Applied
Biopharmaceutics &
Pharmacokinetics
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Applied
Biopharmaceutics &
Pharmacokinetics
Seventh Edition
EDITORS
Leon Shargel, PhD, RPh
Applied Biopharmaceutics, LLC
Raleigh, North Carolina
Aliate Professor, School of Pharmacy
Virginia Commonwealth University, Richmond, Virginia
Adjunct Associate Professor, School of Pharmacy
University of Maryland, Baltimore, Maryland
Andrew B.C. Yu, PhD, RPh
Registered Pharmacist
Gaithersburg, Maryland
Formerly Associate Professor of Pharmaceutics
Albany College of Pharmacy
Albany, New York
Formerly CDER, FDA
Silver Spring, Maryland
New York Chicago San Francisco Athens London Madrid Mexico City
Milan New Delhi Singapore Sydney Toronto
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Contents
Contributors xi
Preface xv
Preface to First Edition xvii
1. Introduction to Biopharmaceutics and Measures of Central Tendency 53
Pharmacokinetics 1 Measures of Variability 54
Hypothesis Testing 56
Drug Product Performance 1 Statistically Versus Clinically Signicant
Biopharmaceutics 1 Differences 58
Pharmacokinetics 4 Statistical Inference Techniques in Hypothesis
Pharmacodynamics 4 Testing for Parametric Data 59
Clinical Pharmacokinetics 5 Goodness of Fit 63
Practical Focus 8 Statistical Inference Techniques for Hypothesis
Pharmacodynamics 10 Testing With Nonparametric Data 63
Drug Exposure and Drug Response 10 Controlled Versus Noncontrolled Studies 66
Toxicokinetics and Clinical Toxicology 10 Blinding 66
Measurement of Drug Concentrations 11 Confounding 66
Basic Pharmacokinetics and Pharmacokinetic Validity 67
Models 15 Bioequivalence Studies 68
Chapter Summary 21 Evaluation of Risk for Clinical Studies 68
Learning Questions 22 Chapter Summary 70
Answers 23 Learning Questions 70
References 25 Answers 72
Bibliography 25 References 73
2. Mathematical Fundamentals in 4. One-Compartment Open Model:
Pharmacokinetics 27 Intravenous Bolus Administration 75
Calculus 27 Elimination Rate Constant 76
Graphs 29 Apparent Volume of Distribution 77
Practice Problem 31 Clearance 80
Mathematical Expressions and Units 33 Clinical Application 85
Units for Expressing Blood Concentrations 34 Calculation of k From Urinary Excretion Data 86
Measurement and Use of Signicant Figures 34 Practice Problem 87
Practice Problem 35 Practice Problem 88
Practice Problem 36 Clinical Application 89
Rates and Orders of Processes 40 Chapter Summary 90
Chapter Summary 42 Learning Questions 90
Learning Questions 43 Answers 92
Answers 46 Reference 96
References 50 Bibliography 96
3. Biostatistics 51 5. Multicompartment Models:
Variables 51 Intravenous Bolus Administration 97
Types of Data (Nonparametric Versus Parametric) 51 Two-Compartment Open Model 100
Distributions 52 Clinical Application 105
v
vi CONTENTS
Practice Problem 107 References 175
Practical Focus 107 Bibliography 175
Practice Problem 110
Practical Focus 113 8. Pharmacokinetics of Oral
Three-Compartment Open Model 114
Clinical Application 115 Absorption 177
Clinical Application 116 Introduction 177
Determination of Compartment Models 116 Basic Principles of Physiologically Based
Practical Focus 117 Absorption Kinetics (Bottom-Up Approach) 178
Clinical Application 118 Absoroption Kinetics
Practical Problem 120 (The Top-Down Approach) 182
Clinical Application 121 Pharmacokinetics of Drug Absorption 182
Practical Application 121 Signicance of Absorption Rate Constants 184
Clinical Application 122 Zero-Order Absorption Model 184
Chapter Summary 123 Clinical Application—Transdermal Drug
Learning Questions 124 Delivery 185
Answers 126 First-Order Absorption Model 185
References 128 Practice Problem 191
Bibliography 129 Chapter Summary 199
Answers 200
Application Questions 202
6. Intravenous Infusion 131 References 203
One-Compartment Model Drugs 131 Bibliography 204
Infusion Method for Calculating Patient Elimination
Half-Life 135
Loading Dose Plus IV Infusion—One-Compartment 9. Multiple-Dosage Regimens 205
Model 136 Drug Accumulation 205
Practice Problems 138 Clinical Example 209
Estimation of Drug Clearance and V From Infusion Repetitive Intravenous Injections 210
D
Data 140 Intermittent Intravenous Infusion 214
Intravenous Infusion of Two-Compartment Model Clinical Example 216
Drugs 141 Estimation of k and V of Aminoglycosides in
D
Practical Focus 142 Clinical Situations 217
Chapter Summary 144 Multiple-Oral-Dose Regimen 218
Learning Questions 144 Loading Dose 219
Answers 146 Dosage Regimen Schedules 220
Reference 148 Clinical Example 222
Bibliography 148 Practice Problems 222
Chapter Summary 224
Learning Questions 225
7. Drug Elimination, Clearance, and Answers 226
Renal Clearance 149 References 228
Drug Elimination 149 Bibliography 228
Drug Clearance 150
Clearance Models 152 10. Nonlinear Pharmacokinetics 229
The Kidney 157 Saturable Enzymatic Elimination Processes 231
Clinical Application 162 Practice Problem 232
Practice Problems 163 Practice Problem 233
Renal Clearance 163 Drug Elimination by Capacity-Limited
Determination of Renal Clearance 168 Pharmacokinetics: One-Compartment
Practice Problem 169 Model, IV Bolus Injection 233
Practice Problem 169 Practice Problems 235
Relationship of Clearance to Elimination Half-Life Clinical Focus 242
and Volume of Distribution 170 Clinical Focus 243
Chapter Summary 171 Drugs Distributed as One-Compartment
Learning Questions 171 Model and Eliminated by Nonlinear
Answers 172 Pharmacokinetics 243
CONTENTS vii
Clinical Focus 244 Practical Focus 311
Chronopharmacokinetics and Time-Dependent Hepatic Clearance 311
Pharmacokinetics 245 Extrahepatic Metabolism 312
Clinical Focus 247 Enzyme Kinetics—Michaelis–Menten
Bioavailability of Drugs That Follow Nonlinear Equation 313
Pharmacokinetics 247 Clinical Example 317
Nonlinear Pharmacokinetics Due to Drug–Protein Practice Problem 319
Binding 248 Anatomy and Physiology of the Liver 321
Potential Reasons for Unsuspected Hepatic Enzymes Involved in the Biotransformation
Nonlinearity 251 of Drugs 323
Dose-Dependent Pharmacokinetics 252 Drug Biotransformation Reactions 325
Clinical Example 253 Pathways of Drug Biotransformation 326
Chapter Summary 254 Drug Interaction Example 331
Learning Questions 254 Clinical Example 338
Answers 255 First-Pass Effects 338
References 257 Hepatic Clearance of a Protein-Bound Drug:
Bibliography 258 Restrictive and Nonrestrictive Clearance From
Binding 344
11. Physiologic Drug Distribution and Biliary Excretion of Drugs 346
Clinical Example 348
Protein Binding 259 Role of Transporters on Hepatic Clearance
Physiologic Factors of Distribution 259 and Bioavailability 348
Clinical Focus 267 Chapter Summary 350
Apparent Volume Distribution 267 Learning Questions 350
Practice Problem 270 Answers 352
Protein Binding of Drugs 273 References 354
Clinical Examples 275 Bibliography 355
Effect of Protein Binding on the Apparent Volume
of Distribution 276
Practice Problem 279 13. Pharmacogenetics and Drug
Clinical Example 280 Metabolism 357
Relationship of Plasma Drug–Protein Binding to Genetic Polymorphisms 358
Distribution and Elimination 281 Cytochrome P-450 Isozymes 361
Clinical Examples 282 Phase II Enzymes 366
Clinical Example 284 Transporters 367
Determinants of Protein Binding 285 Chapter Summary 368
Clinical Example 285 Glossary 369
Kinetics of Protein Binding 286 Abbreviations 369
Practical Focus 287 References 370
Determination of Binding Constants and Binding
Sites by Graphic Methods 287 14. Physiologic Factors Related to Drug
Clinical Signicance of Drug–Protein
Binding 290 Absorption 373
Clinical Example 299 Drug Absorption and Design
Clinical Example 300 of a Drug Product 373
Modeling Drug Distribution 301 Route of Drug Administration 374
Chapter Summary 302 Nature of Cell Membranes 377
Learning Questions 303 Passage of Drugs Across Cell Membranes 378
Answers 304 Drug Interactions in the Gastrointestinal
References 306 Tract 389
Bibliography 307 Oral Drug Absorption 390
Oral Drug Absorption During Drug Product
Development 401
12. Drug Elimination and Hepatic Methods for Studying Factors That Affect Drug
Clearance 309 Absorption 402
Route of Drug Administration and Extrahepatic Effect of Disease States on Drug Absorption 405
Drug Metabolism 309 Miscellaneous Routes of Drug Administration 407
viii CONTENTS
Chapter Summary 408 Other Approaches Deemed Acceptable
Learning Questions 409 (by the FDA) 482
Answers to Questions 410 Bioequivalence Studies Based on Multiple
References 411 Endpoints 482
Bibliography 414 Bioequivalence Studies 482
Design and Evaluation of Bioequivalence
15. Biopharmaceutic Considerations in Studies 484
Study Designs 490
Drug Product Design and In Vitro Drug Crossover Study Designs 491
Product Performance 415 Clinical Example 496
Biopharmaceutic Factors and Rationale for Drug Clinical Example 496
Product Design 416 Pharmacokinetic Evaluation of the Data 497
Rate-Limiting Steps in Drug Absorption 418 The Partial AUC in Bioequivalence
Physicochemical Properties of the Drug 420 Analysis 498
Formulation Factors Affecting Drug Product Examples of Partial AUC Analyses 499
Performance 423 Bioequivalence Examples 500
Drug Product Performance, In Vitro: Dissolution Study Submission and Drug Review Process 502
and Drug Release Testing 425 Waivers of In Vivo Bioequivalence Studies
Compendial Methods of Dissolution 429 (Biowaivers) 503
Alternative Methods of Dissolution Testing 431 The Biopharmaceutics Classication System
Dissolution Prole Comparisons 434 (BCS) 507
Meeting Dissolution Requirements 436 Generic Biologics (Biosimilar Drug
Problems of Variable Control in Dissolution Products) 510
Testing 437 Clinical Signicance of Bioequivalence
Performance of Drug Products: In Vitro–In Vivo Studies 511
Correlation 437 Special Concerns in Bioavailability and
Approaches to Establish Clinically Relevant Drug Bioequivalence Studies 512
Product Specications 441 Generic Substitution 514
Drug Product Stability 445 Glossary 517
Considerations in the Design of a Drug Chapter Summary 520
Product 446 Learning Questions 520
Drug Product Considerations 450 Answers 525
Clinical Example 456 References 526
Chapter Summary 461
Learning Questions 462
Answers 462 1 7. Biopharmaceutical Aspects of the
References 463 Active Pharmaceutical Ingredient and
Bibliography 466 Pharmaceutical Equivalence 529
Introduction 529
16. Drug Product Performance, In Vivo: Pharmaceutical Alternatives 533
Bioavailability and Bioequivalence 469 Practice Problem 534
Drug Product Performance 469 Bioequivalence of Drugs With Multiple
Purpose of Bioavailability and Bioequivalence Indications 536
Studies 471 Formulation and Manufacturing Process
Relative and Absolute Availability 472 Changes 536
Practice Problem 474 Size, Shape, and Other Physical Attributes of
Methods for Assessing Bioavailability and Generic Tablets and Capsules 536
Bioequivalence 475 Changes to an Approved NDA or ANDA 537
In Vivo Measurement of Active Moiety or Moieties The Future of Pharmaceutical Equivalence and
in Biological Fluids 475 Therapeutic Equivalence 538
Bioequivalence Studies Based on Pharmacodynamic Biosimilar Drug Products 539
Endpoints—In Vivo Pharmacodynamic (PD) Historical Perspective 540
Comparison 478 Chapter Summary 541
Bioequivalence Studies Based on Clinical Learning Questions 541
Endpoints—Clinical Endpoint Study 479 Answers 542
In Vitro Studies 481 References 542
CONTENTS ix
18. Impact of Biopharmaceutics on Pharmacokinetics of Biopharmaceuticals 630
Bioequivalence of Biotechnology-Derived
Drug Product Quality and Clinical
Drug Products 631
Efficacy 545 Learning Questions 632
Risks From Medicines 545 Answers 632
Risk Assessment 546 References 633
Drug Product Quality and Drug Product Bibliography 633
Performance 547
Pharmaceutical Development 547 21. Relationship Between Pharmacokinetics
Example of Quality Risk 550
Excipient Effect on Drug Product and Pharmacodynamics 635
Performance 553 Pharmacokinetics and Pharmacodynamics 635
Practical Focus 554 Relationship of Dose to Pharmacologic Effect 640
Quality Control and Quality Assurance 554 Relationship Between Dose and Duration of
Practical Focus 555 Activity (t ), Single IV Bolus Injection 643
eff
Risk Management 557 Practice Problem 643
Scale-Up and Postapproval Changes (SUPAC) 558 Effect of Both Dose and Elimination Half-Life on
Practical Focus 561 the Duration of Activity 643
Product Quality Problems 561 Effect of Elimination Half-Life on Duration of
Postmarketing Surveillance 562 Activity 644
Glossary 562 Substance Abuse Potential 644
Chapter Summary 563 Drug Tolerance and Physical Dependency 645
Learning Questions 564 Hypersensitivity and Adverse Response 646
Answers 564 Chapter Summary 673
References 565 Learning Questions 674
Bibliography 565 Answers 677
References 678
1 9. Modified-Release Drug Products and
2 2. Application of Pharmacokinetics to
Drug Devices 567
Modied-Release (MR) Drug Products and Clinical Situations 681
Conventional (Immediate-Release, IR) Medication Therapy Management 681
Drug Products 567 Individualization of Drug Dosage Regimens 682
Biopharmaceutic Factors 572 Therapeutic Drug Monitoring 683
Dosage Form Selection 575 Clinical Example 690
Advantages and Disadvantages of Extended- Clinical Example 692
Release Products 575 Design of Dosage Regimens 692
Kinetics of Extended-Release Dosage Forms 577 Conversion From Intravenous Infusion to
Pharmacokinetic Simulation of Extended-Release Oral Dosing 694
Products 578 Determination of Dose 696
Clinical Examples 580 Practice Problems 696
Types of Extended-Release Products 581 Effect of Changing Dose ond Dosing Interval on
Ç Ç Ç
Considerations in the Evaluation of C , C , and C 697
max min av
Modied-Release Products 601 Determination of Frequency of Drug
Evaluation of Modied-Release Products 604 Administration 698
Evaluation of In Vivo Bioavailability Data 606 Determination of Both Dose and Dosage
Chapter Summary 608 Interval 698
Learning Questions 609 Practice Problem 699
References 609 Determination of Route of Administration 699
Bibliography 613 Dosing Infants and Children 700
Practice Problem 702
2 Dosing the Elderly 702
0. Targeted Drug Delivery Systems and
Practice Problems 703
Biotechnological Products 615 Clinical Example 704
Biotechnology 615 Dosing the Obese Patients 705
Drug Carriers and Targeting 624 Pharmacokinetics of Drug Interactions 706
Targeted Drug Delivery 627 Inhibition of Drug Metabolism 710
x CONTENTS
Inhibition of Monoamine Oxidase (MAO) 712 General Approaches for Dose Adjustment in Renal
Induction of Drug Metabolism 712 Disease 777
Inhibition of Drug Absorption 712 Measurement of Glomerular Filtration Rate 779
Inhibition of Biliary Excretion 713 Serum Creatinine Concentration and
Altered Renal Reabsorption Due to Changing Creatinine Clearance 780
Urinary pH 713 Practice Problems 782
Practical Focus 713 Dose Adjustment for Uremic Patients 785
Effect of Food on Drug Disposition 713 Practice Problem 787
Adverse Viral Drug Interactions 714 Practice Problem 792
Population Pharmacokinetics 714 Practice Problems 793
Clinical Example 722 Practice Problem 795
Regional Pharmacokinetics 724 Extracorporeal Removal of Drugs 796
Chapter Summary 725 Practice Problem 799
Learning Questions 725 Clinical Examples 800
Answers 728 Effect of Hepatic Disease
References 731 on Pharmacokinetics 803
Bibliography 732 Practice Problem 805
Chapter Summary 809
23. Application of Pharmaco kinetics to Learning Questions 810
Answers 811
Specific Populations: Geriatric, Obese, References 813
and Pediatric Patients 735 Bibliography 815
Specic and Special Populations 735
Module I: Application of Pharmacokinetics to the 25. Empirical Models, Mechanistic
Geriatric Patients 736
Summary 749 Models, Statistical Moments, and
Learning Questions 749 Noncompartmental Analysis 817
Answers 750 Empirical Models 818
References 751 Mechanistic Models 822
Further Reading 754 Noncompartmental Analysis 835
Module II: Application of Pharmacokinetics to the Comparison of Different Approaches 842
Obese Patients 754 Selection of Pharmacokinetic Models 844
Summary 760 Chapter Summary 845
Learning Questions 760 Learning Questions 845
Answers 761 Answers 846
References 761 References 847
Module III: Application of Pharmacokinetics to the Bibliography 848
Pediatric Patients 763
Summary 769 Appendix A Applications of
Learning Questions 770
Answers 771 Software Packages in
References 773 Pharmacokinetics 851
24. Dose Adjustment in Renal and Hepatic Appendix B Glossary 875
Disease 775
Renal Impairment 775 Index 879
Pharmacokinetic Considerations 775
Contributors
S. Thomas Abraham, PhD Philippe Colucci, PhD
Associate Professor Principal Scientist
Department of Pharmaceutical Sciences Learn and Confirm Inc.
College of Pharmacy & Health Sciences Sr. Laurent, QC, Canada
Campbell University
Buies Creek, North Carolina Dale P. Conner, Pharm.D.
Director
Michael L. Adams, PharmD, PhD Office of Bioequivalence
Associate Professor Office of Generic Drugs
Department of Pharmaceutical Sciences CDER, FDA
College of Pharmacy & Health Sciences Silver Spring, Maryland
Campbell University
Buies Creek, North Carolina Barbara M. Davit, PhD, JD
Executive Director
Antoine Al-Achi, PhD Biopharmaceutics
Associate Professor Merck & Co.
Campbell University Kenilworth, New Jersey
College of Pharmacy & Health Sciences
Buies Creek, North Carolina Hong Ding, PhD
Assistant Professor
Lily K. Cheung, PharmD Department of Immunology
Assistant Professor Herbert Wertheim College of Medicine
Department of Pharmacy Practice Florida International University
College of Pharmacy & Health Sciences Miami, Florida
Texas Southern University
Houston, Texas John Z. Duan, PhD
Master Reviewer
Diana Shu-Lian Chow, PhD Office of New Drug Products
Professor of Pharmaceutics Office of Pharmaceutical Quality
Director FDA/CDER
Institute for Drug Education and Research (IDER) Silver Spring, Maryland
College of Pharmacy
University of Houston
Houston, Texas
xi
xii CONTRIBUTORS
Murray P. Ducharme, PharmD, FCCP, FCP Minerva A. Hughes, PhD, RAC (US)
President and CEO Senior Pharmacologist
Learn and Confirm Inc. Food and Drug Administration
Sr. Laurent, QC, Canada Center for Drug Evaluation and Research
Professeur Associé Silver Spring, Maryland
Faculté de Pharmacie
University of Montreal, Canada Manish Issar, PhD
Visiting Professor Assistant Professor of Pharmacology
Faculty of Pharmacy College of Osteopathic Medicine of the Pacific
Rhodes University, South Africa Western University of Health Sciences
Pomona, California
Mathangi Gopalakrishnan, MS, PhD
Research Assistant Professor Vipul Kumar, PhD
Center for Translational Medicine Senior Scientist I
School of Pharmacy Nonclinical Development Department
University of Maryland Cubist Pharmaceuticals Inc.
Baltimore, Maryland Lexington, Massachusetts
Phillip M. Gerk, PharmD, PhD S.W. Johnny Lau, RPh, PhD
Associate Professor Senior Clinical Pharmacologist
Department of Pharmaceutics Food and Drug Administration
Virginia Commonwealth University Office of Clinical Pharmacology
MCV Campus Silver Spring, Maryland
School of Pharmacy
Richmond, Virginia David S.H. Lee, PharmD, PhD
Assistant Professor
Charles Herring, BSPharm, PharmD, BCPS, CPP Department of Pharmacy Practice
Associate Professor Oregon State University/Oregon Health and Science
Department of Pharmacy Practice University College of Pharmacy
College of Pharmacy & Health Sciences Portland, Oregon
Campbell University
Clinical Pharmacist Practitioner Patrick J Marroum, PhD
Adult Medicine Team Director
Downtown Health Plaza of Wake Forest Baptist Clinical Pharmacology and Pharmacometrics
Health AbbVie
Winston-Salem, North Carolina North Chicago, Illinois
Christine Yuen-Yi Hon, PharmD, BCOP Shabnam N. Sani, PharmD, PhD
Clinical Pharmacology Reviewer Assistant Professor
Division of Clinical Pharmacology III Department of Pharmaceutical and Administrative
Office of Clinical Pharmacology Sciences
Office of Translational Sciences College of Pharmacy
Center for Drug Evaluation and Research Western New England University
Food and Drug Administration Springfield, Massachusetts
Silver Spring, Maryland
CONTRIBUTORS xiii
Leon Shargel, PhD, RPh Vincent H. Tam, PharmD, BCPS (Infectious Diseases)
Manager and Founder Professor Department of Clinical Sciences and
Applied Biopharmaceutics, LLC Administration
Raleigh, North Carolina University of Houston College of Pharmacy
Affiliate Professsor Texas Medical Center Campus
School of Pharmacy Houston, Texas
Virginia Commonwealth University
Richmond, Virginia Dr. Susanna Wu-Pong, PhD
Associate Professor
Sandra Suarez Sharp, PhD Director
Master Biopharmaceutics Reviewer/Biopharmaceutics Pharmaceutical Sciences Graduate Program
Lead VCU School of Pharmacy
Office of New Drug Products/Division of Richmond, Virginia
Biopharmaceutics
Office of Pharmaceutical Quality Andrew B.C. Yu, PhD, RPh
Food and Drug Administration Registered Pharmacist
Silver Spring, Maryland Formerly senior reviewer, CDER, FDA
Associate Pharmaceutics Professor
Rodney Siwale, PhD, MS Albany College of Pharmacy
Assistant Professor Albany, New York
Department of Pharmaceutical and Administrative
Sciences Corinne Seng Yue, BPharm, MSc, PhD
College of Pharmacy Principal Scientist
Western New England University Learn and Confirm Inc.
Springfield, Massachusetts Sr. Laurent, QC, Canada
Changquan Calvin Sun, PhD Hong Zhao, PhD
Associate Professor of Pharmaceutics Clinical Pharmacology Master Reviewer
University of Minnesota Clinical Pharmacology Team Leader
Department of Pharmaceutics Office of Clinical Pharmacology (OCP)
College of Pharmacy Office of Translational Sciences (OTS)
Minneapolis, Minnesota Center for Drug Evaluation and Research (CDER)
U.S. Food and Drug Administration (FDA)
He Sun, PhD Silver Spring, Maryland
President and CEO
Tasly Pharmaceuticals Inc. HaiAn Zheng, PhD
Rockville, Maryland Associate Professor
Professor and Chairman Department of Pharmaceutical Sciences
Department of Pharmaceutical Economics and Policy Albany College of Pharmacy and Health Sciences
School of Pharmaceutical Science and Technology Albany, New York
Tianjin University
Tianjin, P. R. China
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Preface
The publication of this seventh edition of Applied in teaching basic concepts that may be applied to
Biopharmaceutics and Pharmacokinetics represents understanding complex issues associated with in vivo
over three decades in print. Since the introduction drug delivery that are essential for safe and efficacious
of classic pharmacokinetics in the first edition, the drug therapy.
discipline has expanded and evolved greatly. The The primary audience is pharmacy students
basic pharmacokinetic principles and biopharma- enrolled in pharmaceutical science courses in phar-
ceutics now include pharmacogenetics, drug recep- macokinetics and biopharmaceutics. This text fulfills
tor theories, advances in membrane transports, and course work offered in separate or combined courses
functional physiology. These advances are applied to in these subjects. Secondary audiences for this text-
the design of new active drug moieties, manufacture book are research, technological and development
of novel drug products, and drug delivery systems. scientists in pharmaceutics, biopharmaceutics, and
Biopharmaceutics and pharmacokinetics play a key pharmacokinetics.
role in the development of safer drug therapy in This edition represents many significant changes
patients, allowing individualizing dosage regimens from previous editions.
and improving therapeutic outcomes.
• The book is an edited textbook with the collabo-
In planning for the seventh edition, we realized
ration of many experts well known in biopharma-
that we needed expertise for these areas. This sev-
ceutics, drug disposition, drug delivery systems,
enth edition is our first edited textbook in which an
manufacturing, clinical pharmacology, clinical
expert with intimate knowledge and experience in
trials, and regulatory science.
the topic was selected as a contributor. We would
• Many chapters have been expanded and updated
like to acknowledge these experts for their precious
to reflect current knowledge and application of
time and effort. We are also grateful to our readers
biopharmaceutics and pharmacokinetics. Many
and colleagues for their helpful feedback and support
new topics and updates are listed in Chapter 1.
throughout the years.
• Practical examples and questions are included
As editors of this edition, we kept the original
to encourage students to apply the principles in
objectives, starting with fundamentals followed by
patient care and drug consultation situations.
a holistic integrated approach that can be applied to
• Learning questions and answers appear at the end
practice (see scope and objectives in Preface to the
of each chapter.
first edition). This textbook provides the reader with
• Three new chapters have been added to this edi-
a basic and practical understanding of the principles
tion including, Biostatistics which provides intro-
of biopharmaceutics and pharmacokinetics that can be
duction for popular topics such as risk concept,
applied to drug product development and drug ther-
non-inferiority, and superiority concept in new
apy. Practice problems, clinical examples, frequently
drug evaluation, and Application of Pharmaco-
asked questions and learning questions are included in
kinetics in Specific Populations which discusses
each chapter to demonstrate how these concepts relate
issues such as drug and patient related pharmacy
to practical situations. This textbook remains unique
xv
xvi PREFACE
topics in during therapy in various patient popula- bioavailability of the drug from the drug product
tions, and Biopharmaceutic Aspects of the Active and clinical efficacy.
Pharmaceutical Ingredient and Pharmaceutical
Equivalence which explains the synthesis, Leon Shargel
quality and physical/chemical properties of the Andrew B.C. Yu
active pharmaceutical ingredients affect the
Preface to First Edition
The publication of the twelfth edition of this book Online features now supplement the printed
is a testament to the vision and ideals of the original edition. The entire text, updates, reviews of newly
authors, Alfred Gilman and Louis Goodman, who, approved drugs, animations of drug action, and
in 1941set forth the principles that have guided the hyper links to relevant text in the prior edition are
book through eleven editions: to correlate pharma- available on the Goodman & Gilman section of
cology with related medical sciences, to reinterpret McGraw-Hill’s websites, AccessMedicine.com and
the actions and uses of drugs in light of advances AccessPharmacy.com. An Image Bank CD accom-
in medicine and the basic biomedical sciences, to panies the book and makes all tables and figures
emphasize the applications of pharmacodynamics to available for use in presentations.
therapeutics, and to create a book that will be use- The process of editing brings into view many
ful to students of pharmacology and to physicians. remarkable facts, theories, and realizations. Three
These precepts continue to guide the current edition. stand out: the invention of new classes of drugs has
As with editions since the second, expert schol- slowed to a trickle; therapeutics has barely begun
ars have contributed individual chapters. A multiau- to capitalize on the information from the human
thored book of this sort grows by accretion, posing genome project; and, the development of resistance
challenges editors but also offering memorable pearls to antimicrobial agents, mainly through their overuse
to the reader. Thus, portions of prior editions persist in medicine and agriculture, threatens to return us to
in the current edition, and I hasten to acknowledge the the pre-antibiotic era. We have the capacity and inge-
contributions of previous editors and authors, many nuity to correct these shortcomings.
of whom will see text that looks familiar. However, Many, in addition to the contributors, deserve
this edition differs noticeably from its immediate thanks for their work on this edition; they are
predecessors. Fifty new scientists, including a num- acknowledged on an accompanying page. In addition,
ber from out-side. the U.S., have joined as contribu- I am grateful to Professors Bruce Chabner (Harvard
tors, and all chapters have been extensively updated. Medical School/Massachusetts General Hospital)
The focus on basic principles continues, with new and Björn Knollmann (Vanderbilt University Medical
chapters on drug invention, molecular mechanisms School) for agreeing to be associate editors of this
of drug action, drug toxicity and poisoning, princi- edition at a late date, necessitated by the death of my
ples of antimicrobial therapy and pharmacotherapy colleague and friend Keith Parker in late 2008. Keith
of obstetrical and gynecological disorders. Figures and I worked together on the eleventh edition and on
are in full color. The editors have continued to stan- planning this edition. In anticipation of the editorial
dardize the organization of chapters: thus, students work ahead, Keith submitted his chapters before any-
should easily find the basic physiology, biochemis- one else and just a few weeks before his death; thus,
try, and pharmacology set forth in regular type; bullet he is well represented in this volume, which we dedi-
points highlight important lists within the text; the cate to his memory.
clinician and expert will find details in extract type
under clear headings. Laurence L. Brunton
xvii
About the Authors
Dr. Leon Shargel is a consultant for the pharmaceuti- Association Pharmaceutical Scientists (AAPS),
cal industry in biopharmaceutics and pharmacokinetics. American Pharmacists Association (APhA), and the
Dr. Shargel has over 35 years experience in both aca- American Society for Pharmacology and Experi-
demia and the pharmaceutical industry. He has been mental Therapeutics (ASPET).
a member or chair of numerous national committees
Dr. Andrew Yu has over 30 years of experience
involved in state formulary issues, biopharmaceutics
in academia, government, and the pharmaceutical
and bioequivalence issues, institutional review boards,
industry. Dr. Yu received a BS in pharmacy from
and a member of the USP Biopharmaceutics Expert
Albany College of Pharmacy and a PhD in pharma-
Committee. Dr. Shargel received a BS in pharmacy
cokinetics from the University of Connecticut. He is
from the University of Maryland and a PhD in phar-
a registered pharmacist and has over 30 publications
macology from the George Washington University
and a patent in novel drug delivery. He had lectured
Medical Center. He is a registered pharmacist and
internationally on pharmaceutics, drug disposition,
has over 150 publications including several leading
and drug delivery.
textbooks in pharmacy. He is a member of vari-
ous professional societies, including the American
Introduction to
1 Biopharmaceutics and
Pharmacokinetics
Leon Shargel and Andrew B.C. Yu
Chapter Objectives DRUG PRODUCT PERFORMANCE
»» Define drug product Drugs are substances intended for use in the diagnosis, cure, mitiga-
performance and tion, treatment, or prevention of disease. Drugs are given in a variety
biopharmaceutics. of dosage forms or drug products such as solids (tablets, capsules),
»» Describe how biopharmaceutics semisolids (ointments, creams), liquids, suspensions, emulsions, etc,
affects drug product for systemic or local therapeutic activity. Drug products can be con-
performance. sidered to be drug delivery systems that release and deliver drug to
the site of action such that they produce the desired therapeutic
»» Define pharmacokinetics and
effect. In addition, drug products are designed specifically to meet
describe how pharmacokinetics
the patient’s needs including palatability, convenience, and safety.
is related to pharmacodynamics
Drug product performance is defined as the release of the
and drug toxicity.
drug substance from the drug product either for local drug action
»» Define the term clinical or for drug absorption into the plasma for systemic therapeutic
pharmacokinetics and explain activity. Advances in pharmaceutical technology and manufactur-
how clinical pharmacokinetics ing have focused on developing quality drug products that are
may be used to develop dosage safer, more effective, and more convenient for the patient.
regimens for drugs in patients.
»» Define pharmacokinetic model BIOPHARMACEUTICS
and list the assumptions that
are used in developing a Biopharmaceutics examines the interrelationship of the physical/
pharmacokinetic model. chemical properties of the drug, the dosage form (drug product) in
which the drug is given, and the route of administration on the rate
»» Explain how the prescribing
and extent of systemic drug absorption. The importance of the
information or approved
drug substance and the drug formulation on absorption, and in vivo
labeling for a drug helps the
distribution of the drug to the site of action, is described as a
practitioner to recommend an
sequence of events that precede elicitation of a drug’s therapeutic
appropriate dosage regimen for
effect. A general scheme describing this dynamic relationship is
a patient.
illustrated in Fig. 1-1.
First, the drug in its dosage form is taken by the patient by an
oral, intravenous, subcutaneous, transdermal, etc, route of adminis-
tration. Next, the drug is released from the dosage form in a predict-
able and characterizable manner. Then, some fraction of the drug is
absorbed from the site of administration into either the surrounding
tissue for local action or into the body (as with oral dosage forms),
or both. Finally, the drug reaches the site of action. A pharmacody-
namic response results when the drug concentration at the site of
1
2 Chapter 1
Absorption Distribution
Drug release and Drug in systemic Drug in
dissolution circulation tissues
Elimination
Excretion and Pharmacologic or
metabolism clinical effect
FIGURE 11 Scheme demonstrating the dynamic relationship between the drug, the drug product, and the pharmacologic effect.
action reaches or exceeds the minimum effective con- product manufacturers must characterize their drug
centration (MEC). The suggested dosing regimen, and drug product and demonstrate that the drug prod-
including starting dose, maintenance dose, dosage uct performs appropriately before the products can
form, and dosing interval, is determined in clinical become available to consumers in the United States.
trials to provide the drug concentrations that are Biopharmaceutics provides the scientific basis for
therapeutically effective in most patients. This drug product design and drug product development.
sequence of events is profoundly affected—in fact, Each step in the manufacturing process of a finished
sometimes orchestrated—by the design of the dosage dosage form may potentially affect the release of the
form and the physicochemical properties of the drug. drug from the drug product and the availability of the
Historically, pharmaceutical scientists have eval- drug at the site of action. The most important steps in
uated the relative drug availability to the body in vivo the manufacturing process are termed critical manu-
after giving a drug product by different routes to an facturing variables. Examples of biopharmaceutic
animal or human, and then comparing specific phar- considerations in drug product design are listed in
macologic, clinical, or possible toxic responses. For Table 1-1. A detailed discussion of drug product
example, a drug such as isoproterenol causes an design is found in Chapter 15. Knowledge of physio-
increase in heart rate when given intravenously but logic factors necessary for designing oral products is
has no observable effect on the heart when given discussed in Chapter 14. Finally, drug product quality
orally at the same dose level. In addition, the bio- of drug substance (Chapter 17) and drug product testing
availability (a measure of systemic availability of a is discussed in later chapters (18, 19, 20, and 21). It is
drug) may differ from one drug product to another important for a pharmacist to know that drug product
containing the same drug, even for the same route of selection from multisources could be confusing and
administration. This difference in drug bioavailability needs a deep understanding of the testing procedures
may be manifested by observing the difference in the and manufacturing technology which is included in the
therapeutic effectiveness of the drug products. Thus, chemistry, manufacturing, and control (CMC) of the
the nature of the drug molecule, the route of delivery, product involved. The starting material (SM) used to
and the formulation of the dosage form can determine make the API (active pharmaceutical ingredient), the
whether an administered drug is therapeutically processing method used during chemical synthesis,
effective, is toxic, or has no apparent effect at all. extraction, and the purification method can result in
The US Food and Drug Administration (FDA) differences in the API that can then affect drug product
approves all drug products to be marketed in the performance (Chapter 17). Sometimes a by-product of
United States. The pharmaceutical manufacturers the synthetic process, residual solvents, or impurities
must perform extensive research and development that remain may be harmful or may affect the product’s
prior to approval. The manufacturer of a new drug physical or chemical stability. Increasingly, many drug
product must submit a New Drug Application (NDA) sources are imported and the manufacturing of these
to the FDA, whereas a generic drug pharmaceutical products is regulated by codes or pharmacopeia in other
manufacturer must submit an Abbreviated New Drug countries. For example, drugs in Europe may be meet-
Application (ANDA). Both the new and generic drug ing EP (European Pharmacopeia) and since 2006,
Introduction to Biopharmaceutics and Pharmacokinetics 3
TABLE 11 Biopharmaceutic Considerations in Drug Product Design
Items Considerations
Therapeutic objective Drug may be intended for rapid relief of symptoms, slow extended action given once per day, or
longer for chronic use; some drug may be intended for local action or systemic action
Drug (active pharmaceutical Physical and chemical properties of API, including solubility, polymorphic form, particle size;
ingredient, API) impurities
Route of administration Oral, topical, parenteral, transdermal, inhalation, etc
Drug dosage and dosage Large or small drug dose, frequency of doses, patient acceptance of drug product, patient compliance
regimen
Type of drug product Orally disintegrating tablets, immediate release tablets, extended release tablets, transdermal, topical,
parenteral, implant, etc
Excipients Although very little pharmacodynamic activity, excipients may affect drug product performance
including release of drug from drug product
Method of manufacture Variables in manufacturing processes, including weighing accuracy, blending uniformity, release tests,
and product sterility for parenterals
agreed uniform standards are harmonized in ICH guid- pharmaceutical equivalence, bioavailability, bioequiv-
ances for Europe, Japan, and the United States. In the alence, and therapeutic equivalence often evolved by
US, the USP-NF is the official compendia for drug necessity. The implications are important regarding
quality standards. availability of quality drug product, avoidance of
Finally, the equipment used during manufactur- shortages, and maintaining an affordable high-quality
ing, processing, and packaging may alter important drug products. The principles and issues with regard
product attribute. Despite compliance with testing and to multisource drug products are discussed in subse-
regulatory guidance involved, the issues involving quent chapters:
Chapter 14 Physiologic Factors How stomach emptying, GI residence time, and gastric window affect drug absorption
Related to Drug
Absorption
Chapter 15 Biopharmaceutic How particle size, crystal form, solubility, dissolution, and ionization affect in vivo dissolution and
Considerations in absorption. Modifications of a product with excipient with regard to immediate or delayed action
Drug Product Design are discussed. Dissolution test methods and relation to in vivo performance
Chapter 16 Drug Product Bioavailability and bioequivalence terms and regulations, test methods, and analysis exam-
Performance, In Vivo: ples. Protocol design and statistical analysis. Reasons for poor bioavailability. Bioavailability
Bioavailability and reference, generic substitution. PE, PA, BA/BE, API, RLD, TE
Bioequivalence SUPAC (Scale-up postapproval changes) regarding drug products. What type of changes will result
in changes in BA, TE, or performances of drug products from a scientific and regulatory viewpoint
Chapter 17 Biopharmaceutic Physicochemical differences of the drug, API due to manufacturing and synthetic pathway.
Aspects of the How to select API from multiple sources while meeting PE (pharmaceutical equivalence) and
Active Pharmaceuti- TE (therapeutic equivalence) requirement as defined in CFR. Examples of some drug failing TE
cal Ingredient and while apparently meeting API requirements. Formulation factors and manufacturing method
Pharmaceutical affecting PE and TE. How particle size and crystal form affect solubility and dissolution. How
Equivalence pharmaceutical equivalence affects therapeutic equivalence. Pharmaceutical alternatives.
How physicochemical characteristics of API lead to pharmaceutical inequivalency
Chapter 18 Impact of Drug Drug product quality and drug product performance
Product Quality and Pharmaceutical development. Excipient effect on drug product performance. Quality control
Biopharmaceutics on and quality assurance. Risk management
Clinical Efficacy
Scale-up and postapproval changes (SUPAC)
Product quality problems. Postmarketing surveillance
4 Chapter 1
Thus, biopharmaceutics involves factors that analytical methods for the measurement of drugs
influence (1) the design of the drug product, (2) stabil- and metabolites, and procedures that facilitate data
ity of the drug within the drug product, (3) the manu- collection and manipulation. The theoretical aspect
facture of the drug product, (4) the release of the drug of pharmacokinetics involves the development of
from the drug product, (5) the rate of dissolution/ pharmacokinetic models that predict drug disposi-
release of the drug at the absorption site, and (6) deliv- tion after drug administration. The application of
ery of drug to the site of action, which may involve statistics is an integral part of pharmacokinetic stud-
targeting the drug to a localized area (eg, colon for ies. Statistical methods are used for pharmacokinetic
Crohn disease) for action or for systemic absorption parameter estimation and data interpretation ulti-
of the drug. mately for the purpose of designing and predicting
Both the pharmacist and the pharmaceutical sci- optimal dosing regimens for individuals or groups of
entist must understand these complex relationships to patients. Statistical methods are applied to pharma-
objectively choose the most appropriate drug product cokinetic models to determine data error and struc-
for therapeutic success. tural model deviations. Mathematics and computer
The study of biopharmaceutics is based on fun- techniques form the theoretical basis of many phar-
damental scientific principles and experimental macokinetic methods. Classical pharmacokinetics is
methodology. Studies in biopharmaceutics use both a study of theoretical models focusing mostly on
in vitro and in vivo methods. In vitro methods are model development and parameterization.
procedures employing test apparatus and equipment
without involving laboratory animals or humans.
In vivo methods are more complex studies involving PHARMACODYNAMICS
human subjects or laboratory animals. Some of these
methods will be discussed in Chapter 15. These Pharmacodynamics is the study of the biochemical
methods must be able to assess the impact of the and physiological effects of drugs on the body; this
physical and chemical properties of the drug, drug includes the mechanisms of drug action and the rela-
stability, and large-scale production of the drug and tionship between drug concentration and effect.
drug product on the biologic performance of the drug. A typical example of pharmacodynamics is how a
drug interacts quantitatively with a drug receptor to
PHARMACOKINETICS produce a response (effect). Receptors are the mole-
cules that interact with specific drugs to produce a
After a drug is released from its dosage form, the pharmacological effect in the body.
drug is absorbed into the surrounding tissue, the The pharmacodynamic effect, sometimes referred
body, or both. The distribution through and elimina- to as the pharmacologic effect, can be therapeutic
tion of the drug in the body varies for each patient but and/or cause toxicity. Often drugs have multiple
can be characterized using mathematical models and effects including the desired therapeutic response as
statistics. Pharmacokinetics is the science of the well as unwanted side effects. For many drugs, the
kinetics of drug absorption, distribution, and elimina- pharmacodynamic effect is dose/drug concentration
tion (ie, metabolism and excretion). The description related; the higher the dose, the higher drug concen-
of drug distribution and elimination is often termed trations in the body and the more intense the phar-
drug disposition. Characterization of drug disposition macodynamic effect up to a maximum effect. It is
is an important prerequisite for determination or desirable that side effects and/or toxicity of drugs
modification of dosing regimens for individuals and occurs at higher drug concentrations than the drug
groups of patients. concentrations needed for the therapeutic effect.
The study of pharmacokinetics involves both Unfortunately, unwanted side effects often occur con-
experimental and theoretical approaches. The exper- currently with the therapeutic doses. The relationship
imental aspect of pharmacokinetics involves the between pharmacodynamics and pharmacokinetics is
development of biologic sampling techniques, discussed in Chapter 21.
Introduction to Biopharmaceutics and Pharmacokinetics 5
CLINICAL PHARMACOKINETICS TABLE 12 Ratio of Age-Adjusted Death
Rates, by Male/Female Ratio from the
During the drug development process, large numbers 10 Leading Causes of Death* in the US, 2003
of patients are enrolled in clinical trials to determine
efficacy and optimum dosing regimens. Along with Disease Rank Male:Female
safety and efficacy data and other patient information, Disease of heart 1 1.5
the FDA approves a label that becomes the package
Malignant neoplasms 2 1.5
insert discussed in more detail later in this chapter. The
approved labeling recommends the proper starting Cerebrovascular diseases 3 4.0
dosage regimens for the general patient population and Chronic lower respiration 4 1.4
may have additional recommendations for special diseases
populations of patients that need an adjusted dosage Accidents and others* 5 2.2
regimen (see Chapter 23). These recommended dosage
Diabetes mellitus 6 1.2
regimens produce the desired pharmacologic response
in the majority of the anticipated patient population. Pneumonia and influenza 7 1.4
However, intra- and interindividual variations will Alzheimers 8 0.8
frequently result in either a subtherapeutic (drug con-
Nephrotis, nephrotic 9 1.5
centration below the MEC) or a toxic response (drug syndrome, and nephrosis
concentrations above the minimum toxic concentra-
tion, MTC), which may then require adjustment to Septicemia 10 1.2
the dosing regimen. Clinical pharmacokinetics is the *Death due to adverse effects suffered as defined by CDC.
application of pharmacokinetic methods to drug Source: National Vital Statistics Report Vol. 52, No. 3, 2003.
therapy in patient care. Clinical pharmacokinetics
involves a multidisciplinary approach to individually
optimized dosing strategies based on the patient’s
therapeutic drug monitoring (TDM) for very potent
disease state and patient-specific considerations.
drugs, such as those with a narrow therapeutic range,
The study of clinical pharmacokinetics of drugs
in order to optimize efficacy and to prevent any
in disease states requires input from medical and
adverse toxicity. For these drugs, it is necessary to
pharmaceutical research. Table 1-2 is a list of 10 age
monitor the patient, either by monitoring plasma drug
adjusted rates of death from 10 leading causes of
concentrations (eg, theophylline) or by monitoring a
death in the United States in 2003. The influence of
specific pharmacodynamic endpoint such as pro-
many diseases on drug disposition is not adequately
thrombin clotting time (eg, warfarin). Pharmacokinetic
studied. Age, gender, genetic, and ethnic differences
and drug analysis services necessary for safe drug
can also result in pharmacokinetic differences that may
monitoring are generally provided by the clinical
affect the outcome of drug therapy (see Chapter 23).
pharmacokinetic service (CPKS). Some drugs fre-
The study of pharmacokinetic differences of drugs in
quently monitored are the aminoglycosides and anti-
various population groups is termed population
convulsants. Other drugs closely monitored are those
pharmacokinetics (Sheiner and Ludden, 1992; see
used in cancer chemotherapy, in order to minimize
Chapter 22). Application of Pharmacokinetics to
adverse side effects (Rodman and Evans, 1991).
Specific Populations, Chapter 23, will discuss many
of the important pharmacokinetic considerations for
dosing subjects due to age, weight, gender, renal,
and hepatic disease differences. Despite advances in Labeling For Human Prescription Drug and
modeling and genetics, sometimes it is necessary to Biological Products
monitor the plasma drug concentration precisely in a In 2013, the FDA redesigned the format of the
patient for safety and multidrug dosing consider- prescribing information necessary for safe and
ation. Clinical pharmacokinetics is also applied to effective use of the drugs and biological products
6 Chapter 1
(FDA Guidance for Industry, 2013). This design was pharmacognosy, pharmacokinetics, pharmacody-
developed to make information in prescription drug namics, pharmacotherapeutics, and toxicology. The
labeling easier for health care practitioners to access application of pharmacology in clinical medicine
and read. The practitioner can use the prescribing including clinical trial is referred to as clinical phar-
information to make prescribing decisions. The macology. For pharmacists and health profession-
labeling includes three sections: als, it is important to know that NDA drug labels
report many important study information under
• Highlights of Prescribing Information (Highlights)—
Clinical Pharmacology in Section 12 of the standard
contains selected information from the Full Pre-
prescription label (Tables 1-3A and 1-3B).
scribing Information (FPI) that health care prac-
titioners most commonly reference and consider
most important. In addition, highlights may contain 12 CLINICAL PHARMACOLOGY
any boxed warnings that give a concise summary 12.1 Mechanism of Action
of all of the risks described in the Boxed Warning 12.2 Pharmacodynamics
section in the FPI. 12.3 Pharmacokinetics
• Table of Contents (Contents)—lists the sections
and subsections of the FPI. Question
• Full Prescribing Information (FPI)—contains the Where is toxicology information found in the pre-
detailed prescribing information necessary for safe scription label for a new drug? Can I find out if a
and effective use of the drug. drug is mutagenic under side-effect sections?
An example of the Highlights of Prescribing Answer
Information and Table of Contents for Nexium Nonclinical toxicology information is usefully in
(esomeprazole magnesium) delayed release capsules Section 13 under Nonclinical Toxicology if avail-
appears in Table 1-3B. The prescribing information able. Mutagenic potential of a drug is usually
sometimes referred to as the approved label or the reported under animal studies. It is unlikely that a
package insert may be found at the FDA website, drug with known humanly mutagenicity will be mar-
Drugs@FDA (http://www.accessdata.fda.gov/scripts keted, if so, it will be labeled with special warning.
/cder/drugsatfda/). Prescribing information is updated Black box warnings are usually used to give warn-
periodically as new information becomes available. ings to prescribers in Section 5 under Warnings and
The prescribing information contained in the label Precautions.
recommends dosage regimens for the average patient
from data obtained from clinical trials. The indica-
tions and usage section are those indications that the Pharmacogenetics
FDA has approved and that have been shown to be Pharmacogenetics is the study of drug effect includ-
effective in clinical trials. On occasion, a practitioner ing distribution and disposition due to genetic differ-
may want to prescribe the drug to a patient drug for a ences, which can affect individual responses to
non-approved use or indication. The pharmacist must drugs, both in terms of therapeutic effect and adverse
decide if there is sufficient evidence for dispensing the effects. A related field is pharmacogenomics, which
drug for a non-approved use (off-label indication). emphasizes different aspects of genetic effect on
The decision to dispense a drug for a non-approved drug response. This important discipline is discussed
indication may be difficult and often made with con- in Chapter 13. Pharmacogenetics is the main reason
sultation of other health professionals. why many new drugs still have to be further studied
after regulatory approval, that is, postapproval phase
Clinical Pharmacology 4 studies. The clinical trials prior to drug approval
Pharmacology is a science that generally deals with are generally limited such that some side effects and
the study of drugs, including its mechanism, effects, special responses due to genetic differences may not
and uses of drugs; broadly speaking, it includes be adequately known and labeled.
Introduction to Biopharmaceutics and Pharmacokinetics 7
TABLE 13A Highlights of Prescribing Information for Nexium (Esomeprazole Magnesium)
Delayed Release Capsules
HIGHLIGHTS OF PRESCRIBING INFORMATION
These highlights do not include all the information needed to use NEXIUM safely and effectively. See full prescribing
information for NEXIUM.
NEXIUM (esomeprazole magnesium) delayed-release capsules, for oral use
NEXIUM (esomeprazole magnesium) for delayed-release oral suspension
Initial U.S. Approval: 1989 (omeprazole)
RECENT MAJOR CHANGES
Warnings and Precautions. Interactions with Diagnostic
Investigations for Neuroendocrine Tumors (5.8) 03/2014
INDICATIONS AND USAGE
NEXIUM is a proton pump inhibitor indicated for the following:
• Treatment of gastroesophageal reflux disease (GERD) (1.1)
• Risk reduction of NSAID-associated gastric ulcer (1.2)
• H. pylori eradication to reduce the risk of duodenal ulcer recurrence (1.3)
• Pathological hypersecretory conditions, including Zollinger-Ellison syndrome (1.4)
DOSAGE AND ADMINISTRATION
Indication Dose Frequency
Gastroesophageal Reflux Disease (GERD)
Adults 20 mg or 40 mg Once daily for 4 to 8 weeks
12 to 17 years 20 mg or 40 mg Once daily for up to 8 weeks
1 to 11 years 10 mg or 20 mg Once daily for up to 8 weeks
1 month to less than 1 year 2.5 mg, 5 mg or 10 mg (based on weight). Once daily, up to 6 weeks for erosive esophagitis (EE) due
to acid-mediated GERD only.
Risk Reduction of NSAID-Associated Gastric Ulcer
20 mg or 40 mg Once daily for up to 6 months
H. pylori Eradication (Triple Therapy):
NEXIUM 40 mg Once daily for 10 days
Amoxicillin 1000 mg Twice daily for 10 days
Clarithromycin 500 mg Twice daily for 10 days
Pathological Hypersecretory Conditions
40 mg Twice daily
See full prescribing information for administration options (2)
Patients with severe liver impairment do not exceed dose of 20 mg (2)
DOSAGE FORMS AND STRENGTHS
• NEXIUM Delayed-Release Capsules: 20 mg and 40 mg (3)
• NEXIUM for Delayed-Release Oral Suspension: 2.5 mg, 5 mg, 10 mg, 20 mg, and 40 mg (3)
CONTRAINDICATIONS
Patients with known hypersensitivity to proton pump inhibitors (PPIs) (angioedema and anaphylaxis have occurred) (4)
(Continued)
8 Chapter 1
TABLE 13A Highlights of Prescribing Information for Nexium (Esomeprazole Magnesium)
Delayed Release Capsules (Continued)
HIGHLIGHTS OF PRESCRIBING INFORMATION
WARNINGS AND PRECAUTIONS
• Symptomatic response does not preclude the presence of gastric malignancy (5.1)
• Atrophic gastritis has been noted with long-term omeprazole therapy (5.2)
• PPI therapy may be associated with increased risk of Clostriodium difficle-associated diarrhea (5.3)
• Avoid concomitant use of NEXIUM with clopidogrel (5.4)
• Bone Fracture: Long-term and multiple daily dose PPI therapy may be associated with an increased risk for
osteoporosis-related fractures of the hip, wrist, or spine (5.5)
• Hypomagnesemia has been reported rarely with prolonged treatment with PPIs (5.6)
• Avoid concomitant use of NEXIUM with St John’s Wort or rifampin due to the potential reduction in esomeprazole levels
(5.7,7.3)
• Interactions with diagnostic investigations for Neuroendocrine Tumors: Increases in intragastric pH may result in hypergas-
trinemia and enterochromaffin-like cell hyperplasia and increased chromogranin A levels which may interfere with diagnostic
investigations for neuroendocrine tumors (5.8,12.2)
ADVERSE REACTIONS
Most common adverse reactions (6.1):
• Adults (≥18 years) (incidence ≥1%) are headache, diarrhea, nausea, flatulence, abdominal pain, constipation, and dry mouth
• Pediatric (1 to 17 years) (incidence ≥2%) are headache, diarrhea, abdominal pain, nausea, and somnolence
• Pediatric (1 month to less than 1 year) (incidence 1%) are abdominal pain, regurgitation, tachypnea, and increased ALT
To report SUSPECTED ADVERSE REACTIONS, contact AstraZeneca at 1-800-236-9933 or FDA at 1-800-FDA-1088 or
www.fda.gov/medwatch.
DRUG INTERACTIONS
• May affect plasma levels of antiretroviral drugs – use with atazanavir and nelfinavir is not recommended: if saquinavir is used
with NEXIUM, monitor for toxicity and consider saquinavir dose reduction (7.1)
• May interfere with drugs for which gastric pH affects bioavailability (e.g., ketoconazole, iron salts, erlotinib, and digoxin)
Patients treated with NEXIUM and digoxin may need to be monitored for digoxin toxicity. (7.2)
• Combined inhibitor of CYP 2C19 and 3A4 may raise esomeprazole levels (7.3)
• Clopidogrel: NEXIUM decreases exposure to the active metabolite of clopidogrel (7.3)
• May increase systemic exposure of cilostazol and an active metabolite. Consider dose reduction (7.3)
• Tacrolimus: NEXIUM may increase serum levels of tacrolimus (7.5)
• Methotrexate: NEXIUM may increase serum levels of methotrexate (7.7)
USE IN SPECIFIC POPULATIONS
• Pregnancy: Based on animal data, may cause fetal harm (8.1)
See 17 for PATIENT COUNSELING INFORMATION and FDA-approved Medication Guide.
Revised: 03/2014
PRACTICAL FOCUS pharmacogenetics) or pharmacokinetics, the recom-
mended dosage regimen drug may not provide the
Relationship of Drug Concentrations to desired therapeutic outcome. The measurement of
Drug Response plasma drug concentrations can confirm whether the
The initiation of drug therapy starts with the manu- drug dose was subtherapeutic due to the patient’s
facturer’s recommended dosage regimen that individual pharmacokinetic profile (observed by
includes the drug dose and frequency of doses (eg, low plasma drug concentrations) or was not respon-
100 mg every 8 hours). Due to individual differences sive to drug therapy due to genetic difference in
in the patient’s genetic makeup (see Chapter 13 on receptor response. In this case, the drug concentrations
Introduction to Biopharmaceutics and Pharmacokinetics 9
TABLE 13B Contents for Full Prescribing Information for Nexium (Esomeprazole Magnesium)
Delayed Release Capsules
FULL PRESCRIBING INFORMATION: CONTENTS*
1. INDICATIONS AND USAGE
1.1 Treatment of Gastroesophageal Reflux Disease (GERD)
1.2 Risk Reduction of NSAID-Associated Gastric Ulcer
1.3 H. pylori Eradication to Reduce the Risk of Duodenal Ulcer Recurrence
1.4 Pathological Hypersecretory Conditions Including Zollinger-Ellison Syndrome
2. DOSAGE AND ADMINISTRATION
3. DOSAGE FORMS AND STRENGTHS
4. CONTRAINDICATIONS
5. WARNINGS AND PRECAUTIONS
5.1 Concurrent Gastric Malignancy
5.2 Atrophic Gastritis
5.3 Clostridium difficile associated diarrhea
5.4 Interaction with Clopidogrel
5.5 Bone Fracture
5.6 Hypomagnesemia
5.7 Concomitant Use of NEXIUM with St John’s Wort or rifampin
5.8 Interactions with Diagnostic Investigations for Neuroendocrine Tumors
5.9 Concomitant Use of NEXIUM with Methotrexate
6. ADVERSE REACTIONS
6.1 Clinical Trials Experience
6.2 Postmarketing Experience
7. DRUG INTERACTIONS
7.1 Interference with Antiretroviral Therapy
7.2 Drugs for Which Gastric pH Can Affect Bioavailability
7.3 Effects on Hepatic Metabolism/Cytochrome P-450 Pathways
7.4 Interactions with Investigations of Neuroendocrine Tumors
7.5 Tacrolimus
7.6 Combination Therapy with Clarithromycin
7.7 Methotrexate
8. USE IN SPECIFIC POPULATIONS
8.1 Pregnancy
8.3 Nursing Mothers
8.4 Pediatric Use
8.5 Geriatric Use
10. OVERDOSAGE
11. DESCRIPTION
12. CLINICAL PHARMACOLOGY
12.1 Mechanism of Action
12.2 Pharmacodynamics
12.3 Pharmacokinetics
12.4 Microbiology
13. NONCLINICAL TOXICOLOGY
13.1 Carcinogenesis, Mutagenesis, Impairment of Fertility
13.2 Animal Toxicology and/or Pharmacology
14. CLINICAL STUDIES
14.1 Healing of Erosive Esophagitis
14.2 Symptomatic Gastroesophageal Reflux Disease (GERD)
14.3 Pediatric Gastroesophageal Reflux Disease (GERD)
14.4 Risk Reduction of NSAID-Associated Gastric Ulcer
14.5 Helicobacter pylori (H. Pylon) Eradication in Patients with Duodenal Ulcer Disease
14.6 Pathological Hypersecretory Conditions Including Zollinger-Ellison Syndrome
16. HOW SUPPLIED/STORAGE AND HANDLING
17. PATIENT COUNSELING INFORMATION
*Sections or subsections omitted from the full prescribing information are not listed.
Source: FDA Guidance for Industry (February 2013).
10 Chapter 1
and physiologic effects that influence the interaction of
TOXIC drug with the receptor. The interaction of a drug mole-
cule with a receptor causes the initiation of a sequence
POTENTIALLY TOXIC
of molecular events resulting in a pharmacologic or
toxic response. Pharmacokinetic–pharmacodynamic
models are constructed to relate plasma drug level to
drug concentration at the site of action and establish the
THERAPEUTIC intensity and time course of the drug. Pharmacodynamics
and pharmacokinetic–pharmacodynamic models are
discussed more fully in Chapter 21.
POTENTIALLY SUBTHERAPEUTIC DRUG EXPOSURE AND DRUG
RESPONSE
SUBTHERAPEUTIC
Drug exposure refers to the dose (drug input to the
FIGURE 12 Relationship of drug concentrations to drug body) and various measures of acute or integrated
response. drug concentrations in plasma and other biological
fluid (eg, Cmax, Cmin, Css, AUC) (FDA Guidance for
are in the therapeutic range but the patient does not Industry, 2003). Drug response refers to a direct
respond to drug treatment. Figure 1-2 shows that the measure of the pharmacologic effect of the drug.
concentration of drug in the body can range from Response includes a broad range of endpoints or
subtherapeutic to toxic. In contrast, some patients biomarkers ranging from the clinically remote bio-
respond to drug treatment at lower drug doses that markers (eg, receptor occupancy) to a presumed
result in lower drug concentrations. Other patients mechanistic effect (eg, ACE inhibition), to a poten-
may need higher drug concentrations to obtain a tial or accepted surrogate (eg, effects on blood pres-
therapeutic effect, which requires higher drug doses. sure, lipids, or cardiac output), and to the full range
It is desirable that adverse drug responses occur at of short-term or long-term clinical effects related to
drug concentrations higher relative to the therapeutic either efficacy or safety.
drug concentrations, but for many potent drugs, Toxicologic and efficacy studies provide infor-
adverse effects can also occur close to the same drug mation on the safety and effectiveness of the drug
concentrations as needed for the therapeutic effect. during development and in special patient popula-
tions such as subjects with renal and hepatic insuffi-
ciencies. For many drugs, clinical use is based on
weighing the risks of favorable and unfavorable out-
Frequently Asked Questions
comes at a particular dose. For some potent drugs, the
»»Which is more closely related to drug response, the
doses and dosing rate may need to be titrated in order
total drug dose administered or the concentration
of the drug in the body? to obtain the desired effect and be tolerated.
»»Why do individualized dosing regimens need to be
determined for some patients? TOXICOKINETICS AND CLINICAL
TOXICOLOGY
Toxicokinetics is the application of pharmacoki-
PHARMACODYNAMICS
netic principles to the design, conduct, and inter-
Pharmacodynamics refers to the relationship between pretation of drug safety evaluation studies (Leal et al,
the drug concentration at the site of action (receptor) 1993) and in validating dose-related exposure in
and pharmacologic response, including biochemical animals. Toxicokinetic data aid in the interpretation
DRUG CONCENTRATION
Introduction to Biopharmaceutics and Pharmacokinetics 11
of toxicologic findings in animals and extrapolation include sampling blood, spinal fluid, synovial fluid,
of the resulting data to humans. Toxicokinetic stud- tissue biopsy, or any biologic material that requires
ies are performed in animals during preclinical parenteral or surgical intervention in the patient. In
drug development and may continue after the drug contrast, noninvasive methods include sampling of
has been tested in clinical trials. urine, saliva, feces, expired air, or any biologic mate-
Clinical toxicology is the study of adverse effects rial that can be obtained without parenteral or surgi-
of drugs and toxic substances (poisons) in the body. cal intervention.
The pharmacokinetics of a drug in an overmedicated The measurement of drug and metabolite con-
(intoxicated) patient may be very different from the centration in each of these biologic materials yields
pharmacokinetics of the same drug given in lower important information, such as the amount of drug
therapeutic doses. At very high doses, the drug con- retained in, or transported into, that region of the tis-
centration in the body may saturate enzymes involved sue or fluid, the likely pharmacologic or toxicologic
in the absorption, biotransformation, or active renal outcome of drug dosing, and drug metabolite forma-
secretion mechanisms, thereby changing the pharma- tion or transport. Analytical methods should be able
cokinetics from linear to nonlinear pharmacokinetics. to distinguish between protein-bound and unbound
Nonlinear pharmacokinetics is discussed in parent drug and each metabolite, and the pharmaco-
Chapter 10. Drugs frequently involved in toxicity logically active species should be identified. Such
cases include acetaminophen, salicylates, opiates (eg, distinctions between metabolites in each tissue and
morphine), and the tricylic antidepressants (TCAs). fluid are especially important for initial pharmacoki-
Many of these drugs can be assayed conveniently by netic modeling of a drug.
fluorescence immunoassay (FIA) kits.
Drug Concentrations in Blood, Plasma,
MEASUREMENT OF DRUG or Serum
CONCENTRATIONS Measurement of drug and metabolite concentrations
(levels) in the blood, serum, or plasma is the most
Because drug concentrations are an important ele- direct approach to assessing the pharmacokinetics of
ment in determining individual or population phar- the drug in the body. Whole blood contains cellular
macokinetics, drug concentrations are measured in elements including red blood cells, white blood
biologic samples, such as milk, saliva, plasma, and cells, platelets, and various other proteins, such as
urine. Sensitive, accurate, and precise analytical albumin and globulins (Table 1-4). In general, serum
methods are available for the direct measurement of or plasma is most commonly used for drug measure-
drugs in biologic matrices. Such measurements are ment. To obtain serum, whole blood is allowed to
generally validated so that accurate information is clot and the serum is collected from the supernatant
generated for pharmacokinetic and clinical monitor- after centrifugation. Plasma is obtained from the
ing. In general, chromatographic and mass spectro- supernatant of centrifuged whole blood to which an
metric methods are most frequently employed for anticoagulant, such as heparin, has been added.
drug concentration measurement, because chroma- Therefore, the protein content of serum and plasma
tography separates the drug from other related mate- is not the same. Plasma perfuses all the tissues of the
rials that may cause assay interference and mass body, including the cellular elements in the blood.
spectrometry allows detection of molecules or mol- Assuming that a drug in the plasma is in dynamic
ecule fragments based on their mass-to-charge ratio. equilibrium with the tissues, then changes in the
drug concentration in plasma will reflect changes in
Sampling of Biologic Specimens tissue drug concentrations. Drugs in the plasma are
Only a few biologic specimens may be obtained often bound to plasma proteins, and often plasma
safely from the patient to gain information as to the proteins are filtered from the plasma before drug
drug concentration in the body. Invasive methods concentrations are measured. This is the unbound
12 Chapter 1
TABLE 14 Blood Components
Blood Component How Obtained Components
Whole blood Whole blood is generally obtained by venous Whole blood contains all the cellular and protein
puncture and contains an anticoagulant such as elements of blood
heparin or EDTA
Serum Serum is the liquid obtained from whole blood Serum does not contain the cellular elements,
after the blood is allowed to clot and the clot is fibrinogen, or the other clotting factors from
removed the blood
Plasma Plasma is the liquid supernatant obtained after Plasma is the noncellular liquid fraction of
centrifugation of non-clotted whole blood that whole blood and contains all the proteins
contains an anticoagulant including albumin
drug concentration. Alternatively, drug concentration involved, such as elimination in the feces, sweat, or
may be measured from unfiltered plasma; this is the exhaled air.
total plasma drug concentration. When interpreting The relationship of the drug level–time curve
plasma concentrations, it is important to understand and various pharmacologic parameters for the drug
what type of plasma concentration the data reflect. is shown in Fig. 1-3. MEC and MTC represent the
minimum effective concentration and minimum toxic
concentration of drug, respectively. For some drugs,
Frequently Asked Questions such as those acting on the autonomic nervous sys-
»»Why are drug concentrations more often measured tem, it is useful to know the concentration of drug
in plasma rather than whole blood or serum? that will just barely produce a pharmacologic effect
(ie, MEC). Assuming the drug concentration in the
»»What are the differences between bound drug,
plasma is in equilibrium with the tissues, the MEC
unbound drug, total drug, parent drug, and metabolite
reflects the minimum concentration of drug needed
drug concentrations in the plasma?
Plasma Drug Concentration–Time Curve
MTC
The plasma drug concentration (level)–time curve is
generated by obtaining the drug concentration in
plasma samples taken at various time intervals after
a drug product is administered. The concentration of
drug in each plasma sample is plotted on rectangular-
coordinate graph paper against the corresponding
time at which the plasma sample was removed. Duration MEC
As the drug reaches the general (systemic) circula-
tion, plasma drug concentrations will rise up to a
maximum if the drug was given by an extravascular
route. Usually, absorption of a drug is more rapid
than elimination. As the drug is being absorbed into
the systemic circulation, the drug is distributed to all
the tissues in the body and is also simultaneously Onset
time
being eliminated. Elimination of a drug can proceed Time
by excretion, biotransformation, or a combination of FIGURE 13 Generalized plasma level–time curve after
both. Other elimination mechanisms may also be oral administration of a drug.
Plasma level
Intensity
Introduction to Biopharmaceutics and Pharmacokinetics 13
at the receptors to produce the desired pharmaco- level or maximum drug concentration is related to
logic effect. Similarly, the MTC represents the drug the dose, the rate constant for absorption, and the
concentration needed to just barely produce a toxic elimination constant of the drug. The AUC is related
effect. The onset time corresponds to the time to the amount of drug absorbed systemically. These
required for the drug to reach the MEC. The inten- and other pharmacokinetic parameters are discussed
sity of the pharmacologic effect is proportional to in succeeding chapters.
the number of drug receptors occupied, which is
reflected in the observation that higher plasma drug
Frequently Asked Questions
concentrations produce a greater pharmacologic
»»At what time intervals should plasma drug con-
response, up to a maximum. The duration of drug
centration be taken in order to best predict drug
action is the difference between the onset time and response and side effects?
the time for the drug to decline back to the MEC.
The therapeutic window is the concentrations »»What happens if plasma concentrations fall outside
between the MEC and the MTC. Drugs with a wide of the therapeutic window?
therapeutic window are generally considered safer
than drugs with a narrow therapeutic window.
Sometimes the term therapeutic index is used. This Drug Concentrations in Tissues
term refers to the ratio between the toxic and thera- Tissue biopsies are occasionally removed for diag-
peutic doses. nostic purposes, such as the verification of a malig-
In contrast, the pharmacokineticist can also nancy. Usually, only a small sample of tissue is
describe the plasma level–time curve in terms of removed, making drug concentration measurement
such pharmacokinetic terms as peak plasma level difficult. Drug concentrations in tissue biopsies may
(Cmax), time for peak plasma level (Tmax), and area not reflect drug concentration in other tissues nor the
under the curve, or AUC (Fig. 1-4). The time for drug concentration in all parts of the tissue from
peak plasma level is the time of maximum drug which the biopsy material was removed. For exam-
concentration in the plasma and is a rough marker ple, if the tissue biopsy was for the diagnosis of a
of average rate of drug absorption. The peak plasma tumor within the tissue, the blood flow to the tumor
cells may not be the same as the blood flow to other
cells in this tissue. In fact, for many tissues, blood
MTC
flow to one part of the tissues need not be the same
Peak concentration
as the blood flow to another part of the same tissue.
The measurement of the drug concentration in tissue
biopsy material may be used to ascertain if the drug
reached the tissues and reached the proper concen-
tration within the tissue.
MEC
Drug Concentrations in Urine and Feces
Measurement of drug in urine is an indirect method
AUC
to ascertain the bioavailability of a drug. The rate
and extent of drug excreted in the urine reflects the
rate and extent of systemic drug absorption. The use
Peak of urinary drug excretion measurements to establish
time
Time various pharmacokinetic parameters is discussed in
FIGURE 14 Chapter 4.
Plasma level–time curve showing peak time
and concentration. The shaded portion represents the AUC Measurement of drug in feces may reflect drug
(area under the curve). that has not been absorbed after an oral dose or may
Plasma level
14 Chapter 1
reflect drug that has been expelled by biliary secre- methods, such as gas chromatography coupled with
tion after systemic absorption. Fecal drug excretion mass spectrometry, provides information regarding
is often performed in mass balance studies, in which past drug exposure. A study by Cone et al (1993)
the investigator attempts to account for the entire showed that the hair samples from subjects who were
dose given to the patient. For a mass balance study, known drug abusers contained cocaine and 6-acetyl-
both urine and feces are collected and their drug morphine, a metabolite of heroin (diacetylmorphine).
content measured. For certain solid oral dosage
forms that do not dissolve in the gastrointestinal tract Significance of Measuring Plasma Drug
but slowly leach out drug, fecal collection is per- Concentrations
formed to recover the dosage form. The undissolved
The intensity of the pharmacologic or toxic effect of
dosage form is then assayed for residual drug.
a drug is often related to the concentration of the
drug at the receptor site, usually located in the tissue
Drug Concentrations in Saliva
cells. Because most of the tissue cells are richly per-
Saliva drug concentrations have been reviewed for fused with tissue fluids or plasma, measuring the
many drugs for therapeutic drug monitoring plasma drug level is a responsive method of monitor-
(Pippenger and Massoud, 1984). Because only free ing the course of therapy.
drug diffuses into the saliva, saliva drug levels tend Clinically, individual variations in the pharma-
to approximate free drug rather than total plasma cokinetics of drugs are quite common. Monitoring
drug concentration. The saliva/plasma drug concen- the concentration of drugs in the blood or plasma
tration ratio is less than 1 for many drugs. The saliva/ ascertains that the calculated dose actually delivers
plasma drug concentration ratio is mostly influenced the plasma level required for therapeutic effect. With
by the pKa of the drug and the pH of the saliva. some drugs, receptor expression and/or sensitivity in
Weak acid drugs and weak base drugs with pKa sig- individuals varies, so monitoring of plasma levels is
nificantly different than pH 7.4 (plasma pH) gener- needed to distinguish the patient who is receiving
ally have better correlation to plasma drug levels. too much of a drug from the patient who is supersen-
The saliva drug concentrations taken after equilib- sitive to the drug. Moreover, the patient’s physiologic
rium with the plasma drug concentration generally functions may be affected by disease, nutrition, envi-
provide more stable indication of drug levels in the ronment, concurrent drug therapy, and other factors.
body. The use of salivary drug concentrations as a Pharmacokinetic models allow more accurate inter-
therapeutic indicator should be used with caution pretation of the relationship between plasma drug
and preferably as a secondary indicator. levels and pharmacologic response.
In the absence of pharmacokinetic information,
Forensic Drug Measurements plasma drug levels are relatively useless for dosage
Forensic science is the application of science to per- adjustment. For example, suppose a single blood
sonal injury, murder, and other legal proceedings. sample from a patient was assayed and found to con-
Drug measurements in tissues obtained at autopsy or tain 10 mg/mL. According to the literature, the maxi-
in other bodily fluids such as saliva, urine, and blood mum safe concentration of this drug is 15 mg/mL. In
may be useful if a suspect or victim has taken an over- order to apply this information properly, it is important
dose of a legal medication, has been poisoned, or has to know when the blood sample was drawn, what dose
been using drugs of abuse such as opiates (eg, heroin), of the drug was given, and the route of administration.
cocaine, or marijuana. The appearance of social drugs If the proper information is available, the use of phar-
in blood, urine, and saliva drug analysis shows short- macokinetic equations and models may describe the
term drug abuse. These drugs may be eliminated rap- blood level–time curve accurately and be used to
idly, making it more difficult to prove that the subject modify dosing for that specific patient.
has been using drugs of abuse. The analysis for drugs Monitoring of plasma drug concentrations
of abuse in hair samples by very sensitive assay allows for the adjustment of the drug dosage in order
Introduction to Biopharmaceutics and Pharmacokinetics 15
to individualize and optimize therapeutic drug regi- The predictive capability of a model lies in the
mens. When alterations in physiologic functions proper selection and development of mathematical
occur, monitoring plasma drug concentrations may function(s) that parameterizes the essential factors
provide a guide to the progress of the disease state governing the kinetic process. The key parameters in
and enable the investigator to modify the drug dos- a process are commonly estimated by fitting the
age accordingly. Clinically, sound medical judgment model to the experimental data, known as variables.
and observation are most important. Therapeutic A pharmacokinetic parameter is a constant for the
decisions should not be based solely on plasma drug drug that is estimated from the experimental data.
concentrations. For example, estimated pharmacokinetic parameters
In many cases, the pharmacodynamic response to such as k depend on the method of tissue sampling,
the drug may be more important to measure than just the timing of the sample, drug analysis, and the pre-
the plasma drug concentration. For example, the elec- dictive model selected.
trophysiology of the heart, including an electrocardio- A pharmacokinetic function relates an indepen-
gram (ECG), is important to assess in patients dent variable to a dependent variable, often through
medicated with cardiotonic drugs such as digoxin. For the use of parameters. For example, a pharmacoki-
an anticoagulant drug, such as dicumarol, prothrom- netic model may predict the drug concentration in the
bin clotting time may indicate whether proper dosage liver 1 hour after an oral administration of a 20-mg
was achieved. Most diabetic patients taking insulin dose. The independent variable is the time and the
will monitor their own blood or urine glucose levels. dependent variable is the drug concentration in the
For drugs that act irreversibly at the receptor liver. Based on a set of time-versus-drug concentra-
site, plasma drug concentrations may not accurately tion data, a model equation is derived to predict the
predict pharmacodynamic response. Drugs used in liver drug concentration with respect to time. In this
cancer chemotherapy often interfere with nucleic case, the drug concentration depends on the time
acid or protein biosynthesis to destroy tumor cells. after the administration of the dose, where the time–
For these drugs, the plasma drug concentration does concentration relationship is defined by a pharmaco-
not relate directly to the pharmacodynamic response. kinetic parameter, k, the elimination rate constant.
In this case, other pathophysiologic parameters and Such mathematical models can be devised to
side effects are monitored in the patient to prevent simulate the rate processes of drug absorption, distri-
adverse toxicity. bution, and elimination to describe and predict drug
concentrations in the body as a function of time.
Pharmacokinetic models are used to:
BASIC PHARMACOKINETICS AND
PHARMACOKINETIC MODELS 1. Predict plasma, tissue, and urine drug levels
with any dosage regimen
Drugs are in a dynamic state within the body as they 2. Calculate the optimum dosage regimen for each
move between tissues and fluids, bind with plasma patient individually
or cellular components, or are metabolized. The 3. Estimate the possible accumulation of drugs
biologic nature of drug distribution and disposition and/or metabolites
is complex, and drug events often happen simulta- 4. Correlate drug concentrations with pharmaco-
neously. Such factors must be considered when logic or toxicologic activity
designing drug therapy regimens. The inherent and 5. Evaluate differences in the rate or extent of
infinite complexity of these events requires the use availability between formulations
of mathematical models and statistics to estimate (bioequivalence)
drug dosing and to predict the time course of drug 6. Describe how changes in physiology or disease
efficacy for a given dose. affect the absorption, distribution, or elimina-
A model is a hypothesis using mathematical tion of the drug
terms to describe quantitative relationships concisely. 7. Explain drug interactions
16 Chapter 1
Simplifying assumptions are made in pharmacoki- in separate chapters under the topics of drug absorp-
netic models to describe a complex biologic system tion, drug distribution, drug elimination, and pharma-
concerning the movement of drugs within the body. cokinetic drug interactions involving one or all of the
For example, most pharmacokinetic models assume above processes. Theoretically, an unlimited number
that the plasma drug concentration reflects drug con- of models may be constructed to describe the kinetic
centrations globally within the body. processes of drug absorption, distribution, and elimi-
A model may be empirically, physiologically, or nation in the body, depending on the degree of
compartmentally based. The model that simply detailed information considered. Practical consider-
interpolates the data and allows an empirical formula ations have limited the growth of new pharmacoki-
to estimate drug level over time is justified when netic models.
limited information is available. Empirical models A very simple and useful tool in pharmacokinet-
are practical but not very useful in explaining the ics is compartmentally based models. For example,
mechanism of the actual process by which the drug assume a drug is given by intravenous injection and
is absorbed, distributed, and eliminated in the body. that the drug dissolves (distributes) rapidly in the body
Examples of empirical models used in pharmacoki- fluids. One pharmacokinetic model that can describe
netics are described in Chapter 25. this situation is a tank containing a volume of fluid
Physiologically based models also have limita- that is rapidly equilibrated with the drug. The concen-
tions. Using the example above, and apart from the tration of the drug in the tank after a given dose is
necessity to sample tissue and monitor blood flow to governed by two parameters: (1) the fluid volume of
the liver in vivo, the investigator needs to understand the tank that will dilute the drug, and (2) the elimina-
the following questions. What is the clinical implica- tion rate of drug per unit of time. Though this model
tion of the liver drug concentration value? Should is perhaps an overly simplistic view of drug disposi-
the drug concentration in the blood within the tissue tion in the human body, a drug’s pharmacokinetic
be determined and subtracted from the drug in the properties can frequently be described using a fluid-
liver tissue? What type of cell is representative of the filled tank model called the one-compartment open
liver if a selective biopsy liver tissue sample can be model (see below). In both the tank and the one-
collected without contamination from its surround- compartment body model, a fraction of the drug
ings? Indeed, depending on the spatial location of would be continually eliminated as a function of time
the liver tissue from the hepatic blood vessels, tissue (Fig. 1-5). In pharmacokinetics, these parameters are
drug concentrations can differ depending on distance assumed to be constant for a given drug. If drug con-
to the blood vessel or even on the type of cell in the centrations in the tank are determined at various time
liver. Moreover, changes in the liver blood perfusion intervals following administration of a known dose,
will alter the tissue drug concentration. If heteroge- then the volume of fluid in the tank or compartment
neous liver tissue is homogenized and assayed, the (VD, volume of distribution) and the rate of drug
homogenized tissue represents only a hypothetical elimination can be estimated.
concentration that is an average of all the cells and In practice, pharmacokinetic parameters such as
blood in the liver at the time of collection. Since tis- k and VD are determined experimentally from a set of
sue homogenization is not practical for human sub- drug concentrations collected over various times and
jects, the drug concentration in the liver may be
estimated by knowing the liver extraction ratio for
the drug based on knowledge of the physiologic and
Fluid replenished
biochemical composition of the body organs. Fluid
automatically to keep outlet
A great number of models have been developed volume constant
to estimate regional and global information about
FIGURE 15 Tank with a constant volume of fluid equili-
drug disposition in the body. Some physiologic phar-
brated with drug. The volume of the fluid is 1.0 L. The fluid
macokinetic models are also discussed in Chapter 25. outlet is 10 mL/min. The fraction of drug removed per unit of
Individual pharmacokinetic processes are discussed time is 10/1000, or 0.01 min–1.
Introduction to Biopharmaceutics and Pharmacokinetics 17
known as data. The number of parameters needed to compartments, that communicate reversibly with each
describe the model depends on the complexity of the other. A compartment is not a real physiologic or ana-
process and on the route of drug administration. In tomic region but is considered a tissue or group of
general, as the number of parameters required to tissues that have similar blood flow and drug affinity.
model the data increases, accurate estimation of Within each compartment, the drug is considered to
these parameters becomes increasingly more diffi- be uniformly distributed. Mixing of the drug within a
cult. With complex pharmacokinetic models, com- compartment is rapid and homogeneous and is con-
puter programs are used to facilitate parameter sidered to be “well stirred,” so that the drug concentra-
estimation. However, for the parameters to be valid, tion represents an average concentration, and each
the number of data points should always exceed the drug molecule has an equal probability of leaving the
number of parameters in the model. compartment. Rate constants are used to represent
Because a model is based on a hypothesis and the overall rate processes of drug entry into and exit
simplifying assumptions, a certain degree of caution from the compartment. The model is an open system
is necessary when relying totally on the pharmacoki- because drug can be eliminated from the system.
netic model to predict drug action. For some drugs, Compartment models are based on linear assump-
plasma drug concentrations are not useful in predict- tions using linear differential equations.
ing drug activity. For other drugs, an individual’s
genetic differences, disease state, and the compensa-
Mammillary Model
tory response of the body may modify the response
to the drug. If a simple model does not fit all the A compartmental model provides a simple way of
experimental observations accurately, a new, more grouping all the tissues into one or more compart-
elaborate model may be proposed and subsequently ments where drugs move to and from the central or
tested. Since limited data are generally available in plasma compartment. The mammillary model is the
most clinical situations, pharmacokinetic data should most common compartment model used in pharma-
be interpreted along with clinical observations rather cokinetics. The mammillary model is a strongly con-
than replacing sound judgment by the clinician. nected system, because one can estimate the amount
Development of pharmacometric statistical models of drug in any compartment of the system after drug
may help to improve prediction of drug levels among is introduced into a given compartment. In the one-
patients in the population (Sheiner and Beal, 1982; compartment model, drug is both added to and
Mallet et al, 1988). However, it will be some time eliminated from a central compartment. The central
before these methods become generally accepted. compartment is assigned to represent plasma and
highly perfused tissues that rapidly equilibrate with
drug. When an intravenous dose of drug is given, the
Compartment Models drug enters directly into the central compartment.
If the tissue drug concentrations and binding are Elimination of drug occurs from the central compart-
known, physiologic pharmacokinetic models, which ment because the organs involved in drug elimination,
are based on actual tissues and their respective blood primarily kidney and liver, are well-perfused tissues.
flow, describe the data realistically. Physiologic phar- In a two-compartment model, drug can move
macokinetic models are frequently used in describing between the central or plasma compartment to and
drug distribution in animals, because tissue samples from the tissue compartment. Although the tissue
are easily available for assay. On the other hand, tissue compartment does not represent a specific tissue, the
samples are often not available for human subjects, mass balance accounts for the drug present in all
so most physiological models assume an average set the tissues. In this model, the total amount of drug in
of blood flow for individual subjects. the body is simply the sum of drug present in the cen-
In contrast, because of the vast complexity of tral compartment plus the drug present in the tissue
the body, drug kinetics in the body are frequently compartment. Knowing the parameters of either the
simplified to be represented by one or more tanks, or one-compartment or the two-compartment model,
18 Chapter 1
one can estimate the amount of drug left in the body k1 k
k 2 23
a
and the amount of drug eliminated from the body at any 1 2 3
time. The compartmental models are particularly useful k21 k32
when little information is known about the tissues.
FIGURE 17 Example of caternary model.
Several types of compartment models are
described in Fig. 1-6. The pharmacokinetic rate con-
stants are represented by the letter k. Compartment 1 more compartments around a central compartment
represents the plasma or central compartment, and like satellites. Because the catenary model does not
compartment 2 represents the tissue compartment. apply to the way most functional organs in the body
The drawing of models has three functions. The are directly connected to the plasma, it is not used as
model (1) enables the pharmacokineticist to write often as the mammillary model.
differential equations to describe drug concentration
changes in each compartment, (2) gives a visual Physiologic Pharmacokinetic Model
representation of the rate processes, and (3) shows (Flow Model)
how many pharmacokinetic constants are necessary Physiologic pharmacokinetic models, also known as
to describe the process adequately. blood flow or perfusion models, are pharmacoki-
netic models based on known anatomic and physi-
Catenary Model ologic data. The models describe the data kinetically,
In pharmacokinetics, the mammillary model must be with the consideration that blood flow is responsible
distinguished from another type of compartmental for distributing drug to various parts of the body.
model called the catenary model. The catenary Uptake of drug into organs is determined by the
model consists of compartments joined to one
another like the compartments of a train (Fig. 1-7).
In contrast, the mammillary model consists of one or EXAMPLE »» »
Two parameters are needed to describe model 1
MODEL 1. One-compartment open model, IV injection. (Fig. 1-6): the volume of the compartment and
k the elimination rate constant, k. In the case of
1
model 4, the pharmacokinetic parameters consist
of the volumes of compartments 1 and 2 and the
MODEL 2. One-compartment open model with rst-order absorption. rate constants—ka, k, k12, and k21—for a total of
six parameters.
ka k
1 In studying these models, it is important to
know whether drug concentration data may be
MODEL 3. Two-compartment open model, IV injection. sampled directly from each compartment. For mod-
k els 3 and 4 (Fig. 1-6), data concerning compartment
12
1 2 2 cannot be obtained easily because tissues are
k21 not easily sampled and may not contain homoge-
k neous concentrations of drug. If the amount of drug
absorbed and eliminated per unit time is obtained
MODEL 4. Two-compartment open model with rst-order absorption. by sampling compartment 1, then the amount of
k drug contained in the tissue compartment 2 can be
k 12
a
1 2 estimated mathematically. The appropriate math-
k21 ematical equations for describing these models and
k evaluating the various pharmacokinetic parameters
are given in subsequent chapters.
FIGURE 16 Various compartment models.
Introduction to Biopharmaceutics and Pharmacokinetics 19
binding of drug in these tissues. In contrast to an IV injection
estimated tissue volume of distribution, the actual QH
tissue volume is used. Because there are many tissue Heart
organs in the body, each tissue volume must be
obtained and its drug concentration described. The QM
model would potentially predict realistic tissue drug Muscle
concentrations, which the two-compartment model
fails to do. Unfortunately, much of the information QS
required for adequately describing a physiologic SET
pharmacokinetic model is experimentally difficult
to obtain. In spite of this limitation, the physiologic QR
pharmacokinetic model does provide much better RET
insight into how physiologic factors may change
k
drug distribution from one animal species to another. e
Urine QK
Other major differences are described below. Kidney
First, no data fitting is required in the perfusion
model. Drug concentrations in the various tissues are QL
predicted by organ tissue size, blood flow, and Liver
experimentally determined drug tissue–blood ratios km
(ie, partition of drug between tissue and blood). FIGURE 18 Pharmacokinetic model of drug perfu-
Second, blood flow, tissue size, and the drug sion. The ks represent kinetic constants: ke is the first-order
tissue–blood ratios may vary due to certain patho- rate constant for urinary drug excretion and km is the rate
physiologic conditions. Thus, the effect of these constant for hepatic elimination. Each “box” represents a tissue
variations on drug distribution must be taken into compartment. Organs of major importance in drug absorption
are considered separately, while other tissues are grouped as
account in physiologic pharmacokinetic models.
RET (rapidly equilibrating tissue) and SET (slowly equilibrating
Third, and most important of all, physiologically tissue). The size or mass of each tissue compartment is deter-
based pharmacokinetic models can be applied to sev- mined physiologically rather than by mathematical estimation.
eral species, and, for some drugs, human data may be The concentration of drug in the tissue is determined by the
extrapolated. Extrapolation from animal data is not ability of the tissue to accumulate drug as well as by the rate of
blood perfusion to the tissue, represented by Q.
possible with the compartment models, because the
volume of distribution in such models is a mathemati-
cal concept that does not relate simply to blood volume would make the model very complex and mathemat-
and blood flow. To date, numerous drugs (including ically difficult. A simpler but equally good approach
digoxin, lidocaine, methotrexate, and thiopental) have is to group all the tissues with similar blood perfu-
been described with perfusion models. Tissue levels of sion properties into a single compartment.
some of these drugs cannot be predicted successfully A physiologic based pharmacokinetic model
with compartment models, although they generally (PBPK) using known blood flow was used to describe
describe blood levels well. An example of a perfusion the distribution of lidocaine in blood and various
model is shown in Fig. 1-8. organs (Benowitz et el 1974) and applied in anesthe-
The number of tissue compartments in a perfu- siology in man (Tucker et el 1971). In PBKB models,
sion model varies with the drug. Typically, the tis- organs such as lung, liver, brain, and muscle were
sues or organs that have no drug penetration are individually described by differential equations as
excluded from consideration. Thus, such organs as shown in Fig. 1-8, sometimes tissues were grouped as
the brain, the bones, and other parts of the central RET (rapidly equilibrating tissue) and SET (slowly
nervous system are often excluded, as most drugs equilibrating tissue) for simplicity to account for the
have little penetration into these organs. To describe mass balance of the drug. A general scheme showing
each organ separately with a differential equation blood flow for typical organs is shown in Fig. 1-8.
Venous blood
Arterial blood
20 Chapter 1
20 drug metabolism capacity, and blood flow in humans
and other species are often known or can be deter-
10 mined. Thus, physiologic and anatomic parameters
5 can be used to predict the effects of drugs on humans
from the effects on animals in cases where human
experimentation is difficult or restricted.
1
Frequently Asked Questions
0.5
»»What are the reasons to use a multicompartment
Observed
Simulated model instead of a physiologic model?
perfusion model
»»What do the boxes in the mammillary model mean?
0.1
0 60 120 180 240
Time (minutes)
More sophisticated models are introduced as the
FIGURE 19 Observed mean (•) and simulated (—) understanding of human and animal physiology
arterial lidocaine blood concentrations in normal volunteers
receiving 1 mg/kg/min constant infusion for 3 minutes. (From improves. For example, in Chapter 25, special com-
Tucker GT, Boas RA: Pharmacokinetic aspects of intravenous partment models that take into account transporter-
regional anesthesia. Anesthesiology 34(6):538–549, 1971, with mediated drug disposition are introduced for specific
permission.) drugs. This approach is termed Physiologic Pharmaco-
kinetic Model Incorporating Hepatic Transporter-
The data showing blood concentration of lidocaine Mediated Clearance. The differences between the
after an IV dose declining biexponentially (Fig. 1-9) physiologic pharmacokinetic model, the classical
was well predicted by the model. A later PBPK compartmental model, and the noncompartmental
model was applied to model cyclosporine (Fig. 1-10). approach are discussed. It is important to note that
Drug level in various organs were well predicted and mass transfer and balances of drug in and out of the
scaled to human based on this physiologic model body or body organs are fundamentally a kinetic pro-
(Kawai R et al, 1998). The tissue cyclosporine levels cess. Thus, the model may be named as physiologi-
in the lung, muscle, and adipose and other organs are cally based when all drug distributed to body organs
shown in Fig. 1-10. For lidocaine, the tissue such as are identified. For data analysis, parameters are
adipose (fat) tissue accumulates drugs slowly because obtained quantitatively with different assumptions.
of low blood supply. In contrast, vascular tissues, like The model analysis may be compartmental or non-
the lung, equilibrate rapidly with the blood and start compartmental (Chapter 25). One approach is to clas-
to decline as soon as drug level in the blood starts to sify models simply as empirically based models and
fall resulting in curvature of plasma profile. The mechanistic models. Although compartment models
physiologic pharmacokinetic model provides a real- are critically referred to as a “black box” approach
istic means of modeling tissue drug levels. However, and not physiological. The versatility of compartment
drug levels in tissues are not available. A criticism of models and their easy application are based on simple
physiologic pharmacokinetic models in general has mass transfer algorithms or a system of differential
been that there are fewer data points than parameters equations. This approach has allowed many body
that one tries to fit. Consequently, the projected data processes such as binding, transport, and metabolic
are not well constrained. clearance to be monitored. The advantage of a non-
The real significance of the physiologically compartmental analysis is discussed in Chapter 25. In
based model is the potential application of this model Appendix B, softwares used for various type of model
in the prediction of human pharmacokinetics from analysis are discussed, for example, noncompartmen-
animal data (Sawada et al, 1985). The mass of vari- tal analysis is often used for pharmacokinetic and
ous body organs or tissues, extent of protein binding, bioavailability data analysis for regulatory purpose.
Lidocaine hydrochloride (mg/mL blood)
Introduction to Biopharmaceutics and Pharmacokinetics 21
1998 Tissue Distribution Kinetics of IV Cyclosporine A (CyA)
Blood Lung Heart Kidney
100 100 100 100
10
10 10 10
1
0.1 1 1 1
0 4 8 12 16 20 24 28 32 0 4 8 12 16 20 24 28 32 0 4 8 12 16 20 24 28 32 0 4 8 12 16 20 24 28 32
Time (h) Time (h) Time (h) Time (h)
Spleen Liver Gut Skin
100 100 100 10
10 10 10
0.1 1 1 1
0 4 8 12 16 20 24 28 32 0 4 8 12 16 20 24 28 32 0 4 8 12 16 20 24 28 32 0 4 8 12 16 20 24 28 32
Time (h) Time (h) Time (h) Time (h)
Bone Muscle Fat Thymus
10 10 100 10
1 10
1 0.1 1 1
0 4 8 12 16 20 24 28 32 0 4 8 12 16 20 24 28 32 0 4 8 12 16 20 24 28 32 0 4 8 12 16 20 24 28 32
Time (h) Time (h) Time (h) Time (h)
FIGURE 110 Measured and best fit predictions of CyA concentration in arterial blood and various organs/tissues in rat. Each
plot and vertical bar represent the mean and standard deviation, respectively. Solid and dotted lines are the physiological-based
pharmacokinetic (PBPK) best fit predictions based on the parameters associated with the linear or nonlinear model, respectively.
(Reproduced with permission from Kawai R, Mathew D, Tanaka C, Rowland M: Physiologically based pharmacokinetics of cyclospo-
rine A: Extension to tissue distribution kinetics in rats and scale-up to human. JPET 287:457–468, 1998.)
CHAPTER SUMMARY
Drug product performance is the release of the drug route of administration on the rate and extent of sys-
substance from the drug product leading to bioavail- temic drug absorption. Pharmacokinetics is the sci-
ability of the drug substance and eventually leading ence of the dynamics (kinetics) of drug absorption,
to one or more pharmacologic effects, both desirable distribution, and elimination (ie, excretion and
and undesirable. Biopharmaceutics provides the sci- metabolism), whereas clinical pharmacokinetics
entific basis for drug product design and drug prod- considers the applications of pharmacokinetics to
uct performance by examining the interrelationship drug therapy.
of the physical/chemical properties of the drug, the The quantitative measurement of drug concen-
drug product in which the drug is given, and the trations in the plasma after dose administration is
Tissue concentration (mg/g) Tissue concentration (mg/g) Blood concentration (mg/mL)
Tissue concentration (mg/g) Tissue concentration (mg/g) Tissue concentration (mg/g)
Tissue concentration (mg/g) Tissue concentration (mg/g) Tissue concentration (mg/g)
Tissue concentration (mg/g) Tissue concentration (mg/g) Tissue concentration (mg/g)
22 Chapter 1
important to obtain relevant data of systemic drug drug concentration to the pharmacodynamic effect
exposure. The plasma drug concentration-versus- or adverse response, and enables the development of
time profile provides the basic data from which vari- individualized therapeutic dosage regimens and new
ous pharmacokinetic models can be developed that and novel drug delivery systems.
predict the time course of drug action, relates the
LEARNING QUESTIONS
1. What is the significance of the plasma level– d. Write an expression describing the
time curve? How does the curve relate to the rate of change of drug concentration in
pharmacologic activity of a drug? compartment 1 (dC1/dt).
2. What is the purpose of pharmacokinetic models? 5. Give two reasons for the measurement of
3. Draw a diagram describing a three-compartment the plasma drug concentration, Cp, assuming
model with first-order absorption and drug (a) the Cp relates directly to the pharma-
elimination from compartment 1. codynamic activity of the drug and (b) the
4. The pharmacokinetic model presented in Cp does not relate to the pharmacodynamic
Fig. 1-11 represents a drug that is eliminated activity of the drug.
by renal excretion, biliary excretion, and drug 6. Consider two biologic compartments separated
metabolism. The metabolite distribution is by a biologic membrane. Drug A is found in
described by a one-compartment open model. compartment 1 and in compartment 2 in a
The following questions pertain to Fig. 1-11. concentration of c1 and c2, respectively.
a. How many parameters are needed to a. What possible conditions or situations
describe the model if the drug is injected would result in concentration c1 > c2 at
intravenously (ie, the rate of drug absorp- equilibrium?
tion may be neglected)? b. How would you experimentally demonstrate
b. Which compartment(s) can be sampled? these conditions given above?
c. What would be the overall elimination rate c. Under what conditions would c1 = c2 at
constant for elimination of drug from equilibrium?
compartment 1? d. The total amount of Drug A in each biologic
compartment is A1 and A2, respectively.
Metabolite Describe a condition in which A1 > A2, but
Drug compartment
c1 = c2 at equilibrium.
2 Include in your discussion, how the physico-
chemical properties of Drug A or the biologic
k12 k21 properties of each compartment might influ-
k ence equilibrium conditions.
e km ku
1 3
7. Why is it important for a pharmacist to keep
up with possible label revision in a drug newly
kb
approved? Which part of the label you expect
to be mostly likely revised with more phase 4
FIGURE 111 Pharmacokinetic model for a drug eliminated
information?
by renal and biliary excretion and drug metabolism. km = rate
constant for metabolism of drug; k a. The chemical structure of the drug
u = rate constant for urinary
excretion of metabolites; kb = rate constant for biliary excretion b. The Description section
of drug; and ke = rate constant for urinary drug excretion. c. Adverse side effect in certain individuals
Introduction to Biopharmaceutics and Pharmacokinetics 23
8. A pharmacist wishing to find if an excipient 9. A pregnant patient is prescribed pantoprazole
such as aspartame in a product is mostly found sodium (Protonix) delayed release tablets
under which section in the SPL drug label? for erosive gastroesophageal reflux disease
a. How supplied (GERD). Where would you find information
b. Patient guide concerning the safety of this drug in pregnant
c. Description women?
ANSWERS
Frequently Asked Questions What are the reasons to use a multicompartment
Why are drug concentrations more often measured model instead of a physiologic model?
in plasma rather than whole blood or serum? • Physiologic models are complex and require more
• Blood is composed of plasma and red blood cells information for accurate prediction compared to
(RBCs). Serum is the fluid obtained from blood compartment models. Missing information in the
after it is allowed to clot. Serum and plasma do physiologic model will lead to bias or error in the
not contain identical proteins. RBCs may be con- model. Compartment models are more simplistic
sidered a cellular component of the body in which in that they assume that both arterial and venous
the drug concentration in the serum or plasma is drug concentrations are similar. The compartment
in equilibrium, in the same way as with the other model accounts for a rapid distribution phase and
tissues in the body. Whole blood samples are gen- a slower elimination phase. Physiologic clearance
erally harder to process and assay than serum or models postulate that arterial blood drug levels are
plasma samples. Plasma may be considered a liq- higher than venous blood drug levels. In practice,
uid tissue compartment in which the drug in the only venous blood samples are usually sampled.
plasma fluid equilibrates with drug in the tissues Organ drug clearance is useful in the treatment of
and cellular components. cancers and in the diagnosis of certain diseases in-
volving arterial perfusion. Physiologic models are
At what time intervals should plasma drug concen- difficult to use for general application.
tration be taken in order to best predict drug response
and side effects? Learning Questions
• The exact site of drug action is generally un- 1. The plasma drug level–time curve describes the
known for most drugs. The time needed for the pharmacokinetics of the systemically absorbed
drug to reach the site of action, produce a phar- drug. Once a suitable pharmacokinetic model
macodynamic effect, and reach equilibrium are is obtained, plasma drug concentrations may be
deduced from studies on the relationship of the predicted following various dosage regimens
time course for the drug concentration and the such as single oral and IV bolus doses, multiple-
pharmacodynamic effect. Often, the drug concen- dose regimens, IV infusion, etc. If the pharma-
tration is sampled during the elimination phase cokinetics of the drug relates to its pharmaco-
after the drug has been distributed and reached dynamic activity (or any adverse drug response
equilibrium. For multiple-dose studies, both the or toxicity), then a drug regimen based on the
peak and trough drug concentrations are fre- drug’s pharmacokinetics may be designed to
quently taken. provide optimum drug efficacy. In lieu of a direct
24 Chapter 1
pharmacokinetic–pharmacodynamic relation- cell (eg, purine drug). Other explanations for
ship, the drug’s pharmacokinetics describes the C1 > C2 may be possible.
bioavailability of the drug including inter- and b. Several different experimental conditions are
intrasubject variability; this information allows needed to prove which of the above hypoth-
for the development of drug products that consis- eses is the most likely cause for C1 > C2.
tently deliver the drug in a predictable manner. These experiments may use in vivo or in vitro
2. The purpose of pharmacokinetic models is to methods, including intracellular electrodes to
relate the time course of the drug in the body to measure pH in vivo, protein-binding studies
its pharmacodynamic and/or toxic effects. The in vitro, and partitioning of drug in chloro-
pharmacokinetic model also provides a basis form/water in vitro, among others.
for drug product design, the design of dosage c. In the case of protein binding, the total
regimens, and a better understanding of the concentration of drug in each compartment
action of the body on the drug. may be different (eg, C1 > C2) and, at the
3. (Figure A-1) same time, the free (nonprotein-bound)
4. a. Nine parameters: V1, V2, V3, k12, k21, ke, kb, drug concentration may be equal in each
km, ku compartment—assuming that the free or
b. Compartment 1 and compartment 3 may be unbound drug is easily diffusible. Similarly,
sampled. if C1 > C2 is due to differences in pH and the
c. k = kb + km + ke nonionized drug is easily diffusible, then the
dC nonionized drug concentration may be the
d. 1
= k21C2 − (k12 + k + k + kb )Cdt m e 1 same in each compartment. The total drug
concentrations will be C1 = C2 when there
6. Compartment 1 Compartment 2 is similar affinity for the drug and similar
C conditions in each compartment.
1 C2
d. The total amount of drug, A, in each com-
a. C1 and C2 are the total drug concentration in partment depends on the volume, V, of the
each compartment, respectively. C1 > C2 may compartment and the concentration, C, of the
occur if the drug concentrates in compart- drug in the compartment. Since the amount
ment 1 due to protein binding (compartment of drug (A) = concentration (C) times volume
1 contains a high amount of protein or special (V), any condition that causes the product,
protein binding), due to partitioning (compart- C1V1 ≠ C2V2, will result in A1 ≠ A2. Thus, if
ment 1 has a high lipid content and the drug is C1 = C2 and V1 ≠ V2, then A1 ≠ A2.
poorly water soluble), if the pH is different in 7. A newly approved NDA generally contains
each compartment and the drug is a weak elec- sufficient information for use labeled. However,
trolyte (the drug may be more ionized in com- as more information becomes available through
partment 1), or if there is an active transport postmarketing commitment studies, more
mechanism for the drug to be taken up into the information is added to the labeling, including
Warnings and Precautions.
8. An excipient such as aspartame in a product
ka
is mostly found under the Description section,
k12 k13 which describes the drug chemical structure
2 1 3 and the ingredients in the drug product.
k21 k31 9. Section 8, Use in Specific Populations, reports
k information for geriatric, pediatric, renal, and
hepatic subjects. This section will report dosing
FIGURE A1 for pediatric subjects as well.
Introduction to Biopharmaceutics and Pharmacokinetics 25
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heroin and metabolites in hair of drug abusers. Forensic Sci Biopharm 16:311–327, 1988.
Int 63:55–68, 1993. Pippenger CE, Massoud N: Therapeutic drug monitoring. In Benet
FDA Guidance for Industry: Exposure-Response Relationships— LZ, et al (eds). Pharmacokinetic Basis for Drug Treatment.
Study Design, Data Analysis, and Regulatory Applications, New York, Raven, 1984, chap 21.
FDA, Center for Drug Evaluation and Research, April 2003 Rodman JH, Evans WE: Targeted systemic exposure for pediatric
(http://www.fda.gov/cder/guidance/5341fnl.htm). cancer therapy. In D’Argenio DZ (ed). Advanced Methods of
FDA Guidance for Industry: Labeling for Human Prescription Pharmacokinetic and Pharmacodynamic Systems Analysis.
Drug and Biological Products – Implementing the PLR Con- New York, Plenum Press, 1991, pp 177–183.
tent and Format Requirements, February 2013. Sawada Y, Hanano M, Sugiyama Y, Iga T: Prediction of the disposi-
Kawai R, Mathew D, Tanaka C, Rowland M: Physiologically tion of nine weakly acidic and six weekly basic drugs in humans
based pharmacokinetics of cyclosporine. from pharmacokinetic parameters in rats. J Pharmacokinet
Leal M, Yacobi A, Batra VJ: Use of toxicokinetic principles in Biopharm 13:477–492, 1985.
drug development: Bridging preclinical and clinical studies. In Sheiner LB, Beal SL: Bayesian individualization of pharmaco-
Yacobi A, Skelly JP, Shah VP, Benet LZ (eds). Integration of kinetics. Simple implementation and comparison with non
Pharmacokinetics, Pharmacodynamics and Toxicokinetics in Bayesian methods. J Pharm Sci 71:1344–1348, 1982.
Rational Drug Development. New York, Plenum Press, 1993, Sheiner LB, Ludden TM: Population pharmacokinetics/dynamics.
pp 55–67. Annu Rev Pharmacol Toxicol 32:185–201, 1992.
Mallet A, Mentre F, Steimer JL, Lokiec F: Pharmacometrics: Tucker GT, Boas RA: Pharmacokinetic aspects of intravenous
Nonparametric maximum likelihood estimation for population regional anesthesia.
BIBLIOGRAPHY
Benet LZ: General treatment of linear mammillary models with Gibaldi M: Estimation of the pharmacokinetic parameters of the
elimination from any compartment as used in pharmacokinet- two-compartment open model from post-infusion plasma con-
ics. J Pharm Sci 61:536–541, 1972. centration data. J Pharm Sci 58:1133–1135, 1969.
Benowitz N, Forsyth R, Melmon K, Rowland M: Lidocaine dis- Himmelstein KJ, Lutz RJ: A review of the applications of physio-
position kinetics in monkey and man. Clin Pharmacol Ther logically based pharmacokinetic modeling. J Pharm Biopharm
15:87–98, 1974. 7:127–145, 1979.
Bischoff K, Brown R: Drug distribution in mammals. Chem Eng Lutz R, Dedrick RL: Physiologic pharmacokinetics: Relevance to
Med 62:33–45, 1966. human risk assessment. In Li AP (ed). Toxicity Testing: New
Tucker GT, Boas RA:Pharmacokinetic aspects of intravenous Applications and Applications in Human Risk Assessment.
regional anesthesia. New York, Raven, 1985, pp 129–149.
Bischoff K, Dedrick R, Zaharko D, Longstreth T: Methotrexate Lutz R, Dedrick R, Straw J, et al: The kinetics of methotrexate
pharmacokinetics. J Pharm Sci 60:1128–1133, 1971. distribution in spontaneous canine lymphosarcoma. J Pharm
Chiou W: Quantitation of hepatic and pulmonary first-pass effect and Biopharm 3:77–97, 1975.
its implications in pharmacokinetic study, I: Pharmacokinetics of Metzler CM: Estimation of pharmacokinetic parameters: Statisti-
chloroform in man. J Pharm Biopharm 3:193–201, 1975. cal considerations. Pharmacol Ther 13:543–556, 1981.
Colburn WA: Controversy III: To model or not to model. J Clin Montandon B, Roberts R, Fischer L: Computer simulation of sulfo-
Pharmacol 28:879–888, 1988. bromophthalein kinetics in the rat using flow-limited models
Cowles A, Borgstedt H, Gilles A: Tissue weights and rates of with extrapolation to man. J Pharm Biopharm 3:277–290, 1975.
blood flow in man for the prediction of anesthetic uptake and Rescigno A, Beck JS: The use and abuse of models. J Pharm Bio-
distribution. Anesthesiology 35:523–526, 1971. pharm 15:327–344, 1987.
Dedrick R, Forrester D, Cannon T, et al: Pharmacokinetics of Ritschel WA, Banerjee PS: Physiologic pharmacokinetic models:
1-β-d-arabinofurinosulcytosine (ARA-C) deamination in sev- Applications, limitations and outlook. Meth Exp Clin Pharmacol
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Gerlowski LE, Jain RK: Physiologically based pharmacoki- Rowland M, Tozer T: Clinical Pharmacokinetics—Concepts and
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Segre G: Pharmacokinetics: Compartmental representation. Wagner JG: Do you need a pharmacokinetic model, and, if so,
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Tozer TN: Pharmacokinetic principles relevant to bioavailability Welling P, Tse F: Pharmacokinetics. New York, Marcel Dekker,
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Mathematical
2 Fundamentals in
Pharmacokinetics
Antoine Al-Achi
Chapter Objectives1 CALCULUS
»» Algebraically solve mathematical Pharmacokinetic models consider drugs in the body to be in a
expressions related to dynamic state. Calculus is an important mathematic tool for ana-
pharmacokinetics. lyzing drug movement quantitatively. Differential equations are
»» Express the calculated and used to relate the concentrations of drugs in various body organs
theoretical pharmacokinetic over time. Integrated equations are frequently used to model the
values in proper units. cumulative therapeutic or toxic responses of drugs in the body.
»» Represent pharmacokinetic
data graphically using Cartesian Differential Calculus
coordinates (rectangular Differential calculus is a branch of calculus that involves finding
coordinate system) and the rate at which a variable quantity is changing. For example, a
semilogarithmic graphs. specific amount of drug X is placed in a beaker of water to dis-
solve. The rate at which the drug dissolves is determined by the
»» Use the least squares method
rate of drug diffusing away from the surface of the solid drug and
to find the best fit straight line
is expressed by the Noyes–Whitney equation:
through empirically obtained
data.
dX DA
»» Define various models Dissolution rate = = (C − C
dt l 1 2 )
representing rates and order
of reactions and calculate
where d denotes a very small change; X = drug X; t = time; D =
pharmacokinetic parameters
diffusion coefficient; A = effective surface area of drug; l = length
(eg, zero- and first-order) from
of diffusion layer; C1 = surface concentration of drug in the diffu-
experimental data based on
sion layer; and C2 = concentration of drug in the bulk solution.
these models.
The derivative dX/dt may be interpreted as a change in X (or a
derivative of X) with respect to a change in t.
In pharmacokinetics, the amount or concentration of drug in
the body is a variable quantity (dependent variable), and time is
considered to be an independent variable. Thus, we consider the
amount or concentration of drug to vary with respect to time.
1It is not the objective of this chapter to provide a detailed description of mathematical functions, algebra, or statistics. Readers who are
interested in learning more about these topics are encouraged to consult textbooks specically addressing these subjects.
27
28 Chapter 2
y
EXAMPLE »» »
The concentration C of a drug changes as a func-
tion of time t:
dx
C = f (t ) (2.1)
Consider the following data:
Time Plasma Concentration
(hours) of Drug C (μg/mL)
0 12
1 10
2 8 a b x
3 6 FIGURE 2-1 Integration of y = ax or ∫ax·dx.
4 4
5 2 A definite integral of a mathematical function is
the sum of individual areas under the graph of that
The concentration of drug C in the plasma is function. There are several reasonably accurate
declining by 2 mg/mL for each hour of time. The numerical methods for approximating an area. These
rate of change in the concentration of the drug methods can be programmed into a computer for
with respect to time (ie, the derivative of C ) may rapid calculation. The trapezoidal rule is a numerical
be expressed as method frequently used in pharmacokinetics to cal-
culate the area under the plasma drug concentration-
dc
= 2 µg/mL/h versus-time curve, called the area under the curve
dt
(AUC). For example, Fig. 2-2 shows a curve depict-
Here, f(t) is a mathematical equation that describes ing the elimination of a drug from the plasma after a
how C changes, expressed as single intravenous injection. The drug plasma levels
and the corresponding time intervals plotted in
C =12 −2t (2.2) Fig. 2-2 are as follows:
Integral Calculus 40
Integration is the reverse of differentiation and is con-
sidered the summation of f (x) ⋅ dx; the integral sign ∫ 30
implies summation. For example, given the function
y = ax, plotted in Fig. 2-1, the integration is ∫ ax ⋅ dx. 20
Compare Fig. 2-1 to a second graph (Fig. 2-2), where
the function y = Ae–x is commonly observed after an 10
intravenous bolus drug injection. The integration pro-
cess is actually a summing up of the small individual 0
pieces under the graph. When x is specified and is 0 1 2 3 4 5
given boundaries from a to b, then the expression Time (hours)
becomes a definite integral, that is, the summing up FIGURE 2-2 Graph of the elimination of drug from the
of the area from x = a to x = b. plasma after a single IV injection.
Plasma drug level (mg/mL)
Mathematical Fundamentals in Pharmacokinetics 29
estimated by back extrapolation of the data points
Plasma Drug Level
Time (hours) (μg/mL) using a log linear plot (ie, log y vs x). The last plasma
level–time curve is extrapolated to t = ∞. In this case
0.5 38.9 the residual area t
[AUC] ∞
t is calculated as follows:
n
1.0 30.3
t Cpn
2.0 18.4 [AUC] ∞ = (2.4)
tn k
3.0 11.1
4.0 6.77 where Cpn = last observed plasma concentration at tn
and k = slope obtained from the terminal portion of
5.0 4.10
the curve.
The trapezoidal rule written in its full form to
The area between time intervals is the area of a calculate the AUC from t = 0 to t = ∞ is as follows:
trapezoid and can be calculated with the following
formula: ∞ t Cpn
[AUC] = Σ[AUC] n +
0 tn−1 k
t C
[ ] n 1 + C
AUC n − n
= (t − t
t 2 n n 1) (2.3)
−
n−1 This numerical method of obtaining the AUC is
fairly accurate if sufficient data points are available.
where [AUC] = area under the curve, tn = time of As the number of data points increases, the trapezoi-
observation of drug concentration Cn, and tn–1 = time dal method of approximating the area becomes more
of prior observation of drug concentration corre- accurate.
sponding to Cn–1. The trapezoidal rule assumes a linear or straight-
To obtain the AUC from 1 to 4 hours in Fig. 2-2, line function between data points. If the data points
each portion of this area must be summed. The AUC are spaced widely, then the normal curvature of the
between 1 and 2 hours is calculated by proper substi- line will cause a greater error in the area estimate.
tution into Equation 2.3:
t 30.3+18.4 Frequently Asked Questions
[AUC] 2 = (2 −1) = 24.35 µg ⋅h/mL
t1 2 »»What are the units for logarithms?
»»What is the difference between a common log and a
Similarly, the AUC between 2 and 3 hours is calcu- natural log (ln)?
lated as 14.75 mg·h/mL, and the AUC between 3 and
4 hours is calculated as 8.94 mg·h/mL. The total
AUC between 1 and 4 hours is obtained by adding
the three smaller AUC values together. GRAPHS
The construction of a curve or straight line by plot-
t4 t t t
[AUC] = [AUC] 2 + [AUC] 3 + AUC
t t t [ ] 4 ting observed or experimental data on a graph is an
1 1 2 t3
important method of visualizing relationships
= 24.3+14.3+ 8.94
between variables. By general custom, the values of
= 48.04 µg ⋅h/mL the independent variable (x) are placed on the hori-
zontal line in a plane, or on the abscissa (x axis),
The total area under the plasma drug level–time whereas the values of the dependent variable are
curve from time zero to infinity (Fig. 2-2) is obtained placed on the vertical line in the plane, or on the
by summation of each individual area between each ordinate (y axis). The values are usually arranged so
pair of consecutive data points using the trapezoidal that they increase linearly or logarithmically from
rule. The value on the y axis when time equals 0 is left to right and from bottom to top.
30 Chapter 2
6 100
5
50
4
3
2 10
1
5
0
0 1 2 3 4 5 6 7 8
FIGURE 2-3 Rectangular coordinates. 1
0 1 2 3 4 5 6 7
FIGURE 2-4 Semilog coordinates.
In pharmacokinetics, time is the independent
variable and is plotted on the abscissa (x axis),
whereas drug concentration is the dependent variable observed data. If the relationship between x and y is
and is plotted on the ordinate (y axis). Two types of linearly related, then the relationship between the
graphs or graph papers are usually used in pharma- two can be expressed as a straight line.
cokinetics. These are Cartesian or rectangular coor- Physiologic variables are not always linearly
dinate (Fig. 2-3) and semilogarithmic graph or graph related. However, the data may be arranged or trans-
paper (Fig. 2-4). Semilogarithmic allows placement formed to express the relationship between the vari-
of the data at logarithmic intervals so that the num- ables as a straight line. Straight lines are very useful
bers need not be converted to their corresponding log for accurately predicting values for which there are
values prior to plotting on the graph. no experimental observations. The general equation
of a straight line is
Curve Fitting
Fitting a curve to the points on a graph implies that y = mx + b (2.5)
there is some sort of relationship between the vari-
ables x and y, such as dose of drug versus pharmaco- where m = slope and b = y intercept. Equation 2.5
logic effect (eg, lowering of blood pressure). could yield any one of the graphs shown in Fig. 2-5,
Moreover, when using curve fitting, the relationship depending on the value of m. The absolute magnitude
is not confined to isolated points but is a continuous of m gives some idea of the steepness of the curve.
function of x and y. In many cases, a hypothesis is For example, as the value of m approaches 0, the line
made concerning the relationship between the vari- becomes more horizontal. As the absolute value of m
ables x and y. Then, an empirical equation is formed becomes larger, the line slopes farther upward or
that best describes the hypothesis. This empirical downward, depending on whether m is positive or
equation must satisfactorily fit the experimental or negative, respectively.
y y y
m = 0 m < 0
b
b
b m > 0
x x x
FIGURE 2-5 Graphic demonstration of variations in slope (m).
Mathematical Fundamentals in Pharmacokinetics 31
Linear Regression/Least Squares Method between the variables. If a linear line deviates sub-
This method is often encountered and used in clinical stantially from the data, it may suggest the need for a
pharmacy studies to construct a linear relationship nonlinear regression model, although several vari-
between an independent variable (also known as the ables (multiple linear regression) may be involved.
input factor or the x factor) and a dependent variable Nonlinear regression models are complex mathemati-
(commonly known as an output variable, an outcome, cal procedures that are best performed with a com-
or the y factor). In pharmacokinetics, the relationship puter program.
between the plasma drug concentrations versus time
can be expressed as a linear function. Because of the
availability of computing devices (computer pro-
Frequently Asked Questions
grams, scientific calculators, etc), the development of
»»How is the area under the curve, AUC, calculated?
a linear equation has indeed become a simple task.
What are the units for AUC?
A general format for a linear relationship is often
expressed as: »»How do you know that the line that you fit to pro-
duce a curve on a graph is the line of best fit?
y = mx + b (2.6)
»»What assumptions are made when a line is fitted to
the points on a graph?
where y is the dependent variable, x is the indepen-
dent variable, m is the slope, and b is the y intercept.
The value of the slope and the y intercept may be
positive, negative, or zero. A positive linear relation-
ship has a positive slope, and a negative slope PRACTICE PROBLEM
belongs to a negative linear relationship (Gaddis and
Gaddis, 1990; Munro, 2005). Plot the following data and obtain the equation for
The strength of the linear relationship is the line that best fits the data by (a) using a ruler and
assessed by the correlation coefficient (r). The value (b) using the method of least squares. Data can be
of r is positive when the slope is positive and it is plotted manually or by using a computer spreadsheet
negative when the slope is negative. When r takes program such as Microsoft Excel.
the value of either +1 or −1, a perfect relationship
exists between the variables. A zero value for the
x (mg) y (hours) x (mg) y (hours)
slope (or for r) indicates that there is no linear rela-
tionship existing between y and x. In addition to r, 1 3.1 5 15.3
the coefficient of determination (r2) is often com- 2 6.0 6 17.9
puted to express how much variability in the out-
come is explained by the input factor. For example, 3 8.7 7 22.0
if r is 0.90, then r2 equals to 0.81. This means that 4 12.9 8 23.0
the input variable explains 81% of the variability
observed in y. It should be noted, however, that a
high correlation between the two variables does not Solution
necessarily mean causation. For example, the pas- Many computer programs have a regression analy-
sage of time is not really the cause for the drug sis, which fits data to a straight line by least squares.
concentration in the plasma to decrease. Rather it is In the least squares method, the slope m and the y
the distribution and the elimination functions that intercept b (Equation 2.7) are calculated so that the
cause the level of the drug to decrease over time average sum of the deviations squared is minimized.
(Gaddis and Gaddis, 1990; Munro, 2005). The deviation, d, is defined by
The linear regression/least squares method
assumes, for simplicity, that there is a linear relationship b + mx − y = d (2.7)
32 Chapter 2
If there are no deviations from linearity, then d = 0 Problems of Fitting Points to a Graph
and the exact form of Equation 2.7 is as follows: When x and y data points are plotted on a graph, a
relationship between the x and y variables is sought.
b + mx − y = 0
Linear relationships are useful for predicting values
for the dependent variable y, given values for the
To find the slope, m, and the intercept, b, the follow-
independent variable x.
ing equations are used:
The linear regression calculation using the least
squares method is used for calculating a straight line
Σ(x)Σ(y) − nΣ(xy)
m = (2.8) through a given set of points. However, it is impor-
2
[Σ(x)] − nΣ(x2 ) tant to realize that, when using this method, one has
already assumed that the data points are related lin-
where n = number of data points. early. Indeed, for three points, this linear relationship
may not always be true. As shown in Fig. 2-6, Riggs
Σ(x)Σ(xy) (1963) calculated three different curves that fit the
− Σ(x2 )Σy
b = (2.9)
2 data accurately. Generally, one should consider the
[Σ(x)] − nΣ(x2 ) law of parsimony, which broadly means “keep it
simple”; that is, if a choice between two hypotheses
where Σ is the sum of n data points. is available, choose the more simple relationship.
The following graph was obtained by using a If a linear relationship exists between the x and
Microsoft Excel spreadsheet and calculating a y variables, one must be careful as to the estimated
regression line (sometimes referred to as a trendline value for the dependent variable y, assuming a value
in the computer program): for the independent variable x. Interpolation, which
30 means filling the gap between the observed data on
y = 2.9679x + 0.2571
25
R2
= 0.99231 15
20
15
10
10 A
5
0 y
0 2 4 6 8 10
Therefore, the linear equation that best fits the 5
data is
y = 2.97x + 0.257 B
C
0
Although an equation for a straight line is obtained 0 2 4 6 8
by the least squares procedure, the reliability of the x
values should be ascertained. A correlation coeffi- FIGURE 2-6 Three points equally well fitted by different
cient, r, is a useful statistical term that indicates the curves. The parabola, y = 10.5 – 5.25x + 0.75×2 (curve A); the
relationship of the x, y data fit to a straight line. For exponential, y = 12.93e–1.005x + 1.27 (curve B); and the rectangular
a perfect linear relationship between x and y, r = +1. hyperbola, y = 6/x (curve C) all fit the three points (1,6), (2,3), and
(4,1.5) perfectly, as would an infinite number of other curves.
Usually, r ≥ 0.95 demonstrates good evidence or a
(Reprinted with permission from Riggs DS: The Mathematical
strong correlation that there is a linear relationship Approach to Physiological Problems. Baltimore, Williams &
between x and y. Wilkins, 1963.)
Mathematical Fundamentals in Pharmacokinetics 33
a graph, is usually safe and assumes that the trend An important rule in using equations with dif-
between the observed data points is consistent and ferent units is that the units may be added or sub-
predictable. In contrast, the process of extrapolation tracted as long as they are alike, but divided or
means predicting new data beyond the observed multiplied if they are different. When in doubt,
data, and assumes that the same trend obtained check the equation by inserting the proper units.
between two data points will extend in either direc- For example,
tion beyond the last observed data points. The use of
extrapolation may be erroneous if the regression
FD
line no longer follows the same trend beyond the AUC 0
= = concentration × time
kV
measured points. D
Graphs should always have the axes (abscissa (2.11)
µg 1mg µg ⋅h
and ordinate) properly labeled with units. For h = =
mL h−1 L mL
example, the amount of drug on the ordinate (y axis)
is given in milligrams and the time on the abscissa
(x axis) is given in hours. The equation that best fits Certain terms have no units. These terms include
the points on this curve is the equation for a straight logarithms and ratios. Percent may have no units
line, or y = mx + b. Because the slope m = ∆y/∆x, the and is expressed mathematically as a decimal
units for the slope should be milligrams per hour between 0 and 1 or as 0% to 100%, respectively.
(mg/h). Similarly, the units for the y intercept b On occasion, percent may indicate mass/volume,
should be the same units as those for y, namely, mil- volume/volume, or mass/mass. Table 2-1 lists com-
ligrams (mg). mon pharmacokinetic parameters with their sym-
bols and units.
A constant is often inserted in an equation to
MATHEMATICAL EXPRESSIONS quantify the relationship of the dependent variable
AND UNITS to the independent variable. For example, Fick’s
Mathematics is a basic science that helps to explain law of diffusion relates the rate of drug diffusion,
relationships among variables. For an equation to be dQ/dt, to the change in drug concentration, C, the
valid, the units or dimensions must be constant on surface area of the membrane, A, and the thick-
both sides of the equation. Many different units are ness of the membrane, h. In order to make this
used in pharmacokinetics, as listed in Table 2-1. For relationship an equation, a diffusion constant D is
an accurate equation, both the integers and the units inserted:
must balance. For example, a common expression
for total body clearance is dQ DA
= × ∆C (2.12)
dt h
Cl = kV 2 1 )
T d ( . 0
To obtain the proper units for D, the units for each of
After insertion of the proper units for each term in the other terms must be inserted:
the above equation from Table 2-1,
mg D(cm2 ) mg
= ×
h cm cm3
mL 1
= mL
h h D = cm2 /h
Thus, the above equation is valid, as shown by the The diffusion constant D must have the units of area/
equality mL/h = mL/h. time or cm2/h if the rate of diffusion is in mg/h.
34 Chapter 2
TABLE 2-1 Common Units Used in Pharmacokinetics
Parameter Symbol Unit Example
Rate dD Mass mg/h
dt Time
dC Concentration ug/mL/h
dt Time
Zero-order rate constant K Concentration
0 mg/mL/h
Time
Mass mg/h
Time
First-order rate constant k 1 1/h or h–1
Time
Drug dose D0 Mass mg
Concentration C Mass mg/mL
Volume
Plasma drug concentration Cp Drug mg/mL
Volume
Volume V Volume mL or L
Area under the curve AUC Constration × time mg·h/mL
Fraction of drug absorbed F No units 0 to 1
Clearance Cl Volume mL/h
Time
Half-life t1/2 Time H
UNITS FOR EXPRESSING BLOOD MEASUREMENT AND USE OF
CONCENTRATIONS SIGNIFICANT FIGURES
Various units have been used in pharmacology, toxi- Every measurement is performed within a certain
cology, and the clinical laboratory to express drug degree of accuracy, which is limited by the instru-
concentrations in blood, plasma, or serum. Drug con- ment used for the measurement. For example, the
centrations or drug levels should be expressed as weight of freight on a truck may be measured accu-
mass/volume. The expressions mcg/mL, mg/mL, and rately to the nearest 0.5 kg, whereas the mass of drug
mg/L are equivalent and are commonly reported in the in a tablet may be measured to 0.001 g (1 mg).
literature. Drug concentrations may also be reported Measuring the weight of freight on a truck to the
as mg% or mg/dL, both of which indicate milligrams nearest milligram is not necessary and would require
of drug per 100 mL (1 deciliter). Two older expres- a very costly balance or scale to detect a change in a
sions for drug concentration occasionally used in milligram quantity.
veterinary medicine are the terms ppm and ppb, which Significant figures are the number of accurate
indicate the number of parts of drug per million parts digits in a measurement. If a balance measures the
of blood (ppm) or per billion parts of blood (ppb), mass of a drug to the nearest milligram, measure-
respectively. One ppm is equivalent to 1.0 mg/mL. The ments containing digits representing less than 1 mg
accurate interconversion of units is often necessary to are inaccurate. For example, in reading the weight or
prevent confusion and misinterpretation. mass of a drug of 123.8 mg from this balance, the
Mathematical Fundamentals in Pharmacokinetics 35
0.8 mg is only approximate; the number is therefore A pharmacist is interested in learning the time
rounded to 124 mg and reported as the observed mass. needed for 90% of ASA to be released from the
For practical calculation purposes, all figures tablet. To answer her inquiry the following steps are
may be used until the final number (answer) is taken:
obtained. However, the answer should retain only the
1. Calculate the amount of ASA in milligrams
number of significant figures in the least accurate
representing 90% of the drug present in the
initial measurement.
tablet.
2. Replace the value found in step (1) in
PRACTICE PROBLEM Equation 2.14 and solve for time (t):
90% of 325 = (0.9)(325 mg) = 292.5 mg
When a patient swallows a tablet containing 325 mg 292.5 mg = 0.86t − 0.04
of aspirin (ASA), the tablet comes in contact with the 292.5 + 0.04 = 0.86t
contents of the gastrointestinal tract and the ASA is Dividing both sides of the equation by 0.86:
released from the tablet. Assuming a constant amount (292.5 + 0.04)/0.86 = (0.86t)/0.86
of the drug release over time (t), the rate of drug release 340.07 minutes = t
is expressed as: Or it takes 5.7 hours for this amount of ASA
(90%) to be released from the tablet.
d(ASA)
Rate of drug (ASA) release (mg/min) =
dt The above calculations show that this tablet
= k0 releases the drug very slowly over time and it may
not be useful in practice when the need for the drug
where k0 is a rate constant. is more immediate. It should also be emphasized that
Integration of the rate expression above gives only the amount of the drug released and soluble in
Equation 2.13: the GI juices is available for absorption. If the drug
precipitates out in the GI tract, it will not be absorbed
Amount of ASA released (mg) = at + b (2.13) by the GI mucosa. It is also assumed that the unab-
sorbed portion of the drug in the GI tract is consid-
ered to be “outside the body” because its effect
The symbol “a” represents the slope (equivalent to k0), cannot be exerted systematically.
t is time, and b is the y intercept. Assuming that time
To calculate the amount of ASA that was imme-
was measured in minutes, the following mathematical
diately released from the tablet upon contact with
expression is obtained representing Equation 2.13:
gastric juices, the time in Equation 2.14 is set to the
value zero:
Amount of ASA released (mg) = 0.86t − 0.04
(2.14)
Amount of ASA released (mg) = 0.86(0) − 0.04
To calculate the amount of ASA released at
180 seconds, the following algebraic manipulations Amount of ASA released (mg) = −0.04 mg
are needed:
1. Convert 180 seconds to minutes: 3 minutes.
2. Replace t in Equation 2.14 by the value 3. Since an amount released cannot be negative, this
3. Solve the equation for the amount of ASA indicates that no amount of ASA is released from
released. the tablet instantly upon coming in touch with the
juices. Equation 2.14 may be represented graphi-
Amount of ASA released (mg) = 0.86(3) − 0.04 cally using Cartesian or rectangular coordinates
= 2.54 mg (Fig. 2-7).
36 Chapter 2
60 the area under the moment curve, whereas MRT is
the mean residence time, which is estimated from the
50
ratio of AUMC(0–infinity)/AUC(0–infinity). These
40 pharmacokinetic terms are discussed in more details
throughout this textbook.
30 The below table (Ravi Shankar et al., 2012)
shows pharmacokinetic data obtained from a study
20
conducted in rabbits following administration of
10 various formulations of rectal suppositories contain-
ing aspirin (600 mg each). Various formulations
0
0 10 20 30 40 50 60 70 were prepared in a suppository base made of a mix-
Time (minutes) ture of gelatin and glycerin. Formulation Fas9 had
the same composition as Fs9 with the exception that
FIGURE 2-7 Amount of ASA released versus time (minutes) Fas9 contained ASA in the form of nanoparticles,
plotted on Cartesian coordinates.
whereas Fs9 had ASA in its free form (so did formu-
lations Fs2, Fs4, and Fs11, but varied in their gelatin/
glycerin composition). The authors concluded that
PRACTICE PROBLEM the incorporation of ASA in the form of nanoparti-
cles increased the Tmax. The other pharmacokinetic
Briefly, Cmax is the maximum drug concentration in parameters taken together indicate that nanoparticles
the plasma and Tmax is the time associated with Cmax. produced a sustained-release profile of ASA when
First-order elimination rate constant signifies the given in this dosage form. In this study, the plasma
fraction of the drug that is eliminated per unit time. concentration was expressed in “micrograms per
The biological half-life of the drug is the time needed milliliter.” If the mg/mL were not specified, it would
for 50% of the drug to be eliminated. The AUC term have been difficult to compare the results from this
or the area under the drug plasma concentration- study with other similar studies. It is imperative,
versus-time curve reflects the extent of absorption therefore, that pharmacokinetic parameters such as
from the site of administration. The term AUMC is Cmax be properly defined by units.
Pharmacokinetic
Parameters Fs2 Fs4 Fs9 Fs11 Fas9
Cmax (mg/mL) 34.93 ± 0.60 31.16 ± 1.04 32.66 ± 1.52 35.33 ± 0.57 31.86 ± 0.41
Tmax (hours) 1 ± 0.01 1 ± 0.03 1 ± 0.06 1 ± 0.09 6 ± 0.03
Elimination rate constant (h–1) 0.14 ± 0.02 0.19 ± 0.06 0.205 ± 0.03 0.17 ± 0.01 0.133 ± 0.004
Half-life (hours) 1.88 ± 0.76 1.9 ± 1.19 1.43 ± 0.56 1.99 ± 0.24 5.11 ± 0.15
AUC(0–t) 127.46 ± 8.9 126.62 ± 2.49 132.11 ± 3.88 127.08 ± 1.95 260.62 ± 4.44
AUC(0–infinity)(ng·h/mL) 138.36 ± 13.87 131.61 ± 0.27 136.89 ± 4.40 133.07 ± 2.97 300.48 ± 24.06
AUMC(0–t)(ng·h2/mL) 524.51 ± 69.64 516.04 ± 28.25 557.84 ± 16.25 501.29 ± 26.65 2006.07 ± 38.00
AUMC(0–infinity)(ng·h2/mL) 382.09 ± 131.45 237.74 ± 64.37 232.93 ± 28.16 257.71 ± 30.04 1494.71 ± 88.21
MRT (hours) 2.45 ± 0.36 2.31 ± 0.80 1.41 ± 0.31 2.95 ± 0.17 8.23 ± 0.06
Ravi Sankar V, Dachinamoorthi D, Chandra Shekar KB: A comparative pharmacokinetic study of aspirin suppositories and aspirin nanoparticles loaded
suppositories. Clinic Pharmacol Biopharm 1:105, 2012.
Amount of ASA released (mg)
Mathematical Fundamentals in Pharmacokinetics 37
Expressing the Cmax value by equivalent units units is ([amount][time]/[volume]). Together, the rate
is also possible. For example, converting mg/mL to and extent of absorption refers to the bioavailability
mg/dL follows these steps: of the drug from the site of administration. The term
“absolute bioavailability” is used when the reference
1. Convert micrograms (also written as mcg) to
route of administration is the intravenous injection
milligrams.
(ie, the IV route). If the reference route is different
2. Convert milliliters to deciliters:
from the intravenous route, then the term “relative
Since:
bioavailability” is used. The value for the AUC (0 to
1 mg = 1000 mg, then 31.86 mg/mL = 0.03186
+∞) following the administration of Fs2, Fs4, and
mg/mL
Fas9 was 138.36, 131.61, and 300.48 ng·h/mL,
1 dL = 100 mL, then 31.86 mg/mL = 3186
respectively (Ravi Sankar et al, 2012). The origin of
mg/dL
the AUC units is based on the trapezoidal rule. The
We have to divide the value of Cmax by 1000
trapezoidal rule is a numerical method frequently
and multiply it by 100. The net effect is to divide
used in pharmacokinetics to calculate the area under
the number by 10, or (31.86)(100/1000) =
the plasma drug concentration-versus-time curve,
3.19 mg/dL.
called the area under the curve (AUC). This rule
Expressing the Cmax value 34.93 mg/mL in nano- computes the average concentration value of each
grams per microliter (ng/mL) is done as follows: consecutive concentration and multiplies them by the
difference in their time values. To compute the AUC
1. Convert the number of micrograms to nano-
(0 to time t), the sum of all these products is calcu-
grams.
lated. For example, AUC(0–t) = 127.46 ng·h/mL can
2. Convert milliliters to microliters:
be written as 127.46 (ng/mL)(h).
1 mg = 1000 ng, or 34.93 mg/mL = 34,930 To convert 260.62 ng·h/mL to mg·-h/mL, divide
ng/mL the value by 1000 (recall that 1 mg is 1000 ng).
1 mL = 1000 mL, or 34.93 mg/mL = Therefore, the AUC value becomes 0.26 mg·h/mL.
0.03493 mg/mL Expressing the AUC (0 to +∞) value 300.48
As 34.93 was multiplied and divided by the ng·h/mL in ng·min/mL can be accomplished by
same number (1000), the final answer is dividing 300.48 by 60 (1 hour is 60 min). Thus, the
34.93 ng/mL. AUC value becomes 5.0 ng·min/mL.
Consider the following data:
Express the Cmax value 35.33 mg/mL in %w/v (this is
defined as the number of grams of ASA in 100 mL
plasma). Plasma Time AUC
Concentration (ng/L) (hours) (ng·h/L)
(35.33 mg/mL)(100 mL) = 3533 mg/dL = 0 0 0
3.533 mg/dL = 0.0035 g/dL, or 0.0035% w/v 0.05 1 0.025
(This means that there is 0.0035 g of ASA
0.10 2 0.075
in every 100 mL plasma.)
0.18 3 0.140
The data (Tmax, Cmax) represent a maximum point on 0.36 5 0.540
the plasma drug level-versus-time curve. This point 0.13 7 0.490
reflects the rate of absorption of the drug from its
site of administration. Another pharmacokinetic 0.08 9 0.210
measure obtained from the same curve is the area
under the curve (AUC). It reflects the extent of To compute the AUC value from initial to 9
absorption for a drug from the site of administration hours, sum up the values under the AUC column
into the circulation. The general format for the AUC above (0.025 + 0.075 + … + 0.210 = 1.48 ng·h/L).
38 Chapter 2
To convert the AUC value 1.48 ng·h/L to 0.4
mg·min/dL, use the following steps: 0.35
1. Divide the value by 106 to convert the nano- 0.3
grams to milligrams.
2. Divide the value by 60 to convert the hours to 0.25
minutes. 0.2
3. Divide the value by 10 to convert the liters to
0.15
deciliters.
0.1
AUC = (1.48)/[(106 )(60)(10)] 0.05
5 6 7 8 9
–9
= 2.47 ×10 mg·min/dL (2.15) Time (hours)
FIGURE 2-9 The exponential decline in plasma concen-
Figure 2-8 represents the data in a rectangular tration over time portion in Fig. 2-8.
coordinate–type graph. Time is placed on the x axis
(the abscissa) and plasma concentration is placed on bases or weak acids, the pH of the biological fluid
the y axis (the ordinate). The highest point on the determines the degree of ionization of the drug and
graph can simply be determined by spotting it on the this in turns influences the pharmacokinetic profile of
graph. Note that the plasma concentration declines the drug. The pH scale is a logarithmic scale:
exponentially from the apex point on the curve over
time. Figure 2-9 shows the exponential portion of the
pH = −log[H O+ ]= log(1/[H +
3 3O ]) (2.16)
graph on its own.
Exponential and Logarithmic Functions where the symbol “log” is the logarithm to base 10.
The natural logarithm has the symbol “ln,” which is
These two mathematical functions are related to each
the logarithm to base e (the value of e is approxi-
other. For example, the pH of biological fluids (eg,
mately 2.71828). The two functions are linked by the
plasma or urine) can influence all pharmacokinetic
following expression:
aspects including drug dissolution/release in vitro
as well as systemic absorption, distribution, metabo-
lism, and excretion. Since most drugs are either weak ln x = 2.303 log x (2.17)
The concentration of hydronium ions [H3O+]
0.4
can be calculated from Equation 2.16 as follows:
0.35
0.3
[H3O
+ ] 10−pH
= (2.18)
0.25
0.2
For example, the pH of a patient’s plasma is 7.4 at
0.15
room temperature. Therefore, the hydronium ion
0.1
concentration in plasma is:
0.05
0
[H3O
+ ] = 10−7.4
= 3.98 10−8
× M
–0.05
0 2 4 6 8 10
Time (hours) The value (3.98 × 10–8) is the antilogarithm of 7.4.
FIGURE 2-8 Plasma concentration (g/L)-versus-time With the availability of scientific calculators and
(hours) curve plotted on Cartesian coordinates. computers, these functions can be easily calculated.
Plasma concentration (g/L)
Plasma concentration (g/L)
Mathematical Fundamentals in Pharmacokinetics 39
–1 The slope of the line is (−0.38). Thus,
Slope = −0.38 = −k
–1.5 1
Multiplying both sides of the equation by (−1)
–2 results in:
k1 = 0.38 h–1
–2.5
5 6 7 8 9 where k1 is the first-order elimination rate constant.
Time (hours) The units for this constant are reciprocal time, such
as h–1 or 1/h. The value 0.38 h–1 means that 38% of
FIGURE 2-10 ln (Plasma concentration)-versus-time the concentration remaining of the drug in plasma is
curve plotted on Cartesian coordinates.
eliminated every hour.
Using Equation 2.17, Equation 2.19 can be con-
Oftentimes, converting plasma concentrations verted to the following expression:
to logarithmic values and plotting the logarithmic
values against time would convert an exponential
relationship to a linear function between the two 2.303 [log (Plasma concentration)] = 0.77 − 0.38
variables. Consider, for example, Fig. 2-9. When the Time (hours)
concentration values are converted to logarithmic
values, the graph now becomes linear (Fig. 2-10).
Dividing both sides of the equation by 2.303:
This same linear function may be obtained by plotting
the actual values of the plasma concentration versus
time using a semilogarithmic graph (Fig. 2-11). The 2.303 [log (Plasma concentration)]/2.303 =
following equation represents the straight line: [0.77 − 0.38 Time (hours)]/2.303
log (Plasma concentration) = 0.334 − 0.17
ln (Plasma concentration) = 0.77 − 0.38 Time (hours) Time (hours)
(2.19) (2.20)
0.4 Equation 2.20 is mathematically equivalent to
Equation 2.19.
0.3 The value 0.77 in Equation 2.19 equals (ln C0),
where C0 is the initial concentration of the drug in
0.2 plasma. Thus,
ln C0 = 0.77
0.1 C0 = e0.77 = 2.16 g/L
0.09
0.08
0.07
5 6 7 8 9 Once k1 is known, the AUC from the last data point
Time (hours) to t–infinity can be calculated as follows:
FIGURE 2-11 Plasma concentration-versus-time curve
using a semilogarithmic graph. AUC = CLast/k1 (2.21)
Plasma concentration (g/L) In (plasma concentration)
40 Chapter 2
Applying Equation 2.21 on the data used to obtain the may be defined in terms of specifying its order. In
AUC value in Equation 2.15 results in the following pharmacokinetics, two orders are of importance, the
value: zero order and the first order.
AUC = 0.08/0.38 = 0.21 g·h/L
Zero-Order Process
And the total AUC (t = 0 to t = infinity): The rate of a zero-order process is one that proceeds
over time (t) independent from the concentration of
the drug (c). The negative sign for the rate indicates
AUCTotal = 1.48 + 0.21 = 1.69 g·h/L
that the concentration of the drug decreases over time.
The following rules may be useful in handling
exponential and logarithmic functions. For this, if m −dc/dt = k0 (2.22)
and n are positive, then for the real numbers q and s
dc = −k
(Howard, 1980): 0 dt
c = c0 − k0t (2.23)
Exponent rules:
1. m0 = 1 where c0 is the initial concentration of the drug at
2. m1 = m t = 0 and k0 is the zero-order rate constant. The units
3. m–1 = 1/m1
for k0 are concentration per unit time (eg, [mg/mL]/h)
4. mq/ms = mq–s
or amount per unit time (eg, mg/h).
5. (mq)(ms) = mq+s
For example, calculate the zero-order rate con-
6. (mq)s = mqs
stant ([ng/mL]/min) if the initial concentration of
7. (mq/nq) = (m/n)q
the drug is 200 ng/mL and that at t = 30 minutes is
8. (mq)(nq) = (mn)q
35 ng/mL.
If z is any positive number other than 1 and if
zy = x, then following logarithmic rules apply:
c = c0 − k0 t
Logarithm rules:
35 = 200 − k0 (30)
1. y = logz x (y is the logarithm to the base z of x)
−k0 = (35 − 200)/30 = −5.5
2. For x > 1, then loge x = ln x (where e is approxi-
mately 2.71828) k0 = 5.5 (ng/mL)/min
3. logz x = (ln x/ln z)
4. logz mn = logz m + logz n
5. logq (m/n) = logq m − logq n
When does the concentration of drug equal to 100
6. logz (1/m) ng/mL?
= −logz m
7. ln e = 1
8. For z = 10, then logz 1 = 0 100 = 200 − 5.5 t
9. logz mh = h logz m
10. For z = 10, then (2.303) logz x = ln x (100 − 200)/5.5 = −t
−18.2 = −t
t = 18.2 min
RATES AND ORDERS OF PROCESSES
Oftentimes a process such as drug absorption or drug In pharmacokinetics, the time required for one-
elimination may be described by the rate by which half of the drug concentration to disappear is known
the process proceeds. The rate of a process, in turn, as t½. Thus, for this drug the t½ is 18.2 minutes.
Mathematical Fundamentals in Pharmacokinetics 41
In general, t½ may be calculated as follows for a ln 0.5/−k1 = t½
zero-order process:
t½ = −0.693/−k1
c = c0 − k0t t½ = 0.693/k1 (2.27)
(0.5 c0 ) = c0 − k0t12
(0.5 c0 ) − c0 = −k0t1 Unlike a zero-order rate process, the t1/2 for a first-
2
order rate process is always a constant, independent
−0.5 c0 = −k0t12 of the initial drug concentration or amount (Table 2-2,
Fig. 2-12).
t1 = (0.5 c0 )/k0 (2.24)
2 A plot between ln c versus t produces a straight
line. A semilogarithmic graph also produces a
Applying Equation 2.24 to the example above straight line between c and t. The units of the first-
should yield the same result: order rate constant (k1) are in reciprocal time.
t½ = (0.5 c0)/k0 TABLE 2-2 Comparison of Zero- and First-
t½ = (0.5)(200)/5.5 = 18.2 minutes Order Reactions
Zero-Order First-Order
A plot of x versus time on rectangular coordinates Reaction Reaction
produces a straight line with a slope equal to (−k0) Equation –dC/dt = k0 –dC/dt = kC
and a y intercept as c0. In a zero-order process the t1/2 C = –k0t + C0 C = C –
0 e kt
is not constant and depends upon the initial amount
or concentration of drug. Rate constant— (mg/L)/h 1/h
units
First-Order Process Half-life, t1/2 t1/2 = 0.5C/k0 t1/2 = 0.693/k
(units = time) (not constant) (constant)
The rate of a first-order process is dependent upon
the concentration of the drug: Effect of time Zero-order rate First-order rate
on rate is constant with will change with
respect to time respect to time
−dc/dt = k c
1 as concentration
(2.25)
changes
−dc/c = k dt
1
Effect of time on Rate constant Rate con-
rate constant with respect to stant remains
lnc = lnc t (2.26) time changes as constant with
0 − k1
the concentra- respect to time
tion changes
While the rate of the process is a function of the drug
Drug concen- Drug concentra- Drug concentra-
concentration, the t½ is not: trations versus tions decline tions decline
time—plotted linearly for a nonlinearly for
on rectangular zero-order rate a first-order rate
ln c = ln c0 − k1t coordinates process process
ln (0.5 c ug concen- Drug concentra- Drug concentra-
0) = ln c0 − k Dr
1t½
trations versus tions decline tions decline
ln (0.5 c linearly for a
0) − ln c0 = −k time—plotted nonlinearly for a
1t½
on a semiloga- zero-order rate single first-order
ln (0.5 c rithmic graph process rate process
0 /c0) = −k1t½
42 Chapter 2
ln 0.3/−k1 = t
100
t = −1.2/−0.04 = 30 hours
50
The value 30 hours may be written as t30 = 30 hours
(it is t30 because 70% of the drug is eliminated).
t1/2
10 Determination of Order
Graphical representation of experimental data pro-
5 vides a visual relationship between the x values
t1/2 (generally time) and the y axis (generally drug
concentrations). Much can be learned by inspecting
the line that connects the data points on a graph.
The relationship between the x and y data will
1
0 4 8 12 14 20 24 determine the order of the process, data quality,
Time (hours) basic kinetics, and number of outliers, and provide
FIGURE 2-12 The t1/2 in a first-order rate process is a the basis for an underlying pharmacokinetic model.
constant. To determine the order of reaction, first plot the
data on a rectangular graph. If the data appear to be a
For a drug with k1 = 0.04 h–1, find t½. curve rather than a straight line, the reaction rate
for the data is non-zero order. In this case, plot the
data on a semilog graph. If the data now appear to
t½ = 0.693/k1 form a straight line with good correlation using
linear regression, then the data likely follow first-
t½ = 0.693/0.04 = 17.3 hours
order kinetics. This simple graph interpretation is
true for one-compartment, IV bolus (Chapter 4).
The value 0.04 h–1 for the first-order rate constant Curves that deviate from this format are discussed
indicates that 4% of the drug disappears every in other chapters in terms of route of administration
hour. and pharmacokinetic model.
Calculate the time needed for 70% of the drug
to disappear.
Frequently Asked Questions
»»How is the rate and order of reaction determined
ln c = ln c0 − k1t graphically?
ln (0.3 c0) = ln c0 − k1t »»What is the difference between a rate and a rate
constant?
ln (0.3 c0) − ln c0 = −k1t
CHAPTER SUMMARY
Pharmacokinetic calculations require basic skills in line by plotting observed or experimental data on a
mathematics. Although the availability of computer graph is an important method of visualizing relation-
programs and scientific calculators facilitate pharma- ships between variables. The linear regression calcu-
cokinetic calculations, the pharmaceutical scientist lation using the least squares method is used for
should be familiar with fundamental rules pertaining calculation of a straight line through a given set of
to calculus. The construction of a curve or straight points. However, it is important to realize that, when
Drug concentration (mg/mL)
Mathematical Fundamentals in Pharmacokinetics 43
using this method, one has already assumed that the order. In pharmacokinetics, two orders are of impor-
data points are related linearly. For all equations, both tance, the zero order and the first order. Mathematical
the integers and the units must balance. The rate of a skills are important in pharmacokinetics in particular
process may be defined in terms of specifying its and in pharmacy in general.
LEARNING QUESTIONS
1. Plot the following data on both semilog graph 3. A pharmacist dissolved a few milligrams of
paper and standard rectangular coordinates. a new antibiotic drug into exactly 100 mL of
distilled water and placed the solution in a
Time (minutes) Drug A (mg) refrigerator (5°C). At various time intervals,
the pharmacist removed a 10-mL aliquot from
10 96.0
the solution and measured the amount of drug
20 89.0 contained in each aliquot. The following data
40 73.0 were obtained:
60 57.0
Time (hours) Antibiotic (μg/mL)
90 34.0
0.5 84.5
120 10.0
1.0 81.2
130 2.5
2.0 74.5
a. Does the decrease in the amount of drug A 4.0 61.0
appear to be a zero-order or a first-order
6.0 48.0
process?
b. What is the rate constant k? 8.0 35.0
c. What is the half-life t1/2? 12.0 8.7
d. Does the amount of drug A extrapolate to
zero on the x axis? a. Is the decomposition of this antibiotic a first-
e. What is the equation for the line produced order or a zero-order process?
on the graph? b. What is the rate of decomposition of this
2. Plot the following data on both semilog graph antibiotic?
paper and standard rectangular coordinates. c. How many milligrams of antibiotics were
in the original solution prepared by the
Time (minutes) Drug A (mg) pharmacist?
4 70.0 d. Give the equation for the line that best fits
the experimental data.
10 58.0
4. A solution of a drug was freshly prepared at a
20 42.0 concentration of 300 mg/mL. After 30 days at
30 31.0 25°C, the drug concentration in the solution
was 75 mg/mL.
60 12.0
a. Assuming first-order kinetics, when will
90 4.5 the drug decline to one-half of the original
120 1.7 concentration?
b. Assuming zero-order kinetics, when will
Answer questions a, b, c, d, and e as stated in the drug decline to one-half of the original
Question 1. concentration?
44 Chapter 2
5. How many half-lives (t1/2) would it take for 12. The following information was provided by
99.9% of any initial concentration of a drug to Steiner et al (2013):
decompose? Assume first-order kinetics.
“ACT-335827 hydrobromide (Actelion Phar-
6. If the half-life for decomposition of a drug is
maceuticals Ltd., Switzerland) was freshly
12 hours, how long will it take for 125 mg of
prepared in 10% polyethylene glycol 400/0.5%
the drug to decompose by 30%? Assume first-
methylcellulose in water, which served as
order kinetics and constant temperature.
vehicle (Veh). It was administered orally at
7. Exactly 300 mg of a drug is dissolved into an
300 mg/kg based on the weight of the free base,
unknown volume of distilled water. After com-
in a volume of 5 mL/kg, and administered daily
plete dissolution of the drug, 1.0-mL samples
2 h before the onset of the dark phase.”
were removed and assayed for the drug. The
following results were obtained: How many milligrams of ACT-335827 hydro-
bromide would be given orally to a 170-g rat?
13. Refer to Question 12; how many milliliters
Time (hours) Concentration (mg/mL)
of drug solution would be needed for the
0.5 0.45 170-g rat?
2.0 0.3 14. Refer to Question 12; express 0.5% methylcel-
lulose (%w/v) as grams in 1 L solution.
15. The t½ value for aceclofenac tablet following
Assuming zero-order decomposition of the oral administration in Wistar male rats was
drug, what was the original volume of water in reported to be 4.35 hours (Shakeel et al, 2009).
which the drug was dissolved? Assuming a first-order process, what is the
8. For most drugs, the overall rate of drug elimination rate constant value in hours–1?
elimination is proportional to the amount of
16. Refer to Question 15; express the value of t½
drug remaining in the body. What does in minutes.
this imply about the kinetic order of drug
17. Refer to Question 15; the authors reported
elimination? that the relative bioavailability of aceclofenac
9. A single cell is placed into a culture tube from a transdermally applied gel is 2.6 folds
containing nutrient agar. If the number of cells higher compared to that of an oral tablet. The
doubles every 2 minutes and the culture tube following equation was used by the authors to
is completely filled in 8 hours, how long does calculate the relative bioavailability:
it take for the culture tube to be only half full
of cells? F% = {[(AUC sample)(Dose oral)]/
10. Cunha (2013) reported the following: “…CSF
[(AUC oral)(Dose sample)]}*100 (2.28)
levels following 2 g of ceftriaxone are
approximately 257 mcg/mL, which is well
above the minimal inhibitory concentration where AUC/Dose sample is for the gel and
(MIC) of even highly resistant (PRSP) in AUC/Dose oral is for the tablet. F% is the rela-
CSF…” What is the value of 257 mcg/mL tive bioavailability expressed in percent. If
in mg/mL? oral and transdermal doses were the same,
11. Refer to Question 10 above; express the value calculate AUC sample given AUC oral of
257 mcg/mL in mcg/dL. 29.1 mg·h/mL. What are the units for AUC
sample in (mg·day/mL)?
Mathematical Fundamentals in Pharmacokinetics 45
18. 300
DMAA_Concentration vs Time
1
200 2
3
4
5
6
100 7
8
Mean
0
0 5 10 15 20 25
Time (hours)
The above figure (from Basu Sarkar et al, The equation in the graph is that for the standard
2013) shows the plasma concentration–time curve generated for progesterone using a high-
profile of DMAA (1,3-dimethylamylamine) in performance liquid chromatography method.
eight men following a single oral dose of the In the equation, y is the area under the curve of
DMAA (25 mg). progesterone peak and x represents the concen-
What type of graph paper is the above graph? tration of the drug in mg/mL. Using this equa-
(Semilogarithmic or rectangular?) tion, predict the AUC for a drug concentration
19. Refer to Question 18; what are the C of 35 mg/mL.
max
and Tmax values for subject #1? (subject #1) 24. Refer to Question 23; predict the concentration
occurred at Tmax of ____ hour. of progesterone (mg/L) for a peak area (AUC)
20. Refer to Question 18; what is the average C of 145.
max
value for all eight subjects? Please use the cor- 25. Consider the following function dc/dt = 0.98
rect units for your answer. with c and t being the concentration of the drug
21. Refer to Question 18; what are the units for and time, respectively. This equation can also
AUC obtained from the graph? be written as ______.
22. Refer to Question 18; for subject #3, the C a. x = x0 − 0.98 t
max
value is approximately 105 ng/mL. Express b. x = 0.98 − t
this concentration in %w/v. c. x = x0 + 0.98 t
23. Consider the following graph (Figure 2a in the d. x = t/0.98
original article) presented in Schilling et al (2013):
180
y = 1.6624x – 0.3
160 R2 = 0.9998
140
120
100
80
60
40
20
0
0 25 50 75 100 125
DMAA_Concentration (ng/mL)
46 Chapter 2
ANSWERS
Learning Questions Notice that the answer differs in accordance
with the method used.
1. a. Zero-order process (Fig. A-1). c. t1/2
For zero-order kinetics, the larger the initial
100
amount of drug A0, the longer the t1/2.
Method 1
80 0.5A
t 0
1/2 =
k0
60 0.5(103.5)
t1/2 = = 66 min
0.78
40 Method 2
The zero-order t1/2 may be read directly from
the graph (see Fig. A-1):
20
At t = 0, A0 = 103.5 mg
At t1/2 , A = 51.8 mg
0
0 20 40 60 80 100 120 140
Minutes Therefore, t1/2 = 66 min.
d. The amount of drug, A, does extrapolate to
FIGURE A-1
zero on the x axis.
b. Rate constant, k The equation of the line is
0: e.
Method 1 A = −k0t + A0
Values obtained from the graph (see Fig. A-1): A = −0.78t +103.5
2. a. First-order process (Fig. A-2).
t (minutes) A (mg)
40 70 100
80 41
50
∆Y y − y
lope 1
−k 2
0 = s = =
∆X x
2 − x1
20
41 − 71
−k0 = k0 = 0.75 mg/min
80 − 40
10
Notice that the negative sign shows that the
slope is declining. 5
Method 2
By extrapolation: 2
A0 = 103.5 at t = 0; A = 71 at t = 40 min
A 1
= k0t + A0 0 20 40 60 80 100 120
71= −40k Minutes
0 +103.5
k0 = 0.81 mg/min FIGURE A-2
A (mg)
A (mg)
Mathematical Fundamentals in Pharmacokinetics 47
b. Rate constant, k: 3. a. Zero-order process (Fig. A-3).
Method 1
Obtain the first-order t1/2 from the semilog 100
graph (see Fig. A-2):
80
t (minutes) A (mg)
30 30
60
53 15
t1/2 = 23 min 40
0.693 0.693
k = = = 0.03 min−1
t1/2 23 20
Method 2
0
0 2 4 6 8 10 12
−k logY2 − logY
Slope 1 Hours
= =
2.3 X2 − X1 FIGURE A-3
−2.3 (log15− log 30)
k 0.03 min−1
= =
53− 30
∆Y
b. k0 = slope =
∆X
c. t1/2 = 23 min (see Method 1 above). Values obtained from the graph (see
d. The amount of drug, A, does not extrapolate Fig. A-3):
to zero on the x axis.
e. The equation of the line is
t (hours) C (μg/mL)
−kt 1.2 80
log A = − + log A
2.3 0
4.2 60
0.03t
log A = − + log78
2.3 It is always best to plot the data. Obtain a
regression line (ie, the line of best fit), and
A − t
= 78e 0.03
then use points C and t from that line.
On a rectangular plot, the same data show a 60 − 80
−k0 =
curve (not plotted). 4.2 −1.2
k0 = 6.67 µg/mL/h
c. By extrapolation:
At t0, C0 = 87.5 mg/mL.
d. The equation (using a ruler only) is
A = −k0t + A0 = −6.67t + 87.5
A better fit to the data may be obtained by
using a linear regression program. Linear
regression programs are available on spread-
sheet programs such as Excel.
mg/mL
48 Chapter 2
4. Given: Method 3
A t1/2 value of 20 days may be obtained
C (mg/mL) t (days) directly from the graph by plotting C against
300 0 t on rectangular coordinates.
5. Assume the original concentration of drug to be
75 30
1000 mg/mL.
−kt Method 1
a. logC = − + logC
2.3 0
No. of Half- No. of Half-
−30k
log75 = − + log300 mg/mL Lives mg/mL Lives
2.3
1000 0 15.6 6
k = 0.046 days−1
500 1 7.81 7
0.693 0.693
t 250 2 3.91 8
1/2 = = = 15 days
k 0.046
125 3 1.95 9
b. Method 1 62.5 4 0.98 10
300 mg/mL 31.3 5
= C0 at t = 0
75 mg/mL = C at t = 30 days 99.9% of 1000 = 999
225 mg/mL = difference between initial and Concentration of drug remaining = 0.1% of
final drug concentration 1000
225 mg/mL 1000 − 999 = 1 mg/mL
k0 = = 7.5 mg/mL/d
30 days It takes approximately 10 half-lives to eliminate
all but 0.1% of the original concentration of
The time, t1/2, for the drug to decompose drug.
to one-half C0 (from 300 to 150 mg/mL) is
Method 2
calculated by (assuming zero order):
Assume any t1/2 value:
150 mg/mL
t1/2 = = 20 days
75 mg/mL/day 0.693
t1/2 =
k
Method 2 Then
C = −k0t + C0 0.693
k =
75 30k 300 t
= − 1/2
0 +
k mg/mL/d −kt
0 = 7.5 logC = + logC
2.3 0
At t1/2 ,C = 150 mg/mL
−kt
log1.0 = + log1000
150 = −7.5t 2.3
1/2 + 300
t = 9.96 t
t 1/2
1/2 = 20 days
Mathematical Fundamentals in Pharmacokinetics 49
Substituting 0.693/t1/2 for k: Alternatively, at t = 0.5 hour,
−0.693 t 0.45 = –0.1(0.5) –C0
log1.0 = + log1000
2.3× t1/2 C0 = 0.5 mg/mL
t = 9.96 t1/2 Since the initial mass of drug D0 dissolved is
300 mg and the initial drug concentration C0 is
6. t1/2 = 12 h 0.5 mg/mL, the original volume may be calcu-
0.693 0.693 lated from the following relationship:
k = = = 0.058 h–1
t1/2 12 D
C 0
0 =
V
If 30% of the drug decomposes, 70% is left.
Then 70% of 125 mg = (0.70)(125) = 87.5 mg 300 mg
0.5 mg/mL =
V
A0 = 125 mg V = 600 mL
A = 87.5 mg
8. First order.
k −1
= 0.058 h 9. The volume of the culture tube is not impor-
kt tant. In 8 hours (480 minutes), the culture tube
log A = − + log A
2.3 0 is completely full. Because the doubling time
for the cells is 2 minutes (ie, one t1/2), then in
0.058t
log 87.5 = − + log125 480 minutes less 2 minutes (478 minutes) the
2.3
culture tube is half full of cells.
t = 6.1 hours 10. b. Since 1 mg = 1000 mg, then
(257 mg/mL)/1000 = 0.257 mg/mL.
7. Immediately after the drug dissolves, the drug
11. c. Since 1 dL = 100 mL, then
degrades at a constant, or zero-order rate.
(257 mg/mL) × 100 = 25,700 mg/dL.
Since concentration is equal to mass divided by
12. a. Since 1 kg = 1000 g, then (170 g)/1000 =
volume, it is necessary to calculate the initial
0.17 kg.
drug concentration (at t = 0) to determine the
The oral dose was 300 mg/kg; therefore,
original volume in which the drug was dis-
for 0.17 kg rat, (0.17 kg)(300 mg)/1 kg =
solved. From the data, calculate the zero-order
51 mg.
rate constant, k0: 13. c. The volume given was 5 mL/kg. For
∆Y 0.45− 0.3 0.17 kg rat, (0.17 kg)(5 mL)/1 kg = 0.85 mL.
−k0 = slope = = 14. d. 0.5% of methylcellulose (% w/v) means
∆X 2.0 − 0.5
0.5 g of methylcellulose in 100 mL solution.
k0 = 0.1mg/mL/h Or 5 g of methylcellulose in 1 L solution.
15. b. kel = 0.693/t½ = 0.693/4.35 = 0.16 h–1
Then calculate the initial drug concentration,
16. b. 4.35 hours × 60 min/h = 261 minutes.
C0, using the following equation:
17. c. F%= {[(AUC sample)(Dose oral)]/[(AUC
oral)(Dose sample)]} * 100 (2.28)
C = −k t + C
0 0
F% = [(AUC sample)/AUC oral)] * 100
At t = 2 hours, 2.6 folds higher = 260%
0.3 = −0.1(2) +C 260 = [AUC sample)/29.1] * 100
0
AUC sample = 75.66 mg·h/mL = 0.07566
C0 = 0.5 mg/mL mg·h/mL = 1.8 mg·day/mL
50 Chapter 2
18. b. A rectangular coordinate graph. 23. c. y = 1.6624 × −0.3
19. d. According to the figure, the highest plasma y = 1.6624 (35) − 0.3 = 57.9 = AUC
concentration for subject #1 occurred at 24. a. y = 1.6624 × −0.3
24 hours. 145 = 1.6624 × −0.3
20. b. From the graph, the average Cmax was x = 87.4 mg/mL = 87.4 mg/L
between 50 and 100 ng/mL. 25. c. dc/dt = 0.98
21. c. It is (concentration units) × (time) = dc = 0.98 dt
(ng/mL) × (hours) = (ng·h/mL). ∫dc = 0.98 ∫dt
22. c. 105 ng/mL = 10,500 ng/100 mL = c = c0 + 0.98t
10.5 mg/100 mL = 0.0105 mg/100 mL =
0.0000105 g/100 mL.
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MDPI [http://www.mdpi.org]. Reproduction is permitted.) vocable, worldwide, perpetual right of access and a license to
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Biostatistics
3 Charles Herring
Chapter Objectives VARIABLES1
»» Describe basic statistical Several types of variables will be discussed throughout this text.
methodology and concepts A random variable is “a variable whose observed values may be
»» Describe how basic statistical considered as outcomes of an experiment and whose values cannot be
methodology may be used anticipated with certainty before the experiment is conducted”
in pharmacokinetic and (Herring, 2014). An independent variable is defined as the “interven-
pharmacodynamics study tion or what is being manipulated” in a study (eg, the drug or dose of
design the drug being evaluated) (Herring, 2014). “The number of indepen-
dent variables determines the category of statistical methods that are
»» Describe how basic statistical
appropriate to use” (Herring, 2014). A dependent variable is the
methodology may be used in
“outcome of interest within a study.” In bioavailability and bioequiva-
critically evaluating data
lence studies, examples include the maximum concentration of the
»» Describe how basic statistical drug in the circulation, the time to reach that maximum level, and the
methodology may be used to area under the curve (AUC) of drug level-versus-time curve. These
help minimize error, bias, and are “the outcomes that one intends to explain or estimate” (Herring,
confounding, and, therefore, 2014). There may be multiple dependent (aka outcome) variables. For
promote safe and efficacious example, in a study determining the half-life, clearance, and plasma
drug therapy protein binding of a new drug following an oral dose, the independent
»» Provide examples of how basic variable is the oral dose of the new drug. The dependent variables are
statistical methodology may be the half-life, clearance, and plasma protein binding of the drug
used for study design and data because these variables “depend upon” the oral dose given.
evaluation Discrete variables are also known as counting or nonparamet-
ric variables (Glasner, 1995). Continuous variables are also
known as measuring or parametric variables (Glasner, 1995). We
will explore this further in the next section.
TYPES OF DATA NONPARAMETRIC
VERSUS PARAMETRIC
There are two types of nonparametric data, nominal and ordinal. For
nominal data, numbers are purely arbitrary or without regard to any
order or ranking of severity (Gaddis and Gaddis, 1990a; Glasner,
1The 5th edition of Quick Stats: Basics for Medical Literature Evaluation was
utilized for the majority of the following chapter (Herring, 2014). In order to
discuss basic statistics, some background terminology must be defined.
51
52 Chapter 3
1995). Nominal data may be either dichotomous or level-versus-time curve, drug clearance, and elim-
categorical. Dichotomous (aka binary) nominal data ination half-life.
evaluate yes/no questions. For example, patients lived
or died, were hospitalized, or were not hospitalized.
Examples of categorical nominal data would be things Frequently Asked Questions
like tablet color or blood type; there is no order or »»Is it appropriate to degrade parametric data to
inherent value for nominal, categorical data. nonparametric data for data analysis?
Ordinal data are also nonparametric and cate- »»What occurs if this is done?
gorical, but unlike nominal data, ordinal data are
scored on a continuum, without a consistent level of
magnitude of difference between ranks (Gaddis and
Gaddis, 1990a; Glasner, 1995). Examples of ordinal Data Scale Summary Example
data include a pain scale, New York Heart Association In pharmacokinetic studies, researchers may be inter-
heart failure classification, cancer staging, bruise ested in testing the difference in the oral absorption of
staging, military rank, or Likert-like scales (poor/ a generic versus a branded form of a drug. In this case,
fair/good/very good/excellent) (Gaddis and Gaddis, “generic or branded” is a nominal scale-type variable,
1990a; DeYoung, 2005). whereas expressing the “rate of absorption” numeri-
Parametric data are utilized in biopharmaceu- cally is a ratio-type scale (Gaddis and Gaddis, 1990a;
tics and pharmacokinetic research more so than Ferrill and Brown 1994; Munro, 2005).
are the aforementioned types of nonparametric
data. Parametric data are also known as continu-
ous or measuring data or variables. There is an DISTRIBUTIONS
order and consistent level of magnitude of differ- Normal distributions are “symmetrical on both sides
ence between data units. There are two types of of the mean” sometimes termed as a bell-shaped
parametric data: interval and ratio. Both interval curve, Gaussian curve, curve of error, or normal
and ratio scale parametric data have a predeter- probability curve (Shargel et al, 2012). An example
mined order to their numbering and a consistent of normally distributed data includes drug elimina-
level of magnitude of difference between the tion half-lives in a specific population, as would be
observed data units (Gaddis and Gaddis, 1990a; the case in a sample of men with normal renal and
Glasner, 1995). However, for interval scale data, hepatic function. As will be discussed later in this
there is no absolute zero, for example, Celsius or chapter, parametric statistical tests like t-test and
Fahrenheit (Gaddis and Gaddis, 1990a; Glasner, various types of analysis of variance (ANOVA) are
1995). For ratio scale data, there is an absolute utilized for normally distributed data.
zero, for example, drug concentrations, plasma
glucose, Kelvin, heart rate, blood pressure, dis-
tance, and time (Gaddis and Gaddis, 1990a;
Glasner, 1995). Although the specific definitions
of these two types of parametric data are listed
above, their definitions are somewhat academic
since all parametric data utilize the same statisti-
cal tests. In other words, regardless of whether the
parametric data are interval or ratio scale, the Sometimes in bioequivalence or pharmacokinetic
same tests are used to detect statistical differ- studies, a bimodal distribution is noted. In this case two
ences. Examples of parametric data include plasma peaks of cluster or areas of high frequency occur. For
protein binding, the maximum concentration of example, a medication that is acetylated at different
the drug in the circulation, the time to reach that rates in humans would be a “bimodal distribution, indi-
maximum level, the area under the curve of drug cating two populations consisting of fast acetylators
Biostatistics 53
and slow acetylators” (Gaddis and Gaddis, 1990a;
Glasner, 1995; Shargel et al, 2012).
Mortality
Blood pressure
Skewed distributions occur when data are not MEASURES OF CENTRAL TENDENCY
normally distributed and tail off to either the high or There are several measures of central tendency that
the low end of measurement units. A positive skew are utilized in biopharmaceutical and pharmacoki-
occurs when data cluster on the low end of the x axis netic research. The most common one is the mean,
(Gaddis and Gaddis, 1990a; Glasner, 1995). For or average. It is the “sum of all values divided by the
example, the x axis could be the income of patients total number of values,” is used for parametric data,
seen in inner-city Emergency Department (ED), cost and is affected by outliers or extreme values, which
of generic medications, number of prescribed medica- “deviate far from the majority of the data” (Gaddis
tions in patients younger than 30 years of age. and Gaddis, 1990b; Shargel et al, 2012). Mu (μ) is
the population mean and X-bar (X ) is the sample
mean (Gaddis and Gaddis, 1990b).
Median is also known as the 50th percentile or
y axis mid-most point (Gaddis and Gaddis, 1990b). It is
“the point above which or below which half of the
data points lie” (Gaddis and Gaddis, 1990b). It is not
x axis affected by outliers and may be used for ordinal and
parametric data (Gaddis and Gaddis, 1990b). Median
A negative skew occurs when data cluster on the is used when outliers exist, when a data set spans a
high end of the x axis (Gaddis and Gaddis, 1990a; wide range of values, or “when continuous data are
Glasner, 1995). For example, the x axis could be the not normally distributed” (Gaddis and Gaddis,
income of patients seen in ED of an affluent area, cost 1990b; DeYoung, 2005).
of brand name medications, number of prescribed Mode is the most common value (Gaddis and
medications in patients older than 60 years of age. Gaddis, 1990b). Mode is not affected by outliers
and may be used for nominal, ordinal, or parametric
data (Gaddis and Gaddis, 1990b). As with median,
the mode is not affected by outliers (Gaddis and
y axis Gaddis, 1990b). However, the mode is not helpful
when a data set contains a large range of infre-
quently occurring values (Gaddis and Gaddis,
x axis 1990b).
For normally distributed data, mean, median,
Kurtosis occurs when data cluster on both ends and mode are the same. For positively skewed data,
of the x axis such that the graph tails upward (ie, the mode is less than the median and the median is
clusters on both ends of the graph). For example, the less than the mean. For negatively skewed data, the
J-curve of hypertension treatment; with the J-curve, mode is greater than the median and the median is
mortality increases if blood pressure is either too greater than the mean (Gaddis and Gaddis, 1990b;
high or too low (Glasner, 1995). Glasner, 1995).
54 Chapter 3
Normally distributed data (Gaddis and Gaddis, Range is the interval between lowest and highest
1990b; Glasner, 1995) values (Gaddis and Gaddis, 1990b; Glasner, 1995).
Normally distributed data (2, 8) Range only considers extreme values, so it is affected by
outliers (Gaddis and Gaddis, 1990b). Range is descrip-
tive only, so it is not used to infer statistical significance
(Gaddis and Gaddis, 1990b). Interquartile range is the
interval between the 25th and 75th percentiles, so it is
directly related to median, or the 50th percentile (Gaddis
and Gaddis, 1990b). It is not affected by outliers and,
Mode = median = mean along with the median, is used for ordinal scale data
(Gaddis and Gaddis, 1990b).
Positively skewed data (Gaddis and Gaddis, Variance is deviation from the mean, expressed as
1990b; Glasner, 1995) the square of the units used. The data are squared in the
Positively skewed data (2, 8) variance calculations because some deviations are nega-
tive and squaring provides a positive number (Gaddis
and Gaddis, 1990b; Glasner, 1995). “As sample size (n)
increases, variance decreases” (Herring, 2014). Variance
equals the sum of (mean – data point) squared, divided
by n – 1.
∑(X − X)2
Mode < median < mean Variance = (3.1)
n −1
Negatively skewed data (Gaddis and Gaddis,
Standard deviation (SD) is the square root of
1990b; Glasner, 1995)
variance (Gaddis and Gaddis, 1990b; Glasner, 1995).
Negatively skewed data (2, 8) SD estimates the degree of data scatter around the
sample mean. Sixty-eight percent of data lie within ±1
SD of the mean and 95% of data lie within ±2 SD of
the mean (Gaddis and Gaddis, 1990b; Glasner, 1995).
SD is only meaningful when data are normally or
near-normally distributed and, therefore, is only appli-
Mean < median < mode cable to parametric data (Gaddis and Gaddis, 1990b;
Glasner, 1995). Sigma (s) is the population SD and S
Based upon a data set’s mean, median, and mode is the sample SD (Glasner, 1995).
values, one can determine if the data is normally dis-
tributed or skewed when no graphical representation SD = Variance (3.2)
is provided. For biopharmaceutical and pharmacoki-
netic data, this is important to know so that appropri- “Coefficient of variation (or relative standard
ate logarithmic transformation can be performed for deviation) is another measure used when evaluating
skewed data to restore normality. dispersion from one data set to another. The coefficient
A weakness of measures of central tendency is of variation is the SD expressed as a percentage of the
the data does not describe variability or spread of data. mean. This is useful in comparing the relative difference
in variability between two or more samples, or which
MEASURES OF VARIABILITY group has the largest relative variability of values from
the mean” (Herring, 2014). The smaller the coefficient
Measures of variability describe data spread and, in the of variation, the less the variability in the data set.
case of confidence intervals (CIs), can help one infer
statistical significance (Gaddis and Gaddis, 1990b). Coefficientof variation = 100 × SD/X (3.3)
Biostatistics 55
Standard error of the mean (SEM) is the SD However, the closer the point estimate lies to the
divided by the square root of n (Gaddis and Gaddis, middle of the CI, the more likely the point estimate
1990b; Glasner, 1995). The larger n is, the smaller represents the population.
SEM is (Gaddis and Gaddis, 1990b; Glasner, 1995). For example, if a point estimate and 95% CI for
SEM is always smaller than SD. drug clearance are 3 L/h (95% CI: 1.5–4.5 L/h), all
“The mean of separate samples from a single values including and between 1.5 and 4.5 L/h are
population will give slightly different parameter statistically possible. However, a point estimate of
estimates. The standard error (SE) is the standard 2.5 L/h is a more accurate representation of the stud-
deviation (SD) of the sampling distribution of a ied population than a point estimate of 1.6 L/h since
statistic and should not be confused with SEM. 2.5 is closer to the sample’s point estimate of 3 than
The distribution of means from random samples is is 1.6. As seen in this example, CI shows the degree
approximately normal. The mean of this ‘distribu- of certainty (or uncertainty) in each comparison in an
tion of means’ is the unknown population mean” easily interpretable way.
(Glasner, 1995)
In addition, CIs make it easier to assess clinical
SD for the distribution of means is estimated by the significance and are less likely to mislead one into
SEM. One “could name the SEM as the standard thinking that nonsignificantly different sample val-
deviation of means of random samples of a fixed size ues imply equal population values
drawn from the original population of interest”
(Herring, 2014). The SEM is the quantification of the 95% CI = X ± 1.96 (SEM) (3.5)
spread of the sample means for a study that is repeated
multiple times. The SEM helps to estimate how well Significance of CIs depends upon the objective
a sample represents the population from which it was of the trial being conducted or evaluated.
drawn (Glasner, 1995). However, the SEM should not In superiority trials, all values within a CI are
be used as a measure of variability when publishing a statistically possible. For differences like differ-
study. Doing so is misleading. The only purpose of ences in half-life, differences in area under the
SEM is to calculate CIs, which contain an estimate of curve (AUC), relative risk reductions/increases
the true population mean from which the sample was (RRRs/RRIs), or absolute risk reductions/increases
drawn (Gaddis and Gaddis, 1990b). (ARRs/ARIs), if the CI includes ZERO (0), then
the results are not statistically significant (NSS). In
SEM = SD/ n (3.4)
the case of a 90% CI, if the CI includes ZERO (0)
Confidence interval (CI) is a method of estimat- for this type of data, it can be interpreted as a p >
ing the range of values likely to include the true value 0.10. In the case of a 95% CI, if the CI includes
of a population parameter (Gaddis and Gaddis, ZERO (0) for this type of data, it can be interpreted
1990b). In medical literature, a 95% CI is most fre- as a p > 0.05. In the case of a 97.5% CI, if the CI
quently used. The 95% CI is a range of values that “if includes ZERO (0) for this type of data, it can be
the entire population could be studied, 95% of the interpreted as a p > 0.025.
time the true population value would fall within the CI For superiority trials, since all values within a
estimated from the sample” (Gaddis and Gaddis, CI are statistically possible, for ratios like relative
1990b). For a 95% CI, 5 times out of 100, the true risk (RR), odds ratio (OR), or hazards ratio (HR), if
population parameter may not lie within the CI. For a the CI includes ONE (1.0), then the results are not
97.5% CI, 2.5 times out of 100, the true population statistically significant (NSS). In the case of a 90%
parameter may not lie within the CI. Therefore, a CI, if the CI includes ONE (1.0) for this type of data,
97.5% CI is more likely to include the true population it can be interpreted as a p > 0.10. In the case of a
value than a 95% CI (Gaddis and Gaddis, 1990b). 95% CI, if the CI includes ONE (1.0) for this type of
The true strength of a CI is that it is both data, it can be interpreted as a p > 0.05. In the case
descriptive and inferential. “All values contained in of a 97.5% CI, if the CI includes ONE (1.0) for this
the CI are statistically possible” (Herring, 2014). type of data, it can be interpreted as a p > 0.025.
56 Chapter 3
HYPOTHESIS TESTING are willing to accept and is denoted in trials as a p ≤
0.05 (Gaddis and Gaddis, 1990c). So the p-value is
For superiority trials, the null hypothesis (H0) is that the calculated chance that a type 1 error has occurred
no difference exists between studied populations (Gaddis and Gaddis, 1990c). In other words, it tells us
(Gaddis and Gaddis, 1990c). For superiority trials, the likelihood of obtaining a statistically significant
the alternative hypothesis (H1) is that a difference result if H0 were true. “At p = 0.05, the likelihood is 5%.
does exist between studied populations (Gaddis and At p = 0.10, the likelihood is 10%” (Herring, 2014).
Gaddis, 1990c). A p ≤ a means the observed treatment difference is
H statistically significant, it does not indicate the size or
0: There is no difference in the AUC for drug
formulation A relative to formulation B. direction of the difference. The size of the p-value is
H not related to the importance of the result (Gaddis and
1 (aka Ha): There is a difference in AUC for
drug formulation A relative to formulation B. Gaddis, 1990f; Berensen, 2000). Smaller p-values
simply mean that “chance” is less likely to explain
H1 is sometimes directional. For example, observed differences (Gaddis and Gaddis, 1990f;
H1: We expect AUC for drug formulation A to Berensen, 2000). Also, “a small p-value does not cor-
be 25% higher than that of formulation B. rect for systematic error (bias)” from a poorly designed
H0 is tested instead of H1 because there are an study (DeYoung, 2005).
infinite number of alternative hypotheses. It would be A type 2 error occurs if one accepts the H0 when,
impossible to calculate the required statistics for each in fact, the H0 is false (Gaddis and Gaddis, 1990c).
of the infinite number of possible magnitudes of dif- For superiority trials this is when one concludes there
ference between population samples H1 hypothesizes is no difference between treatment groups, when in
(Gaddis and Gaddis, 1990c). H0 is used to determine fact, a difference does exist. Beta (b) is the probability
“if any observed differences between groups are due of making a type 2 error (Gaddis and Gaddis, 1990c).
to chance alone” or sampling variation. By convention, an acceptable b is 0.2 (20%) or less
Statistical significance is tested (hypothesis test- (Gaddis and Gaddis, 1990c).
ing) to indicate if H0 should be accepted or rejected Regardless of the trial design (superiority,
(Gaddis and Gaddis, 1990c). For superiority trials, if equivalence, or non-inferiority), a and b are interre-
H0 is “rejected,” this means a statistically significant lated (Gaddis and Gaddis, 1990c). All else held
difference between groups exists (results unlikely due constant, a and b are inversely related (Gaddis and
to chance) (Gaddis and Gaddis, 1990c). For superior- Gaddis, 1990c). In other words, as a is decreased, b
ity trials, if H0 is “accepted,” this means no statisti- is increased, and as a is increased, b is decreased (ie,
cally significant difference exists (Gaddis and Gaddis, as risk for a type 1 error is increased, risk for a type
1990c). However, “failing to reject H0 is not sufficient 2 error is decreased and vice versa) (Gaddis and
to conclude that groups are equal” (DeYoung, 2005). Gaddis, 1990c). The most common use of b is in
A type 1 error occurs if one rejects the H0 when, calculating the approximate sample size required for
in fact, the H0 is true (Gaddis and Gaddis, 1990c). a study to keep a and b acceptably small (Gaddis
For superiority trials this is when one concludes and Gaddis, 1990c).
there is a difference between treatment groups, when
in fact, no difference exists (Gaddis and Gaddis,
1990c). Frequently Asked Questions
Alpha (a) is defined as the probability of making
»»For a superiority trial, if a statistically significant
a type 1 error (Gaddis and Gaddis, 1990c). When a difference were detected, is there any way that the
level is set a priori (or before the trial), the H0 is study was underpowered?
rejected when p ≤ a (Gaddis and Gaddis, 1990c). By
»»For a superiority trial, if a statistically significant dif-
convention, an acceptable a is usually 0.05 (5%),
ference were detected, is there any way a type 2 error
which means that 1 time out of 20, a type 1 error will
could have occurred?
be committed. This is a consequence that investigators
Biostatistics 57
TABLE 31 Type 1 and 2 Error for Superiority Trials
Reality
Difference Exists (H0 False) No Difference Exists (H0 True)
Decision from Statistical Test
Difference found (Reject H0) Correct No error Incorrect Type 1 error (false positive)
No difference found (Accept H0) Incorrect Type 2 error (false negative) Correct No error
Delta (∆) is sometimes referred to as the “effect For superiority trials, inadequate power may
size” and is a measure of the degree of difference cause one to conclude that no difference exists when,
between tested population samples (Gaddis and in fact, a difference does exist. As described above,
Gaddis, 1990c). For parametric data, the value of ∆ this would be a type 2 error (Gaddis and Gaddis,
is the ratio of the clinical difference expected to be 1990c). Note that in most cases, power is an issue
observed in the study to the standard deviation (SD) only if one accepts the H0. If one rejects the H0, there
of the variable: is no way that one could have made a type 2 error
(see Table 3-1). Therefore, power to detect a differ-
∆ = (ma − m0)/SD (3.6)
ence would not be an issue in most of these cases. An
where μa is the alternative hypothesis value expected exception to this general rule would be if one wanted
for the mean and μ0 is the null hypothesis value for to decrease data variability or spread. For example,
the mean. if one wanted to narrow the 95% CI, increasing
One-tailed versus two-tailed tests: It is easier to power by increasing sample size could help.
show a statistically significant difference with a For research purposes, power calculations are
one-tailed test than with a two-tailed test, because generally used to determine the required sample size
with a one-tailed test a statistical test result must not when designing a study (ie, prior to the study).
vary as much from the mean to achieve significance Power calculations are generally based upon the
at any level of a chosen (Gaddis and Gaddis, 1990c). primary endpoint of the study and, as is depicted in
However, most reputable journals require that inves- the examples below, the a priori (prespecified) a, b,
tigators perform statistics based upon a two-tailed ∆, SD, and whether a one-tailed or two-tailed design
test even if it innately makes sense that a differ- is used.
ence would only occur unidirectionally (Al-Achi A,
discussions). Parametric Data Sample Size/Power
Power is the ability of an experiment to detect a
Examples
statistically significant difference between samples,
when in fact, a significant difference truly exists The way a study is set up will determine the required
(Gaddis and Gaddis, 1990c). Said another way, sample size. In other words, the preset a, b, ∆, SD,
power is the probability of making a correct decision and tailing (one-tailed vs two-tailed) affect sample
when H0 is false. size required for a study (Drew R, discussions and
provisions).
Power = 1 − b (3.7) Utilizing a larger standard deviation (SD) will
As stated in the section on type 2 error risk, by con- require a larger sample size. Also, a one-tailed test
vention, an acceptable b is 0.2 (20%) or less; there- requires a smaller sample size than a two-tailed test
fore, most investigators set up their studies, and their to detect differences between groups (Drew R, dis-
sample sizes, based upon an estimated power of at cussions and provisions). This is due to the fact that
least 80%. given everything else is the same, a one-tailed test
58 Chapter 3
has more power to reject the null hypothesis than a size required to detect that difference (Drew R, dis-
two-tailed test. cussions and provisions).
Sample Size Sample Size
Statistical Statistical
Differences Limits Differences Limits
One- Two- One- Two-
SD ∆ (%) ` a tailed tailed SD ∆ (%) ` a tailed tailed
1 (68% 10 0.05 0.20 1237 1570 2 (95% 10 0.05 0.20 4947 6280
of data) of data)
2 (95% 10 0.05 0.20 4947 6280 2 (95% 20 0.05 0.20 1237 1570
of data) of data)
An example for estimating the sample size for a
Increasing the accepted type 1 (a) and type 2 (b) study would be as follows:
statistical error risks will decrease the sample size a = 0.05
required. b = 0.20
Decreasing the acceptable type 1 (a) and type ∆ = 0.25
2 (b) statistical error risks will increase the required SD = 2.0
sample size (Drew R, discussions and provisions). Statistical test = two-sided t-test
Single sample
Statistical Sample Size From a statistics table, the total sample size
Differences Limits
One- Two- needed for this study is 128, or 64 in each group.
SD ∆ (%) α β tailed tailed This also indicates that the investigators are inter-
ested in detecting a clinically meaningful difference
2 (95% 10 0.05 0.20 4947 6280
of data) of 0.50 unit:
2 (95% 10 0.10 0.20 3607 4947 ∆ = (ma –m0)/SD
of data)
0.25 = (ma – m0)/2.0
(ma – m0) = (2.0) × (0.25) = 0.50 unit
Power = 1 – b, so a larger sample size is required for
smaller b and higher power (Drew R, discussions and In other words, in order for the researchers to
provisions). significantly detect the difference of 0.50 units, they
would need a sample size of 128 patients. This test
would have an estimated power of 80% (since b =
Sample Size 0.20) and a confidence level of 95% (since a = 0.05).
Statistical
It is important to reemphasize here that the smaller
Differences Limits
One- Two- the value for ∆, the greater would be the sample size
SD ∆ (%) a b tailed tailed needed for the study.
2 (95% 10 0.05 0.10 6852 8406
of data)
STATISTICALLY VERSUS CLINICALLY
2 (95% 10 0.05 0.20 4947 6280
of data) SIGNIFICANT DIFFERENCES
Statistically significant differences do not necessar-
A smaller difference (∆) between groups ily translate into clinically significant differences
increases the sample size required to detect that dif- (Gaddis and Gaddis, 1990c). If the sample size of a
ference. A larger difference (∆) decreases the sample trial is large enough, nonclinically meaningful,
Biostatistics 59
statistically significant differences may be detected. differences between these is solely academic.
For example, grapefruit juice induces enzymatic Parametric tests are more powerful than nonparametric
activity with some drugs such that their elimination tests (Gaddis and Gaddis, 1990d). Also, more infor-
t½ becomes shorter. Current data support that consis- mation about data is generated from parametric tests
tent grapefruit consumption statistically and clini- (Gaddis and Gaddis, 1990d).
cally significantly decreases the elimination t½ of The t-test (aka Student’s t-test) is the method of
these drugs. However, a one-time, single glass of choice when making a single comparison between
grapefruit juice may statistically significantly two groups. A non-paired t-test is used when obser-
decrease the value of t½ by only 1%, which would vations between groups are independent as in the
not be considered clinically meaningful. case of a parallel study as seen in the example below.
Also, lack of statistical significance does not Exp represents the experimental group and Ctrl repre-
necessarily mean the results are not clinically signifi- sents the control group.
cant; consider power, trial design, and populations
Population
studied (Gaddis and Gaddis, 1990f). A nonstatistically
Exp Endpoint
significant difference is more likely to be accepted as
being clinically significant in the instance of safety Sample
issues (like adverse effects), than for endpoint improve-
ments. For example, if a trial were to find a nonsta-
tistically significant increase in the risk for invasive
Ctrl Endpoint
breast cancer with a particular medication, many
clinicians would deem this as being clinically mean-
ingful such that they would avoid using the agent
Randomization Analysis
until further data were obtained. Also, suppose that a
study were conducted to examine the response rate
for a drug in two different populations. The response A paired t-test is used when observations
rates were 55% and 72% for groups 1 and 2, respec- between groups are dependent, as would be the case
tively. This difference in response rate is 17% (72 – 55 in a pretest/posttest study or a crossover study
= 17%) with a 95% CI of –3% to 40%. Since the 95% (Gaddis and Gaddis, 1990d). Initially in a crossover
CI includes zero, the difference is not statistically design, group A receives the experimental drug (Exp)
significant. Let’s also further assume that the mini- while group B receives the control (Ctrl: placebo or
mum clinically acceptable difference in response rate gold standard treatment). After a washout period,
for the particular disease is 15%. Since the response group A receives the control (Ctrl) and group B
rate is 17% (which is greater than 15%), it may very receives the experimental drug (Exp). It is very
well be clinically meaningful (significant) such that important to ensure adequate time for washout to
another, more adequately powered study may be prevent carry-over effects.
worth conducting. Population Washout period
Exp Endpoint Exp Endpoint
STATISTICAL INFERENCE
TECHNIQUES IN HYPOTHESIS Ctrl Endpoint Ctrl Endpoint
TESTING FOR PARAMETRIC DATA
Randomization Analysis
Parametric statistical methods (t-test and ANOVA)
are used for analyzing normally distributed, para- However, when making either multiple com-
metric data (Gaddis and Gaddis, 1990d). Parametric parisons between two groups or a single comparison
data include interval and ratio data, but since the between multiple groups, type 1 error risk increases
same parametric tests are used for both, knowing the if utilizing a t-test. For example, when rolling dice,
60 Chapter 3
think of rolling ones on both dice (snake eyes) as Investigators should make their best effort to
being a type 1 error. For each roll of the dice, there keep the type 1 error risk ≤ 5% (ie, ≤0.05). The best
is a 1 in 36 chances (2.78%) of rolling snake eyes. way of doing so for multiple comparisons is by
For each statistical analysis, we generally accept a avoiding unnecessary comparisons or analyses,
1 in 20 chances (5%) of a type 1 error. Although the using the appropriate statistical test(s) for multiple
chance for snake eyes is the same for each roll and comparisons, and using an alpha spending function
the chance for type 1 error is the same for each for interim analyses. However, if investigators fail to
analysis, increasing the number of rolls and analyses do so, there is a crude method for adjusting the pre-
increases the opportunity for snake eyes and type 1 set a level based upon the number of comparisons
errors, respectively. Said another way, the more being made: the Bonferroni correction. This simply
times one rolls the dice, the more opportunity one divides the preset a level by the number of compari-
has to roll snake eyes. It’s the same with statistical sons being made (Gaddis and Gaddis, 1990d). This
testing. The more times one performs a statistical estimates the a level that is required to reach statisti-
test on a particular data set, whether it be multiple cal significance (Gaddis and Gaddis, 1990d). However,
comparisons of two groups, a single comparison of Bonferroni is very conservative as the number of
multiple groups, or multiple comparisons of multiple comparisons increases. A less conservative and more
groups, the more likely one is to commit a type 1 error. accepted way of minimizing type 1 error risk for
As an example of multiple comparisons of two multiple comparisons with parametric data is through
groups for which the authors and/or statisticians did utilization of one of several types of analysis of vari-
not make type 1 error risk corrections, a trial evalu- ance (ANOVA).
ated chlorthalidone versus placebo for the primary ANOVA holds a level (type 1 error risk) constant
endpoint of blood pressure. In addition to this, there when comparing more than two groups (Gaddis and
were other evaluated endpoints (including potassium Gaddis, 1990d). It tests for statistically significant
concentration, serum creatinine, BUN:SCr ratio, difference(s) among a group’s collective values
calcium concentration, and others), and the authors (Gaddis and Gaddis, 1990d). In other words, intra-
did not control for these additional comparisons. and intergroup variability is what is being analyzed
Let’s say there were a total of 20 comparisons instead of the means of the groups (Gaddis and
including the primary endpoint of blood pressure. If Gaddis, 1990d). It involves calculation of an F-ratio,
the original a level were p = 0.05, the corrected a which answers the question, “is the variability
would be 1 – (1 – 0.05)20 = 0.64. This means that if between the groups large enough in comparison to
the original p-value threshold of 0.05 were used, the variability of data within each group to justify the
there would be a 64% chance of inappropriately conclusion that two or more of the groups differ”
rejecting the null hypothesis (ie, committing a type 1 (Gaddis and Gaddis, 1990d)?
error) for at least one of the 20 comparisons (Gaddis The most commonly used ANOVAs are for inde-
and Gaddis, 1990d). pendent (aka non-paired) samples as is the case for
As an example of a single comparison of multi- a parallel design.
ple groups for which the authors and/or statisticians The first is 1-way ANOVA, which is used if there
did not make type 1 error risk corrections, a trial are no confounders and at least three independent
evaluated the difference in cholesterol among four (aka non-paired) samples. For example, if investiga-
lipid-lowering medications. With four groups, there tors wanted to evaluate the excretion rate (percent of
were six paired comparisons. If the original a level dose excreted unchanged in the urine) of different
were p = 0.05, the corrected a would be 1 – (1 – blood pressure medications, they could use a 1-way
0.05)6 = 0.26. Therefore, if the original p-value ANOVA if (1) each sample were independent (ie, a
threshold of 0.05 were used, there would be a 26% parallel design), (2) there were at least three samples
chance of inappropriately rejecting the null hypothe- (ie, at least three different blood pressure medica-
sis (type 1 error) for at least one of the six compari- tions), and (3) the experimental groups differed in
sons (Gaddis and Gaddis, 1990d). only one factor, which for this case would be the
Biostatistics 61
type of blood pressure drug being used (ie, there blood pressure medications, they could use a 4-way
were no differences between the groups with regard ANOVA if (1) each sample were independent (ie, a
to confounding factors like age, gender, kidney function, parallel design), (2) there were at least two samples
plasma protein binding, etc). (ie, at least two different blood pressure medica-
Multifactorial ANOVAs include any type of tions), and (3) the experimental groups differed in
ANOVA that controls for at least one confounder for four factors, which for this case would be the type of
at least two independent (non-paired) samples as is blood pressure drug being used and three confound-
the case for a parallel design. ing variables (eg, differences between the groups’
A 2-way ANOVA is used if there is one identifiable renal function, plasma protein binding, and average
confounder and at least two independent (aka non- patient age).
paired) samples. For example, if investigators wanted There are also ANOVAs for related (aka paired,
to evaluate the excretion rate (percent of dose matched, or repeated) samples as is the case for a
excreted unchanged in the urine) of different blood crossover design. These include the repeated mea-
pressure medications, they could use a 2-way sures ANOVA, which is used if there are no con-
ANOVA if (1) each sample were independent (ie, a founders and at least three related (aka paired)
parallel design), (2) there were at least two samples samples. For example, if investigators wanted to
(ie, at least two different blood pressure medications), evaluate the bioavailability of different cholesterol-
and (3) the experimental groups differed in only two lowering medications to determine Cmax, they could
factors, which for this case would be the type of use a repeated measures ANOVA if (1) each subject
blood pressure drug being used and one confounding served as his/her own control (ie, a crossover
variable (eg, differences between the groups’ renal design), (2) there were at least three samples (ie, at
function). least three different cholesterol medications), and (3)
Other types of multifactorial ANOVAs include the experimental groups differed in only one factor,
analyses of covariance (ANACOVA or ANCOVA). which for this case would be the type of cholesterol
These are used if there are at least two confounders drug being used (ie, there were no identified con-
for at least two independent (non-paired) samples as founders like fluctuations in renal function, adminis-
is the case for a parallel design. These include the tration times, etc).
3-way ANOVA, 4-way ANOVA, etc. A second type of ANOVA for related (aka
A 3-way ANOVA is used if there are two identifi- paired, matched, or repeated) samples is the 2-way
able confounders and at least two independent (aka repeated measures ANOVA, which is used if there is
non-paired) samples. For example, if investigators one identifiable confounder and at least two related
wanted to evaluate the excretion rate (percent of (aka paired) samples. For example, if investigators
dose excreted unchanged in the urine) of different wanted to evaluate the bioavailability of different
blood pressure medications, they could use a 3-way cholesterol-lowering medications to determine Cmax,
ANOVA if (1) each sample were independent (ie, a they could use a 2-way repeated measures ANOVA if
parallel design), (2) there were at least two samples (1) each subject served as his/her own control (ie, a
(ie, at least two different blood pressure medica- crossover design), (2) there were at least two sam-
tions), and (3) the experimental groups differed in ples (ie, at least two different cholesterol medica-
three factors, which for this case would be the type tions), and (3) the experimental groups differed in
of blood pressure drug being used and two con- only two factors, which for this case would be the
founding variables (eg, differences between the type of cholesterol drug being used and one con-
groups’ renal function and plasma protein binding). founding variable (eg, fluctuations in renal
A 4-way ANOVA is used if there are three iden- function).
tifiable confounders and at least two independent Beyond that, repeated measures regression
(aka non-paired) samples. For example, if investiga- analysis is used if there are two or more related (aka
tors wanted to evaluate the excretion rate (percent of paired) samples and two or more confounders. For
dose excreted unchanged in the urine) of different example, if investigators wanted to evaluate the
62 Chapter 3
bioavailability of different cholesterol-lowering Sometimes, otherwise parametric data are not
medications to determine Cmax, they could use a normally distributed (ie, are skewed) such that afore-
repeated measures regression analysis if (1) each mentioned parametric testing methods, t-test and the
subject served as his/her own control (ie, a crossover various types of ANOVA, would be inaccurate for
design), (2) there were at least two samples (ie, at data analysis. In these cases, investigators can loga-
least two different cholesterol medications), and (3) rithmically transform the data to normalize data
the experimental groups differed in at least three factors, distribution such that t-test or ANOVA can be used
which for this case would be the type of cholesterol for data analysis (Shargel et al, 2012).
drug being used and at least two confounding vari- When performing statistical analyses of subgroup
ables (eg, fluctuations in renal function and adminis- data sets, the term interaction or p for interaction is
tration times). often heard (Shargel et al, 2012). P for interaction (aka
ANOVA will indicate if differences exist p-value for interaction) simply detects heterogeneity or
between groups, but will not indicate where these differences among subgroups. A significant p for inter-
differences exist. For example, if an investigator is action generally ranges from 0.05 to 0.1 depending on
interested in comparing the volume of distribution of the analysis. In other words if a subgroup analysis finds
a drug among various species, both clearance and the a p for interaction <0.05 (or <0.1 for some studies) for
elimination rate constant must be considered. half-life by male versus female patients, then there is
Clearance and the elimination rate constant may be possibly a significant difference in half-life based upon
species dependent (ie, rats vs dogs vs humans) and gender. This difference may be worth investigating in
thus, they are expected to produce different out- future analyses. Just as with other types of subgroup
comes (ie, volumes of distribution). However, a sta- analyses, p for interaction solely detects hypothesis-
tistically significant ANOVA does not point to where generating differences. However, if multiple similar
these differences exist. To find where the differences studies are available, a properly performed meta-
lie, post hoc multiple comparison methods must be analysis may help answer the question of gender and
performed. half-life differences.
Multiple comparison methods are types of post
hoc tests that help determine which groups in a statis-
tically significant ANOVA analysis differ (Gaddis Pharmacokinetic Study Example
and Gaddis, 1990d). These methods are based upon Incorporating Parametric Statistical
the t-test but have built-in corrections to keep a level Testing Principles
constant when >1 comparison is being made. In other The t½ of phenobarbital in a population is 5 days with
words, these help control for type 1 error rate for a standard deviation of 0.5 days. A clinician observed
multiple comparisons (Gaddis and Gaddis, 1990d). that patients who consumed orange juice 2 hours prior
Examples include (1) least significant difference, to dosing with phenobarbital had a reduction in their
which controls individual type 1 error rate for each t½ by 10%. To test this hypothesis, the clinician
comparison, (2) layer (aka stepwise) methods, which selected a group of 9 patients who were already taking
gradually adjust the type 1 error rate and include phenobarbital and asked them to drink a glass of
Newman-Keuls and Duncan, and (3) experiment-wise orange juice 2 hours prior to taking the medication.
methods, which hold type 1 error rate constant for a The average calculated t½ value from this sample of
set of comparisons and include Dunnett, which tests 12 patients was 4.25 days. The clinician has to decide
for contrasts with a control only; Dunn, which tests from the results obtained from the study whether
for small number of contrasts; Tukey, which tests for orange juice consumption decreases the value of t½.
a large number of contrasts when no more than two Assuming that alpha was 0.05 (5%), there are several
means are involved; and Scheffe, which tests for a ways to reach the conclusion. Based on the statement
large number of contrasts when more than two means of the null hypothesis, “drinking orange juice 2 hours
are involved (Gaddis and Gaddis, 1990d). prior to taking phenobarbital does not affect t½ of the
Biostatistics 63
drug” (remember that H0 is a statement of no differ- It is a way to describe the “agreement between model
ence, meaning that whether orange juice was or was and data” (Anonymous, 2003). This is done by plot-
not consumed the t½ of phenobarbital is the same), the ting the residuals (RES; the difference between
conclusion of the test is written with respect to H0. observed and predicted values) versus predicted
The alternative hypothesis is that “orange juice lowers (PRED) data points. In addition to this plot, GOF
the t½ value of phenobarbital.” The alternative hypoth- analysis includes other plots such as PRED versus
esis has the symbol of H1 or Ha. One way to analyze observed (OBS) or PRED versus time (Brendel et al,
the result is to calculate a p-value for the test (Ferrill 2007). GOF methodology is often used in population
and Brown, 1994). The p-value is the exact probability pharmacokinetic studies. For example, the pharma-
of obtaining a test value of 4.25 days or less, given cokinetic profile of the antiretroviral drug nelfinavir
that H0: μ0 = 5 days: and its active metabolite M8 was investigated with
the aim of optimizing treatment in pediatric popula-
Pr. [y-bar ≤ 4.25 µ0 = 5] (3.8) tion (Hirt et al, 2006). The authors used GOF in their
assessment of the proposed pharmacokinetic models
Equation 3.8 can be evaluated by standardizing
to compare the population predicted versus the
the data using a standard normal curve (this curve
observed nelfinavir and M8 concentrations.
has an average of μ = 0 and a standard deviation of
s = 1):
STATISTICAL INFERENCE
Pr. [z ≤ (y-bar − m)/s/(n)0.5] (3.9)
TECHNIQUES FOR HYPOTHESIS
Pr. [z ≤ (4.25 − 5)/0.5/(9)0.5] TESTING WITH NONPARAMETRIC
= Pr. [z ≤ −1.28] = 10.03%
Or DATA
Nonparametric statistical methods are used for analyz-
p = 0.1003
ing data that are not normally distributed and cannot be
Since the p-value for the test is greater than a of 5% defined as parametric data (Gaddis and Gaddis, 1990e).
(p > 0.05), then we conclude that drinking orange For nominal data, the most common tests for propor-
juice 2 hours prior to taking phenobarbital dose does tions and frequencies include chi-square (c 2) and
not decrease the value of t½. It should be noted that Fisher’s exact. These tests are “used to answer ques-
the value calculated from Equation 3.9 is for a one- tions about rates, proportions, or frequencies” (Gaddis
tailed test. In order to calculate the p-value for a and Gaddis, 1990e). Fisher’s exact test is only used for
two-tailed test, the value computed from Equation 3.9 very small data sets (N ≤ 20). Chi-square (c 2) is used
is multiplied by 2 (p = 2 × 0.1003 = 0.2006). for all others. For matrices that are larger than 2 × 2, c 2
While z-test and t-test are used for one-sample tests will detect difference(s) between groups, but will
and two-sample comparisons, they cannot be used if not indicate where the difference(s) lie(s) (Gaddis and
the researcher is interested in comparing more than Gaddis, 1990e). To find this, post hoc tests are needed.
two samples at one time. As was explained earlier in These post hoc tests should only be performed if the c 2
this chapter, the parametric analysis of variance test was statistically significant. Doing otherwise will
(ANOVA) test is used to compare two or more groups increase type 1 error risk.
with respect to their means. For ordinal data, the most appropriate test
depends upon the number of groups being compared,
GOODNESS OF FIT the number of comparisons being made, and whether
the study is of parallel or crossover design. The most
The idea of “goodness of fit” (GOF) in pharmacoki- commonly used ordinal tests are Mann–Whitney U,
netic data analysis is an important concept to assure Wilcoxon Rank Sum, Kolmogorov–Smirnov, Wilcoxon
the reliability of proposed pharmacokinetic models. Signed Rank, Kruskal–Wallis, and Friedman.
64 Chapter 3
The procedure for utilizing all of these tests is the t-distribution are “less pinched.” The mean of the
very similar to the example provided in the paramet- t-distribution is zero, and its standard deviation is a
ric data testing section: function of the sample size (or the degrees of freedom).
The larger the sample size, the closer the value of the
1. State the null and alternate hypotheses at a
standard deviation is to 1 (recall that the standard devia-
given alpha value.
tion for the z distribution, the standard normal curve, is
2. Calculate test statistics (a computed value for
always 1). With the advances in computer technology
Chi-square or z, depending on the test being
and the availability of software programs that readily
used).
calculate these statistics, the function of the researcher
3. Compare the calculated value with a tabulated
is to enter the data in a computer database, calculate the
value.
slope, and find the p-value associated with the slope. If
4. Build a confidence interval on the true propor-
the p-value is less than a, then the slope is different
tion that is expected in the population.
from zero. Otherwise, do not reject the null hypothesis
5. Make a decision whether or not to reject the
and declare the slope is zero. Similar analysis can be
null hypothesis.
done on the y intercept using a t-test. For the signifi-
Many statistical software programs perform the cance of the regression coefficient (r), a critical value is
above tests or other similar tests found in the litera- obtained from statistics tables at a given degrees of
ture. Computer programs calculate a p-value for the freedom (n – 2), a two- or one-tailed test, and a selected
test to determine whether or not the results are sig- a value. If the observed r value equals or exceeds the
nificant. This is, of course, accomplished by compar- critical value, then r is significant (ie, reject H0 of r =
ing the computed p-value with a predetermined a 0); otherwise, r is statistically insignificant. For exam-
value. In the practice of pharmacokinetics, it is rec- ple, a calculated r value of 0.75 was computed based on
ommended to have computer software for calculating 30 pairs of x and y values. The following calculations
pharmacokinetic parameters and another software are taken in the analysis:
program for statistical analysis of experimental data.
1. State the null hypothesis and alternate hypothesis:
H0: r = 0
H1: r is not equal to zero
Frequently Asked Question
Two-tailed test
»»How do nonparametric statistical tests differ from
2. State the alpha value:
parametric statistical test regarding power?
a = 0.05
3. Find the critical value of r (tables for this may
Least Squares method be found in statistical textbooks):
Degrees of freedom = n – 2 = 30 – 2 = 28
Statistical testing is also applicable to the linear least
Critical value = 0.361
squares method (Gaddis and Gaddis, 1990f; Ferrill and
4. Since the calculated value (r = 0.75) is greater
Brown 1994). In this instance, the analysis focuses on
than 0.361, then the null hypothesis is rejected
whether the slope of the line is different from zero as a
5. A linear relationship exists between variables x
slope of zero means that no linear relationship exists
and y
between the variables x and y. To that end, testing for
the significance of the slope (a statistically significant Another way to test the significance of r is to build a
test is that when the H0 is rejected; an insignificant confidence interval on the true value of r in the popu-
result means that the null hypothesis is not rejected) lation. The procedure for this test includes the fol-
requires the use of a Student’s t-test. This test replaces lowing steps:
the z distribution whenever the standard deviation of
the variable in the population is unknown (ie, s is 1. Convert the observed r value to zr value, also
unknown). The t-test uses a bell-shaped distribution known as Fisher’s z:
similar to that of the z distribution; however, the tails of r = 0.75, then zr = 0.973
Biostatistics 65
2. Fisher’s z distribution has a bell-shaped distri- bias occurs when investigators select included and/or
bution with a mean equal to zero and a standard excluded samples or data. Diagnostic or detection
error of the mean (SE) equal to [1/(n – 3)0.5]: bias can occur when outcomes are detected more or
SE = [1/(30 – 3)0.5] = 0.192 less frequently. For example, this can be from changes
in the sensitivity of instruments used to detect drug
3. Construct a confidence interval on the true concentrations. Observer or investigator bias may
value of Fisher’s z in the population: occur when an investigator favors one sample over
95% CIZr = Zr ± 1.96 (SE) another. This is most problematic with “open” or
unblinded study designs. Misclassification bias may
95% CIZr = 0.973 ± 1.96 (0.192)
occur when samples are inappropriately classified and
95% CIZr = [0.60, 1.35]
may bias in favor of one group over another or in
4. Convert the interval found in (3) above to a favor of finding no difference between the groups.
confidence interval on the true value of r in the Bias can also occur when there is a significant dropout
population: rate or loss to follow-up such that data collection is
incomplete. Channeling bias is sometimes called con-
95% CIr = [0.54, 0.88]
founding by indication and can occur when one group
5. If the interval in step (4) contains the value or sample is “channeled” into receiving one treatment
of zero, then do not reject the null hypothesis over another.
(H0: the true value of r in the population is Bias is minimized through a combination of
zero); otherwise, reject H0 and declare that r proper study design, methods, and analysis. Proper
is statistically significantly different from zero analysis cannot “de-flaw” a study with poor design
(this indicates that a linear relationship exists or methodology (DeYoung, 2000). There are several
between the variables x and y): means of minimizing bias. Randomization is some-
times referred to as allocation. In this process, sam-
Since the 95% CI does not contain the value
ples are divided into groups by chance alone such
zero, reject the null hypothesis and conclude
that potential confounders are divided equally among
that r is statistically significant.
the groups and bias is minimized. Doing so helps
ensure that all within a studied sample have an equal
Accuracy Versus Precision and independent opportunity of being selected as
“Accuracy refers to the closeness of the observation to part of the sample. This can be carried a step further
the actual or true value. Precision (or reproducibility) in that once the subject has been selected for a sample,
refers to the closeness of repeated measurements” he/she has an equal opportunity of being selected for
(Shargel et al, 2012). any of the study arms. An example of simple ran-
domization would be drawing numbers from a hat.
Its advantage is that it is simple. Its disadvantage is
Error Versus Bias that if a study were stopped early, there is no assur-
Error occurs when mistakes that neither systemati- ance of similar numbers of subjects in each group at
cally under- nor overestimate effect size are made any given point in time. Block randomization
(Drew, 2003). This is sometimes referred to as ran- involves randomizing subjects into small groups
dom error. An example would be if a coin were tossed called blocks. These blocks generally range from
10 times, yielding 8 “heads,” leading one to conclude 4 to 20 subjects. Block randomization is advanta-
that the probability of heads is 80% (Drew, 2003). geous in that there are nearly equal numbers of subjects
Bias refers to systematic errors or flaws in study in each group at any point during a study. Therefore,
design that lead to incorrect results (Drew, 2003). In if a study is stopped early, equal comparisons and
other words, bias is “error with direction” leading to more valid conclusions can be made.
systematic under- or overestimation of effect size Other means of minimizing bias include utiliz-
(Drew, 2003). There are many types of bias. Selection ing objective study endpoints, proper and accurate
66 Chapter 3
means of defining exposures and endpoints, accurate is/are equally efficacious, non-inferior, or superior to
and complete sources of information, proper controls “standard” treatment.
to allow investigators to minimize outside influences
when evaluating treatments or exposures, proper
selection of study subjects, which would require BLINDING
proper inclusion and exclusion criteria, minimizing
Blinding limits investigators’ treating or assessing one
loss of data, appropriate statistical tests for data analy-
group differently from another. It is especially impor-
sis, blinding as described later in this chapter, and
tant if there is any degree of subjectivity associated
matching, which involves identifying characteristics
with the outcome(s) being assessed. However, it is
that are a potential source of bias and matching con-
expensive and time consuming. There are several types
trols based upon those characteristics (DeYoung,
of blinding but we will only discuss the three most
2000, 2005; Drew, 2003).
common forms. In a single-blind study, someone, usu-
ally the subject, but in rare cases it may be the investi-
gator, is unaware of what treatment or intervention the
CONTROLLED VERSUS subject is receiving. In a double-blind study, neither the
NONCONTROLLED STUDIES investigator nor the subject is aware of what treatment
or intervention the subject is receiving. In a double-
Uncontrolled studies do not utilize a control group
dummy study, if one is comparing two different dosage
such that outside influences may affect study results.
forms (eg, intranasal sumatriptan vs injectable sumat-
Using controls helps minimize bias through keeping
riptan), and doesn’t want the patient or investigator to
study groups as similar as possible and minimizing
know in which arm a patient is participating, then one
outside influences. Ideally, groups will differ only in
group would receive intranasal sumatriptan and a placebo
the factor being studied. There are many types of
injection and the other group would receive intranasal
controls. “Utilizing a placebo control is not always
placebo and a sumatriptan injection. Another example
practical or ethical, but one or more groups receive(s)
would be for a trial evaluating a tablet versus an inhaler.
active treatment(s) while the control group receives
Some trials that claim to be blinded are not. For example,
a placebo” (Drew, 2003). Historical control studies
a medication may have a distinctive taste, physiologic
are generally less expensive to perform but this
effect, or adverse effect that un-blinds patients and/or
design introduces problems with diagnostic, detec-
investigators.
tion, and procedure biases. “Data from a group of
subjects receiving the experimental drug or interven-
tion are compared to data from a group of subjects CONFOUNDING
previously treated during a different time period,
perhaps in a different place” (Herring, 2014). Confounding occurs when variables, other than the
Crossover control is very efficient at minimizing one(s) being studied, influence study results.
bias while maximizing power when used appropri- Confounding variables are difficult to detect some-
ately. Each subject serves as his/her own control. times and are linked to study outcome(s) and may be
Initially, group A receives the experimental drug linked to hypothesized cause(s). As discussed in
while group B receives the control (placebo or gold more detail later in this chapter, validity of a study
standard treatment). After a washout period, group A depends upon how well investigators minimize the
receives the control and group B receives the experi- influence of confounders (DeYoung, 2000).
mental drug. Standard treatment (aka active treat- For example, atherosclerosis and myocardial
ment) control is very practical and ethical. The infarction (MI): There is an association between
control group receives “standard” treatment while atherosclerosis and smoking, smoking and risk for
the other group(s) receives experimental treatment(s). an MI, and atherosclerosis and risk for an MI. The
This type of control is used when the investigator proposed cause is atherosclerosis and the potential
wishes to demonstrate that the experimental treatment(s) confounder is smoking.
Biostatistics 67
Proposed cause Confounder the national cholesterol guidelines utilize multiple
(atherosclerosis) (smoking)
regression to help establish atherosclerotic cardio-
vascular disease (ASCVD) risk for patients based
upon population data. A patient’s ASCVD risk is the
Outcome studied dependent variable because its estimate “depends
(heart attack) upon” several independent variables. The indepen-
dent variables include gender, race, age, total choles-
Another example of confounding is the relation-
terol, HDL-cholesterol, smoking status, systolic
ship between fasting blood glucose (FBG) in patients
blood pressure, and whether or not a patient is being
being treated for diabetes with medication. One
treated for hypertension, or has diabetes. All of these
confounding factor on their FBG is their diet. For
independent variables are used to help predict a
example, dietary cinnamon consumption can lower
patient’s ASCVD risk. Similar factors to those listed
blood glucose. If patients regularly consume cinna-
above can influence a multitude of pharmacokinetic
mon, FBG could be lowered beyond the diabetic
parameters as well.
medication’s capabilities. In this case, although cin-
As previously discussed, various types of
namon may not affect the proposed cause (type of
ANOVAs help account for confounding: multivariate
diabetes medication that is being used), it very well
ANOVAs for non-paired data, and two-way repeated
may affect FBG concentrations, possibly resulting in
measures ANOVA for paired data.
biased results by augmenting the diabetes drug’s
FBG lowering effect, and therefore affecting its
pharmacodynamic profile. VALIDITY
Proposed cause Confounder Internal validity addresses how well a study was
(diabetes drug) (cinnamon intake) conducted: if appropriate methods were used to
minimize bias and confounding and ensure that
exposures, interventions, and outcomes were mea-
sured correctly (DeYoung, 2000). This includes
Outcome studied
(fasting blood glucose) ensuring the study accurately tested and measured
what it claims to have tested and measured (DeYoung,
As with bias, confounding is minimized through 2000; Anonymous, 2003). Internal validity directly
the combination of proper study design and method- affects external validity; without internal validity, a
ology, including randomization, proper inclusion study has no external validity. Presuming internal
and exclusion criteria, and matching if appropriate. validity, external validity addresses the application
However, unlike bias, confounding may also be of study findings to other groups, patients, systems,
minimized through proper statistical analysis. or the general population (DeYoung, 2000; Drew,
Stratification separates subjects into nonoverlapping 2003). “A high degree of internal validity is often
groups called strata, where specific factors (eg, gen- achieved at the expense of external validity” (Drew,
der, ethnicity, race, smoking status, weight, diet) are 2003). For example, excluding diabetic hypertensive
evaluated for any influence on study results (DeYoung, patients from a study may provide very clean statisti-
2000). “Stratification has limits” (Herring, 2014). As cal endpoints. However, clinicians who treat mainly
one stratifies, subgroup sample sizes decrease, so one’s diabetic hypertensive patients may be unable to uti-
ability to detect meaningful influences in each sub- lize the results from such a trial (Drew, 2003).
group will also decrease.
Multivariate (or multiple) regression analysis
(MRA) is a possible solution (DeYoung, 2000). With Frequently Asked Question
MRA, “multiple predictor variables (aka indepen- »»Are there any types of statistical tests that can be
dent variables) can be used to predict outcomes (aka used to correct for a lack of internal validity?
dependent variables)” (Herring, 2014). For example,
68 Chapter 3
BIOEQUIVALENCE STUDIES nominal outcomes, but in rare cases may be applied
to ordinal outcomes. The following calculations for
“Statistics have wide application in bioequiva- cohort and randomized controlled trial (RCT) are the
lence studies for the comparison of drug bio-
same, but nomenclature is different. For a cohort
availability for two or more drug products. The
study, the exposed group is referred to as such. For an
FDA has published Guidance for Industry for the
statistical determination of bioequivalence (1992, RCT, the exposed group may be referred to as the
2001) that describes the comparison between a interventional, experimental, or treatment group. For
test (T) and reference (R) drug product. These a cohort study, the unexposed group is referred to as
trials are needed for approval of new or generic such. For an RCT, the unexposed group is referred to
drugs. If the drug formulation changes, bio- as the control group. For the following examples, the
equivalence studies may be needed to compare subscript “E” will refer to the exposed or experimen-
the new drug formulation to the previous drug tal (treatment, interventional) group and the subscript
formulation. For new drugs, several investiga- “C” will refer to the unexposed or control group.
tional formulations may be used at various Absolute risk (AR) is simply another term for
stages, or one formulation with several strengths
incidence. It is the number of new cases that occur
must show equivalency by extent and rate
during a specified time period divided by the number
(eg, 2 × 250-mg tablet vs 1 × 500-mg tablet,
suspension vs capsule, immediate-release vs of subjects initially followed to detect the outcome(s)
extended-release product). The blood levels of of interest (Gaddis and Gaddis, 1990c).
the drug are measured for both the new and the
reference formulation. The derived pharmacoki- Number who develop
netic parameters, such as maximum concentra- the outcome of interest
during a specified time period
tion (Cmax) and area under the curve (AUC), must AR =
meet accepted statistical criteria for the two Number initially followed to detect
the outcome of interest
drugs to be considered bioequivalent. In bio-
equivalence trials, a 90% confidence interval of (3.10)
the ratio of the mean of the new formulation to Absolute risk reduction (ARR) is a measure of the
the mean of the old formulation (Test/Reference) absolute incidence differences in the event rate
is calculated. That confidence interval needs to between the studied groups. Absolute differences are
be completely within 0.80–1.25 for the drugs to more meaningful than relative differences in out-
be considered bioequivalent. Adequate power comes when evaluating clinical trials (DeYoung,
should be built into the design and validated
2005). When outcomes are worse for the experimental
methods used for analysis of the samples.
group, the absolute risk difference is termed absolute
Typically, both the rate (reflected by Cmax) and
the extent (AUC) are tested. The ANOVA may risk increase (ARI).
also reveal any sequence effects, period effects, ARR (or ARI) = ARC – ARE (3.11)
treatment effects, or inter- and intrasubject vari-
ability. Because of the small subject population Numbers needed to treat (NNT) is the “reciprocal of
usually employed in bioequivalence studies, the the ARR” (DeYoung, 2000).
ANOVA uses log-transformed data to make an
1
inference about the difference of the two groups” NNT = (3.12)
ARR
(Shargel et al, 2012).
When outcomes are worse for the experimental
group, there is an ARI and this calculation is referred
EVALUATION OF RISK FOR to as numbers needed to harm (NNH).
CLINICAL STUDIES 1
NNH =
ARI (3.13)
Risk calculations estimate the magnitude of associa-
tion between exposure and outcome (DeYoung, These calculations help in understanding the magnitude
2000). These effect measurers are mainly used for of an intervention’s effectiveness (DeYoung, 2000).
Biostatistics 69
A weakness of these is that they “assume baseline utilizing logistic or multivariate regression analysis
risk is the same for all patients or that it is unrelated simply because these analyses automatically calculate
to relative risk” (DeYoung, 2000). Although rarely OR. They do so because regression analysis is utilized
seen, “confidence intervals (CIs) may be calculated to adjust for confounding and adjustments are easier
for NNT and NNH” (DeYoung, 2005). to perform with OR than with RR (De Muth, 2006).
Relative risk (RR) compares the AR (incidence) OR is presented differently for case-control studies
of the experimental group to that of the control than for RCTs. For RCTs, OR is presented in the
group (DeYoung, 2000). It is simply a ratio of the same way as RR. For example, in an RCT evaluating
AR for the experimental or exposed group to the AR an association of an intervention and death rate, an
of the control or unexposed group. RR is sometimes OR of 0.75 would be reported as patients receiving
called risk ratio, rate ratio, or incidence rate ratio. the intervention were 25% less likely, or 75% as
AR likely, to have died than controls. Since case-control
E
RR = (31.4)
AR studies identify patients based upon disease rather
C
Relative risk differences are sometimes presented in than intervention, OR is presented differently than for
studies and these estimate the percentage of baseline an RCT; it compares the odds that a case was exposed
risk that is changed between the exposed or experi- to a risk factor to the odds that a control was exposed to
mental group and the unexposed or control group. a risk factor. For example, in a case-control study evalu-
The relative risk difference is termed relative risk ating an association of a rare type of cancer and expo-
reduction (RRR) when risk is decreased. The relative sure to pesticides, an OR of 1.5 would be reported as
risk difference is termed relative risk increase (RRI) cases (those with the rare cancer) were 50% more likely,
when risk is increased. RRR and RRI can be calcu- or 1½ times as likely, to have been exposed to pesticides
lated in two different ways: than controls. CIs should always be provided for RR,
OR, and HR.
RRR (or RRI) = 1 – RR (3.15)
These above calculations and principles are com-
or monly utilized for interpreting data in FDA-approved
ARR (or ARI)
RRR (or RRI) = (3.16) package inserts. For example, in the Coreg®
ARC (carvedilol) package insert, there are several major
Hazard ratio (HR) is used with Cox proportional studies that are presented. The Copernicus trial evalu-
hazards regression analysis. It is used when a study is ated carvedilol’s efficacy against that of placebo for
evaluating the length of time required for an outcome patients with severe systolic dysfunction heart failure
of interest to occur (Katz, 2003). HR is often used over a median of 10 months (GlaxoSmithKline,
similarly to RR, and is a reasonable estimate of RR 2008). The primary endpoint of mortality occurred in
as long as adequate data are collected and outcome 190 out of 1133 patients taking placebo and 130 out
incidence is <15% (Katz, 2003; Shargel et al, 2012). of 1156 patients taking carvedilol. This means that the
However, whereas RR only represents the probability AR for patients taking placebo was 190/1133 = 0.17
of having an event between the beginning and the end or 17% and the AR for patients taking carvedilol was
of a study, HR can represent the probability of having 130/1156 = 0.11 or 11%. The RR would be 0.11/0.17
an event during a certain time interval between the or 11%/17% = 0.65 or 65%. RRR would be 1 – 0.65
beginning and the end of the study (DeYoung, 2005). = 0.35 or 35%. Therefore, patients treated with
Odds ratio (OR) is mainly used in case-control carvedilol were 35% less likely to die than were
studies as an estimate of RR since incidence cannot be patients treated with placebo. However, sometimes
calculated. Estimation accuracy decreases as outcome RR and RRR can be deceptive, so one should always
or disease incidence increases. However, OR is fairly calculate the ARR or ARI and NNT or NNH. In this
accurate as long as disease incidence is <15%, which case, carvedilol improved the death rate, so one would
is usually the case since case-control studies evaluate calculate ARR and NNT. The AAR is simply the dif-
potential risk factors for rare diseases (Katz, 2003). In ference between the AR of each agent: 17% – 11% =
addition, OR is sometimes reported for RCTs 6% or 0.17 – 0.11 = 0.06. NNT is the reciprocal of
70 Chapter 3
ARR, so 1/0.06 = 17. Therefore, since the median Frequently Asked Question
follow-up of this trial was 10 months, one would need »»Which are more important: relative or absolute
to treat 17 patients for 10 months with carvedilol differences?
rather than placebo to prevent 1 death.
CHAPTER SUMMARY
Statistical applications are vital in conducting and In this chapter, we have presented very basic,
evaluating biopharmaceutical and pharmacokinetic practical principles in hopes of guiding the reader
research. Utilization includes, but is not limited to, throughout the research process. For readers who
studies involving hypothesis testing, finding ways to are interested in learning about this topic in more
improve a product, its safety, or performance. Proper depth, we recommend statistics textbooks or
statistics are required for experimental planning, online resources and/or taking a research-based
data collection, analysis, and interpretation of results, statistics course at the college or university of their
allowing for rational decision making throughout choosing.
these processes (Durham, 2008; Shargel et al, 2012).
LEARNING QUESTIONS
The column for concentration (ng/mL) refers to
1. The following data represent the concentration
the concentration of vitamin C in infant urine.
of vitamin C in infant urine:
Calculate the arithmetic mean for vitamin C in
the urine.
Age (months) Gender Conc. (ng/mL) 2. Refer to Question 1; find the standard deviation
for the concentration of vitamin C in urine for
1 F 2.7
the male infants.
3 F 2.8 3. Refer to Question 1; find the coefficient of
4 M 2.9 variation (%) value for the variable age.
4. Refer to Question 1; consider the following
6 M 2.9
graph representing the data:
7 M 2.3
3
9 M 2.3
2.5
12 F 1.5
2
15 F 1.1
16 M 1.3 1.5
17 F 1.3 1
18 F 1.1 0.5
24 F 1.5
0
0 5 10 15 20 25 30 35
25 F 1.0
Age (months)
29 M 0.4
Based on the above graph, the value for the
30 F 0.2
correlation coefcient is most likely_______.
Vitamin C urine
concentration (ng/mL)
Biostatistics 71
5. Refer to Questions 1 and 4. The older the 9. Which statistics did you use in answering
infant, the _______ is the concentration of Question 8?
vitamin C in the urine. 10. Investigators want to perform a study comparing
6. The p-value associated with the slope of the two doses of an investigational anticoagulant
line in Question 4 is less than 0.0001 for prevention of thromboembolism. They
(p < 0.0001). For a of 5%, the slope value is calculate that a sample size of 400 subjects
statistically _______. (200 in each arm) will be needed to show a dif-
7. Find the slop value for the graph in Question 4. ference (based upon an alpha of 0.05 and beta
8. The following results were presented by Chin of 0.20). They predict that given the patient
KH, Sathyyasurya DR, Abu Saad H, Jan population, approximately 50% of subjects will
Mohamed HJB: Effect of ethnicity, dietary drop out of the study. Based upon the dropout
intake and physical activity on plasma rate, how many subjects will be needed in each
adiponectin concentrations among Malaysian treatment arm?
patients with type 2 diabetes mellitus. Int 11. A superiority trial evaluating the doses of a
J Endocrinol Metab 11(3):16–174, 2013. new cholesterol medication was performed
DOI:10.5812/ijem.8298.) (Copyright © 2013, comparing AUC. There were 200 patients in
Research Institute for Endocrine Sciences this trial and differences were statistically
and Iran Endocrine Society; Licensee Kowsar significant. Was this study underpowered?
Ltd. This is an Open Access article distributed 12. A study is planned to evaluate differences
under the terms of the Creative Commons in half-life (t½) of three different metoprolol
Attribution License [http://creativecommons. formulations. The investigators plan to include
org/licenses/by/3.0], which permits unre- 150 subjects (50 in each arm) to reach statisti-
stricted use, distribution, and reproduction in cal significance based upon a beta of 0.20 and
any medium, provided the original work is alpha of 0.05. Which statistical test would
properly cited): be the most appropriate? (Hint: Assume no
confounders.)
Malay Chinese Indian 13. If you conduct a pharmacokinetic study that
utilizes appropriate methodology and a broad
Adiponectin 6.85 (4.66) 6.21 (3.62) 4.98 (2.22) population base for inclusion, how will this
(μg/mL)
affect the strength of internal and external
(Chin KH, Sathyyasurya DR, Abu Saad H, Jan Mohamed HJB: Effect of validity?
ethnicity, dietary intake and physical activity on plasma adiponectin
14. Investigators wish to study the differences in
concentrations among Malaysian patients with type 2 diabetes mellitus.
Int J Endocrinol Metab 11(3):16–174, 2013.) patients with subtherapeutic concentrations
of vancomycin via two difference delivery
The concentration of adiponectin (a protein systems. The results from this 2-week study
produced by adipocytes) in plasma is reported are listed below:
in Malaysian patients with three different ethnici-
ties. The values in the table above are given as
arithmetic mean (standard deviation). The signi- Formulation A Formulation B
cance of adiponectin plasma concentration is that (FA) (n = 55) (FB) (n = 62)
its plasma levels correlate well with the clinical
Subtherapeutic 35 17
response to administered insulin in patients with vancomycin
type 2 diabetes. Referring to the results above, concentrations
which group of patients is more variable with
respect to its mean than the other two groups? How should these results be reported?
72 Chapter 3
ANSWERS
Learning Questions 11. Power is associated with beta: power = 1 – beta.
Beta is the risk of committing a type 2 error. If
1. Using a scientific calculator, the arithmetic mean a statistically significant difference is detected,
for vitamin C in infant urine was 1.69 ng/mL. a type 2 error could not occur. Therefore, the
2. Using a scientific calculator, the standard devia- trial was not underpowered. With this scenario,
tion of vitamin C in urine for male infants was there are only two possibilities: either (1) the
0.98 ng/mL. findings were correct or (2) a type 1 error
3. The coefficient of variation (%) for age was occurred.
(SD/mean) × 100 = (9.49/14.4) × 100 = 66% 12. Differences in half-life (t½) are parametric data
4. The slope of the line depicted in the graph was since they are scored on a continuum and there
negative. Therefore, the correlation coefficient is a consistent level of magnitude of differ-
must be a negative value. ence between data units. Since there are three
5. A negative linear relationship was observed metoprolol formulations being evaluated, and
between age of infants and the concentration of no identified confounders, a 1-way ANOVA is
vitamin C in urine. Thus, the vitamin C concen- appropriate. If there were only two groups and
tration in urine in older infants would be lower no identified confounders, a t-test would be
than that found in younger infants. appropriate.
6. Since p-value is less than 0.05, the results were 13. Utilizing appropriate methodology helps
statistically significant. increase internal validity. Including a broad
7. The slope of the line is negative. The value of the population helps increase external validity.
slope may be obtained by a scientific calculator. 14. There are several ways the results could be
8. The coefficient of variation (%) for Malay, Chi- reported. ARFA = 35/55 = 0.64 or 64%, ARFB =
nese, and Indian patients was 68.03%, 58.29%, 17/62 = 0.27 or 27%, ARI = ARC – ARE = 0.27
and 44.58%, respectively. Recall that CV (%) = – 0.64 = 0.37 or 37%, NNH= 1/0.37 = 2.7, so
(SD/mean) × 100. Since Malay patients had the 3 patients over 2 weeks. In other words, one
highest CV (%) value, then adiponectin plasma would need to treat 3 patients over 2 weeks
concentration was more variable with respect to with formulation A rather than formulation B to
its mean than the other two values. cause one episode of a subtherapeutic vanco-
9. The coefficient of variation (%). mycin concentration. RR = 0.64/0.27 = 2.3.
10. Sample size (corrected for drop-outs) The results could be reported as those utilizing
formulation A were 2.3 times as likely to be
Number of patients subtherapeutic as those being given formula-
=
1–% of expected drop-outs tion B. Since RRI = 1 – RR = 1 – 2.3 = –1.3,
another way of explaining the results would be
200 in each arm/(1 – 0.5) = 200/0.5 = 400 in
that those utilizing formulation A were 130%
each treatment arm. If the question had asked
more likely to have subtherapeutic vancomycin
how many total subjects would be needed
concentrations than those being given
(ie, both arms), the answer would have been
formulation B.
400/(1 – 0.5) = 400/0.5 = 800.
Biostatistics 73
REFERENCES
Anonymous: SOP 13 : Pharmacokinetic data analysis. Onkologie Gaddis ML, Gaddis GM: Introduction to biostatistics: Part 3, Sen-
26(suppl 6):56–59, 2003. sitivity, specificity, predictive value, and hypothesis testing.
Al-Achi A, PhD. Discussions. Ann Emerg Med 19(5):591–597, 1990c.
Berensen NM: Biostatistics review with lecture for the MUSC/ Gaddis ML, Gaddis GM: Introduction to biostatistics: Part 4, Statis-
VAMC BCPS study group, Charleston, SC, July 17, 2000. tical inference techniques in hypothesis testing. Ann Emerg Med
Brendel K, Dartois C, Comets E, et al: Are population 19(7):820–825, 1990d.
pharmacokinetic-pharmacodynamic models adequately evalu- Gaddis ML, Gaddis GM: Introduction to biostatistics: Part 5, Statisti-
ated? A survey of the literature from 2002 to 2004. Clin Phar- cal inference techniques for hypothesis testing with nonparamet-
macokinet 46(3):221–234, 2007. ric data. Ann Emerg Med 19(9):1054–1059, 1990e.
De Muth JE: In Chow SC (ed). Basic Statistics and Pharmaceutical Gaddis ML, Gaddis GM: Introduction to biostatistics: Part 6,
Statistical Applications, 2nd ed. Boca Raton, London, New York, Correlation and regression. Ann Emerg Med 19(12):1462–1468,
Chapman & Hall/CRC, Taylor & Francis Group, 2006. 1990f.
DeYoung GR: Clinical Trial Design (handout). 2000 Updates in Glasner AN: High Yield Biostatistics. PA, Williams & Willkins,
Therapeutics: The Pharmacotherapy Preparatory Course, 2000. 1995.
DeYoung GR: Understanding Statistics: An Approach for the Clini- GlaxoSmithKline. Coreg CR [package insert], https://www.gsk-
cian. Science and Practice of Pharmacotherapy PSAP Book 5, source.com/gskprm/htdocs/documents/COREG-CR-PI-PIL.
5th ed. American College of Clinical Pharmacy, Kansas City, PDF. Research Triangle Park, NC, 2008.
MO, 2005. Herring C: Quick Stats: Basics for Medical Literature Evaluation,
Drew R: Clinical Research Introduction (handout). Drug Literature 5th ed. Massachusetts, USA, Xanedu Publishing Inc., 2014.
Evaluation/Applied Statistics Course. Campbell University Hirt D, Urien S, Jullien V, et al: Age-related effects on nelfina-
School of Pharmacy, 2003. vir and M8 pharmacokinetics: A population study with 182
Durham TA, Turner JR: Introduction to Statistics in Pharmaceutical children. Antimicrob Agents Chemother 50(3):910–916,
Clinical Trials. London, UK, Pharmaceutical Press, RPS Pub- 2006.
lishing, 2008. Katz MH: Multivariable analysis: A primer for readers of medical
Ferrill JM, Brown LD: Statistics for the Nonstatistician: A System- research. Annal Internal Med 138:644–650, 2003.
atic Approach to Evaluating Research Reports. US Pharmacist Munro HB: Statistical Methods for Health Care Research.
July:H-3-H-16, 1994. Lippincott Williams & Wilkins, Philadelphia, PA, 2005.
Gaddis ML, Gaddis GM: Introduction to biostatistics: Part 1, Basic Drew R, PharmD, MS, BCPS. Discussions and provisions.
concepts. Ann Emerg Med 19(1):86–89, 1990a. Shargel L, Wu-Pong S, Yu A: Statistics. Applied Biopharma-
Gaddis ML, Gaddis GM: Introduction to biostatistics: Part 2, ceutics and Pharmacokinetics, 6th ed. New York, NY, USA,
Descriptive statistics. Ann Emerg Med 19(3):309–315, 1990b. McGraw-Hill, 2012, Appendix.
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One-Compartment Open
4 Model: Intravenous Bolus
Administration
David S.H. Lee
Chapter Objectives While the oral route of drug administration is the most convenient,
intravenous (IV) administration is the most desirable for critical
»» Describe a one-compartment
care when reaching desirable drug concentrations quickly is
model, IV bolus injection.
needed. Examples of when IV administration is desirable include
»» Provide the pharmacokinetic antibiotic administration during septic infections or administration
terms that describe a one- of antiarrhythmic drugs during a myocardial infarction. Because
compartment model, IV bolus pharmacokinetics is the science of the kinetics of drug absorption,
injection, and the underlying distribution, and elimination, IV administration is desirable in
assumptions. understanding these processes since it simplifies drug absorption,
»» Explain how drugs follow one- essentially making it complete and instantaneous. This leaves only
compartment kinetics using the processes of drug distribution and elimination left to study. This
drug examples that follow one- chapter will introduce the concepts of drug distribution and elimi-
compartment kinetics. nation in the simplest model, the one-compartment open model.
The one-compartment open model assumes that the body can
»» Calculate pharmacokinetic be described as a single, uniform compartment (ie, one compart-
parameters from drug ment), and that drugs can enter and leave the body (ie, open
concentration–time data using a model). The simplest drug administration is when the entire drug is
one-compartment model. given in a rapid IV injection, also known as an IV bolus. Thus, the
»» Simulate one-compartment one-compartment open model with IV bolus administration is the
plasma drug level graphically simplest pharmacokinetic model. It assumes that the drug is admin-
using the one-compartment istered instantly into the body, it is instantaneously and rapidly
model equation. distributed throughout the body, and drug elimination occurs
immediately upon entering the body. This model is a simplistic
»» Calculate the IV bolus dose
representation of the processes in the body that determine drug
of a drug using the one-
disposition, but nonetheless, it can be useful to describe and predict
compartment model equation.
drug disposition.
»» Relate the relevance of the In reality, when a drug is administered intravenously, the drug
magnitude of the volume of travels through the bloodstream and distributes throughout the
distribution and clearance of bloodstream in the body. While this process is not truly instanta-
various drugs to underlying neous, it is relatively rapid enough that we can make this assump-
processes in the body. tion for most drugs. Through the bloodstream, the drug is
»» Derive model parameters from distributed to the various tissue organs in the body. The rate and
slope and intercept of the extent of distribution to the tissue organs depends on several pro-
appropriate graphs. cesses and properties. Tissues in the body are presented the drug at
various rates, depending on the blood flow to that organ, and the
drug may have different abilities to cross from the vasculature to
75
76 Chapter 4
the organ depending on the molecular weight of the k
drug. Tissues also have different affinity for the drug, IV DB, VD
depending on lipophilicity and drug binding. Finally,
large organs may have a large capacity for drugs to FIGURE 4-1 Pharmacokinetic model for a drug admin-
distribute to. istered by rapid intravenous injection. DB = drug in body; VD =
While drug distribution is complex, if these pro- apparent volume of distribution; k = elimination rate constant.
cesses are rapid enough, we can simplify our con-
ceptualization as if the drug uniformly distributes
into a single (one) compartment of fluid. The volume
of this single compartment is termed the apparent the plasma, but does not predict the concentrations in
volume of distribution, VD. The apparent volume of tissues. However, using this model, which assumes
distribution is not an actual volume in the body, but distribution to tissues is rapid, we can assume the
is a theoretical volume that the drug uniformly dis- declines in drug concentration in the plasma and tis-
tributes to immediately after being injected into the sues will be proportional. For these reasons, the one-
body. This uniform and instantaneous distribution is compartment open model is useful for predicting
termed a well-stirred one-compartment model. The concentrations in the plasma, and declines in plasma
apparent volume of distribution is a proportion concentrations will be proportional to declines in
between the dose and the concentration of the drug tissue concentrations.
in plasma, C0
p , at that time immediately after being
injected.
Most drugs are eliminated from the body by ELIMINATION RATE CONSTANT
liver metabolism and/or renal excretion. All of the The rate of elimination for most drugs from a tissue
processes of drug elimination can be described by or from the body is a first-order process, in which the
the elimination rate constant, k. The elimination rate rate of elimination at any point in time is dependent
constant is the proportion between the rate of drug on the amount or concentration of drug present at
elimination and the amount of drug in the body. that instance. The elimination rate constant, k, is a
Because the amount of drug in the body changes first-order elimination rate constant with units of
over time, the rate of drug elimination changes, but time–1 (eg, h–1 or 1/h). Generally, the injected drug is
the elimination rate constant remains constant for measured in the blood or plasma, sometimes termed
first-order elimination. This makes it convenient to the vascular compartment. Total removal or elimina-
summarize drug elimination from the body indepen- tion of the injected drug from this compartment is
dent of time or the amount of drug in the body. affected by metabolism (biotransformation) and
However, because it’s difficult to measure the amount excretion. The elimination rate constant represents
of drug in the body, DB, pharmacokineticists and the sum of each of these processes:
pharmacists also prefer to convert drug amounts to
drug concentrations in the body using the apparent
k = km + ke (4.1)
volume of distribution. Thus, the elimination rate
constant also describes the proportion between the
rate of change of drug concentration and drug con- where km = first-order rate process of metabolism
centration in the compartment. and ke = first-order rate process of excretion. There
The one-compartment open model with IV may be several routes of elimination of drug by
bolus dosing describes the distribution and elimina- metabolism or excretion. In such a case, each of
tion after an IV bolus administration and is shown in these processes has its own first-order rate constant.
Fig. 4-1. The fluid that the drug is directly injected A rate expression for Fig. 4-1 is
into is the blood, and generally, drug concentrations
are measured in plasma since it is accessible. dD
B
= −kD (4.2)
Therefore, this model predicts the concentrations in dt B
One-Compartment Open Model: Intravenous Bolus Administration 77
This expression shows that the rate of elimination of APPARENT VOLUME
drug in the body is a first-order process, depending
OF DISTRIBUTION
on the overall elimination rate constant, k, and the
amount of drug in the body, DB, remaining at any In general, drug equilibrates rapidly in the body.
given time, t. Integration of Equation 4.2 gives the When plasma or any other biologic compartment is
following expression: sampled and analyzed for drug content, the results are
usually reported in units of concentration instead of
−kt amount. Each individual tissue in the body may con-
log DB = + log D0 (4.
2.3 B 3)
tain a different concentration of drug due to differ-
ences in blood flow and drug affinity for that tissue.
where D 0 The amount of drug in a given location can be related
B = the drug in the body at time t and DB is
the amount of drug in the body at t = 0. When log D to its concentration by a proportionality constant that
B
is plotted against t for this equation, a straight line is reflects the apparent volume of fluid in which the
obtained (Fig. 4-2). In practice, instead of transform- drug is dissolved. The volume of distribution repre-
ing values of DB to their corresponding logarithms, sents a volume that must be considered in estimating
each value of DB is placed at logarithmic intervals on the amount of drug in the body from the concentra-
semilog paper. tion of drug found in the sampling compartment. The
Equation 4.3 can also be expressed as volume of distribution is the apparent volume (VD) in
which the drug is dissolved (Equation 4.5).
Because the value of the volume of distribution does
D D0e−kt
B = B (4.4) not have a true physiologic meaning in terms of an
anatomic space, the term apparent volume of distri-
bution is used.
The amount of drug in the body is not deter-
Frequently Asked Questions mined directly. Instead, blood samples are collected
»»What is the difference between a rate and a rate at periodic intervals and the plasma portion of blood
constant? is analyzed for their drug concentrations. The VD
»»Why does k always have the unit 1/time (eg, h–1), relates the concentration of drug in plasma (Cp) and
regardless of what concentration unit is plotted? the amount of drug in the body (DB), as in the fol-
lowing equation:
DB = VDCp (4.5)
100
D 0
B
Substituting Equation 4.5 into Equation 4.3, a
similar expression based on drug concentration in
plasma is obtained for the first-order decline of drug
0 Slope = –k
1 plasma levels:
2.3
−kt
logCp= + logC0 (4.6)
2.3 p
1 where Cp = concentration of drug in plasma at time t
0 1 2 3 4 5 and C0
p = concentration of drug in plasma at t = 0.
Time Equation 4.6 can also be expressed as
FIGURE 4-2 Semilog graph of the rate of drug elimina-
tion in a one-compartment model. C C0e−kt
p = p (4.7)
Drug in body (DB)
78 Chapter 4
The relationship between apparent volume, drug
concentration, and total amount of drug may be bet- where D = total amount of drug, V = total volume, and
ter understood by the following example. C = drug concentration. From Equation 4.8, which is
similar to Equation 4.5, if any two parameters are
known, then the third term may be calculated.
EXAMPLE »» »
Exactly 1 g of a drug is dissolved in an unknown vol-
ume of water. Upon assay, the concentration of this The one-compartment open model considers the
solution is 1 mg/mL. What is the original volume of body a constant-volume system or compartment.
this solution? Therefore, the apparent volume of distribution for
The original volume of the solution may be any given drug is generally a constant. If both the
obtained by the following proportion, remember- concentration of drug in the plasma and the apparent
ing that 1 g = 1000 mg: volume of distribution for the drug are known, then
the total amount of drug in the body (at the time in
which the plasma sample was obtained) may be cal-
1000mg 1mg
= culated from Equation 4.5.
xmL mL
x =1000mL Calculation of Volume of Distribution
Therefore, the original volume was 1000 mL or 1 L. In a one-compartment model (IV administration),
This is analogous to how the apparent volume of the VD is calculated with the following equation:
distribution is calculated.
Dose D0
If, in the above example, the volume of the V B
D= = (4.9)
C0 0
p C
solution is known to be 1 L, and the amount of drug p
dissolved in the solution is 1 g, what is the concen-
When C0
p is determined by extrapolation, C0
p repre-
tration of drug in the solution?
sents the instantaneous drug concentration after drug
equilibration in the body at t = 0 (Fig. 4-3). The dose
1000 mg
=1mg/mL of drug given by IV bolus (rapid IV injection) repre-
1000 mL
sents the amount of drug in the body, D0
B, at t = 0.
Because both D0
B and C0
p are known at t = 0, then the
Therefore, the concentration of the drug in the
solution is 1 mg/mL. This is analogous to calculat-
ing the initial concentration in the plasma if the 100
0
apparent volume of distribution is known. Cp
From the preceding example, if the volume
of solution in which the drug is dissolved and the
drug concentration of the solution are known, then
the total amount of drug present in the solution 10
may be calculated. This relationship between drug
concentration, volume in which the drug is dis-
solved, and total amount of drug present is given in
the following equation:
1
0 1 2 3 4 5
Dose D0
V B
= 4 8
D=
( . ) Time
C 0 0
p Cp FIGURE 4-3 Semilog graph giving the value of C 0
p by
extrapolation.
Plasma level (Cp )
One-Compartment Open Model: Intravenous Bolus Administration 79
apparent volume of distribution, VD, may be calcu- The calculation of the apparent VD by means of
lated from Equation 4.9. Equation 4.13 is a model-independent or noncom-
From Equation 4.2 (repeated here), the rate of partmental model method, because no pharmacoki-
drug elimination is netic model is considered and the AUC is determined
directly by the trapezoidal rule.
dDB
= −kD
dt B Significance of the Apparent Volume of
Distribution
Substituting Equation 4.5, DB = VDCp, into The apparent volume of distribution is not a true
Equation 4.2, the following expression is obtained: physiologic volume, but rather reflects the space the
drug seems to occupy in the body. Equation 4.9
dD shows that the apparent VD is dependent on C0
p , and
B
= −kV C (4.10)
dt D p thus is the proportionality constant between C0
p and
dose. Most drugs have an apparent volume of distri-
Rearrangement of Equation 4.10 gives bution smaller than, or equal to, the body mass. If a
drug is highly bound to plasma proteins or the mol-
ecule is too large to leave the vascular compartment,
dDB = −kVDCpdt (4.11) then C0
p will be higher, resulting in a smaller appar-
ent VD. For example, the apparent volume of distri-
bution of warfarin is small, approximately 0.14 L/kg,
As both k and V are constants, Equation 4.10
D much less than the total body mass. This is because
may be integrated as follows:
warfarin is highly bound to plasma proteins, making
it hard to leave the vascular compartment.
D0 ∞
∫ dD kV C d
0 B = − D ∫ t (4 12) For some drugs, the volume of distribution may
0 p .
be several times the body mass. In this case, a very
small C0
p may occur in the body due to concentration
Equation 4.12 shows that a small change in time of the drug in peripheral tissues and organs, resulting
(dt) results in a small change in the amount of drug in a large VD. Drugs with a large apparent VD are
in the body, DB. more concentrated in extravascular tissues and less
∞
The integral ∫ C e r s n s t e A C∞
0 pdt r p e e t h U 0 , concentrated intravascularly. For example, the appar-
which is the summation of the area under the curve ent volume of distribution of digoxin is very high,
from t = 0 to t = ∞. Thus, the apparent V may also 7.0 L/kg, much greater than the body mass. This is
D
be calculated from knowledge of the dose, elimina- because digoxin binds extensively to tissues, espe-
tion rate constant, and the area under the curve cially muscle tissues. Consequently, binding of a
(AUC) from t = 0 to t = ∞. This is usually estimated drug to peripheral tissues or to plasma proteins will
by the trapezoidal rule (see Chapter 2). After integra- significantly affect the VD.
tion, Equation 4.12 becomes The apparent VD is a volume term that can be
expressed as a simple volume or in terms of percent
of body weight. In expressing the apparent VD in
∞
D0 = kVD [AUC]0 terms of percent of body weight, a 1-L volume is
assumed to be equal to the weight of 1 kg. For
which upon rearrangement yields the following example, if the VD is 3500 mL for a subject weighing
equation: 70 kg, the VD expressed as percent of body weight is
D
V 0 3.5 kg
D = (4.13)
∞ ×100 = 5%of body weight
k [AUC]0 70 kg
80 Chapter 4
In the example of warfarin above, 0.14 L/kg is For each drug, the apparent VD is a constant. In
estimated to be 14% of body weight. certain pathologic cases, the apparent VD for the drug
If VD is a very large number—that is, >100% of may be altered if the distribution of the drug is
body weight—then it may be assumed that the drug changed. For example, in edematous conditions, the
is concentrated in certain tissue compartments. In total body water and total extracellular water
the digoxin example above, 7.0 L/kg is estimated to increases; this is reflected in a larger apparent VD
be 700% of body weight. Thus, the apparent VD is a value for a drug that is highly water soluble. Similarly,
useful parameter in considering the relative amounts changes in total body weight and lean body mass
of drug in the vascular and in the extravascular (which normally occur with age, less lean mass, and
tissues. more fat) may also affect the apparent VD.
Pharmacologists often attempt to conceptualize
the apparent VD as a true physiologic or anatomic
fluid compartment. By expressing the VD in terms of Frequently Asked Question
percent of body weight, values for the VD may be »»If a drug is distributed in the one-compartment model,
found that appear to correspond to true anatomic does it mean that there is no drug in the tissue?
volumes (Table 4-1). In the example above where the
VD is 5% of body weight, this is approximately the
volume of plasma, and it would be assumed that this
drug occupies the vascular compartment with very CLEARANCE
little distributing to tissues outside the vascular com-
partment. However, it may be only fortuitous that the Clearance is a measure of drug elimination from the
value for the apparent VD of a drug has the same body without identifying the mechanism or process.
value as a real anatomic volume. If a drug is to be Clearance is also discussed in subsequent chapters.
considered to be distributed in a true physiologic Clearance (drug clearance, systemic clearance, total
volume, then an investigation is needed to test this body clearance, ClT) considers the entire body or
hypothesis. compartment (in the case of a one-compartment
Given the apparent VD for a particular drug, the model) as a drug-eliminating system from which
total amount of drug in the body at any time after many elimination processes may occur.
administration of the drug may be determined by the
measurement of the drug concentration in the plasma
(Equation 4.5). Because the magnitude of the appar- Drug Clearance in the One-Compartment
ent VD is a useful indicator for the amount of drug Model
outside the sampling compartment (usually the The body may be considered a system of organs
blood), the larger the apparent VD, the greater the perfused by plasma and body fluids. Drug elimina-
amount of drug in the extravascular tissues. tion from the body is an ongoing process due to both
metabolism (biotransformation) and drug excretion
through the kidney and other routes. The mecha-
TABLE 4-1 Fluid in the Body nisms of drug elimination are complex, but collec-
tively drug elimination from the body may be
Percent of
Water Percent of Total Body quantitated using the concept of drug clearance.
Compartment Body Weight Water Drug clearance refers to the volume of plasma fluid
that is cleared of drug per unit time. Clearance may
Plasma 4.5 7.5
also be considered the fraction of drug removed per
Total extracellular water 27.0 45.0 unit time. The rate of drug elimination may be
Total intracellular water 33.0 55.0 expressed in several ways, each of which essentially
describes the same process, but with different levels
Total body water 60.0 100.0
of insight and application in pharmacokinetics.
One-Compartment Open Model: Intravenous Bolus Administration 81
Drug Elimination Expressed as Clearance is a concept that expresses “the rate of
Amount per Unit Time drug removal” in terms of the volume of drug in
The expression of drug elimination from the body in solution removed per unit time (at whatever drug
terms of mass per unit time (eg, mg/min, or mg/h) is concentration in the body prevailing at that time)
simple, absolute, and unambiguous. For a zero-order (Fig. 4-4B). In contrast to a solution in a bottle, the
elimination process, expressing the rate of drug drug concentration in the body will gradually decline
elimination as mass per unit time is convenient by a first-order process such that the mass of drug
because the elimination rate is constant (Fig. 4-4A). removed over time is not constant. The plasma vol-
However, drug clearance is not constant for a drug ume in the healthy state is relatively constant because
that has zero-order elimination (see Chapter 6). For water lost through the kidney is rapidly replaced
most drugs, the rate of drug elimination is a first- with fluid absorbed from the gastrointestinal tract.
order elimination process, that is, the elimination Since a constant volume of plasma (about
rate is not constant and changes with respect to the 120 mL/min in humans) is filtered through the glom-
drug concentration in the body. For first-order elimi- eruli of the kidneys, the rate of drug removal is
nation, drug clearance expressed as volume per unit dependent on the plasma drug concentration at all
time (eg, L/h or mL/min) is convenient because it is times. This observation is based on a first-order pro-
a constant. cess governing drug elimination. For many drugs,
the rate of drug elimination is dependent on the
plasma drug concentration, multiplied by a constant
Drug Elimination Expressed as
factor (dC/dt = kC). When the plasma drug concen-
Volume per Unit Time tration is high, the rate of drug removal is high, and
The concept of expressing a rate in terms of volume vice versa.
per unit time is common in pharmacy. For example, a Clearance (volume of fluid removed of drug) for
patient may be dosed at the rate of 2 teaspoonfuls a first-order process is constant regardless of the
(10 mL) of a liquid medicine (10 mg/mL) daily, or drug concentration because clearance is expressed in
alternatively, a dose (weight) of 100 mg of the drug volume per unit time rather than drug amount per
daily. Many intravenous medications are adminis- unit time. Mathematically, the rate of drug elimina-
tered as a slow infusion with a flow rate (30 mL/h) tion is similar to Equation 4.10:
of a sterile solution (1 mg/mL).
dD
A. Mass approach B 4 1 )
= −kC
d pV
( . 0
t D
Dose = 100 mg Amount eliminated/minute
Fluid volume = 10 mL = 10 mg/min
Conc. = 10 mg/mL Dividing this expression on both sides by Cp yields
Equation 4.14:
B. Clearance (volume) approach
Dose = 100 mg dD /dt −kC V
B p D
Volume eliminated/minute = (4.14)
Fluid volume = 10 mL = 1 mL/min Cp Cp
Conc. = 10 mg/mL
dD d
C. Fractional approach B / t
= −kV = −Cl (4.15)
C D
p
Dose = 100 mg Fraction eliminated/minute
Fluid volume = 10 mL = 1 mL/10 mL/min
Conc. = 10 mg/mL = 1/10/min
where dDB/dt is the rate of drug elimination from the
body (mg/h), Cp is the plasma drug concentration
FIGURE 4-4 Diagram illustrating three different ways of
(mg/L), k is a first-order rate constant (h–1 or 1/h),
describing drug elimination after a dose of 100 mg injected IV
into a volume of 10 mL (a mouse, for example). and VD is the apparent volume of distribution (L).
82 Chapter 4
Cl is clearance and has the units L/h in this example. Clearance and Volume of Distribution
In the example in Fig. 4-4B, Cl is in mL/min. Ratio, Cl/VD
Clearance, Cl, is expressed as volume/time.
Equation 4.15 shows that clearance is a constant
EXAMPLE »» »
because VD and k are both constants. DB is the amount
of drug in the body, and dDB/dt is the rate of change
Consider that 100 mg of drug is dissolved in 10 mL
(of amount) of drug in the body with respect to time.
of fluid and 10 mg of drug is removed in the first
The negative sign refers to the drug exiting from the
minute. The drug elimination process could be
body. In many ways, Cl expressed as a flow rate
described as:
makes sense since drugs are presented to the elimi-
nating organs at the flow rate of blood to that organ: a. Number of mg of drug eliminated per minute
1000 mL/min to the kidneys and 1500 mL/min to the (mg/min)
liver. Clearance is a reflection of what percentage of b. Number of mL of fluid cleared of drug per minute
drug is eliminated when passing through these organs. c. Fraction of drug eliminated per minute
The relationship of the three drug elimination
Drug Elimination Expressed as Fraction processes is illustrated in Fig. 4-4A–C. Note that in
Eliminated per Unit Time Fig. 4-4C, the fraction Cl/VD is dependent on both
the volume of distribution and the rate of drug
Consider a compartment volume, containing VD
clearance from the body. This clearance concept
liters. If Cl is expressed in liters per minute (L/min),
forms the basis of classical pharmacokinetics and is
then the fraction of drug cleared per minute in the
later extended to flow models in pharmacokinetic
body is equal to Cl/VD.
modeling. If the drug concentration is Cp, the rate
Expressing drug elimination as the fraction of
of drug elimination (in terms of rate of change in
total drug eliminated is applicable regardless of
concentration, dCp/dt) is:
whether one is dealing with an amount or a volume
(Fig. 4-4C). This approach is most flexible and con- dC
p
= −(Cl/V ) ( . 6
dt D ×C 4 1 )
venient because of its dimensionless nature in terms p
of concentration, volume, or amounts. Thus, it is
valid to express drug elimination as a fraction (eg, For a first-order process,
one-tenth of the amount of drug in the body is elimi- dCp
nated or one-tenth of the drug volume is eliminated = −kC = rate of drug elimination (4.17)
dt p
per unit time). Pharmacokineticists have incorpo-
rated this concept into the first-order equation (ie, k) Equating the two expressions yields:
that describes drug elimination from the one-com-
kCp = Cl/V 4 1 )
D × C ( . 8
partment model. Indeed, the universal nature of many p
processes forms the basis of the first-order equation
Cl
of drug elimination (eg, a fraction of the total drug k = (4.19)
V
molecules in the body will perfuse the glomeruli, a D
fraction of the filtered drug molecules will be reab- Thus, a first-order rate constant is the fractional
sorbed at the renal tubules, and a fraction of the fil- constant Cl/VD. Some pharmacokineticists regard
tered drug molecules will be excreted from the body, drug clearance and the volume of distribution as
giving an overall first-order drug elimination rate independent parameters that are necessary to
constant, k). The rate of drug elimination is the prod- describe the time course of drug elimination. They
uct of k and the drug concentration (Equation 4.2a). also consider k to be a secondary parameter that
The first-order equation of drug elimination can also comes about as a result of Cl and VD. Equation 4.19
be based on probability and a consideration of the is a rearrangement of Equation 4.15 given earlier.
statistical moment theory (see Chapter 25).
One-Compartment Open Model: Intravenous Bolus Administration 83
One-Compartment Model Equation in Terms first-order elimination processes are involved, clear-
of Cl and V ance represents the sum of the clearances for both
D
Equation 4.20 may be rewritten in terms of clearance renal and nonrenal clearance, each drug-eliminating
and volume of distribution by substituting Cl/VD for k. organ as shown in Equation 4.22:
The clearance concept may also be applied to a bio-
logic system in physiologic modeling without the need ClT = ClR +ClNR (4.22)
of a theoretical compartment.
C C0e−kt
p = p (4.20) where ClR is renal clearance or drug clearance
through the kidney, and ClNR is nonrenal clearance
C −( D )
p=D0 /V e Cl /V t
D (4.21) through other organs. ClNR is assumed to be due
primarily to hepatic clearance (ClH) in the absence of
Equation 4.21 is applied directly in clinical phar- other significant drug clearances, such as elimina-
macy to determine clearance and volume of distribu- tion through the lung or the bile, as shown in
tion in patients. When only one sample is available, Equation 4.23:
that is, Cp is known at one sample time point, t, after a
given dose, the equation cannot be determined unam- ClT = ClR +ClH (4.23)
biguously because two unknown parameters must be
solved, that is, Cl and VD. In practice, the mean values Drug clearance considers that the drug in the
for Cl and VD of a drug are obtained from the popula- body is uniformly dissolved in a volume of fluid
tion values (derived from a large population of sub- (apparent volume of distribution, VD) from which
jects or patients) reported in the literature. The values drug concentrations can be measured easily.
of Cl and VD for the patient are adjusted using a com- Typically, plasma drug concentration is measured
puter program. Ultimately, a new pair of Cl and VD and drug clearance is then calculated as the fixed
values that better fit the observed plasma drug concen- volume of plasma fluid (containing the drug) cleared
tration is found. The process is repeated through itera- of drug per unit of time. The units for clearance are
tions until the “best” parameters are obtained. Since volume/time (eg, mL/min, L/h).
many mathematical techniques (algorithms) are avail- Alternatively, ClT may be defined as the rate of
able for iteration, different results may be obtained drug elimination divided by the plasma drug concen-
using different iterative programs. An objective test to tration. Thus, clearance is expressed in terms of the
determine the accuracy of the estimated clearance and volume of plasma containing drug that is eliminated
VD values is to monitor how accurately those parame- per unit time. This clearance definition is equivalent
ters will predict the plasma level of the drug after a to the previous definition and provides a practical
new dose is given to the patient. In subsequent chap- way to calculate clearance based on plasma drug
ters, mean predictive error will be discussed and cal- concentration data.
culated in order to determine the performance of
various drug monitoring methods in practice. Elimination rate
The ratio of Cl/VD may be calculated regardless ClT = (4.24)
Plasma concentration (Cp )
of compartment model type using minimal plasma
samples. Clinical pharmacists have applied many
variations of this approach to therapeutic drug moni- (dDE /dt)
ClT = = (µg/min)/(µg/mL) = mL/min
toring and drug dosage adjustments in patients. Cp
(4.25)
Clearance from Drug-Eliminating Tissues
Clearance may be applied to any organ that is involved where DE is the amount of drug eliminated and
in drug elimination from the body. As long as dDE/dt is the rate of drug elimination.
84 Chapter 4
Rearrangement of Equation 4.25 gives ∞
Because [AUC] is calculated from the plasma
0
Equation 4.26: drug concentration–time curve from 0 to infinity (∞)
using the trapezoidal rule, no compartmental model
dD is assumed. However, to extrapolate the data to infin-
Rate of Drug elimination E
= C
dt pClT (4.26)
∞
ity to obtain the residual [AUC] or (Cpt/k), first-
0
order elimination is usually assumed. In this case, if
Therefore, ClT is a constant for a specific drug the drug follows the kinetics of a one-compartment
and represents the slope of the line obtained by plot- model, the ClT is numerically similar to the product
ting dDE/dt versus Cp, as shown in Equation 4.26. of VD and k obtained by fitting the data to a one-
For drugs that follow first-order elimination, the compartment model.
∞
rate of drug elimination is dependent on the amount The approach (Equation 4.29) of using [AUC]0
of drug remaining in the body. to calculate body clearance is preferred by some
statisticians/pharmacokineticists who desire an
alternative way to calculate drug clearance without
dD
E
= kDB = kC 2 )
p V (4. 7 a compartmental model. The alternative approach
dt D
is often referred to as a noncompartmental method
of analyzing the data. The noncompartmental
Substituting the elimination rate in Equation 4.26 approach may be modified in different ways in order
for kC to avoid subjective interpolation or extrapolation
pVD in Equation 4.27 and solving for ClT gives
Equation 4.28: (see Chapters 7 and 25 for more discussion). While
the advantage of this approach is not having to
make assumptions about the compartmental model,
kC
Cl P VD the disadvantage of the noncompartmental approach
T = = kV 4.2 )
C D ( 8
p is that it does not allow for predicting the concentra-
tion at any specific time.
Equation 4.28 shows that clearance, ClT, is the In the noncompartmental approach, the two
product of VD and k, both of which are constant. This model parameters, (1) clearance and (2) volume of
Equation 4.28 is similar to Equation 4.19 shown ear- distribution, govern drug elimination from the physi-
lier. As the plasma drug concentration decreases dur- ologic (plasma) fluid directly and no compartment
ing elimination, the rate of drug elimination, dDE/dt, model is assumed. The preference to replace k with
will decrease accordingly, but clearance will remain Cl/VD was prompted by Equation 4.19 as rearranged
constant. Clearance will be constant as long as the in the above section:
rate of drug elimination is a first-order process. Cl
For some drugs, the elimination rate processes k = (4.19)
V
D
are not well known and few or no model assumptions
are desirable; in this situation, a noncompartment For a drug to be eliminated from the body fluid,
method may be used to calculate certain pharmaco- the volume cleared of drug over the size of the pool
kinetic parameters such as clearance, which can be indicates that k is really computed from Cl and VD.
determined directly from the plasma drug concentra- In contrast, the classical one-compartment model
tion–time curve by is described by two model parameters: (1) elimination
constant, k, and (2) volume of distribution, VD.
Clearance is derived from Cl = kVD. The classical
D approach considers VD the volume in which the drug
Cl 0
T = (4.29)
∞
[AUC] appears to dissolve, and k reflects how the drug
0
declines due to excretion or metabolism over time. In
chemical kinetics, the rate constant, k, is related to
∞ ∞
where D0 is the dose and [AUC] = ∫ C dt.
0 0 p “encounters” or “collisions” of the molecules involved
One-Compartment Open Model: Intravenous Bolus Administration 85
when a chemical reaction takes place. An ordinary and the intercept of the plasma drug concentration–
hydrolysis or oxidation reaction occurring in the test time curve obtained after IV bolus injection. This
tube can also occur in the body. Classical pharmaco- approach is particularly useful for a new or investi-
kineticists similarly realized that regardless of whether gational drug when little pharmacokinetic informa-
the reaction occurs in a beaker or in the body fluid, the tion is known. In practice, rapid bolus injection is
drug molecules must encounter the enzyme molecule often not desirable for many drugs and a slow IV
for biotransformation or the exit site (renal glomeruli) drip or IV drug infusion is preferred. Rapid injection
to be eliminated. The probability of getting to the of a large drug dose may trigger adverse drug reac-
glomeruli or metabolic site during systemic circula- tions (ADR) that would have been avoided if the
tion must be first order because both events are prob- body had sufficient time to slowly equilibrate with
ability or chance related (ie, a fraction of drug the drug. This is particularly true for certain classes
concentration will be eliminated). Therefore, the rate of antiarrhythmics, anticonvulsants, antitumor, anti-
of elimination (dC/dt) is related to drug concentration coagulants, oligonucleotide drugs, and some sys-
and is aptly described by temic anesthetics. Immediately after an intravenous
injection, the concentrated drug solution/vehicle is
dC
= k × Cp (4.30) directly exposed to the heart, lung, and other vital
dt
organs before full dilution in the entire body. During
The compartment model provides a useful way to the drug’s first pass through the body, some tissues
track mass balance of the drug in the body. It is virtu- may react adversely to a transient high drug concen-
ally impossible to account for all the drug in the body tration because of the high plasma/tissue drug con-
with a detailed quantitative model. However, keeping centration difference (gradients) that exists prior to
track of systemic concentrations and the mass balance full dilution and equilibration. Most intravenous
of the dose in the body is still important to understand drugs are formulated as aqueous solutions, lightly
a drug’s pharmacokinetic properties. For example, the buffered with a suitable pH for this reason. A poorly
kinetic parameters for drugs such as aspirin and acet- soluble drug may precipitate from solution if injected
aminophen were determined using mass balance, too fast. Suspensions or drugs designed for IM injec-
which indicates that both drugs are over 90% metabo- tion only could cause serious injury or fatality if
lized (acetaminophen urinary excretion = 3%; aspirin injected intravenously. For example, the antibiotic
urinary excretion = 1.4%). It is important for a phar- Bicillin intended for IM injection has a precaution
macist to apply such scientific principles during drug that accompanies the packaging to ensure that the
modeling in order to optimize dosing, such as if a drug will not be injected accidentally into a vein.
patient has liver failure and metabolism is decreased. Pharmacists should be especially alert to verify
Drug metabolism may be equally well described by extravascular injection when drugs are designed for
applying clearance and first-order/saturation kinetics IM injection.
concepts to kinetic models. With many drugs, the initial phase or transient
plasma concentrations are not considered as impor-
tant as the steady-state “trough” level during long-
Frequently Asked Question term drug dosing. However, drugs with the
»»How is clearance related to the volume of distribu- therapeutic endpoint (eg, target plasma drug concen-
tion and k? tration) that lie within the steep initial distributive
phase are much harder to dose accurately and not
overshoot the target endpoint. This scenario is par-
CLINICAL APPLICATION ticularly true for some drugs used in critical care
where rapid responses are needed and IV bolus
IV bolus injection provides a simple way to study the routes are used more often. Many new biotechno-
pharmacokinetics of a drug. The pharmacokinetic logical drugs are administered intravenously because
parameters of the drug are determined from the slope of instability or poor systemic absorption by the oral
86 Chapter 4
route. The choice of a proper drug dose and rate of
Log keD
0
infusion relative to the elimination half-life of the B
drug is an important consideration for safe drug
administration. Individual patients may behave very
Slope = –k
differently with regard to drug metabolism, drug 2.3
transport, and drug efflux in target cell sites. Drug
receptors and enzymes may have genetic variability
making some people more prone to allergic reac-
tions, drug interactions, and side effects. Simple
kinetic half-life determination coupled with a careful
Time
review of the patient’s chart by a pharmacist can
greatly improve drug safety and efficacy. FIGURE 4-5 Graph of Equation 4.33: log rate of drug
excretion versus t on regular paper.
Frequently Asked Question
»»If we use a physiologic model, are we dealing with A straight line is obtained from this equation by
actual volumes of blood and tissues? Why do vol- plotting log dDu/dt versus time on regular paper or
umes of distribution emerge for drugs that often are on semilog paper dDu/dt against time (Figs. 4-5 and
greater than the real physical volume?
4-6). The slope of this curve is equal to –k/2.3 and
the y intercept is equal to k D0
e B. For rapid intravenous
administration, D0
B is equal to the dose D0. Therefore,
if D0
B is known, the renal excretion rate constant (ke)
CALCULATION OF k FROM URINARY can be obtained. Because both ke and k can be deter-
EXCRETION DATA mined by this method, the nonrenal rate constant
(knr) for any route of elimination other than renal
The elimination rate constant k may be calculated excretion can be found as follows:
from urinary excretion data. In this calculation the
excretion rate of the drug is assumed to be first order. k − ke = knr (4.34)
The term ke is the renal excretion rate constant, and
Du is the amount of drug excreted in the urine.
dD
u 1000
= k D 4 3 )
dt e B ( . 1
keD 0
B
From Equation 4.4, DB can be substituted for
D0 e–kt
B : Slope = –k
2.3
100
dD
u k D0e−kt
=
dt e B (4.32)
Taking the natural logarithm of both sides and
10
then transforming to common logarithms, the fol- 0 1 2 3 4 5
lowing expression is obtained: Time (hours)
FIGURE 4-6 Semilog graph of rate of drug excretion
dD kt
log u −
0
= + log k D (4.33) versus time according to Equation 4.33 on semilog paper
dt 2.3 e B (intercept = k D0).
e B
Rate of drug excretion (dDu/dt)
Log dDu/dt
One-Compartment Open Model: Intravenous Bolus Administration 87
Substitution of km for knr in Equation 4.34 gives Solution
Equation 4.1. Because the major routes of elimina- Set up the following table:
tion for most drugs are renal excretion and metabo-
lism (biotransformation), knr is approximately equal
Time
to km. (hours) Du (mg) Du/t mg/h t* (hours)
0.25 160 160/0.25 640 0.125
k = k (4.35)
nr m
0.50 140 140/0.25 560 0.375
There are practical considerations of collecting 1.0 200 200/0.5 400 0.750
urine for drug analysis since urine is produced at an 2.0 250 250/1 250 1.50
approximate rate of 1 mL/min and collected in the
4.0 188 188/2 94 3.0
bladder until voided for collection. Thus, the drug
urinary excretion rate (dDu/dt) cannot be determined 6.0 46 46/2 23 5.0
experimentally for any given instant. In practice, Here t* = midpoint of collection period and t = time interval for collection
urine is collected over a specified time interval, and of urine sample.
the urine specimen is analyzed for drug. An average
Construct a graph on a semilogarithmic scale of
urinary excretion rate is then calculated for that col-
D
lection period. Therefore, the average rate of uri- u/t versus t*. The slope of this line should equal
–k/2.3. It is usually easier to determine the elimination
nary drug excretion, Du/t, is plotted against the time
t
corresponding to the midpoint of the collection ½ directly from the curve and then calculate k from
interval, t*, for the collection of the urine sample. 0.693
k =
The average value of dDu/dt is plotted on a semiloga- t1/2
rithmic scale against the time that corresponds to the
In this problem, t1/2 = 1.0 hour and k = 0.693 h–1. Note
midpoint (average time) of the collection period.
that the slope of the log excretion rate constant is a
function of the elimination rate constant k and not of
the urinary excretion rate constant ke (Fig. 4-6).
PRACTICE PROBLEM
A similar graph of the Cp values versus t should
A single IV dose of an antibiotic was given to a yield a curve with a slope having the same value as
50-kg woman at a dose level of 20 mg/kg. Urine and that derived from the previous curve. Note that this
blood samples were removed periodically and method uses the time of plasma sample collection,
assayed for parent drug. The following data were not the midpoint of collection.
obtained: An alternative method for the calculation of the
elimination rate constant k from urinary excretion data
is the sigma-minus method, or the amount of drug
Time (hours) Cp (µg/mL) Du (mg)
remaining to be excreted method. The sigma-minus
0.25 4.2 160 method is sometimes preferred over the previous
method because fluctuations in the rate of elimination
0.50 3.5 140
are minimized.
1.0 2.5 200 The amount of unchanged drug in the urine can
2.0 1.25 250 be expressed as a function of time through the fol-
lowing equation:
4.0 0.31 188
6.0 0.08 46 k
eDD 0
u = (1 e−kt
− ) (4.36)
k
What is the elimination rate constant, k, for this where Du is the cumulative amount of unchanged
antibiotic? drug excreted in the urine.
88 Chapter 4
The amount of unchanged drug that is ulti- PRACTICE PROBLEM
mately excreted in the urine, D∞
u , can be determined
by making time t equal to ∞. Thus, the term e–kt Using the data in the preceding problem, determine
becomes negligible and the following expression is the elimination rate constant.
obtained:
Solution
k
∞ eD
D 0
u = (4.37) Construct the following table:
k
Time Cumulative
Substitution of D∞
u for keD0/k in Equation 4.36 (hours) Du (mg) D ∞
u D −D
u u
and rearrangement yields
0.25 160 160 824
0.50 140 300 684
D∞ D D∞ e−kt
u − u = u (4.38)
1.0 200 500 484
2.0 250 750 234
Equation 4.38 can be written in logarithmic
form to obtain a linear equation: 4.0 188 938 46
6.0 46 984 0
−kt
log(D∞
u − Du )
∞
= + log D
2.3 u (4.39)
Plot log (D∞
u − Du ) versus time. Use a semiloga-
rithmic scale for ( ∞
Du − Du ). Evaluate k and t1/2 from
Equation 4.39 describes the relationship for the the slope.
amount of drug remaining to be excreted (D∞
u − Du )
versus time.
Comparison of the Rate and the
A linear curve is obtained by graphing the loga-
Sigma-Minus Methods
rithm scale of the amount of unchanged drug yet to
be eliminated, log ( ∞
Du − Du ), versus time. On semi- The rate method is highly dependent on the accurate
log paper, the slope of this curve is –k/2.3 and the y measurement of drug in the urine at each time point.
intercept is (D∞
u ) (Fig. 4-7). Fluctuations in the rate of drug elimination and
experimental errors including incomplete bladder
emptying for a collection period cause appreciable
departure from linearity using the rate method,
1000 whereas the accuracy of the sigma-minus method is
less affected. The rate method is applicable to zero-
order drug elimination process, while the sigma-
minus method is not. Lastly, the renal drug excretion
rate constant may be obtained from the rate method
100
but not from the sigma-minus method.
The sigma-minus method requires knowing the
D∞
u and even a single missed urine collection will
invalidate the entire urinary drug excretion study.
This method also requires the collection of urine until
10
0 1 2 3 4 urinary drug excretion is complete; prematurely end-
Time ing the study early will invalidate the study. Finally,
∞
FIGURE 4-7 a small error in the assessment of D introduces an
Sigma-minus method, or the amount of drug u
remaining to be excreted method, for the calculation of the error in terms of curvature of the plot, because each
elimination rate constant according to Equation 4.39. point is based on log ( ∞
Du − Du ) versus time.
D
∞
u − Du
One-Compartment Open Model: Intravenous Bolus Administration 89
CLINICAL APPLICATION 30 hours. However, the urinary drug excretion rate
method data were more scattered (variable) and the
The sigma-minus method and the excretion rate correlation coefficient r was equal to 0.744 (Fig. 4-9),
method were applied to the urinary drug excretion in compared to the correlation coefficient r of 0.992
subjects following the smoking of a single marijuana using the sigma-minus method (Fig. 4-8).
cigarette (Huestis et al, 1996). The urinary excretion
curves of 11-nor-carboxy 9-tetrahydrocannabinol
Problems in Obtaining Valid Urinary
(THCCOOH), a metabolite of marijuana, in one
Excretion Data
subject from 24 to 144 hours after smoking one
marijuana cigarette are shown in Figs. 4-8 and 4-9. Certain factors can make it difficult to obtain valid
A total of 199.7 mg of THCCOOH was excreted in urinary excretion data. Some of these factors are as
the urine over 7 days, which represents 0.54% of the follows:
total 9-tetrahydrocannabinol available in the ciga- 1. A significant fraction of the unchanged drug
rette. Using either urinary drug excretion method, must be excreted in the urine.
the elimination half-life was determined to be about 2. The assay technique must be specific for the
unchanged drug and must not include interfer-
ence due to drug metabolites that have similar
chemical structures.
5.5 3. Frequent sampling is necessary for a good
5.0 Subject B curve description.
4.5 4. Urine samples should be collected periodically
4.0 until almost all of the drug is excreted. A graph
3.5 t1/2 = 29.9 h of the cumulative drug excreted versus time
3.0 r = 0.992 will yield a curve that approaches an asymp-
2.5 tote at “infinite” time (Fig. 4-10). In practice,
0 24 48 72 96 120 144 168
approximately seven elimination half-lives are
Time (hours)
needed for 99% of the drug to be eliminated.
FIGURE 4-8 Amount remaining to be excreted method. 5. Variations in urinary pH and volume may cause
The half-life of THCCOOH was calculated to be 29.9 hours from significant variation in urinary excretion rates.
the slope of this curve; the correlation coefficient r was equal
6. Subjects should be carefully instructed as to the
to 0.992. (Data from Huestis et al, 1996.)
necessity of giving a complete urine specimen
(ie, completely emptying the bladder).
4.0
3.5 Subject B
3.0
2.5
t1/2 = 30.7 h
2.0 r = 0.744
1.5
0 24 48 72 96 120 144 168
Time (hours)
FIGURE 4-9 Excretion rate method. The half-life of Time
THCCOOH was calculated to be 30.7 hours from the slope of
this curve; the correlation coefficient r was equal to 0.744. FIGURE 4-10 Graph showing the cumulative urinary
(Data from Huestis et al, 1996.) excretion of drug as a function of time.
Log excretion rate Log THCCOOH
remaining to be excreted
Cumulative amount of drug in urine
90 Chapter 4
CHAPTER SUMMARY
The one-compartment model assumes that the drug This approach is most flexible and convenient
is uniformly distributed within a single hypothetical because of its dimensionless nature in terms of
compartment volume from which the drug concen- amount or volume (k is expressed as h–1 or min–1).
tration can be sampled and assayed easily. The one- Clearance may be computed by Cl = kVD. This
compartment model, IV bolus drug injection, method is preferred by many pharmacists since it can
provides the simplest approach for estimating the be calculated from two concentration measurements,
apparent volume of distribution, VD, and the elimina- making it more clinically feasible than a full pharma-
tion rate constant, k. If VD, k, and the drug dose are cokinetic study. Many pharmacokineticists do not
known, the model equation allows drug concentra- prefer this method since k is considered a secondary
tion in the compartment (body) at any time to be model parameter, while VD and Cl are considered to
calculated. The volumes of plasma fluid and extra- be independent model parameters. That is, VD and Cl
cellular fluid may be relatively constant under nor- give k its properties. Instead, many prefer the non-
mal conditions. However, these volumes added compartmental approach using area under the con-
together do not usually numerically equal to the centration-time curve to calculate Cl; this method
(apparent) volume of distribution of the drug, which avoids the basic assumptions inherent in the one-
may be larger or smaller depending on how widely compartmental model but requires a full pharmacoki-
the drug distributes into tissues. netic study to determine the area under the curve.
The one-compartment model may be described Drug clearance is constant for a first-order process
with the two model parameters, clearance and vol- regardless of the drug concentration. Clearance is
ume of distribution. Alternatively, the one-compart- expressed as the apparent volume of fluid of the dis-
ment model can also be described by two model solved drug that is removed per unit time. The one-
parameters, the elimination constant, k, and volume compartment model may assume either a first-order
of distribution. The latter model explains that drugs or a zero-order elimination rate depending on whether
are fractionally removed at any time, whatever the the drug follows linear kinetics or not. The disadvan-
initial drug concentration is, and k as a ratio of Cl/VD. tage of the noncompartmental approach is that pre-
Expressing drug elimination as the fraction of total dicting concentrations at specific times may not hold
drug eliminated per time is applicable regardless of true, while using a one-compartmental model allows
whether one is dealing with an amount or a volume. for predicting the concentration at any time point.
LEARNING QUESTIONS
1. A 70-kg volunteer is given an intravenous dose
of an antibiotic, and serum drug concentrations t (hours) Cp (µg/mL)
were determined at 2 hours and 5 hours after
0.25 8.21
administration. The drug concentrations were
1.2 and 0.3 mg/mL, respectively. What is the 0.50 7.87
biologic half-life for this drug, assuming first- 1.00 7.23
order elimination kinetics?
3.00 5.15
2. A 50-kg woman was given a single IV dose of
an antibacterial drug at a dose level of 6 mg/kg. 6.00 3.09
Blood samples were taken at various time inter- 12.0 1.11
vals. The concentration of the drug (Cp) was
18.0 0.40
determined in the plasma fraction of each blood
sample and the following data were obtained:
One-Compartment Open Model: Intravenous Bolus Administration 91
a. What are the values for VD, k, and t1/2 for this 6. A drug has an elimination t1/2 of 6 hours and
drug? follows first-order kinetics. If a single 200-mg
b. This antibacterial agent is not effective dose is given to an adult male patient (68 kg)
at a plasma concentration of less than by IV bolus injection, what percent of the dose
2 mg/mL. What is the duration of activity is lost in 24 hours?
for this drug? 7. A rather intoxicated young man (75 kg, age
c. How long would it take for 99.9% of this 21 years) was admitted to a rehabilitation cen-
drug to be eliminated? ter. His blood alcohol content was found to be
d. If the dose of the antibiotic was doubled 210 mg%. Assuming the average elimination
exactly, what would be the increase in dura- rate of alcohol is 10 mL of ethanol per hour,
tion of activity? how long would it take for his blood alcohol
3. A new drug was given in a single intravenous concentration to decline to less than the legal
dose of 200 mg to an 80-kg adult male patient. blood alcohol concentration of 100 mg%?
After 6 hours, the plasma drug concentration of (Hint: Alcohol is eliminated by zero-order
drug was 1.5 mg/100 mL of plasma. Assuming kinetics.) The specific gravity of alcohol is 0.8.
that the apparent VD is 10% of body weight, The apparent volume of distribution for alcohol
compute the total amount of drug in the body is 60% of body weight.
fluids after 6 hours. What is the half-life of this 8. A single IV bolus injection containing 500 mg
drug? of cefamandole nafate (Mandol, Lilly) is given
4. A new antibiotic drug was given in a single to an adult female patient (63 years, 55 kg) for
intravenous bolus of 4 mg/kg to 5 healthy male a septicemic infection. The apparent volume
adults ranging in age from 23 to 38 years of distribution is 0.1 L/kg and the elimination
(average weight 75 kg). The pharmacokinetics half-life is 0.75 hour. Assuming the drug is
of the plasma drug concentration–time curve eliminated by first-order kinetics and may be
for this drug fits a one-compartment model. The described by a one-compartment model, calcu-
equation of the curve that best fits the data is late the following:
a. The C0
p
Cp 78e−0.46t
= b. The amount of drug in the body 4 hours after
the dose is given
Determine the following (assume units of mg/mL c. The time for the drug to decline to 0.5 mg/mL,
for Cp and hours for t): the minimum inhibitory concentration for
a. What is the t1/2? streptococci
b. What is the VD? 9. If the amount of drug in the body declines from
c. What is the plasma level of the drug after 100% of the dose (IV bolus injection) to 25%
4 hours? of the dose in 8 hours, what is the elimination
d. How much drug is left in the body after half-life for this drug? (Assume first-order
4 hours? kinetics.)
e. Predict what body water compartment this 10. A drug has an elimination half-life of 8 hours
drug might occupy and explain why you and follows first-order elimination kinetics. If a
made this prediction. single 600-mg dose is given to an adult female
f. Assuming the drug is no longer effective patient (62 kg) by rapid IV injection, what per-
when levels decline to less than 2 mg/mL, cent of the dose is eliminated (lost) in 24 hours
when should you administer the next dose? assuming the apparent VD is 400 mL/kg? What
5. Define the term apparent volume of distribution. is the expected plasma drug concentration (Cp)
What criteria are necessary for the measure- at 24 hours postdose?
ment of the apparent volume of distribution to 11. For drugs that follow the kinetics of a one-
be useful in pharmacokinetic calculations? compartment open model, must the tissues
92 Chapter 4
and plasma have the same drug concentration?
t (hours) Amount of Drug in Urine (mg)
Why?
12. An adult male patient (age 35 years, weight 0 0
72 kg) with a urinary tract infection was 4 100
given a single intravenous bolus of an
8 26
antibiotic (dose = 300 mg). The patient was
instructed to empty his bladder prior to being
medicated. After dose administration, the a. Assuming first-order elimination, calculate
patient saved his urine specimens for drug the elimination half-life for the antibiotic in
analysis. The urine specimens were analyzed this patient.
for both drug content and sterility (lack of b. What are the practical problems in obtaining
bacteriuria). The drug assays gave the follow- valid urinary drug excretion data for the deter-
ing results: mination of the drug elimination half-life?
ANSWERS
Frequently Asked Questions • The first-order rate constant k has no concentration
What is the difference between a rate and a rate or mass units. In the calculation of the slope, k, the
constant? unit for mass or concentration is canceled when
taking the log of the number:
• A rate represents the change in amount or concen-
tration of drug in the body per time unit. For exam- ln y2 − ln y1 ln (y2 /y )Slope 1
= =
ple, a rate equal to –5 mg/h means the amount of x2 − x1 x2 − x1
drug is decreasing at 5 mg/h. A positive or negative
sign indicates that the rate is increasing or decreas- If a drug is distributed in the one-compartment model,
ing, respectively. Rates may be zero order, first does it mean that there is no drug in the tissue?
order, or higher orders. For a first-order rate, the • The one-compartment model uses a single homo-
rate of change of drug in the body is determined by
geneous compartment to represent the fluid and
the product of the elimination rate constant, k, and
the vascular tissues. This model ignores the het-
the amount of drug remaining in the body, that is,
erogeneity of the tissues in the body, so there is
rate = –kDB, where k represents “the fraction” of
no merit in predicting precise tissue drug levels.
the amount of drug in the body that is eliminated
However, the model provides useful insight into
per hour. If k = 0.1 h–1 and DB = 10 mg, then the
the mass balance of drug distribution in and out
rate = 0.1 h–1 × 10 mg = 1 mg/h. The rate constant
of the plasma fluid in the body. If VD is larger than
in this example shows that one-tenth of the drug
the physiologic vascular volume, the conclusion is
is eliminated per hour, whatever amount of drug is
that there is some drug outside the vascular pool,
present in the body. For a first-order rate, the rate
that is, in the tissues. If VD is small, then there is
states the absolute amount eliminated per unit
little extravascular tissue drug storage, except
time (which changes with the amount of drug in
perhaps in the lung, liver, kidney, and heart. With
the body), whereas the first-order rate constant, k,
some knowledge about the lipophilicity of the drug
gives a constant fraction of drug that is eliminated
and an understanding of blood flow and perfusion
per unit time (which does not change with the
within the body, a postulation may be made as to
amount of drug in the body).
which organs are involved in storing the extravas-
Why does k always have the unit 1/time (eg, h–1), cular drug. The concentration of a biopsy sample
regardless of what concentration unit is plotted? may support or refute the postulation.
One-Compartment Open Model: Intravenous Bolus Administration 93
How is clearance related to the volume of distribution These data may also be plotted on a semilog
and k? graph and t1/2 obtained from the graph.
2. Dose (IV bolus) = 6 mg/kg × 50 kg = 300 mg
• Clearance is the volume of plasma fluid that is
cleared of drug per unit time. Clearance may also dose 300 mg 300 mg
a. VD = = =
be derived for the physiologic model as the frac- C0 8.4 µg/mL 8.4 mg/L
P
tion of drug that is eliminated by an organ as blood
= 35.7 L
flows through it. The former definition is equiva-
lent to Cl = kVD and is readily adapted to dosing (1) Plot the data on semilog graph paper
since VD is the volume of distribution. If the drug is and use two points from the line of
eliminated solely by metabolism in the liver, then best fit.
ClH = Cl. ClH is usually estimated by the differ-
ence between Cl and ClR. ClH is directly estimated t (hours) Cp (µg/mL)
by the product of the hepatic blood flow and the
2 6
extraction ratio.
6 3
If we use a physiologic model, are we dealing with
actual volumes of blood and tissues? Why do vol- (2) t1/2 (from graph) = 4 hours
umes of distribution emerge for drugs that often are
greater than the real physical volume? 0.693
k = = 0.173 h−1
4
• Since mass balance (ie, relating dose to plasma
drug concentration) is based on volume of distri- b. C0
p = 8.4 µg/mL Cp = 2 µg/mL k = 0.173 h−1
bution rather than blood volume, the compartment
model is used in determining dose. Generally, the kt
logC logC0
p = − +
total blood concentrations of most drugs are not 2.3 P
known, since only the plasma or serum concentra-
0.173t
tion is assayed. Some drugs have an RBC/plasma log 2 = − + log 8.4
2.3
drug ratio much greater than 1, making the appli-
cation of the physiologic model difficult without t = 8.29 h
knowing the apparent volume of distribution.
Alternatively, time t may be found from a
Learning Questions graph of Cp versus t.
1. The Cp decreased from 1.2 to 0.3 mg/mL in c. Time required for 99.9% of the drug to be
3 hours. eliminated:
(1) Approximately 10 t1/2
t (hours) Cp (µg/mL)
t = 10(4) = 40 h
2 1.2
5 0.3 (2) C0
p = 8.4 µg/mL
kt
logCp logC0
= − + With 0.1% of drug remaining,
2.3 P
k(3) Cp = 0.001 (8.4 µg/mL) = 0.0084 µg/mL
log 0.3 = − + log 1.2
2.3
k = 0.173 h−1
k = 0.462 h−1
−0.173t
0.693 0.693 log 0.0084 = + log 8.4
t1/2 = = 2.3
k 0.462
t1/2 = 1.5 h t = 39.9 h
94 Chapter 4
d. If the dose is doubled, then C0 will also
p 0.693 0.693
double. However, the elimination half-life a. t1/2 = = = 1.5 h
k 0.46
or first-order rate constant will remain the
same. Therefore, dose 300,000 µg
b. VD = = = 3846 mL
C0 78 µg/mL
p
C0 = µ C k 1
p 16.8 g/mL p = 2µg/mL = 0.173 h−
Dose = 4 mg/kg × 75 kg = 300 mg
0.173t
log 2 = + log16.8 c.
2.3 0.46(4)
(1) logCp = + log78 = 1.092
t = 12.3 h−1 2.3
Cp = 12.4 µg/mL
Notice that doubling the dose does not
double the duration of activity. (2) C = 78e−0.46(4) = 78e−18.4
p = 78 (0.165)
3. D0 = 200 mg Cp = 12.9 µg/mL
VD = 10% of body weight = 0.1 (80 kg) d. At 4 hours:
DB = CpVD = 12.4 µg/mL × 3846 mL
= 8000 mL = 8 L
= 47.69 mg
At 6 hours:
Cp = 1.5 mg/100 mL e. VD = 3846 mL
Average weight = 75 kg
drug in body (D )
V B
D = Percent body wt = (3.846 kg/75 kg) ×100
Cp
= 5.1%
1.5
DB = CpVD = (8000 mL) = 120 mg The apparent VD approximates the plasma
100 mL
volume.
kt f. Cp = 2 mg/mL
log D D0
B = − + log
2.3 B
Find t.
k(6) 0.46t
log120 = − + log 200 log 2 = − + log 78
2.3 2.3
2.3 (log 2− log 78)
k −1
= 0.085 h t = −
0.46
0.693 0.693 t = 7.96 h ≈ 8 h
t1/2 = = = 8.1 h
k 0.085
Alternate Method
4. Cp = 78e–0.46t (the equation is in the form
2 78e−0.46t
=
C C0e−kt
= )
p p
2
0.0256 e−0.46t
ln Cp = ln 78 − 0.46t = =
78
0.46t −37 = −0.46t
logCp = − + log 78
2.3
37
Thus, k = 0.46 h−1,C0 t = = 8 h
p = 78 µg/mL. 0.46
One-Compartment Open Model: Intravenous Bolus Administration 95
6. For first-order elimination kinetics, one-half of where
the initial quantity is lost each t1/2. The follow- DB = amount of drug remaining in the body
ing table may be developed: D0 = dose = 200 mg
k = elimination rate constant
Amount 0.693
= = 0.1155 h−1
of Drug Percent Percent
t1/2
Time Number in Body of Drug of Drug
(hours) of t1/2 (mg) in Body Lost t = 24 h
0 0 200 100 0 −0.1155(24)
logDB = + log200
2.3
6 1 100 50 50
DB = 12.47 mg ≈12.5 mg
12 2 50 25 75
200 −12.512 2 50 25 75 % of drug lost = ×100 = 93.75%
200
18 3 25 12.5 87.5
7. The zero-order rate constant for alcohol is
24 4 12.5 6.25 93.75 10 mL/h. Since the specific gravity for alcohol
is 0.8,
Method 1 x(g)
From the above table the percent of drug remaining 0.8 g/mL =
10 mL
in the body after each t1/2 is equal to 100% times
x = 8 g
(1/2)n, where n is the number of half-lives, as shown
below: Therefore, the zero-order rate constant, k0,
is 8 g/h.
Percent of Drug
Drug in body at t = 0:
Number Percent of Remaining in Body
of t1/2 Drug in Body after n t1/2 210 mg
D0
B = CpVD = × (0.60)(75 L) = 94.5 g
0 100 0.100 L
1 50 100 × 1/2
Drug in body at time t:
2 25 100 × 1/2 × 1/2
100 mg
3 12.5 100 × 1/2 × 1/2 × 1/2 DB = CpVD = × (0.60)(75 L) = 45.0 g
0.100 L
N 100 × (1/2)n
For a zero-order reaction:
100
Percent of drug remaining n , where n = number D k t D0
B = − 0 + B
2
of t1/2 45 = −8t + 94.5
100
Percent of drug lost = 100 −
2n t = 6.19 h
At 24 hours, n = 4, since t1/2 = 6 hours.
100 dose 500 mg
Percent of drug lost = 100 − = 93.75% 8. a. C0
p = = = 90.9 mg/L
16 VD (0.1L/kg)(55 kg)
Method 2
−kt
The equation for a first-order elimination after IV b. logD D0
B = + log
2.3 B
bolus injection is
(0.693/0.75)(4)
logDB = + log500
−kt 2.3
logDB = + logD
2.3 0 DB = 12.3 mg
96 Chapter 4
−(0.693/0.75)t the body (in plasma and tissues). At equilib-
c. log 0.5 = + log 90.0
2.3 rium, the drug concentration in the tissues may
differ from the drug concentration in the body
t = 5.62 h
because of drug protein binding, partitioning
−kt of drug into fat, differences in pH in different
9. log D 0
B = + log D
2.3 B regions of the body causing a different degree
−k(8) of ionization for a weakly dissociated electro-
log 25 = + log100
2.3 lyte drug, an active tissue uptake process, etc.
12. Set up the following table:
k = 0.173 h−1
0.693 Time (hours) Du (mg) dDu/t mg/h t*
t1/2 = = 4 h
0.173
0 0
−kt
10. logD logD0 4 100 100/4 25 2
B = +
2.3 B
8 26 26/4 6.5 6
(−0.693/8)(24)
= + log 600
2.3
The elimination half-life may be obtained
DB = 74.9 mg graphically after plotting mg/h versus t*.
600 t aphically is approximately
− 74.9 The 1/2 obtained gr
Percent drug lost = ×100
600 2 hours.
= 87.5%
dDu −kt
C log k 0
= + log
p at t = 24 hours: dt 2.3 eDB
74.9 mg
−k logY logY log 6.5 log 2.5
Cp = = 3.02 mg/L Slope 2 − 1 −
= = =
(0.4 L/kg)(62 kg) 2.3 X2 − X1 6− 2
11. The total drug concentration in the plasma is k 0.336 h−1
=
not usually equal to the total drug concentra-
tion in the tissues. A one-compartment model 0.693 0.693
t
implies that the drug is rapidly equilibrated in 1/2 = = = 2.06 h
k 0.336
REFERENCE
Huestis MA, Mitchell J, Cone EJ: Prolonged urinary excretion of
marijuana metabolite (abstract). Committee on Problems of
Drug Dependence, San Juan, PR, June 25, 1996.
BIBLIOGRAPHY
Gibaldi M, Nagashima R, Levy G: Relationship between drug Riegelman S, Loo J, Rowland M: Concepts of volume of distribu-
concentration in plasma or serum and amount of drug in the tion and possible errors in evaluation of this parameter. Science
body. J Pharm Sci 58:193–197, 1969. 57:128–133, 1968.
Riegelman S, Loo JCK, Rowland M: Shortcomings in pharmaco- Wagner JG, Northam JI: Estimation of volume of distribution
kinetic analysis by conceiving the body to exhibit properties of and half-life of a compound after rapid intravenous injection.
a single compartment. J Pharm Sci 57:117–123, 1968. J Pharm Sci 58:529–531, 1975.
Multicompartment Models:
5 Intravenous Bolus
Administration
Shabnam N. Sani and Rodney C. Siwale
Chapter Objectives Pharmacokinetic models are used to simplify all the complex pro-
cesses that occur during drug administration that include drug
»» Define the pharmacokinetic
distribution and elimination in the body. The model simplification
terms used in a two- and three-
is necessary because of the inability to measure quantitatively all
compartment model.
the rate processes in the body, including the lack of access to bio-
»» Explain using examples why logical samples from the interior of the body. As described in
drugs follow one-compartment, Chapter 1, pharmacokinetic models are used to simulate drug
two-compartment, or three- disposition under different conditions/time points so that dosing
compartment kinetics. regimens for individuals or groups of patients can be designed.
»» Use equations and graph Compartmental models are classic pharmacokinetic models
to simulate plasma drug that simulate the kinetic processes of drug absorption, distribution,
concentration at various and elimination with little physiologic detail. In contrast, the more
time periods after an IV bolus sophisticated physiologic model is discussed in Chapter 25. In
injection of a drug that follows compartmental models, drug tissue concentration, Ct, is assumed to
the pharmacokinetics of a two- be uniform within a given hypothetical compartment. Hence, all
and three-compartment model muscle mass and connective tissues may be lumped into one hypo-
drug. thetical tissue compartment that equilibrates with drug from the
central (composed of blood, extracellular fluid, and highly per-
»» Relate the relevance of the fused organs/tissues such as heart, liver, and kidneys) compart-
magnitude of the volume of ment. Since no data are collected on the tissue mass, the theoretical
distribution and clearance of tissue concentration cannot be confirmed and used to forecast
various drugs to underlying actual tissue drug levels. Only a theoretical, Ct, concentration of
processes in the body. drug in the tissue compartment can be calculated. Moreover, drug
»» Estimate two-compartment concentrations in a particular tissue mass may not be homoge-
model parameters by using the neously distributed. However, plasma concentrations, Cp, are
method of residuals. kinetically simulated by considering the presence of a tissue or a
group of tissue compartments. In reality, the body is more complex
»» Calculate clearance and alpha
than depicted in the simple one-compartment model and the elimi-
and beta half-lives of a two-
nating organs, such as the liver and kidneys, are much more com-
compartment model drug.
plex than a simple extractor. Thus, to gain a better appreciation
»» Explain how drug metabolic regarding how drugs are handled in the body, multicompartment
enzymes, transportors, and models are found helpful. Contrary to the monoexponential decay
binding proteins in the body in the simple one-compartment model, most drugs given by IV
may modify the distribution bolus dose decline in a biphasic fashion, that is, plasma drug con-
and/or elimination phase of a centrations rapidly decline soon after IV bolus injection, and then
drug after IV bolus. decline moderately as some of the drug that initially distributes
(equilibrates) into the tissue moves back into the plasma. The early
97
98 Chapter 5
decline phase is commonly called the distribution 50
phase (because distribution into tissues primarily
determines the early rapid decline in plasma concen-
tration) and the latter phase is called the terminal or
10
elimination phase. During the distribution phase, se
E
changes in the concentration of drug in plasma pri- l
5 imi
a na
marily reflect the movement of drug within the body, tion ph
rather than elimination. However, with time, distribu- ase
tion equilibrium is established in more and more tis- b
sues between the tissue and plasma, and eventually 1
0 3 6 9 12
changes in plasma concentration reflect proportional Time
changes in the concentrations of drug in all other tis-
FIGURE 5-1 Plasma level–time curve for the two-
sues. During this proportionality phase, the body
compartment open model (single IV dose) described in Fig. 5-2
kinetically acts as a single compartment and because (model A).
decline of the plasma concentration is now associated
solely with elimination of drug from the body, this
phase is often called the elimination phase. is completed, the plasma drug concentrations decline
Concentration of the drug in the tissue compart- more gradually when eventually plasma drug equilib-
ment (Ct), is not a useful parameter due to the non- rium with peripheral tissues occurs. Drug kinetics
homogenous tissue distribution of drugs. However, after distribution is characterized by the composite
amount of the drug in the tissue compartment (Dt) is rate constant, b (or b), which can be obtained from
useful because it is an indication of how much drug the terminal slope of the plasma level–time curve in
accumulates extravascularly in the body at any given a semilogarithmic plot (Fig. 5-1).
time. The two-compartment model provides a simple Nonlinear plasma drug level–time decline occurs
way to keep track of the mass balance of the drug in because some drugs distribute at various rates into
the body. different tissue groups. Multicompartment models
Multicompartment models provide answers to were developed to explain and predict plasma and
such questions as: (1) How much of a dose is elimi- tissue concentrations for those types of drugs. In con-
nated? (2) How much drug remains in the plasma trast, a one-compartment model is used when a drug
compartment at any given time? and (3) How much appears to distribute into tissues instantaneously and
drug accumulates in the tissue compartment? The uniformly or when the drug does not extensively dis-
latter information is particularly useful for drug tribute into extravascular tissues such as aminoglyco-
safety since the amount of drug in a deep tissue com- sides. Extent of distribution is partially determined by
partment may be harder to eliminate by renal excre- the physical-chemical properties of the drug. For
tion or by dialysis after drug overdose. instance, aminoglycosides are polar molecules; there-
Multicompartment models explain the observa- fore, their distribution is primarily limited to extracel-
tion that, after a rapid IV bolus drug injection, the lular water. Lipophilic drugs with more extensive
plasma level–time curve does not decline linearly, distribution into tissues such as the benzodiazepines
implying that the drug does not equilibrate rapidly in or those with extensive intracellular uptake may be
the body, as observed for a single first-order rate better described by more complex models. For both
process in a one-compartment model. Instead, a one- and multicompartment models, the drug in those
biphasic or triphasic drug concentration decline is tissues that have the highest blood perfusion equili-
often observed. The initial decline phase represents brates rapidly with the drug in the plasma. These
the drug leaving the plasma compartment and enter- highly perfused tissues and blood make up the central
ing one or more tissue compartments as well as being compartment (often called the plasma compartment).
eliminated. Later, after drug distribution to the tissues While this initial drug distribution is taking place,
Plasma level
Distrib
utio
n p
ha
Multicompartment Models: Intravenous Bolus Administration 99
multicompartment drugs are delivered concurrently MDR1, a common transport protein of the ABC
to one or more peripheral compartments (often con- [ATP-binding cassette] transporter subfamily found
sidered as the tissue compartment that includes fat, in the body). Drug transporters are now known to
muscle, and cerebrospinal fluid) composed of groups influence the curvature in the log plasma drug con-
of tissues with lower blood perfusion and different centration–time graph of drugs. The drug isotretinoin
affinity for the drug. A drug will concentrate in a tis- has a long half-life because of substantial distribution
sue in accordance with the affinity of the drug for that into lipid tissues.
particular tissue. For example, lipid-soluble drugs Kinetic analysis of a multicompartment model
tend to accumulate in fat tissues. Drugs that bind assumes that all transfer rate processes for the pas-
plasma proteins may be more concentrated in the sage of drug into or out of individual compartments
plasma, because protein-bound drugs do not diffuse are first-order processes. On the basis of this assump-
easily into the tissues. Drugs may also bind with tis- tion, the plasma level–time curve for a drug that
sue proteins and other macromolecules, such as DNA follows a multicompartment model is best described
and melanin. by the summation of a series of exponential terms,
Tissue sampling often is invasive, and the drug each corresponding to first-order rate processes
concentration in the tissue sample may not represent associated with a given compartment. Most multi-
the drug concentration in the entire organ due to the compartment models used in pharmacokinetics are
nonhomogenous tissue distribution of drugs. In mamillary models. Mamillary models are well con-
recent years, the development of novel experimental nected and dynamically exchange drug concentra-
methods such as magnetic resonance spectroscopy tion between compartments making them very
(MRS), single photon emission computed tomogra- suitable for modeling drug distribution.
phy (SPECT), and tissue microdialysis has enabled Because of all these distribution factors, drugs
us to study the drug distribution in the target tissues will generally concentrate unevenly in the tissues,
of animals and humans (Eichler and Müller, 1998, and different groups of tissues will accumulate the
and Müller, 2009). These innovative technologies drug at very different rates. A summary of the
have enabled us to follow the path of the drug from approximate blood flow to major human tissues is
the plasma compartment into anatomically defined presented in Table 5-1. Many different tissues and
regions or tissues. More importantly, for some classes rate processes are involved in the distribution of any
of drugs the concentration in the interstitial fluid drug. However, limited physiologic significance has
space of the target tissue can be measured. This also been assigned to a few groups of tissues (Table 5-2).
affords a means to quantify, for the first time, the The nonlinear profile of plasma drug concentra-
inter- or intraindividual variability associated with tion–time is the result of many factors interacting
the in vivo distribution process. Although these novel together, including blood flow to the tissues, the per-
techniques are promising, measurement of drug or meability of the drug into the tissues (fat solubility),
active metabolite concentrations in target tissues and partitioning, the capacity of the tissues to accumulate
the subsequent development of associated pharmaco- drug, and the effect of disease factors on these pro-
kinetic models is not a routine practice in standard cesses (see Chapter 11). Impaired cardiac function
drug development and certainly is not mandated by may produce a change in blood flow and these affect
regulatory requirements. Occasionally, tissue sam- the drug distributive phase, whereas impairment of the
ples may be collected after a drug overdose episode. kidney or the liver may decrease drug elimination as
For example, the two-compartment model has been shown by a prolonged elimination half-life and cor-
used to describe the distribution of colchicine, even responding reduction in the slope of the terminal
though the drug’s toxic tissue levels after fatal over- elimination phase of the curve. Frequently, multiple
doses have only been recently described (Rochdi factors can complicate the distribution profile in such
et al, 1992). Colchicine distribution is now known to a way that the profile can only be described clearly
be affected by P-gp (also known as ABCB1 or with the assistance of a simulation model.
100 Chapter 5
TABLE 5-1 Blood Flow to Human Tissues
Percent Percent Blood Flow
Tissue Body Weight Cardiac Output (mL/100 g tissue per min)
Adrenals 0.02 1 550
Kidneys 0.4 24 450
Thyroid 0.04 2 400
Liver
Hepatic 2.0 5 20
Portal 20 75
Portal-drained viscera 2.0 20 75
Heart (basal) 0.4 4 70
Brain 2.0 15 55
Skin 7.0 5 5
Muscle (basal) 40.0 15 3
Connective tissue 7.0 1 1
Fat 15.0 2 1
Data from Spector WS: Handbook of Biological Data, Saunders, Philadelphia, 1956; Glaser O: Medical Physics, Vol II, Year Book Publishers, Chicago,
1950; Butler TC: Proc First International Pharmacological Meeting, vol 6, Pergamon Press, 1962.
TABLE 5-2 General Grouping of Tissues According to Blood Supplya
Blood Supply Tissue Group Percent Body Weight
Highly perfused Heart, brain, hepatic-portal system, kidney, and endocrine glands 9
Skin and muscle 50
Adipose (fat) tissue and marrow 19
Slowly perfused Bone, ligaments, tendons, cartilage, teeth, and hair 22
aTissue uptake will also depend on such factors as fat solubility, degree of ionization, partitioning, and protein binding of the drug.
Adapted with permission from Eger (1963).
TWO-COMPARTMENT OPEN MODEL distributes into two compartments, the central com-
partment and the tissue, or peripheral, compartment.
Many drugs given in a single intravenous bolus dose The drug distributes rapidly and uniformly in the
demonstrate a plasma level–time curve that does not central compartment. A second compartment, known
decline as a single exponential (first-order) process. as the tissue or peripheral compartment, contains tis-
The plasma level–time curve for a drug that follows a sues in which the drug equilibrates more slowly.
two-compartment model (Fig. 5-1) shows that the Drug transfer between the two compartments is
plasma drug concentration declines biexponentially assumed to take place by first-order processes.
as the sum of two first-order processes—distribution There are several possible two-compartment
and elimination. A drug that follows the pharmacoki- models (Fig. 5-2). Model A is used most often and
netics of a two-compartment model does not equili- describes the plasma level–time curve observed in
brate rapidly throughout the body, as is assumed for Fig. 5-1. By convention, compartment 1 is the cen-
a one-compartment model. In this model, the drug tral compartment and compartment 2 is the tissue
Multicompartment Models: Intravenous Bolus Administration 101
Model A increases up to a maximum in a given tissue, whose
k
Central compartment 12 Tissue compartment value may be greater or less than the plasma drug
Dp Vp Cp Dt Vt Ct
k21 concentration. At maximum tissue concentrations,
k10 the rate of drug entry into the tissue equals the rate
of drug exit from the tissue. The fraction of drug in
Model B
k the tissue compartment is now in equilibrium (distri-
Central compartment 12 Tissue compartment
Dp Vp Cp Dt Vt Ct bution equilibrium) with the fraction of drug in the
k21
k20 central compartment (Fig. 5-3), and the drug concen-
trations in both the central and tissue compartments
Model C decline in parallel and more slowly compared to the
k
Central compartment 12 Tissue compartment distribution phase. This decline is a first-order pro-
Dp Vp Cp Dt Vt Ct
k21 cess and is called the elimination phase or the beta
k10 k20
(b) phase (Fig. 5-1, line b). Since plasma and tissue
FIGURE 5-2 concentrations decline in parallel, plasma drug con-
Two-compartment open models, intrave-
nous injection. centrations provide some indication of the concen-
tration of drug in the tissue. At this point, drug
compartment. The rate constants k12 and k21 repre- kinetics appears to follow a one-compartment model
sent the first-order rate transfer constants for the in which drug elimination is a first-order process
movement of drug from compartment 1 to com- described by b (also known as b). A typical tissue
partment 2 (k12) and from compartment 2 to com- drug level curve after a single intravenous dose is
partment 1 (k21). The transfer constants are sometimes shown in Fig. 5-3.
termed microconstants, and their values cannot be Tissue drug concentrations in the pharmacoki-
estimated directly. Most two-compartment models netic model are theoretical only. The drug level in the
assume that elimination occurs from the central theoretical tissue compartment can be calculated
compartment model, as shown in Fig. 5-2 (model A), once the parameters for the model are estimated.
unless other information about the drug is known. However, the drug concentration in the tissue com-
Drug elimination is presumed to occur from the cen- partment represents the average drug concentration
tral compartment, because the major sites of drug in a group of tissues rather than any real anatomic
elimination (renal excretion and hepatic drug metab- tissue drug concentration. In reality, drug concentra-
olism) occur in organs such as the kidney and liver, tions may vary among different tissues and possibly
which are highly perfused with blood. within an individual tissue. These varying tissue
The plasma level–time curve for a drug that fol-
lows a two-compartment model may be divided into
two parts, (a) a distribution phase and (b) an elimina-
300
tion phase. The two-compartment model assumes 200
that, at t = 0, no drug is in the tissue compartment. 100
After an IV bolus injection, drug equilibrates rapidly 50 Plasma
in the central compartment. The distribution phase
of the curve represents the initial, more rapid decline
10
of drug from the central compartment into the tissue 5
compartment (Fig. 5-1, line a). Although drug elimi- Tissue
nation and distribution occur concurrently during the
distribution phase, there is a net transfer of drug 1
Time
from the central compartment to the tissue compart-
FIGURE 5-3 Relationship between tissue and plasma
ment because the rate of distribution is faster than
drug concentrations for a two-compartment open model. The
the rate of elimination. The fraction of drug in the maximum tissue drug concentration may be greater or less
tissue compartment during the distribution phase than the plasma drug concentration.
Drug concentration
102 Chapter 5
drug concentrations are due to differences in the The relationship between the amount of drug in each
partitioning of drug into the tissues, as discussed in compartment and the concentration of drug in that
Chapter 11. In terms of the pharmacokinetic model, compartment is shown by Equations 5.3 and 5.4:
the differences in tissue drug concentration are
reflected in the k12/k21 ratio. Thus, tissue drug con- Dp
Cp = (5.3)
centration may be higher or lower than the plasma Vp
drug concentrations, depending on the properties of
D
the individual tissue. Moreover, the elimination rates t
Ct = (5.4)
V
of drug from the tissue compartment may not be the t
same as the elimination rates from the central com-
partment. For example, if k12·Cp is greater than k21·Ct where Dp = amount of drug in the central compart-
(rate into tissue > rate out of tissue), tissue drug ment, Dt = amount of drug in the tissue compartment,
concentrations will increase and plasma drug con- Vp = volume of drug in the central compartment, and
centrations will decrease. Real tissue drug concen- Vt = volume of drug in the tissue compartment.
tration can sometimes be calculated by the addition
of compartments to the model until a compartment
dC
that mimics the experimental tissue concentrations is p D Dp D
= t p
k2 − k k
dt 1 V 12 − (5.5)
t V 10
p V
found. d
In spite of the hypothetical nature of the tissue
dC D
t p D
compartment, the theoretical tissue level is still valu- = t
k12 − k21 (5.6)
dt Vp Vt
able information for clinicians. The theoretical tissue
concentration, together with the blood concentra-
tion, gives an accurate method of calculating the Solving Equations 5.5 and 5.6 using Laplace trans-
total amount of drug remaining in the body at any forms and matrix algebra will give Equations 5.7 and
given time (see digoxin example in Table 5-5). This 5.8, which describe the change in drug concentration
information would not be available without pharma- in the blood and in the tissue with respect to time:
cokinetic models.
D0
In practice, a blood sample is removed periodi- = p k21 − α k2 β
C
− α e−α t 1 −
+ −β
e t
p Vp β α β ( .7)
−
5
cally from the central compartment and the plasma is
analyzed for the presence of drug. The drug plasma
level–time curve represents a phase of initial rapid k 0
21DP
equilibration with the central compartment (the dis- C = α β (e−βt
t − e−α t) (5.8)
Vt ( − )
tribution phase), followed by an elimination phase
after the tissue compartment has also equilibrated
with drug. The distribution phase may take minutes k2 − α −α k − β
DP = D0 1 2 β
P e t
β − α + 1
e− t
α − β (5.9)
or hours and may be missed entirely if the blood is
sampled too late or at wide intervals after drug
administration.
k 0
21DIn the model depicted above, k12 and k21 are P
D β −α
t =
( β (e− t − e t
α ) (5.10)
− )
first-order rate constants that govern the rate of drug
distribution into and out of the tissues and plasma:
where D0
P = dose given intravenously, t = time after
administration of dose, and a and b are constants
dC
t = k12Cp − k21C (5.1)
dt t that depend solely on k12, k21, and k10. The amount of
drug remaining in the plasma and tissue compart-
dC ments at any time may be described realistically by
p
= k21Ct − k12Cp − k 0C (5 2
dt 1 p . ) Equations 5.9 and 5.10.
Multicompartment Models: Intravenous Bolus Administration 103
The rate constants for the transfer of drug Method of Residuals
between compartments are referred to as microcon- The method of residuals (also known as feathering,
stants or transfer constants. They relate the amount peeling, or curve stripping) is a commonly employed
of drug being transferred per unit time from one technique for resolving a curve into various expo-
compartment to the other. The values for these micro- nential terms. This method allows the separation of
constants cannot be determined by direct measure- the monoexponential constituents of a biexponential
ment, but they can be estimated by a graphic method. plot of plasma concentration against time and there-
fore, it is a useful procedure for fitting a curve to the
α + β = k + k + k10 (5.11) experimental data of a drug when the drug does not
12 21
clearly follow a one-compartment model. For exam-
αβ = k k (5.12) ple, 100 mg of a drug was administered by rapid IV
21 10
injection to a healthy 70-kg adult male. Blood sam-
ples were taken periodically after the administration
The constants a and b are hybrid first-order rate of drug, and the plasma fraction of each sample was
constants for the distribution phase and elimination assayed for drug. The following data were obtained:
phase, respectively. The mathematical relationships
of a and b to the rate constants are given by
Equations 5.11 and 5.12, which are derived after Plasma Concentration
Time (hour) (μg/mL)
integration of Equations 5.5 and 5.6. Equation 5.7
can be transformed into the following expression: 0.25 43.00
0.5 32.00
C = Ae−α t Be−βt
p + (5.13) 1.0 20.00
1.5 14.00
The constants a and b are rate constants for the
2.0 11.00
distribution phase and elimination phase, respec-
tively. The constants A and B are intercepts on the 4.0 6.50
y axis for each exponential segment of the curve in 8.0 2.80
Equation 5.13. These values may be obtained graph-
12.0 1.20
ically by the method of residuals or by computer.
Intercepts A and B are actually hybrid constants, as 16.0 0.52
shown in Equations 5.14 and 5.15, and do not have
actual physiologic significance. When these data are plotted on semilogarithmic
graph paper, a curved line is observed (Fig. 5-4). The
curved-line relationship between the logarithm of the
D0 (α − k
21)
A = (5.14)
VP (α − β plasma concentration and time indicates that the drug
)
is distributed in more than one compartment. From
these data a biexponential equation, Equation 5.13,
D (k − )
0 21 β
B = (5.15) may be derived, either by computer or by the method
VP (α − β)
of residuals.
As shown in the biexponential curve in Fig. 5-4,
Please note that the values of A and B are empirical the decline in the initial distribution phase is
constants directly proportional to the dose admin- more rapid than the elimination phase. The rapid
istered. All the rate constants involved in two- distribution phase is confirmed with the constant a
compartment model will have units consistent with being larger than the rate constant b. Therefore, at
the first-order process (Jambhekar SS and Breen JP. some later time (generally at a time following the
2009). attainment of distribution equilibrium), the term
104 Chapter 5
50 From Equation 5.17, the rate constant can be
Cp = 45e–1.8t + 15e–0.21t obtained from the slope (−b/2.3) of a straight line
representing the terminal exponential phase (Fig. 5-4).
10 The t1/2 for the elimination phase (beta half-life) can
be derived from the following relationship:
5
0.693
a b t1/2β = (5.18)
β
1
0.5 In the sample case considered here, b was found
to be 0.21 h−1. From this information the regression
line for the terminal exponential or b phase is extrap-
0.1 olated to the y axis; the y intercept is equal to B, or
0 4 8 12 16 15 mg/mL. Values from the extrapolated line are then
Time (hours) subtracted from the original experimental data points
FIGURE 5-4 Plasma level–time curve for a two- (Table 5-3) and a straight line is obtained. This line
compartment open model. The rate constants and intercepts represents the rapidly distributed a phase (Fig. 5-4).
were calculated by the method of residuals. The new line obtained by graphing the loga-
rithm of the residual plasma concentration (Cp −Cp′ )
Ae−a t will approach 0, while Be−b t will still have a against time represents the a phase. The value for a
finite value. At this later time Equation 5.13 will is 1.8 h−1, and the y intercept is 45 mg/mL. The elimi-
reduce to: nation t1/2b is computed from b by the use of
Equation 5.18 and has the value of 3.3 hours.
A number of pharmacokinetic parameters may
Cp = Be−βt (5.16)
be derived by proper substitution of rate constants
a and b and y intercepts A and B into the following
which, in common logarithms, is: equations:
βt αβ(A + B)
logCp = logB − (5.17) k10 = (5.19)
2.3 Aβ + Bα
TABLE 5-3 Application of the Method of Residuals
Time Cp Observed Plasma Cp Extrapolated Cp – Cp Residual
(hour) Level Plasma Concentration Plasma Concentration
0.25 43.0 14.5 28.5
0.5 32.0 13.5 18.5
1.0 20.0 12.3 7.7
1.5 14.0 11.0 3.0
2.0 11.0 10.0 1.0
4.0 6.5
8.0 2.8
12.0 1.2
16.0 0.52
Blood level (mg/mL)
Multicompartment Models: Intravenous Bolus Administration 105
AB(β − α )2 TABLE 5-4 Two-Compartment Model
k12 = (5.20)
(A + B)(Aβ + Bα ) Pharmacokinetic Parameters of Digoxin
Parameters Unit Normal Renal Impaired
Aβ + Bα
k21 = (5.21)
A + B k12 h–1 1.02 0.45
k21 h–1 0.15 0.11
When an administered drug exhibits the characteris-
k h–1 0.18 0.04
tics of a two-compartment model, the difference
between the distribution rate constant a and the slow Vp L/kg 0.78 0.73
post-distribution/elimination rate constant b plays a D mg/kg 3.6 3.6
critical role. The greater the difference between a and
a 1/h 1.331 0.593
b, the greater is the need to apply two-compartment
model. Failure to do so will result in false clinical b 1/h 0.019 0.007
predictions (Jambhekar SS and Breen JP. 2009). On
the other hand, if this difference is small, it will not myocardium digoxin level. In the simulation below,
cause any significant difference in the clinical predic- the amount of the drug in the plasma compartment at
tions, regardless of the model chosen to describe the any time divided by Vp (54.6 L for the normal subject)
pharmacokinetics of a drug. Then, it may be prudent will yield the plasma digoxin level. At 4 hours after
to follow the principle of PARSIMONY when select-
ing the compartment model by choosing the simpler
1000.00
of the two available models (eg, one-compartment Two-Compartment Model Parameters of Digoxin
versus two) (Jambhekar SS and Breen JP. 2009). Parameter Unit NORM RF
k12 t/h 1.02 0.45
k21 t/h 0.15 0.11
CLINICAL APPLICATION k t/h 0.18 0.04
Vp L/kg 0.76 0.73
D mcg/kg 3.6 3.6
Digoxin in a Normal Patient and in a
a t/h 1.331 0.593
Renal-Failure Patient—Simulation of Plasma b t/h 0.019 0.007
and Tissue Level of a Two-Compartment RF tissue
Model Drug
Once the pharmacokinetic parameters are determined NORM tissue
for an individual, the amount of drug remaining in the
100.00
plasma and tissue compartments may be calculated
using Equations 5.9 and 5.10. The pharmacokinetic
data for digoxin were calculated in a normal and in a
renal-impaired, 70-kg subject using the parameters in RF
Table 5-4 as reported in the literature. The amount of
digoxin remaining in the plasma and tissue compart-
ments is tabulated in Table 5-5 and plotted in Fig. 5-5.
It can be seen that digoxin stored in the plasma NORM
declines rapidly during the initial distributive phase,
while drug amount in the tissue compartment takes
3–4 hours to accumulate for a normal subject. It is
interesting that clinicians have recommended that 10.00
0 5 10 15 20 25
digoxin plasma samples be taken at least several hours Hour
after IV bolus dosing (3–4+ hours, Winters, 1994, and FIGURE 5-5 Amount of digoxin (simulated) in the plasma
4–8 hours, Schumacher, 1995) for a normal subject, and tissue compartment after an IV dose to a normal and a
since the equilibrated level is more representative of renal-failure (RF) patient.
Digoxin amount in plasma (mcg)
106 Chapter 5
an IV dose of 0.25 mg, Cp = Dp/Vp = 24.43 µg/54.6 L = since the amount of drug is calculated using mass
0.45 ng/mL, corresponding to 3 × 0.45 ng/mL = balance. The rate of drug entry into the tissue in
1.35 ng/mL if a full loading dose of 0.75 mg is given micrograms per hour at any time is k12Dp, while the
in a single dose. Although the initial plasma drug levels rate of drug leaving the tissue is k21Dt in the same
were much higher than after equilibration, the digoxin units. Both of these rates may be calculated from
plasma concentrations are generally regarded as not Table 5-5 using k12 and k21 values listed in Table 5-4.
toxic, since drug distribution is occurring rapidly. Although some clinicians assume that tissue and
The tissue drug levels were not calculated. The plasma concentrations are equal when at full equili-
tissue drug concentration represents the hypothetical bration, tissue and plasma drug ratios are determined
tissue pool, which may not represent actual drug by the partition coefficient (a drug-specific physical
concentrations in the myocardium. In contrast, the ratio that measures the lipid/water affinity of a
amount of drug remaining in the tissue pool is real, drug) and the extent of protein binding of the drug.
TABLE 5-5 Amount of Digoxin in Plasma and Tissue Compartment after an IV Dose of
0.252 mg in a Normal and a Renal-Failure Patient Weighing 70 kga
Digoxin Amount
Normal Renal Function Renal Failure (RF)
Time (hour) Dp (µg) Dt (µg) Dp (μg) Dt (μg)
0.00 252.00 0.00 252.00 0.00
0.10 223.68 24.04 240.01 11.01
0.60 126.94 105.54 189.63 57.12
1.00 84.62 140.46 158.78 85.22
2.00 40.06 174.93 107.12 131.72
3.00 27.95 181.45 78.44 156.83
4.00 24.43 180.62 62.45 170.12
5.00 23.17 177.91 53.48 176.88
6.00 22.53 174.74 48.39 180.04
7.00 22.05 171.50 45.45 181.21
8.00 21.62 168.28 43.69 181.29
9.00 21.21 165.12 42.59 180.77
10.00 20.81 162.01 41.85 179.92
11.00 20.42 158.96 41.32 178.89
12.00 20.03 155.97 40.89 177.77
13.00 19.65 153.04 40.53 176.60
16.00 18.57 144.56 39.62 173.00
24.00 15.95 124.17 37.44 163.59
aDp drug in plasma compartment; D
t′ drug in tissue compartment.
Source: Data generated from parameters published by Harron (1989).
Multicompartment Models: Intravenous Bolus Administration 107
Figure 5-5 shows that the time for the RF (renal- reproducible because they are affected by short-term
failure or renal-impaired) patient to reach stable tis- physiologic changes. For example, stress may result
sue drug levels is longer than the time for the normal in short-term change of the hematocrit or plasma
subject due to changes in the elimination and trans- volume and possibly other hemodynamic factors.
fer rate constants. As expected, a significantly higher
amount of digoxin remains in both the plasma and
tissue compartments in the renally impaired subject Frequently Asked Questions
compared to the normal subject. »»Are “hypothetical” or “mathematical” compartment
models useful in designing dosage regimens in the
clinical setting? Does “hypothetical” mean “not real”?
PRACTICE PROBLEM
»»If physiologic models are better than compartment
From Figure 5-5 or Table 5-4, how many hours does models, why not just use physiologic models?
it take for maximum tissue concentration to be »»Since clearance is the term most often used in clinical
reached in the normal and the renal-impaired patient? pharmacy, why is it necessary to know the other
pharmacokinetic parameters?
Solution
At maximum tissue concentration, the rate of drug
entering the tissue compartment is equal to the rate Apparent Volumes of Distribution
of leaving (ie, at the peak of the tissue curve, where As discussed in Chapter 4, the apparent VD is a use-
the slope = 0 or not changing). This occurs at about ful parameter that relates plasma concentration to the
3–4 hours for the normal patient and at 7–8 hours amount of drug in the body. For drugs with large
for the renal-impaired patient. This may be verified extravascular distribution, the apparent volume of
by examining at what time Dpk12 = Dtk21 using the distribution is generally large. Conversely, for polar
data from Tables 5-4 and 5-5. Before maximum Ct drugs with low lipid solubility, the apparent VD is
is reached, there is a net flux of drug into the tissue, generally small. Drugs with high peripheral tissue
that is, Dpk12 > Dtk21, and beyond this point, there is binding also contribute to a large apparent VD. In
a net flux of drug out of the tissue compartment, multiple-compartment kinetics, such as the two-
that is, Dtk12 > Dpk12. compartment model, several types of volumes of
distribution, each based on different assumptions,
can be calculated. Volumes of distribution generally
PRACTICAL FOCUS
reflect the extent of drug distribution in the body on
The distribution half-life of digoxin is about 31 minutes a relative basis, and the calculations depend on the
(t availability of data. In general, it is important to refer
½a = 0.694/a = 0.694/1.331 = 31 min) based on
Table 5-4. Both clinical experience and simulated tis- to the same volume parameter when comparing
sue amount in Table 5-4 recommend “several hours” kinetic changes in disease states. Unfortunately, val-
for equilibration, longer than 5t½a or 5 × 32 minutes. ues of apparent volumes of distribution of drugs
(1) Is digoxin elimination in tissue adequately mod- from tables in the clinical literature are often listed
eled in this example? (2) Digoxin was not known to without specifying the underlying kinetic processes,
be a P-gp substrate when the data were analyzed; can model parameters, or methods of calculation.
the presence of a transporter at the target site change
tissue drug concentration, necessitating a longer Volume of the Central Compartment
equilibration time? This is a proportionality constant that relates the
Generally, the ability to obtain a blood sample amount or mass of drug and the plasma concentration
and get accurate data in the alpha (distribution) immediately (ie, at time zero) following the adminis-
phase is difficult for most drugs because of its short tration of a drug. The volume of the central compart-
duration. Moreover, the alpha phase may not be very ment is useful for determining the drug concentration
108 Chapter 5
directly after an IV injection into the body. In clinical volume of distribution will be 3 L; if it is not, then
pharmacy, this volume is also referred to as Vi or the distribution of drug may also occur outside the vas-
initial volume of distribution as the drug distributes cular pool into extra- and intracellular fluid.
within the plasma and other accessible body fluids.
This volume is generally smaller than the terminal D
0
Vp = (5.22)
C0
volume of distribution after drug distribution to tissue p
is completed. The volume of the central compartment
is generally greater than 3 L, which is the volume of At zero time (t = 0), the entire drug in the body is in
the plasma fluid for an average adult. For many polar the central compartment. C0
p can be shown to be equal
drugs, an initial volume of 7–10 L may be interpreted to A + B by the following equation:
as rapid drug distribution within the plasma and some
extracellular fluids. For example, the Vp of moxalac- C = Ae−α t + Be−βt
p (5.23)
tam ranges from 0.12 to 0.15 L/kg, corresponding to
about 8.4–10.5 L for a typical 70-kg patient At t = 0, e0 = 1. Therefore,
(Table 5-6). In contrast, the Vp of hydromorphone is
about 24 L, possibly because of its rapid exit from the C0
p = A + B (5.24)
plasma into tissues even during the initial phase.
As in the case of the one-compartment model, Vp Vp is determined from Equation 5.25 by measuring
may be determined from the dose and the instanta-
0 A and B after feathering the curve, as discussed
neous plasma drug concentration, Cp . Vp is also use-
previously:
ful in the determination of drug clearance if k (or t½)
is known, as in Chapter 4. D
0
V
In the two-compartment model, Vp may also be p = (5.25)
A + B
considered a mass balance factor governed by the
mass balance between dose and concentration, that Alternatively, the volume of the central compart-
∞
is, drug concentration multiplied by the volume of ment may be calculated from the [AUC] in a manner
0
the fluid must equal the dose at time = 0. At time = 0, similar to the calculation for the apparent VD in the one-
no drug is eliminated, D0 = VpCp. The basic model compartment model. For a one-compartment model
assumption is that plasma drug concentration is rep-
resentative of drug concentration within the distribu- D
∞
[AUC] 0
=
0 (5.26)
tion fluid of plasma. If this statement is true, then the kVD
TABLE 5-6 Pharmacokinetic Parameters (mean ± SD) of Moxalactam in Three Groups of Patients
A B ` a k
Group μg/mL μg/mL h–1 h–1 h–1
1 138.9 ± 114.9 157.8 ± 87.1 6.8 ± 4.5 0.20 ± 0.12 0.38 ± 0.26
2 115.4 ± 65.9 115.0 ± 40.8 5.3 ± 3.5 0.27 ± 0.08 0.50 ± 0.17
3 102.9 ± 39.4 89.0 ± 36.7 5.6 ± 3.8 0.37 ± 0.09 0.71 ± 0.16
Cl Vp Vt (VD)ss (VD)β
Group mL/min L/kg L/kg L/kg L/kg
1 40.5 ± 14.5 0.12 ± 0.05 0.08 ± 0.04 0.20 ± 0.09 0.21 ± 0.09
2 73.7 ± 13.1 0.14 ± 0.06 0.09 ± 0.04 0.23 ± 0.10 0.24 ± 0.12
3 125.9 ± 28.0 0.15 ± 0.05 0.10 ± 0.05 0.25 ± 0.08 0.29 ± 0.09
Multicompartment Models: Intravenous Bolus Administration 109
∞
In contrast, [AUC] for the two-compartment Substituting Equation 5.31 into Equation 5.32, and
0
model is: expressing Dp as VpCp, a more useful equation for
the calculation of (VD)ss is obtained:
D
∞
[AUC] 0
=
0 (5.27)
kVp CpVp + k12VpCp /k21
(VD )ss = (5.33)
Cp
Rearrangement of this equation yields:
D which reduces to
0
Vp = (5.28)
∞
k [AUC]0 k
(V 2
D )
1
ss = Vp + V (5 34)
k p .
21
Apparent Volume of Distribution at
Steady State In practice, Equation 5.34 is used to calculate
This is a proportionality constant that relates the plasma (VD)ss. The (VD)ss is a function of the transfer con-
concentration and the amount of drug remaining in the stants, k12 and k21, which represent the rate constants
body at a time, following the attainment of practical of drug going into and out of the tissue compartment,
steady state (which is reached at a time greater by at respectively. The magnitude of (VD)ss is dependent on
least four elimination half-lives of the drug). At steady- the hemodynamic factors responsible for drug distri-
state conditions, the rate of drug entry into the tissue bution and on the physical properties of the drug,
compartment from the central compartment is equal to properties which, in turn, determine the relative
the rate of drug exit from the tissue compartment into amount of intra- and extravascular drug remaining in
the central compartment. These rates of drug transfer the body.
are described by the following expressions:
Extrapolated Volume of Distribution
The extrapolated volume of distribution (V
= D)exp is
Dtk21 Dpk12 (5.29)
calculated by the following equation:
k12Dp
D = (5.30) D
t k (VD ) = 0
21 exp (5.35)
B
Because the amount of drug in the central compart-
where B is the y intercept obtained by extrapolation
ment, Dp, is equal to VpCp, by substitution in the above
of the b phase of the plasma level curve to the y axis
equation,
(Fig. 5-4). Because the y intercept is a hybrid con-
k stant, as shown by Equation 5.15, (VD)exp may also
12CpVp
D = (5.31)
t k be calculated by the following expression:
21
The total amount of drug in the body at steady α − β
(V =
D )state is equal to the sum of the amount of drug in the exp Vp k2 − β
(5.36)
1
tissue compartment, Dt, and the amount of drug in
the central compartment, Dp. Therefore, the apparent This equation shows that a change in the distribution
volume of drug at steady state (VD)ss may be calcu- of a drug, which is observed by a change in the value
lated by dividing the total amount of drug in the for Vp, will be reflected in a change in (VD)exp.
body by the concentration of drug in the central
compartment at steady state: Volume of Distribution by Area
The volume of distribution by area (VD)area, also
Dp + Dt
( known as (VD)b, is obtained through calculations
VD )ss = (5.32)
Cp similar to those used to find Vp, except that the rate
110 Chapter 5
constant b is used instead of the overall elimination Substituting kVp for clearance in Equation 5.38, one
rate constant k. This volume represents a proportion- obtains:
ality factor between plasma concentrations and
amount of drug in body during the terminal or b kVp
(VD )β = (5.39)
phase of disposition. (VD)b is often calculated from β
total body clearance divided by b and is influenced
by drug elimination in the beta, or b, phase. This
Theoretically, the value for b may remain
volume will be considered a time-dependent and
unchanged in patients showing various degrees of
clearance-dependent volume of distribution parameter.
moderate renal impairment. In this case, a reduction
The value of (VD)b is affected by elimination, and it
in (VD)b may account for all the decrease in Cl, while
changes as clearance is altered. Reduced drug clear-
b is unchanged in Equation 5.39. Within the body, a
ance from the body may increase AUC (area under
redistribution of drug between the plasma and the
the curve), such that (VD)b is either reduced or
tissue will mask the expected decline in b. The fol-
unchanged depending on the value of b, as shown by
lowing example in two patients shows that the b
Equation 5.36.
elimination rate constant remains the same, while
the distributional rate constants change. Interestingly,
D
(V 7
D )β = (V 4 3
D )
area = 0 ( . ) Vp is unchanged, while (VD)b would be greatly
∞
β [AUC]0 changed in the simulated example. An example of a
drug showing a constant b slope while the renal
A slower clearance allows more time for drug equili- function as measured by Clcr decreases from 107 to
bration between plasma and tissues yielding a 56, 34, and 6 mL/min (see Chapter 7) has been
smaller (VD)b. The lower limit of (VD)b is Vss: observed with the aminoglycoside drug gentamicin
in various patients after IV bolus dose (Schentag
Lim(VD )β = Vss et al, 1977). Gentamicin follows polyexponential
decline with a significant distributive phase. The
Cl → 0
following simulation problem may help clarify the
situation by changing k and clearance while keeping
Thus, (VD)b has value in representing Vss for low-
b constant.
clearance drugs as well as estimating terminal or b
phase. Smaller (VD)b values than normal are often
observed in patients with renal failure because of the PRACTICE PROBLEM
reduced Cl. This is a consequence of the Cl-dependent
time of equilibration between plasma and tissue. Thus, Simulated plasma drug concentrations after an IV
Vss is preferred in separating alterations in elimina- bolus dose (100 mg) of an antibiotic in two patients,
tion from those in distribution. patient 1 with a normal k, and patient 2 with a
Generally, reduced drug clearance is also reduced k, are shown in Fig. 5-6. The data in the two
accompanied by a decrease in the constant b (ie, an patients were simulated with parameters using the
increase in the b elimination half-life). For example, two-compartment model equation. The parameters
in patients with renal dysfunction, the elimination used are as follows:
half-life of the antibiotic amoxacillin is longer
Normal subject, k = 0.3 h−1, Vp = 10 L, Cl = 3 L/h
because renal clearance is reduced.
Because total body clearance is equal to k12 = 5 h−1, k21 = 0.2 h−1
∞
D0 / [AUC] , (V ) y b x r s e
0 D β ma e e p e s d in terms of
clearance and the rate constant b: Subject with moderate renal impairment,
k = 0.1 h−1, Vp = 10 L, Cl = 1 L/h
Cl
(VD )β = (5.38)
β k12 = 2 h−1, k21 = 0.25 h−1
Multicompartment Models: Intravenous Bolus Administration 111
10 reflects the data. A decrease in the (VD)b with b
unchanged is possible, although this is not the
common case. When this happens, the termi-
Patient 2 nal data (see Fig. 5-6) conclude that the beta
elimination half-lives of patients 1 and 2 are
1
the same due to a similar b. Actually, the real
Patient 1 elimination half-life of the drug derived from
k is a much better parameter, since k reflects
the changes in renal function, but not b, which
0.1 remains unchanged since it is masked by the
1 2
Time (hours) changes in (VD)b.
3. Both patients have the same b value (b =
FIGURE 5-6 Simulation of plasma drug concentration 0.011 h−1); the terminal slopes are identical.
after an IV bolus dose (100 mg) of an antibiotic in two patients,
Ignoring early points by only taking terminal
one with a normal k (patient 1) and the other with reduced k
(patient 2). data would lead to an erroneous conclusion
that the renal elimination process is unchanged,
while the volume of distribution of the renally
Questions impaired patient is smaller. In this case, the
1. Is a reduction in drug clearance generally renally impaired patient has a clearance of
accompanied by an increase in plasma drug 1 L/h compared with 3 L/h for the normal
concentration, regardless of which compart- subject, and yet the terminal slopes are the
ment model the drug follows? same. The rapid distribution of drug into the
2. Is a reduction in drug clearance generally tissue in the normal subject causes a longer and
accompanied by an increase in the b elimina- steeper distribution phase. Later, redistribution
tion half-life of a drug? [Find (VD)b using of drug out of tissues masks the effect of rapid
Equation 5.38, and then b using Equation 5.39.] drug elimination through the kidney. In the
3. Many antibiotics follow multiexponential renally impaired patient, distribution to tissue is
plasma drug concentration profiles indicating reduced; as a result, little drug is redistributed
drug distribution into tissue compartments. In out from the tissue in the b phase. Hence, it
clinical pharmacokinetics, the terminal half- appears that the beta phases are identical in the
life is often determined with limited early data. two patients.
Which patient has a greater terminal half-life
based on the simulated data?
Significance of the Volumes of Distribution
From Equations 5.38 and 5.39 we can observe that
Solutions (VD)b is affected by changes in the overall elimina-
1. A reduction in drug clearance results in less tion rate (ie, change in k) and by change in total body
drug being removed from the body per unit clearance of the drug. After the drug is distributed,
time. Drug clearance is model independent. the total amount of drug in the body during the
Therefore, the plasma drug concentration elimination of b phase is calculated by using (VD)b.
should be higher in subjects with decreased Vp is sometimes called the initial volume of
drug clearance compared to subjects with distribution and is useful in the calculation of drug
normal drug clearance, regardless of which clearance. The magnitudes of the various apparent
compartment model is used (see Fig. 5-6). volumes of distribution have the following relation-
2. Clearance in the two-compartment model is ships to each other:
affected by the elimination rate constant, b, and
the volume of distribution in the b phase, which (VD )exp > (VD )β >Vp
Plasma drug
concentration (mg/mL)
112 Chapter 5
Calculation of another VD, (VD)ss, is possible in mul- changes in pharmacokinetic parameters should not
tiple dosing or infusion (see Chapters 6 and 9). (VD)ss be attributed to physiologic changes without careful
is much larger than Vp; it approximates (VD)b but consideration of method of curve fitting and inter-
differs somewhat in value, depending on the transfer subject differences. Equation 5.39 shows that, unlike
constants. a simple one-compartment open model, (VD)b may
In a study involving a cardiotonic drug given be estimated from k, b, and Vp. Errors in fitting are
intravenously to a group of normal and congestive easily carried over to the other parameter estimates
heart failure (CHF) patients, the average AUC for even if the calculations are performed by computer.
CHF was 40% higher than in the normal subjects. The terms k12 and k21 often fluctuate due to minor
The b elimination constant was 40% less in CHF fitting and experimental difference and may affect
patients, whereas the average (VD)b remained essen- calculation of other parameters.
tially the same. In spite of the edematous conditions
of these patients, the volume of distribution appar-
ently remained constant. No change was found in the Frequently Asked Questions
Vp or (VD)b. In this study, a 40% increase in AUC in »»What is the significance of the apparent volume of
the CHF subjects was offset by a 40% smaller b distribution?
elimination constant estimated by using computer
»»Why are there different volumes of distribution in the
methods. Because the dose was the same, the (VD)b multiple-compartment models?
would not change unless the increase in AUC is not
accompanied by a change in b elimination constant.
From Equation 5.38, the clearance of the drug in Drug in the Tissue Compartment
CHF patients was reduced by 40% and accompanied
The apparent volume of the tissue compartment (Vt) by a corresponding decrease in the b elimination
is a conceptual volume only and does not represent
constant, possibly due to a reduction in renal blood
true anatomic volumes. The Vt may be calculated
flow as a result of reduced cardiac output in CHF
from knowledge of the transfer rate constants and Vp:patients. In physiologic pharmacokinetics, clearance
(Cl) and volume of distribution (VD) are assumed to
be independent parameters that explain the impact of Vpk12
Vt = (5.40)
disease factors on drug disposition. Thus, an increase k21
in AUC of a cardiotonic in a CHF patient was
assumed to be due to a reduction in drug clearance, The calculation of the amount of drug in the tis-
since the volume of distribution was unchanged. The sue compartment does not entail the use of Vt.
elimination half-life was reduced due to reduction in Calculation of the amount of drug in the tissue com-
drug clearance. In reality, pharmacokinetic changes partment provides an estimate for drug accumulation
in a complex system are dependent on many factors in the tissues of the body. This information is vital in
that interact within the system. Clearance is affected estimating chronic toxicity and relating the duration
by drug uptake, metabolism, binding, and more; all of pharmacologic activity to dose. Tissue compart-
of these factors can also influence the drug distribu- ment drug concentration is an average estimate of the
tion volume. Many parameters are assumed to be tissue pool and does not mean that all tissues have
constant and independent for simplification of the this concentration. The drug concentration in a tissue
model. Blood flow is an independent parameter that biopsy will provide an estimate for drug in that tissue
will affect both clearance and distribution. However, sample. Due to differences in blood flow and drug
blood flow is, in turn, affected and regulated by partitioning into the tissue, and heterogenicity, even
many physiologic compensatory factors. a biopsy from the same tissue may have different
For drugs that follow two-compartment model drug concentrations. Together with Vp and Cp, used to
kinetics, changes in disease states may not result in calculate the amount of drug in the plasma, the com-
different pharmacokinetic parameters. Conversely, partment model provides mass balance information.
Multicompartment Models: Intravenous Bolus Administration 113
Moreover, the pharmacodynamic activity may cor- 6–8 hours apart to minimize potential side effects
relate better with the tissue drug concentration–time from overdigitization. If the entire loading dose were
curve. To calculate the amount of drug in the tissue administered intravenously, the plasma level would
compartment Dt, the following expression is used: be about 4–5 ng/mL after 1 hour, while the level
would drop to about 1.5 ng/mL at about 4 hours. The
k 0
12Dp exact level after a given IV dose may be calculated
D ( −β
= e t − e−α t
t ) (5.41)
α − β using Equation 5.7 at any time desired. The pharma-
cokinetic parameters for digoxin are available in
Table 5-4.
PRACTICAL FOCUS In addition to metabolism, digoxin distribution is
affected by a number of processes besides blood
The therapeutic plasma concentration of digoxin is flow. Digoxin and many other drugs are P-gp
between 1 and 2 ng/mL; because digoxin has a long (P-glycoprotein) substrates, a transporter that is often
elimination half-life, it takes a long time to reach a located in cell membranes that efflux drug in and out
stable, constant (steady-state) level in the body. A of cells, and can theoretically affect k12 (cell uptake)
loading dose is usually given with the initiation of and k21 (cell efflux). Some transporters such as P-gp
digoxin therapy. Consider the implications of the or ABC transporters exhibit genetic variability and
loading dose of 1 mg suggested for a 70-kg subject. therefore can contribute to pharmacokinetic varabil-
The clinical source cited an apparent volume of dis- ity between patients. For example, if drug transport-
tribution of 7.3 L/kg for digoxin in determining the ers avidly carry drug to metabolic sites, then
loading dose. Use the pharmacokinetic parameters metabolism would increase, and plasma levels AUC
for digoxin in Table 5-4. would decrease. The converse is also true; examples
of drugs that are known to increase digoxin level
Solution include amidiodarone, quinidine, and verapamil.
The loading dose was calculated by considering the Verapamil is a potent P-gp inhibitor and a common
body as one compartment during steady state, at agent used to test if an unknown substrate can be
which time the drug well penetrates the tissue com- blocked by a P-gp inhibitor.
partment. The volume of distribution (VD)b of digoxin Many anticancer drugs such as taxol, vincris-
is much larger than Vp, or the volume of the plasma tine, and vinblastine are P-gp substrates. P-gp can
compartment. be located in GI, kidney, liver, and entry to BBB
Using Equation (5.39), (see Chapter 11 for distribution and Chapter 13 for
genetically expressed transporters). There are other
organic anion and cation transporters in the body that
kVp
(VD )β = contribute to efflux of drug into and out of cells.
β
Efflux and translocation of a drug can cause a drug to
lose efficacy (MDR resistance) in many anticancer
0.18/h × 0.78 L/kg
= = 7.39 L/kg
0.019/h drugs. It may not always be possible to distinquish a
specific drug transporter in a specific organ or tissue
mL ng
DL = 7390 × 70 kg ×1.5 in vivo due to ongoing perfusion and the potential for
kg mL multiple transporter/carriers involved. These factors;
drug binding to proteins in blood, cell, and cell mem-
where DL = (VD)b ⋅ (Cp)ss. The desired steady plasma branes; and diffusion limiting processes contribute to
concentration, (Cp)ss, was selected by choosing a “multiexponential” drug distribution kinetically for
value in the middle of the therapeutic range. The many drugs. Much of in vivo kinetics information
loading dose is generally divided into two or three can be learned by examining the kinetics of the IV
doses or is administered as 50% in the first dose bolus time-concentration profile when a suitable sub-
with the remaining drug given in two divided doses strate probe is administered.
114 Chapter 5
Drug Clearance consideration in understanding drug permeation and
The definition of clearance of a drug that follows a toxicity. For example, the plasma–time profiles of
two-compartment model is similar to that of the one- aminoglycosides, such as gentamicin, are more use-
compartment model. Clearance is the volume of ful in explaining toxicity than average plasma or
plasma that is cleared of drug per unit time. Clearance drug concentration taken at peak or trough time.
may be calculated without consideration of the com-
partment model. Thus, clearance may be viewed as a Elimination Rate Constant
physiologic concept for drug removal, even though In the two-compartment model (IV administration),
the development of clearance is rooted in classical the elimination rate constant, k, represents the elimi-
pharmacokinetics. nation of drug from the central compartment, whereas
Clearance is often calculated by a noncompart- b represents drug elimination during the beta or
mental approach, as in Equation 5.37, in which the elimination phase, when distribution is mostly com-
bolus IV dose is divided by the area under the plete. Because of redistribution of drug out of the
plasma concentration–time curve from zero to infin- tissue compartment, the plasma drug level curve
∞ ∞
ity, [AUC] . In evaluating the AUC
0 [ ] , early time
0 declines more slowly in the b phase. Hence b is
points must be collected frequently to observe the smaller than k; thus k is a true elimination constant,
rapid decline in drug concentrations (distribution whereas b is a hybrid elimination rate constant that is
phase) for drugs with multicompartment pharmaco- influenced by the rate of transfer of drug into and out
kinetics. In the calculation of clearance using the of the tissue compartment. When it is impractical to
noncompartmental approach, underestimating the determine k, b is calculated from the b slope. The t1/2b
area can inflate the calculated value of clearance. is often used to calculate the drug dose.
D
0
Cl = (5.42)
∞
[AUC] THREE-COMPARTMENT
0
OPEN MODEL
Equation 5.42 may be rearranged to Equation 5.43
to show that Cl in the two-compartment model is the The three-compartment model is an extension of the
product of (VD)b and b. two-compartment model, with an additional deep
tissue compartment. A drug that demonstrates the
necessity of a three-compartment open model is
Cl = (VD )β β (5.43) distributed most rapidly to a highly perfused central
compartment, less rapidly to the second or tissue
If both parameters are known, then calculation of compartment, and very slowly to the third or deep
clearance is simple and more accurate than using the tissue compartment, containing such poorly per-
trapezoidal rule to obtain area. Clearance calculations fused tissue as bone and fat. The deep tissue com-
that use the two-compartment model are viewed as partment may also represent tightly bound drug in
model dependent because more assumptions are the tissues. The three-compartment open model is
required, and such calculations cannot be regarded as shown in Fig. 5-7.
noncompartmental. However, the assumptions pro- A solution of the differential equation describ-
vide additional information and, in some sense, spe- ing the rates of flow of drug into and out of the
cifically describe the drug concentration–time profile central compartment gives the following equation:
as biphasic.
Clearance is a term that is useful in calculating C = Ae−α t + Be−βt
p +Ce−δ t (5.44)
average drug concentrations. With many drugs, a
biphasic profile suggests a rapid tissue distribution where A, B, and C are the y intercepts of extrapolated
phase followed by a slower elimination phase. lines for the central, tissue, and deep tissue compart-
Multicompartment pharmacokinetics is an important ments, respectively, and a, b, and g are first-order
Multicompartment Models: Intravenous Bolus Administration 115
k21 k13
Tissue compartment Central compartment Deep tissue compartment
Vt C t Dt Vp Cp Dp Vdt Cdt Ddt
k12 k31
k
FIGURE 5-7 Three-compartment open model. This model, as with the previous two-compartment
models, assumes that all drug elimination occurs via the central compartment.
rate constants for the central, tissue, and deep tissue rate constant k, volume of the central compartment,
compartments, respectively. and area are shown in the following equations:
A three-compartment equation may be written
by statisticians in the literature as (A + B +C)αβδ
k = (5.45)
Aβδ + Bαδ +Cαβ
= −λ1t + −λ2t −λ t
Cp Ae Be +Ce 3 (5.44a)
D
0
Vp = (5.46)
Instead of a, b, g, etc, l1, l2, l3 are substituted to A + B +C
express the triexponential feature of the equation.
A B C
Similarly, the n-compartment model may be expressed [AUC] = + + (5.47)
α β δ
with l1, l2, …, ln. The preexponential terms are some-
times expressed as C1, C2, and C3.
The parameters in Equation 5.44 may be solved
CLINICAL APPLICATION
graphically by the method of residuals (Fig. 5-8) or
by computer. The calculations for the elimination Hydromorphone (Dilaudid)
Three independent studies on the pharmacokinetics
100 of hydromorphone after a bolus intravenous injection
reported that hydromorphone followed the pharma-
Cp = 70e–1.5t + 20e–0.2t + 24e–0.03t
cokinetics of a one-compartment model (Vallner et al,
50
1981), a two-compartment model (Parab et al, 1988),
or a three-compartment model (Hill et al, 1991),
respectively. A comparison of these studies is listed in
20 Table 5-7.
A C
10 Comments
The adequacy of the pharmacokinetic model will
5 B depend on the sampling intervals and the drug assay.
The first two studies showed a similar elimination
half-life. However, both Vallner et al (1981) and Parab
2 et al (1988) did not observe a three-compartment
pharmacokinetic model due to lack of appropriate
description of the early distribution phases for
1
0 10 20 30 40 50 hydromorphone. After an IV bolus injection, hydro-
Time (hours) morphone is very rapidly distributed into the tissues.
FIGURE 5-8 Hill et al (1991) obtained a triexponential function
Plasma level–time curve for a three-
compartment open model. The rate constants and intercepts by closely sampling early time periods after the
were calculated by the method of residuals. dose. Average distribution half-lives were 1.27 and
Blood level (mg/mL)
116 Chapter 5
TABLE 5-7 Comparison of Hydromorphone Pharmacokinetics
Study Timing of Blood Samples Pharmacokinetic Parameters
6 Males, 25–29 years; mean weight, 76.8 kg 0, 15, 30, 45 minutes One-compartment model
Dose, 2-mg IV bolus (Vallner et al, 1981) 1, 1.5, 2, 3, 4, 6, 8, 10, 12 hours Terminal t1/2 = 2.64 (± 0.88) hours
8 Males, 20–30 years; weight, 50–86 kg 0, 3, 7, 15, 30, 45 minutes Two-compartment model
Dose, 2-mg IV bolus (Parab et al, 1988) 1, 1.5, 2, 3, 4, 6, 8, 10, 12 hours Terminal t1/2 = 2.36 (± 0.58) hours
10 Males, 21–38 years; mean weight, 72.7 kg 1, 2, 3, 4, 5, 7, 10, 15, 20, 30, 45 minutes Three-compartment model
Dose, 10, 20, and 40 mg/kg IV bolus 1, 1.5, 2, 2.5, 3, 4, 5 hours Terminal t1/2 = 3.07 (± 0.25) hours
(Hill et al, 1991)
14.7 minutes, and the average terminal elimination concentration often lies close to the distributive phase,
was 184 minutes (t1/2b). The average value for sys- since its beta elimination half-life is very short, and
temic clearance (Cl) was 1.66 L/min; the initial dilu- ignoring the alpha phase will result in a large error in
tion volume was 24.4 L. If distribution is rapid, the dosing projection.
drug becomes distributed during the absorption
phase. Thus, hydromorphone pharmacokinetics fol-
lows a one-compartment model after a single oral CLINICAL APPLICATION
dose. Loperamide (Imodium®) is an opioid anti-diarrhea
Hydromorphone is administered to relieve acute agent that is useful for illustrating the importance of
pain in cancer or postoperative patients. Rapid pain understanding drug distribution. Loperamide has lit-
relief is obtained by IV injection. Although the drug is tle central opiate effect. Loperamide is a P-gp (an
effective orally, about 50%–60% of the drug is cleared efflux transporter) substrate. The presence of P-gp
by the liver through first-pass effects. The pharmaco- transporter at the blood–brain barrier allows the drug
kinetics of hydromorphone after IV injection suggests to be pumped out of the cell at the cell membrane
a multicompartment model. The site of action is prob- surface without the substrate (loperamide) entering
ably within the central nervous system, as part of the into the interior of the cell. Mice that have had the
tissue compartment. The initial volume or initial dilu- gene for P-gp removed experimentally show pro-
tion volume, Vp, is the volume into which IV injec- found central opioid effects when administered loper-
tions are injected and diluted. Hydromorphone follows amide. Hypothesizing the presence of a tissue
linear kinetics, that is, drug concentration is propor- compartment coupled with a suitable molecular
tional to dose. Hydromorphone systemic clearance is probe can provide a powerful approach toward eluci-
much larger than the glomerular filtration rate (GFR) dating the mechanism of drug distribution and
of 120 mL/min (see Chapter 7), hence the drug is improving drug safety.
probably metabolized significantly by the hepatic
route. A clearance of 1.66 L/min is faster than the
blood flow of 1.2–1.5 L/min to the liver. The drug DETERMINATION OF
must be rapidly extracted or, in addition, must have COMPARTMENT MODELS
extrahepatic elimination. When the distribution phase
is short, the distribution phase may be disregarded Models based on compartmental analysis should
provided that the targeted plasma concentration is suf- always use the fewest number of compartments neces-
ficiently low and the terminal elimination phase is sary to describe the experimental data adequately.
relatively long. If the drug has a sufficiently high tar- Once an empirical equation is derived from the experi-
get plasma drug concentration and the elimination mental observations, it becomes necessary to examine
half-life is short, the distributive phase must not be how well the theoretical values that are calculated
ignored. For example, lidocaine’s effective target from the derived equation fit the experimental data.
Multicompartment Models: Intravenous Bolus Administration 117
The observed number of compartments or expo- dose or the assay for the drug cannot measure very
nential phases will depend on (1) the route of drug low plasma drug concentrations.
administration, (2) the rate of drug absorption, (3) the The total time for collection of blood samples is
total time for blood sampling, (4) the number of usually estimated from the terminal elimination half-
samples taken within the collection period, and (5) the life of the drug. However, lower drug concentrations
assay sensitivity. If drug distribution is rapid, then, may not be measured if the sensitivity of the assay is
after oral administration, the drug will become distrib- not adequate. As the assay for the drug becomes
uted during the absorption phase and the distribution more sensitive in its ability to measure lower drug
phase will not be observed. For example, theophylline concentrations, then another compartment with a
follows the kinetics of a one-compartment model after smaller first-order rate constant may be observed.
oral absorption, but after intravenous bolus (given as In describing compartments, each new compart-
aminophylline), theophylline follows the kinetics of a ment requires an additional first-order plot.
two-compartment model. Furthermore, if theophyl- Compartment models having more than three com-
line is given by a slow intravenous infusion rather than partments are rarely of pharmacologic significance.
by intravenous bolus, the distribution phase will not In certain cases, it is possible to “lump” a few com-
be observed. Hydromorphone (Dilaudid), which fol- partments together to get a smaller number of com-
lows a three-compartment model, also follows a one- partments, which, together, will describe the data
compartment model after oral administration, since adequately.
the first two distribution phases are rapid. An adequate description of several tissue com-
Depending on the sampling intervals, a com- partments can be difficult. When the addition of a
partment may be missed because samples may be compartment to the model seems necessary, it is
taken too late after administration of the dose to important to realize that the drug may be retained or
observe a possible distributive phase. For example, slowly concentrated in a deep tissue compartment.
the data plotted in Fig. 5-9 could easily be mistaken
for those of a one-compartment model, because the
distributive phase has been missed and extrapola- PRACTICAL FOCUS
tion of the data to C0
p will give a lower value than
was actually the case. Slower drug elimination Two-Compartment Model: Relation Between
compartments may also be missed if sampling is Distribution and Apparent (Beta) Half-Life
not performed at later sampling times, when the The distribution half-life of a drug is dependent on the
type of tissues the drug penetrates as well as blood
supply to those tissues. In addition, the capacity of the
300 tissue to store drug is also a factor. Distribution half-
200
life is generally short for many drugs because of the
100 ample blood supply to and rapid drug equilibration in
the tissue compartment. However, there is some sup-
porting evidence that a drug with a long elimination
half-life is often associated with a longer distribution
10
phase. It is conceivable that a tissue with little blood
supply and affinity for the drug may not attain a suf-
ficiently high drug concentration to exert its impact on
the overall plasma drug concentration profile during
1
Time (hours) rapid elimination. In contrast, drugs such as digoxin
have a long elimination half-life, and drug is elimi-
FIGURE 5-9 The samples from which data were obtained
nated slowly to allow more time for distribution to
for this graph were taken too late to show the distributive
phase; therefore, the value of C 0
p obtained by extrapolation tissues. Human follicle-stimulating hormone (hFSH)
(straight broken line) is deceptively low. injected intravenously has a very long elimination
Plasma level (mcg/mL)
118 Chapter 5
half-life, and its distribution half-life is also quite CLINICAL APPLICATION
long. Drugs such as lidocaine, theophylline, and mil-
rinone have short elimination half-lives and generally Moxalactam Disodium—Effect of Changing
relatively short distributional half-lives. Renal Function in Patients with Sepsis
In order to examine the effect of changing k The pharmacokinetics of moxalactam disodium, a
(from 0.6 to 0.2 h−1) on the distributional (alpha phase) recently discontinued antibiotic (see Table 5-6), was
and elimination (beta phase) half-lives of various examined in 40 patients with abdominal sepsis
drugs, four simulations based on a two-compartment (Swanson et al, 1983). The patients were grouped
model were generated (Table 5-8). The simulations according to creatinine clearances into three groups:
show that a drug with a smaller k has a longer beta
Group 1: Average creatinine clearance = 35.5 mL/
elimination half-life. Keeping all other parameters
min/1.73 m2
(k12, k21, Vp) constant, a smaller k will result in a
Group 2: Average creatinine clearance = 67.1 ± 6.7 mL/
smaller a, or a slower distributional phase. Examples
min/1.73 m2
of drugs with various distribution and elimination
Group 3: Average creatinine clearance = 117.2 ±
half-lives are shown in Table 5-8.
29.9 mL/min/1.73 m2
TABLE 5-8 Comparison of Beta Half-Life and After intravenous bolus administration, the
Distributional Half-Life of Selected Drugs serum drug concentrations followed a biexponential
decline (Fig. 5-10). The pharmacokinetics at steady
Beta Distributional state (2 g every 8 hours) was also examined in these
Drug Half-Life Half-Life
300
Lidocaine 1.8 hours 8 minutes
Cocaine 1 hours 18 minutes 200
Theophylline 4.33 hours 7.2 minutes
Ergometrine 2 hours 11 minutes
100
Hydromorphone 3 hours 14.7 minutes Group 1
Milrinone 3.6 hours 4.6 minutes
Procainamide 2.5–4.7 hours 6 minutes 50
Quinidine 6–8 hours 7 minutes
Group 2
Lithium 21.39 hours 5 hours
Digoxin 1.6 days 35 minutes
Human FSH 1 day 60 minutes
IgG1 kappa MAB 9.6 days 6.7 hours
(monkey) 10
Simulation 1 13.26 hours 36.24 minutes
Group 3
Simulation 2 16.60 hours 43.38 minutes
0 2 4 6 8
Simulation 3 26.83 hours 53.70 minutes
Time (hours)
Simulation 4 213.7 hours 1.12 hours
FIGURE 5-10 Moxalactam serum concentration in three
Simulation was performed using Vp of 10 L; dose = 100 mg; k12 = 0.5 h–1; groups of patients: group 1, average creatinine concentration =
k21 = 0.1 h–1; k = 0.6, 0.4, 0.2, and 0.02 hour for simulations 1–4, respec- 35.5 mL/min/1.73 m2; group 2, average creatinine concentra-
tively (using Equations 5.11 and 5.12). tion = 67.1 ± 6.7 mL/min/1.73 m2; group 3, average creatinine
Source: Data from manufacturer and Schumacher (1995). concentration = 117.2 ± 29.9 mL/min/1.73 m2.
Moxalactam Cp (mcg/mL)
Multicompartment Models: Intravenous Bolus Administration 119
patients. Mean steady-state serum concentrations Clinical Example—Azithromycin
ranged from 27.0 to 211.0 mg/mL and correlated Pharmacokinetics
inversely with creatinine clearance (r = 0.91, Following oral administration, azithromycin
p < 0.0001). The terminal half-life ranged from 1.27 (Zithromax®) is an antibiotic that is rapidly absorbed
to 8.27 hours and reflected the varying renal func- and widely distributed throughout the body.
tion of the patients. Moxalactam total body clear- Azithromycin is rapidly distributed into tissues, with
ance (Cl) had excellent correlation with creatinine high drug concentrations within cells, resulting in
clearance (r2 = 0.92). Cl determined by noncom- significantly higher azithromycin concentrations in
partmental data analysis was in agreement with tissue than in plasma. The high values for plasma
Cl determined by nonlinear least squares regression clearance (630 mL/min) suggest that the prolonged
(r = 0.99, p < 0.0001). Moxalactam total body clear- half-life is due to extensive uptake and subsequent
ance was best predicted from creatinine clearance release of drug from tissues.
corrected for body surface area. Plasma concentrations of azithromycin decline
in a polyphasic pattern, resulting in an average termi-
Questions (Refer to Table 5-6) nal half-life of 68 hours. With this regimen, Cmin and
1. Calculate the beta half-life of moxalactam in Cmax remained essentially unchanged from day 2
the most renally impaired group. through day 5 of therapy. However, without a loading
2. What indicator is used to predict moxalactam dose, azithromycin Cmin levels required 5–7 days to
clearance in the body? reach desirable plasma levels.
3. What is the beta volume of distribution of The pharmacokinetic parameters of azithromycin
patients in group 3 with normal renal function? in healthy elderly male subjects (65–85 years) were
4. What is the initial volume (V similar to those in young adults. Although higher
i) of moxalactam?
peak drug concentrations (increased by 30%–50%)
Solutions were observed in elderly women, no significant accu-
mulation occurred.
1. Mean beta half-life is 0.693/0.20 = 3.47 hours
in the most renally impaired group.
2. Creatinine is mainly filtered through the kidney, Questions
and creatinine clearance is used as an indicator 1. Do you agree with the following statements for
of renal glomerular filtration rate. Group 3 has a drug that is described by a two-compartment
normal renal function (average creatinine clear- pharmacokinetic model? At peak Ct, the drug
ance = 117.2 mL/min/1.73 m2) (see Chapter 7). is well equilibrated between the plasma and the
3. Beta volume of distribution: Moxalactam tissue compartment, Cp = Ct, and the rates of
clearance in group 3 subjects is 125.9 mL/min. drug diffusion into and from the plasma com-
From Equation 5.38, partment are equal.
2. What happens after peak Ct?Cl
(VD )β = 3. Why is a loading dose used?
β
4. What is Vi? How is this volume related to Vp?
125.9 mL/min × 60min /h 5. What population factors could affect the con-
=
0.37 h−1 centration of azithromycin?
= 20,416 mL or 20.4 L
4. The volume of the plasma compartment, Vp, is Solutions
sometimes referred to as the initial volume. V 1. For a drug that follows a multicompartment
p
ranges from 0.12 to 0.15 L/kg among the three model, the rates of drug diffusion into the tissues
groups and is considerably smaller than the from the plasma and from the tissues into the
steady-state volume of distribution. plasma are equal at peak tissue concentrations.
120 Chapter 5
However, the tissue drug concentration is gener- plasma compartment (also referred to as the ini-
ally not equal to the plasma drug concentration. tial volume by some clinicians), which includes
2. After peak Ct, the rate out of the tissue exceeds some extracellular fluid.
the rate into the tissue, and Ct falls. The decline 3. Etoposide is a drug that follows a two-
of Ct parallels that of Cp, and occurs because compartment model with a beta elimination
distribution equilibrium has occurred. phase. Within the first few minutes after an intra-
3. When drugs are given in a multiple-dose regi- venous bolus dose, most of the drug is distributed
men, a loading dose may be given to achieve in the plasma fluid. Subsequently, the drug will
desired therapeutic drug concentrations more diffuse into tissues and drug uptake may occur.
rapidly (see Chapter 9). Eventually, plasma drug levels will decline due
4. The volume of the plasma compartment, Vp, is to elimination, and some redistribution as etopo-
sometimes referred to as the initial volume. side in tissue diffuses back into the plasma fluid.
5. Age and gender may affect the Cmax level of the The real tissue drug level will differ from
drug. the plasma drug concentration, depending on
the partitioning of drug in tissues and plasma.
PRACTICAL PROBLEM This allows the AUC, the volume distribution
(VD)b, to be calculated, an area that has been
Clinical Example—Etoposide related to toxicities associated with many cancer
Pharmacokinetics chemotherapy agents.
Etoposide is a drug used for the treatment of lung The two-compartment model allows contin-
cancer. Understanding the distribution of etoposide uous monitoring of the amount of the drug pres-
in normal and metastatic tissues is important to avoid ent in and out of the vascular system, including
drug toxicity. Etoposide follows a two-compartment the amount of drug eliminated. This information
model. The (VD)b is 0.28 L/kg, and the beta elimina- is important in pharmacotherapy.
tion half-life is 12.9 hours. Total body clearance is 4. (VD)b may be determined from the total drug
0.25 mL/min/kg. clearance and beta:
Questions Cl = β × (VD )β
1. What is the (VD)b in a 70-kg subject?
(VD)b is also calculated from Equation 5.37 where
2. How is the (VD)b different than the volume of
the plasma fluid, Vp? D
3. Why is the (V (VD )β = (VD )area = 0
∞
D)b useful if it does not represent β [AUC]
a real tissue volume? 0
4. How is (VD)b calculated from plasma time–
This method for (VD)b determination using
concentration profile data for etoposide? Is ∞ ∞
[AUC] is popular because AUC
0 [ ] is easily cal-
(V 0
D)b related to total body clearance?
5. Etopside was recently shown to be a P-gp culated using the trapezoidal rule. Many values
substrate. How may this affect drug tolerance in for apparent volumes of distribution reported in
different patients? the clinical literature are obtained using the area
equation. In general, both volume terms reflect
Solutions extravascular drug distribution. (VD)b appears
1. (VD)b of etoposide in a 70-kg subject is 0.28 L/kg × to be affected by the dynamics of drug disposi-
70 kg = 19.6 L. tion in the beta phase. In clinical practice, many
2. The plasma fluid volume is about 3 L in a potent drugs are not injected by bolus dose.
70-kg subject and is much smaller than (VD)b. Instead, these drugs are infused over a short
The apparent volume of distribution, (VD)b, is interval, making it difficult to obtain accurate
also considerably larger than the volume of the information on the distributive phase. As a result,
Multicompartment Models: Intravenous Bolus Administration 121
many drugs that follow a two-compartment The distributive phase is not a major issue if the distri-
model are approximated using a single compart- bution phase has a short duration (Fig. 5-11) relative to
ment. It should be cautioned that there are sub- the beta phase for chronic dosing. However, from the
stantial deviations in some cases. When in doubt, adverse reaction perspective, injury may occur even
the full equation with all parameters should be with short exposure to sensitive organs or enzyme
applied for comparison. A small bolus (test) dose sites. The observation of where the therapeutically
may be injected to obtain the necessary data if effective levels are relative to the time-concentration
a therapeutic dose injected rapidly causes side profile presents an interesting case below.
effects or discomfort to the subject.
PRACTICAL APPLICATION
Frequently Asked Questions
Drugs A, B, and C are investigated for the treatment of
»»What is the error assumed in a one-compartment
arrhythmia (Fig. 5-12). Drug A has a very short dis-
model compared to a two-compartment or multi-
tributive phase. The short distributive phase does not
compartment model?
distort the overall kinetics when drug A is modeled by
»»What kind of improvement in terms of patient care or the one-compartment model. Simple one-compart-
drug therapy is made using the compartment model? ment model assumptions are often made in practice
and published in the literature for simplicity.
Drugs B and C have different distributive pro-
CLINICAL APPLICATION files. Drug B has a gradual distributive phase fol-
lowed by a slower elimination (beta phase). The
Dosing of Drugs with Different pharmacokinetic profile for drug C shows a longer
Biexponential Profiles and steeper distributive phase. Both drugs are well
Drugs are usually dosed according to clearance described by the two-compartment model.
principles with an objective of achieving a steady- Assuming drugs A and B both have the same
state therapeutic level after multiple dosing (see effective level of 0.1 mg/mL, which drug would you
Chapter 9). The method uses a simple well-stirred prefer for dosing your patient based on the above
one-compartment or noncompartmental approach. plasma profiles provided and assuming that both
100
10
1
0.1
0.01
0.001
0 1 2 3 4 5 6 7 8 9
Time (hours)
FIGURE 5-11 A two-compartment model drug showing a short distributive phase.
The graph shows the log of the drug concentrations (mg/mL) versus time (hours). Drug
mass rapidly distributes within the general circulation and highly vascular organs (central
compartment) and is gradually distributed into other tissues or bound to cellular trans-
porters or proteins.
Drug concentration (mg/mL)
122 Chapter 5
100
10
1
Drug A
0.1
Drug B
0.01
Drug C
0.001
0 1 2 3 4 5 6 7 8 9
Time (hours)
FIGURE 5-12 Plasma drug concentration profile of three drugs after IV bolus injec-
tion. Plasma drug concentration (Cp)–time profiles of three drugs (A, B, C) with different
distributive (α) phase after single IV bolus injection are plotted on a semilogarithmic
scale. Plasma concentrations are in mg/mL (x axis) and time in hours (y axis). Drugs A, B,
and C are each given at a dose of 10 mg/kg to subjects by IV bolus injection, and each
drug has minimum effective concentration of 0.1 mg/mL.
drugs have the same toxic endpoint (as measured by However, for a drug with the therapeutic endpoint (eg,
plasma drug level)? target plasma drug concentration) that lies within the
At what time would you recommend giving a steep initial distributive phase, it is much harder to
second dose for each drug? Please state your support- dose accurately and not overshoot the target endpoint.
ive reasons. Hints: Draw a line at 0.1 mg/mL and see This scenario is particularly true for some drugs used
how it intersects the plasma curve for drugs B and C. in critical care where rapid responses are needed and
If you ignore the distributive phase and dose a IV bolus routes are used more often. Many new bio-
drug based only on clearance or the terminal half- technological drugs are administered intravenously
life, how would this dose affect the duration above because of instability by oral route. The choice of a
minimum effective drug concentration of 0.1 mg/mL proper dose and rate of infusion relative to the half-life
for each drug after an IV bolus dose? of the drug is an important consideration for safe drug
Drug A represents a drug that has limited tissue administration. Individual patients may behave very
distribution with mostly a linear profile and is dosed differently with regard to drug metabolism, drug
by the one-compartment model. Can you recognize transport, and drug efflux in target cell sites. Drug
when the terminal phase starts for drugs B and C? receptors can be genetically expressed differently
Drug A—short distribution, drug B—intermediate making some people more prone to allergic reactions
distribution, drug C—long distribution phase due to and side effects. Simple kinetic half-life determination
transporter or efflux. coupled with a careful review of the patient’s chart by
a pharmacist can greatly improve drug safety.
• Which drug is acceptable to be modeled by a simple
one compartment model?
• When re-dosed (ie, at 0.1 mg/mL), which drug was CLINICAL APPLICATION
equilibrated with the tissue compartment?
Lidocaine is a drug with low toxicity and a long his-
tory of use for anesthetization and for treating ven-
Significance of Distribution Phase tricular arrhythmias. The drug has a steep distributive
With many drugs, the initial phase or transient concen- phase and is biphasic. The risk of adverse effects is
tration is not considered as important as the steady- dose related and increases at intravenous infusion
state “trough” level during long-term drug dosing. rates of above 3 mg/min. Dosage and dose rate are
Drug concentration (mg/mL)
Multicompartment Models: Intravenous Bolus Administration 123
important for proper use (Greenspon et al, 1989). the site of application even if the route is not directly
A case of inappropriate drug use was reported intravenous. It is important to note that for a drug
(Avery, 1998). with a steeply declining elimination plasma profile, it
An overdose of lidocaine was given to a patient is harder to maintain a stable target level with dosing
to anesthetize the airway due to bronchoscopy by an because a small change on the time scale (x axis) can
inexperienced hospital personnel. The patient was greatly alter the drug concentration (y axis). Some
then left unobserved and subsequently developed drugs that have a steep distributive phase may easily
convulsions and cardiopulmonary arrest. He survived cause a side effect in a susceptible subject.
with severe cerebral damage. His lidocaine concen-
tration was 24 mg/mL about 1 hour after initial
administration (a blood concentration over 6 mg/mL
is considered to be toxic). What is the therapeutic Frequently Asked Questions
plasma concentration range? Is the drug highly pro- »»A new experimental drug can be modeled by a two-
tein bound? Is VD sufficiently large to show extra- compartment model. What potential adverse event
vascular distribution? could occur for this drug if given by single IV bolus
A second case of adverse drug reaction (ADR) injection?
based on inappropriate use of this drug due to rapid
»»A new experimental drug can be modeled by a three-
absorption was reported by Pantuck et al (1997). A compartment model. What potential adverse event
40-year-old woman developed seizures after lido- could occur for this drug if given by multiple IV bolus
caine gel 40 mL was injected into the ureter. Vascular injections?
absorption can apparently be very rapid depending on
CHAPTER SUMMARY
Compartment is a term used in pharmacokinetic time. Pharmacokinetic parameters are numerical
models to describe a theoreticized region within the values of model descriptors derived from data that
body in which the drug concentrations are presumed are fitted to a model. These parameters are initially
to be uniformly distributed. estimated and later refined using computing curve-
fitting techniques such as least squares.
• A two-compartment model typically shows a biex-
ponential plasma drug concentration–time curve • Mamillary models are pharmacokinetic models
with an initial distributive phase and a later termi- that are well connected or dynamically exchange
nal phase. drug concentration between compartments. The
• One or more tissue compartments may be present two- and three-compartment models are examples.
in the model depending on the shape of the poly- • Compartment models are useful for estimating
exponential curve representing log plasma drug the mass balance of the drug in the body. As more
concentration versus time. physiological and genetic information is known,
• The central compartment refers to the volume of the model may be rened. Efux and special trans-
the plasma and body regions that are in rapid equi- porters are now known to inuence drug distri-
librium with the plasma. bution and plasma prole. The well-known ABC
• The amount of drug within each compartment transporters (eg, P-gp) are genetically expressed
after a given dose at a given time can be calculated and vary among individuals. These drug trans-
once the model is developed and model parameters porters can be kinetically simulated using trans-
are obtained by data tting. fer constants in a compartment model designed to
mimic drug efux in and out of a cell or compart-
A pharmacokinetic model is a quantitative
ment model.
description of how drug concentrations change over
124 Chapter 5
During curve fitting, simplifying the two- • An important consideration is whether the effec-
compartment model after an IV bolus dose and tive concentration lies near the distributive phase
ignoring the presence of the distributive phase may after the IV bolus dose is given.
cause serious errors unless the beta phase is very
long relative to the distributive phase.
LEARNING QUESTIONS
1. A drug was administered by rapid IV injection 3. Mitenko and Ogilvie (1973) demonstrated
into a 70-kg adult male. Blood samples were that theophylline followed a two-compartment
withdrawn over a 7-hour period and assayed pharmacokinetic model in human subjects.
for intact drug. The results are tabulated below. After administering a single intravenous dose
Using the method of residuals, calculate the (5.6 mg/kg) in nine normal volunteers, these
values for intercepts A and B and slopes a, b, investigators demonstrated that the equation
k, k12, and k21. best describing theophylline kinetics in humans
was as follows:
Time Cp Time Cp
C = 12e−.58t 6
p 18e−0.1 t
+
(hours) (µg/mL) (hours) (µg/mL)
What is the plasma level of the drug 3 hours
0.00 70.0 2.5 14.3
after the IV dose?
0.25 53.8 3.0 12.6 4. A drug has a distribution that can be described
0.50 43.3 4.0 10.5 by a two-compartment open model. If the drug
is given by IV bolus, what is the cause of the
0.75 35.0 5.0 9.0
initial or rapid decline in blood levels (a phase)?
1.00 29.1 6.0 8.0 What is the cause of the slower decline in blood
1.50 21.2 7.0 7.0 levels (b phase)?
5. What does it mean when a drug demonstrates a
2.00 17.0
plasma level–time curve that indicates a three-
2. A 70-kg male subject was given 150 mg of compartment open model? Can this curve be
a drug by IV injection. Blood samples were described by a two-compartment model?
removed and assayed for intact drug. Calculate 6. A drug that follows a multicompartment
the slopes and intercepts of the three phases of pharmacokinetic model is given to a patient
the plasma level–time plot from the results tab- by rapid intravenous injection. Would the drug
ulated below. Give the equation for the curve. concentration in each tissue be the same after
the drug equilibrates with the plasma and all
Time Cp Time Cp the tissues in the body? Explain.
(hours) (μg/mL) (hours) (μg/mL) 7. Park and associates (1983) studied the pharma-
cokinetics of amrinone after a single IV bolus
0.17 36.2 3.0 13.9
injection (75 mg) in 14 healthy adult male
0.33 34.0 4.0 12.0 volunteers. The pharmacokinetics of this drug
0.50 27.0 6.0 8.7 followed a two-compartment open model and
fit the following equation:
0.67 23.0 7.0 7.7
C = Ae−α t
+ Be−βt
1.00 20.8 18.0 3.2 p
where
1.50 17.8 23.0 2.4
A = 4.62 ± 12.0 mg/mL
2.00 16.5 B = 0.64 ± 0.17 mg/mL
Multicompartment Models: Intravenous Bolus Administration 125
a = 8.94 ± 13 h−1 10. The toxicokinetics of colchicine in seven
b = 0.19 ± 0.06 h−1 cases of acute human poisoning was studied
by Rochdi et al (1992). In three further cases,
From these data, calculate:
postmortem tissue concentrations of colchi-
a. The volume of the central compartment
cine were measured. Colchicine follows the
b. The volume of the tissue compartment
two-compartment model with wide distribution
c. The transfer constants k12 and k21 in various tissues. Depending on the time of
d. The elimination rate constant from the cen-
patient admission, two disposition processes
tral compartment
were observed. The first, in three patients,
e. The elimination half-life of amrinone after
admitted early, showed a biexponential plasma
the drug has equilibrated with the tissue
colchicine decrease, with distribution half-
compartment
lives of 30, 45, and 90 minutes. The second, in
8. A drug may be described by a three-compartment
four patients, admitted late, showed a mono-
model involving a central compartment and two
exponential decrease. Plasma terminal half-
peripheral tissue compartments. If you could
lives ranged from 10.6 to 31.7 hours for both
sample the tissue compartments (organs), in
groups.
which organs would you expect to find a drug
11. Postmortem tissue analysis of colchicine
level corresponding to the two theoretical periph-
showed that colchicine accumulated at high
eral tissue compartments?
concentrations in the bone marrow (more than
9. A drug was administered to a patient at 20 mg
600 ng/g), testicle (400 ng/g), spleen (250 ng/g),
by IV bolus dose and the time–plasma drug
kidney (200 ng/g), lung (200 ng/g), heart
concentration is listed below. Use a suitable
(95 ng/g), and brain (125 ng/g). The pharmaco-
compartment model to describe the data and list
kinetic parameters of colchicine are:
the fitted equation and parameters. What are the
Fraction of unchanged colchicine in
statistical criteria used to describe your fit?
urine = 30%
Renal clearance = 13 L/h
Hour mg/L
Total body clearance = 39 L/h
0.20 3.42 Apparent volume of distribution = 21 L/kg
0.40 2.25 a. Why is colchicine described by a mono-
0.60 1.92 exponential profile in some subjects and a
biexponential in others?
0.80 1.80
b. What is the range of distribution of half-life
1.00 1.73 of colchicine in the subjects?
2.00 1.48 c. Which parameter is useful in estimating
tissue drug level at any time?
3.00 1.28
d. Some clinical pharmacists assumed that, at
4.00 1.10 steady state when equilibration is reached
6.00 0.81 between the plasma and the tissue, the tissue
drug concentration would be the same as the
8.00 0.60
plasma. Do you agree?
10.00 0.45 e. Which tissues may be predicted by the tissue
12.00 0.33 compartment?
14.00 0.24
18.00 0.13
20.00 0.10
126 Chapter 5
ANSWERS
Frequently Asked Questions storage (DB = Dt + Dp). Assuming steady state, the
Are “hypothetical” or “mathematical” compart- tissue drug concentration is equal to the plasma
ment models useful in designing dosage regimens in drug concentration, (Cp)ss, and one may determine
the clinical setting? Does “hypothetical” mean “not size of the tissue volume using Dt /(Cp)ss. This vol-
real”? ume is really a “numerical factor” that is used to
describe the relationship of the tissue storage drug
• Mathematical and hypothetical are indeed vague relative to the drug in the blood pool. The sum of the
and uninformative terms. Mathematical equations two volumes is the steady-state volume of distribu-
are developed to calculate how much drug is in the tion. The product of the steady-state concentration,
vascular fluid, as well as outside the vascular fluid (Cp)ss, and the (VD)ss yields the amount of drug in
(ie, extravascular or in the tissue pool). Hypotheti- the body at steady state. The amount of drug in the
cal refers to an unproven model. The assumptions body at steady state is considered vital information
in the compartmental models simply imply that the in dosing drugs clinically. Students should realize
model simulates the mass transfer of drug between that tissue drug concentrations are not predicted
the circulatory system and the tissue pool. The mass by the model. However, plasma drug concentra-
balance of drug moving out of the plasma fluid is tion is fully predictable after any given dose once
described even though we know the tissue pool is the parameters become known. Initial pharmacoki-
not real (the tissue pool represents the virtual tissue netic parameter estimation may be obtained from the
mass that receives drug from the blood). While the literature using comparable age and weight for a
model is a less-than-perfect representation, we can specific individual.
interpret it, knowing its limitations. All pharmaco-
kinetic models need interpretation. We use a model If physiologic models are better than compartment
when there are no simple ways to obtain needed models, why not just use physiologic models?
information. As long as we know the model limi- • A physiologic model is a detailed representation of
tations (ie, that the tissue compartment is not the drug disposition in the body. The model requires
brain or the muscle!) and stay within the bounds of blood flow, extraction ratio, and specific tissue
the model, we can extract useful information from and organ size. This information is not often avail-
it. For example, we may determine the amount of able for the individual. Thus, the less sophisticated
drug that is stored outside the plasma compartment compartment models are used more often.
at any desired time point. After an IV bolus drug
injection, the drug distributes rapidly throughout Since clearance is the term most often used in clini-
the plasma fluid and more slowly into the fluid- cal pharmacy, why is it necessary to know the other
filled tissue spaces. Drug distribution is initially pharmacokinetic parameters?
rapid and confined to a fixed fluid volume known • Clearance is used to calculate the steady-state drug
as the Vp or the initial volume. As drug distribution concentration and to calculate the maintenance
expands into other tissue regions, the volume of the dose. However, clearance alone is not useful in
penetrated spaces increases, until a critical point determining the maximum and minimum drug
(steady state) is obtained when all penetrable tissue concentrations in a multiple-dosing regimen.
regions are equilibrated with the drug. Knowing
that there is heterogenous drug distribution within What is the significance of the apparent volume of
and between tissues, the tissues are grouped into distribution?
compartments to determine the amount of drugs in • Apparent volumes of distribution are not real tis-
them. Mass balance, including drug inside and out- sue volumes, but rather reflect the volume in which
side the vascular pool, accounts for all body drug the drug is contained. For example,
Multicompartment Models: Intravenous Bolus Administration 127
V ion for the curve:
p = initial or plasma volume 2. Equat
Vt = tissue volume C 28e−0.63t 077t
p = +10.5e−0.46t
+14e−0.
(VD)ss = steady-state volume of distribution (most Note: When feathering curves by hand, a
often listed in the literature). minimum of three points should be used to
The steady-state drug concentration multiplied determine the line. Moreover, the rate constants
by (VD)ss yields the amount of drug in the body. and y intercepts may vary according to the indi-
(VD)b is a volume usually determined from area un- vidual’s skill. Therefore, values for Cp should
der the curve (AUC), and differs from (VD)ss some- be checked by substitution of various times for
what in magnitude. (VD)b multiplied by b gives t, using the derived equation. The theoretical
clearance of the drug. curve should fit the observed data.
3. C
t is the error assumed in a one-compartment p = 11.14 mg/mL.
Wha
4. The initial decline in the plasma drug concen-
model compared to a two-compartment or multicom-
tration is due mainly to uptake of drug into
partment model?
tissues. During the initial distribution of drug,
• If the two-compartment model is ignored and the some drug elimination also takes place. After
data are treated as a one-compartment model, the the drug has equilibrated with the tissues, the
estimated values for the pharmacokinetic param- drug declines at a slower rate because of drug
eters are distorted. For example, during the dis- elimination.
tributive phase, the drug declines rapidly according 5. A third compartment may indicate that the
to distribution a half-life, while in the elimina- drug has a slow elimination component. If
tion (terminal) part of the curve, the drug declines the drug is eliminated by a very slow elimina-
according to a b elimination half-life. tion component, then drug accumulation may
occur with multiple drug doses or long IV drug
What kind of improvement in terms of patient care
infusions. Depending on the blood sampling,
or drug therapy is made using the compartment
a third compartment may be missed. However,
model?
some data may fit both a two-compartment and
• Compartment models have been used to develop a three-compartment model. In this case, if the
dosage regimens and pharmacodynamic models. fit for each compartment model is very close
Compartment models have improved the dosing of statistically, the simpler compartment model
drugs such as digoxin, gentamicin, lidocaine, and should be used.
many others. The principal use of compartment 6. Because of the heterogeneity of the tissues,
models in dosing is to simulate a plasma drug con- drug equilibrates into the tissues at different
centration profile based on pharmacokinetic (PK) rates and different drug concentrations are
parameters. This information allows comparison usually observed in the different tissues. The
of PK parameters in patients with only two or three drug concentration in the “tissue” compartment
points to a patient with full profiles using gener- represents an “average” drug concentration and
ated PK parameters. does not represent the drug concentration in
any specific tissue.
Learning Questions 7. C = Ae−α t + Be−βt
p
After substitution,
1. Equation for the curve:
Cp 4.62e−8.94t
= + 0.64e−019t
C 52e–1.39t 18e–0.135tp = +
D0 75,000
k = 0.41 h–1 a. V
k12 = 0.657 h–1 k21 = 0.458 h–1 p = = = 14,259 mL
A + B 4.62 + 0.64
128 Chapter 5
Vp k12 (14,259)(6.52) A (1) = 2.0049 A (2) = 6.0057 (two preexponential
b. Vt = = = 74,375 mL
k21 (1.25) values)
AB(β −α )2
k (1) = 0.15053 k (2) = 7.0217 (two exponential
c. k12 = values)
(A+ B)(Aβ + Bα )
The equation that describes the data is:
(4.62)(064)(0.19−8.94)2
k12 =
(4.62+ 0.64)[(4.62)(0.19) + (0.64)(8.94)] C e−
p 2.0049 0.15053t 6.0057e−7.0217t
= +
k = −1
12 6.52 h The coefficient of correlation = 0.999 (very
good fit).
Aβ + Bα (4.62)(0.19)(4.64)(8.94) The model selection criterion = 11.27 (good
k21 = =
A+ B 4.62 + 0.64 model).
The sum of squared deviations = 9.3 × 10−5
k = −1
21 1.25 h
(there is little deviation between the observed
αβ( data and the theoretical value).
A + B)
d. k =
Aβ + Bα α = 7.0217 h–1, β = 0.15053 h–1.
(8.94)(0.19)(4.62 + 0.64) 10. a. Late-time samples were taken in some
=
(4.62)(0.19) + (0.64)(8.94) patients, yielding data that resulted in a
monoexponential elimination profile. It is
1.35 h−1
=
also possible that a patient’s illness contrib-
8. The tissue compartments may not be sampled utes to impaired drug distribution.
directly to obtain the drug concentration. b. The range of distribution half-lives is
Theoretical drug concentration, Ct, represents 30–45 minutes.
the average concentration in all the tissues c. None. Tissue concentrations are not generally
outside the central compartment. The amount well predicted from the two-compartment
of drug in the tissue, Dt, represents the total model. Only the amount of drug in the tissue
amount of drug outside the central or plasma compartment may be predicted.
compartment. Occasionally Ct may be equal d. No. At steady state, the rate in and the rate
to a particular tissue drug concentration in an out of the tissues are the same, but the drug
organ. However, this Ct may be equivalent by concentrations are not necessarily the same.
chance only. The plasma and each tissue may have differ-
9. The data were analyzed using computer soft- ent drug binding.
ware called RSTRIP, and found to fit a two- e. None. Only the pooled tissue is simulated
compartment model: by the tissue compartment.
REFERENCES
Avery JK: Routine procedure—bad outcome. Tenn Med 91(7): Eichler HG, Müller M: Drug distribution; the forgotten relative in
280–281, 1998. clinical pharmacokinetics. Clin Pharmacokinet 34(2): 95–99,
Butler TC: The distribution of drugs. In LaDu BN, et al (eds). Fun- 1998.
damentals of Drug Metabolism and Disposition. Baltimore, Greenspon AJ, Mohiuddin S, Saksena S, et al: Comparison of
Williams & Wilkins, 1972. intravenous tocainide with intravenous lidocaine for treat-
Eger E: In Papper EM and Kitz JR (eds). Uptake and Distribution ing ventricular arrhythmias. Cardiovasc Rev Rep 10:55–59,
of Anesthetic Agents. New York, McGraw-Hill, 1963, p. 76. 1989.
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Harron DWG: Digoxin pharmacokinetic modelling—10 years Rochdi M, Sabouraud A, Baud FJ, Bismuth C, Scherrmann JM:
later. Int J Pharm 53:181–188, 1989. Toxicokinetics of colchicine in humans: Analysis of tis-
Hill HF, Coda BA, Tanaka A, Schaffer R: Multiple-dose evalua- sue, plasma and urine data in ten cases. Hum Exp Toxicol
tion of intravenous hydromorphone pharmacokinetics in nor- 11(6):510–516, 1992.
mal human subjects. Anesth Analg 72:330–336, 1991. Schentag JJ, Jusko WJ, Plaut ME, Cumbo TJ, Vance JW, Abutyn E:
Jambhekar SS, Breen JP: Two compartment model. Basic Phar- Tissue persistence of gentamicin in man. JAMA 238:327–329,
macokinetics. London, Chicago, Pharmaceutical Press, 2009, 1977.
p. 269. Schumacher GE: Therapeutic Drug Monitoring. Norwalk, CT,
Mitenko PA, Ogilvie RI: Pharmacokinetics of intravenous theoph- Appleton & Lange, 1995.
ylline. Clin Pharmacol Ther 14:509, 1973. Swanson DJ, Reitberg DP, Smith IL, Wels PB, Schentag JJ: Steady-
Müller M: Monitoring tissue drug levels by clinical microdialysis. state moxalactam pharmacokinetics in patients: Noncompart-
Altern Lab Anim 37(suppl 1):57–59, 2009. mental versus two-compartmental analysis. J Pharmacokinet-
Pantuck AJ, Goldsmith JW, Kuriyan JB, Weiss RE: Seizures Biopharm 11(4):337–353, 1983.
after ureteral stone manipulation with lidocaine. J Urol Vallner JJ, Stewart JT, Kotzan JA, Kirsten EB, Honiger IL: Phar-
157(6):2248, 1997. macokinetics and bioavailability of hydromorphone following
Parab PV, Ritschel WA, Coyle DE, Gree RV, Denson DD: Phar- intravenous and oral administration to human subjects. J Clin
macokinetics of hydromorphone after intravenous, peroral and Pharmacol 21:152–156, 1981.
rectal administration to human subjects. Biopharm Drug Dispos Winters ME: Basic Clinical Pharmacokinetics, 3rd ed. Vancouver,
9:187–199, 1988. WA, Applied Therapeutics, 1994, p. 23.
Park GP, Kershner RP, Angellotti J, et al: Oral bioavailability
and intravenous pharmacokinetics of amrinone in humans.
J Pharm Sci 72:817, 1983.
BIBLIOGRAPHY
Dvorchick BH, Vessell ES: Significance of error associated with Mayersohn M, Gibaldi M: Mathematical methods in pharmacoki-
use of the one-compartment formula to calculate clearance of netics, II: Solution of the two compartment open model. Am J
38 drugs. Clin Pharmacol Ther 23:617–623, 1978. Pharm Ed 35:19–28, 1971.
Jusko WJ, Gibaldi M: Effects of change in elimination on various Riegelman S, Loo JCK, Rowland M: Concept of a volume of dis-
parameters of the two-compartment open model. J Pharm Sci tribution and possible errors in evaluation of this parameter.
61:1270–1273, 1972. J Pharm Sci 57:128–133, 1968.
Loughman PM, Sitar DS, Oglivie RI, Neims AH: The two- Riegelman S, Loo JCK, Rowland M: Shortcomings in pharmaco-
compartment open-system kinetic model: A review of its clini- kinetics analysis by conceiving the body to exhibit properties
cal implications and applications. J Pediatr 88:869–873, 1976. of a single compartment. J Pharm Sci 57:117–123, 1968.
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Intravenous Infusion
6 HaiAn Zheng
Chapter Objectives Drugs may be administered to patients by oral, topical, parenteral,
or other various routes of administration. Examples of parenteral
»» Describe the concept of steady
routes of administration include intravenous, subcutaneous, and
state and how it relates to
intramuscular. Intravenous (IV) drug solutions may be either
continuous dosing.
injected as a bolus dose (all at once) or infused slowly through a
»» Determine optimum dosing for vein into the plasma at a constant rate (zero order). The main
an infused drug by calculating advantage for giving a drug by IV infusion is that it allows precise
pharmacokinetic parameters control of plasma drug concentrations to fit the individual needs of
from clinical data. the patient. For drugs with a narrow therapeutic window (eg, hepa-
»» Calculate loading doses to rin), IV infusion maintains an effective constant plasma drug con-
be used with an intravenous centration by eliminating wide fluctuations between the peak
infusion. (maximum) and trough (minimum) plasma drug concentration.
Moreover, the IV infusion of drugs, such as antibiotics, may be
»» Describe the purpose of a given with IV fluids that include electrolytes and nutrients.
loading dose. Furthermore, the duration of drug therapy may be maintained or
»» Compare the pharmacokinetic terminated as needed using IV infusion.
outcomes and clinical The plasma drug concentration−time curve of a drug given by
implications after giving a constant IV infusion is shown in Fig. 6-1. Because no drug was
loading dose for a drug that present in the body at zero time, drug level rises from zero drug
follows a one-compartment concentration and gradually becomes constant when a plateau or
model to a drug that follows a steady-state drug concentration is reached. At steady state, the rate
two-compartment model. of drug leaving the body is equal to the rate of drug (infusion rate)
entering the body. Therefore, at steady state, the rate of change in
the plasma drug concentration dCp/dt = 0, and
Rate of drug input = rate of drug output
(infusion rate) (elimination rate)
Based on this simple mass balance relationship, a pharmaco-
kinetic equation for infusion may be derived depending on whether
the drug follows one- or two-compartment kinetics.
ONE-COMPARTMENT MODEL DRUGS
The pharmacokinetics of a drug given by constant IV infusion fol-
lows a zero-order input process in which the drug is directly
infused into the systemic blood circulation. For most drugs,
131
132 Chapter 6
elimination of drug from the plasma is a first-order Steady-State Drug Concentration (Css) and
process. Therefore, in this one-compartment model, Time Needed to Reach Css
the infused drug follows zero-order input and first- Once the steady state is reached, the rate of drug
order output. The change in the amount of drug in leaving the body is equal to the rate of drug entering
the body at any time (dDB/dt) during the infusion is the body (infusion rate). In other words, there is no
the rate of input minus the rate of output.
net change in the amount of drug in the body, DB, as
dD
B a function of time during steady state. Drug elimina-
= R − kD (6.1)
dt B
tion occurs according to first-order elimination
where DB is the amount of drug in the body, R is the kinetics. Whenever the infusion stops, either before
infusion rate (zero order), and k is the elimination or after steady state is reached, the drug concentra-
rate constant (first order). tion always declines according to first-order kinetics.
Integration of Equation 6.1 and substitution of The slope of the elimination curve equals to −k/2.3
DB = CpVD gives: (Fig. 6-2). Even if the infusion is stopped before
R steady state is reached, the slope of the elimination
C (1 e−kt
p = − ) (6.2)
VDk
curve remains the same (Fig. 6-2B).
Mathematically, the time to reach true steady-
Equation 6.2 gives the plasma drug concentration at state drug concentrations, Css, would take an infinite
any time during the IV infusion, where t is the time time. The time required to reach the steady-state
for infusion. The graph for Equation 6.2 appears in drug concentration in the plasma is dependent on the
Figs. 6-1 and 6-2. As the drug is infused, the value elimination rate constant of the drug for a constant
for certain time (t) increases in Equation 6.2. At infi- volume of distribution, as shown in Equation 6.4.
nite time t = ∞, e−kt approaches zero, and Equation 6.2 Because drug elimination is exponential (first order),
reduces to Equation 6.4, as the steady-state drug the plasma drug concentration becomes asymptotic
concentration (Css). to the theoretical steady-state plasma drug concen-
R
tration. For zero-order elimination processes, if rate
Cp = (1− e−∞ ) (6.3)
VDk of input is greater than rate of elimination, plasma
R drug concentrations will keep increasing and no
Css = (6.4)
V steady state will be reached. This is a potentially
Dk
dangerous situation that will occur when saturation
The body clearance, Cl, is equal to VDk, therefore: of metabolic process occurs.
R R
Css = = (6.5)
VDk Cl
80
Steady state A
B
60
Steady-state level
40
20
0
0 4 8 12 16 20 24 28 32 36
Time (hours)
FIGURE 6-2 Plasma drug concentration−time profiles
Time
after IV infusion. IV infusion is stopped at steady state (A) or prior
FIGURE 6-1 Plasma level−time curve for constant to steady state (B). In both cases, plasma drug concentrations
IV infusion. decline exponentially (first order) according to a similar slope.
Plasma level
Plasma drug level
Intravenous Infusion 133
In clinical practice, a plasma drug concentration
2R
prior to, but asymptotically approaching, the theo-
retical steady state is considered the steady-state
plasma drug concentration (Css). In a constant IV R
infusion, drug solution is infused at a constant or
zero-order rate, R. During the IV infusion, the
plasma drug concentration increases and the rate of
Time
drug elimination increases because rate of elimina-
tion is concentration dependent (ie, rate of drug FIGURE 6-3 Plasma level−time curve for IV infusions
elimination = kCp). Cp keeps increasing until steady given at rates of R and 2R, respectively.
state is reached at which time the rate of drug input
(IV infusion rate) equals rate of drug output (elimi-
nation rate). The resulting plasma drug concentra-
tion at steady state (Css) is related to the rate of An increase in the infusion rate will not shorten
infusion and inversely related to the body clearance the time to reach the steady-state drug concentration.
of the drug as shown in Equation 6.5. If the drug is given at a more rapid infusion rate, a
In clinical practice, the drug activity will be higher steady-state drug level will be obtained, but
observed when the drug concentration is close to the time to reach steady state is the same (Fig. 6-3).
the desired plasma drug concentration, which is This equation may also be obtained with the fol-
usually the target or desired steady-state drug con- lowing approach. At steady state, the rate of infu-
centration. For therapeutic purposes, the time for sion equals the rate of elimination. Therefore, the
the plasma drug concentration to reach more than rate of change in the plasma drug concentration is
95% of the steady-state drug concentration in the equal to zero.
plasma is often estimated. The time to reach 90%,
95%, and 99% of the steady-state drug concentra-
tion, Css, may be calculated. As detailed in dCp
= 0
Table 6-1, after IV infusion of the drug for 5 half- dt
lives, the plasma drug concentration will be
between 95% (4.32 t1/2) and 99% (6.65 t1/2) of the dCp R
= − kC
dt V p = 0
steady-state drug concentration. Thus, the time for a D
drug whose t1/2 is 6 hours to reach 95% of the steady-
state plasma drug concentration will be approxi- (Ratein )− (Rateout ) = 0
mately 5 t1/2, or 5 × 6 hours = 30 hours. The calculation
of the values in Table 6-1 is given in the example R
= kC
that follows. V p
D
R
C = (6.6)
ss
TABLE 6-1 Number of t1/2 to Reach a VDk
Fraction of Css
Percent of Css Reacheda Number of Half-Lives
Equation 6.6 is the same as Equation 6.5 that
90 3.32 shows that the steady-state concentration (Css) is
95 4.32 dependent on the volume of distribution, the elimi-
nation rate constant, and the infusion rate. Altering
99 6.65
any one of these factors can affect steady-state
aCss is the steady-state drug concentration in plasma. concentration.
Plasma level
134 Chapter 6
EXAMPLES »» » Take the natural logarithm on both sides:
−kt = ln 0.01
1. An antibiotic has a volume of distribution of 10 L ln0.01 −4.61 4.61
t
and a k of 0.2 h−1. A steady-state plasma concen- 99%ss = = =
−k −k k
tration of 10 μg/mL is desired. The infusion rate
Substituting (0.693/t1/2) for k,
needed to maintain this concentration can be
determined as follows: 4.61 4.61
t99%ss = = t
(0.693/t ) 1/2
Equation 6.6 can be rewritten as 1/2 0.693
R = t99%ss = 6.65t
C 1/2
ssVDk
= (10 µg/mL)(10)(1000 mL)(0.2 h−1 Notice that in the equation directly above,
)
the time needed to reach steady state is not
=20 mg/h dependent on the rate of infusion, but only
on the elimination half-life. Using similar cal-
Assume the patient has a uremic condi-
culations, the time needed to reach any per-
tion and the elimination rate constant has
centage of the steady-state drug concentra-
decreased to 0.1 h−1. To maintain the steady-
tion may be obtained (Table 6-1).
state concentration of 10 μg/mL, we must
IV infusion may be used to determine
determine a new rate of infusion as follows:
total body clearance if the infusion rate and
R = (10 mg/mL)(10)(1000 mL)(0.1 h−1) = 10 mg/h the steady-state level are known, as with
Equation 6.6 repeated here:
When the elimination rate constant decreases,
then the infusion rate must decrease propor- R
Css = (6.6)
tionately to maintain the same Css. However, VDk
because the elimination rate constant is R
smaller (ie, the elimination t1/2 is longer), the VDk =
Css
time to reach Css will be longer.
Because total body clearance, ClT, is equal
2. An infinitely long period of time is needed to
to VDk,
reach steady-state drug levels. However, in
practice it is quite acceptable to reach 99% Css R
ClT = (6.7)
(ie, 99% steady-state level). Using Equation 6.6, Css
we know that the steady-state level is
3. A patient was given an antibiotic (t1/2 = 6 hours)
R
C = by constant IV infusion at a rate of 2 mg/h. At
ss
VDk the end of 2 days, the serum drug concentra-
and 99% steady-state level would be equal to tion was 10 mg/L. Calculate the total body
R clearance ClT for this antibiotic.
99%
VDk
Solution
Substituting into Equation 6.2 for Cp, we can
find out the time needed to reach steady state The total body clearance may be estimated from
by solving for t. Equation 6.7. The serum sample was taken after
2 days or 48 hours of infusion, which time repre-
R R
99% (1 e−kt
= − ) sents 8 × t1/2; therefore, this serum drug concen-
VDk VDk
tration approximates the Css.
99% 1 e−kt
= − R 2 mg/h
ClT = = =200 mL/h
e−kt
=1% Css 10 mg/L
Intravenous Infusion 135
Frequently Asked Questions EXAMPLE »» »
»»How does one determine whether a patient has
1. An antibiotic has an elimination half-life of
reached steady state during an IV infusion?
3−6 hours in the general population. A patient
»»What is the clinical relevance of steady state? was given an IV infusion of an antibiotic at an
»»How can the steady-state drug concentration be infusion rate of 15 mg/h. Blood samples were
achieved more quickly? taken at 8 and 24 hours, and plasma drug con-
centrations were 5.5 and 6.5 mg/L, respectively.
Estimate the elimination half-life of the drug in
this patient.
INFUSION METHOD FOR
Solution
CALCULATING PATIENT
Because the second plasma sample was taken
ELIMINATION HALF-LIFE
at 24 hours, or 24/6 = 4 half-lives after infusion,
The Cp-versus-time relationship that occurs during the plasma drug concentration in this sample is
an IV infusion (Equation 6.2) may be used to calcu- approaching 95% of the true plasma steady-state
late k, or indirectly the elimination half-life of the drug concentration, assuming the extreme case of
drug in a patient. Some information about the elimi- t1/2 = 6 hours.
nation half-life of the drug in the population must be By substitution into Equation 6.8:
known, and one or two plasma samples must be 6 − .5 (8)
lo .5 5 k
g = −
taken at a known time after infusion. Knowing the 6.5 2.3
half-life in the general population helps determine if
k = 0.234 h−1
the sample is taken at steady state in the patient. To
simplify calculation, Equation 6.2 is arranged to t1/2 = 0.693/0.234 =2.96 hours
solve for k:
The elimination half-life calculated in this
R
manner is not as accurate as the calculation of t1/2
C (1 e−kt
p = − ) (6.2)
VDk using multiple plasma drug concentration time
points after a single IV bolus dose or after stop-
Since
ping the IV infusion. However, this method may
R be sufficient in clinical practice. As the second
Css =
VDk blood sample is taken closer to the time for steady
state, the accuracy of this method improves. At the
substituting into Equation 6.2: 30th hour, for example, the plasma concentration
would be 99% of the true steady-state value (cor-
C (1 −k
p C t
= ss − e )
responding to 30/6 or 5 elimination half-lives), and
Rearranging and taking the log on both sides: less error would result in applying Equation 6.8.
When Equation 6.8 was used in the example
C above to calculate the drug t1/2 of the patient, the
ss −C
p kt
log = − and
Css 2.3 second plasma drug concentration was assumed to
be the theoretical Css. As demonstrated below, when
−2.3 Css −C k and the corresponding values are substituted,
= p
k log (6.8)
t Css Css −5.5 (0.234)(8)
log = −
Css 2.3
where Cp is the plasma drug concentration taken at
time t, and Css is the approximate steady-state plasma Css −5.5
= 0.157
drug concentration in the patient. Css
136 Chapter 6
LOADING DOSE PLUS IV INFUSION—
Css = 6.5 mg/L ONE-COMPARTMENT MODEL
(Note that Css is in fact the same as the concentra- The loading dose DL, or initial bolus dose of a drug,
tion at 24 hours in the example above.) is used to obtain desired concentrations as rapidly as
possible. The concentration of drug in the body for a
one-compartment model after an IV bolus dose is
In practice, before starting an IV infusion, an
described by
appropriate infusion rate (R) is generally calculated
from Equation 6.8 using literature values for Css, k, D
C C e−kt L e−kt
= = (6.9)
and VD or ClT. Two plasma samples are taken and the 1 0 V
D
sampling times recorded. The second sample should
be taken near the theoretical time for steady state. and concentration by infusion at the rate R is
Equation 6.8 would then be used to calculate a k and
then t1/2. If the elimination half-life calculated con- R
C (1 e−kt
firms that the second sample was taken at steady 2 = − ) (6.10)
VDk
state, the plasma concentration is simply assumed as
the steady-state concentration and a new infusion
Assume that an IV bolus dose DL of the drug is given
rate may be calculated.
and that an IV infusion is started at the same time.
The total concentration Cp at t hours after the start of
EXAMPLE »» » infusion would be equal to C1 + C2 due to the sum
contributions of bolus and infusion, or
1. If the desired therapeutic plasma concentration
is 8 mg/L for the above patient (Example 1),
Cp =C1 +C2
what is the suitable infusion rate for the patient?
D R
Solution C = L
e−kt
p + (1− e−kt )
VD VDk
From Example 1, the trial infusion rate was 15 mg/h.
Assuming the second blood sample is the steady- D R R
= L
e−kt + − e−kt
state level, 6.5 mg/mL, the clearance of the patient is VD VDk VDk
Css = R/Cl R D R
= + L
e−kt − e−kt (6.11)
Cl = R/C VDk VD VDk
ss =15/6.5=2.31 L/h
The new infusion rate should be
R = Css ×Cl = 8×2.31=18.48 mg/h Let the loading dose (DL) equal the amount of drug
in the body at steady state
In this example, the t1/2 of this patient is a lit-
tle shorter, about 3 hours compared to 3−6 hours DL =CssVD
reported for the general population. Therefore, the
infusion rate should be a little greater in order to
From Equation 6.4, CssVD = R/k. Therefore,
maintain the desired steady-state level of 15 mg/L.
Equation 6.7 or the steady-state clearance
method has been applied to the clinical infusion DL = R/k (6.12)
of drugs. The method was regarded as simple and
accurate compared with other methods, including Substituting DL = R/k in Equation 6.11 makes the
the two-point method (Hurley and McNeil, 1988). expression in parentheses cancel out. Equation 6.11
reduces to Equation 6.13, which is the same
Intravenous Infusion 137
expression for Css or steady-state plasma concentra- By differentiating this equation at steady state, we
tions (Equation 6.14 is identical to Equation 6.6): obtain:
R dC
p −D k
Cp = (6.13) Rk
= 0 = L
e−kt + e−kt (6.16)
VDk dt VD VDk
R
Css = (6.14) −D
0 = − Lk R
e kt
VDk
+
VD VD
Therefore, if an IV loading dose of R/k is given, fol-
DLk R
lowed by an IV infusion, steady-state plasma drug = (6.17)
V
D VD
concentrations are obtained immediately and main-
tained (Fig. 6-4). In this situation, steady state is R
DL = = loading dose
also achieved in a one-compartment model, since the k
rate in = rate out (R = dDB/dt). In order to maintain instant steady-state level
The loading dose needed to get immediate ([dCp/dt] = 0), the loading dose should be equal to R/k.
steady-state drug levels can also be found by the fol- For a one-compartment drug, if the DL and infu-
lowing approach. sion rate are calculated such that C0 and Css are the
Loading dose equation: same and both DL and infusion are started concur-
D rently, then steady state and C
L ss will be achieved
C1 e−kt
=
V immediately after the loading dose is administered
D
(Fig. 6-4). Similarly, in Fig. 6-5, curve b shows the
Infusion equation:
blood level after a single loading dose of R/k plus
R
C infusion from which the concentration desired at
2 (1 e−kt
= − )
VDk steady state is obtained. If the DL is not equal to R/k,
Adding up the two equations yields Equation 6.15, then steady state will not occur immediately. If the
an equation describing simultaneous infusion after a loading dose given is larger than R/k, the plasma drug
loading dose. concentration takes longer to decline to the concentra-
D tion desired at steady state (curve a). If the loading
L R
C e−kt t
p = + (1− e−k ) (6.15)
VD VDk
dose is lower than R/k, the plasma drug concentrations
will increase slowly to desired drug levels (curve c),
but more quickly than without any loading dose.
IV infusion plus loading dose combined
Steady-
state a
IV infusion level
b
IV bolus loading dose
c
Time (hours)
d
FIGURE 6-4 IV infusion with loading dose DL. The loading
dose is given by IV bolus injection at the start of the infusion.
Plasma drug concentrations decline exponentially after DL
Time
whereas they increase exponentially during the infusion. The
resulting plasma drug concentration−time curve is a straight FIGURE 6-5 Intravenous infusion with loading doses a, b,
line due to the summation of the two curves. and c. Curve d represents an IV infusion without a loading dose.
Plasma drug concentration (µg/mL)
Plasma level
138 Chapter 6
Another method for the calculation of loading 3. Calculate the drug concentration in the blood
dose DL is based on knowledge of the desired steady- after infusion has been stopped.
state drug concentration Css and the apparent volume of
distribution VD for the drug, as shown in Equation 6.18. Solution
This concentration can be calculated in two
D ( 8
L =C .
ssV
6 1 )
D parts (see Fig. 6-2A). First, calculate the con-
For many drugs, the desired Css is reported in the centration of drug during infusion, and second,
literature as the effective therapeutic drug concentra- calculate the concentration after the stop of
tion. The VD and the elimination half-life are also the infusion, C. Then use the IV bolus dose
available for these drugs. equation (C = C0e
−kt) for calculations for any
further point in time. For convenience, the two
equations can be combined as follows:
PRACTICE PROBLEMS
R
C −
p = (1 e−kb
− )e k (t−b) (6.19)
V
1. A physician wants to administer an anesthetic Dk
agent at a rate of 2 mg/h by IV infusion. The where b = length of time of infusion period, t =
elimination rate constant is 0.1 h−1 and the volume total time (infusion and postinfusion), and t − b =
of distribution (one compartment) is 10 L. How length of time after infusion has stopped. Here,
much is the drug plasma concentration at the we assume no bolus loading dose was given.
steady state? What loading dose should be recom-
4. A patient was infused for 6 hours with a drug
mended to reach steady state immediately?
(k = 0.01 h−1; VD = 10 L) at a rate of 2 mg/h.
Solution What is the concentration of the drug in the
body 2 hours after cessation of the infusion?
R 2000
Css = = = 2 µg/mL
V 3
Dk (10×10 )(0.1) Solution
Using Equation 6.19,
To reach Css instantly,
2000
R 2 mg/h Cp = (1− e−0.01(6) )e−0.01(8−6)
D (0.01)(10,000)
L = = DL = 20 mg
k 0.1/h
C
2. What is the concentration of a drug at 6 hours p =1.14 µg/mL
after infusion administration at 2 mg/h, with an
Alternatively, when infusion stops, Cp′ is
initial loading dose of 10 mg (the drug has a t1/2 calculated:
of 3 hours and a volume of distribution of 10 L)?
Solution R
Cp′ (1 −kt
= − e )
VDk
0.693
k = 2000
3 h C′ −
p = (1− e 0.01(6) )
0.01×10,000
D
= L R
C e−kt
p + (1− e−kt ) C C e−0.01(2)
=
V p′
D VDk
10,000 C =1.14 µg/mL
C = (e−(0.693/3)(6)
p )
10,000
The two approaches should give the same answer.
2000
+ (1− e−(0.693/3)(6) ) 5. An adult male asthmatic patient (78 kg, 48 years
(10,000)(0.693/3)
old) with a history of heavy smoking was given
Cp = 0.90 µg/mL an IV infusion of aminophylline at a rate of
Intravenous Infusion 139
0.75 mg/kg/h. A loading dose of 6 mg/kg was (equivalent to 0.75 × 0.8 = 0.6 mg theoph-
given by IV bolus injection just prior to the ylline) per kg was given to the patient, the
start of the infusion. Two hours after the start plasma theophylline concentration of 5.8 mg/L
of the IV infusion, the plasma theophylline con- is the steady-state Css. Total clearance may be
centration was measured and found to contain estimated by
5.8 mg/mL of theophylline. The apparent VD
for theophylline is 0.45 L/kg. (Aminophylline R (0.6 mg/h/kg)(78 kg)
Cl
is the ethylenediamine salt of theophylline and T = =
Css,present 5.8 mg/L
contains 80% of theophylline base.)
Because the patient was responding poorly ClT = 8.07 L/h or 1.72 mL/min/kg
to the aminophylline therapy, the physician
wanted to increase the plasma theophylline
The usual ClT for adult, nonsmoking patients
concentration in the patient to 10 mg/mL. What
with uncomplicated asthma is approximately
dosage recommendation would you give the
0.65 mL/min/kg. Heavy smoking is known to
physician? Would you recommend another
increase ClT for theophylline.
loading dose?
The new IV infusion rate, R′ in terms of
Solution theophylline, is calculated by
If no loading dose is given and the IV infu- R′ = Css,desired ClT
sion rate is increased, the time to reach R′ = 10 mg/L × 8.07 L/h = 80.7 mg/h or
steady-state plasma drug concentrations 1.03 mg/h/kg of theophylline, which is equiva-
will be about 4 to 5 t1/2 to reach 95% of Css. lent to 1.29 mg/h/kg of aminophylline.
Therefore, a second loading dose should be 6. An adult male patient (43 years, 80 kg) is to be
recommended to rapidly increase the plasma given an antibiotic by IV infusion. According to
theophylline concentration to 10 mg/mL. The the literature, the antibiotic has an elimination
infusion rate must also be increased to main- t1/2 of 2 hours and VD of 1.25 L/kg, and is effec-
tain this desired Css. tive at a plasma drug concentration of 14 mg/L.
The calculation of loading dose DL must The drug is supplied in 5-mL ampuls contain-
consider the present plasma theophylline ing 150 mg/mL.
concentration. a. Recommend a starting infusion rate in milli-
grams per hour and liters per hour.
VD (Cp,desired −Cp,present )
DL = (6.20)
(S)(F) Solution
where S is the salt form of the drug and F is Assume the effective plasma drug concentra-
the fraction of drug bioavailable. For amino- tion is the target drug concentration or Css.
phylline S is equal to 0.80 and for an IV bolus
R =C
injection F is equal to 1. sskVD
= (14 mg/L)(0.693/2 h)(1.5 L/kg)(80 kg)
(0.45 L/kg)(78 kg)(10−5.8 mg/L)
DL =
(0.8)(1) = 485.1 mg/h
DL =184 mg aminophylline
Because the drug is supplied at a concentration
of 150 mg/mL,
The maintenance IV infusion rate may be
calculated after estimation of the patient’s (485.1 mg)(mL/150 mg) = 3.23 mL
clearance, ClT. Because a loading dose and
an IV infusion of 0.75 mg/h aminophylline Thus, R = 3.23 mL/h.
140 Chapter 6
b. Blood samples were taken from the patient d. After reviewing the pharmacokinetics of the
at 12, 16, and 24 hours after the start of the antibiotic in this patient, should the infusion
infusion. Plasma drug concentrations were rate for the antibiotic be changed?
as shown below:
Solution
To properly decide whether the infusion rate
t (hours) Cp (mg/L)
should be changed, the clinical pharmacist must
12 16.1 consider the pharmacodynamics and toxicity of
16 16.3 the drug. Assuming the drug has a wide thera-
peutic window and shows no sign of adverse
24 16.5
drug toxicity, the infusion rate of 485.1 mg/h,
calculated according to pharmacokinetic litera-
From these additional data, calculate the ture values for the drug, appears to be correct.
total body clearance ClT for the drug in this
R
patient. Cl V t
Cp (1 −( / )
= −e D )
Cl
Solution
Because the plasma drug concentrations at 12, ESTIMATION OF DRUG CLEARANCE
16, and 24 hours were similar, steady state has
AND VD FROM INFUSION DATA
essentially been reached. (Note: The continu-
ous increase in plasma drug concentrations The plasma concentration of a drug during constant
could be caused by drug accumulation due to a infusion was described in terms of volume of distri-
second tissue compartment, or could be due to bution VD and elimination constant k in Equation 6.2.
variation in the drug assay.) Assuming a Css of Alternatively, the equation may be described in terms
16.3 mg/mL, ClT is calculated. of clearance by substituting for k into Equation 6.2
with k = Cl/V
R 485.1 mg/h D:
ClT = = = 29.8 L/h
Css 16.3 mg/L R
(1 −(Cl /V t
C e D )
p = − ) (6.21)
Cl
c. From the above data, estimate the elimi- The drug concentration in this physiologic
nation half-life for the antibiotics in this model is described in terms of volume of distribution
patient. VD and total body clearance Cl. The independent
Solution parameters are clearance and volume of distribution;
k is viewed as a dependent variable that depends on
Generally, the apparent volume of distribution
Cl and VD. In this model, the time for steady state
(VD) is less variable than t1/2. Assuming that
and the resulting steady-state concentration will be
the literature value for VD is 1.25 L/kg, then t1/2 dependent on both clearance and volume of distribu-
may be estimated from the ClT.
tion. When a constant volume of distribution is evi-
Cl dent, the time for steady state is then inversely
T 29.9 L/h
k 0.299 h−1
= = =
VD (1.25 L/kg)(80 kg) related to clearance. Thus, drugs with small clear-
ance will take a long time to reach steady state.
0.693 Although this newer approach is preferred by some
t1/2 = = 2.32 h
0.299 h−1
clinical pharmacists, the alternative approach to
parameter estimation was known for some time in
Thus the t1/2 for the antibiotic in this patient is classical pharmacokinetics. Equation 6.21 has been
2.32 hours, which is in good agreement with applied in population pharmacokinetics to estimate
the literature value of 2 hours. both Cl and VD in individual patients with one or
Intravenous Infusion 141
more data points. However, clearance in patients By rearranging this equation, the infusion rate for a
may differ greatly from subjects in the population, desired steady-state plasma drug concentration may
especially subjects with different renal functions. be calculated.
Unfortunately, the plasma samples taken at time
R =CssVpk (6.24)
equivalent to less than 1 half-life after infusion was
started may not be very discriminating due to the
small change in the drug concentration. Blood sam- Loading Dose for Two-Compartment
ples taken at 3−4 half-lives later are much more Model Drugs
reflective of their difference in clearance. Drugs with long half-lives require a loading dose to
more rapidly attain steady-state plasma drug levels. It
is clinically desirable to achieve rapid therapeutic
INTRAVENOUS INFUSION OF TWO- drug levels by using a loading dose. However, for a
COMPARTMENT MODEL DRUGS drug that follows the two-compartment pharmacoki-
netic model, the drug distributes slowly into extravas-
Many drugs given by IV infusion follow two- cular tissues (compartment 2). Thus, drug equilibrium
compartment kinetics. For example, the respective is not immediate. The plasma drug concentration of a
distributions of theophylline and lidocaine in humans drug that follows a two-compartment model after
are described by the two-compartment open model. various loading doses is shown in Fig. 6-6. If a load-
With two-compartment-model drugs, IV infusion ing dose is given too rapidly, the drug may initially
requires a distribution and equilibration of the drug give excessively high concentrations in the plasma
before a stable blood level is reached. During a con- (central compartment), which then decreases as drug
stant IV infusion, drug in the tissue compartment is equilibrium is reached (Fig. 6-6). It is not possible to
in distribution equilibrium with the plasma; thus, maintain an instantaneous, stable steady-state blood
constant Css levels also result in constant drug con- level for a two-compartment model drug with a zero-
centrations in the tissue, that is, no net change in the order rate of infusion. Therefore, a loading dose
amount of drug in the tissue occurs during steady produces an initial blood level either slightly higher
state. Although some clinicians assume that tissue or lower than the steady-state blood level. To over-
and plasma concentrations are equal when fully come this problem, several IV bolus injections given
equilibrated, kinetic models only predict that the as short intermittent IV infusions may be used as a
rates of drug transfer into and out of the compart-
ments are equal at steady state. In other words, drug
concentrations in the tissue are also constant, but
may differ from plasma concentrations.
The time needed to reach a steady-state blood d
level depends entirely on the distribution half-life of
c Css
the drug. The equation describing plasma drug con-
b
centration as a function of time is as follows:
R k − b − a − k
Cp = 1− −
− e at e−bt
P −
(6.22) a
V k a b a b
where a and b are hybrid rate constants and R is the rate
Time
of infusion. At steady state (ie, t = ∞), Equation 6.22
reduces to FIGURE 6-6 Plasma drug level after various loading
doses and rates of infusion for a drug that follows a two-
R compartment model: a, no loading dose; b, loading dose = R/k
Css = (6.23) (rapid infusion); c, loading dose = R/b (slow infusion); and d,
Vpk loading dose = R/b (rapid infusion).
Plasma level
142 Chapter 6
method for administering a loading dose to the patient which reduces to
(see Chapter 9).
k
(VD )
12
ss =Vp + V (6 30)
k p .
Apparent Volume of Distribution at Steady 21
State, Two-Compartment Model In practice, Equation 6.30 is used to calculate
After administration of any drug that follows two- (VD)ss. The (VD)ss is a function of the transfer con-
compartment kinetics, plasma drug levels will decline stants, k12 and k21, which represent the rate constants
due to elimination, and some redistribution will occur of drug going into and out of the tissue compartment,
as drug in tissue diffuses back into the plasma fluid. respectively. The magnitude of (VD)ss is dependent
The volume of distribution at steady state, (V on the hemodynamic factors responsible for drug
D)ss, is the
“hypothetical space” in which the drug is assumed to distribution and on the physical properties of the
be distributed. The product of the plasma drug concen- drug, properties which, in turn, determine the rela-
tration with (VD)ss will give the total amount of drug in tive amount of intra- and extravascular drug.
the body at that time period, such that (Cp)ss × (VD) Another volume term used in two-compartment
ss =
amount of drug in the body at steady state. At steady- modeling is (VD)b (see Chapter 5). (VD)b is often
state conditions, the rate of drug entry into the tissue calculated from total body clearance divided by b,
compartment from the central compartment is equal to unlike the steady-state volume of distribution, (VD)ss,
the rate of drug exit from the tissue compartment into (VD)b is influenced by drug elimination in the beta
the central compartment. These rates of drug transfer “b ” phase. Reduced drug clearance from the body
are described by the following expressions: may increase AUC, such that (VD)b is either reduced
or unchanged depending on the value of b as shown
Dtk21 = Dpk12 (6.25) in Equation 5.37 (see Chapter 5):
k12Dp D0
D V
t = (6.26) ( D )β = (VD )area = (5.37)
b ∞
k21 [AUC]0
Because the amount of drug in the central compart- Unlike (VD)b, (VD)ss is not affected by changes in
ment Dp is equal to VpCp, by substitution in the above drug elimination. (VD)ss reflects the true distributional
equation, volume occupied by the plasma and the tissue pool when
steady state is reached. Although this volume is not use-
k12CpVp
Dt = (6.27) ful in calculating the amount of drug in the body during
k21 pre-steady state, (VD)ss multiplied by the steady-state
The total amount of drug in the body at steady plasma drug concentration, Css, yields the amount of
state is equal to the sum of the amount of drug in the drug in the body. This volume is often used to determine
tissue compartment, Dt, and the amount of drug in the loading dose necessary to upload the body to a desired
the central compartment, Dp. Therefore, the apparent plasma drug concentration. As shown by Equation 6.30,
volume of drug at steady state (VD)ss may be calcu- (VD)ss is several times greater than Vp, which represents
lated by dividing the total amount of drug in the the volume of the plasma compartment, but differs
body by the concentration of drug in the central somewhat in value depending on the transfer constants.
compartment at steady state:
Dp +Dt
(VD )ss = (6.28) PRACTICAL FOCUS
Cp
Questions
Substituting Equation 6.27 into Equation 6.28, and
expressing Dp as VpCp, a more useful equation for 1. Do you agree with the following statements for
the calculation of (VD)ss is obtained: a drug that is described by a two-compartment
pharmacokinetic model? At steady state, the drug
C is well equilibrated between the plasma and the
pVp+ k12VpCp /k21
(V (6 2
D ) . 9)
ss =
Cp tissue compartment, Cp = Ct, and the rates of drug
Intravenous Infusion 143
diffusion into and from the plasma compartment biopharmaceutic studies, the factors that account
are equal. for high tissue concentrations include diffusion
2. Azithromycin may be described by a plasma constant, lipid solubility, and tissue binding to
and a tissue compartment model (refer to cell components. A ratio measuring the relative
Chapter 5). The steady-state volume of distribu- drug concentration in tissue and plasma is the
tion is much larger than the initial volume, Vi, partition coefficient, which is helpful in predict-
or the original plasma volume, Vp, of the central ing the distribution of a drug into tissues. Ulti-
compartment. Why? mately, studies of tissue drug distribution using
3. “Rapid distribution of azithromycin into cells radiolabeled drug are much more useful.
causes higher concentration in the tissues than in The real tissue drug level will differ from
the plasma. …” Does this statement conflict with the plasma drug concentration depending on
the steady-state concept? Why is the loading dose the partitioning of drug in tissues and plasma.
often calculated using the (VD)ss instead of Vp. (VD)b is a volume of distribution often calculated
4. Why is a loading dose used? because it is easier to calculate than (VD)ss. This
volume of distribution, (VD)b, allows the area
under the curve to be calculated, an area which
Solutions
has been related to toxicities associated with
1. For a drug that follows a multiple-compartment many cancer chemotherapy agents. Many values
model, the rates of drug diffusion into the tis- for apparent volumes of distribution reported
sues from the plasma and from the tissues into in the clinical literature are obtained using the
the plasma are equal at steady state. However, area equation. Some early pharmacokinetic
the tissue drug concentration is generally not literature only includes the steady-state volume
equal to the plasma drug concentration. of distribution, which approximates the (VD)b
2. When plasma drug concentration data are used but is substantially smaller in many cases. In
alone to describe the disposition of the drug, general, both volume terms reflect extravascular
no information on tissue drug concentration is drug distribution. (VD)b appears to be much more
known, and no model will predict actual tissue affected by the dynamics of drug disposition
drug concentrations. To account for the mass in the beta phase, whereas (VD)ss reflects more
balance (drug mass/volume = body drug concen- accurately the inherent distribution of the drug.
tration) of drug present in the body (tissue and 4. When drugs are given in a multiple-dose regi-
plasma pool) at any time after dosing, the body men, a loading dose may be given to achieve
drug concentration is assumed to be the plasma steady-state drug concentrations more rapidly.
drug concentration. In reality, azithromycin tis-
sue concentration is much higher. Therefore, the
Frequently Asked Questions
calculated volume of the tissue compartment is
»»What is the main reason for giving a drug by slow
much bigger (31.1 L/kg) than its actual volume.
IV infusion?
3. The product of the steady-state apparent (VD)ss
and the steady-state plasma drug concentration »»Why do we use a loading dose to rapidly achieve
C therapeutic concentration for a drug with a long elim-
ss estimates the amount of drug present in the
body. The amount of drug present in the body ination half-life instead of increasing the rate of drug
may be important information for toxicity con- infusion or increasing the size of the infusion dose?
siderations, and may also be used as a therapeutic »»Explain why the application of a loading dose as a
end point. In most cases, the therapeutic drug at single IV bolus injection may cause an adverse event
the site of action accounts for only a small frac- or drug toxicity in the patient if the drug follows a two-
tion of total drug in the tissue compartment. The compartment model with a slow elimination phase.
pharmacodynamic profile may be described as a »»What are some of the complications involved with
separate compartment (see effect compartment IV infusion?
in Chapter 21). Based on pharmacokinetic and
144 Chapter 6
CHAPTER SUMMARY
An IV bolus injection puts the drug into the systemic A loading dose given as an IV bolus injection may
circulation almost instantaneously. For some drugs, be used at the start of an infusion to quickly achieve
IV bolus injections can result in immediate high the desired steady-state plasma drug concentration.
plasma drug concentrations and drug toxicity. An IV For drugs that follow a two-compartment model,
drug infusion slowly inputs the drug into the circula- multiple small loading doses or intermittent IV infu-
tion and can provide stable drug concentrations in sions may be needed to prevent plasma drug concen-
the plasma for extended time periods. Constant IV trations from becoming too high. Pharmacokinetic
drug infusions are considered to have zero-order parameters may be calculated from samples taken
drug absorption because of direct input. Once the during the IV infusion and after the infusion is
drug is infused, the drug is eliminated by first-order stopped, regardless of whether steady state has been
elimination. Steady state is achieved when the rate of achieved. These calculated pharmacokinetic param-
drug infusion (ie, rate of drug absorption) equals the eters are then used to optimize dosing for that patient
rate of drug elimination. Four to five elimination when population estimates do not provide outcomes
half-lives are needed to achieve 95% of steady state. suitable for the patient.
LEARNING QUESTIONS
1. A female patient (35 years old, 65 kg) with The serum drug concentrations are as presented
normal renal function is to be given a drug by in Table 6-2.
IV infusion. According to the literature, the a. What is the steady-state plasma drug level?
elimination half-life of this drug is 7 hours and b. What is the time for 95% steady-state
the apparent VD is 23.1% of body weight. The plasma drug level?
pharmacokinetics of this drug assumes a first- c. What is the drug clearance?
order process. The desired steady-state plasma d. What is the plasma concentration of the drug
level for this antibiotic is 10 mg/mL. 4 hours after stopping infusion (infusion was
a. Assuming no loading dose, how long after stopped after 24 hours)?
the start of the IV infusion would it take to
reach 95% of the Css? TABLE 6-2 Serum Drug Concentrations for a
b. What is the proper loading dose for this Hypothetical Anticonvulsant Drug
antibiotic?
c. What is the proper infusion rate for this TIME Single IV dose Constant IV Infusion
(hour) (1 mg/kg) (0.2 mg/kg per hour)
drug?
d. What is the total body clearance? 0 10.0 0
e. If the patient suddenly develops partial renal 2 6.7 3.3
failure, how long would it take for a new
4 4.5 5.5
steady-state plasma level to be established
(assume that 95% of the Css is a reasonable 6 3.0 7.0
approximation)? 8 2.0 8.0
f. If the total body clearance declined 50% due
10 1.35 8.6
to partial renal failure, what new infusion rate
would you recommend to maintain the desired 12 9.1
steady-state plasma level of 10 mg/mL. 18 9.7
2. An anticonvulsant drug was given as (a) a single
24 9.9
IV dose and then (b) a constant IV infusion.
Intravenous Infusion 145
e. What is the infusion rate for a patient weigh- 6. Calculate the excretion rate at steady state for a
ing 75 kg to maintain a steady-state drug drug given by IV infusion at a rate of 30 mg/h.
level of 10 mg/mL? The Css is 20 mg/mL. If the rate of infusion
f. What is the plasma drug concentration were increased to 40 mg/h, what would be
4 hours after an IV dose of 1 mg/kg the new steady-state drug concentration, Css?
followed by a constant infusion of Would the excretion rate for the drug at the
0.2 mg/kg/h? new steady state be the same? Assume first-order
3. An antibiotic is to be given by IV infusion. elimination kinetics and a one-compartment
How many milliliters per hour should a sterile model.
25 mg/mL drug solution be given to a 75-kg 7. An antibiotic is to be given to an adult male
adult male patient to achieve an infusion rate patient (58 years, 75 kg) by IV infusion. The
of 1 mg/kg/h? elimination half-life is 8 hours and the apparent
4. An antibiotic drug is to be given to an adult volume of distribution is 1.5 L/kg. The drug is
male patient (75 kg, 58 years old) by IV supplied in 60-mL ampules at a drug concen-
infusion. The drug is supplied in sterile vials tration of 15 mg/mL. The desired steady-state
containing 30 mL of the antibiotic solution drug concentration is 20 mg/mL.
at a concentration of 125 mg/mL. What rate a. What infusion rate in mg/h would you rec-
in milliliters per hour would you infuse this ommend for this patient?
patient to obtain a steady-state concentration b. What loading dose would you recommend
of 20 mg/mL? What loading dose would you for this patient? By what route of admin-
suggest? Assume the drug follows the pharma- istration would you give the loading dose?
cokinetics of a one-compartment open model. When?
The apparent volume of distribution of this c. Why should a loading dose be
drug is 0.5 L/kg and the elimination half-life recommended?
is 3 hours. d. According to the manufacturer, the recom-
5. According to the manufacturer, a steady- mended starting infusion rate is 15 mL/h. Do
state serum concentration of 17 mg/mL was you agree with this recommended infusion
measured when the antibiotic, cephradine rate for your patient? Give a reason for your
(Velosef®) was given by IV infusion to 9 adult answer.
male volunteers (average weight, 71.7 kg) at a e. If you were to monitor the patient’s serum
rate of 5.3 mg/kg/h for 4 hours. drug concentration, when would you request a
a. Calculate the total body clearance for this blood sample? Give a reason for your answer.
drug. f. The observed serum drug concentration is
b. When the IV infusion was discontinued, the higher than anticipated. Give two possible
cephradine serum concentration decreased reasons based on sound pharmacokinetic
exponentially, declining to 1.5 mg/mL at principles that would account for this
6.5 hours after the start of the infusion. Cal- observation.
culate the elimination half-life. 8. Which of the following statements (a−e) is/are
c. From the information above, calculate the true regarding the time to reach steady-state for
apparent volume of distribution. the three drugs below?
d. Cephradine is completely excreted
unchanged in the urine, and studies have Drug A Drug B Drug C
shown that probenecid given concurrently Rate of infusion 10 20 15
causes elevation of the serum cephradine (mg/h)
concentration. What is the probable mecha-
k (h−1) 0.5 0.1 0.05
nism for this interaction of probenecid with
cephradine? Cl (L/h) 5 20 5
146 Chapter 6
a. Drug A takes the longest time to reach 9. If the steady-state drug concentration of a
steady state. cephalosporin after constant infusion of 250 mg/h
b. Drug B takes the longest time to reach is 45 mg/mL, what is the drug clearance of this
steady state. cephalosporin?
c. Drug C takes the longest time to reach 10. Some clinical pharmacists assumed that, at
steady state. steady state when equilibration is reached
d. Drug A takes 6.9 hours to reach steady state. between the plasma and the tissue, the tissue
e. None of the above is true. drug concentration would be the same as the
plasma. Do you agree?
ANSWERS
Frequently Asked Questions administered if the initial steady-state drug level is
What is the main reason for giving a drug by slow inadequate for the patient.
IV infusion? What are some of the complications involved with
• IV infusion?
Slow IV infusion may be used to avoid side effects
due to rapid drug administration. For example, • The common complications associated with intra-
intravenous immune globulin (human) may cause venous infusion include phlebitis and infections at
a rapid fall in blood pressure and possible ana- the infusion site caused by poor intravenous tech-
phylactic shock in some patients when infused niques or indwelling catheters.
rapidly. Some antisense drugs also cause a rapid
fall in blood pressure when injected via rapid IV Learning Questions
into the body. The rate of infusion is particularly
important in administering antiarrhythmic agents 1. a. To reach 95% of Css:
in patients. The rapid IV bolus injection of many 4.32t1/2 = (4.32)(7) = 30.2 hours
drugs (eg, lidocaine) that follow the pharmacoki-
netics of multiple-compartment models may cause
an adverse response due to the initial high drug b. DL = CssVD
concentration in the central (plasma) compartment = (10)(0.231)(65,000) = 150 mg
before slow equilibration with the tissues.
c. R = CssVDk = (10)(15,000)(0.099)
Why do we use a loading dose to rapidly achieve
therapeutic concentration for a drug with a long elimi- = 14.85 mg/h
nation half-life instead of increasing the rate of drug
infusion or increasing the size of the infusion dose? d. ClT =VDk = (15,000)(0.099) =1485 mL/h
• The loading drug dose is used to rapidly attain the e. To establish a new Css will still take 4.32t1/2.
target drug concentration, which is approximately However, the t1/2 will be longer in renal
the steady-state drug concentration. However, the failure.
loading dose will not maintain the steady-state f. If ClT is decreased by 50%, then the infusion
level unless an appropriate IV drug infusion rate rate R should be decreased proportionately:
or maintenance dose is also used. If a larger IV R =10(0.50)(1485) = 7.425 mg/h
drug infusion rate or maintenance dose is given,
the resulting steady-state drug concentration will 2. a. The steady-state level can be found by
be much higher and will remain sustained at plotting the IV infusion data. The plasma
the higher level. A higher infusion rate may be drug−time curves plateau at 10 mg/mL.
Intravenous Infusion 147
Alternatively, VD and k can be found from 3. Infusion rate R for a 75-kg patient:
the single IV dose data:
R = (1 mg/kg ⋅ h)(75 kg) = 75 mg/h
V 100 mL/kg k 0.2 h−1
D = =
Sterile drug solution contains 25 mg/mL.
b. Using equations developed in Example 2 in Therefore, 3 mL contains (3 mL) × (25 mg/mL),
the first set of examples in this chapter: or 75 mg. The patient should receive 3 mL
(75 mg/h) by IV infusion.
R R
0.95 (1 e−kt
= − )
VDk VDk
R
4. Css = R = C V k
V k ss D
D
0.95 1 e−0.2t
= −
0.693
0.05 e−0.2t R = (20 mg/L)(0.5L/kg)(75 kg) 3 h =
ln 0.05 = 173.25 mg/h
t95% = =15 hours
SS −0.2
Drug is supplied as 125 mg/mL. Therefore,
D
c. 0
ClT =VDk VD =
C0 173.25 mg
P 125 mg/mL = X = 1.386 mL
X
1000 100 mL
ClT =100× 0.2 VD = = R = 1.386 mL/h
10 kg
DL = CssVD = (20 mg/L)(0.5 L/kg)(75 kg)
ClT = 20 mL/kg ⋅ h
= 750 mg
d. The drug level 4 hours after stopping the IV
infusion can be found by considering the drug
concentration at the termination of infusion R R
5. Css = =
as C0
p . At the termination of the infusion, the kVD ClT
drug level will decline by a first-order process. R 5.3 mg/kg ⋅h × 71.71 kg
a. ClT = =
C = C0e− Css 17 mg/L
kt
p p
= 22.4 L/h
C = 9.9 −(0.2)(4)
p e
b. At the end of IV infusion, Cp = 17 mg/mL.
Cp = 4.5 µg/mL
Assuming first-order elimination kinetics:
e. The infusion rate to produce a Css of
C C0 −
p = pe
kt
10 mg/mL is 0.2 mg/kg/h. Therefore, the
infusion rate needed for this patient is 1.5 −
= 17e kt(2.5)
0.2 mg/kg ⋅h× 75 kg =15 mg/h 0.0882 e−2.5k
=
f. From the data shown, at 4 hours after the start ln 0.0882 = −2.5 k
of the IV infusion, the drug concentration is
5.5 mg/mL; the drug concentration after an −2.43 = −2.5 k
IV bolus of 1 mg/kg is 4.5 mg/mL. Therefore,
k 0.971 h−1
=
if a 1-mg dose is given and the drug is then
infused at 0.2 mg/kg/h, the plasma drug con- 0.693
t1/2 = = 0.714 hour
centration will be 4.5 + 5.5 = 10 mg/mL. 0.971
148 Chapter 6
Cl 7. a.
c. T
ClT = kVD VD =
k R = CsskVD
22.4
VD = = 23.1 L R = (20 mg/L)(0.693/8 h)(1.5 L/kg)(75 kg)
0.971
= 194.9 mg/h
d. Probenecid blocks active tubular secretion of
cephradine. 195 mg/h
R = = 13 mL/h
6. At steady state, the rate of elimination should 15 mg/mL
equal the rate of absorption. Therefore, the rate
of elimination would be 30 mg/h. The C b. DL
ss is = CssVD = (20)(1.5)(75) = 2250 mg given
directly proportional to the rate of infusion R, by IV bolus injection.
as shown by c. The loading dose is given to obtain steady-state
drug concentrations as rapidly as possible.
R R d. 15 mL of the antibiotic solution contains
Css = kVD =
kV 225 mg of drug. Thus, an IV infusion rate of
D Css
15 mL/h is equivalent to 225 mg/h. The Css
Rold Rnew achieved by the manufacturer’s recommen-
=
Css,old Css, new dation is
30 mg/h 40 mg/h R 225
= Css = = = 23.1 mg/L
20 kV
µg/mL C D (0.0866)(112.5)
ss,new
The theor
Css,new = 26.7 µg/mL etical Css of 23.1 mg/L is close to the desired
Css of 20 mg/L. Assuming a reasonable therapeutic
window, the manufacturer’s suggested starting infusion
The new elimination rate will be 40 mg/h. rate is satisfactory.
REFERENCE
Hurley SF, McNeil JJ: A comparison of the accuracy of a least-
squares regression, a Bayesian, Chiou’s and the steady-state
clearance method of individualizing theophylline dosage.
Clin Pharmacokinet 14:311−320, 1988.
BIBLIOGRAPHY
Gibaldi M: Estimation of the pharmacokinetic parameters of the Mitenko P, Ogilvie R: Rapidly achieved plasma concentration
two-compartment open model from postinfusion plasma con- plateaus, with observations on theophylline kinetics. Clin
centration data. J Pharm Sci 58:1133−1135, 1969. Pharmacol Ther 13:329−335, 1972.
Koup J, Greenblatt D, Jusko W, et al: Pharmacokinetics of digoxin Riegelman JS, Loo JC: Assessment of pharmacokinetic constants
in normal subjects after intravenous bolus and infusion dose. from postinfusion blood curves obtained after IV infusion.
J Pharmacokinet Biopharm 3:181−191, 1975. J Pharm Sci 59:53, 1970.
Loo J, Riegelman S: Assessment of pharmacokinetic constants Sawchuk RJ, Zaske DE: Pharmacokinetics of dosing regimens
from postinfusion blood curves obtained after IV infusion. which utilize multiple intravenous infusions: Gentamicin
J Pharm Sci 59:53−54, 1970. in burn patients. J Pharmacokinet Biopharm 4:183−195,
Loughnam PM, Sitar DS, Ogilvie RI, Neims AH: The two- 1976.
compartment open system kinetic model: A review of its clini- Wagner J: A safe method for rapidly achieving plasma concentra-
cal implications and applications. J Pediatr 88:869−873, 1976. tion plateaus. Clin Pharmacol Ther 16:691−700, 1974.
Drug Elimination,
7 Clearance, and
Renal Clearance
Murray P. Ducharme
Chapter Objectives DRUG ELIMINATION
»» Describe the main routes of drug Drugs are removed from the body by various elimination pro-
elimination from the body. cesses. Drug elimination refers to the irreversible removal of drug
»» Understand the importance from the body by all routes of elimination. The declining plasma
of the role of clearance as a PK drug concentration observed after systemic drug absorption shows
parameter. that the drug is being eliminated from the body but does not neces-
sarily differentiate between distribution and elimination, and does
»» Define clearance and its
not indicate which elimination processes are involved.
relationship to a corresponding
Drug elimination is usually divided into two major components:
half-life and a volume of
excretion and biotransformation. Drug excretion is the removal of
distribution.
the intact drug. Nonvolatile and polar drugs are excreted mainly by
»» Differentiate between clearance renal excretion, a process in which the drug passes through the
and renal clearance. kidney to the bladder and ultimately into the urine. Other pathways
»» Describe the processes for renal for drug excretion may include the excretion of drug into bile,
drug excretion and explain sweat, saliva, milk (via lactation), or other body fluids. Volatile
which renal excretion process drugs, such as gaseous anesthetics, alcohol, or drugs with high
predominates in the kidney for volatility, are excreted via the lungs into expired air.
a specific drug, given its renal Biotransformation or drug metabolism is the process by
clearance. which the drug is chemically converted in the body to a metabolite.
Biotransformation is usually an enzymatic process. A few drugs
»» Describe the renal clearance may also be changed chemically1 by a nonenzymatic process
model based on renal blood (eg, ester hydrolysis). The enzymes involved in the biotransforma-
flow, glomerular filtration, and tion of drugs are located mainly in the liver (see Chapter 12). Other
drug reabsorption. tissues such as kidney, lung, small intestine, and skin also contain
»» Describe organ drug clearance biotransformation enzymes.
in terms of blood flow and Drug elimination in the body involves many complex rate
extraction. processes. Although organ systems have specific functions, the
tissues within the organs are not structurally homogeneous, and
»» Calculate clearance
elimination processes may vary in each organ. In Chapter 4, drug
using different methods
elimination was modeled by an overall first-order elimination rate
including the physiological,
process. In this chapter, drug elimination is described in terms of
noncompartmental, and
clearance from a hypothetical well-stirred compartment containing
compartmental approaches.
1 Nonenzymatic breakdown of drugs may also be referrered to as degradation. For
example, some drugs such as aspirin (acetylsalicylic acid) may break down in the
stomach due to acid hydrolysis at pH 1–3.
149
150 Chapter 7
uniform drug distribution. The term clearance or more generally
describes the process of drug elimination from the
DOSE = Cl/F × AUC0-inf (7.2)
body or from a single organ without identifying the
individual processes involved. Clearance may be in which Cl/F can be called the “apparent clearance”
defined as the volume of fluid removed of the drug when the absolute bioavailability (F) is unknown or
from the body per unit of time. The units for clearance simply not specified or assumed.
are sometimes in milliliters per minute (mL/min) but
most often reported in liters per hour (L/h). The vol-
ume concept is simple and convenient, because all Frequently Asked Question
drugs are dissolved and distributed in the fluids of
»»Why is clearance a useful pharmacokinetic
the body. parameter?
Clearance is even more important clinically than
a half-life for several reasons. First and foremost,
clearance directly relates to the systemic exposure of
a drug (eg, AUCinf), making it the most useful PK DRUG CLEARANCE
parameter clinically as it will be used to calculate Drug clearance is a pharmacokinetic term for
doses to administer in order to reach a therapeutic describing drug elimination from the body without
goal in terms of exposure. While the terminal half- identifying the mechanism of the process. Drug
life gives information only on the terminal phase of clearance (also called body clearance or total body
drug disposition, clearance takes into account all clearance, and abbreviated as Cl or ClT) considers
processes of drug elimination regardless of their the entire body as a single drug-eliminating system
mechanism. When the PK behavior of the drug fol- from which many unidentified elimination processes
lows linear PK, clearance is a constant, whereas the may occur. Instead of describing the drug elimina-
rate of drug elimination is not. For example, first- tion rate in terms of amount of drug removed per unit
order elimination processes consider that a certain of time (eg, mg/h), drug clearance is described in
portion or fraction (percent) of the distribution vol- terms of volume of fluid removed from the drug per
ume is cleared of drug over a given time period. This unit of time (eg, L/h).
basic concept (see also Chapter 3) will be elaborated There are several definitions of clearance, which
along with a review of the anatomy and physiology are similarly based on a volume removed from the
of the kidney. drug per unit of time. The simplest concept of clear-
As will be seen later on in this chapter and in the ance regards the body as a space that contains a defi-
noncompartmental analysis chapter (Chapter 25), nite volume of apparent body fluid (apparent volume
the clearance of a drug (Cl) is directly related to of distribution, V or VD) in which the drug is dis-
the dose administered and to the overall systemic solved. Drug clearance is defined as the fixed volume
exposure achieved with that dose as per the equation of fluid (containing the drug) removed from the drug
Cl = DOSE/AUC0-inf. The overall systemic exposure per unit of time. The units for clearance are volume/
(AUC0-inf) of a drug resulting from an administered time (eg, mL/min, L/h). For example, if the Cl of
dose correlates with its efficacy and toxicity. The penicillin is 15 mL/min in a patient and penicillin
drug clearance (Cl) is therefore the most important has a VD of 12 L, then from the clearance definition,
PK parameter to know in a given patient. If the thera- 15 mL of the 12 L will be removed from the drug
peutic goal in terms of AUC0-inf is known for a drug, per minute.
then the dose to administer to this patient is com- Alternatively, Cl may be defined as the rate of
pletely dictated by the clearance value (Cl). drug elimination divided by the plasma drug concen-
tration. This definition expresses drug elimination in
Hence, after IV administration
terms of the volume of plasma eliminated of drug
DOSE = Cl × AUC0-inf (7.1) per unit time. This definition is a practical way to
Drug Elimination, Clearance, and Renal Clearance 151
calculate clearance based on plasma drug concentra-
tion data. From Equation 7.4, the rate of drug elimination is
dD
Elimination rate E =10 µg/mL×15 mL/min=150 µg/min
Cl = dt
Plasma concentration (Cp ) (7.3)
Thus, 150 mg/min of penicillin is eliminated from
dD µg/min the body when the plasma penicillin concentra-
Cl = E /dt = = min (7.4)
Cp µ mL/
g/mL tion is 10 mg/mL.
Clearance may be used to estimate the rate
where DE is the amount of drug eliminated and of drug elimination at any given concentration.
dDE/dt is the rate of elimination. Using the same example, if the elimination rate of
Rearrangement of Equation 7.4 gives Equation 7.5. penicillin was measured as 150 mg/min when the
dD plasma penicillin concentration was 10 mg/mL,
Elimination rate E
= = C Cl (7.5)
dt p then the clearance of penicillin is calculated from
Equation 7.4:
The two definitions for clearance are similar because
150 µg/min
dividing the elimination rate by the Cp yields the Cl = 15 mL/min
10 µ =
g/mL
volume of plasma cleared of drug per minute, as
shown in Equation 7.4.
As discussed in previous chapters, a first-order
Just as the elimination rate constant (k or k
elimination rate, dD el) represents
E/dt, is equal to kDB or kCpVD.
the total sum of all of the different rate constants for
Based on Equation 7.3, substituting elimination rate
drug elimination, including for example the renal (k
for kC R)
pVD,
and liver (kH) elimination rate constants, Cl is the total
kCpVD sum of all of the different clearance processes in the
Cl = = kVD (7.6)
C body that are occurring in parallel in terms of cardiac
p
blood flow (therefore excepting lung clearance),
Equation 7.6 shows that clearance is the product of a
including for example clearance through the kidney
volume of distribution, VD, and a rate constant, k,
(renal clearance abbreviated as Cl
both of which are constants when the PK is linear. As R), and through the
liver (hepatic clearance abbreviated as Cl
the plasma drug concentration decreases during H):
elimination, the rate of drug elimination, dDE/dt, Elimination rate constant:
decreases accordingly, but clearance remains con- k or kel where k = kR + kH + kother (7.7)
stant. Clearance is constant as long as the rate of
Clearance:
drug elimination is a first-order process.
Cl where Cl = ClR + ClH + Clother (7.8)
EXAMPLE »» » where
Penicillin has a Cl of 15 mL/min. Calculate the elim- Renal clearance: ClR = kR × V (7.9)
ination rate for penicillin when the plasma drug
Hepatic clearance: Cl
concentration, C H = kH × V (7.10)
p, is 2 mg/mL.
Total clearance:
Solution
Cl = k × V = (kR + kH + kother) × V (7.11)
Elimination rate = Cp × Cl (from Equation 7.5)
dD From Equation 7.11, for a one-compartment model
E =2 µg/mL×15 mL/min=30 µg/min
dt (ie, where V = Vss and where k = lz), the total body
clearance Cl of a drug is the product of two con-
Using the previous penicillin example, assume that
stants, l
the plasma penicillin concentration is 10 mg/mL. z and Vss, which reflect all the distribution
and elimination processes of the drug in the body.
152 Chapter 7
Distribution and elimination are affected by blood
flow, which will be considered below (and in 0.693 0.693
k 1h−1
= = = 0.23
Chapter 11) using a physiologic model. t1/2 3
For a multicompartment model (eg, where the Cl = 0.23 h−1 × 100 mL/kg = 23.1 mL/(kg⋅h)
total volume of distribution [Vss] includes a central
volume of distribution [Vc], and one [Vp] or more For a 70-kg patient, Cl = 23.1 × 70 = 1617 mL/h
peripheral volumes of distributions), the total body
clearance of a drug will be the product of the elimi- CLEARANCE MODELS
nation rate constant from the central compartment
(k10) and Vc. The equations become: The calculation of clearance from a rate constant
(eg, k or k10) and a volume of distribution (eg, V or Vc)
Renal clearance: ClR = kR × VC (7.12) assumes (sometimes incorrectly) a defined compart-
Hepatic clearance: ClH = kH × VC (7.13) mental model, whereas clearance estimated directly
from the plasma drug concentration−time curve using
Total clearance:
noncompartmental PK approaches does not need one
Cl = k10 × VC = (kR + kH + kother) × VC (7.14) to specify the number of compartments that would
describe the shape of the concentration−time curve.
Clearance values are often adjusted on a per-kilogram- Although clearance may be regarded as the product of
of-actual-body-weight (ABW) or on a per-meter- a rate constant k and a volume of distribution V,
square-of-surface-area basis, such as L/h per kilogram Equation 7.11 is far more general because the reaction
or per m2, or normalized for a “typical” adult of 72 kg order for the rate of drug elimination, dDE/dt, is not
or 1.72 m2. This approach is similar to the method for specified, and the elimination rate may or may not
expressing V, because both pharmacokinetic param- follow first-order kinetics. The various approaches for
eters vary with body weight or body size. It has estimating a drug clearance are described in Fig. 7-1
been found, however, that when expressing clearance and will be explored one by one below:
between individuals of varying ABW, such as predict-
ing Cl between children and adults, Cl varies best allo- Compartmental model
metrically with ABW, meaning that Cl is best expressed IV k10
Vc (Cp)with an allometric exponent (most often 0.75 is rec-
ommended) relating it to ABW as per the following Static volume and
rst-order processes are assumed in
expression (see also Chapter 25): simpler models. Here Cl = k10 x Vc.
Cl (predicted in a patient) Physiologic model
= Cl(population value for a 72-kg patient) × (ABW/72)0.75 Q Ca Q Cv
(7.15)
EXAMPLE »» » Elimination
Clearance is the product of the ow through an organ (Q)
and the extraction ratio of that organ (E). For example, the
Determine the total body clearance for a drug in a hepatic clearance is ClH = QH x EH.
70-kg male patient. The drug follows the kinetics Noncompartmental approach
of a one-compartment model and has an elimina- Cp
tion half-life of 3 hours with an apparent volume of AUC0-inf
distribution of 100 mL/kg.
Time (h)
Solution
Volume of distribution does not need to be de
ned.
First determine the elimination rate constant (k) Cl = DOSE/AUCinf.
and then substitute properly into Equation 7.11. FIGURE 71 General approaches to clearance. Volume
and elimination rate constant not defined.
Drug Elimination, Clearance, and Renal Clearance 153
Q Ca Elimination Q C Equation 7.16 adapted for the liver as an organ yields
v
organ the hepatic clearance (ClH)
ClH = QH × EH (7.19)
Elimination Therefore, if Cl = ClH + ClNH (where ClNH is the
drug
nonhepatic clearance), then
FIGURE 72 Drug clearance model. (Q = blood flow,
Ca = incoming drug concentration [usually arterial drug con- Cl = (QH × EH) + ClNH (7.20)
centration], Cv = outgoing drug concentration [venous drug
concentration].) For some drugs Cl ~ ClH, and so Cl ~ QH × EH.
The physiologic approach to organ clearance
Physiologic/Organ Clearance
shows that the clearance from an organ depends on
Clearance may be calculated for any organ involved its blood flow rate and its ability at eliminating the
in the irreversible removal of drug from the body. drug, whereas the total clearance is that of a constant
Many organs in the body have the capacity for drug or static fraction of the volume in which the drug is
elimination, including drug excretion and biotrans- distributed or is removed from the drug per unit of
formation. The kidneys and liver are the most com- time. Organ clearance measurements using the phys-
mon organs involved in excretion and metabolism, iologic approach require invasive techniques to
respectively. Physiologic pharmacokinetic models obtain measurements of blood flow and extraction
are based on drug clearance through individual ratio. The physiologic approach has been used to
organs or tissue groups (Fig. 7-2). describe hepatic clearance, which is discussed fur-
For any organ, clearance may be defined as the ther under hepatic elimination (Chapter 12). More
fraction of blood volume containing drug that flows classical definitions of clearance have been applied
through the organ and is eliminated of drug per unit to renal clearance because direct measurements of
time. From this definition, clearance is the product plasma drug concentration and urinary drug excre-
of the blood flow (Q) to the organ and the extraction tion may be obtained. Details will be presented in the
ratio (E). The E is the fraction of drug extracted by Renal Clearance section of this chapter.
the organ as drug passes through.
Cl (organ) = Q (organ) × E (organ) (7.16) Noncompartmental Methods
If the drug concentration in the blood (Ca) entering Clearance is commonly used to describe first-order
the organ is greater than the drug concentration of drug elimination from compartment models such as
blood (C the one-compartment model, C(t) = Cp = C0e−kt
p in
v) leaving the organ, then some of the drug
has been extracted by the organ (Fig. 7-2). The E is which the distribution volume and elimination rate
C constant are well defined. Clearance estimated directly
a − Cv divided by the entering drug concentration
(Ca), as shown in Equation 7.17. from the area under the plasma drug concentration−
time curve using the noncompartmental method is
C −C
a v
E = (7.17) often called a “model-independent” approach as it
C
a does not need any assumption to be set in terms of
E is a ratio with no units. The value of E may range the number of compartments describing the kinetics
from 0 (no drug removed by the organ) to 1 (100% of or concentration−time profile of the drug under study.
the drug is removed by the organ). An E of 0.25 indi- It is not exactly true that this method is a “model-
cates that 25% of the incoming drug concentration is independent” one, though, as this method still assumes
removed by the organ as the drug passes through. that the terminal phase decreases in a log-linear fash-
Substituting for E into Equation 7.16 yields ion that is model dependent, and many of its parame-
ters can be calculated only when one assumes PK
C −C
Cl (organ) =Q (organ) a v
(7.18) linearity. Referring to this method as “noncompart-
Ca mental” is therefore more appropriate.
154 Chapter 7
The noncompartmental approach is based on described as the “observed” AUC and calculated
statistical moment theory and is presented in more using the linear or mixed log-linear trapezoidal rule,
details in Chapter 25. The main advantages of this while the AUC that needs to be extrapolated from
approach are that (1) clearance can be easily calcu- time t to infinity (AUCt-inf) is often described as the
lated without making any assumptions relating to “extrapolated” AUC. It is good pharmacokinetic
rate constants (eg, distribution vs. elimination rate practice for the clearance to be calculated robustly to
constants), (2) volume of distribution is presented in never extrapolate the AUC0-t by more than 20%. In
a clinically useful context as it is related to systemic addition, it is also good pharmacokinetic practice for
exposure and the dose administered, and (3) its esti- the AUC0-t to be calculated using a rich sampling
mation is robust in the context of rich sampling data strategy, meaning a minimum of 12 concentration−
as very little modeling is involved, if any (eg, no time points across the concentration−time curve
modeling at steady-state data, and only very limited from zero to Ct.
modeling by way of linear regression of the terminal At steady state, when the concentration−time
phase after single dose administration). profiles between administered doses become con-
Clearance can be determined directly from the stant, the amount of drug administered over the dos-
time−concentration curve by ing interval is exactly equal to the amount eliminated
over that dosing interval (t). The formula for clear-
∞
Cl = ∫ D × F /C(t)dt (7.21) ance therefore becomes:
0
where D is the dose administered, F is the bioavail- F × D
Cl or Cl = (7.22)
(ss)
ability factor associated with the administration route AUC
τ (ss)
used of the drug product, and C(t) is an unknown If the drug exhibits linear pharmacokinetics in terms
function that describes the changing plasma drug of time, then the clearance calculated after single
concentrations. dose administration (Cl) using Equation 7.2 and the
Using the noncompartmental approach, the gen- clearance calculated from steady-state data (Cl(ss))
eral equation therefore uses the area under the drug using Equation 7.22 will be the same.
concentration curve, [AUC]∞0 , for the calculation of From Equation 7.22, it can be derived that follow-
clearance. ing a constant intravenous infusion (see Chapter 6), the
F × D steady-state concentration (Css) will then be equal to
Cl = (as presented before
AUC “rate in,” the administration dosing rate (R0), divided
0-inf in Equation 7.2)
by “rate out” or the clearance:
∞
where AUC0-inf = [AUC]∞0 = ∫ C t nd s t e t tal
0 p d a i h o F × R
C 0 F × R0
(ss) = or Cl = (7.23)
systemic exposure obtained after a single dose (D) Cl Css
until infinity.
where R0 is the constant dosing rate (eg, in mg/h), C
Because [AUC]∞0 is calculated from the drug ss
is the steady-state concentration (eg, in mg/L), and
concentration−time curve from zero to infinity using
Cl is the total body clearance (eg, in L/h).
the trapezoidal rule, no model is assumed until the
terminal phase after the last detectable concentration
is obtained (Ct). To extrapolate the data to infinity to Compartmental Methods
obtain the residual [AUC]∞ or (Cp /k), first-order Clearance is a direct measure of elimination from the
t t
elimination is usually assumed. central compartment, regardless of the number of
Equation 7.2 is used to calculate clearance after compartments. The central compartment consists of
administration of a single dose, and where concen- the plasma and highly perfused tissues in which drug
trations would be obtained in a rich sampling fashion equilibrates rapidly (see Chapter 5). The tissues for
until a last detectable concentration time point, Ct. drug elimination, namely, kidney and liver, are con-
The AUC from time zero to t (AUC0-t) is often sidered integral parts of the central compartment.
Drug Elimination, Clearance, and Renal Clearance 155
Clearance is always the product of a rate con- rate constant instead of assuming it is the “elimina-
stant and a volume of distribution. There are different tion” rate constant.
clearance formulas depending on the pharmacoki- Cl V
ss
netic model that would describe appropriately the = λ ×
F z F
concentration-versus-time profiles of a drug product.
Relationship with the noncompartmental approach
The clearance formulas depend upon whether the
after IV administration:
drug is administered intravenously or extravascularly
Dose
and range from simple to more complicated scenarios: Cl = λz ×Vss and Cl =
AUC
0-inf
Drug that is well described pharmacokinetically
with a one-compartment model and Vss = Cl × MRT
After intravenous administration, such a drug Therefore, MRT (mean residence time2) = 1/lz and
will exhibit a concentration−time profile that Vss = Dose/(AUC0-inf × lz).
decreases in a straight line when viewed on a semilog Relationship with the noncompartmental approach
plot and would therefore be well described by a after extravascular administration:
monoexponential decline. This is the simplest model
Cl V
ss Cl Dose
that can be used and often will describe well the phar- = λz × and =
F F F AUC
macokinetics of drugs that are very polar and that are 0-inf
readily eliminated in the urine. Clinically, aminogly- MRT and Vss /F are not computable directly using
coside antibiotics are relatively well characterized noncompartmental methods after extravascular
and predicted by a one-compartment model. administration, but only MTT (mean transit time),
which is the sum of MAT (mean absorption time)
Cl = lz × Vss and MRT.
But we have seen that MRT = 1/lz and Vss/F =
where lz is the only rate constant describing the fate
Dose/(AUC0-inf × lz). MAT can then be calculated by
of the concentration−time profile and dividing 0.693
subtracting MRT from the MTT.
by its value, therefore, estimates the terminal half-
life. Vss is the total volume of distribution, and in this Drug that is well described pharmacokinetically
case, there is only one volume that is describing the with a two-compartment model
pharmacokinetic behavior of the drug. After intravenous administration, such a drug will
Calculated parameters: exhibit a concentration−time profile that decreases
in a profile that can be characterized by two different
The terminal half-life of the drug is T1/2 = 0.693/l exponentials or two different straight lines when
z
viewed on a semilog plot (see Chapter 5). This
After oral administration the formula for clearance is model will describe well the pharmacokinetics of
exactly the same but a Cl/F is calculated. There is drugs that are not so polar and distribute in a second
also an absorption process in addition to an elimina- compartment that is not so well perfused by blood or
tion one. If the absorption process is faster than the plasma. Clinically, the antibiotic vancomycin is rela-
elimination, the terminal rate constant, lz, will tively well characterized and predicted by a two-
describe the elimination of the drug. If the drug compartment model.
exhibits a “flip-flop” profile because the absorption
Cl = k10 × Vc (7.24)
of the drug is much slower than the elimination pro-
cess (eg, often the case with modified release formu- where k10 is the rate constant describing the disap-
lations), then the terminal rate constant, l pearance of the drug from its central volume of dis-
z, will be
reflective of the absorption and not the elimination. tribution (Vc).
It is sometimes not possible to know if a drug exhib-
its a slower absorption than elimination. In these 2MRT is mean residence time and is discussed more fully in
cases, it is always best to refer to lz as the “terminal” Chapter 25.
156 Chapter 7
The distributional clearance (Cld) describes the It is often stated that clearances and volumes are
clearance occurring between the central (Vc) and the “independent” parameters, while rate constants are
peripheral compartment (Vp), and where the central “dependent” parameters. This assumption is made in
compartment includes the plasma and the organs that PK models to facilitate data analysis of the underly-
are very well perfused, while the peripheral compart- ing kinetic processes. Stated differently, a change in
ment includes organs that are less well perfused. a patient in its drug clearance may not result in a
The concentration−time curve profile will fol- change in its volume of distribution or vice versa,
low a biexponential decline on a semilog graph and while a change in clearance or in the volume of dis-
the distributional rate constant (l1) will be describ- tribution will result in a change in the appropriate
ing the rapid decline after IV administration that rate constant (eg, k10, lz). While mostly true, this
describes the distribution process, and the second statement can be somewhat confusing, as there are
and last exponential (lz) will describe the terminal clinical instances where a change can lead to both
elimination phase. volume of distribution and clearance changes, without
The distribution (l1) and terminal elimination a resulting change in the rate constant (eg, k10, lz).
(lz) rate constants can be obtained with the follow- A common example is a significant abrupt change
ing equations: in actual body weight (ABW) as both clearances
and volumes of distribution correlate with ABW.
° l1 = [((Cl + Cld)/Vc + Cld/Vp) + SQRT (((Cl +
A patient becoming suddenly edematous will not
Cld)/Vc + Cld/Vp)
2 − 4 × Cl/Vc*Cld/Vp))]/2 see his or her liver or renal function necessarily
° lz = [((Cl + Cld)/Vc + Cld/Vp) − SQRT (((Cl +
affected. In that example, both the patient’s clear-
Cld)/Vc + Cld/Vp)
2 − 4 × Cl/Vc*Cld/Vp))]/2 ance and volume of distribution will be increased,
The distribution and terminal elimination half-lives while half-life or half-lives will remain relatively
are therefore: unchanged. In that situation the dosing interval will
not need to be changed, as the half-life will stay
° T1/2(l1) = 0.693/l1 constant, but the dose to be given will need to be
° T1/2(lz) = 0.693/lz increased due to the greater volume of distribution
The total volume of distribution Vss will be the sum and clearance.
of Vc and Vp:
Summary Regarding Clearance Calculations
Vss = Vc + Vp (7.25)
Clearance can be calculated using physiologic, com-
Relationship with the noncompartmental approach partmental, or noncompartmental methods. What is
after IV administration: important to remember is that all methods will lead
Dose to the same results if they are applied correctly and
Cl = and Vss = Cl × MRT
AUC if there are enough data supporting the calculations.
0-inf
Clearance can therefore be calculated:
(noncompartmental equations)
• After a single dose administration using the area
Cl = k10 × Vc and Vss = Vc + Vp under the concentration−time curve from time zero
(compartmental equations) to infinity using a noncompartmental approach:
Cl = (Dose × F)/AUC
Therefore, MRT = (Vc + Vp)/(k10 × Vc)
0-inf.
• At steady-state conditions using the area under the
concentration−time curve during a dosing interval
Relationship between Rate Constants, using a noncompartmental approach: Cl = (Dose ×
Volumes of Distribution, and Clearances F)/AUCt (ss).
As seen previously in Equation 7.24, Cl = k10 × Vc, • When a constant infusion is administered until
which for a drug well described by a one-compart- steady-state concentrations (Css) are achieved:
ment model can be simplified to Cl = lz × Vss. Cl = F × R0 /Css.
Drug Elimination, Clearance, and Renal Clearance 157
• At any time using a compartmental approach with Medulla
Renal artery Cortex
the appropriate volume(s) of distribution and rate
Renal
constant(s): vein
° Cl = k10 × Vc when the PK of a drug is well Renal
described by any compartment model when the pelvis LEFT
drug displays linear pharmacokinetics. RIGHT KIDNEY
KIDNEY Ureters (cut
° Which equation can be simplified to Cl = lz × Vss surface)
when the PK of a drug is well described by only
a one-compartment model as lz is then equal to
k10, and Vss to Vc.
• For an organ using its blood ow and its extraction
Urinary
ratio. For example, the hepatic clearance could be bladder
Direction of
calculated as ClH = QH × EH. For a drug that would urine ow
be only eliminated via the liver, then Cl would be
FIGURE 73 The general organizational plan of the
equal to ClH.
urinary system. (Reproduced with permission from Guyton
AC: Textbook of Medical Physiology, 8th ed. Philadelphia,
Saunders, 1991.)
THE KIDNEY
The liver (see Chapter 12) and the kidney are the two nephrons have long loops of Henle that extend into
major drug-eliminating organs in the body, though the medulla (Fig. 7-5). The longer loops of Henle
drug elimination can also occur almost anywhere in allow for a greater ability of the nephron to reabsorb
the body. The kidney is the main excretory organ for water, thereby producing more concentrated urine.
the removal of metabolic waste products and plays a
major role in maintaining the normal fluid volume Blood Supply
and electrolyte composition in the body. To maintain
The kidneys represent about 0.5% of the total body
salt and water balance, the kidney excretes excess
weight and receive approximately 20%−25% of the
electrolytes, water, and waste products while con-
cardiac output. The kidney is supplied by blood via
serving solutes necessary for proper body function.
the renal artery, which subdivides into the interlobar
In addition, the kidney has two endocrine functions:
(1) secretion of renin, which regulates blood pres-
sure, and (2) secretion of erythropoietin, which Medulla Cortex
Capsule
stimulates red blood cell production.
Renal pyramid
Papilla
Anatomic Considerations Interlobar arteries
Minor calyx
The kidneys are located in the peritoneal cavity. A Major calyx Arcuate arteries
general view is shown in Fig. 7-3 and a longitudinal Renal
artery Interlobular
view in Fig. 7-4. The outer zone of the kidney is arteries
HILUS Renal vein
called the cortex, and the inner region is called the Renal Segmental
pelvis arteries
medulla. The nephrons are the basic functional units,
Column of Bertin
collectively responsible for the removal of metabolic
waste and the maintenance of water and electrolyte
balance. Each kidney contains 1−1.5 million neph- Ureter
rons. The glomerulus of each nephron starts in the FIGURE 74 Longitudinal section of the kidney, illustrat-
cortex. Cortical nephrons have short loops of Henle ing major anatomical features and blood vessels. (From West,
that remain exclusively in the cortex; juxtamedullary 1985, with permission.)
158 Chapter 7
JUXTAMEDULLARY CORTICAL Interlobular Afferent Efferent Peritubular
NEPHRON NEPHRON artery arteriole arteriole capillaries
Bowman’s capsule
Proximal Distal
tubule tubule Afferent arteriole
Glomerular
Glomerular capillaries
capillaries
Arcuate vein
(outer Arcuate artery
stripe)
(inner Efferent
stripe) arteriole
Loop of Collecting
Henle tubule/duct
Vasa recta
Interlobar
A B artery and vein
FIGURE 75 Cortical and juxtamedullary nephrons and their vasculature. (From West, 1985, p. 452, with permission.)
arteries penetrating within the kidney and branching The relationship of RBF to RPF is given by a rear-
further into the afferent arterioles. Each afferent arteri- rangement of Equation 7.26:
ole carries blood toward a single nephron into the glo-
RPF = RBF (1 − Hct) (7.27)
merular portion of the nephron (Bowman’s capsule).
The filtration of blood occurs in the glomeruli in Assuming a hematocrit of 0.45 and an RBF of 1.2 L/min
Bowman’s capsule. From the capillaries (glomerulus) and using the above equation, RPF = 1.2 − (1.2 ×
within Bowman’s capsule, the blood flows out via the 0.45) = 0.66 L/min or 660 mL/min, or approximately
efferent arterioles and then into a second capillary 950 L/d. The average glomerular filtration rate (GFR)
network that surrounds the tubules (peritubule capil- is about 120 mL/min in an average adult,3 or about
laries and vasa recti), including the loop of Henle, 20% of the RPF. The ratio GFR/RPF is the filtration
where some water is reabsorbed. fraction.
The renal blood flow (RBF) is the volume of
blood flowing through the renal vasculature per unit Regulation of Renal Blood Flow
of time. RBF exceeds 1.2 L/min or 1700 L/d. Renal
Blood flow to an organ is directly proportional to the
plasma flow (RPF) is the RBF minus the volume of
arteriovenous pressure difference (perfusion pressure)
red blood cells present. RPF is an important factor in
across the vascular bed and indirectly proportional to
the rate of drug filtration at the glomerulus.
the vascular resistance. The normal renal arterial pres-
RPF = RBF − (RBF × Hct) (7.26) sure (Fig. 7-6) is approximately 100 mm Hg and falls
to approximately 45−60 mm Hg in the glomerulus
where Hct is the hematocrit.
Hct is the fraction of blood cells in the blood, 3GFR is often based on average body surface, 1.73 m2. GFR is less
about 0.45 or 45% of the total blood volume. in women and also decreases with age.
Medulla Cortex
Inner zone Outer
(papilla) zone
Drug Elimination, Clearance, and Renal Clearance 159
18 mm Hg autoregulation refers to the maintenance of a con-
10 mm Hg stant blood flow in the presence of large fluctuations
60 mm Hg in arterial blood pressure. Because autoregulation
maintains a relatively constant blood flow, the filtra-
18 mm Hg
tion fraction (GFR/RPF) also remains fairly constant
13 mm Hg in this pressure range.
10 mm Hg Glomerular Filtration and Urine Formation
100 mm Hg A normal adult subject has a GFR of approxi-
mately 120 mL/min. About 180 L of fluid per day are
filtered through the kidneys. In spite of this large fil-
tration volume, the average urine volume is 1−1.5 L.
Up to 99% of the fluid volume filtered at the glom-
8 mm Hg
Intersitial uid erulus is reabsorbed. Besides fluid regulation, the
pressure 6 mm Hg 0 mm Hg
kidney also regulates the retention or excretion of
FIGURE 76 Approximate pressures at different points in various solutes and electrolytes (Table 7-1). With the
the vessels and tubules of the functional nephron and in the exception of proteins and protein-bound substances,
interstitial fluid. (Reproduced with permission from Guyton most small molecules are filtered through the glom-
AC: Textbook of Medical Physiology, 8th ed. Philadelphia, erulus from the plasma. The filtrate contains some
Saunders, 1991.)
ions, glucose, and essential nutrients as well as waste
products, such as urea, phosphate, sulfate, and other
(glomerular capillary hydrostatic pressure). This pres- substances. The essential nutrients and water are
sure difference is probably due to the increasing vas- reabsorbed at various sites, including the proximal
culature resistance provided by the small diameters of tubule, loops of Henle, and distal tubules. Both active
the capillary network. Thus, the GFR is controlled by reabsorption and secretion mechanisms are involved.
changes in the glomerular capillary hydrostatic The urine volume is reduced, and the urine generally
pressure. contains a high concentration of metabolic wastes
In the normal kidney, RBF and GFR remain and eliminated drug products. Advances in molec-
relatively constant even with large differences in ular biology have shown that transporters such as
mean systemic blood pressure (Fig. 7-7). The term P-glycoprotein and other efflux proteins are pres-
ent in the kidney, and can influence urinary drug
excretion. Further, CYP enzymes are also present
1000
RPF in the kidney, and can impact drug clearance by
800 metabolism.
600 Renal Drug Excretion
Renal excretion is a major route of elimination for
400
many drugs. Drugs that are nonvolatile, are water
200 GFR soluble, have a low molecular weight (MW), or are
slowly biotransformed by the liver are eliminated by
0 renal excretion. The processes by which a drug is
0 80 160 240 excreted via the kidneys may include any combination
Mean arterial pressure (mm Hg) of the following:
FIGURE 77 Schematic representation of the effect
• Glomerular filtration
of mean arterial pressure on GFR and RPF, illustrating the
phenomenon of autoregulation. (From West, 1985, p. 465, with • Active tubular secretion
permission.) • Tubular reabsorption
GFR or RPF (mL/min)
160 Chapter 7
TABLE 71 Quantitative Aspects of Urine Formationa
Per 24 Hours
Substance Filtered Reabsorbed Secreted Excreted Percent Reabsorbed
Sodium ion (mEq) 26,000 25,850 150 99.4
Chloride ion (mEq) 18,000 17,850 150 99.2
Bicarbonate ion (mEq) 4,900 4,900 0 100
Urea (mM) 870 460b 410 53
Glucose (mM) 800 800 0 100
Water (mL) 180,000 179,000 1000 99.4
Hydrogen ion Variable Variablec
Potassium ion (mEq) 900 900d 100 100 100d
aQuantity of various plasma constituents filtered, reabsorbed, and excreted by a normal adult on an average diet.
bUrea diffuses into, as well as out of, some portions of the nephron.
cpH or urine is on the acid side (4.5−6.9) when all bicarbonate is reabsorbed.
dPotassium ion is almost completely reabsorbed before it reaches the distal nephron. The potassium ion in the voided urine is actively secreted into
the urine in the distal tubule in exchange for sodium ion.
From Levine (1990), with permission.
Glomerular filtration is a unidirectional process Active tubular secretion is an active transport
that occurs for most small molecules (MW < 500), process. As such, active renal secretion is a carrier-
including undissociated (nonionized) and dissoci- mediated system that requires energy input,
ated (ionized) drugs. Protein-bound drugs behave as because the drug is transported against a concen-
large molecules and do not get filtered at the glom- tration gradient. The carrier system is capacity
erulus. The major driving force for glomerular filtra- limited and may be saturated. Drugs with similar
tion is the hydrostatic pressure within the glomerular structures may compete for the same carrier sys-
capillaries. The kidneys receive a large blood supply tem. Among the active renal secretion systems that
(approximately 25% of the cardiac output) via the have been identified, there are some for weak acids
renal artery, with very little decrease in the hydro- (organic anion transporter, OAT) and some for
static pressure. weak bases (organic cation transporter, OCT).
Glomerular filtration rate (GFR) is measured Active tubular secretion rate is dependent on RPF.
by using a drug that is eliminated primarily by filtra- Drugs commonly used to measure active tubular
tion only (ie, the drug is neither reabsorbed nor secretion include p-amino-hippuric acid (PAH)
secreted). Clinically inulin and creatinine are often and iodopyracet (Diodrast). These substances are
used for this purpose, although creatinine is also both filtered by the glomeruli and secreted by the
secreted. The clearance of inulin is approximately tubular cells. Active secretion is extremely rapid
equal to the GFR, which can equal 120 mL/min. The for these drugs, and practically all the drug carried
value for the GFR correlates fairly well with body to the kidney is eliminated in a single pass. The
surface area. Glomerular filtration of drugs is directly clearance for these drugs therefore reflects the
related to the free or nonprotein-bound drug concen- effective renal plasma flow (ERPF), which varies
tration in the plasma. As the free drug concentration from 425 to 650 mL/min. The ERPF is determined by
in the plasma increases, the glomerular filtration for both RPF and the fraction of drug that is effectively
the drug increases proportionately, thus increasing extracted by the kidney relative to the concentration
renal drug clearance for some drugs. in the renal artery.
Drug Elimination, Clearance, and Renal Clearance 161
For a drug that is excreted solely by glomerular may decrease (acidify) or increase (alkalinize) the
filtration, the elimination half-life may change mark- urinary pH, respectively, when administered in large
edly in accordance with the binding affinity of the quantities. By far the most important changes in
drug for plasma proteins. In contrast, drug protein urinary pH are caused by fluids administered intra-
binding has very little effect on the elimination half- venously. Intravenous fluids, such as solutions of
life of the drug excreted mostly by active secretion. bicarbonate or ammonium chloride, are used in
Because drug protein binding is reversible, drug acid−base therapy to alkalinize or acidify the urine,
bound to plasma protein rapidly dissociates as free respectively. Excretion of these solutions may drasti-
drug is secreted by the kidneys. For example, some cally change urinary pH and alter drug reabsorption
of the penicillins are extensively protein bound, but and drug excretion by the kidney.
their elimination half-lives are short due to rapid The percentage of ionized weak acid drug cor-
elimination by active secretion. responding to a given pH can be obtained from the
Tubular reabsorption occurs after the drug is Henderson−Hasselbalch equation.
filtered through the glomerulus and can be an active
or a passive process involving transporting back into Ionized
pH = pKa + log (7.28)
the plasma. If a drug is completely reabsorbed (eg, Nonionized
glucose), then the value for the clearance of the drug
Rearrangement of this equation yields:
is approximately zero. For drugs that are partially
reabsorbed without being secreted, clearance values Ionized
are less than the GFR of 120 mL/min. 10pH−pKa
= (7.29)
Nonionized
The reabsorption of drugs that are acids or weak
bases is influenced by the pH of the fluid in the renal Fraction of drug ionized
tubule (ie, urine pH) and the pKa of the drug. Both of
these factors together determine the percentage of [Ionized]
=
dissociated (ionized) and undissociated (nonionized) [Ionized]+ [Nonionized]
drug. Generally, the undissociated species is more 10pH−pKa
lipid soluble (less water soluble) and has greater = (7.30)
1 10pH−pK
+ a
membrane permeability. The undissociated drug is
easily reabsorbed from the renal tubule back into the The fraction or percent of weak acid drug ionized in
body. This process of drug reabsorption can signifi- any pH environment may be calculated with Equation
cantly reduce the amount of drug excreted, depend- 7.30. For acidic drugs with pKa values from 3 to 8, a
ing on the pH of the urinary fluid and the pKa of the change in urinary pH affects the extent of dissocia-
drug. The pKa of the drug is a constant, but the nor- tion (Table 7-2). The extent of dissociation is more
mal urinary pH may vary from 4.5 to 8.0, depending greatly affected by changes in urinary pH for drugs
on diet, pathophysiology, and drug intake. In addi- with a pKa of 5 than with a pKa of 3. Weak acids with
tion, the initial morning urine generally is more
acidic and becomes more alkaline later in the day.
Vegetable and fruit diets (alkaline residue diet4) TABLE 72 Effect of Urinary pH and pKa on
result in higher urinary pH, whereas diets rich in the lonization of Drugs
protein result in lower urinary pH. Drugs such as Percent of Drug Percent of Drug
ascorbic acid and antacids such as sodium carbonate pH of Urine Ionized: pKa53 Ionized: pKa55
4The alkaline residue diet (also known as the alkaline ash diet) is a 7.4 100 99.6
diet composed of foods, such as fruits and vegetables, from which 5 99 50.0
the carbohydrate portion of the diet is metabolized in the body
leaving an alkaline residue containing cations such as sodium, 4 91 9.1
potasium, calcium, etc. These cations are excreted through the
3 50 0.99
kidney and cause the urine to become alkaline.
162 Chapter 7
TABLE 73 Properties of Renal Drug Elimination Processes
Active/Passive Location in Drug Protein
Process Transport Nephron Drug Ionization Binding Influenced by
Filtration Passive Glomerulus Either Only free drug Protein binding
Secretion Active Proximal tubule Mostly weak acids No effect Competitive inhibitors
and weak bases
Reabsorption Passive/Active Distal tubule Nonionized Not applicable Urinary pH and flow
pKa values of less than 2 are highly ionized at all acid), acidification of the urine causes greater reab-
urinary pH values and are only slightly affected by sorption of the drug and alkalinization of the urine
pH variations. causes more rapid excretion of the drug.
For a weak base drug, the Henderson−Hasselbalch In summary, renal drug excretion is a composite
equation is given as of passive filtration at the glomerulus, active secretion
in the proximal tubule, and passive and/or active
Nonionized
pH = pKa + log (7.31) reabsorption in the distal tubule (Table 7-3). Active
Ionized
secretion is an enzyme (transporter)-mediated pro-
and cess that is saturable. Although reabsorption of drugs
is mostly a passive process, the extent of reabsorp-
10pKa −pH
Percent of drug ionized = (7.32) tion of weak acid or weak base drugs is influenced
1 10pKa −pH
+
by the pH of the urine and the degree of ionization
The greatest effect of urinary pH on reabsorption of the drug. In addition, an increase in blood flow to
occurs for weak base drugs with pKa values of the kidney, which may be due to diuretic therapy or
7.5−10.5. large alcohol consumption, decreases the extent of
From the Henderson−Hasselbalch relationship, drug reabsorption in the kidney and increases the
a concentration ratio for the distribution of a weak rate of drug excreted in the urine.
acid or basic drug between urine and plasma may be
derived. The urine−plasma (U/P) ratios for these CLINICAL APPLICATION
drugs are as follows.
For weak acids, Both sulfisoxazole (Gantrisin) tablets and the com-
bination product, sulfamethoxazole/trimethoprim
U 1 p −
+10 Hurine pKa
= (7.33) (Bactrim) tablets, are used for urinary tract infec-
P pHp −pK
1+10 lasma a
tions. Sulfisoxazole and sulfamethoxazole are sul-
For weak bases, fonamides that are well absorbed after oral
administration and are excreted in high concentra-
1 1 pK − H
U + 0 a p urine
= (7.34) tions in the urine. Sulfonamides are N-acetylated to
P pK −pH
1+10 a plasma
a less water-soluble metabolite. Both sulfonamides
For example, amphetamine, a weak base, will be reab- and their corresponding N-acetylated metabolite are
sorbed if the urine pH is made alkaline and more less water soluble in acid and more soluble in alka-
lipid-soluble nonionized species are formed. In con- line conditions. In acid urine, renal toxicity can
trast, acidification of the urine will cause the amphet- occur due to precipitation of the sulfonamides in the
amine to become more ionized (form a salt). The salt renal tubules. To prevent crystalluria and renal com-
form is more water soluble, less likely to be reab- plications, patients are instructed to take these drugs
sorbed, and tends to be excreted into the urine more with a high amount of fluid intake and to keep the
quickly. In the case of weak acids (such as salicylic urine alkaline.
Drug Elimination, Clearance, and Renal Clearance 163
a constant fraction of the central volume of distribu-
Frequently Asked Questions tion in which the drug is contained that is excreted
»»Which renal elimination processes are influenced by by the kidney per unit of time. More simply, renal
protein binding? clearance is defined as the urinary drug excretion
»»Is clearance a first-order process? Is clearance a rate (dDu/dt) divided by the plasma drug concentra-
better parameter to describe drug elimination and tion (Cp).
exposure than half-life? Why is it necessary to use
both parameters in the literature? Excretion rate dDu /dt Cl = = (7.35)
R Plasma concentration Cp
PRACTICE PROBLEMS As seen earlier in this chapter, most clearances
besides that of the lung are additive, and therefore,
Let pKa = 5 for an acidic drug. Compare the U/P at the total body clearance can be defined as the sum of
urinary pH (a) 3, (b) 5, and (c) 7. the renal clearance (ClR) and the nonrenal clearance
(ClNR), whatever it may consist of (eg, hepatic or
Solution other):
a. At pH = 3,
Cl = ClR + ClNR (7.36)
U 1 −
+103 5 1.01 1.01 1
= = = =
P 1 107.4−5
+ 1+102.4 252 252 Therefore, ClR = fe × Cl (7.37)
b. At pH = 5, where fe is the proportion of the bioavailable dose
that is eliminated unchanged in the urine. Using the
U 1 105−5
+ 2 2 noncompartmental formula for Cl studied earlier
= = =
P 1 −
+107.4 5 1+102.4 252 (Equation 7.2), we obtain
c. At pH = 7, fe × F × Dose
ClR =
AUC0-inf
U 1 07−5
+1 101 101
= = =
P 1 1 −
+ 07.4 5 1+102.4 252
and consequently
In addition to the pH of the urine, the rate of urine flow
Ae
influences the amount of filtered drug that is reabsorbed. 0-inf
ClR = (7.38)
AUC
The normal flow of urine is approximately 1−2 mL/min. 0-inf
Nonpolar and nonionized drugs, which are normally well where Ae0-inf is the amount of drug eliminated
reabsorbed in the renal tubules, are sensitive to changes in unchanged in the urine from time 0 to infinity after a
the rate of urine flow. Drugs that increase urine flow, such single dose. In practice it is not possible to measure
as ethanol, large fluid intake, and methylxanthines (such the amount of drug excreted unchanged in the urine
as caffeine or theophylline), decrease the time for drug until infinity, and so in order to get a reasonable
reabsorption and promote their excretion. Thus, forced estimate of the renal clearance with this noncompart-
diuresis through the use of diuretics may be a useful mental approach formula using the amount excreted
adjunct for removing excessive drug in an intoxicated unchanged in the urine and the systemic exposure,
patient, by increasing renal drug excretion. one has to collect the urine and observe the AUC for
the longest time period possible, ideally more than
RENAL CLEARANCE 3−4 terminal half-lives, so that the error made using
this formula is less than 10%. So if, for example, a
Renal clearance, ClR, is defined as the volume that is drug product has a terminal half-life of 12 hours,
removed from the drug per unit of time through the then one may need to collect the urine for 48 hours
kidney. Similarly, renal clearance may be defined as and calculate the ratio of Ae0-48 divided by AUC0-48.
164 Chapter 7
In essence for that particular drug product one could It can therefore be appreciated that the nonrenal
say that: clearance can be readily calculated when the drug
Ae product is administered intravenously, as ClNR =
0-inf Ae
R ~ 0-48
Cl =
AUC Cl − ClR. However, this calculation is not possible
0-inf AUC0-48
after extravascular administration if the exact rela-
At steady-state conditions it is easier to calculate tive bioavailability is not known or assumed as the
renal clearance, as at steady state all of the excreted exact renal clearance can be calculated (ClR), but
drug eliminated unchanged in the urine from one only the apparent clearance can (Cl/F). The non-
dose occurs over one dosing interval. Equation 7.38 renal clearance can only be estimated if the relative
therefore becomes: bioavailability is assumed. For example, if the rela-
Ae tive bioavailability is estimated to be hypothetically
τ (ss)
ClR(ss) = (7.39)
AUC between 75% and 100%, then the nonrenal clearance
τ (ss)
could be presented in the following manner:
where t is the dosing interval at which the drug is
administered until steady state (ss) conditions are Cl
= 10 L/h and ClR = 5 L/h
seen, and Ae F
t (ss) is the amount of drug excreted
unchanged in the urine during a dosing interval at Therefore,
steady state and AUCt (ss) is the area under the sys-
If F~100%, then ClNR = 5 L/h (eg, ClNR =
temic concentration−time curve over the same dos-
(Cl/F × 1) − ClR)
ing interval at steady state.
One important note is that by virtue of its method But if F ~ 75%, then ClNR = 2.5 L/h (eg, ClNR =
of calculation, the relative bioavailability (F) of the (Cl/F × 0.75) − ClR)
drug is not present in the renal clearance calculations
An alternative approach to obtaining Equation 7.38
while it always is for the total body clearance. So this
is to consider the mass balance of drug cleared by
means that if systemic concentrations and collected
the kidney and ultimately excreted in the urine. For
urinary excretion are only obtained after a drug prod-
any drug cleared through the kidney, the rate of the
uct is administered extravascularly, for example orally,
drug passing through kidney (via filtration, reabsorp-
then only an apparent clearance will be calculated
tion, and/or active secretion) must equal the rate of
(eg, Cl/F and not Cl) while the true renal clearance
drug excreted in the urine.
will be (eg, ClR and not ClR/F).
Rate of drug passing through kidney = rate of
Total clearance will be reported as an “apparent”
drug excreted:
clearance:
ClR × Cp = Qu × Cu (7.40)
Cl Dose
= (after single dose administration)
F AUC0-inf where ClR is renal clearance, Cp is plasma drug con-
centration, Qu is the rate of urine flow, and Cu is the
Cl Dose (at steady state during a dosing
= urine drug concentration. Rearrangement of
F AUC
τ (ss) interval) Equation 7.40 gives
While the renal clearance will not be “apparent”: Qu ×Cu Excretion rate
ClR = = (7.41)
ClR = Ae0-x/AUC0-x (after single dose adminis- Cp Cp
tration and where x is the maximum length of time
during which both urinary excreted amounts and the Because the excretion rate = QuCu = dDu/dt,
AUC can be observed; as mentioned earlier it should Equation 7.41 is the equivalent of Equation 7.38.
be a minimum of 3−4 terminal half-lives) Renal clearance can also be obtained using data
modeling and fitting with compartmental methods.
Ae
τ (ss)
Cl (at steady state during a dosing The most accurate method to obtain renal clearance
R =
AUC
τ (ss) interval) as well as total clearance with this method will be to
Drug Elimination, Clearance, and Renal Clearance 165
• The apparent total volume of distribution, Vss/F,
ka
T would be the addition of Vc/F to the Vp/Flag Cld/F
• The distribution (l1) and terminal elimination (lz)
Vc/F Vp/F rate constants would be:
Cl/F – Cl ° l1 = [((Cl + Cld)/Vc + Cld/Vp) + SQRT(((Cl +
R
ClR Cld)/Vc + Cld/Vp)
2 − 4 × Cl/Vc*Cld/Vp))]/2
° lz = [((Cl + Cld)/Vc + Cld/Vp) − SQRT(((Cl +
Urine Cld)/Vc + Cld/Vp)
2 − 4 × Cl/Vc*Cld/Vp))]/2
• The distribution and terminal elimination half-
FIGURE 78 Schematic description of a hypothetical lives would be:
two-compartment PK model in which plasma concentrations
° T1/2(l1) = 0.693/l1
and urinary excreted data would be simultaneously fitted and
° T1/2(lz) = 0.693/l
explained. z
model simultaneously observed systemic concentra- Comparison of Drug Excretion Methods
tions with observed excreted urinary amounts over a Renal clearance may be measured without regard to the
period of time that allows for robust estimates, so physiologic mechanisms involved in the process. From
ideally over 3−4 terminal half-lives or longer. As a physiologic viewpoint, however, renal clearance may
with any data modeling exercise, it is critical to use be considered the ratio of the sum of the glomerular
the simplest model that can explain all the data filtration and active secretion rates less the reabsorption
appropriately and to use a model that is identifiable. rate divided by the plasma drug concentration:
So using the example of a drug administered via Filtration rate + Secretion rate − Reabsorption rate
the oral route and where the plasma concentration C lR =
Cp
profile is fitted to a two-compartment model and
where the excreted urinary amounts are fitted simul- (7.42)
taneously, a typical model would look like Fig. 7-8,
The renal clearance of a drug is often related to the
where the “fitted” pharmacokinetic parameters by
renal glomerular filtration rate, GFR, when reabsorp-
the model would be:
tion is negligible and the drug is not actively secreted.
• T The renal clearance value for the drug is compared to
lag would be the time elapsed after dosing before
the beginning of the absorption process that of a standard reference, such as inulin, which is
• ka would be the first-order absorption rate constant cleared completely through the kidney by glomerular
• Vc/F would be the apparent central volume of filtration only. The clearance ratio, which is the ratio
distribution of drug clearance to inulin clearance, may give an
• (Cl/F − ClR) would be the apparent total clearance indication for the mechanism of renal excretion of the
that does not include the renal clearance drug (Table 7-4). However, further renal drug excre-
• Cl tion studies are necessary to confirm unambiguously
R would be the renal clearance
• Cld/F would be the apparent distributional clear- the mechanism of excretion.
ance between the central and peripheral volumes
of distribution Filtration Only
• Vp/F would be the apparent peripheral volume of If glomerular filtration is the sole process for drug
distribution excretion, the drug is not bound to plasma proteins,
and is not reabsorbed, then the amount of drug filtered
And where the subsequently “derived” or “calculated”
at any time (t) will always be C
pharmacokinetic parameters would be: p × GFR (Table 7-5).
Likewise, if the ClR of the drug is by glomerular filtra-
• The apparent total clearance, Cl/F, would be the tion only, as in the case of inulin, then ClR = GFR.
addition of ClR to the (Cl/F − ClR) Otherwise, ClR represents all the processes by which
166 Chapter 7
TABLE 74 Comparison of Clearance of a Total excretion
Sample Drug to Clearance of a Reference
Drug, Inulin
Probable Mechanism of Renal Filtration only
Clearance Ratio Excretion
Cl Drug is partially reabsorbed
drug <1 Active
Clinulin secretion only
Cl Drug is filtered only
drug
=1
Clinulin
Cl Drug is actively secreted
drug
>1
Clinulin Plasma level (Cp)
FIGURE 79 Excretion rate−plasma level curves for a drug
the drug is cleared through the kidney, including any that demonstrate active tubular secretion and a drug that is
secreted by glomerular filtration only.
combination of filtration, reabsorption, and active
secretion. Using compartmental PK even when lacking
any knowledge of GFR, active secretion, or the reab-
Filtration and Active Secretion
sorption process, modeling the data allows the pro-
For a drug that is primarily filtered and secreted, with cess of drug elimination to be described quantitatively.
negligible reabsorption, the overall excretion rate will If a change to a higher-order elimination rate process
exceed GFR (Table 7-4). At low drug plasma concen- occurs, then an additional process besides GFR may
trations, active secretion is not saturated, and the drug be involved. The compartmental analysis aids the
is excreted by filtration and active secretion. At high ultimate development of a model consistent with
concentrations, the percentage of drug excreted by physiologic functions of the body.
active secretion decreases due to saturation. Clearance We often relate creatinine clearance (CrCl) to the
decreases because excretion rate decreases (Fig. 7-9). overall clearance of a drug in clinical practice. This
Clearance decreases because the total excretion rate allows clinicians to adjust dosage of drugs depending
of the drug increases to the point where it is approxi- on a patient’s observed renal function. As the renal
mately equal to the filtration rate (Fig. 7-10). clearance is the summation of filtration, secretion, and
reabsorption, it can be simplified to:
TABLE 75 Urinary Drug Excretion Ratea
ClR = Slope × CrCl + Intercept (7.43)
Excretion Rate ( lg/min)
Time (Drug Filtered by Active secretion plus
(minutes) Cp ( lg/mL) GFR per Minute) passive ltration
0 (Cp)0 (Cp)0 × 125
1 (Cp)1 (Cp)1 × 125
2 (Cp)2 (Cp)2 × 125 Filtration
only
T (Cp)t (Cp)t = 125
aAssumes that the drug is excreted by filtration only, is not plasma Plasma drug concentration, Cp
protein bound, and that the GFR is 125 mL/min.
FIGURE 710 Graph representing the decline of renal
Note that the quantity of drug excreted per minute is always the
plasma concentration (Cp) multiplied by a constant (eg, 125 mL/min), clearance. As the drug plasma level increases to a concentra-
which in this case is also the renal clearance for the drug. The glomeru- tion that saturates the active tubular secretion, glomerular
lar filtration rate may be treated as a first-order process relating to Cp. filtration becomes the major component for renal clearance.
Excretion rate (dDu/dt)
Renal clearance, ClR
Drug Elimination, Clearance, and Renal Clearance 167
where the intercept reflects the reabsorption and
secretion processes, assuming that the CrCl only helps identify the mechanism of drug elimination. In
reflects GFR. this example, both drugs have the same clearance.
Because Cl = ClR + ClNR, then Basing the calculation on the elimination con-
cept and applying Equation 7.14, kR and lz are eas-
Cl = (Slope × CrCl + Intercept) + ClNR ily determined, resulting in an obvious difference
An assumption that is often made when adjusting in the elimination t1/2 between the two drugs—in
doses based on differing renal function is that spite of similar drug clearance.
decreasing renal function does not change the nonre- Cl
nal clearance (eg, hepatic and/or other clearances). kR(drug A) = k10(drug A) = λZ(drug A) =
Vss
This is a reasonable assumption to make until quite-
125
severe renal impairment is observed at which point = = 0.0125 min−1
10×1000
changes in protein binding capacity and affinity as
well as changes in enzymatic and transporter affinity Cl
kR(drug B) = k10(drug B) = λZ(drug B) =
and/or activity may be seen. Because ClNR and the Vss
intercept are both constants, then overall clearance 125
= = 0.00625 min−1
formula can therefore be simplified to: 20×1000
Cl = (Slope × CrCl) + Intercept2 (7.44) In spite of identical drug clearances, the lz for drug
The intercept2 is often simplified to ClNR, but in A is twice that of drug B. Drug A has an elimina-
reality if CrCl is assumed to only reflect GFR func- tion half-life of 55.44 minutes, while that of drug
tion, then it is really representative of the clearance B is 110.88 minutes—much longer because of the
from kidney secretion and reabsorption as well as bigger volume of distribution.
from nonrenal routes. 2. In a subject with a normal GFR (eg, a CrCl of
125 mL/min), the renal clearance of a drug is
EXAMPLES »» » 10 L/h while the nonrenal clearance is 5 L/h.
Assuming no significant secretion and reab-
1. Two drugs, A and B, are entirely eliminated sorption, how should we adjust the dosing regi-
through the kidney by glomerular filtration men of the drug if the renal function and the
(125 mL/min), with no reabsorption, and are GFR decrease in half (eg, CrCl = 62.5 mL/min)?
well described by a one-compartment model.
Solution
Drug A has half the distribution volume of drug
B, and the Vss of drug B is 20 L. What are the For a patient with “normal GFR”:
drug clearances for each drug using both the
Cl = ClR + ClNR, so Cl = 15 L/h
compartmental and physiologic approaches?
ClR = Slope × CrCl, therefore,
Solution slope = 10/(125 × 60/1000) = 1.33
Since glomerular filtration of the two drugs is the For a patient with a GFR that decreases in half:
same, and both drugs are not eliminated by other
means, clearance for both drugs depends on renal ClR = Slope × CrCl = 1.33 × (62.5 × 60/1000)
plasma flow and extraction by the kidney only. = 5 L/h
Basing the clearance calculation on the physi- Cl = ClR + ClNR = 5 + 5 = 10 L/h
ologic definition and using Equation 7.18 results in
The clearance therefore decreased by 33%. In
Q(Ca −Cv ) order to reach the same target exposure of the
Cl = =125 mL/min
Ca drug (AUCinf), the dose per day will need to be
Interestingly, known drug clearance tells little about decreased by 33% as Dose = Cl/AUCinf.
the dosing differences of the two drugs, although it
168 Chapter 7
Frequently Asked Question Slope = renal clearance A
(ClR)
»»What is the relationship between drug clearance and
creatinine clearance?
DETERMINATION OF RENAL
CLEARANCE
Graphical Methods B
Clearance is given by the slope of the curve obtained
Plasma level (Cp)by plotting the rate of drug excretion in urine
(dDu/dt) against Cp (Equation 7.45). For a drug that FIGURE 712 Rate of drug excretion versus concentra-
is excreted rapidly, dDu/dt is large, the slope is tion of drug in the plasma. Drug A has a higher clearance than
steeper, and clearance is greater (Fig. 7-11, line A). drug B, as shown by the slopes of line A and line B.
For a drug that is excreted slowly through the kidney,
the slope is smaller (Fig. 7-11, line B). estimated by the trapezoidal rule or by other measure-
From Equation 7.35, ment methods. The disadvantage of this method is
dD that if a data point is missing, the cumulative amount
u /dt
ClR =
C of drug excreted in the urine is difficult to obtain.
p
However, if the data are complete, then the determina-
Multiplying both sides by Cp gives tion of clearance is more accurate by this method.
ClR × C By plotting cumulative drug excreted in the urine
p = dDu/dt (7.45)
t t
from t1 to t2, (D
2
u ) versus (AUC) 2 , one ob
1 t tains an
t
By rearranging Equation 7.45 and integrating, one 1
equation similar to that presented previously:
obtains
[Du] [D t1−t2 = ClR × AUCt1−t2 (7.47)
u]0-t = ClR × AUC0-t (7.46)
The slope is equal to the renal clearance (Fig. 7-13).
A graph is then plotted of cumulative drug excreted in
the urine versus the area under the concentration−time
Midpoint Method
curve (Fig. 7-12). Renal clearance is obtained from
the slope of the curve. The area under the curve can be From Equation 7.35,
dDu /dt Cl
R =
Cp
Slope = renal clearance (ClR)
t (AUC)t2(AUC)0 t1
FIGURE 711 Cumulative drug excretion versus AUC. FIGURE 713 t
Drug excreted versus (AUC) 2 . The slope is
t1
The slope is equal to ClR. equal to ClR.
Drug excreted in urine (Du)
Rate of drug excretion (dDu/dt)
(Du)
t2
t1
Drug Elimination, Clearance, and Renal Clearance 169
which can be simplified to 1000 L. From the information given, find (a) the
X apparent clearance and the clearance, (b) the renal and
u(0-24) /Cp12
ClR = (7.48) nonrenal clearance, (c) the formation clearance of the
24
drug to the metabolite, and (d) if the drug undergoes
where Xu(0-24) is the 24-hour excreted urinary amount
another systemic metabolic or elimination route.
of the drug obtained by multiplying the collected
24-hour urine volume (Vu(0-24)) by the measured uri- Solution
nary concentration (Cu(0-24)) and Cp12 is the midpoint a. Apparent clearance and clearance:
plasma concentration of the drug measured at the
Cl V
midpoint of the collected interval, here at 12 hours. = K ×
F F
This equation is obviously not very robust as it is
on only one measured plasma concentration, Cl 0.693
based = ×1000 = 210 L/h
F 3.3
but it is often very useful in the clinic when very few
plasma concentrations of drugs can be collected and Cl
Cl = × F = 210 × 0.9 = 189 L/h
measured. The overall duration of urinary collection F
is typically 24 hours, but different collection intervals b. Renal and nonrenal clearance:
can obviously be used. Ae0-inf
ClR =
AUC0-inf
PRACTICE PROBLEM and,
DOSE 100
Consider a drug that is eliminated by first-order renal AUC0-inf = = = 0.4762 mg ⋅h/L
Cl /F 210
excretion and hepatic metabolism. The drug follows a
Therefore,
one-compartment model and is given in a single intra-
60
venous or oral dose (Fig. 7-14). Working with the ClR = = 126 L/h
odel presented, assume that a single dose (100 mg) 0.4762
m
of this drug is given orally. The drug has a 90% oral ClNR = 189 −126 = 63 L/h
bioavailability. The total amount of unchanged drug c. Formation clearance of the parent drug to the
recovered in the urine is 60 mg, and the total amount metabolite:
of metabolite recovered in the urine is 30 mg (expressed Ae0-inf 30
as milligram equivalents to the parent drug). According Clf = = = 63 L/h
AUC0-inf 0.4762
to the literature, the elimination half-life for this drug
d. Does the drug undergo other elimination or
is 3.3 hours and its apparent volume of distribution is
metabolic routes?
Cl
= ClR +ClNR = ClR + (Cl
F f +Clother )
Dose Clf
Vss (Cp) Vss(m) (Cm)
F Then, Clother = Cl − ClR − Clf = 189 − 126 − 63 =
Cl-ClR-Clf Cl 0 L/h
R
The drug does not undergo additional elimina-
tion or metabolic routes.
Urine Urine
(parent) (metabolite)
PRACTICE PROBLEM
FIGURE 714 Model of a drug eliminated by first-order
renal excretion and hepatic transformation into a metabolite also An antibiotic is given by IV bolus injection at a dose of
excreted in the urine. (ClR = renal clearance of parent drug, Clf = 500 mg. The drug follows a one-compartment model.
formation clearance of parent drug to metabolite, Cm = plasma The total volume of distribution was 21 L and the elimi-
concentration of the metabolite, Cp = plasma concentration of nation half-life was 6 hours. Urine was collected for
the parent drug, Vss = total volume of distribution of parent drug,
V 48 hours, and 400 mg of unchanged drug was recov-
ss(m) = apparent volume of distribution of metabolite,
(Cl − Cl − Cl of parent drug minus the renal and ered. What is the fraction of the dose excreted unchanged
R f) clearance
formation clearances, F = absolute bioavailability of parent drug.) in the urine? Calculate k, kR, Cl, ClR, and ClNR.
170 Chapter 7
Solution Cl = k × Vss = 0.1155 × 21 = 2.43 L/h
Since the elimination half-life, t1/2, for this drug is ClR = kR × Vss = 0.0924 × 21 = 1.94 L/h
6 hours, a urine collection for 48 hours represents
ClNR = Cl − ClR = 2.43 − 1.94 = 0.49 L/h
8 × t1/2, which allows for greater than 99% of the
drug to be eliminated from the body. The fraction of
drug excreted unchanged in the urine, fe, is obtained
by using Equation 7.37 and recalling that F = 1 for RELATIONSHIP OF CLEARANCE
drugs given by IV bolus injection. TO ELIMINATION HALF-LIFE AND
400 VOLUME OF DISTRIBUTION
fe = = 0.8
500 A common area of confusion for students is the
relationship between half-lives, volumes of distri-
Therefore, 80% of the bioavailable dose is excreted
bution, clearances, and noncompartmental-versus-
in the urine unchanged. Calculations for k, kR, ClT,
compartmental approaches.
ClR, and ClNR are given here:
As seen previously, clearances are always
related to a rate constant (k) and a volume of distri-
0.693
k = 0.1155 h−1 bution (Vd) but these will vary according to the math-
=
6 ematical model that describes appropriately the PK
kR = fe × k = 0.8 × 0.1155 = 0.0924 h−1 of the drug. Table 7-6 aims at reconciling this.
TABLE 76 Relationships between Clearance, Volumes of Distribution, and Half-Life
Appearance of
Cp Versus Time Compartmental Method Noncompartmental Method
Monoexponen- Model after IV administration: Single dose IV administration:
tial decline
Cl = k10 × Vc
AUC
V 0-t typically calculated with linear or mixed
ss = Vc as there is only one compartment
linear/log-linear trapezoidal rule
lz = k10 as there is only one compartment
Cl = ClR + ClNR
C
Cl t is the last detectable concentration time point.
R = kR × Vc
T1/2 = 0.693/lz
lz is the negative slope using linear regression of
Biexponential Model after IV administration: the terminal elimination log-linear phase of the
decline
Cl = k10 × V concentration-versus-time profile.
c
Vp = k12 × Vc/k21
Vss = Vc + V Cl = DOSE/AUC
p 0-inf
l1 = [((Cl + Cl AUC
d)/Vc + Cld/Vp) + SQRT(((Cl + Cld)/Vc 0-inf = AUC0-t + Ct/lz
+ Cld/Vp)2 − 4 × Cl/Vc∗Cld/Vp))]/2 MRT = AUMC0-inf/AUC0-inf − (Duration of infusion/2)
lz = [((Cl + Cld)/Vc + Cld/Vp) − SQRT(((Cl+Cld)/Vc Vss = Cl × MRT
+ Cld/Vp)2 − 4 × Cl/Vc∗Cld/Vp))]/2
T1/2 (elimination) = 0.693/lz
T1/2 (distribution) = 0.693/l1
T1/2 (elimination) = 0.693/lz
Drug Elimination, Clearance, and Renal Clearance 171
CHAPTER SUMMARY
Clearance refers to the irreversible removal of drug the clearance will be the product of the terminal
from the systemic circulation of the body by all elimination rate constant and the total volume of
routes of elimination. Clearance may be defined as distribution. Clearance is therefore inversely related
the volume of fluid removed from the drug per unit to the elimination half-life of a drug. Organ clear-
of time. The clearance of a drug is a very clinically ances are additive, except for lung, and so the total
useful parameter as it is related to the systemic expo- body clearance is often described in terms of renal
sure of a drug, which dictates efficacy and safety, and nonrenal clearance. The renal clearance is depen-
and its administered dose. Clearance is a constant dent on renal blood flow, glomerular filtration, drug
when the PK behavior of a drug is linear in terms of secretion, and reabsorption. Reabsorption of drugs is
time and dose. Clearance can be calculated by many often a passive process and the extent of reabsorp-
different methods, including noncompartmental, tion of weak acid or weak base drugs is influenced
compartmental, and physiological. Assuming a spe- by the pH of the urine and the degree of ionization
cific compartment model, clearance will be the prod- of the drug. In addition, an increase in blood flow to
uct of an elimination rate constant and a volume of the kidney, which may be due to diuretic therapy or
distribution. In the simplest case, a one-compartment large beer consumption, decreases the extent of drug
model for drugs whose concentration−time profile reabsorption in the kidney and increases the rate of
decreases according to a monoexponential decline, drug excreted in the urine.
LEARNING QUESTIONS
1. Theophylline is effective in the treatment of b. What is the renal clearance for this drug?
bronchitis at a blood level of 10−20 mg/mL. At c. What is the probable mechanism for renal
therapeutic range, theophylline follows linear clearance of this drug?
pharmacokinetics. The average t1/2 is 3.4 hours, 3. A drug with an elimination half-life of 1 hour
and the range is 1.8−6.8 hours. The average was given to a male patient (80 kg) by intrave-
volume of distribution is 30 L. nous infusion at a rate of 300 mg/h. At 7 hours
a. What are the average upper and lower after infusion, the plasma drug concentration
clearance limits for theophylline assuming a was 11 mg/mL.
one-compartment model? a. What is the total body clearance for this drug?
b. The renal clearance of theophylline is 0.36 L/h. b. What is the apparent Vss for this drug assum-
What are the kNR and kR? ing a one-compartment model?
2. A single 250-mg oral dose of an antibiotic c. If the drug is not metabolized and is elimi-
is given to a young man (age 32 years, nated only by renal excretion, what is the
creatinine clearance CrCl = 122 mL/min, renal clearance of this drug?
ABW = 78 kg). From the literature, the d. What would then be the probable mecha-
drug is known to have an apparent Vss equal nism for renal clearance of this drug?
to 21% of body weight and an elimination 4. In order to rapidly estimate the renal clearance
half-life of 2 hours. The dose is normally of a drug in a patient, a 2-hour postdose urine
90% bioavailable and is not bound signifi- sample was collected and found to contain
cantly to plasma proteins. Urinary excretion 200 mg of drug. A midpoint plasma sample
of the unchanged drug is equal to 70% of the was taken (1 hour postdose) and the drug con-
bioavailable dose. centration in plasma was found to be 2.5 mg/L.
a. What is the total body clearance for this Estimate the renal clearance for this drug in
drug assuming a one-compartment model? this patient.
172 Chapter 7
5. According to the manufacturer, after the the drug using urinary data. (b) Determine the
antibiotic cephradine (Velosef), given by IV clearance using the noncompartmental method.
infusion at a rate of 5.3 mg/kg/h to 9 adult (c) Is there any nonrenal clearance of the drug in
male volunteers (average weight, 71.7 kg), a this patient? What would be the nonrenal clear-
steady-state serum concentration of 17 μg/mL ance, if any? How would you determine clear-
was measured. Calculate the average clearance ance using a compartmental approach and com-
for this drug in adults. pare that with the noncompartmental method?
6. Cephradine is completely excreted unchanged 9. Ciprofloxacin hydrochloride (Cipro) is a
in the urine, and studies have shown that pro- fluoroquinolone antibacterial drug used to
benecid given concurrently causes elevation of treat urinary tract infections. Ciprofloxacin
the serum cephradine concentration. What is contains several pKas (basic amine and car-
the probable mechanism for the interaction of boxylic group) and may be considered a weak
probenecid with cephradine? acid and eliminated primarily by renal excre-
7. When deciding on a dosing regimen of a drug tion, although about 15% of a drug dose is
to administer to a patient, what information can metabolized. The serum elimination half-life in
be obtained from knowing only the elimination subjects with normal renal function is approxi-
half life? The clearance? mately 4 hours. The renal clearance of cip-
8. A patient was given 2500 mg of a drug by rofloxacin is approximately 300 mL/min. By
IV bolus dose, and periodic urinary data were what processes of renal excretion would you
collected. (a) Determine the renal clearance of conclude that ciprofloxacin is excreted? Why?
ANSWERS
Frequently Asked Questions saturated, then the clearance cannot be described
by a constant.
Why is clearance a useful pharmacokinetic parameter? Clearance is related to the administered dose
• Clearance is very useful clinically as it is the and the overall exposure of a drug as per the formula
only PK parameter that relates to dose and the Cl/F = DOSE/AUC0-inf. As the exposure of a drug
overall exposure of a drug, for example, Cl/F correlates with its efficacy and toxicity, clearance is
=
DOSE/AUC a much more useful parameter clinically than the
0-inf.
terminal half-life as it will directly dictate what dose
Which renal elimination processes are influenced by to administer to a patient in order to reach a cer-
protein binding? tain systemic exposure. Although it will not dictate
• what dose to administer, the terminal half-life will
Only the free drug can be filtered by the kidney, so
be important in deciding how often to administer a
protein binding influences the filtration of drugs,
drug. Both parameters are therefore important.
but it has no significant influences on secretion
and reabsorption.
What is the relationship between drug clearance and
Is clearance a first-order process? Is clearance a creatinine clearance?
better parameter to describe drug elimination and
• The Cl of a drug is composed of the renal (ClR)
exposure than half-life? Why is it necessary to use
and of the nonrenal (ClNR) components. The ClR
both parameters in the literature?
is composed of filtration, reabsorption, and secre-
• The clearance of a drug is a constant only if the tion components. Creatinine is mostly filtrated but
drug exhibits linear pharmacokinetic characteris- also secreted, so the creatinine clearance (CrCl),
tics. If the clearance changes with drug concen- whether estimated by the Cockcroft and Gault
trations, for example, when metabolism becomes formula or calculated by collecting its urinary
Drug Elimination, Clearance, and Renal Clearance 173
excretion, is used in clinical practice to give us an R0 300
indication of the filtration capacity (eg, GFR) of Cl = = = 27.27 mg/L
Css 11
the kidney in a given patient.
Because Cl = ClR + ClNR, and because the Cl = λz ×Vss
CrCl directly correlates with ClR, the clearance
of a drug can often be expressed as Cl = (Slope × b. Cl 27.27
Vss = = = 39.354 L
CrCl) + Intercept, where the intercept can often be λ 0.693/1
z
assumed to mostly reflect the nonrenal clearance
component. c. ClR ~ Cl = 27.27 L/h
d. ClR = 27.27 × 1000/60 = 454.54 mL/min
Learning Questions
The binding to plasma protein is unknown
1. a. Cl = k × V, where V = 30 L and k = 0.693/T (eg, only free drug is filtered), the renal
1/2
function of the patient is unknown, and the
Average Cl = 30 × 0.693/3.4 = 6.11 L/h molecular weight of the drug is unknown
Upper Cl = 30 × 0.693/1.8 = 11.55 L/h (drugs with large molecular weight are not
Lower Cl = 30 × 0.693/6.8 = 3.06 L/h filtered). So at this point, this drug is likely
filtered but we cannot be sure based on the
b. ClR = kR × V limited information available.
Because the ClR > GFR, we know for
kR = ClR/V = 0.36/30 = 0.36 L/h
sure, though, that the drug is actively
Cl = ClR + ClNR secreted. It could also be reabsorbed, but
ClNR = Cl − ClR = 6.11 × 0.36 = 5.75 L/h we cannot be sure based on the information
available.
kNR = ClNR/V = 5.75/30 = 0.192 h−1
4. The renal clearance can be calculated using the
2. a. Cl = lz × Vss as the drug PK is well described midpoint clearance formula,
by a one-compartment model
Curine × Volume urine
lz = 0.693/2 = 0.3465 h−1 ClR =
Cp(midpoint)
Vss = 0.21 × 78 = 16.38 L
where (Curine × Volume urine) = 200 mg.
Cl = 0.3465 × 16.38 = 5.68 L/h
200
b. fe = 70% ClR = = 80 L per 2 hours, or 40 L/h
2.5
ClR = fe × Cl = 0.7 × 5.68 = 3.97 L/h
R
C 0
5. ss =
c. ClR = 3.97 L/h = 66.2 mL/min Cl
This man has a CrCl of 122 mL/min. Because
R0 5.3× 71.7
the ClR is less than the CrCl, and because the Cl = = = 22.4 L/h
Css 17
drug is not bound to plasma protein, then we
can expect that the drug is filtered but also
6. Probenecid is likely decreasing the renal secre-
reabsorbed with or without being secreted.
tion of cephradine.
3. a. During intravenous infusion, the drug levels
will reach more than 99% of the plasma steady- 7. Cl/F = DOSE/AUC0-inf, so if the target AUC0-inf
state concentration after 7 half-lives of the is known in order to achieve a desired level of
drug, 7 hours in this case. So we can assume efficacy without significant toxicity, then the
that steady-state conditions are reached. At dose to administer per day to a patient will be
steady state, dictated by its Cl/F value.
174 Chapter 7
For example, if the targeted AUC per day
is 100 mg/L and the Cl/F in a patient is 400 y = –1.4824 + 1493.4x
R2 = 1.000
1 L/h, then the drug has to be adminis-
tered at a dose of 100 mg per day. 300
The elimination half-life will not help us under-
stand what dose per day to administer, but will help
200
us decide how frequently to administer the drug.
For example, if the minimum level of effi-
cacy of the previous drug is seen at 1 mg/L, 100
if its Cmax at steady state after 100-mg dose
per day is 4 mg/L, then the drug can be 0
given every 2 half-lives in order to reach 0 100 200 300
a Cmax of 4 and a minimum concentration Cp between time points (average)
of 1 mg/L at steady state. If the half-life in FIGURE A1
a patient is 12 hours, then the drug can be
administered as 100 mg every 24 hours. concentration curve [AUC] must be calculated
and summed. The tailpiece is extrapolated
8. because the data are not taken to the end. A plot
of log Cp versus t (Fig. A-2) yields a slope of
Plasma Urinary Urinary Urinary
k = 0.23 h−1. The tailpiece of area is extrapo-
Time Concentration Volume Concentration
(hours) (lg/mL) (mL) (lg/mL) lated using the last data point divided by k or
31.55/0.23 = 137.17 mg/mL/h.
0 250.00 100.00 0.00
1 198.63 125.00 2880.00 1000
2 157.82 140.00 1901.20
3 125.39 100.00 2114.80
4 99.63 80.00 2100.35
5 79.16 250.00 534.01 100 k = –2.3x slope
6 62.89 170.00 623.96
7 49.97 160.00 526.74
8 39.70 90.00 744.03
9 31.55 400.00 133.01 10
0 2 4 6 8 10 12
10 25.06 240.00 176.13 Time
From the data, determine urinary rate of drug FIGURE A2
excretion per time period by multiplying
urinary volume by the urinary concentration Subtotal area (0−9 h) 953.97
for each point. Average Cp for each period by
Tailpiece (9−∞ h) 137.17
taking the mean of two consecutive points (see
table). Plot dDu/dt versus Cp to determine renal Total area (0−∞) 1091.14
clearance from the slope. The renal clearance
FD 2,500,000
from the slope is 1493.4 mL/h (Fig. A-1). Total clearance 0
= ClT = =
[AUC]∞ 1091.14
To determine the total body clearance by 0
the area method, the area under the plasma
= 2291.2 mL/h
Cp dDu/dt (thousands)
Drug Elimination, Clearance, and Renal Clearance 175
Time Plasma Concentration Urinary Urinary Concentration Urinary Rate,
(hours) (mg/mL) Volume (mL) (lg/mL) dDu/dt (lg/h) Average Cp
0 250.00 100.00 0 0
1 198.63 125.00 2680.00 334,999.56 224.32
2 157.82 140.00 1901.20 266,168.41 178.23
3 125.39 100.00 2114.80 211,479.74 141.61
4 99.63 80.00 2100.35 168,027.76 112.51
5 79.16 250.00 534.01 133,503.70 89.39
6 62.89 170.00 623.96 106,073.18 71.03
7 49.97 160.00 526.74 84,278.70 56.43
8 39.70 90.00 744.03 66,962.26 44.84
9 31.55 400.00 133.01 53,203.77 35.63
Because total body clearance is much larger from the graph. VD is 10 L and k is 0.23 h−1. Total
than renal clearance, the drug is probably also clearance is 2300 mL/min (a slightly different
excreted by a nonrenal route. value when compared with the area method).
Nonrenal clearance = 2291.2−1493.4 9. The ClR of Ciprofloxacin is larger than the GFR
(eg, 300 mL/min) and so the drug is at least
= 797.8 mL/h secreted in addition to be filtered. Weak acids
The easiest way to determine clearance by a are known to be secreted.
compartmental approach is to estimate k and VD
REFERENCES
Guyton AC: Textbook of Medical Physiology, 8th ed. Philadelphia, West JB (ed): Best and Taylor’s Physiological Basis of Medical
Saunders, 1991. Practice, 11th ed. Baltimore, Williams & Wilkins, 1985.
Levine RR: Pharmacology: Drug Actions and Reactions, 4th ed.
Boston, Little, Brown, 1990.
BIBLIOGRAPHY
Benet LZ: Clearance (née Rowland) concepts: A downdate and Smith H: The Kidney: Structure and Function in Health and Disease.
an update. J Pharmacokinet Pharmacodyn 37:529−539, 2010. New York, Oxford University Press, 1951.
Cafruny EJ: Renal tubular handling of drugs. Am J Med 62: Thomson P, Melmon K, Richardson J, et al: Lidocaine pharma-
490−496, 1977. cokinetics in advanced heart failure, liver disease and renal
Hewitt WR, Hook JB: The renal excretion of drugs. In Bridges VW, failure in humans. Ann Intern Med 78:499−508, 1973.
Chasseaud LF (eds.), Progress in Drug Metabolism, vol. 7. Tucker GT: Measurement of the renal clearance of drugs. Br J
New York, Wiley, 1983, chap 1. Clin Pharm 12:761−770, 1981.
Holford N, Heo YA, Anderson B. A pharmacokinetic standard for Weiner IM, Mudge GH: Renal tubular mechanisms for excretion
babies and adults. J Pharm Sci 102(9):2941−2952, 2013. and organic acids and bases. Am J Med 36:743−762, 1964.
Renkin EM, Robinson RR: Glomerular filtration. N Engl J Med Wilkinson GR: Clearance approaches in pharmacology. Pharmacol
290:785−792, 1974. Rev 39:1−47, 1987.
Rowland M, Benet LZ, Graham GG: Clearance concepts in phar-
macokinetics. J Pharm Biopharm 1:123−136, 1973.
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Pharmacokinetics of
8 Oral Absorption
John Z. Duan
Chapter Objectives INTRODUCTION
»» Define oral drug absorption Extravascular delivery routes, particularly oral dosing, are impor-
and describe the absorption tant and popular means of drug administration. Unlike intravenous
process. administration, in which the drug is injected directly into the gen-
»» Introduce two general eral circulation (see Chapters 4–7), pharmacokinetic models after
approaches used for studying extravascular drug administration must consider drug absorption
absorption kinetics and their from the site of administration, for example, the gut, the lung, etc.
similarities and differences. The aim of this chapter is to study the kinetics of absorption.
Before delving into the details, it is important to clarify the defini-
»» Understand the basic principles
tion of absorption.
for physiologically based
There are three different definitions of absorption in exis-
absorption kinetics.
tence. Traditionally, absorption occurs when drug reaches the
»» Describe the oral one- systemic circulation, or sometimes when it reaches the portal vein
compartment model and blood stream. In recent years, a new definition is presented, in which
explain how this model drug is assumed to be absorbed when it leaves the lumen and
simulates drug absorption from crosses the apical membrane of the enterocytes lining the intestine
the gastrointestinal tract. (GastroPlus manual). It is important to distinguish among these
»» Calculate the pharmacokinetic definitions when the kinetics study is performed, especially during
parameters of a drug comparisons of the study results.
that follows the oral one- Drug absorption from the gastrointestinal (GI) tract or any
compartment model. other extravascular site is dependent on (1) the physicochemical
properties of the drug and the environment in the small intestine,
»» Calculate the fraction of drug (2) the dosage form used, and (3) the anatomy and physiology of
absorbed in a one-compartment the absorption site, such as surface area of the GI tract, stomach-
model using the Wagner–Nelson emptying rate, GI mobility, and blood flow to the absorption site.
method. Extravascular drug delivery is further complicated by variables at
»» Calculate the fraction of drug the absorption site, including possible drug degradation and sig-
absorbed in a two-compartment nificant inter- and intrapatient differences in the rate and extent
model using the Loo–Riegelman of absorption. The variability in drug absorption can be mini-
method. mized to some extent by proper biopharmaceutical design of the
dosage form to provide predictable and reliable drug therapy
»» Describe the conditions that
(Chapters 15–18). Although this chapter will focus primarily on
may lead to flip-flop of ka and k
oral dosing, the concepts discussed here may be easily extrapo-
during pharmacokinetics (PK)
lated to other extravascular routes.
data analysis.
There are generally two methodologies to study the kinetics of
absorption. Pharmacokinetic models can be built based mainly on
177
178 Chapter 8
»» Describe the model parameters the observed clinical data (“top-down” approach) or based on the
that form the foundation of drug broader understanding of the human body and its mechanisms
absorption and bioavailability of (“bottom-up” approach) (Jamei et al, 2009). A top-down model is
oral dosage forms. often specified with the assistance of “black boxes” (such as the
compartment model). In a bottom-up approach the elements of the
»» Discuss how ka and k may
system are first specified in great detail. These elements are then
influence Cmax, tmax, and AUC
linked together to form larger subsystems, which in turn are
and how changes in these
linked, sometimes in many levels, until a complete top-level sys-
parameters may affect drug
tem is formed. The goals of the two approaches are the same: to
safety in a clinical situation.
make physiologically plausible predictions.
This chapter will introduce the basic concept of the physiolog-
ically based absorption kinetics (the bottom-up approach) with
some examples followed by the detailed explanation of the tradi-
tional top-down approach, and finally, the combination of the two
approaches is proposed.
BASIC PRINCIPLES OF PHYSIOLOGICALLY
BASED ABSORPTION KINETICS
(BOTTOM-UP APPROACH)
The physiologically based absorption models provide a quantita-
tive mechanistic framework by which scaled drug-specific param-
eters can be used to predict the plasma and, importantly, tissue
concentration–time profiles of drugs following oral administra-
tion. The main advantage of physiology-based pharmacokinetic
(PBPK) models is that they can be used to extrapolate outside the
studied population and experimental conditions. For example,
PBPK can be used to extrapolate the absorption process in healthy
volunteers to that in a disease population if the relevant physiologi-
cal properties of the target population are available. The trade-off for
this advantage is a complex system of differential equations with a
considerable number of model parameters. When these parameters
cannot be informed from in vitro or in silico1 experiments, PBPK
models are usually optimized with respect to observed clinical data.
Parameter estimation in complex models is a challenging task asso-
ciated with many methodological issues.
Historically, PBPK approach stemmed from a natural thinking
for elucidating the kinetics of absorption. The first pharmacoki-
netic model described in the scientific literature was in fact a
PBPK model (Teorell, 1937). However, this model led to great
difficulty in computations due to lack of computers. Additionally,
the in vitro science was not advanced enough to obtain the neces-
sary key information. Therefore, the lack of in vitro and in silico
techniques hindered the development of PBPK approach for many
1In silico refers to computer-based models.
Pharmacokinetics of Oral Absorption 179
years. Recently, PBPK development has been accel- two directions, indicating the drug transit among
erated mainly due to the explosion of computer sci- these compartments. Each transit process, repre-
ence and the increasing availability of in vitro sented by an arrow in Fig. 8-1, can be expressed by
systems that act as surrogates for in vivo reactions a differential equation. The model equations follow
relevant to absorption. the principles of mass transport, fluid dynamics, and
Parameter estimation in PBPK models is chal- biochemistry in order to simulate the fate of a sub-
lenging because of the large number of parameters stance in the body. Most of the equations involve
involved and the relative small amount of observed linear kinetics. For example, for non-eliminating
data usually available. An absorption model consists tissues, the following principles are followed: the
of a set of values for the absorption scale factors, “rate of change of drug in the tissue” is equal to the
transit times, pH assignments, compartment geome- “rate in” (QT · CA) minus the “rate out” (QT · CvT) as
tries (individual compartment radii and lengths, and shown in Equation 8.1.
volume), and pharmacokinetic parameters that pro-
vide the best predictions for a compound in human. dC
V T
= Q C −Q C (8.1)
For example, an advanced absorption transit model T dt T A T vT
developed in GastroPlus™2 contains nine compart-
ments, which represent the five segments of the GI where Q = blood flow (L/h), C = concentration
tract—stomach, duodenum, jejunum, ileum, and (mg/L), V = volume (L), T = tissues, A = arterial, v =
colon. The fluid content, carrying dissolved and venous, CvT = CT/(Kp/B:P), B:P = blood-to-plasma
undissolved compound, passes from one compart- ratio. On the other hand, Michaelis–Menten nonlin-
ment to the next, simulating the action of peristaltic ear kinetics is used to describe saturable metabolism
motion. Within each compartment, the dynamic and carrier-mediated transport.
interconversion between dissolved and undissolved The PBPK approach can specifically define the
compound is modeled. Dissolved compound can be absorption for a specific drug product. Figure 8-2
absorbed across the GI tract epithelium. The volume shows the simulation results using PBPK software
of each compartment, which represents the fluid GastroPlus for several drugs with different physico-
content, is modeled dynamically, simulating the fol- chemical properties. The first column lists the drug
lowing processes: names and the second column is the pKa of the com-
pound. The solubility factor (Sol Factor) is the ratio
• Transit of the fluid with characteristic rate con-
of the solubility of the completely ionized form of an
stants through each compartment
ionizable group to the completely unionized form.
• Gastric secretion into the stomach, and biliary and
The figure also lists the solubility and logD pH pro-
pancreatic secretions into the duodenum
files for each drug (two green vertical lines indicate
• Absorption of uid from duodenum, jejunum, ileum,
pH 1.2 and 7.5, respectively). Notice that the color of
and large intestine
the cells for dose number (Dose No), absorption
Figure 8-1 shows the graphic representation of number (Abs No), and dissolution number (Dis No)
this model. As seen, each of the nine compartments changes depending on the physicochemical and bio-
is divided into four subcompartments: unreleased, pharmaceutical properties of the drug selected. The
undissolved, dissolved, and enterocyte. colors approximate the four Biopharmaceutical
In the figure, the compartments and subcom- Classification System (BCS) categories. All green
partments in GI tract are connected to each other by indicates high permeability, high solubility, and
arrows. These arrows are of either one direction or rapid dissolution (BCS Class I). Red absorption
number and green dose number may indicate low
permeability and high solubility (BCS Class III). All
2GastroPlus is a mechanistically based simulation software package
red may indicate low permeability and low solubility
that simulates absorption, pharmacokinetics, and pharmacodynamics
in human and animals (http://www.simulations-plus.com/Products (BCS Class VI). These color systems are not perfect
.aspx?GastroPlus&grpID=3&cID=16&pID=11). cutoffs for the BCS, but they represent most drugs.
ch
Stoma
Asc C
olon
Cecu
m
Ileu
m 3
Ileu
m 2
Ileu
m 1
Jeju
num 2
Jeju
num 1
Duodenum
Hepatic Hepatic Unreleased
Vein Artery
Liver Undissolved
Dissolved
Portal
Vein
Enterocyte
GI Tract
Venous Arterial
Portal Vein
Flow Flow
FIGURE 81 A graphic representation of drug absorption from the GI tract.
180
Solubility pH LogD pH Prole Absorption & Dissolution Compartmental
absorption Plasma Concentration
prole
Metoprolol
1.0 Metoprolol
AmtDiss AmtPV
150
0.5 AmtAbs Total SC Metoprolol
150 93.0% 93% 0.25
150
0.0 0.20
100 100
100 0.15
36.7%
–0.5 50 20.4% 17.6% 0.10
50 –1.0 50 8.9% 4.7%
0% 2.6% 0.4% 1.7% 0.05
0.00
–1.5 0
0 0 5 10 15 20 25
5 10 15 20
0 2 4 6 8 10 0 2 4 6 8 10 Time (h)
pH Time (h)
pH
3 Ketoprofen
Ketoprofen
AmtDiss AmtPV
60 AmtAbs Total SC Ketoprofen
2.5
2 50 50 99.9% 99.9%
2.0
40 40
40
30 55.7%
30 1.5
1 20 31.6% 1.0
20
20 10 6.8%
0% 1.6% 0.4% 0.2% 2.7% 0.8% 0.5
10
0 0.0
0
0 0 5 10 15 20 25
5 10 15 20
0 2 4 6 8 10 0 2 4 6 8 10 Time (h)
Time (h)
pH pH
Carbamazepine
1.5 Carbamazepine
20 AmtDiss AmtPV
AmtAbs Total SC 99.5% Carbamazepine
200 99.3% 1.5
15 200
1.0 150
150 1.0
10 100
100 31.6%
50 21.4%
0.5 10.5% 12.7% 0.5
5 7.1% 4% 8.6%
50 0% 3.6%
0.0
0
0
0.0
0 2 4 6 8 10 0 2 4 6 8 10 5 10 15 20 0 5 10 15 20 25
pH pH Time (h) Time (h)
–0.5 Atenolol Atenolol
150 AmtDiss AmtPV
Atenolol
–1.0 AmtAbs Total SC
100 40 37.9% 0.3
37.9%
100 80 30 0.2
–1.5
60 20
11.9%
40 10 8.5% 0.1
3.8% 6%
50 –2.0 4.1%
0% 2.8% 0.1% 0.6%
20
0.0
0
–2.5 0 5 10 15 20 25
5 10 15 20
0 2 4 6 8 10 0 2 4 6 8 10 Time (h)
pH pH Time (h)
Furosemide Furosemide
1.5
4 AmtDiss AmtPV Furosemide
1.0 AmtAbs Total SC 60
3 100 .1%
50 52.1% 52
0.5 80 40 1.0
2 60 30
0.0
20 16.4%
40 11.3%
10 7.7% 0.5
4% 5.1%
1 –0.5 3.3% 3.2%
20 0% 1%
–1.0 0 0.0
0
5 10 15 20 0 5 10 15 20 25
0 2 4 6 8 10 0 2 4 6 8 10 Time (h) Time (h)
pH pH
FIGURE 82 The modeling results for several drugs using GastroPlus software.
Furosemide Atenolol Carbamazepine Ketoprofen Metoprolol tartrate Drug
–0.59, 3.88, 9.37 9.33 11.83 4.39 9.39 pka
36.7 16.2 503 35.3 35.9 Sol Factor
64.9565 0.0025 6.8376 0.9792 0.0064 Dose No
0.261 5.761 × 103 5.299 9.075 6.257 × 103 Dis No
0.596 0.367 8.546 17.29 2.663 Abs No
Solubility (mg/mL) Solubility (mg/mL) Solubility (mg/mL) Solubility (mg/mL) Solubility (mg/mL)
logD logD logD logD logD
Mass (mg) Mass (mg) Mass (mg) Mass (mg) Mass (mg)
Amount (mg) Amount (mg) Amount (mg) Amount (mg) Amount (mg)
Stomach Stomach Stomach Stomach Stomach
Duodenum Duodenum Duodenum Duodenum Duodenum
Jejunum 1 Jejunum 1 Jejunum 1 Jejunum 1 Jejunum 1
Jejunum 2 Jejunum 2 Jejunum 2 Jejunum 2 Jejunum 2
IIeum 1 IIeum 1 IIeum 1 IIeum 1 IIeum 1
IIeum 2 IIeum 2 IIeum 2 IIeum 2 IIeum 2
IIeum 3 IIeum 3 IIeum 3 IIeum 3 IIeum 3
Caecum Caecum Caecum Caecum Caecum
Asc colon Asc colon Asc colon Asc colon Asc colon
AmtAbs AmtAbs AmtAbs AmtAbs AmtAbs
Concentration (µg/mL) Concentration (µg/mL) Concentration (µg/mL) Concentration (µg/mL) Concentration (µg/mL)
181
182 Chapter 8
Based on the in vitro properties and assuming a ABSOROPTION KINETICS
set of general physiological conditions, the absorp-
(THE TOP-DOWN APPROACH)
tion profiles, the absorption amount in each of the
nine compartments, and the plasma concentration The top-down approach is a traditional methodology
profiles are predicted in the last three columns, to study the kinetics of drug absorption. With the
respectively. In the “Absorption & Dissolution” col- advances of statistical methods and computer sci-
umn, the profiles for the total dissolved (red), the ence, many software packages are available to calcu-
absorbed (cyan, the absorption is defined as the drug late the pharmacokinetic parameters. The following
leaves the lumen and crosses the apical membrane of sections provide the basic concepts and rationales.
the enterocytes lining the intestine), the cumulative
amount entering portal vein (blue), and the cumula-
tive amount entering systemic circulation (green) are PHARMACOKINETICS
characterized. These profiles along with the informa-
OF DRUG ABSORPTION
tion about the amount absorbed in each compartment
give the plasma concentration profiles as shown in In pharmacokinetics, the overall rate of drug absorp-
the last column. As seen, due to the physicochemical tion may be described as either a first-order or a zero-
property differences, the rate and the extent of order input process. Most pharmacokinetic models
absorption vary among the drugs listed. assume first-order absorption unless an assumption
Drug absorption from the gastrointestinal tract of zero-order absorption improves the model signifi-
is a highly complex process dependent upon numer- cantly or has been verified experimentally.
ous factors. In addition to the physicochemical The rate of change in the amount of drug in the
properties of the drug as shown in Fig. 8-2 (with body, dDB/dt, is dependent on the relative rates of
limited extents), characteristics of the formulation drug absorption and elimination (Fig. 8-3). The net
and interplay with the underlying physiological rate of drug accumulation in the body at any time is
properties of the GI tract play important roles. In equal to the rate of drug absorption less the rate of
GastroPlus, the formulation types that can be drug elimination, regardless of whether absorption
selected include both immediate release (IR) formu- rate is zero-order or first-order.
lations (solution, suspension, tablet, and capsule)
and controlled release (CR) formulations (enteric- dD dD dD
B GI E
= − (8.2)
coated or other form of delayed release [DR]). For dt dt dt
CR, release of either dissolved material (drug in
where DGI is the amount of drug in the gastrointestinal
solution) or undissolved material (solid particles,
tract and DE is the amount of drug eliminated. A
which then dissolve according to the selected dis-
plasma level–time curve showing drug absorption and
solution model) can be evoked.
elimination rate processes is given in Fig. 8-4. During
In addition to GastroPlus, there are several other
the absorption phase of a plasma level–time curve
physiologically based softwares available for studying
(Fig. 8-4), the rate of drug absorption3 is greater than
absorption kinetics, such as SimCyp (http://www
.simcyp.com/) and PK-Sim (http://www.systems
-biology.com/products/pk-sim.html).
Absorption Elimination
The major advantage of the PBPK approach is D D V D
GI B D E
that if adequate information of physicochemical
properties of a drug is available, a reasonable predic-
FIGURE 83 Model of drug absorption and elimination.
tion for the performance of the drug product can be
made with certain assumptions according to previ-
ous experience. With little or no human PK data 3The rate of drug absorption is dictated by the product of the drug
generated, the predictions would be very valuable in the gastrointestinal tract, DGI times the rst-order absorption
for further drug development. rate constant, ka.
Pharmacokinetics of Oral Absorption 183
or dDGI/dt = 0. The plasma level–time curve (now the
elimination phase) then represents only the elimina-
tion of drug from the body, usually a first-order pro-
Postabsorption
phase cess. Therefore, during the elimination phase the rate
of change in the amount of drug in the body is
described as a first-order process:
Elimination dDB
phase = −kD
dt B (8.6)
Absorption
phase
where k is the first-order elimination rate constant.
Clinical Application
Peak
concentration, Cmax Time Manini et al (2005) reported a case of adverse drug
reaction in a previously healthy young man who
FIGURE 84 Plasma level–time curve for a drug given in
ingested a recommended dose of an over-the-counter
a single oral dose. The drug absorption and elimination phases
of the curve are shown. (OTC) cold remedy containing pseudoephedrine.
Forty-five minutes later, he had an acute myocardial
infarction (MI). Elevations of cardiac-specific creatinine
the rate of drug elimination.4 Note that during the kinase and cardiac troponin I confirmed the diagnosis.
absorption phase, elimination occurs whenever drug Cardiac magnetic resonance imaging (MRI) confirmed
is present in the plasma, even though absorption a regional MI. Cardiac catheterization 8 hours later
predominates. revealed normal coronary arteries, suggesting a mech-
dD dD anism of vasospasm.
GI E
> (8.3)
dt dt 1. Could rapid drug absorption (large ka) contrib-
At the peak drug concentration in the plasma ute to high-peak drug concentration of pseudo-
(Fig. 8-4), the rate of drug absorption just equals the ephedrine in this subject?
rate of drug elimination, and there is no net change 2. Can an adverse drug reaction (ADR) occur
in the amount of drug in the body. before absorption is complete or, before Cmax
dD dD is reached?
GI = E (8.4)
dt dt 3. What is the effect of a small change in k on the
time and magnitude of Cmax (maximum plasma
Immediately after the time of peak drug absorp- concentration)? (Remember to correctly assign ka
tion, some drug may still be at the absorption site and k values when computing ka and k from patient
(ie, in the GI tract or other site of administration). data. See Flip-flop in oral absorption model in
However, the rate of drug elimination at this time is the next section.) In addition, see Chapter 13 for
faster than the rate of absorption, as represented by reasons why some subjects may have a smaller k.
the postabsorption phase in Fig. 8-4. 4. Do you believe that therapeutic drug concentra-
dD dD tion and toxic plasma concentration are always
GI < E (8.5)
dt dt clearly defined for individual subjects as intro-
duced in Fig. 1-2 (see Chapter 1)?
When the drug at the absorption site becomes
depleted, the rate of drug absorption approaches zero,
Discussion
4 From past experience, generally transient high plasma
The rate of drug elimination is dictated by the product of the
amount of drug in the body, DB times the rst-order elimination drug concentrations are not considered unsafe as long
rate constant, k. as the steady-state plasma concentration is within a
Plasma drug level
184 Chapter 8
recommended range. This is generally true for OTC plasma drug concentrations following multiple dos-
drugs. This case highlights a potential danger of some ing. In bioequivalence studies, drug products are
sympathomimetic drugs such as pseudoephedrine and given in chemically equivalent (ie, pharmaceutical
should alert the pharmacist that even drugs with a equivalents) doses, and the respective rates of sys-
long history of safe use may still exhibit dangerous temic absorption may not differ markedly. Therefore,
ADRs in some susceptible subjects. for these studies, tmax, or time of peak drug concen-
Do you believe that pseudoephedrine can be tration, can be very useful in comparing the respec-
sold safely without advice from a pharmacist? What tive rates of absorption of a drug from chemically
other types of medication are important to monitor equivalent drug products.
where a large ka may present transient high drug
concentrations in the blood?
A small elimination rate constant, k may be ZERO-ORDER ABSORPTION MODEL
caused by reduced renal drug excretion as discussed in Zero-order drug absorption from the dosing site into the
Chapter 7, but a small k may also be due to reduced plasma usually occurs when either the drug is absorbed
hepatic clearance caused by relatively inactive meta- by a saturable process or a zero-order controlled-release
bolic enzymes such as CYPs for some patients (see delivery system is used (see Chapter 19). The pharma-
Chapter 12). What are the kinetic tools that will allow cokinetic model assuming zero-order absorption is
one to make this differentiation? described in Fig. 8-5. In this model, drug in the gastro-
The pharmacokinetic concepts presented in this intestinal tract, DGI, is absorbed systemically at a con-
chapter will allow you to decide whether an unusual stant rate, k0. Drug is simultaneously and immediately
peak plasma drug concentration, Cmax is caused by a eliminated from the body by a first-order rate process
large ka, a small k (or Cl), both, or neither. defined by a first-order rate constant, k. This model is
analogous to that of the administration of a drug by
intravenous infusion (see Chapter 6).
SIGNIFICANCE OF ABSORPTION The rate of first-order elimination at any time is
RATE CONSTANTS equal to DBk. The rate of input is simply k0.
Therefore, the net change per unit time in the body
The overall rate of systemic drug absorption from an can be expressed as
orally administered solid dosage form encompasses
many individual rate processes, including dissolution dD
B
= k − kD
dt 0 B (8.7)
of the drug, GI motility, blood flow, and transport of
the drug across the capillary membranes and into the Integration of this equation with substitution of VDCp
systemic circulation. The rate of drug absorption rep- for DB produces
resents the net result of all these processes. The selec-
tion of a model with either first-order or zero-order k
C 0 (1 e−kt
p = − )
V (8.8)
absorption is generally empirical. Dk
The actual drug absorption process may be zero-
The rate of drug absorption is constant until the
order, first-order, or a combination of rate processes
amount of drug in the gut, DGI, is depleted. The time
that is not easily quantitated. For many immediate-
for complete drug absorption to occur is equal to
release dosage forms, the absorption process is first-
DGI/k0. After this time, the drug is no longer available
order due to the physical nature of drug diffusion.
For certain controlled-release drug products, the rate
of drug absorption may be more appropriately k k
0
described by a zero-order rate constant. D D V
GI B D
The calculation of ka is useful in designing a
multiple-dosage regimen. Knowledge of the ka and k FIGURE 85 One-compartment pharmacokinetic model
values allows for the prediction of peak and trough for zero-order drug absorption and first-order drug elimination.
Pharmacokinetics of Oral Absorption 185
for absorption from the gut, and Equation 8.7 no FIRST-ORDER ABSORPTION MODEL
longer holds. The drug concentration in the plasma
subsequently declines in accordance with a first- Although zero-order drug absorption can occur, sys-
order elimination rate process. temic drug absorption after oral administration of a
drug product (eg, tablet, capsule) is usually assumed
to be a first-order process. This model assumes a
first-order input across the gut wall and first-order
CLINICAL APPLICATION—
elimination from the body (Fig. 8-7). This model
TRANSDERMAL DRUG DELIVERY applies mostly to the oral absorption of drugs in
solution or rapidly dissolving dosage (immediate
The stratum corneum (horny layer) of the epidermis
release) forms such as tablets, capsules, and supposi-
of the skin acts as a barrier and rate-limiting step for
tories. In addition, drugs given by intramuscular or
systemic absorption of many drugs. After applica-
subcutaneous aqueous injections may also be
tion of a transdermal system (patch), the drug dis-
described using a first-order process.
solves into the outer layer of the skin and is absorbed
After oral administration of a drug product, the
by a pseudo first-order process due to high concen-
drug is relased from the drug product and dissolves
tration and is eliminated by a first-order process.
into the fluids of the GI tract. In the case of an
Once the patch is removed, the residual drug concen-
immediate-release compressed tablet, the tablet first
trations in the skin continues to decline by a first-
disintegrates into fine particles from which the drug
order process.
then dissolves into the fluids of the GI tract. Only
Ortho Evra is a combination transdermal contra-
drug in solution is absorbed into the body. The rate
ceptive patch with a contact surface area of 20 cm2.
of disappearance of drug from the gastrointestinal
Each patch contains 6.00 mg norelgestromin
tract is described by
(NGMN) and 0.75 mg ethinyl estradiol (EE) and is
designed to deliver 0.15 mg of NGMN and 0.02 mf
EE to the systemic circulation daily. As shown in dD
GI
= −kaD F (8.9)
Fig. 8-6, serum EE (ethinyl estradiol) is absorbed dt GI
from the patch at a zero-order rate.
where ka is the first-order absorption rate constant
from the GI tract, F is the fraction absorbed, and
70 DGI is the amount of drug in solution in the GI
60 tract at any time t. Integration of the differential
Equation (8.8) gives
50
40
dDGI = D e−kat
0 (8.10)
30
20 where D0 is the dose of the drug.
10 The rate of drug elimination is described by a
first-order rate process for most drugs and is equal
0
0 24 48 72 96 120 144 158 192 216 240 to −kDB. The rate of drug change in the body, dDB/dt,
Time (hours)
Cycle 1 week 1 Cycle 3 week 2
Cycle 3 week 1 Cycle 3 week 3
k k
FIGURE 86 Mean serum EE concentrations (pg/mL) in a
D D V
GI B D
healthy female volunteers following application of Ortho Evra
on the buttock for three consecutive cycles (vertical arrow
indicates time of patch removal). (Adapted from approved label for FIGURE 87 One-compartment pharmacokinetic model
Ortho Evra, September, 2009.) for first-order drug absorption and first-order elimination.
EE Concentration (pg/mL)
186 Chapter 8
is therefore the rate of drug in, minus the rate of The maximum plasma concentration after oral
drug out—as given by the differential equation, dosing is Cmax, and the time needed to reach maximum
Equation 8.10: concentration is tmax. The tmax is independent of dose
and is dependent on the rate constants for absorption
dDB
= rate in − rate out (k and elimination (k) (Equation 8.13). At C
dt a) max, some-
(8.11) times called peak concentration, the rate of drug
dDB absorbed is equal to the rate of drug eliminated.
= FkaDGI − kD
dt B Therefore, the net rate of concentration change is equal
to zero. At Cmax, the rate of concentration change can be
where F is the fraction of drug absorbed systemi-
obtained by differentiating Equation 8.11, as follows:
cally. Since the drug in the gastrointestinal tract
also follows a first-order decline (ie, the drug is dCp Fk D
absorbed across the gastrointestinal wall), the = a 0 (−ke−kt + k e−kat
a ) = 0 (8.13)
dt VD (ka − k)
amount of drug in the gastrointestinal tract at any
time t is equal to D e−kat. This can be simplified as follows:
0
dD kt −k
B at −k
Fk D e−kat − +
= a = 0 or ke−kt
= k e at
a
dt a 0 − kD ke− k e
B
ln k − kt = ln ka − kat
The value of F may vary from 1 for a fully
absorbed drug to 0 for a drug that is completely ln ka − ln k ln (ka /k)
tmax = =
unabsorbed. This equation can be integrated to give ka − k ka − k
the general oral absorption equation for calculation 2.3 log ( .14)
ka /k)
(8
of the drug concentration (Cp) in the plasma at any tmax =
ka − k
time t, as shown below.
Fk shown in Equation 8.13, the time for maxi-
aD
As
0 kt
C = (e−
− e−kat
p )
VD (ka k) (8.12) mum drug concentration, tmax, is dependent only on
−
the rate constants ka and k. In order to calculate Cmax,
A typical plot of the concentration of drug in the the value for tmax is determined via Equation 8.13
body after a single oral dose is presented in Fig. 8-8. and then substituted into Equation 8.11, solving for
Cmax. Equation 8.11 shows that Cmax is directly pro-
portional to the dose of drug given (D0) and the frac-
tion of drug absorbed (F). Calculation of tmax and
Cmax
Cmax is usually necessary, since direct measurement
of the maximum drug concentration may not be pos-
sible due to improper timing of the serum samples.
The first-order elimination rate constant may be
determined from the elimination phase of the plasma
level–time curve (Fig. 8-4). At later time intervals,
when drug absorption has been completed, that is,
e−kat
AUC ≈ 0, Equation 8.11 reduces to
FkaD0
Cp = e−kt (8.15)
VD (ka − k)
tmax Taking the natural logarithm of this expression,
Time
Fk D
FIGURE 88 Typical plasma level–time curve for a drug lnCp ln a 0
= − kt (8.16)
given in a single oral dose. VD (ka − k)
Plasma level
Pharmacokinetics of Oral Absorption 187
Substitution of common logarithms gives A
Fk D kt
logCp log a 0
= − (8.17)
VD (ka − k) 2.3 20
With this equation, a graph constructed by plotting 15
log Cp versus time will yield a straight line with a
slope of −k/2.3 (Fig. 8-9A). 10
With a similar approach, urinary drug excretion
5
data may also be used for calculation of the first-
order elimination rate constant. The rate of drug
0
excretion after a single oral dose of drug is given by 0 5 10 15 20 25
Time (hours)
dDu FkakeD0
(e−kt e−kat
= − − ) (8.18) B
dt ka − k
where dDu/dt = rate of urinary drug excretion, ke = 20
first-order renal excretion constant, and F = fraction
of dose absorbed. 15
10
A
5
100
FD
I 0kntercept = a
VD(ka – k) 0
0 5 10 15 20 25
10 Time (hours)
Slope = –k FIGURE 810 A. Plasma drug concentration versus time,
2.3 single oral dose. B. Rate of urinary drug excretion versus time,
1
single oral dose.
0.1
0 5 10 15 20 25 A graph constructed by plotting dDu/dt versus
Time (hours) time will yield a curve identical in appearance to the
B plasma level–time curve for the drug (Fig. 8-10B).
After drug absorption is virtually complete, −e−kat
100
FkekaDIntercept = 0 approaches zero, and Equation 8.18 reduces to
ka – k
10 dD Fk k
u eDa 0
e−kt
= (8.19)
dt k − k
a
Slope = –k
2.3
1 Taking the natural logarithm of both sides of this
expression and substituting for common logarithms,
Equation 8.19 becomes
0.1
0 5 10 15 20 25 dD Fk k D kt
log u
= log a e 0
− (8.20)
Time (hours) dt ka − k 2.3
FIGURE 89 A. Plasma drug concentration versus time,
single oral dose. B. Rate of urinary drug excretion versus time, When log(dDu/dt) is plotted against time, a
single oral dose. graph of a straight line is obtained with a slope of
Rate of drug excretion (dDu/dt) Concentration (mg/mL)
Rate of drug excretion, dDu/dt (mg/h) Plasma drug concentration, Cp (µg/mL)
188 Chapter 8
−k/2.3 (Fig. 8-9B). Because the rate of urinary drug virtually complete. Equation 8.12 then reduces to
excretion, dDu/dt, cannot be determined directly for Equation 8.23.
any given time point, an average rate of urinary drug
excretion is obtained (see also Chapter 4), and this Fk
C aD0 e−kt
p = (8.23)
value is plotted against the midpoint of the collection VD (ka − k)
period for each urine sample.
To obtain the cumulative drug excretion in the From this, one may also obtain the intercept of
urine, Equation 8.18 must be integrated, as shown the y axis (Fig. 8-12).
below.
Fk
aD0
Fk k D −e−kat e−kt = A
Fk D
D a e 0
= VD (ka − k)
− − + e 0
u (8.21)
k k k k k
a a
where A is a constant. Thus, Equation 8.23 becomes
A plot of Du versus time will give the urinary
drug excretion curve described in Fig. 8-11. When all C Ae−kt
p = (8.24)
of the drug has been excreted, at t = ∞, Equation 8.21
reduces to This equation, which represents first-order drug
elimination, will yield a linear plot on semilog paper.
Fk
∞ eDD 0 . 2
u = (8 2 ) The slope is equal to − k/2.3. The value for ka can be
k obtained by using the method of residuals or a feath-
ering technique, as described in Chapter 5. The value
where D∞
u is the maximum amount of active or par-
of ka is obtained by the following procedure:
ent drug excreted.
1. Plot the drug concentration versus time on
Determination of Absorption Rate Constants semilog paper with the concentration values on
from Oral Absorption Data the logarithmic axis (Fig. 8-12).
2. Obtain the slope of the terminal phase (line BC,
Method of Residuals Fig. 8-12) by extrapolation.
Assuming ka >> k in Equation 8.12, the value for the
second exponential will become insignificantly
small with time (ie, e−kat ≈ 0) and can therefore be A X1′
omitted. When this is the case, drug absorption is 40 X2′
X3′
20 Cp = 43(e–0.40t – e–1.5t)
X
250 3
200 10 X2 B
150
100 5
X1
50
0
0 5 10 15 20 25 2
C
Time (hours)
FIGURE 811 Cumulative urinary drug excretion versus 1
0 2 4 6 8 10
time, single oral dose. Urine samples are collected at various
Time
time periods after the dose. The amount of drug excreted in
each sample is added to the amount of drug recovered in the FIGURE 812 Plasma level–time curve for a drug dem-
previous urine sample (cumulative addition). The total amount onstrating first-order absorption and elimination kinetics. The
of drug recovered after all the drug is excreted is D∞
u . equation of the curve is obtained by the method of residuals.
Cumulative drug
excretion (Du)
Plasma level
Pharmacokinetics of Oral Absorption 189
3. Take any points on the upper part of line BC
(eg, x′1, x′2, x′3, …) and drop vertically to obtain
corresponding points on the curve (eg, x1, x2,
x3, …).
4. Read the concentration values at x1 and x′1, x2
and x′2, x3 and x′3, and so on. Plot the values of
the differences at the corresponding time points
∆1, ∆2, ∆3, … . A straight line will be obtained
with a slope of −ka/2.3 (Fig. 8-12).
When using the method of residuals, a mini-
mum of three points should be used to define the
straight line. Data points occurring shortly after tmax Lag time
Time
may not be accurate, because drug absorption is
still continuing at that time. Because this portion of FIGURE 813 The lag time can be determined graphi-
the curve represents the postabsorption phase, only cally if the two residual lines obtained by feathering the plasma
level–time curve intersect at a point where t > 0.
data points from the elimination phase should be
used to define the rate of drug absorption as a first-
order process. The lag time, t0, represents the beginning of drug
If drug absorption begins immediately after absorption and should not be confused with the phar-
oral administration, the residual lines obtained by macologic term onset time, which represents latency,
feathering the plasma level–time curve (as shown in that is, the time required for the drug to reach mini-
Fig. 8-12) will intersect on the y axis at point A. The mum effective concentration.
value of this y intercept, A, represents a hybrid constant Two equations can adequately describe the curve
composed of ka, k, VD, and FD0. The value of A has no in Fig. 8-13. In one, the lag time t0 is subtracted from
direct physiologic meaning (see Equation 8.24). each time point, as shown in Equation 8.25.
FkaD0 Fk
A = C aD0 (e−k (t−t0 ) e−ka (t−t0 )
p = − ) (8.25)
VD (ka − k) VD (ka − k)
The value for A, as well as the values for k and ka, where FkaD0/VD(ka − k) is the y value at the point of
may be substituted back into Equation 8.11 to obtain intersection of the residual lines in Fig. 8-13.
a general theoretical equation that will describe the The second expression that describes the curve
plasma level–time curve. in Fig. 8-13 omits the lag time, as follows:
C Be−kt A −kat
p = − e (8.26)
Lag Time
In some individuals, absorption of drug after a single where A and B represent the intercepts on the y axis
oral dose does not start immediately, due to such after extrapolation of the residual lines for absorp-
physiologic factors as stomach-emptying time and tion and elimination, respectively.
intestinal motility. The time delay prior to the com-
mencement of first-order drug absorption is known
as lag time. Frequently Asked Question
The lag time for a drug may be observed if the »»If drug absorption is simulated using the oral one-
two residual lines obtained by feathering the oral compartment model, would a larger absorption
absorption plasma level–time curve intersect at a point rate constant result in a greater amount of drug
greater than t = 0 on the x axis. The time at the point of absorbed?
intersection on the x axis is the lag time (Fig. 8-13).
Plasma level
190 Chapter 8
Flip-Flop of ka and k 1.38 h−1 or 0.69 h−1). Because most of the drugs used
In using the method of residuals to obtain estimates orally have longer elimination half-lives compared to
of k rption half-lives, the assumption that the smaller
a and k, the terminal phase of an oral absorption abso
curve is usually represented by k, whereas the steeper slope or smaller rate constant (ie, the terminal phase
slope is represented by k ed as the elimi-
a (Fig. 8-14). In a few cases, of the curve in Fig. 8-14) should be us
the elimination rate constant k obtained from oral nation constant is generally correct.
absorption data does not agree with that obtained For drugs that have a large elimination rate
after intravenous bolus injection. For example, the k constant (k > 0.69 h−1), the chance for flip-flop of ka
obtained after an intravenous bolus injection of a and k is much greater. The drug isoproterenol, for
bronchodilator was 1.72 h−1, whereas the k calculated example, has an oral elimination half-life of only a
after oral administration was 0.7 h−1 (Fig. 8-14). few minutes, and flip-flop of ka and k has been noted
When ka was obtained by the method of residuals, the (Portmann, 1970). Similarly, salicyluric acid was
rather surprising result was that the ka was 1.72 h−1. flip-flopped when oral data were plotted. The k for
Apparently, the k was much larger than its ka (Levy
a and k obtained by the method salicyluric acid
of residuals have been interchanged. This phenome- et al, 1969). Many experimental drugs show flip-
non is called flip-flop of the absorption and elimina- flop of k and ka, whereas few marketed oral drugs
tion rate constants. Flip-flop, or the reversal of the do. Drugs with a large k are usually considered to be
rate constants, may occur whenever ka and k are unsuitable for an oral drug product due to their large
estimated from oral drug absorption data. Use of elimination rate constant, corresponding to a very
computer methods does not ensure against flip-flop short elimination half-life. An extended-release
of the two constants estimated. drug product may slow the absorption of a drug,
In order to demonstrate unambiguously that the such that the ka is smaller than the k and producing
steeper curve represents the elimination rate for a a flip-flop situation.
drug given extravascularly, the drug must be given
by intravenous injection into the same patient. After Frequently Asked Question
intravenous injection, the decline in plasma drug »»How do you explain that ka is often greater than k
levels over time represents the true elimination rate. with most drugs?
The relationship between ka and k on the shape of the
plasma drug concentration–time curve for a constant
dose of drug given orally is shown in Fig. 8-14. Determination of ka by Plotting Percent
Most of the drugs observed to have flip-flop char- of Drug Unabsorbed Versus Time
acteristics are drugs with fast elimination (ie, k > ka). (Wagner–Nelson Method)
Drug absorption of most drug solutions or fast-
The Wagner–Nelson method may be used as an
dissolving products is essentially complete or at
alternative means of calculating k his method
least half-complete within an hour (ie, absorption a. T
estimates the loss of drug from the GI over time,
half-life of 0.5 or 1 hour, corresponding to a ka of
whose slope is inversely proportional to ka. After a
single oral dose of a drug, the total dose should be
completely accounted for for the amount present in
the body, the amount present in the urine, and the
amount present in the GI tract. Therefore, dose (D0)
k = 0.7 h–1 ka = 0.7 h–1 is expressed as follows:
ka = 1.72 h–1
k = 1.72 h–1
Time Time D0 = DGI +DB +Du (8.27)
A. Incorrect B. Correct
FIGURE 814 Flip-flop of k Let Ab = DB + Du = amount of drug absorbed and let
a and k. Because k > ka, the
right-hand figure and slopes represent the correct values for Ab∞ = amount of drug absorbed at t = ∞. At any
ka and k. given time the fraction of drug absorbed is Ab/Ab∞,
log Cp
log Cp
Pharmacokinetics of Oral Absorption 191
and the fraction of drug unabsorbed is 1 − (Ab/Ab∞). 10
The amount of drug excreted at any time t can be
calculated as 1
Du = kVD[AUC]t0 (8.28)
0.1
The amount of drug in the body (DB) at any time =
CpVD. At any time t, the amount of drug absorbed
(Ab) is 0
0 5 10 15
Time (hours)
Ab =CpVD + kVD[AUC]t0 (8.29)
FIGURE 815 Semilog graph of data in Table 8-2, depict-
At t = C∞
∞, p = 0 (ie, plasma concentration is negli- ing the fraction of drug unabsorbed versus time using the
gible), and the total amount of drug absorbed is Wagner–Nelson method.
Ab∞ k ∞
= 0+ VD[AUC]0 (8.30)
5. Find k by adding up all the [AUC] pieces, from
The fraction of drug absorbed at any time is
t = 0 to t = ∞.
C 6. Determine the 1 − (Ab/Ab∞) value correspond-
pV kV t
Ab D + D[AUC]0
= (8.31)
Ab∞ kVD[AUC]∞ ing to each time point t by using Table 8-1.
0
7. Plot 1 − (Ab/Ab∞) versus time on semilog paper,
C k t
Ab p + [AUC] with 1 − (Ab/Ab∞) on the logarithmic axis.
0
= (8.32)
Ab∞ k[AUC]∞0 If the fraction of drug unabsorbed, 1 − Ab/Ab∞,
gives a linear regression line on a semilog graph,
The fraction unabsorbed at any time t is
then the rate of drug absorption, dDGI/dt, is a first-
C + k[ t
Ab p AUC] order process. Recall that 1 − Ab/Ab∞ is equal to
0
1− =1− (8.33)
Ab∞ k[AUC]∞ dDGI/dt (Fig. 8-15).
0
As the drug approaches 100% absorption, Cp
The drug remaining in the GI tract at any time t is becomes very small and difficult to assay accurately.
Consequently, the terminal part of the line described
D D e−kat
GI = 0 (8.34) by 1 − Ab/Ab∞ versus time tends to become scattered
or nonlinear. This terminal part of the curve is excluded,
Therefore, the fraction of drug remaining is
and only the initial linear segment of the curve is used
D for the estimate of the slope.
GI D −k t
= e−kat log GI a
= (8.35)
D0 D0 2.3
Because DGI/D0 is actually the fraction of drug PRACTICE PROBLEM
unabsorbed—that is, 1 − (Ab/Ab∞)—a plot of 1 − (Ab/
Ab∞) versus time gives −ka/2.3 as the slope (Fig. 8-15). Drug concentrations in the blood at various times are
The following steps should be useful in determi- listed in Table 8-1. Assuming the drug follows a one-
nation of ka:
compartment model, find the ka value, and compare it
with the ka value obtained by the method of residuals.
1. Plot log concentration of drug versus time.
2. Find k from the terminal part of the slope when
Solution
the slope = −k/2.3.
3. Find [AUC]t0 by plotting C The AUC is approximated by the trapezoidal rule.
p versus t.
4. Find k [AUC]t by multiplying each [AUC]t This method is fairly accurate when there are suffi-
0 0
by k. cient data points. The area between each time point
Ion of drug unabsorbed
[1 – (Ab/Ab∞)]
192 Chapter 8
TABLE 81 Blood Concentrations and Associated Data for a Hypothetical Drug
Time tn Concentration Ab Ab
(h) C tn [AUC]t k[AUC t + [AU ]
p (lg/mL) [AUC]
t 0 ] 1−
C t ∞
0 p k C
0
– Ab∞ Ab
n 1
0 0 0 0 1.000
1 3.13 1.57 1.57 0.157 3.287 0.328 0.672
2 4.93 4.03 5.60 0.560 5.490 0.548 0.452
3 5.86 5.40 10.99 1.099 6.959 0.695 0.305
4 6.25 6.06 17.05 1.705 7.955 0.794 0.205
5 6.28 6.26 23.31 2.331 8.610 0.856 0.140
6 6.11 6.20 29.51 2.951 9.061 0.905 0.095
7 5.81 5.96 35.47 3.547 9.357 0.934 0.066
8 5.45 5.63 41.10 4.110 9.560 0.955 0.045
9 5.06 5.26 46.35 4.635 9.695 0.968 0.032
10 4.66 4.86 51.21 5.121
12 3.90 8.56 59.77 5.977
14 3.24 7.14 66.91 6.691
16 2.67 5.92 72.83 7.283
18 2.19 4.86 77.69 7.769
24 1.20 10.17 87.85 8.785
28 0.81 4.02 91.87 9.187
32 0.54 2.70 94.57 9.457
36 0.36 1.80 96.37 9.637
48 0.10 2.76 99.13 9.913
k = 0.1 h–1.
is calculated as has fallen to an insignificant drug concentration,
0.1 μg/mL. The rest of the needed information is
t C
[AU n n +C
C] −1 n
t = (t − )
1 2 n t
n n 1 (8.36)
− given in Table 8-1. Notice that k is obtained from the
−
plot of log Cp versus t; k was found in this example to
where Cn and Cn−1 are concentrations. For example, be 0.1 h−1. The plot of 1− (Ab/Ab∞) versus t on semi-
at n = 6, the [AUC] is log paper is shown in Fig. 8-15.
A more complete method of obtaining ka is to
6.28+6.11
(6− 5) = 6.20 estimate the residual area from the last observed
2
plasma concentration, Cp at tn to time equal to infinity.
This equation for the residual AUC from Cp to time
To obtain [AUC]∞0 , add all the area portions
equal to infinity is
under the curve from zero to infinity. In this case,
48 hours is long enough to be considered infinity, C
p
[AUC]∞ n
t = (8.37)
because the blood concentration at that point already k
Pharmacokinetics of Oral Absorption 193
The total [AUC]∞0 is the sum of the areas obtained Substituting for dCp/dt into Equation 8.42 and kDu/ke
by the trapezoidal rule, [AUC]t0 , and the residual for DE,
area [AUC]∞t , as described in the following
dAb d(dDu /dt) k dD
expression: u
= + (8.45)
dt ke dt ke dt
[AUC]∞ t
0 = [AUC]0 + [AUC]∞t (8.38)
When the above expression is integrated from zero
to time t,
Estimation of ka from Urinary Data
1 dD k
The absorption rate constant may also be estimated Abt = ( u ) + (D )
ke dt t k u t (8.46)
from urinary excretion data, using a plot of percent of e
drug unabsorbed versus time. For a one-compartment At t = ∞, all the drug that is ultimately absorbed is
model: expressed as Ab∞ and dDu/dt = 0. The total amount
Ab = total amount of drug absorbed—that is, the of drug absorbed is
amount of drug in the body plus the amount of
k
drug excreted Ab∞ = D∞
k u
DB = amount of drug in the body e
Du = amount of unchanged drug excreted in the urine where D∞ is the total amount of unchanged drug
u
Cp = plasma drug concentration excreted in the urine.
DE = total amount of drug eliminated (drug and The fraction of drug absorbed at any time t is
metabolites) equal to the amount of drug absorbed at this time, Abt,
divided by the total amount of drug absorbed, Ab∞.
Ab = DB + DE (8.39)
Abt (dDu /dt)t + k(Du )t
The differential of Equation 8.39 with respect to = (8.47)
Ab∞ kD∞
time gives u
dAb dD dD A plot of the fraction of drug unabsorbed, 1 −
B E
= + (8.40)
dt dt dt Ab/Ab∞, versus time gives −ka/2.3 as the slope
from which the absorption rate constant is obtained
Assuming first-order elimination kinetics with renal
(Fig. 8-15; refer to Equation 8.35).
elimination constant ke, When collecting urinary drug samples for the
dD determination of pharmacokinetic parameters, one
u = k .
eDB = keVDC (8 41)
dt p should obtain a valid urine collection as discussed in
Chapter 4. If the drug is rapidly absorbed, it may be
Assuming a one-compartment model, difficult to obtain multiple early urine samples to
V describe the absorption phase accurately. Moreover,
DCp = DB
drugs with very slow absorption will have low con-
Substituting VDCp into Equation 8.40, centrations, which may present analytical problems.
dAb dCp dD
=V E
+ (8.42) Effect of ka and k on Cmax, tmax, and AUC
dt D dt dt
Changes in ka and k may affect tmax, Cmax, and AUC as
And rearranging Equation 8.41, shown in Table 8-2. If the values for ka and k are
1 dD reversed, then the same tmax is obtained, but the Cmax
C u
p =
k V 4
e D dt (8. 3) and AUC are different. If the elimination rate constant
is kept at 0.1 h−1 and the ka changes from 0.2 to 0.6 h−1
dCp d(dDu /dt) (absorption rate increases), then the tmax becomes
=
dt dt keV
(8.44)
D shorter (from 6.93 to 3.58 hours), the Cmax increases
194 Chapter 8
TABLE 82 Effects of the Absorption Rate Constant and Elimination Ratea
Absorption Rate Elimination Rate
Constant, ka (h–1) Constant, k (h–1) tmax (h) Cmax (lg/mL) AUC (lg . h/mL)
0.1 0.2 6.93 2.50 50
0.2 0.1 6.93 5.00 100
0.3 0.1 5.49 5.77 100
0.4 0.1 4.62 6.29 100
0.5 0.1 4.02 6.69 100
0.6 0.1 3.58 6.99 100
0.3 0.1 5.49 5.77 100
0.3 0.2 4.05 4.44 50
0.3 0.3 3.33 3.68 33.3
0.3 0.4 2.88 3.16 25
0.3 0.5 2.55 2.79 20
atmax = peak plasma concentration, Cmax = peak drug concentration, AUC = area under the curve. Values are based on a single oral dose (100 mg) that
is 100% bioavailable (F = 1) and has an apparent VD of 10 L. The drug follows a one-compartment open model. tmax is calculated by Equation 8.14 and
Cmax is calculated by Equation 8.12. The AUC is calculated by the trapezoidal rule from 0 to 24 hours.
(from 5.00 to 6.99 μg/mL), but the AUC remains con- (from 5.77 to 2.79 μg/mL), and the AUC decreases
stant (100 μg h/mL). In contrast, when the absorption (from 100 to 20 μg h/mL). Graphical representations
rate constant is kept at 0.3 h−1 and k changes from 0.1 for the relationships of ka and k on the time for peak
to 0.5 h−1 (elimination rate increases), then the tmax absorption and the peak drug concentrations are
decreases (from 5.49 to 2.55 hours), the Cmax decreases shown in Figs. 8-16 and 8-17.
8 2.8
2.4 0.2/h
0.5/h
6 2.0
0.3/h
1.5
4 0.2/h
1.2
0.3/h 0.8 0.5/h
2
0.4
0 0
0 4 8 12 15 20 0 4 8 12 15 20
Time (hours) Time (hours)
FIGURE 816 Effect of a change in the absorption rate FIGURE 817 Effect of a change in the elimination rate
constant, ka, on the plasma drug concentration–time curve. constant, k, on the plasma drug concentration–time curve.
Dose of drug is 100 mg, VD is 10 L, and k is 0.1 h–1. Dose of drug is 100 mg, VD is 10 L, and ka is 0.1 h–1.
Concentration (mg/mL)
Concentration (mg/mL)
Pharmacokinetics of Oral Absorption 195
Modified Wagner–Nelson Method Models for Estimation of Drug Absorption
Hayashi et al (2001) introduced a modified Wagner– There are many models and approaches that have
Nelson method to study the subcutaneous absorption been used to predict drug absorption since the intro-
of a drug with nonlinear kinetics from the central duction of the classical approaches by John Wagner
compartment. Nonlinear kinetics occurs in some (1967) and Jack Loo. Deconvolution and convolu-
drugs where the kinetic parameter such as k change tion approaches are used to predict plasma drug
with dose. The method was applicable to a biotech- concentration of oral dosage forms. Several com-
nological drug (recombinant human granulocyte- mercial software (eg, GastroPlus, iDEA, Intellipharm
colony stimulating factors, rhG-CSF) which is PK, and PK-Sim) are now available for formulation
eliminated nonlinearly. The drug was absorbed into and drug development or to determine the extent of
the blood from the dermal site after subcutaneous drug absorption. The new software allows the char-
injection. Because of nonlinear kinetics the extent of acteristics of the drug, physiologic factors, and the
absorption was not easily determined. The amount dosage form to be inputed into the software. An impor-
of drug absorbed, Ab for each time sample, tn, is tant class of programs involves the Compartmental
given by Equation 8.48. V1 and Vss are central com- Absorption and Transit (CAT) models. This model
partment and steady-state volume of distribution, integrates the effect of solubility, permeability, as well
respectively. as gastric emptying and GI transit time in the estima-
Vmax and Km are Michaelis–Menten parameters tion of in vivo drug absorption. CAT models were
that describe the saturable elimination (see Chapter 10) successfully used to predict the fraction of drug oral
of the drug. ti is the sample time which = 0,1,2,4… absorption of 10 common drugs based on a small
48 hours in this example, and C(t) is the average intestine transit time (Yu, 1999). The CAT models
serum drug concentraton between time points, that is, compared well overall with other plausible models
ti and ti+1. such as the dispersion model, the single mixing tank
model, and some flow models. It is important to note
n−1 that the models discussed earlier in this chapter are
ti+1
( ) = ∑ VmaxC(t)
Aab tn ∫ +
=
kV
C t K 1C(t) dt +VssC(tn )
t ( ) + used to compute extent of absorption after the plasma
i 1 i m drug concentrations are measured. In contrast, the
(8.48) later models/software allow a comprehensive way to
simulate or predict drug (product) performance in vivo.
From the mass balance of the above equation, The subjects of dissolution, dosage form design, and
the authors did account for the amount of drug pres- drug absorption will be discussed in more detail in
ent in the tissue compartment. (Note the authors Chapters 14 and 15.
stated that the central compartment V1 is 4.56 L and
that of Vss is 4.90 L.) To simplify the model, the
Determination of ka from Two-Compartment
authors used convolution to show that the contribu-
Oral Absorption Data (Loo–Riegelman
tion of the tissue compartment is not significant and
therefore may be neglected. Thus, the Loo– Method)
Riegelman method which requires a tissue compart- Plotting the percent of drug unabsorbed versus time
ment was not used by the authors. Convolution is an to determine ka may also be calculated for a drug
analytical method that predicts plasma time drug exhibiting a two-compartment kinetic model. As in
concentration using input and disposition functions the method used previously to obtain an estimate of
for drugs with linear kinetics. The disposition func- the ka, no limitation is placed on the order of the
tion may be first obtained by deconvolution of sim- absorption process. However, this method does
ple IV plasma drug concentration data or from the require that the drug be given intravenously as well as
terminal phase of an oral solution. Alternatively, the orally to obtain all the necessary kinetic constants.
method of Lockwood and Gillespie (1996) abbrevi- After oral administration of a dose of a drug that
ated the need for the simple solution. exhibits two-compartment model kinetics, the amount
196 Chapter 8
k
k 12 A plot of the fraction of drug unabsorbed, 1 −
a Central compartment Tissue compartment
Dp Vp Cp Dt Vt Ct Ab/Ab∞, versus time gives −ka/2.3 as the slope from
k21 which the value for the absorption rate constant is
k obtained (refer to Equation 8.35).
The values for k[AUC]t0 are calculated from a plot
FIGURE 818 Two-compartment pharmacokinetic mode. of Cp versus time. Values for (Dt/Vp) can be approxi-
Drug absorption and elimination occur from the central mated by the Loo–Riegelman method, as follows:
compartment.
k12∆Cp ∆ t k
(C ) = + 12 k t k t
t t (Cp )2 t (1− e− 21∆ )+ (C 21
1 t )t e− ∆
n k n− n−1
of drug absorbed is calculated as the sum of the 21
amounts of drug in the central compartment (Dp), in (8.57)
the tissue compartment (Dt), and the amount of drug
where Ct is Dt/Vp, or apparent tissue concentration;
eliminated by all routes (Du) (Fig. 8-18).
t = time of sampling for sample n; tn−1 = time of
Ab = Dp + Dt + Du (8.49) sampling for the sampling point preceding sample n;
and (Cp )t = concentration of drug at central com-
Each of these terms may be expressed in terms of n−1
partment for sample n − 1.
kinetics constants and plasma drug concentrations, Calculation of Ct values is shown in Table 8-3,
as follows: using a typical set of oral absorption data. After calcu-
lation of Ct values, the percent of drug unabsorbed is
Dp = VpCp (8.50)
calculated with Equation 8.56, as shown in Table 8-4.
Dt = VtCt (8.51) A plot of percent of drug unabsorbed versus time
on semilog graph paper gives a ka of approximately
dD
u = kV (8.52)
dt pCp 0.5 h−1.
For calculation of ka by this method, the drug
D must be given intravenously to allow evaluation of the
u = kVp[AUC]t0
distribution and elimination rate constants. For drugs
Substituting the above expression for Dp and Du into that cannot be given by the IV route, the ka cannot be
Equation 8.49, calculated by the Loo–Riegelman method. For drugs
that are given by the oral route only, the Wagner–
Ab = VpCp +Dt + kVp[AUC]t0 (8.53)
Nelson method, which assumes a one-compartment
By dividing this equation by Vp to express the equation model, may be used to provide an initial estimate of
on drug concentrations, we obtain ka. If the drug is given intravenously, there is no way
of knowing whether there is any variation in the values
Ab D
C t for the elimination rate constant, k and the distributive
= p + + k[AUC]t (8 54
p V 0 . )
V p rate constants, k12 and k21. Such variations alter the
rate constants. Therefore, a one-compartment model
At t = ∞, this equation becomes
is frequently used to fit the plasma curves after an oral
Ab or intramuscular dose. The plasma level predicted
= k[AUC]∞0 (8.55)
Vp from the ka obtained by this method does deviate from
the actual plasma level. However, in many instances,
Equation 8.54 divided by Equation 8.55 gives the
this deviation is not significant.
fraction of drug absorbed at any time as shown in
Equation 8.56.
Cumulative Relative Fraction Absorbed
D
C t
p + + k[AUC]t The fraction of drug absorbed at any time t (Equation
0
Ab Vp (8.56) 8.32) may be summed or cumulated for each time
∞ =
Ab k[AUC]∞0 period for which a plasma drug sample was obtained.
Pharmacokinetics of Oral Absorption 197
TABLE 83 Calculation of Ct Valuesa
(k12 /k21)× (Cp )t (k12 / k21)×
(k n−1
12∆Cp∆t)
−k ∆t
(C 2 e−k21∆t ) (1−e−k21∆t ) (C ) e 21
t tn−1
p)tn (t)tn D(Cp) Dt (Cp) (1−
t (C
n-1 t)tn
3.00 0.5 3.0 0.5 0.218 0 0.134 0 0 0.218
5.20 1.0 2.2 0.5 0.160 3.00 0.134 0.402 0.187 0.749
6.50 1.5 1.3 0.5 0.094 5.20 0.134 0.697 0.642 1.433
7.30 2.0 0.8 0.5 0.058 6.50 0.134 0.871 1.228 2.157
7.60 2.5 0.3 0.5 0.022 7.30 0.134 0.978 1.849 2.849
7.75 3.0 0.15 0.5 0.011 7.60 0.134 1.018 2.442 3.471
7.70 3.5 –0.05 0.5 –0.004 7.75 0.134 1.039 2.976 4.019
7.60 4.0 –0.10 0.5 –0.007 7.70 0.134 1.032 3.444 4.469
7.10 5.0 –0.50 1.0 –0.073 7.60 0.250 1.900 3.276 5.103
6.60 6.0 –0.50 1.0 –0.073 7.10 0.250 1.775 3.740 5.442
6.00 7.0 –0.60 1.0 –0.087 6.60 0.250 1.650 3.989 5.552
5.10 9.0 –0.90 2.0 –2.261 6.00 0.432 2.592 2.987 5.318
4.40 11.0 –0.70 2.0 –0.203 5.10 0.432 2.203 2.861 4.861
3.30 15.0 –1.10 4.0 –0.638 4.40 0.720 3.168 1.361 3.891
aCalculated with the following rate constants: k12 = 0.29 h–1, k21 = 0.31 h–1.
Adapted with permission from Loo and Riegelman (1968).
From Equation 8.32, the term Ab/Ab∞ becomes the To determine the real percent of drug absorbed,
cumulative relative fraction absorbed (CRFA). a modification of the Wagner–Nelson equation was
suggested by Welling (1986). A reference drug prod-
Cp + k[AUC]t0
CRFA = (8.58) uct was administered and plasma drug concentra-
k[AUC]∞0 tions were determined over time. CRFA was then
estimated by dividing Ab/Ab∞ , where Ab is the
where Cp is the plasma concentration at time t. ref
cumulative amount of drug absorbed from the drug
In the Wagner–Nelson equation, Ab/Ab∞ or CRFA
product and Ab∞
will eventually equal unity, or 100%, even though the ref is the cumulative final amount of
drug absorbed from a reference dosage form. In this
drug may not be 100% systemically bioavailable. The
case, the denominator of Equation 8.58 is modified
percent of drug absorbed is based on the total amount
as follows:
of drug absorbed (Ab∞) rather than the dose D0.
Because the amount of drug ultimately absorbed, Ab∞ C ∞
p + k[AUC]0
in fractional term, is analogous to CRFA = (8.59)
k[AUC]∞0 , the k ∞
ref [AUC]ref
numerator will always equal the denominator at time
infinity, whether the drug is 10%, 20%, or 100% where kref and [AUC]∞ref are the elimination constant
bioavailable. The percent of drug absorbed based on and the area under the curve determined from the
Ab/Ab∞ is therefore different from the real percent of reference product, respectively. The terms in the
drug absorbed unless F = 1. However, for the calcula- numerator of Equation 8.59 refer to the product, as
tion of k in Equation 8.58.
a, the method is acceptable.
198 Chapter 8
TABLE 84 Calculation of Percentage Unabsorbeda
100% –
t
Time (h) (Cp)t t
[AUC] n [AUC]tn k[AUC] n
n (Ct)tn Ab/Vp %Ab/V
t p Ab/Vp%
n–1 t0 t0
0.5 3.00 0.750 0.750 0.120 0.218 3.338 16.6 83.4
1.0 5.20 2.050 2.800 0.448 0.749 6.397 31.8 68.2
1.5 6.50 2.925 5.725 0.916 1.433 8.849 44.0 56.0
2.0 7.30 3.450 9.175 1.468 2.157 10.925 54.3 45.7
2.5 7.60 3.725 12.900 2.064 2.849 12.513 62.2 37.8
3.0 7.75 3.838 16.738 2.678 3.471 13.889 69.1 30.9
3.5 7.70 3.863 20.601 3.296 4.019 15.015 74.6 25.4
4.0 7.60 3.825 24.426 3.908 4.469 15.977 79.4 20.6
5.0 7.10 7.350 31.726 5.084 5.103 17.287 85.9 14.1
6.0 6.60 6.850 38.626 6.180 5.442 18.222 90.6 9.4
7.0 6.00 6.300 44.926 7.188 5.552 18.740 93.1 6.9
9.0 5.10 11.100 56.026 8.964 5.318 19.382 96.3 3.7
11.0 4.40 9.500 65.526 10.484 4.861 19.745 98.1 1.9
15.0 3.30 15.400 80.926 12.948 3.891 20.139 100.0 0
a t
Ab/V = (C )+ k[AUC] n
p p + (C )
t0 t tn
(C ) = k 21 21
12∆Cp∆t /2+ k12 /k21 (Cp ) (1− e−k ∆t )+ (C ) e−k ∆t
t tn tn t t
−1 n−1
k = 0.16; k12 = 0.29; k21 = 0.31
Each fraction of drug absorbed is calculated and is shown in Fig. 8-20. The data for Fig. 8-21 were
plotted against the time interval in which the plasma obtained from the serum tolazamide levels–time
drug sample was obtained (Fig. 8-19). An example of curves in Fig. 8-20. The CRFA–time graph provides
the relationship of CRFA versus time for the absorp- a visual image of the relative rates of drug absorp-
tion of tolazamide from four different drug products tion from various drug products. If the CRFA–time
1.2
1.0 A
0.8 D
0.8
0.6
0.4 C
0.4
0.2
B
0
0 0 2 4 6 8 12 16
0 5 10 15 20 25 30 Time (hours)
Time (hours)
FIGURE 820 Mean cumulative relative fractions of
FIGURE 819 Fraction of drug absorbed. (Wagner–Nelson tolazamide absorbed as a function of time. (From Welling et al,
method.) 1982, with permission.)
Fraction of drug absorbed
(Ab/Ab)
Cumulative relative
fraction absorbed
Pharmacokinetics of Oral Absorption 199
30 absorption may not differ markedly. Therefore, for
A these studies, tmax, or time of peak drug concentra-
20 tion, can be very useful in comparing the respective
D
rates of absorption of a drug from chemically equiv-
C alent drug products.
10
B
0 Frequently Asked Questions
0 2 4 6 8 12 16 24
Time (hours) »»Can the Wagner–Nelson method be used to calculate
ka for an orally administered drug that follows the
FIGURE 821 Mean serum tolazamide levels as a func- pharmacokinetics of a two-compartment model?
tion of time. (From Welling et al, 1982, with permission.)
»»What is the absorption half-life of a drug and how is
it determined?
curve is a straight line, then the drug was absorbed
from the drug product at an apparent zero-order »»In switching a drug from IV to oral dosing, what is the
most important consideration?
absorption rate.
The calculation of ka is useful in designing a »»Drug clearance is dependent on dose and area under
multiple-dosage regimen. Knowledge of the ka and k the time–drug concentration curve. Would drug
allows for the prediction of peak and trough plasma clearance be affected by the rate of absorption?
drug concentrations following multiple dosing. In »»Does a larger absorption rate constant affect Cmax,
bioequivalence studies, drug products are given in tmax, and AUC if the dose and elimination rate con-
chemically equivalent (ie, pharmaceutical equiva- stant, k remains constant?
lents) doses, and the respective rates of systemic
CHAPTER SUMMARY
Pharmacokinetic absorption models range from two-compartment model using the Loo–Riegelman
being entirely “exploratory” and empirical, to semi- method. The determination of the fraction of drug
mechanistic and ultimately complex physiologically absorbed is an important tool in evaluating drug dos-
based pharmacokinetic (PBPK) models. This choice age form and design. The Wagner–Nelson method
is conditional on the modeling purpose as well as the and Loo–Reigelman method are classical methods for
amount and quality of the available data. determinating absorption rate constants and fraction
Empirically, the pharmacokinetics of drug of drug absorbed. Convolution and deconvolution are
absorption may be described by zero-order or first- powerful alternative tools used to predict a plasma
order kinetics. Drug elimination from the body is drug concentration–time profile from dissolution of
generally described by first-order kinetics. Using the data during drug development.
compartment model, various important pharmacoki- The empirical models presented in this chapter
netics parameters about drug absorption such as ka, are very basic with simple assumptions. More
k, Cmax, tmax, and other parameters may be computed sophisticated methods based on these basic con-
from data by the method of residuals (feathering) or cepts may be extended to include physiological
by computer modeling. The pharmacokinetic param- factors such as GI transit in the physiologically
eters are important in evaluating drug absorption and based models that represent the advance drug
understanding how these parameters affect drug absorption model development. These models are
concentrations in the body. The fraction of drug useful to predict drug absorption over time curves
absorbed may be computed in a one-compartment in designing oral dosage forms (see Chapters 14
model using the Wagner–Nelson method or in a and 15).
Serum tolazamide
concentration (mg/mL)
200 Chapter 8
Although the current development of in vitro increases. Although such an approach has limita-
studies and computer science have allowed rapid tions, further methodology research in this field and
advances of PBPK models, the combination of the advances in computer science can address many
physiologically based modeling with parameter esti- of them. It is apparent that “bottom-up” and “top-
mation techniques seems to be the way forward and down” modeling strategies need to approach and
its impact on the drug development progressively borrow skills from each other.
ANSWERS
Frequently Asked Questions with oral solutions and immediate-release drug
products such as compressed tablets or capsules.
If drug absorption is simulated using the oral one- The determination of the absorption rate constant,
compartment model, would a larger absorption rate ka, is most often calculated by the Wagner–Nelson
constant result in a greater amount of drug absorbed? method for drugs, which follows a one-compartment
• The fraction of drug absorbed, F, and the absorption model with first-order absorption and first-order
rate constant, ka, are independent parameters. A drug elimination.
in an oral solution may have a more rapid rate of In switching a drug from IV to oral dosing, what is
absorption compared to a solid drug product. If the the most important consideration?
drug is released from the drug product slowly or is
formulated so that the drug is absorbed slowly, the • The fraction of drug absorbed may be less than 1
drug may be subjected to first-pass effects, degraded (ie, 100% bioavailable) after oral administration.
in the gastrointestinal tract, or eliminated in the feces In some cases, there may be a different salt form
so that less drug (smaller F) may be absorbed sys- of the drug used for IV infusion compared to the
temically compared to the same drug formulated to salt form of the drug used orally. Therefore, a cor-
be absorbed more rapidly from the drug product. rection is needed for the difference in MW of the
two salt forms.
How do you explain that ka is often greater than k
with most drugs? Drug clearance is dependent on dose and area under
the time–drug concentration curve. Would drug
• A drug with a rate of absorption slower than its rate clearance be affected by the rate of absorption?
of elimination will not be able to obtain optimal
systemic drug concentrations to achieve efficacy. • Total body drug clearance and renal drug clear-
Such drugs are generally not developed into prod- ance are generally not affected by drug absorp-
ucts. However, the apartment ka for drugs absorbed tion from most absorption sites. In the gastroin-
from controlled-release products (Chapter 18) may testinal tract, a drug is absorbed via the hepatic
be smaller, but the initial rate of absorption from portal vein to the liver and may be subject to
the GI tract is faster than the rate of drug elimina- hepatic clearance.
tion since, dDGI/dt = − kaDGI.
Learning Questions
What is the absorption half-life of a drug and how is
1. a. T he elimination rate constant is 0.1 h−1
it determined? (t1/2 =
6.93 h).
• For drugs absorbed by a first-order process, the b. The absorption rate constant, ka, is 0.3 h−1
absorption half-life is 0.693/ka. Although drug (absorption half-life = 2.31 h).
absorption involves many stochastic (system-based
random) steps, the overall rate process is often ln(k /k)
The calculated a
tmax = = 5.49 h
approximated by a first-order process, especially ka − k
Pharmacokinetics of Oral Absorption 201
c. The y intercept was observed to be 60 ng/mL. 5. The equations for a drug that follows the
Therefore, the equation that fits the observed kinetics of a one-compartment model with
data is first-order absorption and elimination are
FD k ln(k /k)
C = 60(e−0.1t e−0.3t
p − ) C 0 a
p = (ekt −kat
− e ) t a
=
VD(k k max
a − ) ka − k
Note: Answers obtained by “hand” feather- As shown by these equations:
ing the data on semilog graph paper may vary a. tmax is influenced by ka and k and not by F,
somewhat depending on graphing skills and D0, or VD.
skill in reading data from a graph. b. Cp is influenced by F, D0, VD, ka, and k.
2. By direct observation of the data, the tmax
6. A drug product that might provide a zero-order
is 6 hours and the Cmax is 23.01 ng/mL. input is an oral controlled-release tablet or a trans-
The apparent volume of distribution, VD, is dermal drug delivery system (patch). An IV drug
obtained from the intercept, I, of the terminal infusion will also provide a zero-order drug input.
elimination phase, and substituting F = 0.8, 7. The general equation for a one-compartment
D = 10,000,000 ng, ka = 0.3 h−1, k = 0.1 h−1: open model with oral absorption is
FD
C 0ka (e−kt e−kat
p = − )
Fk D
I a 0 VD (ka − k)
=
VD (ka − k)
From Cp = 45(e−0.17t − e−1.5t)
(0.8)(0.3)(10,000,000)
60 =
VD (0.3− 0.1) FD0ka
= 45
VD (ka − k)
VD = 200 L
k −1
= 0.17 h
3. The percent-of-drug-unabsorbed method k 1.5 h−1
a =
is applicable to any model with first-order
elimination, regardless of the process of drug ln(ka /k) ln(1.5/0.17)
input. If the drug is given by IV injection, the a. tmax = = =1.64 h
ka − k 1.5− 0.17
elimination rate constant, k, may be deter-
b. Cma = 45(e−(0.17)(1.64) − e−(1.5)(1.64)
mined accurately. If the drug is administered x )
orally, k and ka may flip-flop, resulting in an = 30.2 µg/mL
error unless IV data are available to determine
k. For a drug that follows a two-compartment 0.693 0.693
c. t1/2 = = = 4.08 h
model, an IV bolus injection is used to deter- k 0.17
mine the rate constants for distribution and
elimination. In(1.0/0.2)
8. a. Drug A tmax = = 2.01 h
4. After an IV bolus injection, a drug such as 1.0 −1.2
theophylline follows a two-compartment In(0.2/1.0)
Drug B tmax = = 2.01 h
model with a rapid distribution phase. During 0.2−1.0
oral absorption, the drug is distributed dur-
FD k
ing the absorption phase, and no distribution b. C 0 a ( − tmax −katmax
max = e k
− e )
VD (ka − k)
phase is observed. Pharmacokinetic analy-
sis of the plasma drug concentration data (1)(500)(1)
Drug A Cma = (e−(0.2)(2)− e−(1)(2)
obtained after oral drug administration will x − )
(10)(1 0.2)
show that the drug follows a one-compartment
model. Cmax = 33.4 µg/mL
202 Chapter 8
(1)(500)(0.2) c. The Loo–Riegelman method requires IV
Drug B Cmax =
(20)(0.2 −1.0) data. Therefore, only the Wagner–Nelson
method may be used on these data.
= (e−1(2) − e−(0.2)(2) ) d. Observed tmax and Cmax values are taken
Cmax = 33.4 µ directly from the experimental data. In
g/mL
this example, Cmax is 85.11 ng/mL, which
occurred at a tmax of 1 hour. The theoretical
9. a. The method of residuals using manual
tmax and Cmax are obtained as follows:
graphing methods may give somewhat dif-
ferent answers depending on personal skill 2.3log(k /k)
t a
and the quality of the graph paper. Values max =
ka − k
obtained by the computer program ESTRIP
gave the following estimates: 2.3log(2.84/0.186)
= =1.03 h
2.84 − 0.186
ka = 2.84 h−1 k = 0.186 h−1 t1/2 = 3.73 h
FD k
b. A drug in an aqueous solution is in the most C 0 a − max − a max
max = (e kt e k t
− )
VD (ka − k)
absorbable form compared to other oral dosage
forms. The assumption that k where FD0ka/VD(ka − k) is the y intercept
a > k is generally
true for drug solutions and immediate-release equal to 110 ng/mL and tmax = 1.03 h.
oral dosage forms such as compressed tablets
C (1 −(1.186)(1.0) −(2
max = 10)(e − e .84)(1.03) )
and capsules. Drug absorption from extended-
release dosage forms may have ka < k. To dem- Cmax = 85 ng/mL
onstrate unequivocally which slope represents
e. A more complete model-fitting program, such
the true k, the drug must be given by IV bolus
as WINNONLIN, is needed to fit the data
or IV infusion, and the slope of the elimination
statistically to a one-compartment model.
curve obtained.
APPLICATION QUESTIONS
1. Plasma samples from a patient were collected From the given data:
after an oral bolus dose of 10 mg of a new a. Determine the elimination constant of the
benzodiazepine solution as follows: drug.
b. Determine ka by feathering.
Time (hours) Concentration (ng/mL) c. Determine the equation that describes
0.25 2.85 the plasma drug concentration of the new
benzodiazepine.
0.50 5.43
2. Assuming that the drug in Question 1 is
0.75 7.75 80% absorbed, find (a) the absorption con-
1.00 9.84 stant, ka; (b) the elimination half-life, t1/2;
(c) the tmax, or time of peak drug concentra-
2.00 16.20
tion; and (d) the volume of distribution of
4.00 22.15 the patient.
6.00 23.01 3. Contrast the percent of drug-unabsorbed methods
10.00 19.09 for the determination of rate constant for
absorption, ka, in terms of (a) pharmacokinetic
14.00 13.90
model, (b) route of drug administration, and
20.00 7.97 (c) possible sources of error.
Pharmacokinetics of Oral Absorption 203
4. What is the error inherent in the measure- subjects. The following data represent the
ment of ka for an orally administered drug mean blood phenylpropanolamine hydrochlo-
that follows a two-compartment model when ride concentrations (ng/mL) after the oral
a one-compartment model is assumed in the administration of a single 25-mg dose of
calculation? phenylpropanolamine hydrochloride solution:
5. What are the main pharmacokinetic parameters
that influence (a) time for peak drug concen-
Concen- Concen-
tration and (b) peak drug concentration?
Time tration Time tration
6. Name a method of drug administration that (hours) (ng/mL) (hours) (ng/mL)
will provide a zero-order input.
7. A single oral dose (100 mg) of an antibiotic 0 0 3 62.98
was given to an adult male patient (43 years, 0.25 51.33 4 52.32
72 kg). From the literature, the pharmacokinetics 0.5 74.05 6 36.08
of this drug fits a one-compartment open model.
The equation that best fits the pharmacokinetics 0.75 82.91 8 24.88
of the drug is 1.0 85.11 12 11.83
C 45(e−0.17t e−1.5t
p = − ) 1.5 81.76 18 3.88
2 75.51 24 1.27
From the equation above, calculate (a) tmax,
(b) Cmax, and (c) t1/2 for the drug in this patient.
Assume Cp is in μg/mL and the first-order rate a. From the above data, obtain the rate constant
constants are in h−1. for absorption, ka, and the rate constant for
8. Two drugs, A and B, have the following phar- elimination, k, by the method of residuals.
macokinetic parameters after a single oral dose b. Is it reasonable to assume that ka > k for a
of 500 mg: drug in a solution? How would you deter-
mine unequivocally which rate constant
Drug ka (h−1) k (h−1) VD (mL) represents the elimination constant k?
c. From the data, which method, Wagner–
A 1.0 0.2 10,000
Nelson or Loo–Riegelman, would be more
B 0.2 1.0 20,000 appropriate to determine the order of the rate
constant for absorption?
Both drugs follow a one-compartment pharma- d. From your values, calculate the theoreti-
cokinetic model and are 100% bioavailable. cal tmax. How does your value relate to the
a. Calculate the tmax for each drug. observed tmax obtained from the subjects?
b. Calculate the Cmax for each drug. e. Would you consider the pharmacokinetics of
9. The bioavailability of phenylpropanolamine phenylpropanolamine HCl to follow a one-
hydrochloride was studied in 24 adult male compartment model? Why?
REFERENCES
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for assessing inter-individual variability in pharmacokinetics absorption kinetics after subcutaneous administration using a
using virtual human populations and integrating general modified Wagner–Nelson method with a nonlinear elimination
knowledge of physical chemistry, biology, anatomy, physiol- model. J Pharm Sci 13:151–158, 2001.
ogy and genetics: A tale of “bottom-up” vs “top-down” rec- Lockwood P, Gillespie WR: A convolution approach to in vivo:in
ognition of covariates. Drug Metab Pharmacokinet 24:53–75, vitro correlation (IVIVC) that does not require an IV or solu-
2009. tion reference dose. Pharm Res 34:369, 1996.
204 Chapter 8
Loo JCK, Riegelman S: New method for calculating the intrinsic Wagner JG: Use of computers in pharmacokinetics. Clin Pharma-
absorption rate of drugs. J Pharm Sci 57:918–928, 1968. col Ther 8:201–218, 1967.
Levy G, Amsel LP, Elliot HC: Kinetics of salicyluric acid elimina- Welling PG: Pharmacokinetics: Processes and Mathematics. ACS
tion in man. J Pharm Sci 58:827–829, 1969. monograph 185. Washington, DC, American Chemical Soci-
Manini AF, Kabrhel C, Thomsen TW: Acute myocardial infarction ety, 1986, pp 174–175.
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Med 45(2):213–216, Feb 2005. mide from tablets: Comparison of in vitro and in vivo results.
Portmann G: Pharmacokinetics. In Swarbrick J (ed), Current Con- J Pharm Sci 71:1259, 1982.
cepts in the Pharmaceutical Sciences, vol 1. Philadelphia, Lea Yu LX, Amidon GL: A compartmental absorption and tran-
& Febiger, 1970, Chap 1. sit model for estimating oral drug absorption. Int J Pharm
Teorell T: Kinetics of distribution of substances administered to 186:119–125, 1999.
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BIBLIOGRAPHY
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Ther 174:1–8, 1970. Wagner JG, Nelson E: Kinetic analysis of blood levels and urinary
Dvorchik BH, Vesell ES: Significance of error associated with use excretion in the absorptive phase after single doses of drug.
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Multiple-Dosage Regimens
9 Rodney C. Siwale and Shabnam N. Sani
Chapter Objectives Earlier chapters of this book discussed single-dose drug and
constant-rate drug administration. By far though, most drugs are
»» Define the index for measuring
given in several doses, for example, multiple doses to treat chronic
drug accumulation.
disease such as arthritis, hypertension, etc. After single-dose drug
»» Define drug accumulation and administration, the plasma drug level rises above and then falls
drug accumulation t1/2. below the minimum effective concentration (MEC), resulting in a
»» Explain the principle of decline in therapeutic effect. To treat chronic disease, multiple-
superposition and its dosage or IV infusion regimens are used to maintain the plasma
assumptions in multiple-dose drug levels within the narrow limits of the therapeutic window
regimens. (eg, plasma drug concentrations above the MEC but below the
minimum toxic concentration or MTC) to achieve optimal clinical
»» Calculate the steady-state Cmax effectiveness. These drugs may include antibacterials, cardioton-
and Cmin after multiple IV bolus ics, anticonvulsants, hypoglycemics, antihypertensives, hormones,
dosing of drugs. and others. Ideally, a dosage regimen is established for each drug
»» Calculate k and V to provide the correct plasma level without excessive fluctuation
D of
aminoglycosides in multiple- and drug accumulation outside the therapeutic window.
dose regimens. For certain drugs, such as antibiotics, a desirable MEC can be
determined. For drugs that have a narrow therapeutic range
»» Adjust the steady-state Cmax and
(eg, digoxin and phenytoin), there is a need to define the therapeu-
Cmin in the event the last dose
tic minimum and maximum nontoxic plasma concentrations
is given too early, too late, or
(MEC and MTC, respectively). In calculating a multiple-dose regi-
totally missed following multiple
men, the desired or target plasma drug concentration must be
IV dosing.
related to a therapeutic response, and the multiple-dose regimen
must be designed to produce plasma concentrations within the
therapeutic window.
There are two main parameters that can be adjusted in
developing a dosage regimen: (1) the size of the drug dose and
(2) t, the frequency of drug administration (ie, the time interval
between doses).
DRUG ACCUMULATION
To calculate a multiple-dose regimen for a patient or patients,
pharmacokinetic parameters are first obtained from the plasma
level–time curve generated by single-dose drug studies. With these
pharmacokinetic parameters and knowledge of the size of the dose
and dosage interval (t), the complete plasma level–time curve or
205
206 Chapter 9
the plasma level may be predicted at any time after concentration obtained by adding the residual drug
the beginning of the dosage regimen. concentration obtained after each previous dose. The
For calculation of multiple-dose regimens, it is superposition principle may be used to predict drug
necessary to decide whether successive doses of concentrations after multiple doses of many drugs.
drug will have any effect on the previous dose. The Because the superposition principle is an overlay
principle of superposition assumes that early doses method, it may be used to predict drug concentra-
of drug do not affect the pharmacokinetics of subse- tions after multiple doses given at either equal or
quent doses. Therefore, the blood levels after the unequal dosage intervals. For example, the plasma
second, third, or nth dose will overlay or superim- drug concentrations may be predicted after a drug
pose the blood level attained after the (n−1)th dose. dose is given every 8 hours, or 3 times a day before
∞
In addition, the AUC = ( ∫ C AM, 12 noon, and 6 PM.
p dt) for the first dose is meals at 8
0
There are situations, however, in which the
equal to the steady-state area between doses, that is,
superposition principle does not apply. In these
t
∫ 2
( Cp dt) as shown in Fig. 9-1. cases, the pharmacokinetics of the drug change after
t1
The principle of superposition allows the pharma- multiple dosing due to various factors, including
cokineticist to project the plasma drug concentration– changing pathophysiology in the patient, saturation
time curve of a drug after multiple consecutive doses of a drug carrier system, enzyme induction, and
based on the plasma drug concentration–time curve enzyme inhibition. Drugs that follow nonlinear phar-
obtained after a single dose. The basic assumptions are macokinetics (see Chapter 10) generally do not have
(1) that the drug is eliminated by first-order kinetics predictable plasma drug concentrations after multi-
and (2) that the pharmacokinetics of the drug after a ple doses using the superposition principle.
single dose (first dose) are not altered after taking mul- If the drug is administered at a fixed dose and a
tiple doses. fixed dosage interval, as is the case with many mul-
The plasma drug concentrations after multiple tiple-dose regimens, the amount of drug in the body
doses may be predicted from the plasma drug con- will increase and then plateau to a mean plasma level
centrations obtained after a single dose. In Table 9-1, higher than the peak Cp obtained from the initial
the plasma drug concentrations from 0 to 24 hours dose (Figs. 9-1 and 9-2). When the second dose is
are measured after a single dose. A constant dose given after a time interval shorter than the time
of drug is given every 4 hours and plasma drug con- required to “completely” eliminate the previous
centrations after each dose are generated using the dose, drug accumulation will occur in the body. In
data after the first dose. Thus, the predicted plasma other words, the plasma concentrations following the
drug concentration in the patient is the total drug second dose will be higher than corresponding
plasma concentrations immediately following the
first dose. However, if the second dose is given after
a time interval longer than the time required to elimi-
nate the previous dose, drug will not accumulate
(see Table 9-1).
AUC = As repetitive equal doses are given at a constant
t
∫ 2
t Cpdt frequency, the plasma level–time curve plateaus and
1
a steady state is obtained. At steady state, the plasma
∞
AUC = ∫0C pdt drug levels fluctuate between C∞
max and C∞
min. Once
Time (hours) t steady state is obtained, C∞
t max and C∞
min are constant
1 t2
and remain unchanged from dose to dose. In addi-
t2
Doses tion, the AUC between ( ∫ Cp dt) is constant during
t1
FIGURE 91 a dosing interval at steady state (see Fig. 9-1). The
Simulated data showing blood levels after
administration of multiple doses and accumulation of blood C∞
max is important in determining drug safety. The
levels when equal doses are given at equal time intervals. C∞
max should always remain below the MTC. The C∞
max
Blood level
Multiple-Dosage Regimens 207
TABLE 91 Predicted Plasma Drug Concentrations for Multiple-Dose Regimen Using the
Superposition Principlea
Plasma Drug Concentration ( lg/mL)
Dose
Number Time (h) Dose 1 Dose 2 Dose 3 Dose 4 Dose 5 Dose 6 Total
1 0 0 0
1 21.0 21.0
2 22.3 22.3
3 19.8 19.8
2 4 16.9 0 16.9
5 14.3 21.0 35.3
6 12.0 22.3 34.3
7 10.1 19.8 29.9
3 8 8.50 16.9 0 25.4
9 7.15 14.3 21.0 42.5
10 6.01 12.0 22.3 40.3
11 5.06 10.1 19.8 35.0
4 12 4.25 8.50 16.9 0 29.7
13 3.58 7.15 14.3 21.0 46.0
14 3.01 6.01 12.0 22.3 43.3
15 2.53 5.06 10.1 19.8 37.5
5 16 2.13 4.25 8.50 16.9 0 31.8
17 1.79 3.58 7.15 14.3 21.0 47.8
18 1.51 3.01 6.01 12.0 22.3 44.8
19 1.27 2.53 5.06 10.1 19.8 38.8
6 20 1.07 2.13 4.25 8.50 16.9 0 32.9
21 0.90 1.79 3.58 7.15 14.3 21.0 48.7
22 0.75 1.51 3.01 6.01 12.0 22.3 45.6
23 0.63 1.27 2.53 5.06 10.1 19.8 39.4
24 0.53 1.07 2.13 4.25 8.50 16.9 33.4
aA single oral dose of 350 mg was given and the plasma drug concentrations were measured for 0–24 h. The same plasma drug concentrations are
assumed to occur after doses 2–6. The total plasma drug concentration is the sum of the plasma drug concentrations due to each dose. For this
example, VD = 10 L, t1/2 = 4 h, and ka = 1.5 h−1. The drug is 100% bioavailable and follows the pharmacokinetics of a one-compartment open model.
208 Chapter 9
is also a good indication of drug accumulation. If a 50
drug produces the same C∞
max at steady state, com-
pared with the (C 1) f e h i
n max a t r t e f rst dose, then 45
− 600 mg every 24 h
there is no drug accumulation. If C∞
max is much larger
than (C 1) , t e h r
n max h n t e e is significant accumulation 40
−
during the multiple-dose regimen. Accumulation is
affected by the elimination half-life of the drug and 35
200 mg
the dosing interval. The index for measuring drug every 8 h
accumulation R is 30 IV infusion
(25 mg/h)
(C∞ )
R = max (9.1) 25 300 mg
(C every 12 h
n=1)max
20
Substituting for Cmax after the first dose and at steady
state yields 15
D0 /VD[1/(1− e−kτ )] 10
R = (9.2)
D0 /VD
5
1
R =
1− e−kτ
0
0 10 20 30 40 50
Time (hours)
Equation 9.2 shows that drug accumulation mea-
sured with the R index depends on the elimination FIGURE 93 Simulated plasma drug concentration–time
constant and the dosing interval and is independent curves after IV infusion and oral multiple doses for a drug with an
elimination half-life of 4 hours and apparent VD of 10 L. IV infusion
of the dose. For a drug given in repetitive oral doses,
given at a rate of 25 mg/h, oral multiple doses are 200 mg every
the time required to reach steady state is dependent 8 hours, 300 mg every 12 hours, and 600 mg every 24 hours.
on the elimination half-life of the drug and is inde-
pendent of the size of the dose, the length of the
dosing interval, and the number of doses. For exam-
Furthermore, if the drug is given at the same
ple, if the dose or dosage interval of the drug is
dosing rate but as an infusion (eg, 25 mg/h), the aver-
altered as shown in Fig. 9-2, the time required for the
age plasma drug concentrations will (C∞
drug to reach steady state is the same, but the final av ) be the
same but the fluctuations between C∞
max and C∞
min will
steady-state plasma level changes proportionately.
vary (Fig. 9-3). An average steady-state plasma drug
concentration is obtained by dividing the area under
t
the curve (AUC) for a dosing period (ie, ∫ 2
C dt) by
t p
1000 1
the dosing interval t, at steady state.
800 An equation for the estimation of the time to
600 Max reach one-half of the steady-state plasma levels or
Min
400 the accumulation half-life has been described by van
Rossum and Tomey (1968).
200
0
0 20 40 60 80 100 k
Accumulation 1 3. a
t1/2 = t1/2 + 3log (9.3)
Time (hours) ka − k
FIGURE 92 Amount of drug in the body as a function of
time. Equal doses of drug were given every 6 hours (upper curve) For IV administration, ka is very rapid (approaches ∞);
and every 8 hours (lower curve). ka and k remain constant. k is very small in comparison to ka and can be omitted
Amount of drug in body (mg)
Plasma level (mg/mL)
Multiple-Dosage Regimens 209
in the denominator of Equation 9.3. Thus, Equation 9.3 of the drug and the dosage interval t (see Table 9-3).
reduces to If the drug is given at a dosage interval equal to the
half-life of the drug, then 6.6 doses are required to
k
Accumulation a
t1/2 = t1/2 1+ 3.3log (9.4) reach 99% of the theoretical steady-state plasma
ka drug concentration. The number of doses needed to
reach steady state is 6.6t1/2/t, as calculated in the far
Since ka/ka = 1 and log 1 = 0, the accumulation t1/2 of
right column of Table 9-3. As discussed in Chapter 6,
a drug administered intravenously is the elimination
Table 6-1, it takes 4.32 half-lives to reach 95% of
t1/2 of the drug. From this relationship, the time to
steady state.
reach 50% steady-state drug concentrations is depen-
dent only on the elimination t1/2 and not on the dose
or dosage interval. CLINICAL EXAMPLE
As shown in Equation 9.4, the accumulation
t1/2 is directly proportional to the elimination t1/2. Paroxetine (Prozac) is an antidepressant drug with a
Table 9-2 gives the accumulation t1/2 of drugs with long elimination half-life of 21 hours. Paroxetine is
various elimination half-lives given by multiple well absorbed after oral administration and has a tmax
oral doses (see Table 9-2). of about 5 hours, longer than most drugs. Slow
From a clinical viewpoint, the time needed to elimination may cause the plasma curve to peak
reach 90% of the steady-state plasma concentration is slowly. The tmax is affected by k and ka, as discussed
3.3 times the elimination half-life, whereas the time in Chapter 8. The Cmax for paroxetine after multiple
required to reach 99% of the steady-state plasma dosing of 30 mg of paroxetine for 30 days in one
concentration is 6.6 times the elimination half-life study ranged from 8.6 to 105 ng/mL among 15 sub-
(Table 9-3). It should be noted from Table 9-3 that at jects. Clinically it is important to achieve a stable
a constant dose size, the shorter the dosage interval, steady-state level in multiple dosing that does not
the larger the dosing rate (mg/h), and the higher the “underdose” or overdose the patient. The pharmacist
steady-state drug level. should advise the patient to follow the prescribed
The number of doses for a given drug to reach dosing interval and dose as accurately as possible.
steady state is dependent on the elimination half-life Taking a dose too early or too late contributes to
TABLE 92 Effect of Elimination Half-Life and Absorption Rate Constant on Accumulation
Half-Life after Oral Administrationa
Elimination Elimination Rate Absorption Rate Accumulation
Half-life (h) constant (1/h) Constant (1/h) Half-life (h)
4 0.173 1.50 4.70
8 0.0866 1.50 8.67
12 0.0578 1.50 12.8
24 0.0289 1.50 24.7
4 0.173 1.00 5.09
8 0.0866 1.00 8.99
12 0.0578 1.00 13.0
24 0.0289 1.00 25.0
aAccumulation half-life is calculated by Equation 8.3, and is the half-time for accumulation of the drug to 90% of the steady-state plasma drug
concentration.
210 Chapter 9
TABLE 93 Interrelation of Elimination Half-Life, Dosage Interval, Maximum Plasma
Concentration, and Time to Reach Steady-State Plasma Concentrationa
Elimination Dosage Interval, Time for NO. Doses to Reach 99%
Half-Life (h) s (h) C∞ (lg/mL) C∞b (h) Steady State
max av
0.5 0.5 200 3.3 6.6
0.5 1.0 133 3.3 3.3
1.0 0.5 341 6.6 13.2
1.0 1.0 200 6.6 6.6
1.0 2.0 133 6.6 3.3
1.0 4.0 107 6.6 1.65
1.0 10.0 100c 6.6 0.66
2.0 1.0 341 13.2 13.2
2.0 2.0 200 13.2 6.1
aA single dose of 1000 mg of three hypothetical drugs with various elimination half-lives but equal volumes of distribution (VD = 10 L) were given by
multiple IV doses at various dosing intervals. All time values are in hours; C∞ = maximum steady-state concentration; (C∞b
max av ) = average steady-state
plasma concentration; the maximum plasma drug concentration after the first dose of the drug is (Cn
=1)max = 100 mg/mL.
bTime to reach 99% of steady-state plasma concentration.
cSince the dosage interval, t, is very large compared to the elimination half-life, no accumulation of drug occurs.
variation. Individual variation in metabolism rate The fraction ( f ) of the dose remaining in the body is
can also cause variable blood levels, as discussed related to the elimination constant (k) and the dosage
later in Chapter 13. interval (t) as follows:
D
f B −kτ
= = e (9.7)
D
REPETITIVE INTRAVENOUS 0
INJECTIONS With any given dose, f depends on k and t. If t is
large, f will be smaller because DB (the amount of
The maximum amount of drug in the body follow-
drug remaining in the body) is smaller.
ing a single rapid IV injection is equal to the dose of
the drug. For a one-compartment open model, the
drug will be eliminated according to first-order
EXAMPLES »» »
kinetics.
1. A patient receives 1000 mg every 6 hours by
D D e−kτ
= (9.5)
B 0 repetitive IV injection of an antibiotic with an
elimination half-life of 3 hours. Assume the drug
If t is equal to the dosage interval (ie, the time between is distributed according to a one-compartment
the first dose and the next dose), then the amount of model and the volume of distribution is 20 L.
drug remaining in the body after several hours can be a. Find the maximum and minimum amounts of
determined with drug in the body.
b. Determine the maximum and minimum
D τ plasma concentrations of the drug.
= D e−k (9.6)
B 0
Multiple-Dosage Regimens 211
TABLE 94 Fraction of the Dose in the Body
Solution before and after Intravenous Injections of a
1000-mg Dosea
a. The fraction of drug remaining in the body is
estimated by Equation 9.7. The concentration of Amount of Drug in Body
the drug declines to one-half after 3 hours (t1/2 =
Number of Doses Before Dose After Dose
3 h), after which the amount of drug will again
decline by one-half at the end of the next 3 hours. 1 0 1000
Therefore, at the end of 6 hours, only one-quarter,
2 250 1250
or 0.25, of the original dose remains in the body.
Thus f is equal to 0.25. To use Equation 9.7, we 3 312 1312
must first find the value of k from the t1/2. 4 328 1328
0.693 0.693 5 332 1332
k = = = 0.231h−1
t1/2 3 6 333 1333
The time interval τ is equal to 6 hours. From 7 333 1333
Equation 9.7, ∞ 333 1333
f = e–(0.231)(6)
af = 0.25.
f = 0.25
Substituting known data, we obtain
In this example, 1000 mg of drug is given
intravenously, so the amount of drug in the body ∞ 1000
D =
max − =1333 mg
is immediately increased by 1000 mg. At the end 1 0.25
of the dosage interval (ie, before the next dose), Then, from Equation 9.8,
the amount of drug remaining in the body is 25%
D∞
of the amount of drug present just after the previ-
min =1333 − 1000 = 333 mg
ous dose, because f = 0.25. Thus, if the value of f
The average amount of drug in the body at steady
is known, a table can be constructed relating the
state, D∞
av, can be found by Equation 9.10 or
fraction of the dose in the body before and after
Equation 9.11. F is the fraction of dose absorbed. For
rapid IV injection (Table 9-4).
an IV injection, F is equal to 1.0.
From Table 9-4 the maximum amount of
drug in the body is 1333 mg and the minimum FD
0
D∞
a = (9.10)
v
amount of drug in the body is 333 mg. The differ- kτ
ence between the maximum and minimum val- FD01.44t ∞ 1/2
D (9.1
ues, D0, will always equal the injected dose. av = 1)
τ
Equations 9.10 and 9.11 can be used for repetitive
Dmax −Dmin =D0 (9.8)
dosing at constant time intervals and for any route
of administration as long as elimination occurs from
In this example, the central compartment. Substitution of values
from the example into Equation 9.11 gives
1333 − 333 = 1000 mg
(1)(1000)(1.44)(3)
D∞
av = = 720 mg
D∞ can also be calculated directly by the
max 6
relationship Since the drug in the body declines exponentially
D (ie, first-order drug elimination), the value D∞
av is not
D∞ 0
max = (9.9)
1− f the arithmetic mean of D∞ and D∞
min . The limitation
max
212 Chapter 9
of using D∞
av is that the fluctuations of D∞ and D∞ is dependent on both AUC and t. The C∞
max min av reflects
are not known. drug exposure after multiple doses. Drug expo-
b. To determine the concentration of drug in the sure is often related to drug safety and efficacy as
body after multiple doses, divide the amount discussed later in Chapter 21. For example, drug
of drug in the body by the volume in which it is exposure is closely monitored when a cytotoxic
dissolved. For a one-compartment model, the or immunosuppressive, anticancer drug is admin-
maximum, minimum, and steady-state concen- istered during therapy. AUC may be estimated by
trations of drug in the plasma are found by the sampling several plasma drug concentrations over
following equations: time. Theoretically, AUC is superior to sampling
just the Cmax or Cmin. For example, when cyclospo-
D∞
C∞ = max (9.12) rine dosing is clinically evaluated using AUC, the
max V
D AUC is approximately estimated by two or three
D∞ points. Dosing error is less than using AUC com-
min
C∞ (9.13)
min =
V pared to the trough method alone (Primmett et al,
D
1998). In general, Cmin or trough level is more fre-
D∞
av
C∞
av = (9.14) quently used than C∞ . C is the drug concentra-
V max min
D
tion just before the next dose is given and is less
A more direct approach to finding C∞ , and C∞ ,
max min variable than peak drug concentration, C∞ . The
max
is C∞
av: sample time for C∞ is approximated and the true
max
C 0 C∞ may not be accurately estimated. In some
max
∞ p
Cmax = (9.15)
1 e−kτ cases, the plasma trough level, C∞
− min is considered
by some investigators as a more reliable sample
where C 0
p is equal to D0/VD. since the drug is equilibrated with the surround-
ing tissues, although this may also depend on
0
C e−kτ
∞ p (9.16)
C other factors.
min =
1− e−kτ
The AUC is related to the amount of drug
FD absorbed divided by total body clearance (Cl), as
∞ 0
Cav = (9.17)
V shown in the following equation:
Dkτ
For this example, the values for C∞ , C∞ C∞
max min, and av t FD FD
[AUC] 2 = 0 = 0 (9.19)
t1
are 66.7, 16.7, and 36.1 μg/mL, respectively. Cl kVD
As mentioned, C∞
av is not the arithmetic mean
Substitution of FD0/kVD for AUC in Equation 9.18
of C∞ and C∞
max min because plasma drug concentra-
gives Equation 9.17. Equation 9.17 or 9.18 can be
tion declines exponentially. The C∞
av is equal to
used to obtain C∞
t t2 av after a multiple-dose regimen
[AUC] 2 or ( al at steady
t ∫ Cp dt ) for a dosage interv
1 t regardless of the route of administration.
1
state divided by the dosage interval t. It is sometimes desirable to know the
t plasma drug concentration at any time after the
[AUC] 2
t
∞ 1
C administration of n doses of drug. The general
av = (9.18)
τ
expression for calculating this plasma drug con-
C∞ centration is
av gives an estimate of the mean plasma drug
concentration at steady state. The C∞
av is often the
D0 1− e−nkτ
target drug concentration for optimal therapeu- Cp = e−kt
VD
(9.20)
1− e−kτ
tic effect and gives an indication as to how long
this plasma drug concentration is maintained dur- where n is the number of doses given and t is the
ing the dosing interval (between doses). The C∞ time after the nth dose.
av
Multiple-Dosage Regimens 213
Problem of a Missed Dose
At steady state, e−nkt approaches zero and
Equation 9.22 describes the plasma drug concentra-
Equation 9.20 reduces to
tion t hours after the nth dose is administered; the
D0 1
C∞ −
p = τ e kt
VD 1− e−k (9.21) doses are administered t hours apart according to a
multiple-dose regimen:
where C∞
p is the steady-state drug concentration at
D 1− e−nkτ
time t after the dose. C = 0 e−kt
p V 1− e− (9.22)
kτ
D
2. The patient in the previous example received 1000
mg of an antibiotic every 6 hours by repetitive IV Concentration contributed by the missing dose is
injection. The drug has an apparent volume of dis-
D
tribution of 20 L and elimination half-life of 3 hours. C′ = 0 e−ktmiss
p (9.23)
Calculate (a) the plasma drug concentration, Cp at VD
3 hours after the second dose, (b) the steady-state
in which tmiss = time elapsed since the scheduled
plasma drug concentration, C∞
p at 3 hours after the
dose was missed. Subtracting Equation 9.23 from
last dose, (c) C∞ , (d) C∞
ma min, and (e) CSS.
x Equation 9.20 corrects for the missing dose as shown
Solution in Equation 9.24.
a. The Cp at 3 hours after the second dose—use D 1− − τ
C 0 e nk
Equation 9.20 and let n = 2, t = 3 hours, and make = e−kt − e ktmiss
p (9
V − −kτ − .24)
D 1 e
other appropriate substitutions.
1000 1− e−(2)(0.231)(6) Note: If steady state is reached (ie, either n = large
C = e−0.231(3)
p 20 1− e−(0.231)(6) or after many doses), the equation simplifies to
Equation 9.25. Equation 9.25 is useful when steady
Cp = 31.3 mg/L state is reached.
b. The C∞
p at 3 hours after the last dose—because D −k
C = 0 e t
−
steady state is reached, use Equation 9.21 and mis
p 1 − − e kt s (9.25)
VD − e kt
perform the following calculation:
1000 1
C∞
p =
e−0.231(3) Generally, if the missing dose is recent, it will affect
20 1− e−0.231(6) the present drug level more. If the missing dose is
several half-lives later (>5t1/2), the missing dose
C∞
p = 33.3 mg/L
may be omitted because it will be very small.
c. The C∞ is calculated from Equation 9.15. Equation 9.24 accounts for one missing dose, but
max
several missing doses can be subtracted in a similar
1000/20
C∞ =
max − = 66.7 mg/L way if necessary.
1− e (0.231)(6)
d. The C∞
min may be estimated as the drug concen-
tration after the dosage interval t, or just before
EXAMPLE »» »
the next dose.
C∞ = C∞ e−kt 66.7e (0.231)(6)
min max = − =16.7 mg/L A cephalosporin (k = 0.2 h−1, VD = 10 L) was admin-
istered by IV multiple dosing; 100 mg was injected
e. The C∞
av is estimated by Equation 9.17—because
every 6 hours for 6 doses. What was the plasma
the drug is given by IV bolus injections, F = 1.
drug concentration 4 hours after the sixth dose
1000
C∞
av = = 36.1mg/L (ie, 40 hours later) if (a) the fifth dose was omitted,
(0.231)(20)(6)
(b) the sixth dose was omitted, and (c) the fourth
C∞
av is represented as CSS in some references. dose was omitted?
214 Chapter 9
the late or early dose added back to take into account
Solution the actual time of dosing, using Equation 9.26.
Substitute k = 0.2 h−1, VD = 10 L, D = 100 mg, n = 6,
D
0 1− e−nkt
t = 4 hours, and t = 6 hours into Equation 9.20 and C e kt e−
= − ktmiss e−ktactual
p V e− − +
kt
D − (9.26)
evaluate: 1
Cp = 6.425 mg/L
in which tmiss = time elapsed since the dose (late or
If no dose was omitted, then 4 hours after the sixth early) is scheduled, and tactual = time elapsed since the
injection, Cp would be 6.425 mg/L. dose (late or early) is actually taken. Using a similar
a. Missing the fifth dose, its contribution must be approach, a second missed dose can be subtracted
subtracted off, tmiss = 6 + 4 = 10 hours (the time from Equation 9.20. Similarly, a second late/early
elapsed since missing the dose) using the steady- dose may be corrected by subtracting the scheduled
state equation: dose followed by adding the actual dose. Similarly, if
D0 100 a different dose is given, the regular dose may be
C e−kt
′ = miss = e−(0.2×10)
p V subtracted and the new dose added back.
D 10
Drug concentration correcting for the missing
dose = 6.425 − 1.353 = 5.072 mg/L.
EXAMPLE »» »
b. If the sixth dose is missing, tmiss = 4 hours:
D0 100 Assume the same drug as above (ie, k = 0.2 h−1
C ′ = e−ktmiss = e−(0.2×4) , VD =
p = 4.493 mg/L
VD 10 10 L) was given by multiple IV bolus injections and
Drug concentration correcting for the missing that at a dose of 100 mg every 6 hours for 6 doses.
dose = 6.425 − 4.493 = 1.932 mg/L. What is the plasma drug concentration 4 hours
after the sixth dose, if the fifth dose were given an
c. If the fourth dose is missing, tmiss = 12 + 4 =
hour late?
16 hours:
Substitute into Equation 9.26 for all unknowns:
D0 100
C ′ = e−ktmiss = e−(0.2×16)
p = 0.408 mg/L k = 0.2 h−1, VD = 10 L, D = 100 mg, n = 6, t = 4 h, t = 6 h,
VD 10
tmiss = 6 + 4 = 10 hours, tactual = 9 hours (taken 1 hour
The drug concentration corrected for the missing late, ie, 5 hours before the sixth dose).
dose = 6.425 − 0.408 = 6.017 mg/L.
Note: The effect of a missing dose becomes D k
0 1− e−n τ
−
C = e kτ
− − e−kt miss + e−kt actual
p
VD 1− e kτ less pronounced at a later time. A strict dose
regimen compliance is advised for all drugs.
Cp = 6.425 – 1.353 + 1.653 = 6.725 mg/L
With some drugs, missing a dose can have a
serious effect on therapy. For example, compli- Note: 1.353 mg/L was subtracted and 1.653 mg/mL
ance is important for the anti-HIV1 drugs such was added because the fifth dose was not given as
as the protease inhibitors. planned, but was given 1 hour later.
INTERMITTENT INTRAVENOUS
Early or Late Dose Administration during
Multiple Dosing INFUSION
When one of the drug doses is taken earlier or later Intermittent IV infusion is a method of successive
than scheduled, the resulting plasma drug concentra- short IV drug infusions in which the drug is given by
tion can still be calculated based on the principle of IV infusion for a short period of time followed by a
superposition. The dose can be treated as missing, with drug elimination period, then followed by another
Multiple-Dosage Regimens 215
4.0
EXAMPLE »» »
3.5
3.0
An antibiotic was infused with a 40-mg IV dose
2.5 over 2 hours. Ten hours later, a second dose of
2.0 40 mg was infused, again over 2 hours. (a) What
1.5 is the plasma drug concentration 2 hours after the
1.0 start of the first infusion? (b) What is the plasma
0.5 drug concentration 5 hours after the second dose
0.0 infusion was started? Assume k = 0.2 h−1 and VD =
0 2 4 6 8 10 12 14 16 18 20 10 L for the antibiotic.
Time (hours)
Solution
FIGURE 94 Plasma drug concentration after two doses
by IV infusion. Data from Table 9-5. The predicted plasma drug concentrations after
the first and second IV infusions are shown in
Table 9-5. Using the principle of superposition, the
short IV infusion (Fig. 9-4). In drug regimens
total plasma drug concentration is the sum of the
involving short IV infusion, the drug may not reach
residual drug concentrations due to the first IV infu-
steady state. The rationale for intermittent IV infu- sion (column 3) and the drug concentrations due to
sion is to prevent transient high drug concentrations the second IV infusion (column 4). A graphical rep-
and accompanying side effects. Many drugs are better resentation of these data is shown in Fig. 9-4.
tolerated when infused slowly over time compared to
a. The plasma drug concentration at 2 hours after
IV bolus dosing.
the first IV infusion starts is calculated from Equa-
tion 9.28.
Administering One or More Doses by 40/2
Constant Infusion: Superposition of Several Cp (1 e−0.2/2
= − )= 3.30 mg/L
10× 0.2
IV Infusion Doses
b. From Table 9-5, the plasma drug concentration
For a continuous IV infusion (see Chapter 7):
at 15 hours (ie, 5 hours after the start of the sec-
R R ond IV infusion) is 2.06 μg/mL. At 5 hours after
C = (1− −
p e kt ) = (1− e−kt ) (9.27)
Cl kVD the second IV infusion starts, the plasma drug
concentration is the sum of the residual plasma
Equation 9.27 may be modified to determine drug drug concentrations from the first 2-hour infu-
concentration after one or more short IV infusions sion according to first-order elimination and the
for a specified time period (Equation 9.28). residual plasma drug concentrations from the
D second 2-hour IV infusion as shown in the fol-
Cp = (1− e−kt ) (9.28)
t lowing scheme:
infVDk
where R = rate of infusion = D/tinf, D = size of infu- 10 hours 10 hours
sion dose, and tinf = infusion period.
First Stopped Second Stopped
After the infusion is stopped, the drug concen- infusion (no infusion infusion (no infusion
tration post-IV infusion is obtained using the first- for 2 hours for 8 hours) for 2 hours for 8 hours)
order equation for drug elimination:
The plasma drug concentration is calculated
C = −
p Cstope
kt (9.29) using the first-order elimination equation, where
Cstop is the plasma drug concentration at the stop
where Cstop = concentration when infusion stops, and
of the 2-hour IV infusion.
t = time elapsed since infusion stopped.
mcg/mL
216 Chapter 9
TABLE 95 Drug Concentration after Two Intravenous Infusionsa
Plasma Drug Plasma Drug Total Plasma
Concentration Concentration Drug
Time(h) after Infusion 1 after Infusion 2 Concentration
Infusion 1 begins 0 0 0
1 1.81 1.81
Infusion 1 stopped 2 3.30 3.30
3 2.70 2.70
4 2.21 2.21
5 1.81 1.81
6 1.48 1.48
7 1.21 1.21
8 0.99 0.99
9 0.81 0.81
Infusion 2 begins 10 0.67 0 0.67
11 0.55 1.81 2.36
Infusion 2 stopped 12 0.45 3.30 3.74
13 0.37 2.70 3.07
14 0.30 2.21 2.51
15 0.25 1.81 2.06
aDrug is given by a 2-hour infusion separated by a 10-hour drug elimination interval. All drug concentrations are in lg/mL. The declining
drug concentration after the first infusion dose and the drug concentration after the second infusion dose give the total plasma drug
concentration.
CLINICAL EXAMPLE
The plasma drug concentration after the com-
pletion of the first IV infusion when t = 15 hours is Gentamicin sulfate was given to an adult male
patient (57 years old, 70 kg) by intermittent IV infu-
C = C e–kt = 3.30e–0.2×15
p stop = 0.25 µg/L sions. One-hour IV infusions of 90 mg of gentami-
cin was given at 8-hour intervals. Gentamicin
The plasma drug concentration 5 hours after the
clearance is similar to creatinine clearance and was
second IV infusion is
estimated as 7.2 L/h with an elimination half-life of
C = C e–kt = 3.30e–0.2×3
p stop =1.81µg/mL 3 hours.
a. What is the plasma drug concentration after the
The total plasma drug concentration 5 hours after
first IV infusion?
the start of the second IV infusion is
b. What is the peak plasma drug concentration,
0.25 mg/L + 1.81 mg/L = 2.06 mg/L. Cmax, and the trough plasma drug concentration,
Cmin, at steady state?
Multiple-Dosage Regimens 217
Solution ESTIMATION OF k AND VD OF
a. The plasma drug concentration directly after the AMINOGLYCOSIDES IN CLINICAL
first infusion is calculated from Equation 9.27,
SITUATIONS
where R = 90 mg/h, Cl = 7.2 L/h, and k = 0.231 h−1.
The time for infusion, tint, is 1 hour. As illustrated above, antibiotics are often infused
90 intravenously by multiple doses, so it is desirable to
C = (1− e−(0.231)(1)
p ) = 2.58 mg/L
7.2 adjust the recommended starting dose based on the
patient’s individual k and VD values. According to
b. The C∞
max at steady state may be obtained from Sawchuk and Zaske (1976), individual parameters
Equation 9.30. for aminoglycoside pharmacokinetics may be deter-
∞ R(1− e−ktinf ) 1 mined in a patient by using a limited number of
Cmax = (9.30)
Cl (1− e−kt ) plasma drug samples taken at appropriate time inter-
vals. The equation was simplified by replacing an
where Cmax is the peak drug concentration fol-
elaborate model with the one-compartment model to
lowing the nth infusion, at steady state, tinf is
describe drug elimination and appropriately avoid-
the time period of infusion, and t is the dosage
ing the distributive phase. The plasma sample should
interval. The term 1/(1 − e−kt) is the accumula-
be collected 15–30 minutes postinfusion (with infu-
tion factor for repeated drug administration.
sion lasting about 60 minutes) and, in patients with
Substitution in Equation 9.30 gives
poor renal function, 1–2 hours postinfusion, to allow
90(1 e−(0.231)(1)
− ) 1
C∞ adequate tissue distribution. The second and third
max = ×
7.2 (1 −(0.231)(8)
− e ) blood samples should be collected about 2–3 half-
lives later, in order to get a good estimation of the
= 3.06 mg/L
slope. The data may be determined graphically or by
The plasma drug concentration C∞
p at any time t regression analysis using a scientific calculator or
after the last infusion ends when steady state computer program.
is obtained by Equation 9.31 and assumes that
plasma drug concentrations decline according R(1− e−ktinf )
VD = (9.32)
to first-order elimination kinetics. [C∞ f
max −C∞ e−ktin
min
R(1 −
− e ktinf ) 1
C∞ e−k (t)
p = × × (9.31)
Cl (1 e−kt The dose of aminoglycoside is generally fixed by
− )
the desirable peak, C∞
max, and trough plasma concen-
where tinf is the time for infusion and t is the tration, C∞
min. For example, C∞
max for gentamicin may
time period after the end of the infusion. be set at 6–10 mg/mL with the steady-state trough
The trough plasma drug concentration, level, C∞
min, generally about 0.5–2 mg/mL, depending
C∞
min, at steady state is the drug concentration on the severity of the infection and renal consider-
just before the start of the next IV infusion or ations. The upper range is used only for life-threat-
after a dosage interval equal to 8 hours after ening infections. The infusion rate for any desired
the last infusion stopped. Equation 9.31 can peak drug concentration may be calculated using
be used to determine the plasma drug con- Equation 9.33.
centration at any time after the last infusion is
stopped (after steady state has been reached). V kC∞ (1 −kτ
D max − e )
R = (9.33)
(1 e−kt
− inf
90(1 e−(0.231)(1) −(0.231)(8) )
− ) e
C∞
min = ×
7.2 (1 e−(0.231)(8)
− )
The dosing interval t between infusions may be
= 0.48 mg/L adjusted to obtain a desired concentration.
218 Chapter 9
the dosage interval (t) is shortened, then the value
Frequently Asked Questions for C∞ will increase. The C∞ will be predictably
av av
»»Is the drug accumulation index (R) applicable to any higher for drugs distributed in a small VD (eg, plasma
drug given by multiple doses or only to drugs that are water) or that have long elimination half-lives than
eliminated slowly from the body? for drugs distributed in a large VD (eg, total body
»»What are the advantages/disadvantages for giving water) or that have very short elimination half-lives.
a drug by a constant IV infusion, intermittent IV Because body clearance (ClT) is equal to kVD, substi-
infusion, or multiple IV bolus injections? What drugs tution into Equation 9.17 yields
would most likely be given by each route of adminis- FD
tration? Why? C∞ 0
av = (9.36)
ClTτ
»»Why is the accumulation index, R, not affected by the
Thus, if ClT decreases, C∞ will increase.
dose or clearance of a drug? Would it be possible for av
a drug with a short half-life to have R much greater The C∞ does not give information concerning the
av
than 1? fluctuations in plasma concentration (C∞
max and C∞
min).
In multiple-dose regimens, Cp at any time can be
obtained using Equation 9.34, where n = nth dose. At
steady state, the drug concentration can be determined
MULTIPLE-ORAL-DOSE REGIMEN by letting n equal infinity. Therefore, e−nkt becomes
Figures 9-1 and 9-2 present typical cumulation approximately equal to zero and Equation 9.22 becomes
curves for the concentration of drug in the body after k
∞ = aFD0 1 k 1
C
− − a
p − e t e
VD (k
a k) 1− e k −
− τ τ k t
multiple oral doses given at a constant dosage inter- 1− eka
val. The plasma concentration at any time during an
oral or extravascular multiple-dose regimen, assum- (9.37)
ing a one-compartment model and constant doses The maximum and minimum drug concentrations
and dose interval, can be determined as follows: (C∞
max and C∞
min) can be obtained with the following
Fk D 1 e− aτ
− nk n
t 1− e− kτ equations:
C a 0 e−ka − e−kt
p =
V (k − ka ) 1− e−kaτ 1− e−kτ
D
∞ FD
= 0 1
−kt
C p
max − τ e (9.38)
VD 1− e k
where n = number of doses, t = dosage interval, F =
fraction of dose absorbed, and t = time after admin- ∞ k 1
C = aFD0
min e k (9.39)
V ( −
τ τ
k − k) 1− e−k
istration of n doses.
D a
The mean plasma level at steady state, C∞ , is
av The time at which maximum (peak) plasma concen-
determined by a similar method to that employed for
tration (or tmax) occurs following a single oral dose is
repeat IV injections. Equation 9.17 can be used for
finding C∞ for any route of administration. 2.3 k
av = a
tmax − log (9.40)
FD ka k k
C∞ 0
av = (9.17)
VDkτ whereas the peak plasma concentration, tp, following
Because proper evaluation of F and V multiple doses is given by Equation 9.41.
D requires IV
data, the AUC of a dosing interval at steady state 1 k (1− e−kτ )
tp = − ln a
may be substituted in Equation 9.17 to obtain (9.41)
k k
k(1− e−k τ
a
a )
∞
∫ C dt ∞
∞ 0 p [AUC] ( . 5)
C 0 9
av = = 3 Large fluctuations between C∞
max and C∞
min can be
τ τ hazardous, particularly with drugs that have a narrow
One can see from Equation 9.17 that the magnitude therapeutic index. The larger the number of divided
of C∞ is directly proportional to the size of the dose doses, the smaller the fluctuations in the plasma drug
av
and the extent of drug absorbed. Furthermore, if concentrations. For example, a 500-mg dose of drug
Multiple-Dosage Regimens 219
given every 6 hours will produce the same C∞ value as
av
a 250-mg dose of the same drug given every 3 hours, c. Cp at 4 hours after the seventh dose may be calcu-
while the C∞ d using Equation 9.34, letting n = 7, t = 4, t = 8,
max and C∞
min fluctuations for the latter dose late
will be decreased by one-half (see Fig. 9-3). With drugs and making the appropriate substitutions.
that have a narrow therapeutic index, the dosage inter- (0.75)(250)(0.9)
val should not be longer than the elimination half-life. Cp =
(121.5)(0.07−0.9)
(7)(0.9)(8) −(7)(0.07)(8)
EXAMPLE »» » 1−e− 1−e
× e−0.9(4) − e−0.07(4)
1−e−0.9(8)
1−e−
(0.07)(8)
An adult male patient (46 years old, 81 kg) was given
Cp =2.86 mg/L
250 mg of tetracycline hydrochloride orally every
8 hours for 2 weeks. From the literature, tetracycline d. C ∞ at steady state: t at steady state is obtained
max p
hydrochloride is about 75% bioavailable and has an from Equation 9.41.
apparent volume of distribution of 1.5 L/kg. The elim-
1 ka(1−e−kτ )
ination half-life is about 10 hours. The absorption rate tp = ln
k −
k k − −kaτ
a (1 e )
constant is 0.9 h−1. From this information, calculate
(a) C (0.07)(8)
max after the first dose, (b) Cmin after the first dose,
1 0.9(1−e− )
t = ln
(c) plasma drug concentration C p
p at 4 hours after the −
0.9 0.07 0.07(1−e−(0.9)(8) )
seventh dose, (d) maximum plasma drug concentra-
tion at steady state, C∞ , (e) minimum plasma drug tp =2.05 hours
max
concentration at steady state, C∞
min, and (f) average
Then C∞ is obtained using Equation 9.38.
plasma drug concentration at steady state, max
C∞
av.
Solution ∞ 0.75(250) 1
Cmax = e−0.07(2.05)
121.5 1−e−0.07(8)
a. Cmax after the first dose occurs at tmax—therefore,
using Equation 9.40, C∞
min =3.12 mg/L
2.3 0.9
tmax = log e. C∞
0.9−0.07 0.07 min at steady state is calculated from
Equation 9.39.
tmax =3.07
(0.9)(0.75)(250) 1
C∞ =
Then substitute t e−(0.7)(8)
min
max into the following equa- (121.5)(0.9−0.07) 1−e−0.07(8)
tion for a single oral dose (one-compartment
model) to obtain C C∞
max =2.23 mg/L
max.
FD k f. C∞
C = 0 a (e−ktmax −e−katmax av at steady state is calculated from Equation 9.17.
max )
VD(ka −k)
(0.75)(250)
C∞
av =
(0.75)(250)(0.9)
C (121.5)(0.07)(8)
max = (e−0.07(3.07) −e−0.9(3.07) )
(121.5)(0.9−0.07)
C∞
av =2.76 mg/L
Cmax =1.28 mg/L
b. Cmin after the first dose occurs just before the
administration of the next dose of drug—there-
fore, set t = 8 hours and solve for Cmin. LOADING DOSE
(0.75)(250)(0.9) Since extravascular doses require time for absorption
C = (e−0.07(8) −e−0.9(8)
min )
(121.5)(0.9−0.07) into the plasma to occur, therapeutic effects are
C delayed until sufficient plasma concentrations are
min = 0.95 mg/L
achieved. To reduce the onset time of the drug—that is,
220 Chapter 9
the time it takes to achieve the minimum effective
concentration (assumed to be equivalent to the C∞ )—a D
A L D
av = 3 C L = 1.5
Dm Dm
loading (priming) or initial dose of drug is given. The A
main objective of the loading dose is to achieve desired D
B L D
= 2 D L = 1
Dm D
plasma concentrations, C∞ , as quickly as possible. If m
av
the drug follows one-compartment pharmacokinetics,
B
then in theory, steady state is also achieved immedi-
ately following the loading dose. Thereafter, a mainte- C
nance dose is given to maintain C∞ and steady state so MEC
av
that the therapeutic effect is also maintained. In prac- D
tice, a loading dose may be given as a bolus dose or a
short-term loading IV infusion.
As discussed earlier, the time required for the
drug to accumulate to a steady-state plasma level is 0
0 Time (hours)
dependent mainly on its elimination half-life. The
time needed to reach 90% of C∞ is approximately
av D
3.3 half-lives, and the time required to reach 99% of Doses
C∞ is equal to approximately 6.6 half-lives. For a
av FIGURE 95 Concentration curves for dosage regimens
drug with a half-life of 4 hours, it will take approxi- with equal maintenance doses (D) and dosage intervals (τ)
mately 13 and 26 hours to reach 90% and 99% of and different dose ratios. (From Kruger-Thiemer, 1968, with
permission.)
C∞ , respectively.
av
For drugs absorbed rapidly in relation to elimi-
nation (ka >> k) and that are distributed rapidly, the different loading doses. A rapid approximation of
loading dose DL can be calculated as follows: loading dose, DL, may be estimated from
D V C∞
L 1
= (9.42) D = D av
L (9.45)
D − (S)(F)
0 (1− e kaτ )(1 e−kτ
− )
For extremely rapid absorption, as when the product of where C∞ is the desired plasma drug concentration,
av
k S is the salt form of the drug, and F is the fraction of
at is large or in the case of IV infusion, −k
e aτ becomes
approximately zero and Equation 9.42 reduces to drug bioavailability.
Equation 9.45 assumes very rapid drug absorp-
DL 1
tion from an immediate-release dosage form. The DL
=
D k (9.43)
0 1− e− τ
calculated by this method has been used in clinical
The loading dose should approximate the amount of situations for which only an approximation of the DL
drug contained in the body at steady state. The dose is needed.
ratio is equal to the loading dose divided by the main- These calculations for loading doses are not
tenance dose. applicable to drugs that demonstrate multicompart-
ment kinetics. Such drugs distribute slowly into extra-
D
Dose ratio = L (9.44) vascular tissues, and drug equilibration and steady
D0 state may not occur until after the apparent plateau is
As a general rule of thumb, if the selected dosage reached in the vascular (central) compartment.
interval is equal to the drug’s elimination half-life,
then the dose ratio calculated from Equation 9.44 DOSAGE REGIMEN SCHEDULES
should be equal to 2.0. In other words, the loading
dose will be equal to double the initial drug dose. Predictions of steady-state plasma drug concentra-
Figure 9-5 shows the plasma level–time curve for tions usually assume the drug is given at a constant
dosage regimens with equal maintenance doses but dosage interval throughout a 24-hour day. Very often,
Plasma level
Multiple-Dosage Regimens 221
20 procainamide given with a 1.0-g loading dose on the
first day followed by maintainence doses of 0.5-g four
times a day. On the second, third, and subsequent days,
15 the procainamide plasma levels did not reach the thera-
peutic range until after the second dose of drug.
Ideally, drug doses should be given at evenly
10
spaced intervals. However, to improve patient com-
pliance, dosage regimens may be designed to fit
5 with the lifestyle of the patient. For example, the
patient is directed to take a drug such as amoxicillin
four times a day (QID), before meals and at bed-
0 time, for a systemic infection. This dosage regimen
0 20 40 60 80
Time (hours) will produce unequal dosage intervals during the
day, because the patient takes the drug before
FIGURE 96 Plasma level–time curve for theophylline
breakfast, at 0800 hours (8 AM); before lunch, at
given in doses of 160 mg 3 times a day. Dashed lines indicate
the therapeutic range. (From Niebergall et al, 1974, with 1200 hours (12 noon); before dinner, at 1800 hours
permission.) (6 PM); and before bedtime, at 2300 hours (11 PM).
For these drugs, evenly spaced dosage intervals are not
that critical to the effectiveness of the antibiotic as long
however, the drug is given only during the waking
as the plasma drug concentrations are maintained
hours (Fig. 9-6). Niebergall et al (1974) discussed the
above the minimum inhibitory concentration (MIC) for
problem of scheduling dosage regimens and particu-
the microorganism. In some cases, a drug may be given
larly warned against improper timing of the drug
at a larger dose allowing for a longer duration above
dosage. For drugs with a narrow therapeutic index
MIC if fluctuation is less critical. In Augmentin Bid-875
such as theophylline (Fig. 9-6), large fluctuation
(amoxicillin/clavulanate tablets), the amoxicillin/
between the maximum and minimum plasma levels
clavulanate tablet is administered twice daily.
are undesirable and may lead to subtherapeutic
Patient compliance with multiple-dose regimens
plasma drug concentrations and/or to high, possibly
may be a problem for the patient in following the
toxic, drug concentrations. These wide fluctuations
prescribed dosage regimen. Occasionally, a patient
occur if larger doses are given at wider dosage inter-
may miss taking the drug dose at the prescribed
vals (see Fig. 9-3). For example, Fig. 9-7 shows
dosage interval. For drugs with long elimination half-
lives (eg, levothyroxine sodium or oral contraceptives),
10 the consequences of one missed dose are minimal, since
only a small fraction of drug is lost between daily dos-
8 ing intervals. The patient should either take the next
drug dose as soon as the patient remembers or continue
6 the dosing schedule starting at the next prescribed dos-
ing period. If it is almost time for the next dose, then the
4
skipped dose should not be taken and the regular dosing
2 schedule should be maintained. Generally, the patient
should not double the dose of the medication. For spe-
0 cific drug information on missed doses, USP DI II,
0 20 40 60 80
Time (hours) Advice for the Patient, published annually by the United
States Pharmacopeia, is a good source of information.
FIGURE 97 Plasma level–time curve for procainamide
The problems of widely fluctuating plasma drug
given in an initial dose of 1.0 g followed by doses of 0.5 g 4 times
a day. Dashed lines indicate the therapeutic range. (From concentrations may be prevented by using a con-
Niebergall et al, 1974, with permission.) trolled-release formulation of the drug, or a drug in
Plasma level (mg/mL)
Plasma level (mg/mL)
222 Chapter 9
the same therapeutic class that has a long elimination The effective concentration of this drug is
half-life. The use of extended-release dosage forms 15 mg/mL. After the patient is given a single
allows for less frequent dosing and prevents under- IV dose, the elimination half-life for the drug
medication between the last evening dose and the first is determined to be 3.0 hours and the apparent
morning dose. Extended-release drug products may VD is 196 mL/kg. Determine a multiple IV dose
improve patient compliance by decreasing the number regimen for this drug (assume drug is given
of doses within a 24-hour period that the patient needs every 6 hours).
to take. Patients generally show better compliance with
a twice-a-day (BID) dosage regimen compared to a Solution
three-times-a-day (TID) dosage schedule. FD
C∞ 0
av =
VDkτ
CLINICAL EXAMPLE For IV dose, F = 1,
Bupropion hydrochloride (Wellbutrin) is a noradren-
ergic/dopaminergic antidepressant. Jefferson et al, D = (15 µ 0.693
0 g/mL) (196 mL/kg)(6 h)
3 h
2005, have reviewed the pharmacokinetic properties
of bupropion and its various various formulations and D0 = 4.07 mg/kg every 6 hours
clinical applications, the goal of which is optimization
of major depressive disorder treatment. Bupropion Since patient C.S. weighs 76.6 kg, the dose should
hydrochloride is available in three oral formulations. be as shown:
The immediate-release (IR) tablet is given three times D0 = (4.07 mg/kg)(76.6 kg)
a day, the sustained-release tablet (Wellbutrin SR) is D0 = 312 mg every 6 hours
given twice a day, and the extended-release tablet
(Wellbutrin XL) is given once a day. After the condition of this patient has stabilized,
The total daily dose was 300 mg bupropion HCl. the patient is to be given the drug orally for con-
The area under the curve, AUC, for each dose treatment venience of drug administration. The objective is
was similar showing that the formulations were bio- to design an oral dosage regimen that will produce
equivalent based on extent of absorption. The fluctua- the same steady-state blood level as the mul-
tions between peak and trough levels were greatest for tiple IV doses. The drug dose will depend on the
the IR product given three times a day and least for the bioavailability of the drug from the drug product,
once-a-day XL product. According to the manufac- the desired therapeutic drug level, and the dosage
turer, all three dosage regimens provide equivalent interval chosen. Assume that the antibiotic is 90%
clinical efficacy. The advantage of the extended-release bioavailable and that the physician would like to
product is that the patient needs only to take the drug continue oral medication every 6 hours.
once a day. Often, immediate-release drug products are The average or steady-state plasma drug level
less expensive compared to an extended-release drug is given by
product. In this case, the fluctuating plasma drug levels FD
for buproprion IR tablet given three times a day are not C∞ = 0
av VDkτ
a safety issue and the tablet is equally efficacious as the
150-mg SR tablet given twice a day or the 300-mg XL (15 µg/mL)(193 mL/kg)(0.693)(6 h)
D
tablet given once a day. The patient may also consider 0 =
(0.9)(3 h)
the cost of the medication.
D0 = 454 mg/kg
PRACTICE PROBLEMS Because patient C.S. weighs 76.6 kg, he should
be given the following dose:
1. Patient C.S. is a 35-year-old man weighing
76.6 kg. The patient is to be given multiple D0 = (4.54 mg/kg)(76.6 kg)
IV bolus injections of an antibiotic every 6 hours. D0 = 348 mg every 6 hours
Multiple-Dosage Regimens 223
For drugs with equal absorption but slower absorp- Solution
tion rates (F is the same but ka is smaller), the initial
(0.9)(500,000)(3)
dosing period may show a lower blood level; however, C∞
av =
(196)(76.6)(8)(0.693)
the steady-state blood level will be unchanged.
2. In practice, drug products are usually commer- C∞
av =16.2 µg/mL
cially available in certain specified strengths.
Using the information provided in the pre- Notice that a larger dose is necessary if the drug is
ceding problem, assume that the antibiotic is given at longer intervals.
available in 125-, 250-, and 500-mg tablets. In designing a dosage regimen, one should
Therefore, the pharmacist or prescriber must consider a regimen that is practical and con-
now decide which tablets are to be given to the venient for the patient. For example, for good
patient. In this case, it may be possible to give compliance, the dosage interval should be spaced
the patient 375 mg (eg, one 125-mg tablet and conveniently for the patient. In addition, one
one 250-mg tablet) every 6 hours. However, should consider the commercially available dosage
the C∞ should be calculated to determine if
av strengths of the prescribed drug product.
the plasma level is approaching a toxic value. The use of Equation 9.17 to estimate a dosage
Alternatively, a new dosage interval might be regimen initially has wide utility. The C∞ is equal
av
appropriate for the patient. It is very important to the dosing rate divided by the total body clear-
to design the dosage interval and the dose to be ance of the drug in the patient:
as simple as possible, so that the patient will
not be confused and will be able to comply FD
0 1
C∞
with the medication program properly. av = (9.47)
τ ClT
a. What is the new C∞ if the patient is given
av
375 mg every 6 hours? where FD0/t is equal to the dosing rate R, and
1/ClT is equal to 1/kVD.
Solution In designing dosage regimens, the dosing rate
(0.9)(375,000)(3)
C∞ D0/t is adjusted for the patient’s drug clearance
av =
(196)(76.6)(6)(0.693) to obtain the desired C∞ . For an IV infusion, the
av
zero-order rate of infusion (R) is used to obtain
C∞
av =16.2 µg/mL
the desired steady-state plasma drug concentration
Because the therapeutic objective was to achieve CSS. If R is substituted for FD0/t in Equation 9.47,
a minimum effective concentration (MEC) of then the following equation for estimating CSS
15 mg/mL, a value of 16.2 mg/mL is reasonable. after an IV infusion is obtained:
b. The patient has difficulty in distinguishing
R
tablets of different strengths. Can the patient C = (9.48)
ss Cl
take a 500-mg dose (eg, two 250-mg tablets)? T
Solution From Equations 9.47 and 9.48, all dosage sched-
ules having the same dosing rate D0/t, or R, will
The dosage interval (t) for the 500-mg tablet
have the same C∞ or C
a SS, whether the drug is given
would have to be calculated as follows: v
by multiple doses or by IV infusion. For example,
(0.9)(500,000)(3) dosage schedules of 100 mg every 4 hours, 200 mg
τ =
(196)(76.6)(15)(0.693) every 8 hours, 300 mg every 12 hours, and 600 mg
every 24 hours will yield the same C∞ in the
av
τ = 8.63 h
patient. An IV infusion rate of 25 mg/h in the same
c. A dosage interval of 8.63 hours is difficult patient will give a CSS equal to the C∞ obtained
av
to remember. Is a dosage regimen of 500 mg with the multiple-dose schedule (see Fig. 9-3;
every 8 hours reasonable? Table 9-6).
224 Chapter 9
TABLE 96 Effect of Dosing Schedule on Predicted Steady-State Plasma Drug Concentrationsa
Dosing Schedule Steady-State Drug Concentration (lg/mL)
Dosing Rate, D0/τ
C∞ C∞ C∞
Dose (mg) 1 (h) (mg/h) max av min
— — 25b 14.5 14.5 14.5
100 4 25 16.2 14.5 11.6
200 8 25 20.2 14.5 7.81
300 12 25 25.3 14.5 5.03
600 24 25 44.1 14.5 1.12
400 8 50 40.4 28.9 15.6
600 8 75 60.6 43.4 23.4
aDrug has an elimination half-life of 4 hours and an apparent VD of 10 L.
bDrug given by IV infusion. The first-order absorption rate constant ka is 1.2 h−1 and the drug follows a one-compartment open model.
Frequently Asked Questions »»Why is the Cmin value at steady state less variable
»»Why is the steady-state peak plasma drug concen- than the Cmax value at steady state?
tration measured sometime after an IV dose is given
»»Is it possible to take a single blood sample to mea-
in a clinical situation? sure the Cav value at steady state?
CHAPTER SUMMARY
The purpose of giving a loading dose is to achieve multiple dosing. A clinical example of multiple dos-
desired (therapeutic) plasma concentrations as ing using short, intermittent intravenous infusions
quickly as possible. For a drug with long elimination has been applied to the aminoglycosides and is based
half-life, it may take a long time (several half-lives) on pharmacokinetics and clinical factors for safer
to achieve steady-state levels. The loading dose must dosing. The index for measuring drug accumulation
be calculated appropriately based on pharmacoki- during multiple dosing, R, is related to the dosing
netic parameters to avoid overdosing. When several interval and the half-life of the drug, but not the
doses are administered for a drug with linear kinetics, dose. This parameter compares the steady-state con-
drug accumulation may occur according to the prin- centration with drug concentration after the initial
ciple of superposition. Superposition allows the deri- dose. The plasma concentration at any time during
vation of equations that predict the plasma drug peak an oral or extravascular multiple-dose regimen, for a
and trough concentrations of a drug at steady state one-compartment model and constant doses and
and the theoretical drug concentrations at any time dose interval, is dependent on n = number of doses,
after the dose is given. The principle of superposition t = dosage interval, F = fraction of dose absorbed,
is used to examine the effect of an early, late, or miss- and t = time after administration of n doses.
ing dose on steady-state drug concentration.
C∞ ∞ ∞ or Fk −nkaτ
max, C n, and C are useful parameters f
av aD0 1− e 1 nkaτ
mi C = e−k − e−
aτ
ring the safety and efficacy of a drug during p − e−kt
monito VD (k − k τ
1− e−kτ
a ) 1− e−ka
Multiple-Dosage Regimens 225
The trough steady-state concentration after multiple The relationship between average steady-state con-
oral dosing is centration, the AUC, and dosing interval is
∞
∫ C d
∞ 0 p t [AUC]∞
C 0
∞ kaFD0 1
C k
min = e
V ( k
D ka − − τ av = =
− τ τ τ
k) 1− e This parameter is a good measure of drug exposure.
LEARNING QUESTIONS
1. Gentamicin has an average elimination half- is given at a dose of 200 mg every 4 hours
life of approximately 2 hours and an apparent by multiple IV bolus injections. Predict the
volume of distribution of 20% of body weight. plasma drug concentration at 1 hour after the
It is necessary to give gentamicin, 1 mg/kg third dose.
every 8 hours by multiple IV injections, to 9. The elimination half-life of an antibiotic is
a 50-kg woman with normal renal function. 3 hours and the apparent volume of distribution
Calculate (a) Cmax, (b) Cmin, and (c) C∞ . is 20% of the body weight. The therapeutic
av
2. A physician wants to give theophylline to a window for this drug is from 2 to 10 mg/mL.
young male asthmatic patient (age 29 years, Adverse toxicity is often observed at drug
80 kg). According to the literature, the elimina- concentrations above 15 mg/mL. The drug will
tion half-life for theophylline is 5 hours and be given by multiple IV bolus injections.
the apparent VD is equal to 50% of the body a. Calculate the dose for an adult male patient
weight. The plasma level of theophylline (68 years old, 82 kg) with normal renal func-
required to provide adequate airway ventilation tion to be given every 8 hours.
is approximately 10 mg/mL. b. Calculate the anticipated C∞
max and C∞
min
a. The physician wants the patient to take med- values.
ication every 6 hours around the clock. What c. Calculate the C∞ value.
av
dose of theophylline would you recommend d. Comment on the adequacy of your dosage
(assume theophylline is 100% bioavailable)? regimen.
b. If you were to find that theophylline is avail- 10. Tetracycline hydrochloride (Achromycin V,
able to you only in 225-mg capsules, what Lederle) is prescribed for a young adult male
dosage regimen would you recommend? patient (28 years old, 78 kg) suffering from
3. What pharmacokinetic parameter is most gonorrhea. According to the literature, tetra-
important in determining the time at which the cycline HCl is 77% orally absorbed, is 65%
steady-state plasma drug level (C∞ ) is reached? bound to plasma proteins, has an apparent
av
4. Name two ways in which the fluctuations of volume of distribution of 0.5 L/kg, has an
plasma concentrations (between C∞
max and C∞
min) elimination half-life of 10.6 hours, and is 58%
can be minimized for a person on a multiple-dose excreted unchanged in the urine. The minimum
drug regimen without altering the C∞ . inhibitory drug concentration (MIC) for gonor-
av
5. What is the purpose of giving a loading dose? rhea is 25–30 mg/mL.
6. What is the loading dose for an antibiotic (k = a. Calculate an exact maintenance dose for this
0.23 h−1) with a maintenance dose of 200 mg patient to be given every 6 hours around the
every 3 hours? clock.
7. What is the main advantage of giving a potent b. Achromycin V is available in 250- and
drug by IV infusion as opposed to multiple 500-mg capsules. How many capsules (state
IV injections? dose) should the patient take every 6 hours?
8. A drug has an elimination half-life of 2 hours c. What loading dose using the above capsules
and a volume of distribution of 40 L. The drug would you recommend for this patient?
226 Chapter 9
11. The body clearance of sumatriptan (Imitrex) is 12. Cefotaxime has a volume of distribution
250 mL/min. The drug is about 14% bioavail- of 0.17 L/kg and an elimination half-life
able. What would be the average plasma drug of 1.5 hours. What is the peak plasma drug
concentration after 5 doses of 100 mg PO concentration in a patient weighing 75 kg after
every 8 hours in a patient? (Assume steady receiving 1 g IV of the drug 3 times daily for
state was reached.) 3 days?
ANSWERS
Frequently Asked Questions are more suitable to be administered as an IV bolus
Is the drug accumulation index (R) applicable to any injection. For example, some reports show that an
drug given by multiple doses or only to drugs that aminoglycoside given once daily resulted in fewer
are eliminated slowly from the body? side effects compared with dividing the dose into
two or three doses daily. Due to drug accumulation
• Accumulation index, R, is a ratio that indicates in the kidney and adverse toxicity, aminoglycosides
steady-state drug concentration to the drug concen- are generally not given by prolonged IV infusions.
tration after the first dose. The accumulation index In contrast, a prolonged period of low drug level for
does not measure the absolute size of overdosing; penicillins and tetracyclines may not be so effica-
it measures the amount of drug cumulation that can cious and may result in a longer cure time for an
occur due to frequent drug administration. Factors infection. The pharmacodynamics of the individual
that affect R are the elimination rate constant, k, and drug must be studied to determine the best course of
the dosing interval, t. If the first dose is not chosen action. (2) Drugs such as nitroglycerin are less likely
appropriately, the steady-state level may still be to produce tolerance when administered intermit-
incorrect. Therefore, the first dose and the dosing tently versus continuously.
interval must be determined correctly to avoid any
significant drug accumulation. The accumulation Why is the steady-state peak plasma drug concentra-
index is a good indication of accumulation due to tion often measured sometime after an IV dose is
frequent drug dosing, applicable to any drug, re- given in a clinical situation?
gardless of whether the drug is bound to tissues. • After an IV bolus drug injection, the drug is well
What are the advantages/disadvantages for giving a distributed within a few minutes. In practice, how-
drug by constant IV infusion, intermittent IV infu- ever, an IV bolus dose may be administered slowly
sion, or multiple IV bolus injections? What drugs over several minutes or the drug may have a slow
would most likely be given by each route of adminis- distribution phase. Therefore, clinicians often pre-
tration? Why? fer to take a blood sample 15 minutes or 30 minutes
after IV bolus injection and refer to that drug con-
• Some of the advantages of administering a drug by centration as the peak concentration. In some cases,
constant IV infusion include the following: (1) A a blood sample is taken an hour later to avoid the
drug may be infused continuously for many hours fluctuating concentration in the distributive phase.
without disturbing the patient. (2) Constant infusion The error due to changing sampling time can be
provides a stable blood drug level for drugs that have large for a drug with a short elimination half-life.
a narrow therapeutic index. (3) Some drugs are bet-
Is a loading dose always necessary when placing a
ter tolerated when infused slowly. (4) Some drugs
patient on a multiple-dose regimen? What are the
may be infused simultaneously with electrolytes
determining factors?
or other infusion media in an acute-care setting.
Disadvantages of administering a drug by constant • A loading or priming dose is used to rapidly raise
IV infusion include the following: (1) Some drugs the plasma drug concentration to therapeutic drug
Multiple-Dosage Regimens 227
levels to obtain a more rapid pharmacodynamic FD 1.44
c. C∞ 0 t1/2
response. In addition, the loading dose along with av =
VDτ
the maintenance dose allows the drug to reach
steady-state concentration quickly, particularly for (50)(1.44)(2)
= =1.8 µg/mL
drugs with long elimination half-lives. (10,000)(8)
An alternative way of explaining the load-
C∞
2. a. D avVDτ
ing dose is based on clearance. After multiple IV
0 =
1.44t
dosing, the maintenance dose required is based on 1/2
Cl, Css, and t. (10)(40,000)(6)
=
(1.44)(5)
Dose
CSS =
τCl = 333 mg every 6 h
Dose =CSS τCl FD01.44tb. 1/2
τ =
VDC
∞
av
If Css and t are fixed, a drug with a smaller clear- (225,000)(1.44)(5)
ance requires a smaller maintenance dose. In prac- = = 4.05 h
(40,000)(10)
tice, the dosing interval is adjustable and may be
longer for drugs with a small Cl if the drug does 6. Dose the patient with 200 mg every 3 hours.
not need to be dosed frequently. The steady-state D
0 200
DL = = = 400 mg
drug level is generally determined by the desired 1 − τ
− e k 1 −
− e (0.23)(3)
therapeutic drug. Notice that DL is twice the maintenance dose,
Does a loading dose significantly affect the steady- because the drug is given at a dosage interval
state concentration of a drug given by a constant equal approximately to the t1/2 of 3 hours.
multiple-dose regimen? 8. The plasma drug concentration, Cp, may be cal-
culated at any time after n doses by Equation 9.21
• The loading dose will affect only the initial drug and proper substitution.
concentrations in the body. Steady-state drug
levels are obtained after several elimination half- D
0 1− e−nkτ
Cp =
V − τ e−kt
D 1− e k
lives (eg, 4.32t1/2 for 95% steady-state level).
Only 5% of the drug contributed by the loading
200 1− e−(3)(0.347)(4)
dose will remain at 95% steady state. At 99% Cp = e−(0.347)(1)
40
1− e−(0.347)(4)
steady-state level, only 1% of the loading dose
will remain. = 4.63 mg/L
Alternatively, one may conclude that for a drug
Learning Questions whose elimination t1/2 is 2 hours, the predicted
plasma drug concentration is approximately at
1. VD = 0.20(50 kg) =10,000 mL
steady state after 3 doses or 12 hours. Therefore,
D 50 mg the above calculation may be simplified to the
a. D 0
max = − = =
− − 53.3 mg
1 f 1 e (0.693/2)(8) following:
D D0 1
C max 53.3 mg Cp = e−k
max = = = 5.33 µg/mL
VD 10,000 mL VD 1− e kτ τ
−
b. Dmin = 53.3− 50 = 3.3 mg 200 1
C = e−(0.347)(1)
p −
40 1− e (0.347)(4)
3.3 mg
Cmin = = 0.33 µg/mL
10,000 mL = 4.71 mg/L
228 Chapter 9
D / FD
9. C∞ 0 VD
max = 10. a. C∞ = 0
1 e−kτ av
− kVDτ
where Let C∞
av = 27.5 mg/L
VD = 20% of 82 kg = (0.2)(82) = 16.4 L
C∞
a kV τ (27.5)(0.693/10.6)(0.5)(78)(6)
k −
= (0.693/3) = 0.231 h 1 D v D
0 = =
F 0.77
D V C∞ e−kτ e−(0.231)(8)
0 = D max (1− ) = (16.4)(10)(1− = 546.3 mg
a. D0 = 138.16 mg to be given every 8 hours D0 = 546.3 mg every 6 h
b. C∞ =C∞ (e−kτ ) = (10)(e−(0.231)(8)
min max )
= b. If a 500-mg capsule is given every 6 hours,
1.58 mg/L
D
c. 138.16 FD (0.77)(500)
C∞ 0
av = = C∞ 0
kV av = =
Dτ (0.231)(16.4)(8) kVDτ (0.693/10.6)(0.5)(78)(6)
= 4.56 mg/L = 25.2 mg/L
d. In the above dosage regimen, the C∞
min of
1.59 mg/L is below the desired C∞ D 500
min of 2 mg/L. c. D = M
Alternatively, the dosage interval, L
t, could − = =1543 mg
1− e kτ 1− e(0.654)(6)
be changed to 6 hours.
DL = 3× 500 mg capsules =1500 mg
D = V C∞ (1− e−kτ ) = (16.4)(10)(1− e−(0.231)(6)
0 D max )
D0 = 123 mg to be given every 6 h
C∞ = C∞ (e−kτ ) = (10)(e−(0.231)(6)
min max ) = 2.5 mg/L
D
∞ 123
C = 0
av = = 5.41 mg/L
kVDτ (0.231)(16.4)(6)
REFERENCES
Jefferson JW, Pradko JF, Muir KT: Bupropion for major depressive three-point methods that estimate area under the curve are
disorder: Pharmacokinetic and formulation considerations. Clin superior to trough levels in predicting drug exposure, therapeutic
Ther 27(11):1685–1695, 2005. drug monitoring 20(3):276–283, June 1998.
Kruger-Thiemer E: Pharmacokinetics and dose-concentration Sawchuk RJ, Zaske DE: Pharmacokinetics of dosing regimens
relationships. In Ariens EJ (ed.), Physico-Chemical Aspects of which utilize multiple intravenous infusions: Gentamycin in
Drug Action. New York, Pergamon, 1968, p 97. burn patients. J Pharmacokin Biopharm 4(2):183–195, 1976.
Niebergall PJ, Sugita ET, Schnaare RC: Potential dangers of com- van Rossum JM, Tomey AHM: Rate of accumulation and plateau
mon drug dosing regimens. Am J Hosp Pharm 31:53–59, 1974. concentration of drugs after chronic medication. J Pharm
Primmett D, Levine M, Kovarik, J, Mueller E, Keown, P: Cyclo- Pharmacol 30:390–392, 1968.
sporine monitoring in patients with renal transplants: Two- or
BIBLIOGRAPHY
Gibaldi M, Perrier D: Pharmacokinetics, 2nd ed. New York, Wagner JG: Kinetics of pharmacological response, I: Proposed
Marcel Dekker, 1962, pp 451–457. relationship between response and drug concentration in the
Levy G: Kinetics of pharmacologic effect. Clin Pharmacol Ther intact animal and man. J Theor Biol 20:173, 1968.
7:362, 1966. Wagner JG: Relations between drug concentrations and response.
van Rossum JM: Pharmacokinetics of accumulation. J Pharm Sci J Mond Pharm 14:279–310, 1971.
75:2162–2164, 1968.
Nonlinear Pharmacokinetics
10 Andrew B.C. Yu and Leon Shargel
Chapter Objectives Previous chapters discussed linear pharmacokinetic models using
simple first-order kinetics to describe the course of drug disposi-
»» Describe the differences between
tion and action. These linear models assumed that the pharmaco-
linear pharmacokinetics and
kinetic parameters for a drug would not change when different
nonlinear pharmacokinetics.
doses or multiple doses of a drug were given. With some drugs,
»» Illustrate nonlinear pharmaco- increased doses or chronic medication can cause deviations from
kinetics with drug disposition the linear pharmacokinetic profile previously observed with single
examples. low doses of the same drug. This nonlinear pharmacokinetic
»» Discuss some potential risks behavior is also termed dose-dependent pharmacokinetics.
in dosing drugs that follow Many of the processes of drug absorption, distribution, bio-
nonlinear kinetics. transformation, and excretion involve enzymes or carrier-mediated
systems. For some drugs given at therapeutic levels, one of
»» Explain how to detect nonlinear
these specialized processes may become saturated. As shown in
kinetics using AUC-versus-doses
Table 10-1, various causes of nonlinear pharmacokinetic behavior
plots.
are theoretically possible. Besides saturation of plasma protein-
»» Apply the appropriate equation binding or carrier-mediated systems, drugs may demonstrate non-
and graphical methods, to calculate linear pharmacokinetics due to a pathologic alteration in drug
the Vmax and KM parameters after absorption, distribution, and elimination. For example, aminogly-
multiple dosing in a patient. cosides may cause renal nephrotoxicity, thereby altering renal drug
»» Describe the use of the Michaelis– excretion. In addition, gallstone obstruction of the bile duct will alter
Menten equation to simulate biliary drug excretion. In most cases, the main pharmacokinetic
the elimination of a drug by a outcome is a change in the apparent elimination rate constant.
saturable enzymatic process. A number of drugs demonstrate saturation or capacity-limited
metabolism in humans. Examples of these saturable metabolic
»» Estimate the dose for a nonlinear
processes include glycine conjugation of salicylate, sulfate conju-
drug such as phenytoin in
gation of salicylamide, acetylation of p-aminobenzoic acid, and
multiple-dose regimens.
the elimination of phenytoin (Tozer et al, 1981). Drugs that dem-
»» Describe chronopharmaco- onstrate saturation kinetics usually show the following
kinetics, time-dependent characteristics:
pharmacokinetics, and its
influence on drug disposition. 1. Elimination of drug does not follow simple first-order kinetics—
that is, elimination kinetics are nonlinear.
»» Describe how transporters may
2. The elimination half-life changes as dose is increased. Usually,
cause uneven drug distribution at
the elimination half-life increases with increased dose due
cellular level; and understand that
to saturation of an enzyme system. However, the elimination
capacity-limited or concentration-
half-life might decrease due to “self”-induction of liver bio-
dependent kinetics may occur at
transformation enzymes, as is observed for carbamazepine.
the local level within body organs.
229
230 Chapter 10
TABLE 101 Examples of Drugs Showing Nonlinear Kinetics
Causea Drug
Gl Absorption
Saturable transport in gut wall Riboflavin, gebapentin, L-dopa, baclofen, ceftibuten
Intestinal metabolism Salicylamide, propranolol
Drugs with low solubility in GI but relatively Chorothiazide, griseofulvin, danazol
high dose
Saturable gastric or GI decomposition Penicillin G, omeprazole, saquinavir
Distribution
Saturable plasma protein binding Phenylbutazone, lidocaine, salicylic acid, ceftriaxone,
diazoxide, phenytoin, warfarin, disopyramide
Cellular uptake Methicillin (rabbit)
Tissue binding Imiprimine (rat)
CSF transport Benzylpenicillins
Saturable transport into or out of tissues Methotrexate
Renal Elimination
Active secretion Mezlocillin, para-aminohippuric acid
Tubular reabsorption Riboflavin, ascorbic acid, cephapirin
Change in urine pH Salicylic acid, dextroamphetamine
Metabolism
Saturable metabolism Phenytoin, salicyclic acid, theophylline, valproic acidb
Cofactor or enzyme limitation Acetaminophen, alcohol
Enzyme induction Carbamazepine
Altered hepatic blood flow Propranolol, verapamil
Metabolite inhibition Diazepam
Biliary Excretion
Biliary secretion Iodipamide, sulfobromophthalein sodium
Enterohepatic recycling Cimetidine, isotretinoin
aHypothermia, metabolic acidosis, altered cardiovascular function, and coma are additional causes of dose and time dependencies in drug overdose.
bIn guinea pig and probably in some younger subjects.
Data from Evans et al (1992).
3. The area under the curve (AUC) is not propor- the same enzyme or carrier-mediated system
tional to the amount of bioavailable drug. (ie, competition effects).
4. The saturation of capacity-limited processes 5. The composition and/or ratio of the metabolites of
may be affected by other drugs that require a drug may be affected by a change in the dose.
Nonlinear Pharmacokinetics 231
Because these drugs have a changing apparent
A
elimination constant with larger doses, prediction
of drug concentration in the blood based on a
single small dose is difficult. Drug concentrations C
in the blood can increase rapidly once an elimina-
tion process is saturated. In general, metabolism
(biotransformation) and active tubular secretion of
drugs by the kidney are the processes most usually
saturated. Figure 10-1 shows plasma level–time Dose
curves for a drug that exhibits saturable kinetics.
FIGURE 102 Area under the plasma level–time curve
When a large dose is given, a curve is obtained versus dose for a drug that exhibits a saturable elimination
with an initial slow elimination phase followed by process. Curve A represents dose-dependent or saturable
a much more rapid elimination at lower blood elimination kinetics. Curve C represents dose-independent
concentrations (curve A). With a small dose of the kinetics.
drug, apparent first-order kinetics is observed,
because no saturation kinetics occurs (curve B). If
the pharmacokinetic data were estimated only
from the blood levels described by curve B, then a SATURABLE ENZYMATIC
twofold increase in the dose would give the blood
ELIMINATION PROCESSES
profile presented in curve C, which considerably
underestimates the drug concentration as well as The elimination of drug by a saturable enzymatic
the duration of action. process is described by Michaelis–Menten kinetics.
In order to determine whether a drug is follow- If Cp is the concentration of drug in the plasma, then
ing dose-dependent kinetics, the drug is given at
various dosage levels and a plasma level–time curve dCp VmaxCp
Elimination rate = = (10.1)
is obtained for each dose. The curves should exhibit dt KM +Cp
parallel slopes if the drug follows dose-independent
kinetics. Alternatively, a plot of the areas under the where Vmax is the maximum elimination rate and KM
plasma level–time curves at various doses should be is the Michaelis constant that reflects the capacity of
linear (Fig. 10-2). the enzyme system. It is important to note that KM is
not an elimination constant, but is actually a hybrid
rate constant in enzyme kinetics, representing both
the forward and backward reaction rates and equal to
100
the drug concentration or amount of drug in the body
at 0.5Vmax. The values for KM and Vmax are dependent
A on the nature of the drug and the enzymatic process
10 C involved.
The elimination rate of a hypothetical drug with
B
a KM of 0.1 mg/mL and a Vmax of 0.5 mg/mL per hour
is calculated in Table 10-2 by using Equation 10.1.
1 Because the ratio of the elimination rate to drug con-
Time
centration changes as the drug concentration changes
FIGURE 101 Plasma level–time curves for a drug (ie, dCp/dt is not constant, Equation 10.1), the rate of
that exhibits a saturable elimination process. Curves A and B drug elimination also changes and is not a first-order
represent high and low doses of drug, respectively, given in a
or linear process. In contrast, a first-order elimina-
single IV bolus. The terminal slopes of curves A and B are the
same. Curve C represents the normal first-order elimination of tion process would yield the same elimination rate
a different drug. constant at all plasma drug concentrations. At drug
Plasma level
Area under curve
232 Chapter 10
TABLE 102 Effect of Drug Concentration on PRACTICE PROBLEM
the Elimination Rate and Rate Constanta
Using the hypothetical drug considered in Table 10-2
Drug Elimination Elimination Rate/ (Vmax = 0.5 mg/mL per hour, KM = 0.1 mg/mL), how
Concentration Rate Concentrationb
long would it take for the plasma drug concentration
( lg/mL) ( lg/mL/h) (h−1)
to decrease from 20 to 12 mg/mL?
0.4 0.400 1.000
0.8 0.444 0.556 Solution
1.2 0.462 0.385 Because 12 mg/mL is above the saturable level, as
1.6 0.472 0.294 indicated in Table 10-2, elimination occurs at a zero-
order rate of approximately 0.5 mg/mL per hour.
2.0 0.476 0.238 Time needed for the drug to decrease to
2.4 0.480 0.200
12 µ 20 −12 µg
2.8 0.483 0.172 g/mL = µ =16 h
0.5 g/h
3.2 0.485 0.152
A saturable process can also exhibit linear elimination
10.0 0.495 0.0495 when drug concentrations are much less than enzyme
10.4 0.495 0.0476 concentrations. When the drug concentration Cp is
10.8 0.495 0.0459 small in relation to the KM, the rate of drug elimina-
tion becomes a first-order process. The data generated
11.2 0.496 0.0442 from Equation 10.2 (Cp ≤ 0.05 mg/mL, Table 10-3)
11.6 0.496 0.0427 using KM = 0.8 mg/mL and Vmax = 0.9 mg/mL per hour
shows that enzymatic drug elimination can change
aKM = 0.1 mg/mL, Vmax = 0.5 mg/mL/h.
from a nonlinear to a linear process over a restricted
bThe ratio of the elimination rate to the concentration is equal to the
rate constant.
concentrations of 0.4–10 mg/mL, the enzyme system TABLE 103 Effect of Drug Concentration on
the Elimination Rate and Rate Constanta
is not saturated and the rate of elimination is a mixed
or nonlinear process (Table 10-2). At higher drug Drug Elimination Elimination Rate
concentrations, 11.2 mg/mL and above, the elimina- Concentration Rate Concentration
tion rate approaches the maximum velocity (Vmax) of (Cp) ( lg/mL) ( lg/mL/h) (h−1)b
approximately 0.5 mg/mL per hour. At Vmax, the 0.01 0.011 1.1
elimination rate is a constant and is considered a
zero-order process. 0.02 0.022 1.1
Equation 10.1 describes a nonlinear enzyme 0.03 0.033 1.1
process that encompasses a broad range of drug 0.04 0.043 1.1
concentrations. When the drug concentration Cp is
large in relation to KM (Cp >> KM), saturation of the 0.05 0.053 1.1
enzymes occurs and the value for KM is negligible. 0.06 0.063 1.0
The rate of elimination proceeds at a fixed or con- 0.07 0.072 1.0
stant rate equal to Vmax. Thus, elimination of drug
becomes a zero-order process and Equation 10.1 0.08 0.082 1.0
becomes: 0.09 0.091 1.0
dC V C aKM = 0.8 mg/mL, Vmax = 0.9 mg/mL/h.
p max p
− = =V (10.2)
dt C max bThe ratio of the elimination rate to the concentration is equal to the
p rate constant.
Nonlinear Pharmacokinetics 233
concentration range. This is evident because the rate Because C0
p = 0.05 µg/mL, k =1.1 h−1, and C =
p
constant (or elimination rate/drug concentration) 0.005 mg/mL.
values are constant. At drug concentrations below
0.05 mg/mL, the ratio of elimination rate to drug
concentration has a constant value of 1.1 h−1 2.3(log 0.05− log 0.005)
. t =
1.1
Mathematically, when Cp is much smaller than KM,
Cp in the denominator is negligible and the elimina- 2.3(−1.30+ 2.3)
=
tion rate becomes first order. 1.1
2.3
dCp VmaxCp V = = 2.09 h
max
− = = C 1.1
dt C +K K p
p M M
dC When given in therapeutic doses, most drugs pro-
p
− = k′C (
dt p 10.3) duce plasma drug concentrations well below KM for
all carrier-mediated enzyme systems affecting the
The first-order rate constant for a saturable process, pharmacokinetics of the drug. Therefore, most drugs
k¢, can be calculated from Equation 10.3: at normal therapeutic concentrations follow first-
order rate processes. Only a few drugs, such as
Vmax 0.9 salicylate and phenytoin, tend to saturate the hepatic
k′ = = = ∼ 1.1 h−1
KM 0.8 mixed-function oxidases at higher therapeutic doses.
With these drugs, elimination kinetics is first order
This calculation confirms the data in Table 10-3, with very small doses, is mixed order at higher
because enzymatic drug elimination at drug con- doses, and may approach zero order with very high
centrations below 0.05 mg/mL is a first-order rate therapeutic doses.
process with a rate constant of 1.1 h−1. Therefore,
the t1/2 due to enzymatic elimination can be
calculated: Frequently Asked Questions
»»What kinetic processes in the body can be considered
0.693 saturable?
t1/2 = = 0.63 h
1.1
»»Why is it important to monitor drug levels carefully
for dose dependency?
PRACTICE PROBLEM
How long would it take for the plasma concentration
of the drug in Table 10-3 to decline from 0.05 to DRUG ELIMINATION BY CAPACITY-
0.005 mg/mL? LIMITED PHARMACOKINETICS:
ONE-COMPARTMENT MODEL,
Solution
Because drug elimination is a first-order process for IV BOLUS INJECTION
the specified concentrations, The rate of elimination of a drug that follows capacity-
limited pharmacokinetics is governed by the Vmax
C = 0 −kt
p Cpe and KM of the drug. Equation 10.1 describes the
elimination of a drug that distributes in the body as a
kt
logC = 0
p Cp −
2.3 single compartment and is eliminated by Michaelis–
Menten or capacity-limited pharmacokinetics. If a
logC − logC0
= p single IV bolus injection of drug (D0) is given at t =
t
k 0, the drug concentration (Cp) in the plasma at any
234 Chapter 10
time t may be calculated by an integrated form of 1000
Equation 10.1 described by
C0 −Cp K
M C
l 0
=V 0
t max − n (1 .4)
t Cp
100
Alternatively, the amount of drug in the body after an
IV bolus injection may be calculated by the follow-
ing relationship. Equation 10.5 may be used to simu-
late the decline of drug in the body after various size 10
0 0.5 1.0 1.5 2.0 2.5 3.0
doses are given, provided the KM and Vmax of drug Time (hours)
are known.
FIGURE 104 Amount of drug in the body versus time for
D a capacity-limited drug following an IV dose. Data generated
0 −D
t KM D0
=Vma − ln (
t x 10.5) using KM of 38 mg/L () and 76 mg/L (O). Vmax is kept constant.
t D
t
where D0 is the amount of drug in the body at t = 0.
In order to calculate the time for the dose of the drug was calculated for a drug with a KM of 38 mg/L and a
to decline to a certain amount of drug in the body, Vmax that varied from 200 to 100 mg/h (Table 10-4).
Equation 10.5 must be rearranged and solved for With a Vmax of 200 mg/h, the time for the 400-mg dose
time t: to decline to 20 mg in the body is 2.46 hours, whereas
when the Vmax is decreased to 100 mg/h, the time for
the 400-mg dose to decrease to 20 mg is increased to
1 D
= ln 0 1
t D −D + (
K
Vma 0 t M 0.6)
4.93 hours (see Fig. 10-3). Thus, there is an inverse
x Dt
relationship between the time for the dose to decline
to a certain amount of drug in the body and the Vmax
The relationship of KM and Vmax to the time for an IV as shown in Equation 10.6.
bolus injection of drug to decline to a given amount of Using a similar example, the effect of KM on
drug in the body is illustrated in Figs. 10-3 and 10-4. the time for a single 400-mg dose given by IV bolus
Using Equation 10.6, the time for a single 400-mg injection to decline to 20 mg in the body is
dose given by IV bolus injection to decline to 20 mg described in Table 10-5 and Fig. 10-4. Assuming
Vmax is constant at 200 mg/h, the time for the drug
to decline from 400 to 20 mg is 2.46 hours when KM
is 38 mg/L, whereas when KM is 76 mg/L, the time for
1000 the drug dose to decline to 20 mg is 3.03 hours. Thus,
an increase in KM (with no change in Vmax) will
Vmax = increase the time for the drug to be eliminated from
100 mg/h the body.
100 The one-compartment open model with capacity-
limited elimination pharmacokinetics adequately
Vmax = describes the plasma drug concentration–time pro-
200 mg/h files for some drugs. The mathematics needed to
describe nonlinear pharmacokinetic behavior of
10
0 1 2 3 4 5 drugs that follow two-compartment models and/or
Time (hours) have both combined capacity-limited and first-order
FIGURE 103 kinetic profiles are very complex and have little
Amount of drug in the body versus time for
a capacity-limited drug following an IV dose. Data generated practical application for dosage calculations and
using Vmax of 100 (O) and 200 mg/h (). KM is kept constant. therapeutic drug monitoring.
Amount of drug (mg)
Amount of drug (mg)
Nonlinear Pharmacokinetics 235
TABLE 104 Capacity-Limited Pharmacokinetics: TABLE 105 Capacity-Limited Pharmacokinetics:
Effect of Vmax on the Elimination of Druga Effects of KM on the Elimination of Druga
Time for Drug Elimination (h) Amount of Time for Drug Elimination (h)
Amount of Drug in Body
Drug in Body Vmax = Vmax = (mg) K = 38 mg/L K = 76 mg/L
M M
(mg) 200 mg/h 100 mg/h
400 0 0
400 0 0
380 0.109 0.119
380 0.109 0.219
360 0.220 0.240
360 0.220 0.440
340 0.330 0.361
340 0.330 0.661
320 0.442 0.484
320 0.442 0.884
300 0.554 0.609
300 0.554 1.10
280 0.667 0.735
280 0.667 1.33
260 0.781 0.863
260 0.781 1.56
240 0.897 0.994
240 0.897 1.79
220 1.01 1.12
220 1.01 2.02
200 1.13 1.26
200 1.13 2.26
180 1.25 1.40
180 1.25 2.50
160 1.37 1.54
160 1.37 2.74
140 1.49 1.69
140 1.49 2.99
120 1.62 1.85
120 1.62 3.25
100 1.76 2.02
100 1.76 3.52
80 1.90 2.21
80 1.90 3.81
60 2.06 2.42
60 2.06 4.12
40 2.23 2.67
40 2.23 4.47
20 2.46 3.03
20 2.46 4.93
aA single 400-mg dose is given by IV bolus injection. The drug is
aA single 400-mg dose is given by IV bolus injection. The drug is distributed into a single compartment and is eliminated by capacity-
distributed into a single compartment and is eliminated by capacity- limited pharmacokinetics. Vmax is 200 mg/h. The time for drug to
limited pharmacokinetics. KM is 38 mg/L. The time for drug to decline decline from 400 to 20 mg is calculated from Equation 9.6 assuming
from 400 to 20 mg is calculated from Equation 9.6 assuming the drug the drug has KM = 38 mg/L or KM = 76 mg/L.
has Vmax = 200 mg/h or Vmax = 100 mg/h.
the time for 50% of the dose to be elimi-
PRACTICE PROBLEMS nated. Explain why there is a difference in
the time for 50% elimination of a 400-mg
1. A drug eliminated from the body by capacity- dose compared to a 320-mg dose.
limited pharmacokinetics has a KM of
100 mg/L and a Vmax of 50 mg/h. If 400 mg Solution
of the drug is given to a patient by IV bolus Use Equation 10.6 to calculate the time for the
injection, calculate the time for the drug to dose to decline to a given amount of drug in
be 50% eliminated. If 320 mg of the drug is the body. For this problem, Dt is equal to 50%
to be given by IV bolus injection, calculate of the dose D0.
236 Chapter 10
If the dose is 400 mg, the rate of enzymatic reaction of a drug in vitro
(Equation 10.7). When an experiment is performed
1 400
t = 400 − 200+100 ln = 5.39 h with solutions of various concentration of drug C, a
50 200
series of reaction rates (n) may be measured for
If the dose is 320 mg, each concentration. Special plots may then be used
1 320 to determine KM and Vmax (see also Chapter 12).
t = 320 −160+100 ln = 4.59 h
50 160 Equation 10.7 may be rearranged into
Equation 10.8.
For capacity-limited elimination, the elimina-
V C
max
tion half-life is dose dependent, because the ν = (10.7)
K +C
drug elimination process is partially saturated. M
Therefore, small changes in the dose will pro- 1 KM 1 1
= + (10.8)
duce large differences in the time for 50% drug ν Vmax C Vmax
elimination. The parameters KM and Vmax deter-
mine when the dose is saturated. Equation 10.8 is a linear equation when 1/n is plotted
2. Using the same drug as in Problem 1, calculate against 1/C. The y intercept for the line is 1/Vmax, and
the time for 50% elimination of the dose when the slope is KM/Vmax. An example of a drug reacting
the doses are 10 and 5 mg. Explain why the times enzymatically with rate (n) at various concentrations
for 50% drug elimination are similar even though C is shown in Table 10-6 and Fig. 10-5. A plot of 1/n
the dose is reduced by one-half. versus 1/C is shown in Fig. 10-6. A plot of 1/n versus
1/C is linear with an intercept of 0.33 mmol. Therefore,
Solution 1
= 0.33 min ⋅mL/µmol
As in Practice Problem 1, use Equation 10.6 to V
max
calculate the time for the amount of drug in the
Vmax = 3 µmol/mL ⋅min
body at zero time (D0) to decline 50%.
If the dose is 10 mg, because the slope = 1.65 = KM/Vmax = KM/3 or KM =
1 10 3 × 1.65 mmol/mL = 5 mmol/mL. Alternatively,
t = 10 − 5+100 ln = 1.49 h
50 5 KM may be found from the x intercept, where −1/KM
is equal to the x intercept. (This may be seen by
If the dose is 5 mg, extending the graph to intercept the x axis in the
1 5 negative region.)
t = 5− 2.5+100 ln = 1.44 h
50 2.5 With this plot (Fig. 10-6), the points are clus-
tered. Other methods are available that may spread
Whether the patient is given a 10-mg or a 5-mg the points more evenly. These methods are derived
dose by IV bolus injection, the times for the from rearranging Equation 10.8 into Equations 10.9
amount of drug to decline 50% are approximately and 10.10.
the same. For 10- and 5-mg doses, the amount
of drug in the body is much less than the KM of C 1 KM (10.9)
= C +
100 mg. Therefore, the amount of drug in the ν Vmax Vmax
body is well below saturation of the elimination
process and the drug declines at a first-order rate. ν
ν = −K +V (10.10)
M C max
Determination of KM and Vmax A plot of C/n versus C would yield a straight line
Equation 10.1 relates the rate of drug biotransfor- with 1/Vmax as slope and KM/Vmax as intercept
mation to the concentration of the drug in the body. (Equation 10.9). A plot of n versus n/C would yield a
The same equation may be applied to determine slope of −KM and an intercept of Vmax (Equation 10.10).
Nonlinear Pharmacokinetics 237
TABLE 106 Information Necessary for Graphic Determination of Vmax and K
M
Observation C V 1/V 1/C
Number ( lM/mL) ( lM/mL/min) (mL/min/lM) (mL/lM)
1 1 0.500 2.000 1.000
2 6 1.636 0.611 0.166
3 11 2.062 0.484 0.090
4 16 2.285 0.437 0.062
5 21 2.423 0.412 0.047
6 26 2.516 0.397 0.038
7 31 2.583 0.337 0.032
8 36 2.63 0.379 0.027
9 41 2.673 0.373 0.024
10 46 2.705 0.369 0.021
3.0 The necessary calculations for making the above
plots are shown in Table 10-7. The plots are shown
2.5 in Figs. 10-7 and 10-8. It should be noted that the
data are spread out better by the two latter plots.
2.0
Calculations from the slope show that the same KM
1.5 and Vmax are obtained as in Fig. 10-6. When the data
are more scattered, one method may be more accu-
1.0 rate than the other. A simple approach is to graph the
0.5
0 12 24 36 48
Drug concentration (C )
TABLE 107 Calculations Necessary for
FIGURE 105 Plot of rate of drug metabolism at various Graphic Determination of KM and Vmax
drug concentrations. (KM = 0.5 mmol/mL, Vmax = 3 mmol/mL/min.)
C V C/V V/C
( lM/mL) ( lM/mL/min) (min) (1/min)
2.0
1 0.500 2.000 0.500
1.8
1.6 6 1.636 3.666 0.272
1.4 11 2.062 5.333 0.187
1.2 16 2.285 7.000 0.142
1.0
21 2.423 8.666 0.115
0.8
0.6 26 2.516 10.333 0.096
0.4 31 2.583 12.000 0.083
0.2
0 0.2 0.4 0.6 0.8 1.0 36 2.634 13.666 0.073
1/C
41 2.673 15.333 0.065
FIGURE 106 Plot of 1/n versus 1/C for determining KM
46 2.705 17.000 0.058
and Vmax.
1/u Rate of drug metabolism (u)
238 Chapter 10
18 An example for the determination of KM and
16 Vmax is given for the drug phenytoin. Phenytoin
14 undergoes capacity-limited kinetics at therapeutic
12 drug concentrations in the body. To determine KM
10 and Vmax, two different dose regimens are given at
8 different times, until steady state is reached. The
6 steady-state drug concentrations are then measured
4 by assay. At steady state, the rate of drug metabolism
2 (n) is assumed to be the same as the rate of drug input
0 R (dose/day). Therefore, Equation 10.11 may be writ-
0 12 24 36 48
C ten for drug metabolism in the body similar to the
way drugs are metabolized in vitro (Equation 10.7).
FIGURE 107 Plot of C/n versus C for determining KM and
However, steady state will not be reached if the drug
Vmax.
input rate, R, is greater than the Vmax; instead, drug
accumulation will continue to occur without reaching
a steady-state plateau.
data and examine the linearity of the graphs. The
same basic type of plot is used in the clinical litera-
VmaxCss (10.11)
ture to determine KM and Vmax for individual patients R =
KM +Css
for drugs that undergo capacity-limited kinetics.
where R = dose/day or dosing rate, Css = steady-state
Determination of KM and Vmax in Patients plasma drug concentration, Vmax = maximum meta-
bolic rate constant in the body, and KM = Michaelis–
Equation 10.7 shows that the rate of drug metabo-
Menten constant of the drug in the body.
lism (n) is dependent on the concentration of the
drug (C). This same basic concept may be applied to
the rate of drug metabolism of a capacity-limited EXAMPLE »» »
drug in the body (see Chapter 12). The body may be
regarded as a single compartment in which the drug Phenytoin was administered to a patient at dos-
is dissolved. The rate of drug metabolism will vary ing rates of 150 and 300 mg/d, respectively. The
depending on the concentration of drug Cp as well as steady-state plasma drug concentrations were 8.6
on the metabolic rate constants KM and Vmax of the and 25.1 mg/L, respectively. Find the KM and Vmax
drug in each individual. of this patient. What dose is needed to achieve a
steady-state concentration of 11.3 mg/L?
3.0 Solution
There are three methods for solving this problem, all
2.5
based on the same basic equation (Equation 10.11).
2.0
Method A
1.5 Inverting Equation 10.11 on both sides yields
1 K 1 1
1.0 M
= +
R V C V (10.12)
max ss max
0.5
0.06 0.18 0.30 0.42 0.54 Multiply both sides by CssVmax,
u/C
VmaxCss
FIGURE 108 Plot of n versus n/C for determining KM and = KM + Css
R
Vmax.
u C/u
Nonlinear Pharmacokinetics 239
30
800
Vmax = 630 mg/d
20 600
Vmax = 630 mg/d
Slope KM = 27.5 mg/L
400
10
200
0
0.02 0.04 0.06 0.08 0.10 0
0 5 10 15 20
Css/dose rate (R)
(L/d) Clearance (dose/day/Css) (L/d)
–10
FIGURE 1010 Plot of R versus R/Css or clearance
(method B). (From Witmer and Ritschel, 1984, with
permission.)
–20
KM = 27.6 mg/L 2. Mark points for R of 150 mg/d and Css of 8.6 mg/L
as shown. Connect with a straight line.
–30
3. The point where lines from the first two steps
FIGURE 109 Plot of Css versus Css/R (method A). cross is called point A.
(From Witmer and Ritschel, 1984, with permission.)
4. From point A, read Vmax on the y axis and KM on
Rearranging the x axis. (Again, Vmax of 630 mg/d and KM of
27 mg/L are found.)
V C
Css = max ss − KM (10.13)
R
A plot of Css versus Css/R is shown in Fig. 10-9. Vmax is
700
equal to the slope, 630 mg/d, and KM is found from the Vmax = 630 mg/d
y intercept, 27.6 mg/L (note the negative intercept). A
600
Method B
From Equation 10.11, 500
RKM + RCss =VmaxCss
400
Dividing both sides by Css yields
K R
R =V M
max − 300
(10.14)
Css
A plot of R versus R/Css is shown in Fig. 10-10. The 200
KM and Vmax found are similar to those calculated
by the previous method (Fig. 10-9). 100
Method C
A plot of R versus Css is shown in Fig. 10-11. To 30 20 10 0 10 20 30
determine K Phenytoin Css (mg/L)
M and Vmax:
1. Mark points for R of 300 mg/d and Css of 25.1 mg/L
FIGURE 1011 Plot of R versus Css (method C).
as shown. Connect with a straight line. (From Witmer and Ritschel, 1984, with permission.)
Phenytoin Css (mg/L)
Dose rate (mg/d)
Dose/day (mg/d)
KM = 27 mg/L
240 Chapter 10
is the second dosing rate. To calculate KM and Vmax,
This Vmax and KM can be used in Equation 10.11 to use Equation 10.15 with the values C1 = 8.6 mg/L,
find an R to produce the desired Css of 11.3 mg/L. C2 = 25.1 mg/L, R1 = 150 mg/d, and R2 = 300 mg/d.
Alternatively, join point A on the graph to meet The results are
11.3 mg/L on the x axis; R can be read where this
line meets the y axis (190 mg/d). 300 −150
KM = − = 27.3 mg/L
To calculate the dose needed to keep steady- (150/8.6) (300/25.1)
state phenytoin concentration of 11.3 mg/L in this
patient, use Equation 10.7. Substitute KM into either of the two simultaneous
equations to solve for Vmax.
(630 mg/d)(11.3 mg/L)
R =
27 mg/L+11.3 mg/L V (8.6)
150 max
=
27.3+8.6
7119
= =186 mg/d
38.3 Vmax = 626 mg/d
This answer compares very closely with the value
obtained by the graphic method. All three meth- Interpretation of KM and Vmax
ods have been used clinically. Vozeh et al (1981) An understanding of Michaelis–Menten kinetics
introduced a method that allows for an estimation provides insight into the nonlinear kinetics and helps
of phenytoin dose based on steady-state concentra- avoid dosing a drug at a concentration near enzyme
tion resulting from one dose. This method is based saturation. For example, in the above phenytoin
on a statistically compiled nomogram that makes it dosing example, since KM occurs at 0.5Vmax, KM =
possible to project a most likely dose for the patient. 27.3 mg/L, the implication is that at a plasma con-
centration of 27.3 mg/L, enzymes responsible for
phenytoin metabolism are eliminating the drug at
Determination of KM and Vmax 50% Vmax, that is, 0.5 × 626 mg/d or 313 mg/d. When
by Direct Method the subject is receiving 300 mg of phenytoin per day, the
plasma drug concentration of phenytoin is 8.6 mg/L,
When steady-state concentrations of phenytoin are
which is considerably below the KM of 27.3 mg/L.
known at only two dose levels, there is no advantage
In practice, the KM in patients can range from 1 to
in using the graphic method. KM and Vmax may be
15 mg/L, and V
calculated by solving two simultaneous equations max can range from 100 to 1000 mg/d.
Patients with a low KM tend to have greater changes
formed by substituting Css and R (Equation 10.11)
in plasma concentrations during dosing adjustments.
with C1, R1, C2, and R2. The equations contain two
Patients with a smaller KM (same Vmax) will show a
unknowns, KM and Vmax, and may be solved easily.
greater change in the rate of elimination when plasma
VmaxC1 drug concentration changes compared to subjects
R1 =
K with a higher KM. A subject with the same Vmax, but
M +C1
V different KM, is shown in Fig. 10-12. (For another
maxC2
R2 = example, see the slopes of the two curves generated
KM +C2
in Fig. 10-4.)
Combining the two equations yields Equation 10.15.
Dependence of Elimination Half-Life on Dose
R
2 − R1
KM = (10.
(R For drugs that follow linear kinetics, the elimination
1 /C1)− 15)
(R2 /C2 )
half-life is constant and does not change with dose or
where C1 is steady-state plasma drug concentration drug concentration. For a drug that follows nonlinear
after dose 1, C2 is steady-state plasma drug concen- kinetics, the elimination half-life and drug clearance
tration after dose 2, R1 is the first dosing rate, and R2 both change with dose or drug concentration. Generally,
Nonlinear Pharmacokinetics 241
8.00 Within a certain drug concentration range, an average
or mean clearance (Clav) may be determined. Because
7.00 the drug follows Michaelis–Menten kinetics, Clav
is dose dependent. Clav may be estimated from the
6.00
area under the curve and the dose given (Wagner
5.00 et al, 1985).
According to the Michaelis–Menten equation,
4.00
dC
p VmaxCp
= (10.17)
3.00 dt KM +Cp
2.00
KM = 4 Inverting Equation 10.17 and rearranging yields
1.00
KM = 2
K C
M p
0.00 Cpdt = dC dC
V p − p (10.18)
0 10 20 30 40 50 60 70 80 m′ ax Vm′ ax
Cp
FIGURE 1012 Diagram showing the rate of metabolism The area under the curve, [AUC]∞0 , is obtained by
when Vmax is constant (8 mg/mL/h) and KM is changed (KM = integration of Equation 10.18 (ie, [AUC]∞
∞
0 = ∫ C d
0 p t).
2 mg/mL for top curve and KM = 4 mg/mL for bottom curve).
Note the rate of metabolism is faster for the lower KM, but
∞ ∞ K ∞ C
saturation starts at lower concentration. ∫ M p
C dt dC dC
0 p = ∫ p +
C0 ∫
V 0 p (10.19)
p C
m′ ax p Vm′ ax
the elimination half-life becomes longer, clearance where V ′ is the maximum velocity for metabolism.
max
becomes smaller, and the area under the curve Units for V ′ are mass/compartment volume per
max
becomes disproportionately larger with increasing unit time. Vm′ ax =Vmax /VD; Wagner et al (1985) used
dose. The relationship between elimination half-life Vmax in Equation 10.20 as mass/time to be consistent
and drug concentration is shown in Equation 10.16. with biochemistry literature, which considers the
The elimination half-life is dependent on the initial mass of the substrate reacting with the enzyme.
Michaelis–Menten parameters and concentration. Integration of Equation 10.18 from time 0 to
infinity gives Equation 10.20.
0.693
t1/2 = (K C )
V M + p (10.16) C0
p C0
max [AUC]∞ = p
+K
0 V /V 2 M (10.20)
max D
Some pharmacokineticists prefer not to calculate
the elimination half-life of a nonlinear drug because where VD is the apparent volume of distribution.
the elimination half-life is not constant. Clinically, Because the dose D0 =C0
pVD, Equation 10.20 may
if the half-life is increasing as plasma concentration be expressed as
increases, and there is no apparent change in meta- 0
D C
bolic or renal function, then there is a good possibil- [AUC]∞ = 0 p
0 +K (10.21)
V M
ity that the drug may be metabolized by nonlinear max 2
kinetics. To obtain mean body clearance, Clav is then calcu-
lated from the dose and the AUC.
Dependence of Clearance on Dose D0 V
max
Clav = ∞ = (10.22)
The total body clearance of a drug given by IV bolus [AUC] 0
0 (Cp /2)+KM
injection that follows a one-compartment model
with Michaelis–Menten elimination kinetics changes V
max
Clav = (10.23)
with respect to time and plasma drug concentration. (D0 /2VD )+KM
Rate of metabolism
242 Chapter 10
A. Metoprolol 200 mg B. Timolol 20 mg
600 120
400 80
200 40
0 0
0 4 8 12 16 18 24 0 4 8 12 16 20 24
Time (hours) Time (hours)
FIGURE 1013 Mean plasma drug concentration-versus-time profiles following administration of single oral doses
of (A) metoprolol tartrate 200 mg to 6 extensive metabolizers (EMs) and 6 poor metabolizers (PMs) and (B) timolol maleate 20 mg
to six EMs (O) and four PMs (•). (Data from Lennard MS, et al: Oxidation phenotype—A major determinant of metoprolol metabolism
and response. NEJM 307:1558–1560, 1982; Lennard MS, et al: The relationship between debrisoquine oxidation phenotype and the
pharmacokinetics and pharmacodynamics of propranolol. Br J Clin Pharmac 17(6):679–685, 1984; Lewis RV: Timolol and atenolol:
Relationships between oxidation phenotype, pharmacokinetics and pharmacodynamics. Br J Clin Pharmac 19(3):329–333, 1985.)
Alternatively, dividing Equation 10.17 by Cp gives available supporting variable metabolism due to
Equation 10.24, which shows that the clearance of a genetic polymorphism (Chapter 12). The clearance
drug that follows nonlinear pharmacokinetics is (apparent) of many of these drugs in patients who
dependent on the plasma drug concentration Cp, KM, are slow metabolizers changes with dose, although
and Vmax. these drugs may exhibit linear kinetics in subjects
with the “normal” phenotype. Metoprolol and many
VD (dCp /dt) V
max
Cl = = (10.24) b-adrenergic antagonists are extensively metabolized.
Cp KM +Cp The plasma levels of metoprolol in slow metabolizers
Equation 10.22 or 10.23 calculates the average clear- (Lennard et al, 1986) were much greater than other
ance Cl patients, and the AUC, after equal doses, is several
av for the drug after a single IV bolus dose
over the entire time course of the drug in the body. times greater among slow metabolizers of metoprolol
For any time period, clearance may be calculated (Fig. 10-13). A similar picture is observed with another
(see Chapters 7 and 12) as b-adrenergic antagonist, timolol. These drugs have
smaller clearance than normal.
dD
E /dt
ClT = (10.25)
Cp
CLINICAL FOCUS
In Chapter 12, the physiologic model based on blood
flow and intrinsic clearance is used to describe drug The dose-dependent pharmacokinetics of sodium
metabolism. The extraction ratios of many drugs are valproate (VPA) was studied in guinea pigs at 20,
listed in the literature. Actually, extraction ratios are 200, and 600 mg/kg by rapid intravenous infusion.
dependent on dose, enzymatic system, and blood The area under the plasma concentration–time curve
flow, and for practical purposes, they are often increased out of proportion at the 600-mg/kg dose
assumed to be constant at normal doses. level in all groups (Yu et al, 1987). The total clear-
Except for phenytoin, there is a paucity of KM and ance (ClT) was significantly decreased and the beta
Vmax data defining the nature of nonlinear drug elimi- elimination half-life (t1/2) was significantly increased
nation in patients. However, abundant information is at the 600-mg/kg dose level. The dose-dependent
mg/L
mg/L
Nonlinear Pharmacokinetics 243
kinetics of VPA were due to saturation of metabolism. case of overdose, high liver drug concentrations and
Metabolic capacity was greatly reduced in young an extensive tissue distribution (large VD) made the
guinea pigs. drug difficult to remove. Vermeulen (1998) reported
Clinically, similar enzymatic saturation may be that saturation of CYP2D6 could result in a dispro-
observed in infants and in special patient populations, portionally higher plasma level than could be
whereas drug metabolism may be linear with dose in expected from an increase in dosage. These high
normal subjects. These patients have lower Vmax and plasma drug concentrations may be outside the range
longer elimination half-life. Variability in drug metab- of 20–50 mg normally recommended. Since publica-
olism is described in Chapters 12 and 13. tion of this article, more is known about genotype
CYP2D6*10 (Yoon et al, 2000), which may contrib-
ute to intersubject variability in metabolism of this
Frequently Asked Questions drug (see also Chapter 13).
»»What is the Michaelis–Menten equation? How are
Vmax and KM obtained? What are the units for Vmax
and KM? What is the relevance of V Frequently Asked Questions
max and KM?
»»What does autoinhibition mean? Would you expect
»»What are the main differences in pharmacokinetic paroxetine (Paxil) plasma drug concentrations, Cp, to
parameters between a drug that follows linear be higher or lower after multiple doses? Would the Cp
pharmacokinetics and a drug that follows nonlinear change be predictable among different subjects?
pharmacokinetics?
»»Name an example of SSRI and MAOI drug. Read
Chapter 13 to learn how another CYP2D6 drug may
greatly change the Cp of a drug such as Paxil.
CLINICAL FOCUS
Paroxetine hydrochloride (Paxil) is an orally admin-
istered psychotropic drug. Paroxetine is extensively
metabolized and the metabolites are considered to be DRUGS DISTRIBUTED AS
inactive. Nonlinearity in pharmacokinetics is ONE-COMPARTMENT MODEL
observed with increasing doses. Paroxetine exhibits AND ELIMINATED BY NONLINEAR
autoinhibition. The major pathway for paroxetine
metabolism is by CYP2D6. The elimination half-life PHARMACOKINETICS
is about 21 hours. Saturation of this enzyme at clini- The equations presented thus far in this chapter
cal doses appears to account for the nonlinearity of have been for drugs given by IV bolus, distributed
paroxetine kinetics with increasing dose and increas- as a one-compartment model, and eliminated only
ing duration of treatment. The role of this enzyme in by nonlinear pharmacokinetics. The following are
paroxetine metabolism also suggests potential drug– useful equations describing other possible routes of
drug interactions. Clinical drug interaction studies drug administration and including mixed drug
have been performed with substrates of CYP2D6 elimination, by which the drug may be eliminated
and show that paroxetine can inhibit the metabolism by both nonlinear (Michaelis–Menten) and linear
of drugs metabolized by CYP2D6 including itself, (first-order) processes.
desipramine, risperidone, and atomoxetine.
Paroxetine hydrochloride is known to inhibit
metabolism of selective serotonin reuptake inhibitors Mixed Drug Elimination
(SSRIs) and monoamine oxidase inhibitors (MAOIs) Drugs may be metabolized to several different metab-
producing “serotonin syndrome” (hyperthermia, olites by parallel pathways. At low drug doses corre-
muscle rigidity, and rapid changes in vital signs). sponding to low drug concentrations at the site of the
Three cases of accidental overdosing with paroxetine biotransformation enzymes, the rates of formation
hydrochloride were reported (Vermeulen, 1998). In the of metabolites are first order. However, with higher
244 Chapter 10
doses of drug, more drug is absorbed and higher drug the nonlinear relationship between niacin dose and
concentrations are presented to the biotransformation plasma drug concentrations following multiple doses
enzymes. At higher drug concentrations, the enzyme of Niaspan (niacin) extended-release tablets (Niaspan,
involved in metabolite formation may become satu- FDA-approved label, 2009).
rated, and the rate of metabolite formation becomes
nonlinear and approaches zero order. For example, Zero-Order Input and Nonlinear Elimination
sodium salicylate is metabolized to both a glucuro-
The usual example of zero-order input is constant IV
nide and a glycine conjugate (hippurate). The rate of
infusion. If the drug is given by constant IV infusion
formation of the glycine conjugate is limited by the
and is eliminated only by nonlinear pharmacokinetics,
amount of glycine available. Thus, the rate of forma-
then the following equation describes the rate of
tion of the glucuronide continues as a first-order
change of the plasma drug concentration:
process, whereas the rate of conjugation with glycine
is capacity limited. dCp k V ′
0 maxC
The equation that describes a drug that is elimi- = − p
(10.27)
dt VD KM +Cp
nated by both first-order and Michaelis–Menten kinet-
ics after IV bolus injection is given by where k0 is the infusion rate and VD is the apparent
volume of distribution.
dCp Vm′ axCp
− = kC 2
dt p + (10. 6)
KM +Cp First-Order Absorption and
Nonlinear Elimination
where k is the first-order rate constant representing The relationship that describes the rate of change in
the sum of all first-order elimination processes, while the plasma drug concentration for a drug that is
the second term of Equation 10.26 represents the given extravascularly (eg, orally), absorbed by first-
saturable process. V ′ is simply Vmax expressed as
max order absorption, and eliminated only by nonlinear
concentration by dividing by VD. pharmacokinetics, is given by the following equation.
CGI is concentration in the GI tract.
dCp V ′
CLINICAL FOCUS = −k t maxCp
k C a
dt a GIe − (10.28)
KM +Cp
The pharmacokinetic profile of niacin is complicated
due to extensive first-pass metabolism that is dosing- where ka is the first-order absorption rate constant.
rate specific. In humans, one metabolic pathway is If the drug is eliminated by parallel pathways
through a conjugation step with glycine to form nico- consisting of both linear and nonlinear pharmaco-
tinuric acid (NUA). NUA is excreted in the urine, kinetics, Equation 10.28 may be extended to
although there may be a small amount of reversible Equation 10.29.
metabolism back to niacin. The other metabolic path-
dCp V ′
way results in the formation of nicotinamide adenine = −k maxCp
k C e at
dt a GI − − kC
K p (10.29)
dinucleotide (NAD). It is unclear whether nicotinamide M +Cp
is formed as a precursor to, or following the synthesis
where k is the first-order elimination rate constant.
of, NAD. Nicotinamide is further metabolized to at
least N-methylnicotinamide (MNA) and nicotinamide-
N-oxide (NNO). MNA is further metabolized to two Two-Compartment Model with
other compounds, N-methyl-2-pyridone-5-carboxamide Nonlinear Elimination
(2PY) and N-methyl-4-pyridone-5-carboxamide (4PY). RhG-CSF is a glycoprotein hormone (recombinant
The formation of 2PY appears to predominate over human granulocyte-colony stimulating factors, rhG-
4PY in humans. At doses used to treat hyperlipidemia, CSF, MW about 20,000) that stimulates the growth of
these metabolic pathways are saturable, which explains neutropoietic cells and activates mature neutrophils.
Nonlinear Pharmacokinetics 245
The drug is used in neutropenia occurring during CHRONOPHARMACOKINETICS
chemotherapy or radiotherapy. Similar to many bio-
AND TIME-DEPENDENT
technological drugs, RhG-CSF is administered by
injection. The drug is administered subcutaneously PHARMACOKINETICS
and absorbed into the blood from the dermis site.
Chronopharmacokinetics broadly refers to a tempo-
This drug follows a two-compartment model with
ral change in the rate process (such as absorption or
two elimination processes: (1) a saturable process of
elimination) of a drug. The temporal changes in drug
receptor-mediated elimination in the bone marrow
absorption or elimination can be cyclical over a
and (2) a nonsaturable process of elimination. The
constant period (eg, 24-hour interval), or they may
model is described by two differential equations as
be noncyclical, in which drug absorption or elimi-
shown below:
nation changes over a longer period of time. Chrono-
dC V pharmacokinetics is an important consideration during
= − + + max
1 k X
k12 k + 1 2
C1 + 2 (10.29a)
dt V drug therapy.
1(C1 KM ) V1
Time-dependent pharmacokinetics generally
dX
2 = refers to a noncyclical change in the drug absorp-
k C V − k X (10.29b)
dt 12 1 1 21 2
tion or drug elimination rate process over a period
of time. Time-dependent pharmacokinetics leads to
where k12 and k21 are first-order transfer constants
nonlinear pharmacokinetics. Unlike dose-dependent
between the central and peripheral comparments; k
pharmacokinetics, which involves a change in the rate
is the first-order elimination constant from the cen-
process when the dose is changed, time-dependent
tral compartment; V1 is the volume of the central
pharmacokinetics may be the result of alteration in
compartment and the steady-state volume of distri-
the physiology or biochemistry in an organ or a
bution is Vss; X2 is the amount in the peripheral com-
region in the body that influences drug disposition
partment; C1 is the drug concentration in the central
(Levy, 1983).
compartments at time t; and Vmax and KM are
Michaelis–Menten parameters that describe the satu- Time-dependent pharmacokinetics may be due
rable elimination. to autoinduction or autoinhibition of biotransforma-
The pharmacokinetics of this drug was tion enzymes. For example, Pitlick and Levy (1977)
described by Hayashi et al (2001). Here, a is a func- have shown that repeated doses of carbamazepine
tion of dose with no dimensions, and granulocyte induce the enzymes responsible for its elimination
colony-stimulating factor (G-CSF) takes a value from (ie, auto-induction), thereby increasing the clearance
0 to 1. When the dose approaches 0, a of the drug. Auto-inhibition may occur during the
= 1; when the
dose approaches ∞, a course of metabolism of certain drugs (Perrier et al,
= 0.
According to Hayashi et al (2001), the drug 1973). In this case, the metabolites formed increase
clearance may be considered as two parts as shown in concentration and further inhibit metabolism of
below: the parent drug. In biochemistry, this phenomenon
is known as product inhibition. Drugs undergoing
Dose/AUC = αCl c)
int +Cln =Cl (10.29 time-dependent pharmacokinetics have variable
clearance and elimination half-lives. The steady-state
∞
CK
∫ M
dt concentration of a drug that causes auto-induction
C +K may be due to increased clearance over time. Some
Dose/AUC = 0 M (10.29d)
Clint +Cl
∞ n anticancer drugs are better tolerated at certain times
∫ Cdt of the day; for example, the antimetabolite drug fluo-
0
rouracil (FU) was least toxic when given in the
where Clint is intrinsic clearance for the saturable path- morning to rodents (Von Roemeling, 1991). A list of
way; Cln is nonsaturable clearance; and C is serum drugs that demonstrate time dependence is shown
concentration. in Table 10-8.
246 Chapter 10
TABLE 108 Drugs Showing Circadian or and the incidence of nephrotoxicity were studied in
Time-Dependent Disposition 221 patients (Prins et al, 1997). Each patient received
an IV injection of 2–4 mg/kg gentamicin or tobramy-
Cefodizime Fluorouracil Ketoprofen Theophylline
cin once daily: (1) between midnight and 7:30 am,
Cisplatin Heparin Mequitazine (2) between 8 am and 3:30 pm, or (3) between 4 pm
Data from Reinberg (1991). and 11:30 pm. In this study, no statistically significant
differences in drug trough levels (0–4.2 mg/L) or
peak drug levels (3.6–26.8 mg/L) were found for the
In pharmacokinetics, it is important to recognize
three time periods of drug administration. However,
that many isozymes (CYPs) are involved in drug
nephrotoxicity occurred significantly more frequently
metabolisms. A drug may competitively influence
when the aminoglycosides were given during the rest
the metabolism of another drug within the same
period (midnight–7:30 am). Many factors contribut-
CYP subfamily. Sometimes, an unrecognized effect
ing to nephrotoxicity were discussed; the time of
from the presence of another drug may be misjudged
administration was considered to be an independent
as a time-dependent pharmacokinetics. Drug metab-
risk factor in the multivariate statistical analysis.
olism and pharmacogenetics are discussed more
Time-dependent pharmacokinetics/pharmacodynam-
extensively in Chapter 13.
ics is important, but it may be difficult to detect the
clinical difference in drug concentrations due to
Circadian Rhythms and Influence multivariates.
on Drug Response Another example of circadian changes on drug
Circadian rhythms are rhythmic or cyclical changes response involves observations with chronic obstruc-
in plasma drug concentrations that may occur daily, tive pulmonary disease (COPD) patients. Symptoms
due to normal changes in body functions. Some of hypoxemia may be aggravated in some COPD
rhythmic changes that influence body functions and patients due to changes in respiration during the
drug response are controlled by genes and subject to sleep cycle. Circadian variations have been reported
modification by environmental factors. The mam- involving the incidence of acute myocardial infarc-
malian circadian clock is a self-sustaining oscillator, tion, sudden cardiac death, and stroke. Platelet
usually within a period of ~24 hours, that cyclically aggregation favoring coagulation is increased after
controls many physiological and behavioral systems. arising in the early morning hours, coincident with
The biological clock attempts to synchronize and the peak incidence of these cardiovascular events,
respond to changes in length of the daylight cycle although much remains to be elucidated.
and optimize body functions. Time-dependent pharmacokinetics and physio-
Circadian rhythms are regulated through peri- logic functions are important considerations in the
odic activation of transcription by a set of clock treatment of certain hypertensive subjects, in whom
genes. For example, melatonin onset is associated early-morning rise in blood pressure may increase the
with onset of the quiescent period of cortisol secre- risk of stroke or hypertensive crisis. Verapamil is a
tion that regulates many functions. Some well- commonly used antihypertensive. The diurnal pattern
known circadian physiologic parameters are core of forearm vascular resistance (FVR) between hyper-
body temperature (CBT), heart rate (HR), and other tensive and normotensive volunteers was studied at
cardiovascular parameters. These fundamental phys- 9 pm on 24-hour ambulatory blood pressure monitor-
iologic factors can affect disease states, as well as ing, and the early-morning blood pressure rise was
toxicity and therapeutic response to drug therapy. studied in 23 untreated hypertensives and 10 matched,
The toxic dose of a drug may vary as much as sev- normotensive controls. The diurnal pattern of FVR
eral-fold, depending on the time of drug administra- differed between hypertensives and normotensives,
tion—during either sleep or wake cycle. with normotensives exhibiting an FVR decline
For example, the effects of timing of aminoglyco- between 2 pm and 9 pm, while FVR rose at 9 pm in
side administration on serum aminoglycoside levels hypertensives. Verapamil appeared to minimize the
Nonlinear Pharmacokinetics 247
diurnal variation in FVR in hypertensives, although 2200 versus 1000 hours, indicating that the rate of
there were no significant differences at any single excretion during the night time was slower (Sarveshwer
time point. Verapamil effectively reduced ambulatory Rao et al, 1997).
blood pressure throughout the 24-hour period, but it
did not blunt the early-morning rate of blood pressure Clinical and Adverse Toxicity Due to
rise despite peak S-verapamil concentrations in the Nonlinear Pharmacokinetics
early morning (Nguyen et al, 2000).
The presence of nonlinear or dose-dependent phar-
macokinetics, whether due to saturation of a process
CLINICAL FOCUS involving absorption, first-pass metabolism, binding,
or renal excretion, can have significant clinical con-
Hypertensive patients are sometimes characterized
sequences. However, nonlinear pharmacokinetics
as “dippers” if their nocturnal blood pressure drops
may not be noticed in drug studies that use a narrow
below their daytime pressure. Non-dipping patients
dose range in patients. In this case, dose estimation
appear to be at an increased risk of cardiovascular
may result in disproportionate increases in adverse
morbidity. Blood pressure and cardiovascular events
reactions but insufficient therapeutic benefits.
have a diurnal rhythm, with a peak of both in the
Nonlinear pharmacokinetics can occur anywhere
morning hours, and a decrease during the night. The
above, within, or below the therapeutic window.
circadian variation of blood pressure provides assis-
The problem of a nonlinear dose relationship in
tance in predicting cardiovascular outcome (de la
population pharmacokinetics analysis has been inves-
Sierra et al, 2011).
tigated using simulations (Hashimoto et al, 1994,
The pharmacokinetics of many cardiovascular
1995; Jonsson et al, 2000). For example, nonlinear
acting drugs have a circadian phase dependency
fluvoxamine pharmacokinetics was reported (Jonsson
(Lemmer, 2006). Examples include b-blockers, cal-
et al, 2000) to be present even at subtherapeutic doses.
cium channel blockers, oral nitrates, and ACE inhib-
By using simulated data and applying nonlinear
itors. There is clinical evidence that antihypertensive
mixed-effect models using NONMEM, the authors
drugs should be dosed in the early morning in
also demonstrated that use of nonlinear mixed-effect
patients who are hypertensive “dippers,” whereas for
models in population pharmacokinetics had an impor-
patients who are non-dippers, it may be necessary to
tant application in the detection and characterization
add an evening dose or even to use a single evening
of nonlinear processes (pharmacokinetic and pharma-
dose not only to reduce high blood pressure (BP) but
codynamic). Both first-order (FO) and FO conditional
also to normalize a disturbed non-dipping 24-hour
estimation (FOCE) algorithms were used for the
BP profile. However, for practical purposes, some
population analyses. Population pharmacokinetics is
investigators found diurnal BP monitoring in many
discussed further in Chapter 25.
individuals too variable to distinguish between dip-
pers and non-dippers (Lemmer, 2006).
The issue of time-dependent pharmacokinetics/
pharmacodynamics (PK/PD) may be an important BIOAVAILABILITY OF DRUGS
issue in some antihypertensive care. Pharmacists THAT FOLLOW NONLINEAR
should recognize drugs that exhibit this type of time- PHARMACOKINETICS
dependant PK/PD.
Another example of time-dependent pharmaco- The bioavailability of drugs that follow nonlinear
kinetics involves ciprofloxacin. Circadian variation pharmacokinetics is difficult to estimate accurately.
in the urinary excretion of ciprofloxacin was inves- As shown in Table 10-1, each process of drug absorp-
tigated in a crossover study in 12 healthy male vol- tion, distribution, and elimination is potentially satu-
unteers, ages 19–32 years. A significant decrease in rable. Drugs that follow linear pharmacokinetics
the rate and extent of the urinary excretion of cipro- follow the principle of superposition (Chapter 9). The
floxacin was observed following administrations at assumption in applying the rule of superposition is
248 Chapter 10
that each dose of drug superimposes on the previous 50
dose. Consequently, the bioavailability of subsequent
doses is predictable and not affected by the previous
dose. In the presence of a saturable pathway for drug 10
absorption, distribution, or elimination, drug bio-
5 B A
availability will change within a single dose or with
subsequent (multiple) doses. An example of a drug
with dose-dependent absorption is chlorothiazide
(Hsu et al, 1987). 1
Time
The extent of bioavailability is generally esti-
mated using [AUC]∞0 . If drug absorption is saturation FIGURE 1014 Plasma curve comparing the elimination
of two drugs given in equal IV doses. Curve A represents a drug
limited in the gastrointestinal tract, then a smaller
90% bound to plasma protein. Curve B represents a drug not
fraction of drug is absorbed systemically when the bound to plasma protein.
gastrointestinal drug concentration is high. A drug
with a saturable elimination pathway may also have the protein-bound drug is eliminated at a slower,
a concentration-dependent AUC affected by the nonlinear rate. Because the two drugs are eliminated
magnitude of KM and Vmax of the enzymes involved by identical mechanisms, the characteristically slower
in drug elimination (Equation 10.21). At low Cp, the elimination rate for the protein-bound drug is due to
rate of elimination is first order, even at the begin- the fact that less free drug is available for glomerular
ning of drug absorption from the gastrointestinal filtration in the course of renal excretion.
tract. As more drug is absorbed, either from a single The concentration of free drug, Cf, can be calcu-
dose or after multiple doses, systemic drug concen- lated at any time, as follows:
trations increase to levels that saturate the enzymes
Cf =Cp (1− fraction bound) (10.30)
involved in drug elimination. The body drug clear-
ance changes and the AUC increases disproportion- For any protein-bound drug, the free drug concentra-
ately to the increase in dose (see Fig. 10-2). tion (Cf) will always be less than the total drug con-
centration (Cp).
A careful examination of Fig. 10-14 shows that
NONLINEAR PHARMACOKINETICS the slope of the bound drug decreases gradually as the
DUE TO DRUG–PROTEIN BINDING drug concentration decreases. This indicates that the
percent of drug bound is not constant. In vivo, the per-
Protein binding may prolong the elimination half-life cent of drug bound usually increases as the plasma
of a drug. Drugs that are protein bound must first dis- drug concentration decreases (see Chapter 11). Since
sociate into the free or nonbound form to be elimi- protein binding of drug can cause nonlinear elimina-
nated by glomerular filtration. The nature and extent tion rates, pharmacokinetic fitting of protein-bound
of drug–protein binding affects the magnitude of the drug data to a simple one-compartment model with-
deviation from normal linear or first-order elimina- out accounting for binding results in erroneous esti-
tion rate process. mates of the volume of distribution and elimination
For example, consider the plasma level–time half-life. Sometimes plasma drug data for drugs that
curves of two hypothetical drugs given intravenously are highly protein bound have been inappropriately
in equal doses (Fig. 10-14). One drug is 90% protein fitted to two-compartment models.
bound, whereas the other drug does not bind plasma Valproic acid (Depakene) shows nonlinear phar-
protein. Both drugs are eliminated solely by glo- macokinetics that may be due partially to nonlinear
merular filtration through the kidney. protein binding. The free fraction of valproic acid is
The plasma curves in Fig. 10-14 demonstrate 10% at a plasma drug concentration of 40 mg/mL and
that the protein-bound drug is more concentrated in 18.5% at a plasma drug level of 130 mg/mL. In addi-
the plasma than a drug that is not protein bound, and tion, higher-than-expected plasma drug concentrations
Plasma level
Nonlinear Pharmacokinetics 249
occur in the elderly patients, and in patients with
5000
hepatic or renal disease.
One-Compartment Model Drug 1000
with Protein Binding 500
The process of elimination of a drug distributed in a 100 mg/kg
single compartment with protein binding is illus- 100
trated in Fig. 10-15. The one compartment contains
50
both free drug and bound drug, which are dynami-
cally interconverted with rate constants k 5 mg/kg 20 mg/kg
1 and k2.
Elimination of drug occurs only with the free drug, at 10
a first-order rate. The bound drug is not eliminated. Time
Assuming a saturable and instantly reversible drug- FIGURE 1016 Plasma drug concentrations for various
binding process, where P = protein concentration in doses of a one-compartment model drug with protein binding.
plasma, Cf = plasma concentration of free drug, kd = (Adapted from Coffey et al, 1971, with permission.)
k2/k1 = dissociation constant of the protein drug com-
plex, Cp = total plasma drug concentration, and Cb = This differential equation describes the relationship
plasma concentration of bound drug, of changing plasma drug concentrations during elim-
ination. The equation is not easily integrated but can
Cb (1/kd )C f
= (10.31) be solved using a numerical method. Figure 10-16
P 1+ (1/kd )Cf shows the plasma drug concentration curves for a one-
This equation can be rearranged as follows: compartment protein-bound drug having a volume of
distribution of 50 mL/kg and an elimination half-life
PC
f
Cb = =C −C 1 . 2 of 30 minutes. The protein concentration is 4.4% and
k p f ( 0 3 )
d +Cf the molecular weight of the protein is 67,000 Da. At
Solving for Cf ,
various doses, the pharmacokinetics of elimination of
the drug, as shown by the plasma curves, ranges from
1 linear to nonlinear, depending on the total plasma
C ( ) ( 2
f = − P + kd −Cp + P + kd −Cp ) + 4k
2 dC
p drug concentration.
(10.33) Nonlinear drug elimination pharmacokinetics
occurs at higher doses. Because more free drug is avail-
Because the rate of drug elimination is dCp/dt, able at higher doses, initial drug elimination occurs
more rapidly. For drugs demonstrating nonlinear phar-
dC
p = −kC macokinetics, the free drug concentration may increase
dt f
slowly at first, but when the dose of drug is raised
beyond the protein-bound saturation point, free plasma
dC
p −k
=
−(P + kd −Cp )+ (P + kd −C )2+ 4
k C
dt 2 p d p drug concentrations may rise abruptly. Therefore, the
concentration of free drug should always be calculated
(10.34) to make sure the patient receives a proper dose.
Bound Determination of Linearity in Data Analysis
k1
k During new drug development, the pharmacokinetics
k2
Free of the drug is examined for linear or nonlinear phar-
macokinetics. A common approach is to give several
FIGURE 1015 One-compartment model with drug– graded doses to human volunteers and obtain plasma
protein binding. drug concentration curves for each dose. From these
Plasma level
250 Chapter 10
data, a graph of AUC versus dose is generated as shown When the third AUC point is above the trend line, it
in Fig. 10-2. The drug is considered to follow linear is risky to draw a conclusion. One should verify that
kinetics if AUC versus dose for various doses is propor- the high AUC is not due to a lower elimination or
tional (ie, linear relationship). In practice, the experi- clearance due to saturation.
mental data presented may not be very clear, especially In Fig. 10-18, a regression line was obtained by
when oral drug administration data are presented and forcing the same data through point (0,0). The linear
there is considerable variability in the data. For exam- regression analysis and estimated R2 appears to show
ple, the AUC versus three-graded doses of a new drug is that the drug followed nonlinear pharmacokinetics.
shown in Fig. 10-17. A linear regression line was drawn The line appears to have a curvature upward and the
through the three data points. The conclusion is that the possibility of some saturation at higher doses. This
drug follows dose-independent (linear) kinetics based pharmacokineticist recommends additional study by
upon a linear regression line through the data and a cor- adding a higher dose to more clearly check for dose
relation coefficient, R2 = 0.97. dependency.
• Do you agree with this conclusion after inspecting • What is your conclusion?
the graph?
Considerations
The conclusion for linear pharmacokinetics in
• The experimental data are composed of three dif-
Fig. 10-17 seems reasonable based on the estimated
ferent drug doses.
regression line drawn through the data points.
• The regression line shows that the drug follows
However, another pharmacokineticist noticed that
linear pharmacokinetics from the low dose to the
the regression line in Fig. 10-17 does not pass through
high dose.
the origin point (0,0). This pharmacokineticist consid-
• The use of a (0.0) value may provide additional
ered the following questions:
information concerning the linearity of the
• Are the patients in the study receiving the drug pharmacokinetics. However, extrapolation of
doses well separated by a washout period during curves beyond the actual experimental data can
the trial such that no residual drug remained in the be misleading.
body and carried to the present dose when plasma • The conclusion in using the (0.0) time point shows
samples are collected? that the pharmacokinetics is nonlinear below the
• Is the method for assaying the samples validated? lowest drug dose. This may occur after oral dos-
Could a high sample blank or interfering mate- ing because at very low drug doses some of the
rial be artificially adding to elevate 0 time drug drug is decomposed in the gastrointestinal tract
concentrations? or metabolized prior to systemic absorption. With
• How does the trend line look if the point (0,0) is higher doses, the small amount of drug loss is not
included? observed systemically.
AUC AUC
Dose (mg/kg) Dose (mg/kg)
FIGURE 1017 Plot of AUC versus dose to determine lin- FIGURE 1018 Plot of AUC versus dose to determine
earity. The regression line is based on the three doses of the drug. linearity.
Nonlinear Pharmacokinetics 251
TABLE 109 Some Common Issues during Data Analysis for Linearity
Oral Data Issues during Data Analysis Comments
Last data point may be below the LOD or limit of Last sample point scheduled too late in the study
detection. What should the AUC tailpiece be? protocol.
Last data point still very high, much above the LOD. Last sample point scheduled too early.
What should be the AUC tailpiece? A substantial number of data points may be
incorrectly estimated by the tailpiece method.
Incomplete sample spacing around peak. Total AUC estimated may be quite variable or
unreliable.
Oral AUC data are influenced by F, D, and Cl. When examining D0/Cl vs D0, F must be held
constant. Any factor causing change in F during
the trial will introduce uncertainty to AUC.
F may be affected by efflux, transporters (see Chapter 13), Nonlinearity of AUC vs D0 may not be
and GI CYP enzymes. An increase in F and decrease in Cl evident and one may incorrectly conclude a drug
or vice versa over doses may mask each other. follows linear kinetics when it does not.
IV data AUC data by IV are influenced by D0 and Cl only. When examining D0/Cl vs D0, F is always constant.
Therefore, it is easier to see changes in AUC when
Cl changes by IV route.
LOD, limit of detection.
Note if VD of the drug is known, determining k from POTENTIAL REASONS FOR
the terminal slope of the oral data provides another
UNSUSPECTED NONLINEARITY1
way of calculating Cl (Cl = VD k) to check whether
clearance has changed at higher doses due to satura-
1. Nonlinearity caused by membrane resident
tion. Some common issues during data analysis for
transporters
linearity are listed in Table 10-9.
2. Nonlinearity caused by membrane CYPs
Note: In some cases, with certain drugs, the oral
3. Nonlinearity caused by cellular proteins
absorption mechanism is quite unique and drug
4. Nonlinearity caused by transporter proteins at
clearance by the oral route may involve absorption
the GI tract
site-specific enzymes or transporters located on the
5. Nonlinearity caused by bile acid transport
brush border. Extrapolating pharmacokinetic infor-
(apical/bile canaliculus)
mation from IV dose data should be done cautiously
only after a careful consideration of these factors. It
is helpful to know whether nonlinearity is caused by
distribution, or absorption factors. Frequently Asked Questions
Unsuspected nonlinear drug disposition is one »»What is the cause of nonlinear pharmacokinetics
of the biggest issues concerning drug safety. that is not dose related?
Although pharmacokinetic tools are useful, nonlin-
»»For drugs that have several metabolic pathways,
earity can be easily missed during data analysis
must all the metabolic pathways be saturated for the
when there are outliners or extreme data scattering
drug to exhibit nonlinear pharmacokinetics?
due to individual patient factors such as genetics,
age, sex, and other unknown factors in special popu-
lations. While statistical analysis can help minimize
this, it is extremely helpful to survey for problems
(eg, epidemiological surveillance) and have a good 1Source: Evaluation of hepatotoxic potential of drugs using
understanding of how drugs are disposed in various transporter-based assays. Jasminder Sahi AAPS Transporter Meeting,
parts of the body in the target populations. 2005 at Parsippanny, New Jersey.
252 Chapter 10
DOSE-DEPENDENT transporters may critically enhance or reduce local
cell drug concentrations, allowing influx of drugs into
PHARMACOKINETICS
the cell or removing drug from the cell by efflux trans-
Role of Transporters porters, a defensive mechanism of the body. Many of
Classical pharmacokinetics studied linear pharmaco- the cells express transporters genetically, which may
kinetics of a drug by examining the area under plasma also be triggered on or turned off in disease state.
drug concentration curve at various doses given intra- Whether the overall pharmacokinetic process is linear
venously. The method is simple and definitive. The or nonlinear must be determined locally. The knowl-
method is useful revealing the kinetics in the body as edge of the local effects of transporters on pharmaco-
a whole. However, more useful information must now kinetics can improve safe and effective drug dosing.
be obtained through studies based on regional phar- The impact of transporters are discussed by various
macokinetics by studying the roles of transporters in authors in a review book edited by You and Morris
individual organs. Over the last few decades, trans- (2007). Table 10-10 summarizes some of the trans-
porters have been characterized in individual cells or porters that play an important role in drug distribution
in various types of cells (Chapters 11 and 13). These and how they may impact drug linearity.
TABLE 1010 Drug Transports and Comments on Roles in Altering Linearity of Absorption
or Elimination
Transporters Comments
Xenobiotic transporter Transporters may be age and gender related. These differences may change the linearity
expression of a drug through saturation.
Polymorphisms of drug Polymorphisms may have a clinical relevance affecting toxicity and efficacy in a similar
transporters way through change in pharmacokinetics.
Interplay of drug transporters The role of transporters on hepatic drug is profound and may greatly change the overall
and enzymes in liver linearity of a drug systemically.
The concept of drug clearance, Cl, and intrinsic clearance has to be reexamined as a
result of the translocation of transporters, at cellular membranes as suggested in a recent
review.
Drug–drug interaction change Clinical relevance, pharmacokinetics, pharmacodynamics, and toxicity may decrease
due to transporters or increase if a drug is a transporter substrate or inhibitor. Less clear is the change from
linear to nonlinear kinetics due to drug–drug interaction.
Drug transporters in the ABC transporters are very common and this can alter the absorption nature of a drug
intestine product, for example, the bioavailability and linearity of drug absorption. Bile acid
transporters affect drug movement and elimination by biliary excretion. The nature of the
process must be studied.
Drug transport in the kidney Various organic anion and cation drug transporters have been described. These trans-
porters may alter the linearity of systemic drug elimination if present in large quantity.
Multidrug resistance protein: These proteins may affect drug concentration in a cell or group of cells. Hence, they are
P-glycoprotein important elements in determining PK linearity.
Mammalian oligopeptide These transporters play a role in drug absorption and distribution.
transporters
Breast cancer resistance These transporters play a role in drug linearity and dosing in cancer therapy.
protein
Nonlinear Pharmacokinetics 253
CLINICAL EXAMPLE increase in AUC0–72) compared to the fasted state.
A standard meal also increased the rate of absorption
Zmax® (Pfizer) is an extended-release microsphere for- (119% increase in Cmax), with less effect on the extent
mulation of the antibiotic azithromycin in an oral sus- of absorption (12% increase in AUC0–72) compared to
pension. According to the approved label,2 based on administration of a 2-g Zmax dose in the fasted state.
data obtained from studies evaluating the pharmacoki-
netics of azithromycin in healthy adult subjects, a higher Distribution
peak serum concentration (Cmax) and greater systemic The serum protein binding of azithromycin is concen-
exposure (AUC 0–24) of azithromycin are achieved tration dependent, decreasing from 51% at 0.02 mg/mL
on the day of dosing following a single 2-g dose of to 7% at 2 mg/mL. Following oral administration,
Zmax versus 1.5 g of azithromycin tablets admin- azithromycin is widely distributed throughout the
istered over 3 days (500 mg/d) or 5 days (500 mg body with an apparent steady-state volume of distri-
on day 1, 250 mg/d on days 2–5) (Table 10-11). bution of 31.1 L/kg.
Consequently, due to these different pharmacokinetic Azithromycin concentrates in fibroblasts, epithe-
profiles, Zmax is not interchangeable with azithro- lial cells, macrophages, and circulating neutrophils
mycin tablet 3-day and 5-day dosing regimens. and monocytes. Higher azithromycin concentrations
in tissues than in plasma or serum have been observed.
Absorption Following a 2-g single dose of Zmax, azithromycin
The bioavailability of Zmax relative to azithromycin achieved higher exposure (AUC0–120) in mononuclear
immediate release (IR) (powder for oral suspension) leukocytes (MNL) and polymorphonuclear leuko-
was 83%. On average, peak serum concentrations cytes (PMNL) than in serum. The azithromycin
were achieved approximately 2.5 hours later following exposure (AUC0–72) in lung tissue and alveolar cells
Zmax administration and were lower by 57%, com- (AC) was approximately 100 times than in serum,
pared to 2 g azithromycin IR. Thus, single 2-g doses of and the exposure in epithelial lining fluid (ELF) was
Zmax and azithromycin IR are not bioequivalent and also higher (approximately 2–3 times) than in serum.
are not interchangeable. The clinical significance of this distribution data is
Effect of food on absorption: A high-fat meal unknown.
increased the rate and extent of absorption of a 2-g
dose of Zmax (115% increase in Cmax, and 23% Metabolism
In vitro and in vivo studies to assess the metabolism
2http://labeling.pzer.com/ShowLabeling.aspx?id=650#section-12.3. of azithromycin have not been performed.
TABLE 1011 Mean (SD) Pharmacokinetic Parameters for Azithromycin on Day 1 Following the
Administration of a Single Dose of 2 g Zmax or 1.5 g of Azithromycin Tablets Given over 3 Days
(500 mg/d) or 5 Days (500 mg on Day 1 and 250 mg on Days 2–5) to Healthy Adult Subjects
Azithromycin Regimen
Pharmacokinetic
Parameter * Zmax (N = 41) 3-Day (N = 12) 5-Day (N = 12)
Cmax (mg/mL) 0.821 (0.281) 0.441 (0.223) 0.434 (0.202)
T §
max (h) 5.0 (2.0–8.0) 2.5 (1.0–4.0) 2.5 (1.0–6.0)
AUC0–24 (mg·h/mL) 8.62 (2.34) 2.58 (0.84) 2.60 (0.71)
AUC0–∞¶ (mg·h/mL) 20.0 (6.66) 17.4 (6.2) 14.9 (3.1)
t1/2 (h) 58.8 (6.91) 71.8 (14.7) 68.9 (13.8)
∗Zmax, 3-day and 5-day regimen parameters obtained from separate pharmacokinetic studies
Adapted from Zmax approved label, October 2013.
254 Chapter 10
Excretion Based on the information,
Serum azithromycin concentrations following a single 1. The bioavailability of this drug may be quite
2-g dose of Zmax declined in a polyphasic pattern different for different dosage forms due to
with a terminal elimination half-life of 59 hours. The absorption profile.
prolonged terminal half-life is thought to be due to a 2. Absorption is likely to be affected by GI
large apparent volume of distribution. residence time of the product and the type of
Biliary excretion of azithromycin, predomi- dosage form.
nantly as unchanged drug, is a major route of elimi- 3. The drug is widely distributed.
nation. Over the course of a week, approximately 4. Drug binding may be nonlinear resulting in
6% of the administered dose appears as unchanged different free drug concentrations at different
drug in urine. serum drug concentrations.
CHAPTER SUMMARY
Nonlinear pharmacokinetics refers to kinetic pro- nonlinearity curving. A common cause of overdosing
cesses that result in disproportional changes in in clinical practice is undetected saturation of a meta-
plasma drug concentrations when the dose is bolic enzyme due to genotype difference in a subject,
changed. This is also referred to as dose-dependent for example, CYP2D6. A second common cause of
pharmacokinetics or saturation pharmacokinetics. overdosing in clinical practice is undetected satura-
Clearance and half-life are usually not constant with tion of a metabolic enzyme due to coadministration
dose-dependent pharmacokinetics. Carrier-mediated of a second drug/agent that alters the original linear
processes and processes that depend on the binding elimination process. Drug transporters play an impor-
of the drug to a macromolecule resulting in drug tant role in the body. Membrane-located transporters
metabolism, protein binding, active absorption, and may cause uneven drug distribution at cellular level,
some transporter-mediated processes can potentially and hiding concentration-dependent kinetics may
exhibit dose-dependent kinetics, especially at higher occur at the local level within body organs. These
doses. The Michaelis–Menten kinetic equation may processes include absorption and elimination and are
be applied in vitro or in vivo to describe drug dispo- important in drug therapy. Some transporters are trig-
sition, for example, phenytoin. gered by disease or expressed differently in individu-
An approach to determine nonlinear pharmaco- als and should be recognized by pharmacists during
kinetics is to plot AUC versus doses and observe for dosing regimen recommendation.
LEARNING QUESTIONS
1. Define nonlinear pharmacokinetics. How do 2. What processes of drug absorption, distribution,
drugs that follow nonlinear pharmacokinetics and elimination may be considered “capacity
differ from drugs that follow linear pharmaco- limited,” “saturated,” or “dose dependent”?
kinetics? 3. Drugs, such as phenytoin and salicylates, have
a. What is the rate of change in the plasma been reported to follow dose-dependent elimi-
drug concentration with respect to time, nation kinetics. What changes in pharmacoki-
dCp/dt, when Cp << KM? netic parameters, including t1/2, VD, AUC, and
b. What is the rate of change in the plasma Cp, could be predicted if the amounts of these
drug concentration with respect to time, drugs administered were increased from low
dCp/dt, when Cp >> KM? pharmacologic doses to high therapeutic doses?
Nonlinear Pharmacokinetics 255
4. A given drug is metabolized by capacity-limited 10. Which of the following statements is/are true
pharmacokinetics. Assume KM is 50 mg/mL, regarding the pharmacokinetics of diazepam
Vmax is 20 mg/mL per hour, and the apparent VD (98% protein bound) and propranolol
is 20 L/kg. (87% protein bound)?
a. What is the reaction order for the metabo- a. Diazepam has a long elimination half-life
lism of this drug when given in a single because it is difficult to be metabolized due
intravenous dose of 10 mg/kg? to extensive plasma–protein binding.
b. How much time is necessary for the drug to b. Propranolol is an example of a drug with high
be 50% metabolized? protein binding but unrestricted (unaffected)
5. How would induction or inhibition of the metabolic clearance.
hepatic enzymes involved in drug biotransfor- c. Diazepam is an example of a drug with low
mation theoretically affect the pharmacokinet- hepatic extraction.
ics of a drug that demonstrates nonlinear phar- d. All of the above.
macokinetics due to saturation of its hepatic e. a and c.
elimination pathway? f. b and c.
6. Assume that both the active parent drug and 11. Which of the following statements describe(s)
its inactive metabolites are excreted by active correctly the properties of a drug that follows
tubular secretion. What might be the conse- nonlinear or capacity-limited pharmacokinetics?
quences of increasing the dosage of the drug a. The elimination half-life will remain con-
on its elimination half-life? stant when the dose changes.
7. The drug isoniazid was reported to interfere with b. The area under the plasma curve (AUC) will
the metabolism of phenytoin. Patients taking both increase proportionally as dose increases.
drugs together show higher phenytoin levels in c. The rate of drug elimination = Cp × KM.
the body. Using the basic principles in this chap- d. All of the above.
ter, do you expect KM to increase or decrease in e. a and b.
patients taking both drugs? (Hint: see Fig. 10-4.) f. None of the above.
8. Explain why KM sometimes has units of mM/mL 12. The hepatic intrinsic clearances of two
and sometimes mg/L. drugs are
9. The Vmax for metabolizing a drug is 10 mmol/h. drug A: 1300 mL/min
The rate of metabolism (n) is 5 mmol/h when drug B: 26 mL/min
drug concentration is 4 mmol. Which of the fol- Which drug is likely to show the greatest increase
lowing statements is/are true? in hepatic clearance when hepatic blood ow is
a. KM is 5 mmol for this drug. increased from 1 L/min to 1.5 L/min?
b. KM cannot be determined from the informa- a. Drug A
tion given. b. Drug B
c. KM is 4 mmol for this drug. c. No change for both drugs
ANSWERS
Frequently Asked Questions hepatic enzyme systems. Alcoholics may have liver
Why is it important to monitor drug levels carefully cirrhosis and lack certain coenzymes. Other patients
for dose dependency? may experience enzyme saturation at normal doses
due to genetic polymorphism. Pharmacokinetics
• A patient with concomitant hepatic disease may provides a simple way to identify nonlinear kinet-
have decreased biotransformation enzyme activ- ics in these patients and to estimate an appropriate
ity. Infants and young subjects may have immature dose. Finally, concomitant use of other drugs may
256 Chapter 10
cause nonlinear pharmacokinetics at lower drug the metabolic profile based on Vmax and KM. The
doses due to enzyme inhibition. Michaelis–Menten model was applied mostly to
describe in vitro enzymatic reactions. When Vmax What are the main differences in pharmacokinetic
and KM are estimated in patients, blood flow is not
parameters between a drug that follows linear phar-
explicitly considered. This semiempirical method
macokinetics and a drug that follows nonlinear
was found by many clinicians to be useful in dos-
pharmacokinetics?
ing phenytoin. The organ clearance model was
• A drug that follows linear pharmacokinetics gen- more useful in explaining clearance change due to
erally has a constant elimination half-life and a impaired blood flow. In practice, the physiologic
constant clearance with an increase in the dose. model has limited use in dosing patients because
The steady-state drug concentrations and AUC blood flow data for patients are not available.
are proportional to the size of the dose. Nonlinear
pharmacokinetics results in dose-dependent Cl, t1/2, Learning Questions
and AUC. Nonlinear pharmacokinetics are often
2. Capacity-limited processes for drugs include:
described in terms of Vmax and KM. • Absorption
What is the cause of nonlinear pharmacokinetics Active transport
that is not dose related? Intestinal metabolism by microflora
• Distribution
• Chronopharmacokinetics is the main cause of non-
Protein binding
linear pharmacokinetics that is not dose related. • Elimination
The time-dependent or temporal process of drug
Hepatic elimination
elimination can be the result of rhythmic changes
Biotransformation
in the body. For example, nortriptyline and theoph-
Active biliary secretion
ylline levels are higher when administered between • Renal excretion
7 and 9 am compared to between 7 and 9 pm after
Active tubular secretion
the same dose. Biological rhythmic differences in
Active tubular reabsorption
clearance cause a lower elimination rate in the
morning compared to the evening. Other factors dose 10,000 µg
4. C0
p = = = 0.5 µg/mL
that cause nonlinear pharmacokinetics may result VD 20,000 mL
from enzyme induction (eg, carbamazepine) or
From Equation 10.1,
enzyme inhibition after multiple doses of the drug.
Furthermore, the drug or a metabolite may accu- dCp V C
Elimination rate = − = max p
mulate following multiple dosing and affect the dt KM +Cp
metabolism or renal elimination of the drug.
Because KM = 50 mg/mL, Cp << KM and the reac-
What are the main differences between a model based tion rate is first order. Thus, the above equation
on Michaelis–Menten kinetic (Vmax and KM) and the reduces to Equation 10.3.
physiologic model that describes hepatic metabolism
dCp V
based on clearance? maxCp
− = = k ′C
dt K p
M
• The physiologic model based on organ drug clear-
ance describes nonlinear drug metabolism in Vmax 20 µg/h
k ′ = = = 0.4 h−1
terms of blood flow and intrinsic hepatic clear- KM 50 µg
ance (Chapter 12). Drugs are extracted by the For first-order reactions,
liver as they are presented by blood flow. The
0.693 0.693
physiologic model accounts for the sigmoid pro- t1/2 = = =1.73 h
k ′ 0.4
file with changing blood flow and extraction,
whereas the Michaelis–Menten model simulates The drug will be 50% metabolized in 1.73 hours.
Nonlinear Pharmacokinetics 257
7. When INH is coadminstered, plasma phenytoin per liter, or micromoles per milliliter, because
concentration is increased due to a reduction reactions are expressed in moles and not milli-
in metabolic rate n. Equation 10.1 shows that n grams. In dosing, drugs are given in milligrams
and KM are inversely related (KM in denomi- and plasma drug concentrations are expressed
nator). An increase in KM will be accompanied as milligrams per liter or micrograms per
by an increase in plasma drug concentration. milliliter. The units of KM for pharmacoki-
Figure 10-4 shows that an increase in KM is netic models are estimated from in vivo data.
accompanied by an increase in the amount of They are therefore commonly expressed as
drug in the body at any time t. Equation 10.4 milligrams per liter, which is preferred over
relates drug concentration to KM, and it can be micrograms per milliliter because dose is usu-
seen that the two are proportionally related, ally expressed in milligrams. The two terms
although they are not linearly proportional to may be shown to be equivalent and convert-
each other due to the complexity of the equa- ible. Occasionally, when simulating amount of
tion. An actual study in the literature shows drug metabolized in the body as a function of
that k is increased severalfold in the presence time, the amount of drug in the body has been
of INH in the body. assumed to follow Michaelis–Menten kinetics,
8. The KM has the units of concentration. In and KM assumes the unit of D0 (eg, mg). In this
laboratory studies, KM is expressed in moles case, KM takes on a very different meaning.
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Physiologic Drug
11 Distribution and
Protein Binding
He Sun and Hong Zhao
Chapter Objectives PHYSIOLOGIC FACTORS OF DISTRIBUTION
»» Describe the physiology of drug After a drug is absorbed systemically from the site of administra-
distribution in the body. tion, the drug molecules are distributed throughout the body by the
»» Explain how drug distribution is systemic circulation. The location, extent, and distribution are
affected by blood flow, protein, dependent on the drug’s physicochemical properties and individual
and tissue binding. patient characteristics such as organ perfusion and blood flow. The
drug molecules are carried by the blood to the target site (receptor)
»» Describe how drug distribution
for drug action and to other (nonreceptor) tissues as well, where side
can affect the apparent volume
effects or adverse reactions may occur. These sites may be intra-
of distribution.
and/or extracellular. Drug molecules are distributed to eliminating
»» Explain how volume of organs, such as the liver and kidney, and to noneliminating tissues,
distribution, drug clearance, such as the brain, skin, and muscle. In pregnancy, drugs cross the
and half-life can be affected by placenta and may affect the developing fetus. Drugs can also be
protein binding. secreted in milk via the mammillary glands, into the saliva and into
other secretory pathways. A substantial portion of the drug may be
»» Determine drug–protein binding
constants using in vitro methods. bound to proteins in the plasma and/or in the tissues. Lipophilic
drugs deposit in fat, from which the drug may be slowly released.
»» Evaluate the impact of change Drug distribution throughout the body occurs primarily via
in drug–protein binding or the circulatory system, which consists of a series of blood vessels
displacement on free drug that carry the drug in the blood; these include the arteries that carry
concentration. blood to tissues, and the veins that return the blood back to the
heart. An average subject (70 kg) has about 5 L of blood, which is
equivalent to about 3 L of plasma (Fig. 11-1). About 50% of the
blood is in the large veins or venous sinuses. The volume of blood
pumped by the heart per minute—the cardiac output—is the product
of the stroke volume of the heart and the number of heartbeats per
minute. An average cardiac output is 0.08 L/69 left ventricular
contractions (heart beats)/min, or approximately 5.5 L/min in sub-
jects at rest. The cardiac output may be five to six times higher
during exercise. Left ventricular contraction may produce a sys-
tolic blood pressure of 120 mm Hg, and moves blood at a linear
speed of 300 mm/s through the aorta. Mixing of a drug solution in
the blood occurs rapidly at this flow rate. Drug molecules rapidly
diffuse through a network of fine capillaries to the tissue spaces
259
260 Chapter 11
Blood (4.5–5 L) both the drug and the cell membrane. Cell membranes
are composed of protein and a bilayer of phospho-
Plasma Blood cells lipid, which act as a lipid barrier to drug uptake.
(3 L) (2 L)
Thus, lipid-soluble drugs generally diffuse across
cell membranes more easily than highly polar or
Plasma
Intra- water-soluble drugs. Small drug molecules generally
(3 L) Extracellular
cellular water diffuse more rapidly across cell membranes than
water Interstitial
(15 L)
(27 L) water large drug molecules. If the drug is bound to a
(12 L) plasma protein such as albumin, the drug–protein
complex becomes too large for easy diffusion across
FIGURE 111 Major water volumes (L) in a 70-kg human.
the cell or even capillary membranes. A comparison
of diffusion rates for water-soluble molecules is
given in Table 11-1.
filled with interstitial fluid (Fig. 11-2). The intersti-
tial fluid plus the plasma water is termed extracel-
lular water, because these fluids reside outside the Diffusion and Hydrostatic Pressure
cells. Drug molecules may further diffuse from the The processes by which drugs transverse capillary
interstitial fluid across the cell membrane into the membranes into the tissue include passive diffu-
cell cytoplasm. sion and hydrostatic pressure. Passive diffusion is
Drug distribution is generally rapid, and most the main process by which most drugs cross cell
small drug molecules permeate capillary membranes membranes. Passive diffusion (see Chapter 14) is
easily. The passage of drug molecules across a cell the process by which drug molecules move from
membrane depends on the physicochemical nature of an area of high concentration to an area of low
Arteriole
(from artery)
Intracellular
uid
a
b
Tissue cell
Blood
capillary
Interstitial
uid
Venule
A (to vein)
Plasma Interstitial and Tissues and
lymph uids other body water
Bound Bound Bound
Free Free Free
B
FIGURE 112 Diffusion of drug from capillaries to interstitial spaces.
Physiologic Drug Distribution and Protein Binding 261
TABLE 111 Permeability of Molecules of Various Sizes to Capillaries
Diffusion Coefficient
Radius of Equivalent In Water Across Capillary
Molecular Weight Sphere A (0.1 mm) (cm2/s) × 105 (cm2/s × 100 g)
Water 18 3.20 3.7
Urea 60 1.6 1.95 1.83
Glucose 180 3.6 0.91 0.64
Sucrose 342 4.4 0.74 0.35
Raffinose 594 5.6 0.56 0.24
Inulin 5,500 15.2 0.21 0.036
Myoglobin 17,000 19 0.15 0.005
Hemoglobin 68,000 31 0.094 0.001
Serum albumin 69,000 0.085 <0.001
Data from Pappenheimer, JR: Passage of molecules through capillary walls, Physiol Rev 33(3):387–423, July 1953; Renkin EM: Transport of large molecules
across capillary walls, Physiologist 60:13–28, February 1964.
concentration. Passive diffusion is described by Fick’s pressure that allows small drug molecules to be
law of diffusion: filtered in the glomerulus of the renal nephron
(see Chapter 7).
Blood flow–facilitated drug distribution is rapid
dQ −DKA(Cp −Ct )
Rate of drug diffusion = and efficient, but requires pressure. As blood pres-
dt h sure gradually decreases when arteries branch into
(11.1) the small arterioles, the speed of flow slows and dif-
fusion into the interstitial space becomes diffusion or
where Cp − Ct is the difference between the drug concentration driven and facilitated by the large
concentration in the plasma (Cp) and in the tissue surface area of the capillary network. The average
(Ct); A is the surface area of the membrane; h is the pressure of the blood capillary is higher (+18 mm Hg)
thickness of the membrane; K is the lipid–water par- than the mean tissue pressure (−6 mm Hg), resulting
tition coefficient; and D is the diffusion constant. in a net total pressure of 24 mm Hg higher in the
The negative sign denotes net transfer of drug from capillary over the tissue. This pressure difference is
inside the capillary lumen into the tissue and extra- offset by an average osmotic pressure in the blood of
cellular spaces. Diffusion is spontaneous and tem- 24 mm Hg, pulling the plasma fluid back into the
perature dependent. Diffusion is distinguished from capillary. Thus, on average, the pressures in the tissue
blood flow–initiated mixing, which involves hydro- and most parts of the capillary are equal, with no net
static pressure. flow of water.
Hydrostatic pressure represents the pressure gra- At the arterial end, as the blood newly enters the
dient between the arterial end of the capillaries enter- capillary (Fig. 11-2A), the pressure of the capillary
ing the tissue and the venous capillaries leaving the blood is slightly higher (about 8 mm Hg) than that of
tissue. Hydrostatic pressure is responsible for pene- the tissue, causing fluid to leave the capillary and
tration of water-soluble drugs into spaces between enter the tissues. This pressure is called hydrostatic or
endothelial cells and possibly into lymph. In the filtration pressure. This filtered fluid (filtrate) is later
kidneys, high arterial pressure creates a filtration returned to the venous capillary (Fig. 11-2B) due to a
262 Chapter 11
lower venous pressure of about the same magnitude. electrolyte levels in renal and hepatic diseases,
The lower pressure of the venous blood compared resulting in net flow of plasma water into the inter-
with the tissue fluid is termed as absorptive pressure. stitial space (edema). This change in fluid distribu-
A small amount of fluid returns to the circulation tion may partially explain the increased extravascular
through the lymphatic system. drug distribution during some disease states.
Blood flow, tissue size, and tissue storage (par-
Distribution Half-Life, Blood Flow, titioning and binding) are also important in deter-
and Drug Uptake by Organs mining the time it takes the drug to become
completely distributed. Table 11-2 lists the blood
Because the process of drug transfer from the capil-
flow and tissue mass for many tissues in the human
lary into the tissue fluid is mainly diffusional,
body. Drug affinity for a tissue or organ refers to the
according to Fick’s law, the membrane thickness,
partitioning and accumulation of the drug in the tis-
diffusion coefficient of the drug, and concentration
sue. The time for drug distribution is generally mea-
gradient across the capillary membrane are impor-
sured by the distribution half-life or the time for 50%
tant factors in determining the rate of drug diffusion.
drug distribution. The factors that determine the distri-
Kinetically, if a drug diffuses rapidly across the
bution constant of a drug into an organ are the blood
membrane in such a way that blood flow is the rate-
flow to the organ, the volume of the organ, and the
limiting step in the distribution of drug, then the
process is perfusion or flow limited. A person with
congestive heart failure has a decreased cardiac out- TABLE 112 Blood Flow to Human Tissues
put, resulting in impaired blood flow, which may Percent Percent Blood Flow
reduce renal clearance through reduced filtration Body Cardiac (mL/100 g
pressure and blood flow. In contrast, if drug distribu- Tissue Weight Output tissue/min)
tion is limited by the slow diffusion of drug across Adrenals 0.02 1 550
the membrane in the tissue, then the process is
termed diffusion or permeability limited (Fig. 11-3). Kidneys 0.4 24 450
Drugs that are permeability limited may have an Thyroid 0.04 2 400
increased distribution volume in disease conditions
that cause inflammation and increased capillary Liver
membrane permeability. The delicate osmotic pres- Hepatic 2.0 5 20
sure balance may be altered due to changes in
albumin level and/or blood loss or due to changes in Portal 20 75
Portal-drained 2.0 20 75
Organ Organ viscera
Ct R Ct R
Heart (basal) 0.4 4 70
Ca Cv Ca Cv
Brain 2.0 15 55
Blood Blood Skin 7.0 5 5
V V
b b Muscle (basal) 40.0 15 3
pool pool
Connective 7.0 1 1
Diffusion-limited Perfusion-limited tissue
model model
(Slow diffusion (Rapid diffusion Fat 15.0 2 1
into tissue) into tissue)
Data from Spector WS: Handbook of Biological Data, Saunders,
FIGURE 113 Drug distribution to body organs by blood Philadelphia, 1956; Glaser O: Medical Physics, Vol 11, Year Book
flow (perfusion). Right panel for tissue with rapid permeability; Publishers, Chicago, 1950; Butler TC: Proc First International
Left panel for tissue with slow permeability. Pharmacological Meeting, Vol 6, Pergamon Press, 1962.
Physiologic Drug Distribution and Protein Binding 263
partitioning of the drug into the organ tissue, as
100 3 4 5
shown in Equation 11.2. 1+2
Q 80
k = (11.2)
d VR
where kd is first-order distribution constant, Q is 60
blood flow to the organ, V is volume of the organ, R
is ratio of drug concentration in the organ tissue to 40
drug concentration in the blood (venous). The distri- 1 = adrenal
bution half-life of the drug to the tissue, td1/2, may 2 = kidney
20 3 = skin
easily be determined from the distribution constant 4 = muscle [basal]
in the equation of td1/2 = 0.693/kd.
5 = fat
The ratio R is determined experimentally from 0
0 50 100 150 200 250 300 350
tissue samples. With many drugs, however, only Time (minutes)
animal tissue data are available. The ratio R is usu-
ally estimated based on knowledge of the partition FIGURE 115 Drug distribution in five groups of tissues
at various rates of equilibration.
coefficient of the drug. The partition coefficient is a
physical property that measures the ratio of the solu-
bility of the drug in the oil phase to solubility in
aqueous phase. The partition coefficient (Po/w) is longer time is needed to fill a large organ volume
defined as a ratio of the drug concentration in the oil with drug. Figure 11-5 illustrates the distribution
phase (usually represented by octanol) to the drug time (for 0%, 50%, 90%, and 95% distribution) for
concentration in the aqueous phase measured at the adrenal gland, kidney, muscle (basal), skin, and
equilibrium under specified temperature in vitro in fat tissue in an average human subject (ideal body
an oil/water two-layer system (Fig. 11-4). The parti- weight, IBW = 70 kg). In this illustration, the blood
tion coefficient is one of the most important factors drug concentration is equally maintained at 100 mg/
that determine the tissue distribution of a drug. mL, and the drug is assumed to have equal distribu-
If each tissue has the same ability to store the tion between all the tissues and blood, i.e., when
drug, then the distribution half-life is governed by fully equilibrated, the partition or drug concentration
the blood flow, Q, and volume (size), V, of the organ. ratio (R) between the tissue and the plasma will
A large blood flow, Q, to the organ decreases the equal 1. Vascular tissues such as the kidneys and
distribution time, whereas a large organ size or vol- adrenal glands achieve 95% distribution in less than
ume, V, increases the distribution time because a 2 minutes. In contrast, drug distribution time in fat
tissues takes 4 hours, while less in vascular tissues,
such as the skin and muscles, take between 2 and
Oil Diffusion into oil = k 4 hours (Fig. 11-5). When drug partition of the tissues
12 Cwater
(octanol) is the same, the distribution time is dependent only
on the tissue volume and its blood flow.
Coil
k Blood flow is an important factor in determin-
21
Diffusion into water = k21 Coil ing how rapid and how much drug reaches the
k receptor site. Under normal conditions, limited
12
Cwater blood flow reaches the muscles. During exercise,
the increase in blood flow may change the fraction
Water At steady state, k12 Cwater = k21 Coil of drug reaching the muscle tissues. Diabetic
patients receiving intramuscular injection of insulin
FIGURE 114 Diagram showing equilibration of drug may experience the effects of changing onset of drug
between oil and water layer in vitro. action during exercise. Normally, the blood reserve
mg/mL
264 Chapter 11
of the body stays mostly in the large veins and of the plasma drug concentration; thus, the anti-
sinuses in the abdomen. During injury or when androgen effect of the drug may not be fully
blood is lost, constriction of the large veins redirects achieved until distribution to this receptor site is
more blood to needed areas, and therefore, affects complete. Digoxin is highly bound to myocardial
drug distribution. Accumulation of carbon dioxide membranes. Digoxin has a high tissue/plasma con-
may lower the pH of certain tissues and may affect centration ratio (R = 60 − 130) in the myocardium.
the level of drugs reaching those tissues. This high R ratio for digoxin leads to a long distribu-
Figure 11-6 illustrates the distribution of a drug tional phase (see Chapter 5) despite abundant blood
to three different tissues when the partition of the flow to the heart. It is important to note that if a tis-
drug for each tissue varies. For example, the drug sue has a long distribution half-life, a long time is
partition shows that the drug concentration in the needed for the drug to leave the tissue as the blood
adrenal glands is five times of the drug concentration level decreases. Understanding drug distribution is
in the plasma, while the drug partition for the kidney important because the activities of many drugs are
is R = 3, and for basal muscle, R = 1. In this illustra- not well correlated with plasma drug levels.
tion, the adrenal gland and kidney take 5 and 3 times Kinetically, both drug–protein binding and drug
as long to be equilibrated with drug in the plasma. lipid solubility in the tissue site lead to longer distri-
Thus, it can be seen that, even for vascular tissues, bution times.
high drug partition can take much more time for the Chemical knowledge in molecular structure
tissue to become fully equilibrated. In the example in often helps estimate the lipid solubility of a drug. A
Fig. 11-6, drug administration is continuous (as in drug with large oil/water partition coefficient tends
IV infusion), since tissue drug levels remain constant to have high R values in vivo. A reduction in the
after equilibrium. partition coefficient of a drug often reduces the rate
Some tissues have great ability to store and of drug uptake into the brain. This may decrease
accumulate drug, as shown by large R values. For drug distribution into the central nervous system and
example, the anti-androgen drug, flutamide and its decrease undesirable central nervous system side
active metabolite are highly concentrated in the pros- effects. Extensive tissue distribution is kinetically
tate. The prostate drug concentration is 20 times that evidenced by a large volume of distribution. A sec-
ondary effect is a prolonged drug elimination half-
life, since the drug is distributed within a larger
volume (thus, the drug is more diluted) and there-
600 fore, less efficiently removed by the kidney or the
Top = adrenal liver. For example, etretinate (a retinoate derivative)
R = 5
500 for acne treatment has an unusual long elimination
half-life of about 100 days (Chien et al, 1992), due
400 to its extensive distribution to body fats. Newly syn-
R = 3 Middle = kidney thesized agents have been designed to reduce the
300 lipophilicity and drug distribution. These new agents
have less accumulation in the tissue and less poten-
200 tial for teratogenicity.
R = 1 Bottom = muscle
100
Drug Accumulation
0 The deposition or uptake of the drug into the tissue
0 50 100 150 200 250 300 is generally controlled by the diffusional barrier of
Time (minutes) the capillary membrane and other cell membranes.
FIGURE 116 Drug distribution in three groups of tissues For example, the brain is well perfused with blood,
with various abilities to store drug (R). but many drugs with good aqueous solubility have
mg/mL
Physiologic Drug Distribution and Protein Binding 265
high drug concentrations in the kidney, liver, and lung high doses of phenothiazine to chronic schizo-
and yet little or negligible drug concentration in the phrenic patients. The antibiotic tetracycline forms
brain. The brain capillaries are surrounded by a layer an insoluble chelate with calcium. In growing teeth
of tightly joined glial cells that act as a lipid barrier and bones, tetracycline complexes with the calcium
to impede the diffusion of polar or highly ionized and remain in these tissues.
drugs. A diffusion-limited model can be used to Some tissues have enzyme systems that actively
describe the pharmacokinetics of these drugs that are transport natural biochemical substances into the tis-
not adequately described by perfusion models. sues. For example, various adrenergic tissues have a
Tissues receiving high blood flow equilibrate specific uptake system for catecholamines, such as
quickly with the drug in the plasma. However, at norepinephrine. Thus, amphetamine, which has a
steady state, the drug may or may not accumulate phenylethylamine structure similar to norepineph-
(concentrate) within the tissue. The accumulation of rine, is actively transported into adrenergic tissue.
drug into tissues is dependent on both the blood flow Other examples of drug accumulation are well docu-
and the affinity of the drug for the tissue. Drug affin- mented. For some drugs, the actual mechanism for
ity for the tissue depends on partitioning and also drug accumulation may not be clearly understood.
binding to tissue components, such as receptors. In a few cases, the drug is irreversibly bound
Drug uptake into a tissue is generally reversible. The into a particular tissue. Irreversible binding of drug
drug concentration in a tissue with low capacity may occur when the drug or a reactive intermediate
equilibrates rapidly with the plasma drug concentra- metabolite becomes covalently bound to a macro-
tion and then declines rapidly as the drug is elimi- molecule within the cell, such as to a tissue protein.
nated from the body. Many purine and pyrimidine drugs used in cancer
In contrast, drugs with high tissue affinity tend chemotherapy are incorporated into nucleic acids,
to accumulate or concentrate in the tissue. Drugs causing destruction of the cell.
with a high lipid/water partition coefficient are very
lipid soluble and tend to accumulate in lipid or adi-
pose (fat) tissue. In this case, the lipid-soluble drug Permeability of Cells and
partitions from the aqueous environment of the Capillary Membranes
plasma into the fat. This process is reversible, but Cellular and plasma membranes vary in their perme-
the extraction of drug out of the tissue is so slow ability characteristics, depending on the tissue. For
that the drug may remain for days or even longer in example, capillary membranes in the liver and kid-
adipose tissues, long after the drug is depleted from neys are more permeable to transmembrane drug
the blood. Because the adipose tissue is poorly per- movement than capillaries in the brain. The sinusoi-
fused with blood, drug accumulation is slow. dal capillaries of the liver are very permeable and
However, once the drug is concentrated in fat tissue, allow the passage of large-size molecules. In the
drug removal from fat may also be slow. For exam- brain and spinal cord, the capillary endothelial cells
ple, the insecticide, chlorinated hydrocarbon DDT are surrounded by a layer of glial cells, which have
(dichlorodiphenyltrichloroethane) is highly lipid tight intercellular junctions. This added layer of cells
soluble and remains in fat tissue for years. around the capillary membranes acts effectively to
In addition to partitioning, drugs may accumu- slow the rate of drug diffusion into the brain by act-
late in tissues by other processes. For example, ing as a thicker lipid barrier. This lipid barrier, which
drugs may accumulate by binding to proteins or slows the diffusion and penetration of water-soluble
other macromolecules in a tissue. Digoxin is highly and polar drugs into the brain and spinal cord, is
bound to proteins in cardiac tissue, leading in a called the blood–brain barrier.
large volume of distribution (440 L/70 kg) and long Under certain pathophysiologic conditions, the
elimination t1/2 (approximately 40 hours). Some permeability of cell membranes, including capil-
drugs may complex with melanin in the skin and lary cell membranes, may be altered. For example,
eye, as observed after long-term administration of burns will alter the permeability of skin and allow
266 Chapter 11
drugs and larger molecules to permeate inward or for any of the transporters or enzyme systems. It is
outward. In meningitis, which involves inflamma- also important to determine whether the pharmaco-
tion of the membranes of the spinal cord and/or kinetic models have adequately taken transporter
brain, drug uptake into the brain will be enhanced. information into consideration.
The diameters of the capillaries are very small
and the capillary membranes are very thin. The
high blood flow within a capillary allows for inti- Drug Distribution to Cerebral Spinal Fluid,
mate contact of the drug molecules with the plasma CSF, and Brain: Blood–Brain Barrier
membrane, providing for rapid drug diffusion. For
The blood–brain barrier permits selective entry of
capillaries that perfuse the brain and spinal cord,
drugs into the brain and spinal cord due to (1) ana-
the layer of glial cells functions effectively to
tomical features (as mentioned above) and (2) the
increase the thickness (term h in Equation 11.1),
presence of cellular transporters. Anatomically, the
thereby slowing the diffusion and penetration of
layer of cells around the capillary membranes of
water-soluble and polar drugs into the brain and
the brain acts effectively as a thicker lipid barrier
spinal cord.
that slows the diffusion and penetration of water-
soluble and polar drugs into the brain and spinal
Drug Distribution within Cells and Tissues cord. However, some small hydrophilic molecules
Pharmacokinetic models generally provide a good may cross the blood–brain barrier by simple diffu-
estimation of plasma drug concentrations in the body sion. Efflux transporter is often found at the entry
based on dose, volume of distribution, and clearance. point into vital organs in the body. P-glycoprotein
However, drug concentrations within the cell or expression in the endothelial cells of human capil-
within a special region in the body are also governed lary blood vessels at the blood–brain was detected
by special efflux and metabolizing enzyme systems by special antibodies against the human multidrug-
that prevent and detoxify foreign agents entering the resistance gene product. P-gp may have a physiolog-
body. Some proteins are receptors on cell surfaces ical role in regulating the entry of certain molecules
that react specifically with a drug. The transporters into the central nervous system and other organs
are specialized proteins in the body that can associ- (Cordoncardo et al, 1989). P-gp substrate examples
ate transiently with a substrate drug through the include doxorubicin, inmervectin, and others.
hydrophobic region in the molecule, for example, Knocking out P-gp expression can increase brain
P-glycoprotein, P-gp. Drug-specific transporters are toxicity with inmervectin in probe studies. Kim et al
very important in preventing drug accumulation in (1998) studied transport characteristics of protease
cells and may cause drug tolerance or drug resis- inhibitor drugs, indinavir, nelfinavir, and saquinavir
tance. Transporters can modulate drug absorption in vitro using the model P-gp expressing cell lines
and disposition (see Chapters 13 and 14). Special and in vivo administration in the mouse model. After
families of transporters are important and well docu- IV administration, plasma concentrations of the drug
mented (You and Morris, 2007). For example, mono- in mdr1a (−/−) mice, the brain concentrations were
carboxylate transporters, organic cation transporters, elevated 7 to 36-fold. These data demonstrate that
organic anion transporters, oligopeptide transporters, P-gp can limit the penetration of these drugs into the
nucleoside transporters, bile acid transporters, and brain. Efflux transporters (ie, P-gp) effectively pre-
multidrug resistance protein (eg, P-gp) that modulate vent certain small drug substances from entering into
distribution of many types of drugs. Drug transport- the brain, whereas influx transporters enable small
ers in the liver, kidney, brain, and gastrointestinal are nutrient molecules such as glucose to be actively
discussed by You and Morris (2007) (see also taken into the brain. There is now much interest in
Chapter 13 and Fig. 14-1 in Chapter 14). When con- understanding the mechanisms for drug uptake into
sidering drug utilization and drug–drug interactions, brain in order to deliver therapeutic and diagnostic
it is helpful to know whether the drug is a substrate agents to specific regions of the brain.
Physiologic Drug Distribution and Protein Binding 267
CLINICAL FOCUS that system. The volume of the system may be esti-
mated if the amount of drug added to the system and
Jaundice is a condition marked by high levels of bili- the drug concentration after equilibrium in the sys-
rubin in the blood. New born infants with jaundice tem are known.
are particularly sensitive to the effects of bilirubin
since their blood–brain barrier is not well formed at Volume (L)
birth. The increased bilirubin, if untreated, may
cause jaundice, and damage the brain centers of infants amount (mg) of drug added to system
=
drug concentration (mg/L) in system after equilibrium
caused by increased levels of unconjugated, indirect
bilirubin which is free (not bound to albumin). This (11.3)
syndrome is also known as kernicterus. Depending
on the level of exposure to bilirubin, the effects range Equation 11.3 describes the relationship of concentra-
from unnoticeable to severe brain damage. Treatment tion, volume, and mass, as shown in Equation 11.4.
in some cases may require phototherapy that requires
special blue lights that work by helping to break down Concentration (mg/L) × volume (L) = mass (mg)
bilirubin in the skin. (11.4)
Frequently Asked Questions Considerations in the Calculation of Volume
»»How does a physical property, such as partition coef- of Distribution: A Simulated Example
ficient, affect drug distribution?
The objective of this exercise is to calculate the fluid
»»Why do some tissues rapidly take up drugs, whereas volume in each beaker and to compare the calculated
for other tissues, drug uptake is slower? volume to the real volume of water in the beaker.
»»Does rapid drug uptake into a tissue mean that the Assume that three beakers are each filled with 100 mL
drug will accumulate into that tissue? of aqueous fluid. Beaker 1 contains water only; bea-
kers 2 and 3 each contain aqueous fluid and a small
»»What physical and chemical characteristics of a drug compartment filled with cultured cells. The cells in
that would increase or decrease the uptake of the
beaker 2 can bind the drug, while the cells in beaker 3
drug into the brain or cerebral spinal fluid?
can metabolize the drug. The three beakers represent
the following, respectively:
APPARENT VOLUME DISTRIBUTION Beaker 1. Drug distribution in a fluid (water)
compartment only, without drug binding and
The concentration of drug in the plasma or tissues
metabolism
depends on the amount of drug systemically
Beaker 2. Drug distribution in a fluid compartment
absorbed and the volume in which the drug is dis-
containing cell clusters that reversibly bind
tributed. The apparent volume of distribution, VD in
drugs
a pharmacokinetic model, is used to estimate the
Beaker 3. Drug distribution in a fluid compart-
extent of drug distribution in the body (see Chapters 3
ment containing cell clusters (similar to tissues
and 5). Although the apparent volume of distribu-
in vivo) in which the drug may be metabolized
tion does not represent a true anatomical or physical
and the metabolites bound to cells
volume, the VD represents the result of dynamic
drug distribution between the plasma and the tissues Suppose 100 mg of drug is then added to each
and accounts for the mass balance of the drug in the beaker (Fig. 11-7). After the fluid concentration of
body. To illustrate the use of VD, consider a drug drug in each beaker is at equilibration, and the con-
dissolved in a simple solution. A volume term is centration of drug in the water (fluid) compartment
needed to relate drug concentration in the system has been sampled and assayed, the volume of water
(or human body) to the amount of drug present in may be computed.
268 Chapter 11
Assume that the above measurements were made
Fluid (water) and that the following information was obtained:
compartment
• Drug concentration in fluid compartment =
Cell
compartment 0.5 mg/mL
Beaker 1 Beaker 2 Beaker 3 • Drug concentration in cell cluster = 10 mg/mL
• Volume of cell cluster = 5 mL
FIGURE 117 Experiment simulating drug distribution in • Amount of drug added = 100 mg
the body. Three beakers, each contains 100 mL of water (fluid • Amount of drug taken up by the cell cluster =
compartment) and 100 mg of a water-soluble drug. Beakers 2
and 3 also contain 5 mL of cultured cell clusters. 10 mg/mL × 5 mL = 50 mg
• Amount of drug dissolved in uid (water) com-
partment = 100 mg (total) − 50 mg (in cells) =
Case 1 50 mg (in water)
The volume of water in beaker 1 is calculated from Using the above information, the true volume of the
the amount of drug added (100 mg) and the equili- fluid (water) compartment is calculated using
brated drug concentration using Equation 11.3. Equation 11.3.
After equilibration, the drug concentration was
50 mg
measured to be 1 mg/mL. Volume of fluid compartment = = 100 mL
0.5 mg/mL
Volume = 100 mg/1 mg/mL = 100 mL The value of 100 mL agrees with the volume of fluid
we put into the beaker.
The calculated volume in beaker 1 confirms that the If the tissue cells were not accessible for sam-
system is a simple, homogeneous system and, in this pling as in the case of in vivo drug administration,
case, represents the “true” fluid volume of the beaker. the volume of the fluid (water) compartment is cal-
culated using Equation 11.3, assuming the system is
Case 2 homogenous and that 100 mg drug was added to the
Beaker 2 contains cell clusters stuck to the bottom of system.
the beaker. Binding of drug to the proteins of the cells
occurs on the surface and within the cytoplasmic 100 mg
Apparent volume = = 200 mL
interior. This case represents a heterogeneous system 0.5 mg/mL
consisting of a well-stirred fluid compartment and a
The value of 200 mL is a substantial overestimation
tissue (cell). To determine the volume of this system,
of the true volume (100 mL) of the system.
more information is needed than in Case 1:
When a heterogeneous system is involved, the
1. The amount of drug dissolved in the fluid com- real or true volume of the system may not be accu-
partment must be determined. Because some of rately calculated by monitoring only one compart-
the drug will be bound within the cell compart- ment. Therefore, an apparent volume of distribution
ment, the amount of drug in the fluid compart- is calculated and the infrastructure of the system is
ment will be less than the 100 mg placed in the ignored. The term apparent volume of distribution
beaker. refers to the lack of true volume characteristics. The
2. The amount of drug taken up by the cell cluster apparent volume of distribution is used in pharmaco-
must be known to account for the entire amount kinetics because the tissue (cellular) compartments
of drug in the beaker. Therefore, both the cell are not easily sampled and the true volume is not
and the fluid compartments must be sampled known. When the experiment in beaker 2 is per-
and assayed to determine the drug concentra- formed with an equal volume of cultured cells that
tion in each compartment. have different binding affinity for the drug, then the
3. The volume of the cell cluster must be apparent volume of distribution is very much affected
determined. by the extent of cellular drug binding (Table 11-3).
Physiologic Drug Distribution and Protein Binding 269
TABLE 113 Relationship of Volume of Distribution and Amount of Drug in Tissue (Cellular)
Compartmenta
Total Drug Volume of Cells Drug in Cells Drug in Water Drug Concentration
(mg) (mL) (mg) (mg) in Water (mg/mL) VD in Water (mL)
100 15 75 25 0.25 400
100 10 50 50 0.50 200
100 5 25 75 0.75 133
100 1 5 95 0.95 105
aFor each condition, the true water (fluid) compartment is 100 mL. Apparent volume of distribution (VD) is calculated according to Equation 11.3.
As shown in Table 11-3, as the amount of drug volume of distribution. A true VD that exceeds the
in the cell compartment increases (column 3), the volume of the body is physically impossible. Only if
apparent VD of the fluid compartment increases (col- the drug concentrations in both the tissue and plasma
umn 6). Extensive cellular drug binding effectively compartments are sampled, and the volumes of each
pulls drug molecules out of the fluid compartment, compartment are clearly defined, can a true physical
decreases the drug concentration in the fluid com- volume be calculated.
partment, and increases VD. In biological systems,
the quantity of cells, cell compartment volume, and Case 3
extent of drug binding within the cells affect VD.
The drug in the cell compartment in beaker 3
A large cell volume and/or extensive drug binding in
decreases due to undetected metabolism because the
the cells reduce the drug concentration in the fluid
metabolite formed is bound to be inside the cells.
compartment and increase the apparent volume of
Thus, the apparent volume of distribution is also
distribution.
greater than 100 mL. Any unknown source that
In this example, the fluid compartment is com-
decreases the drug concentration in the fluid com-
parable to the central compartment and the cell
partment will increase the VD, resulting in an overes-
compartment is analogous to the peripheral or tissue
timated apparent volume of distribution. This is
compartment. If the drug is distributed widely into
illustrated with the experiment in beaker 3. In beaker 3,
the tissues or concentrated unevenly in the tissues,
the cell cluster metabolizes the drug and binds the
the VD for a drug may exceed the physical volume of
metabolite to the cells. Therefore, the drug is effec-
the body (about 70 L of total volume or 42 L of body
tively removed from the fluid. The data for this
water for a 70-kg subject). Besides cellular protein
experiment (note that metabolite is expressed as
binding, partitioning of drug into lipid cellular com-
equivalent intact drug) are as follows:
ponents may greatly inflate VD. Many drugs have
oil/water partition coefficients above 10,000. These • Total drug placed in beaker = 100 mg
lipophilic drugs are mostly concentrated in the lipid • Cell compartment:
phase of adipose tissue, resulting in a very low drug Drug concentration = 0.2 mg/mL
concentration in the extracellular water. Generally, Metabolite-bound concentration = 9.71 mg/mL
drugs with very large VD values have very low drug Metabolite-free concentration = 0.29 mg/mL
concentrations in plasma. Cell volume = 5 mL
A large VD is often interpreted as broad drug • Fluid (water) compartment:
distribution for a drug, even though many other fac- Drug concentration = 0.2 mg/mL
tors also lead to the calculation of a large apparent Metabolite concentration = 0.29 mg/mL
270 Chapter 11
To calculate the total amount of drug and metab- drug concentration to the amount of drug in the
olite in the cell compartment, Equation 11.3 is rear- body (Equation 11.3). Equation 11.3 relating
ranged as shown: the total mass of drug to drug concentration
and volume of distribution is important in
Total drug and metabolite in cells = 5 mL pharmacokinetics.
× (0.2 + 9.96 + 0.29 mg/mL) = 52.45 mg
Therefore, the total drug and metabolite in the fluid PRACTICE PROBLEM
compartment is 100 − 52.45 mg = 47.55 mg. The amount of drug in the system calculated from VD
If only the intact drug is considered, VD is calcu- and the drug concentration in the fluid compartment
lated using Equation 11.3. is shown in Table 11-3. Calculate the amount of drug
100 mg in the system using the true volume and the drug
VD = = 500 mL
0.2 mg/mL concentration in the fluid compartment.
Considering that only 100 mL of water was Solution
placed into beaker 3, the calculated apparent volume In each case, the product of the drug concentration
of distribution of 500 mL is an overestimate of the (column 5) and the apparent volume of distribution
true fluid volume of the system. (column 6) yields 100 mg of drug, accurately
The following conclusions can be drawn from accounting for the total amount of drug present in
this beaker exercise: the system. For example, 0.25 mg/mL × 400 mL =
1. Drug must be at equilibrium in the system 100 mg. Notice that the total amount of drug present
before any drug concentration is measured. In cannot be determined using the true volume and the
nonequilibrium conditions, the sample removed drug concentration (column 5).
from the system for drug assay does not repre- The physiologic approach requires detailed
sent all parts of the system. information, including (1) cell drug concentration,
2. Drug binding distorts the true physical volume (2) cell compartment volume, and (3) fluid compart-
of distribution when all components in the ment volume. Using the physiologic approach, the
system are not properly sampled and assayed. total amount of drug is equal to the amount of drug
Extravascular drug binding increases the in the cell compartment and the amount of drug in
apparent V the fluid compartment.
D.
3. Both intravascular and extravascular drug bind-
(15 mg/mL × 5 mL) + (100 mL × 0.25 mg/mL)
ing must be determined to calculate meaningful
volumes of distribution. = 100 mg
4. The apparent VD is essentially a measure of
The two approaches shown above each account
the relative extent of drug distribution outside
correctly for the amount of drug present in the sys-
the plasma compartment. Greater tissue drug
tem. However, the second approach requires more
binding and drug accumulation increases VD,
information than is commonly available. The second
whereas greater plasma protein drug binding
approach does, however, make more physiologic
decreases the VD distribution.
sense. Most physiologic compartment spaces are not
5. Undetected cellular drug metabolism
clearly defined for measuring drug concentrations.
increases VD.
6. An apparent VD larger than the combined vol-
ume of plasma and body water is indicative of Complex Biological Systems and VD
(4) and (5), or both, above. The above example illustrates how the VD repre-
7. Although the VD is not a true physiologic sents the apparent volume into which a drug
volume, the VD is useful to relate the plasma appears to distribute, whether into a beaker of fluid
Physiologic Drug Distribution and Protein Binding 271
or the human body. The human body is a much the drug concentration in the plasma compartment
more complex system than a beaker of water con- (Fig. 11-9A). In a physiological system involving a
taining drug metabolizing cells. Many components drug distributed to a given tissue from the plasma
within cells, tissues, or organs can bind to or fluid (Fig. 11-9B), the two-compartment model is
metabolize drug, thereby influencing the apparent not assumed, and drug distribution from the plasma
VD. Only free, unbound drug diffuses between the to a tissue is equilibrated by perfusion with arterial
plasma and tissue fluids. The tissue fluid, in turn, blood and returned by venous blood. The model
equilibrates with the intracellular water inside the tis- parameter Vapp is used to represent the apparent dis-
sue cells. The tissue drug concentration is influenced tribution volume in this model, which is different
by the partition coefficient (lipid/water affinity) of from VDSS used in the compartment model. Similar
the drug and tissue protein drug binding. The distri- to the apparent volume simulated in the beaker
bution of drug in a biological system is illustrated experiment in Equation 11.3, Vapp is defined by
by Fig. 11-8. Equation 11.5, and the amount of drug in the body
is given by Equation 10.6.
Apparent Volume of Distribution
D
The apparent volume of distribution, in general, Vap = B
p (11.5)
Cp
relates the plasma drug concentration to the amount
of drug present in the body. In classical compart- DB = VpCp + VtCt (11.6)
ment models, VDSS is the volume of distribution
determined at steady state when the drug concentra- where DB is the amount of drug in the body, Vp is the
tion in the tissue compartment is at equilibrium with plasma fluid volume, Vt is the tissue volume, Cp is
TISSUES
Clinical response Drug – Receptor
PLASMA
Receptor Protein Drug – Protein
+ +
Drug Drug
KIDNEY LIVER
Carrier + Drug Drug + Enzymes
Drug – Carrier Metabolites
Excretion Active renal Excretion Excretion
in urine secretion in urine in bile
FIGURE 118 Effect of reversible drug–protein binding on drug distribution and elimination. Drugs may bind reversibly with
proteins. Free (nonbound) drugs penetrate cell membranes, distributing into various tissues including those tissues involved in drug
elimination, such as kidney and liver. Active renal secretion, which is a carrier-mediated system, may have a greater affinity for free
drug molecules compared to plasma proteins. In this case, active renal drug excretion allows for rapid drug excretion despite drug–
protein binding. If a drug is displaced from the plasma proteins, more free drug is available for distribution into tissues and interac-
tion with the receptors responsible for the pharmacologic response. Moreover, more free drug is available for drug elimination.
272 Chapter 11
Plasma Tissue calculations of steady-state VD involve some assump-
tions on how and where the drug distributes in the
k12
Binding? Partition? body; it could involve a physiologic or a compartmen-
k Compartment model
21 Binding? tal approach.
Partition? Adsorption?
For a drug that involves protein binding, some
models assume that the drug distributes from the
plasma water into extracellular tissue fluids, where
the drug binds to extravascular proteins, resulting in
Blood Arterial Tissue a larger VD due to extravascular protein binding.
blood However, drug binding and distribution to lipoid tis-
Albumin and ow
Tissue and sues are generally not distinguishable. If the pharma-
AAG albumin Physiologic model
binding binding (Only one tissue shown) cokineticist suspects distribution to body lipids
Venous because the drug involved is very lipophilic, he or she
blood
ow may want to compare results simulated with different
models before making a final conclusion.
FIGURE 119 A diagram showing (upper panel) a two- Figure 11-10 lists the steady-state volume of dis-
compartment model approach to drug distribution; (lower tribution of 10 common drugs in ascending order.
panel) a physiologic approach to drug distribution.
Most of these drugs follow multicompartment kinetics
with various tissue distribution phases. The physio-
the plasma drug concentration, and Ct is the tissue logic volumes of an ideal 70-kg subject are also plotted
drug concentration. for comparison: (1) the plasma (3 L), (2) the extracel-
For many protein-bound drugs, the ratio of lular fluid (15 L), and (3) the intracellular fluid (27 L).
D Drugs such as penicillin, cephalosporin, valproic acid,
B/Cp is not constant over time, and this ratio
depends on the nature of dissociation of the protein– and furosemide are polar compounds that stay mostly
drug complex and how the free drug is distributed; within the plasma and extracellular fluids and there-
the ratio is best determined at steady state. Protein fore have a relatively low VD.
binding to tissue has an apparent effect of increasing In contrast, drugs with low distribution to the
the apparent volume of distribution. Several V extracellular water are more extensively distributed
D
terms were introduced in the classical compartment inside the tissues and tend to have a large VD. An
models (see Chapter 5). However, protein binding excessively high volume of distribution (greater than
was not introduced in those models. the body volume of 70 L) is due mostly to special
Equation 11.6 describes the amount of drug in tissue storage, tissue protein binding, carrier, or
the body at any time point between a tissue and the efflux system which removes drug from the plasma
plasma fluid. Instead of assuming that the drug dis- fluid. Digoxin, for example, is bound to myocardial
tributes to a hypothetical compartment, it is assumed membrane that has drug levels that are 60 and 130
that, after injection, the drug diffuses from the times the serum drug level in adults and children,
plasma to the extracellular fluid/water, where it fur- respectively (Park et al, 1982). The high tissue bind-
ther equilibrates with the given tissue. One or more ing is responsible for the large steady-state volume
tissue types may be added to the model if needed. If of distribution (see Chapter 5). The greater drug
the drug penetrates inside the cell, distribution into affinity also results in longer distribution half-life
the intracellular water may occur. If the volume of despite the heart’s great vascular blood perfusion.
body fluid and the protein level are known, this Imipramine is a drug that is highly protein bound
information may be incorporated into the model. and concentrated in the plasma, yet its favorable tis-
Such a model may be more compatible with the sue partition and binding accounts for a large volume
physiology and anatomy of the human body. of distribution. Several tricyclic antidepressants
When using pharmacokinetic parameters from (TCAs) also have large volumes of distribution due
the literature, it is important to note that most to tissue (CNS) penetration and binding.
Physiologic Drug Distribution and Protein Binding 273
Plasma
Chlorpropamide
Cefazolin
Furosemide
Valproic acid
Extracellular water
Ampicillin
Intracellular water
Methotrexate
Body water
Phenytoin
Lithium
Cimetidine
Diazepam
Gentamicin
Digoxin
Imiprimine
Chloroquine
0 20 40 60 80 100 120 240 1600 13000
Volume of distribution, VD (liters)
FIGURE 1110 Lists of steady-state volumes of distribution of 10 common drugs in ascending order showing various factors
that affect VD. Drugs with high VD generally have high tissue affinity or low binding to serum albumin. Polar or hydrophilic drugs
tend to have VD similar to the volume of extracellular water.
bonding. Irreversible drug binding accounts for cer-
Frequently Asked Questions tain types of drug toxicity that may occur over a long
»»Why is the volume of distribution, VD, considered time period, as in the case of chemical carcinogene-
an “apparent” volume and not a “true” anatomic or sis, or within a relatively short time period, as in the
physiologic volume? case of drugs that form reactive chemical intermedi-
»»Can the VD have a volume equal to a true anatomic ates. For example, the hepatotoxicity of high doses of
volume in the body? acetaminophen is due to the formation of reactive
metabolite intermediates that interact with liver
proteins.
Most drugs bind or complex with proteins by a
PROTEIN BINDING OF DRUGS reversible process. Reversible drug–protein binding
implies that the drug binds the protein with weaker
Many drugs interact with plasma or tissue proteins or chemical bonds, such as hydrogen bonds or van der
with other macromolecules, such as melanin and Waals forces. The amino acids that compose the
DNA, to form a drug–macromolecule complex. The protein chain have hydroxyl, carboxyl, or other sites
formation of a drug–protein complex is often named available for reversible drug interactions.
drug–protein binding. Drug–protein binding may be Reversible drug–protein binding is of major
a reversible or an irreversible process. Irreversible interest in pharmacokinetics. The protein-bound
drug–protein binding is usually a result of chemical drug is a large complex that cannot easily transverse
activation of the drug, which then attaches strongly to the capillary wall and therefore has a restricted dis-
the protein or macromolecule by covalent chemical tribution (Fig. 11-11). Moreover, the protein-bound
274 Chapter 11
Plasma Extracellular water TABLE 115 Considerations in the Study of
Drug–Protein Binding
Equilibrium between bound and free drug must be
maintained.
The method must be valid over a wide range of drug and
protein concentrations.
Drug Extraneous drug binding or drug adsorption onto the
Albumin apparatus walls, membranes, or other components must
be avoided or considered in the method.
Protein Drug Bound drug Denaturation of the protein or contamination of the pro-
tein must be prevented.
FIGURE 1111 Diagram showing that bound drugs will The method must consider pH and ionic concentrations of
not diffuse across membrane but free drug will diffuse freely the media and Donnan effects due to the protein.
between the plasma and extracellular water.
The method should be capable of detecting both revers-
ible and irreversible drug binding, including fast- and slow-
phase associations and dissociations of drug and protein.
drug is usually pharmacologically inactive. In con-
trast, the free or unbound drug crosses cell mem- The method should not introduce interfering substances,
such as organic solvents.
branes and is therapeutically active. Studies that
critically evaluate drug–protein binding are usually The results of the in vitro method should allow extrapola-
performed in vitro using a purified protein such as tion to the in vivo situation.
albumin. Methods for studying protein binding, Data from Bridges and Wilson (1976).
including equilibrium dialysis and ultrafiltration,
make use of a semipermeable membrane that sepa-
rates the protein and protein-bound drug from the glycoprotein, lipoproteins, immunoglobulins (IgG),
free or unbound drug (Table 11-4). By these in vitro and erythrocytes (RBC).
methods, the concentrations of bound drug, free Albumin is a protein with a molecular weight of
drug, and total protein may be determined. Each 65,000 to 69,000 Da that is synthesized in the liver
method for the investigation of drug–protein binding and is the major component of plasma proteins
in vitro has advantages and disadvantages in terms of responsible for reversible drug binding (Table 11-6).
cost, ease of measurement, time, instrumentation, In the body, albumin is distributed in the plasma and
and other considerations. Various experimental fac- in the extracellular fluids of skin, muscle, and various
tors for the measurement of protein binding are
listed in Table 11-5.
Drugs may bind to various macromolecular TABLE 116 Major Proteins to Which Drugs
components in the blood, including albumin, a1-acid Bind in Plasma
Normal Range of
Molecular Concentrations
Weight
TABLE 114 Methods for Studying Drug– Protein (Da) (g/L) (mol/L)
Protein Binding
Albumin 65,000 35–50 5–7.5 × 10–4
Equilibrium dialysis Gel chromatography
a1-Acid 44,000 0.4–1.0 0.9–2.2 × 10–5
Dynamic dialysis Spectrophotometry glycoprotein
Diafiltration Electrophoresis
Lipoproteins 200,000– Variable
Ultrafiltration Optical rotatory dispersion 3,400,000
and circulatory dichroism
From Tozer (1984), with permission.
Physiologic Drug Distribution and Protein Binding 275
other tissues. Interstitial fluid albumin concentration with severe renal impairment. The authors postulated
is about 60% of that in the plasma. The elimination that reduced protein binding in the renal disease sub-
half-life of albumin is 17 to 18 days. Normally, albu- jects may be responsible for the prolonged sedation.
min concentration is maintained at a relatively con- The drug is mainly cleared by hepatic metabolism
stant level of 3.5% to 5.5% (weight per volume) or and is highly protein bound. The example indicates
4.5 mg/dL. Albumin is responsible for maintaining that simple kinetic extrapolation may be inappropriate
the osmotic pressure of the blood and for the trans- in many clinical situations.
port of endogenous and exogenous substances in the
• Could reduced protein binding change the con-
plasma. Albumin complexes with endogeneous sub-
centration of the active drug in the central nervous
stances such as free fatty acids (FFAs), bilirubin, vari-
system, CNS?
ous hormones (eg, cortisone, aldosterone, thyroxine,
• Is the drug a substrate for a transporter?
tryptophan), and other compounds. Many weak
acidic (anionic) drugs bind to albumin by electro-
static and hydrophobic bonds. Weak acidic drugs Case 2
such as salicylates, phenylbutazone, and penicillins Diazepam (Valium) is a benzodiazepine derivative for
are highly bound to albumin. However, the strength anxiolytic, sedative, muscle-relaxant, and anticonvul-
of the drug binding is different for each drug. sant effects. Diazepam is highly protein bound
Alpha-1-acid glycoprotein (AAG), also known as (98.7%) in plasma. Ochs et al (1981) examined the
orosomucoid, is a globulin with a molecular weight effect of changing protein binding on diazepam distri-
of about 44,000 Da. The plasma concentration of bution in subjects with normal renal function versus
AAG is low (0.4%–1%) and it binds primarily basic patients with renal failure. The authors found no sig-
(cationic) drugs such as saquinavir, propranolol, nificant change in clearance of unbound drug in the
imipramine, and lidocaine (see below). subjects with renal failure. Previous studies have sug-
Globulins (a-, b-, g-globulins) may be respon- gested that changes in protein binding may be associ-
sible for the plasma transport of certain endogenous ated with altered drug disposition for some drugs.
substances such as corticosteroids. These globulins Ochs et al (1981) also studied diazepam disposition in
have a low capacity but high affinity for the binding hyperthyroidism and found no significant difference
of these endogenous substances. in diazepam disposition in hyperthyroid patients ver-
sus matched controls.
It is important to remember that each drug has
CLINICAL EXAMPLES a unique molecular structure. Although one drug
may have comparable protein binding, the capacity
Case 1 to bind proteins and the drug–protein binding con-
Dexmedetomidine hydrochloride injection (Precedex®) stant may be different among similar drugs as dis-
is an a-2-adrenergic agonist with sedative and anal- cussed later in this chapter. Individual patient
gesic properties that is given intravenously using a characteristics and kinetic parameters are also very
controlled infusion device. The pharmacokinetics of important. Qin et al (1999) reported great variation
dexmedetomidine was studied in volunteers with in clearance of diazepam among extensive and poor
and without severe renal impairment (De Wolf et al, metabolizers due to polymorphism of the cyto-
2001). The pharmacokinetics of dexmedetomidine chrome gene (see Chapter 13) that regulates
differed little in the two groups and there were no CYP2C19, which is responsible for variation in the
significant differences in the hemodynamic half-life of this drug.
responses. The elimination half-life in subjects with Lipoproteins are macromolecular complexes of
severe renal impairment was significantly shorter lipids and proteins and are classified according to
than in normal subjects: (113 ± 11 minutes versus their density and separation in the ultracentrifuge.
136 ± 13 minutes; p < 0.05). However, dexmedetomi- The terms VLDL, LDL, and HDL are abbreviations
dine resulted in more prolonged sedation in subjects for very-low-density, low-density, and high-density
276 Chapter 11
lipoproteins, respectively. Lipoproteins are respon- The hepatic expression of MDR1 in females
sible for the transport of plasma lipids to the liver was reported as about one-third to one-half of the
and may be responsible for the binding of drugs if hepatic P-gp level measured in men. However,
the albumin sites become saturated. another study reported no difference in MDR1
Erythrocytes, or red blood cells (RBCs), may bind between females and males. Low P-gp activity in the
both endogenous and exogenous compounds. RBCs liver was suggested to increase hepatic CYP3A
consist of about 45% of the volume of the blood. metabolism in some cases. The important point is
Phenytoin, pentobarbital, and amobarbital are known that a protein such as P-gp can translocate a drug
to have an RBC/plasma water ratio of 4 to 2, indicating away or closer to the site of the hepatic enzyme and
preferential binding of drug to the erythrocytes over therefore affecting the rate of metabolism. A similar
plasma water. Penetration into RBC is dependent on situation can occur within the gastrointestinal (GI)
the free concentration of the drug in the plasma. In the tract. This situation explains why first-pass effect is
case of phenytoin, RBC drug concentrations increase often quite erratic. Pharmacokineticists now use
linearly with an increase in the plasma-free drug con- in vitro methods to study both “apical to basolateral”
centration (Borondy et al, 1973). Increased drug bind- and “basolateral to apical” drug transport to deter-
ing to plasma albumin reduces RBC drug concentration. mine if the drug favors mucosal to serosal movement
With most drugs, however, binding of drug to RBCs or vice versa.
generally does not significantly affect the volume of
distribution, because the drug is often bound to albu-
min reversibly in the plasma water. Even though phe- EFFECT OF PROTEIN BINDING
nytoin has a great affinity for RBCs, only about 25% ON THE APPARENT VOLUME
of the blood drug concentration is present in the blood OF DISTRIBUTION
cells, and 75% is present in the plasma because the
drug is also strongly bound to albumin. For drugs with The extent of drug protein binding in the plasma or
strong erythrocyte binding, the hematocrit will influ- tissue affects VD. Drugs that are highly bound to
ence the total drug concentration in the blood. For plasma proteins have a low fraction of free drug (fu =
these drugs, the total whole-blood drug concentration unbound or free drug fraction) in the plasma water.
should be measured. The plasma protein-bound drug does not diffuse
easily and is therefore less extensively distributed to
tissues (see Fig. 11-11). Drugs with low plasma pro-
Frequently Asked Questions
tein binding have larger fu, generally diffuse more
»»Should drug transporter proteins be considered as a easily into tissues, and have a greater volume of
type of “drug–protein binding” in assessing its role in
distribution. Although the apparent volume of distri-
the drug’s pharmacokinetics?
bution is influenced by lipid solubility in addition to
»»How does a protein transporter modulate drug distri- protein binding, there are some exceptions to this
bution in the body? rule. However, when several drugs are selected from
a single family with similar physical and lipid parti-
tion characteristics, the apparent volume of distribu-
Gender Differences in Drug Distribution tion may be explained by the relative degree of drug
Gender differences in drug distribution are now known binding to tissue and plasma proteins.
for many drugs (Anderson, 2005). For example, The VD of four cephalosporin antibiotics
Meibohm et al (2002) discussed the physiologic impact (Fig. 11-12) in humans and mice (Sawada et al,
of P-glycoprotein (P-gp) binding to substrate drugs. 1984) demonstrates that the differences in volume
The human multidrug-resistance gene 1 (MDR1) gene of distribution of cefazolin, cefotetan, moxalactam,
product P-gp are now known to play a major role in and cefoperazone are due mostly to differences in
absorption, distribution, and/or renal and hepatic excre- the degree of protein binding. For example, the frac-
tion of therapeutic agents. tion of unbound drug, fu, in the plasma is the highest
Physiologic Drug Distribution and Protein Binding 277
intense pharmacodynamic (or toxic) response;
(3) increase the free drug concentration, causing a
transient increase in VD and decreasing partly some
350
of the increase in free plasma drug concentration;
300
(4) increase the free drug concentration, resulting
250 in more drug diffusion into tissues of eliminating
200 organs, particularly the liver and kidney, resulting
150 in a transient increase in drug elimination. The ulti-
Cefoperazone mate drug concentration reaching the target depends
100 Moxalactam on one or more of these four factors dominating in
50 Cefotetan the clinical situation. The effect of drug–protein
0
V Cefazolin binding must be evaluated carefully before dosing
human fu-human Vmouse changes are made (see below).
fu-mouse
FIGURE 1112 Plot of VD of four cephalosporin antibiotics
in humans and mice showing the relationship between the Effect of Changing Plasma Protein Level:
fraction of unbound drug (fu) and the volume of distribution. An Example
(Data from Sawada et al, 1984.)
The effect of increasing the plasma a1-acid glycopro-
tein (AAG) level on drug penetration into tissues may
for cefoperazone in humans and mice, and the vol- be verified with cloned transgenic animals that have
ume of distribution is also the highest among the 8.6 times the normal AAG levels. In an experiment
four drugs in both humans and mice. Conversely, investigating the activity of the tricyclic antidepres-
cefazolin has the lowest fu in humans and is corre- sant drug imipramine, equal drug doses were admin-
sponding to the lowest volume of distribution. istered to both normal and transgenic mice. Since
Interestingly, the volume of distribution per kilo- imipramine is highly bound to AAG, the steady-state
gram in humans (Vhuman) is generally higher than imipramine serum level was greatly increased in the
that in mouse (Vmouse) because the fraction of unbound blood due to protein binding.
drug is also greater, resulting in a greater volume of
distribution. Differences in drug-protein binding Imipramine Level (ng/mL)
contribute to the differences seen in Vd and t1/2 among
various species. An equation (Equation 11.12) relat- Mouse Model Serum Brian
ing quantitatively the effect of protein binding on Normal 319.9 7307.7
apparent volume of distribution is derived in the
Transgenic 859 3862.6
next section.
Drugs such as furosemide, sulfisoxazole, tol-
butamide, and warfarin are bound greater than 90% However, the imipramine concentration was
to plasma proteins and have a VD value ranging greatly reduced in the brain tissue because of
from 7.7 to 11.2 L per 70-kg body weight. Basic higher degree of binding to AAG in the serum,
drugs such as imipramine, nortriptyline, and pro- resulting in reduced drug penetration into the brain
pranolol are extensively bound to both tissue and tissue. The volume of distribution of the drug was
plasma proteins and have very large VD values. reported to be reduced in the transgenic mice. The
Displacement of drugs from plasma proteins can antidepressant effect was observed to be lower in
affect the pharmacokinetics of a drug in several the transgenic mouse due to lower brain imipra-
ways: (1) directly increase the free (unbound) drug mine levels. This experiment illustrates that high
concentration as a result of reduced binding in the drug–protein binding in the serum can reduce drug
blood; (2) increase the free drug concentration that penetration to tissue receptors for some drugs
reaches the receptor sites directly, causing a more (Holladay et al, 1996).
278 Chapter 11
Saquinavir mesylate (Invirase®) is an inhibitor of fut is the unbound drug fraction in the tissue, Cu is
the human immunodeficiency virus (HIV) protease. the unbound drug concentration in the plasma, and
Saquinavir is approximately 98% bound to plasma Cut is the unbound drug concentration in the tis-
proteins over a concentration range of 15 to 700 ng/mL. sues. Substituting for Ct in Equation 11.7 using
Saquinavir binding in human plasma and control Equation 11.9 results in
mouse plasma are similar and approximately 2% to f
3% unbound. Saquinavir is highly bound to AAG and DB =VpCp +Vt Cp u
f (11.10)
has reduced free drug concentrations in transgenic mice ut
that express elevated AAG (Holladay et al, 2001). In Rearranging,
this study, the drug was bound to both albumin and
D f
AAG (2.1% to AAG vs 11.5% to albumin). Elevated B =V +V u
p ( 1 1 )
C t 1 . 1
AAG caused saquinavir’s volume of distribution to be p fut
reduced in this study. In AAG-overexpressing trans- Because DB/Cp = Vapp, by substitution into
genic mice, AAG is genetically increased such that Equation 11.11, Vapp may be estimated by
most saquinavir is bound in plasma and only 1.5% is Equation 11.12:
free to be metabolized. The result is a decrease in sys-
f
temic clearance of saquinavir. This conclusion is con- Vapp =V +V u
p t (11.12)
sistent with the observations that systemic exposure to fut
saquinavir in HIV-1 subjects is greater than that in Equation 11.12 relates the amount of drug in the body
healthy subjects and that AAG levels increase with the to plasma volume, tissue volume, and fraction of free
degree of HIV infection. According to the approved plasma and tissue drug in the body. Equation 11.12
label, HIV-infected patients administered Invirase may be expanded to include several tissue organs with
(600-mg TID) had AUC and maximum plasma con- Vti each with unbound tissue fraction futi.
centration (Cmax) values approximately 2 to 2.5 times
those observed in healthy volunteers receiving the f
Vapp Vp ∑V u
= + ti
same dosing regimen. futi
For a drug that distributes into the plasma and a
where Vti = tissue volume of the ith organ and futi =
given tissue in the body, the amount of drug bound
unbound fraction of the ith organ.
may be found by Equation 11.7. Because drug may
The following are important considerations in
bind to both plasma and tissue proteins, the bound
the calculation of Vapp.and unbound drug concentrations must be consid-
ered. At steady state, unbound drug in plasma and 1. The volume of distribution is a constant only
tissue are in equilibration. when the drug concentrations are in equilibrium
between the plasma and tissue.
DB = VpCp + VtCt (11.7) 2. Values of fu and fut are concentration dependent
and must also be determined at equilibrium
Cu = Cut conditions.
3. Vapp is an indirect measure of drug binding in
Alternatively,
the tissues rather than a measurement of a true
Cp fu = Ct fut (11.8) anatomic volume.
4. When fu and fut are unity, Equation 11.12 is
or simplified to
f DB
C C u =V +V
t = p (11.9)
f C p t
p
ut
where all terms refer to steady-state conditions: fu When no drug binding occurs in tissue and
is the unbound (free) drug fraction in the plasma, plasma, the volume of distribution will not exceed the
Physiologic Drug Distribution and Protein Binding 279
real anatomic volume. Only at steady state are the What is the fraction of tissue binding of the two
unbound plasma drug concentration, Cu, and the tis- drugs? Assume that Vp is 4 L and Vt is 10 L.
sue drug concentration, Cut, equal. At any other time,
Solution
Cu may not equal to Cut. The amount of drug in the
Drug A
body, DB, cannot be calculated easily from Vapp and Cp Applying Equation 11.12,
under nonequilibrium conditions. For simplicity,
some models assume that the drug distributed to a tis- f
Vapp =Vp +V u
sue is approximated by the drug present in the fluid of t
fut
that tissue. The tissue fluid volume is then represented
by the volume of the extracellular/intracellular fluid, Because drug A is 60% bound, the drug is 40%
depending on drug penetration. Such a model fails to free, or fu = 0.4.
consider drug partition into fatty tissues/lipids, and 0.4
simulates extravascular drug distribution based solely 20 = 4+10
fon protein binding. A number of drugs have a large ut
volume of distribution despite high protein binding to 4
plasma proteins. Some possible reasons for this large fut = = 0.25
16
volume of distribution could be due to strong tissue
drug partition and/or high intracellular or receptor The fraction of drug bound to tissues is 1 − 0.25 =
binding within the tissue. Under these situations, the 0.75 or 75%.
model discussed above does not adequately describe Drug B
the in vivo drug distribution.
0.4
In contrast, when the data are analyzed by the 100 = 4+10
fcompartmental model, no specific binding interpreta- ut
tion is made. The analyst may interpret a large appar- fut = 0.042
ent volume due to either partition to fatty tissues or
extravascular binding based on other observations. The fraction of drug bound to tissues is 1 −
Compartment models are based on mass balance and 0.042 = 0.958 = 95.8%.
focus on the amount of drug in each compartment In this problem, the percent free (unbound) drug
and not on the tissue volume or tissue drug concen- for drug A is 25% and the percent free drug for drug
tration. The tissue volume and drug concentrations B is 4.2% in plasma fluid. Drug B is more highly
are theoretical and do not necessarily reflect true bound to tissue, which results in a larger apparent
physiologic values. Even the Ct may not be uniform volume of distribution. This approach assumes a
in local tissues and under disease conditions. pooled tissue group because it is not possible to
identify physically the tissue group to which the
Frequently Asked Questions drug is bound.
»»Is it possible for VD to exceed a patient’s actual Equation 11.12 may explain the wide variation
physiologic volume? If so, why? in the apparent volumes of distribution for drugs
observed in the literature (Tables 11-7–11-9). Drugs
»»How does protein binding influence VD? in Table 11-7 have small apparent volumes of distri-
»»What are fut and fup? Are they constant? bution due to plasma drug binding (less than 10 L
when extrapolated to a 70-kg subject). Drugs in
Table 11-8 show that, in general, as the fraction of
PRACTICE PROBLEM unbound drug, fu, in the plasma increases, the appar-
ent volume increases. Reduced drug binding in the
Drug A and drug B have Vapp of 20 and 100 L, plasma results in increased free drug concentration,
respectively. Both drugs have a Vp of 4 L and a Vt of which diffuses into the extracellular water. Drugs
10 L, and they are 60% bound to plasma protein. showing exceptionally large volumes of distribution
280 Chapter 11
TABLE 117 Relationship between Affinity TABLE 119 Examples of Drugs with Tissue
for Serum Albumin and Volume of Distribution Distribution Apparently Independent of Plasma
for Some Acidic Drugs Protein Binding
Plasma Plasma Fraction
Fraction Affinity Drug Bound (%) VD (L/kg)
Bound Constant
Drug (%) (M–1) VD (L/kg) Desipramine 92 40
Imipramine 95 30
Clofibric acid 97 300,000 0.09
Nortriptyline 94 39
Fluorophenindione 95 3,000,000 0.09
Vinblastine 70 35
Phenylbutazone 99 230,000 0.09
Vincristine 70 11
Warfarin 97 230,000 0.13
From Houin (1985), with permission.
From Houin (1985), with permission.
may have unusual tissue binding. Some drugs move
into the interstitial fluid but are unable to diffuse
across the plasma membrane into the intracellular
TABLE 118 Examples of Drugs with fluids, thereby reducing the volume of distribution.
Diffusion Limited by Binding to Protein Drugs in Table 11-9 apparently do not obey the
general binding rule, because their volumes of distribu-
Plasma Fraction tion are not related to plasma drug binding. These drugs
Drug Unbound (%) VD (L/kg)
have very large volumes of distribution and may have
Carbenoxolone 1 0.10 undiscovered tissue binding or tissue metabolism.
Based on their pharmacologic activities, presumably all
Ibuprofen 1 0.14
these drugs penetrate into the intracellular space.
Phenylbutazone 1 0.10
Naproxen 2 0.09
CLINICAL EXAMPLE
Fusidic acid 3 0.15
The serum protein binding of azithromycin is concen-
Clofibrate 3 0.09
tration dependent, ranging from 51% at 0.02 mg/mL to
Warfarin 3 0.10 7% at 2.0 mg/mL as reported in the literature. Following
Bumetanide 4 0.18 oral administration, azithromycin is widely distributed
throughout the body with an apparent steady-state
Dicloxacillin 4 0.29
volume of distribution of 31.1 L/kg. Higher azithro-
Furosemide 4 0.20 mycin concentrations in tissues than in plasma or
Tolbutamide 4 0.14 serum have been observed.
Nalidixic acid 5 0.35 • What is the apparent VD for a subject weighing
Cloxacillin 5 0.34 70 kg?
• Is the apparent VD greater or lower than the plasma
Sulfaphenazole 5 0.29
volume of the body for this subject?
Chlorpropramide 8 0.20 • Do you think protein binding affect the distribu-
Oxacillin 8 0.44 tion of this drug?
Nafcillin 10 0.63 Solution
From Houin (1985), with permission. VD for a subject weighing 70 kg = 70 × 31.1 = 2191 L
Physiologic Drug Distribution and Protein Binding 281
Electrolyte Balance RELATIONSHIP OF PLASMA
Electrolyte balance affects the movement of fluid in DRUG–PROTEIN BINDING TO
the body. The kidney is the main regulator of electro-
DISTRIBUTION AND ELIMINATION
lyte balance. Albumin is synthesized in the liver and
is the main component of plasma proteins. The In general, drugs that are highly bound to plasma
plasma albumin concentration contributes to osmotic protein have reduced overall drug clearance. For a
pressure in the blood. Plasma albumin concentration drug that is metabolized mainly by the liver, binding
may be increased during hypovolemia (loss of to plasma proteins prevents the drug from entering
plasma volume due to movement fluid into extracel- the hepatocytes, resulting in reduced hepatic drug
lular fluid and other various factors such as dehydra- metabolism. In addition, bound drugs may not be
tion, shocks, excessive blood loss, etc) or decreased available as substrates for liver enzymes, thereby
during hypervolemia (increase in plasma volume further reducing the rate of metabolism.
due to various causes such as excessive fluid intake, Protein-bound drugs act as larger molecules that
sodium retention, congestive heart failure, etc). cannot diffuse easily through the capillary mem-
Changes in plasma protein concentration and in branes in the glomeruli. The elimination half-lives of
plasma drug–protein binding may occur to various some drugs such as the cephalosporins, which are
degree, thus affecting drug disposition. Disease excreted mainly by renal excretion, are generally
conditions may cause changes in protein concentra- increased when the percent of drug bound to plasma
tion and drug–protein binding, thus altering the proteins increases (Table 11-10). Drug protein bind-
protein distribution in the body. An altered protein ing are usually measured in plasma and sometimes
concentration and binding may result in more non- in serum. The effect of serum protein binding on the
protein-bound drug leading to a more intense phar- renal clearance and elimination half-life on several
macodynamic effect and a change in the rate of drug tetracycline analogs is shown in Table 11-11. For
elimination. example, doxycycline, which is 93% bound to serum
TABLE 1110 Influence of Protein Binding on the Pharmacokinetics of Primarily Glomerular
Filtrated Cephalosporins
Renal Clearance
Protein Bound (%) t1/2 (h) (mL/min/1.73 m2)
Ceftriaxone 96 8.0 10
Cefoperazone 90 1.8 19
Cefotetan 85 3.3 28
Ceforanide 81 3.0 44
Cefazolin 70 1.7 56
Moxalactam 52 2.3 64
Cefsulodin 26 1.5 90
Ceftazidime 22 1.9 85
Cephaloridine 21 1.5 125
From Houin (1985), with permission.
282 Chapter 11
TABLE 1111 Comparison of Serum Protein Binding of Several Tetracycline Analogs with Their
Half-Lives in Serum Renal Clearance and Urinary Recovery after Intravenous Injection
Renal Clearance Urinary Recovery
Tetracycline Analogs Serum Binding (%) Half-Life (h) (mL/min) (%)
Oxytetracycline 35.4 9.2 98.6 70
Tetracycline 64.6 8.5 73.5 60
Demeclocycline 90.8 12.7 36.5 45
Doxycycline 93.0 15.1 16.0 45
proteins, has an elimination half-life of 15.1 hours, fluid without protein binding. The equation basically
whereas oxytetracycline, which is 35.4% bound to describes the empirical observation that either a
serum proteins, has an elimination half-life of 9.2 large clearance or large volume of distribution leads
hours. On the other hand, a drug that is both exten- to low plasma drug concentrations after a given dose.
sively bound and actively secreted by the kidneys, Mechanistically, a relatively low plasma drug con-
such as penicillin, has a short elimination half-life, centration from a given dose may be resulted from
because active secretion takes preference in remov- (1) extensive distribution into tissues due to favor-
ing or stripping the drug from the proteins as the able lipophilicity, (2) extensive distribution into tis-
blood flows through the kidney. sues due to protein binding in peripheral tissues,
Some cephalosporins are excreted by both renal and/or (3) lack of drug plasma protein binding.
and biliary secretion. The half-lives of drugs that are Two drug examples are selected to illustrate fur-
significantly excreted in the bile do not correlate ther the relationship between elimination half-life,
well with the extent of plasma protein binding. clearance, and the volume of distribution. Although
the kinetic relationship is straightforward, there is
Relationship between VD and Drug more than one way of explaining the observations.
Elimination Half-Life
Drug elimination is governed mainly by renal and
other metabolic processes in the body. However, CLINICAL EXAMPLES
extensive drug distribution has the effect of diluting
Drug with a Large Volume of Distribution
the drug in a large volume, making it harder for the
and a Long Elimination t
kidney to filter the drug by glomerular filtration. 1/2
Thus, the t1/2 of the drug is prolonged if clearance The macrolide antibiotic dirithromycin is extensively
(Cl) is constant and VD is increased according to distributed in tissues, resulting in a large steady-state vol-
Equation 11.14. Cl is related to apparent volume of ume of distribution of about 800 L (range 504–1041 L).
distribution, VD, and the elimination constant k, as The elimination t1/2 in humans is about 44 hours (range
shown in Equation 11.13 (see also Chapter 3). 16–65 h). The drug has a relatively large total body
clearance of 226 to 1040 mL/min (13.6–62.4 L/hours)
Cl = kV and is given once daily. In this case, clearance is large
D (11.13)
due to a large V
V D, whereas k is relatively small. In this
t 0.69 D case, Cl is large but the elimination half-life is long
1/2 = 3 (11.14)
Cl
because of the large VD. Intuitively, the drug will take
For a first-order process, Cl is the product of VD and a long time to be removed when the drug is distributed
the elimination rate constant, k, according to extensively over a large volume; despite a relatively
Equation 11.13. The equation is derived for a given large clearance, t1/2 accurately describes drug elimina-
drug dose distributed in a single volume of body tion alone.
Physiologic Drug Distribution and Protein Binding 283
Drug with a Small Volume of Distribution by Equation 11.4, clearance is clearly affected by the
and a Long Elimination t volume of distribution and by many variables of the
1/2
Tenoxicam is a nonsteroidal anti-inflammatory drug drug in the biological system. In patients with asci-
(Nilsen, 1994) that is about 99% bound to human tes, clearance is increased but with no increase in
plasma protein. The drug has low lipophilicity, is half-life, reflecting the increase in volume of distri-
highly ionized (approximately 99%), and is distrib- bution in ascitic patients (Stoeckel et al, 1983).
uted in blood. Because tenoxicam is very polar, the
drug penetrates cell membranes slowly. The synovial Frequently Asked Questions
fluid peak drug level is only one-third that of the »»Does a large value for clearance always result in a
plasma drug concentration and occurs 20 hours (range short half-life? Explain.
10–34 h) later than the peak plasma drug level. In
»»What are the causes of a long distribution half-life for
addition, the drug is poorly distributed to body tissues
a body organ if blood flow to the tissue is rapid?
and has an apparent volume of distribution, VD, of
9.6 L (range 7.5–11.5 L). Tenoxicam has a low total »»How long does it take for a tissue organ to be fully
plasma clearance of 0.106 L/h (0.079–0.142 L/h) and an equilibrated with the plasma? How long for a tissue
elimination half-life of 67 hours (range 49–81 hours), organ to be half-equilibrated?
undoubtedly related to the extensive drug binding to »»When a body organ is equilibrated with drug from the
plasma proteins. plasma, the drug concentration in that organ should
According to Equation 11.13, drug clearance be the same as that of the plasma. True or false?
from the body is low if VD is small and k is not too
»»What is the parameter that tells when half of the
large. This relationship is consistent with a small Cl protein-binding sites are occupied?
and a small VD observed for tenoxicam. Equation 11.4,
however, predicts that a small VD would result in a
short elimination t1/2. In this case, the actual elimina- Elimination of Protein-Bound Drug:
tion half-life is long (67 hours) because the plasma Restrictive Versus Nonrestrictive Elimination
tenoxicam clearance is so low that it dominates in
Equation 11.4. The long elimination half-life of tenoxi- When a drug is tightly bound to a protein, only the
cam is better explained by restrictive drug clearance unbound drug is assumed to be metabolized; drugs
due to its binding to plasma proteins, making it diffi- belonging to this category are described as restrictively
cult for the drug to clear rapidly. eliminated. On the other hand, some drugs may be
eliminated even when they are protein bound; drugs
in this category are described as nonrestrictively
Clearance eliminated. Nonrestrictively cleared drugs are nor-
Pharmacokineticists regard Cl and VD as indepen- mally rapidly eliminated since protein binding does
dent model variables based on Equation 11.14. not impede the elimination process. Examples of
Equation 11.13 and its equivalent, Equation 11.14, nonrestrictively cleared drugs include morphine,
are rooted in classical pharmacokinetics. Initially, it metoprolol, and propranolol. Para-aminohippacuric
may be difficult to understand why a drug such as acid is also nonrestrictively cleared by the kidney
dirithromycin, with a rapid clearance of 226 to and useful as a marker for renal blood flow.
1040 mL/min, has a long half-life. In pharmacoki- If a clinician fails to consider the role of restric-
netics, the elimination constant k = 0.0156 h−1 tive versus nonrestrictive elimination, serious dosage
implies that 1/64 (ie, 0.0156 h−1 = 1/64) of the drug miscalculations may be made with regard to response
is cleared per hour (a low-efficiency elimination fac- to the addition of inhibitors or changes in protein
tor). From the elimination rate constant k, one can concentration. Nonrestrictively cleared drugs are less
estimate that it takes 44 hours (t1/2 = 44 hours) to influenced by changes in protein binding since drug
eliminate half the drug in the body, regardless of VD. elimination is not affected. However, free drug diffu-
While t1/2 is dependent on clearance and VD as shown sion may be affected by a change in free fraction.
284 Chapter 11
Therefore, when drugs with varying fractions of plasma body may include a high degree of protein binding,
protein binding are compared, the expected reduction a lower fraction of drug metabolised, and having
in clearance for drugs with low protein binding is drug molecular properties (eg, lipophilicity) that
sometimes absent or very minor. However, restrictively favor extravascular partitioning into tissues.
cleared drugs will exhibit a relationship between total
drug concentration and protein concentration, though CLINICAL EXAMPLE
the free drug concentration may not change because
of the resulting proportional changes in elimination. Diazepam (Valium®) has an average elimination
Therefore, whether a drug is restrictively or nonre- half-life of 37 hours and VD of 77 L and is mainly
strictively eliminated must be considered when deter- eliminated by demethylation.
mining the role of changes in protein binding or
• Is diazepam slowly eliminated due to the extensive
inhibitors. The effect of protein binding on the kinet-
binding to protein, a large VD or simply because
ics of drug clearance in an organ system is discussed
diazepam has a low metabolic rate (or low extrac-
in detail in Chapter 12.
tion ratio, ER)?
In practice, the molecular effect of protein bind-
ing on elimination is not always predictable. Drugs Recent studies with CYP 2C9 have shown that
with restrictive elimination are recognized by very drug protein binding is not the only reason for small
small plasma clearances and extensive plasma pro- clearance and a long t1/2 of diazepam (Qin et al, 1999).
tein binding. The hepatic extraction ratios (ERs) for Diazepam demethylation varies greatly among indi-
drugs that are restrictively eliminated are generally viduals due to genetic polymorphism (see Chapter 13).
small, because of strong protein binding. Their In some subjects, slow metabolism is the main cause
hepatic extraction ratios are generally smaller than for a longer elimination half-life. The half-lives of
their unbound fractions in plasma (ie, ER < fu). For diazepam ranged from 20 to 84 hours (Qin et al,
example, phenylbutazone and the oxicams, includ- 1999). Clearance ranged from 2.8 ± 0.9 mL/min
ing piroxicam, isoxicam, and tenoxicam, all have (slow metabolizer) to 19.5 ± 9.8 mL/min (fast metab-
hepatic extraction ratios smaller than their unbound olizers). The long half-life is, in part, due to the small
fraction in plasma (Verbeeck and Wallace, 1994). ER in some subjects. The elimination half-lives are
The hepatic elimination for these drugs is therefore shorter in subjects who are fast metabolizers, although
restrictive. A series of nonsteroid anti-inflammatory the elimination half-lives are still quite long due to
drugs (NSAIDs) were reported by the same authors the large volume of distribution of this drug (small k
to be nonrestrictive with the following characteris- and large VD). It is important to keep in mind that free
tics: (1) drug elimination is exclusively hepatic, (2) drug concentration and how it sustains ultimately
bioavailability of the drug from an oral dosage form determines pharmacologic effect and duration of
is complete, and (3) these drugs do not undergo action. Based on a well-stirred venous equilibrium
extensive reversible biotransformation or enterohe- model (Benet and Hoener, 2002), and a given set of
patic circulation. assumptions, one can predict that the free AUC or
Propranolol is a drug that has low bioavailability systemic exposure of an orally administered drug
with a hepatic extraction ratio, ER, of 0.7 to 0.9. will not be affected by protein binding despite its
Propranolol is 89% bound, that is, 11% free (or fu = 0.11) high degree of binding since the free AUC is not
so that ER > fu. Thus, propranolol is considered to be affected by fu. In general, the approach is quite use-
nonrestrictively eliminated. The bioavailability of ful for many drugs with receptor sites within the
propranolol is very low because of the large first-pass plasma compartment discussed earlier. In the case
effect, and its elimination half-life is relatively short. of diazepam, pharmacological effect occurs in the
In contrast, highly bound drugs such as warfarin brain and penetration across the central nervous
(99% bound) and diazepam (98% bound) each has system (CNS) may not be adequately considered by
an average long half-life of about 37 hours (see the equations of one-compartment model. The risk
Appendix E). Reasons for a long half-life drug in the of unknown metabolism or uptake within cells
Physiologic Drug Distribution and Protein Binding 285
outside the plasma compartment is always present. 2. The protein
(See illustrated in vitro examples for VD in the begin- • Quantity of protein available for drug–protein
ning of this chapter.) binding
Schmidt et al (2010) recently reviewed the effect • Quality or physicochemical nature of the pro-
of protein binding of various drugs and they charac- tein synthesized
terized various situations in which steady-state free 3. The affinity between drug and protein
drug concentrations may or may not be affected by • The magnitude of the association constant
protein binding. The article discussed a group of ben- 4. Drug interactions
zodiazepines with different degrees of protein binding • Competition for the drug by other substances
and reported that penetration into CNS is better at a protein-binding site
related to the free drug concentration, that is, after • Alteration of the protein by a substance that
correcting for protein binding. The benzodiazepines modifies the affinity of the drug for the protein;
studied were (1) flunitrazepam, 85% bound, (2) mid- for example, aspirin acetylates lysine residues
azolam, 96%, (3) oxazepam, 91%, and (4) clobazam, of albumin
69%. The authors concluded that for each drug, the 5. The pathophysiologic condition of the patient
pharmacokinetics and pharmacodynamics should be • For example, drug–protein binding may be
considered instead of a generalized “one-size-fit-all” reduced in uremic patients and in patients with
approach. Schmidt et al (2010) also discuss various hepatic disease
situations that may cause changes in half-life as a
Plasma drug concentrations are generally
result of changes in protein–drug binding. Furthermore,
reported as the total drug concentration in the
Schmidt et al (2010) conclude that “plasma protein
plasma, including both protein-bound drug and
binding can have multiple effects on the pharmacoki-
unbound (free) drug. Most literature values for the
netics and pharmacodynamics of a drug and a simple,
therapeutic effective drug concentrations refer to the
generalized guideline for the evaluation of the clinical
total plasma or serum drug concentration. For thera-
significance of protein binding frequently cannot be
peutic drug monitoring, the total plasma drug con-
applied.” These authors propose that a careful analysis
centrations are generally used in the development of
of protein-binding effects must be made on a drug-by-
the appropriate drug dosage regimen for the patient.
drug basis.
In the past, measurement of free drug concentration
was not routinely performed in the laboratory. More
recently, free drug concentrations may be measured
Frequently Asked Question quickly using ultrafiltration thereby allowing the
»»Why is it important to report detailed information of measure of the drug concentration available to the
the pharmacokinetics of a drug including the num- drug receptor. Because of the high plasma protein
ber and demographics of the subjects and the nature binding of phenytoin and the narrow therapeutic
of drug elimination when citing mean clearance or index of the drug, more hospital laboratories are
half-life data from a table in the literature? measuring both free and total phenytoin plasma
levels.
DETERMINANTS OF PROTEIN
BINDING CLINICAL EXAMPLE
Macfie et al (1992) studied the disposition of intra-
Drug–protein binding is influenced by a number of
venous dosing of alfentanil in six patients who suf-
important factors, including the following:
fered 10% to 30% surface area burns compared a
1. The drug control group of six patients matched for age, sex,
• Physicochemical properties of the drug and weight. Alfentanil binding to plasma proteins
• Total concentration of the drug in the body was measured by equilibrium dialysis. The burn
286 Chapter 11
patients had significantly greater concentrations of To study the binding behavior of drugs, a determin-
AAG and smaller concentrations of albumin. The able ratio r is defined, as follows:
mean protein binding of alfentanil was 94.2% ± 0.05
moles of drug bound
(SEM) in the burn group and 90.7% ± 0.4 in the r =
total moles of protein
control group (p = 0.004). A good correlation was
found between AAG concentration and protein bind- As moles of drug bound is [PD] and the total moles
ing. The greater AAG concentrations in the burn of protein is [P] + [PD], this equation becomes
group corresponded with significantly reduced vol-
ume of distribution and total clearance of alfentanil. [PD]
r = (1 . 7
[PD]+ 1 1 )
The clearance of the unbound fraction and the elimi- [P]
nation half-life of alfentanil were not decreased
According to Equation 11.16, [PD] = Ka [P] [D];
significantly.
by substitution into Equation 11.17, the following
expression is obtained:
KINETICS OF PROTEIN BINDING K
= a [P][D]r
The kinetics of reversible drug–protein binding for a Ka [P][D]+ [P]
protein with one simple binding site can be described (11.18)
K
by the law of mass action, as follows: a [D]r =
1+Ka [D]
Protein + drug ⇔ drug–protein complex
This equation describes the simplest situation, in
or which 1 mole of drug binds to 1 mole of protein in a
1:1 complex. This case assumes only one indepen-
[P] + [D] ⇔ [PD] (11.15) dent binding site for each molecule of drug. If there
are n identical independent binding sites per protein
From Equation 11.15 and the law of mass action, an
molecule, then the following equation is used:
association constant, Ka (also called the affinity con-
stant), can be expressed as the ratio of the molar nKa [D] r = ( 1 1 )
1+ 1 . 9
concentration of the products and the molar concen- Ka [D]
tration of the reactants. This equation assumes only
one binding site per protein molecule. In terms of Kd, which is 1/Ka, Equation 11.19
reduces to
[PD]
Ka = (11.16)
[P][D] n[D]
r = (1 0
Kd + 1.2 )
[D]
The extent of the drug–protein complex formed is
dependent on the association binding constant, Ka. Protein molecules are quite large compared to
The magnitude of Ka yields information on the degree drug molecules and may contain more than one type
of drug–protein binding. Drugs strongly bound to of binding site for the drug. If there is more than one
protein have a very large Ka and exist mostly as the type of binding site and the drug binds indepen-
drug–protein complex. With such drugs, a large dose dently to each binding site with its own association
may be needed to obtain a reasonable therapeutic constant, then Equation 11.20 expands to
concentration of free drug.
n1K1[P] n K
Most kinetic studies in vitro use purified albumin r 2 2[P] = + +… (11.21)
1+K1[D] 1+K2[D]as a standard protein source because this protein is
responsible for the major portion of plasma drug– where the numerical subscripts represent different
protein binding. Experimentally, both the free drug [D] types of binding sites, the Ks represent the binding
and the protein-bound drug [PD], as well as the total constants, and the ns represent the number of bind-
protein concentration [P] + [PD], may be determined. ing sites per molecule of albumin.
Physiologic Drug Distribution and Protein Binding 287
These equations assume that each drug mole- When n = 1 and the unbound (free) drug con-
cule binds to the protein at an independent binding centration is equal to Kd, the protein binding of
site, and the affinity of a drug for one binding site the drug is half-saturated. Interestingly, when
does not influence binding to other sites. In reality, [D] is much greater than Kd, Kd is negligible in
drug–protein binding sometimes exhibits a phenom- Equation 11.21, and r = n (that is, r is indepen-
enon of cooperativity. For these drugs, the binding dent of concentration or fully saturated).
of the first drug molecule at one site on the protein When Kd > [D], [D] is negligible in the
molecule influences the successive binding of other denominator of Equation 11.21, and r is depen-
drug molecules. The binding of oxygen to hemoglo- dent on n/Kd[D], or nKa[D]. In this case, the
bin is an example of drug cooperativity. number of sites bound is directly proportional
Each method for the investigation of drug– to n, Ka, and the free drug concentration [D].
protein binding in vitro has advantages and disad- This relationship also explains why a drug with
vantages in terms of cost, ease of measurement, a higher Ka may not necessarily have a higher
time, instrumentation, and other considerations. percent of drug bound, because the number
Various experimental factors for the measurement of of binding sites, n, may be different from one
protein binding are listed in Table 11-10. Drug–protein drug to another. At higher [D], the relationship
binding kinetics yield valuable information concern- between [PD] and [D] may no longer be linear.
ing proper therapeutic use of the drug and predic-
tions of possible drug interactions.
DETERMINATION OF BINDING
CONSTANTS AND BINDING SITES
PRACTICAL FOCUS BY GRAPHIC METHODS
In Vitro Methods (Known Protein
1. How is r related to the fraction of drug bound Concentration)
(fu), a term that is often of clinical interest?
A plot of the ratio of r (moles of drug bound per
Solution mole of protein) versus free drug concentration [D]
r is the ratio of number of moles of drug bound/ is shown in Fig. 11-13. Equation 11.20 shows that as
number of moles of albumin. r determines the free drug concentration increases, the number of
fraction of drug binding sites that are occupied. moles of drug bound per mole of protein becomes
fu is based on the fraction of drug which is free saturated and plateaus. Thus, drug protein binding
in the plasma. The value of fu is often assumed
to be fixed. However, fu may change, especially
with drugs that have therapeutic levels close to
Kd. (See examples on diazoxide.)
2. At maximum drugs binding, the number of Saturation of binding sites at high concentration
binding sites is n (see Equation 11.21). The
drug disopyramide has a Kd = 1 × 10−6 M/L.
How close to saturation is the drug when the
free drug concentration is 1 × 10−6 M/L?
Solution
Substitution for [D] = 1 × 10−6 M/L and Kd = 1 ×
10−6 M/L in Equation 11.21 gives Free drug concentration (D)
n
FIGURE 1113 Graphical representation of Equation 11.20,
r =
2 showing saturation of protein at high drug concentrations.
Moles of drug bound per
mole of protein (r)
288 Chapter 11
for the estimation of the binding constants and bind-
ing sites. From Equation 11.20, we obtain
nKa [D]r =
1+Ka [D]Slope = 1
nKa
1 r + rKa [D]= nK
n a [D]
(11.23)
1/ [ r = nKa [D]− rKa [D]D]
FIGURE 1114 Hypothetical binding of drug to r
= nK
D a − rK
protein. The line was obtained with the double reciprocal a
equation.
A graph constructed by plotting r/[D] versus r
yields a straight line with the intercepts and slope
shown in Figs. 11-15 and 11-16.
resembles a Langmuir adsorption isotherm, which is Some drug–protein binding data produce
also similar to the process where adsorption of a Scatchard graphs of curvilinear lines (Figs. 11-17
drug to an adsorbent becomes saturated as the drug and 11-18). The curvilinear line represents the sum-
concentration increases. Because of nonlinearity in mation of two straight lines that collectively form the
drug–protein binding, Equation 11.20 is rearranged curve. The binding of salicylic acid to albumin is an
for the estimation of n and Ka. example of this type of drug–protein binding in
The values for the association constants and the which there are at least two different, independent
number of binding sites are obtained by various binding sites (n1 and n2), each with its own indepen-
graphic methods. The reciprocal of Equation 11.20 dent association constant (k1 and k2). Equation 11.21
gives the following equation: best describes this type of drug–protein interaction.
1 1+Ka [D]= In Vivo Methods (Unknown Protein
r nKa [D] Concentration)
(11.22)
1 1 1 Reciprocal and Scatchard plots cannot be used if the
= +
r nKa [D] n exact nature and amount of protein in the experimen-
tal system are unknown. The percent of drug bound
is often used to describe the extent of drug–protein
A graph of 1/r versus 1/[D] is called a double
binding in the plasma. The fraction of drug bound, b,
reciprocal plot. The y intercept is 1/n and the slope is
can be determined experimentally and is equal to the
1/nKa. From this graph (Fig. 11-14), the number of
ratio of the concentration of bound drug, [Db], and
binding sites may be determined from the y intercept,
and the association constant may be determined from
the slope, if the value for n is known.
If the graph of 1/r versus 1/[D] does not yield a nKa
straight line, then the drug–protein binding process
is probably more complex. Equation 11.20 assumes Slope = –Ka
one type of binding site and no interaction among
the binding sites. Frequently, Equation 11.22 is used
to estimate the number of binding sites and binding
constants, using computerized iteration methods. n
r
Another graphic technique called the Scatchard
plot, is a rearrangement of Equation 11.20. The FIGURE 1115 Hypothetical binding of drug to protein.
Scatchard plot spreads the data to give a better line The line was obtained with the Scatchard equation.
1/r
r/D
Physiologic Drug Distribution and Protein Binding 289
LEGEND: 18
LEGEND:
Sulphaphenylpyrazole pH 7.4
25 16 Theoretical curve
Phenylbutazone pH 7.4 Experimental points
Sulphamethoxypyridazine pH 8.0 14 n1 = 0.72
k1n1 = 18,000
Sulphamethoxypyridazine pH 7.0
12 n2 = 5.3
20 k2n2 = 800
10 k1 = 25,000
k2 = 150
8
15
6
I I + II
4
10
2
II
0
0 0.5 1.0 1.5 2.0 2.5
5
r
FIGURE 1118 Binding curves for salicylic acid to crystal-
0 line bovine serum albumin. Curve I, plot for one class, n1 = 0.72,
0 0.5 1.0 1.5 2.0
k1 = 25,000. Curve II, plot for second class, n2 = 5.3, k2 = 150.
r
Curve I + II, plot for both binding sites, sum of the above. (From
FIGURE 1116 Davison, 1971, with permission.)
Graphic determination of number of
binding sites and association constants for interaction of
sulfonamides and phenylbutazone with albumin. (From Thorp,
Equation 11.24 into Equation 11.25:
1964, with permission.)
[D ] nK
a [D]= β
r =
[PT ] 1+ (11.25)
the total drug concentration, [D K
T], in the plasma, as a [D]
follows: [Dβ ]
β = where [Db] is the bound drug concentration; [D] is
[D
T ] (11.24) the free drug concentration; and [PT] is the total pro-
tein concentration. Rearrangement of this equation
The value of the association constant, Ka, can be gives the following expression, which is analogous
determined, even though the nature of the plasma to the Scatchard equation:
proteins binding the drug is unknown, by rearranging
[Dβ ]
= nKa [PT ]− Ka [Dβ ] (11.26)
[D]
n k
1 1 Concentrations of both free and bound drug
may be measured experimentally, and a graph
obtained by plotting [Db]/[D] versus [Db] will yield
a straight line for which the slope is the association
constant Ka. Equation 11.26 shows that the ratio of
k
1
bound Cp to free Cp is influenced by the affinity con-
k stant, the protein concentration, [PT], which may
2
n k
2 2 change during disease states, and the drug concen-
n n tration in the body.
1 2
r The values for n and Ka give a general estimate
of the affinity and binding capacity of the drug, as
FIGURE 1117 Hypothetical binding of drug to protein.
The k’s represent independent binding constants and the n’s plasma contains a complex mixture of proteins. The
represent the number of binding sites per molecule of protein. drug–protein binding in plasma may be influenced by
r/[D] x 10–4
r/[D ]
r/[D] x 10–3
290 Chapter 11
competing substances such as ions, free fatty acids,
100 A B
drug metabolites, and other drugs. Measurements of
drug–protein binding should be obtained over a wide C
75
drug concentration range, because at low drug con-
centrations a high-affinity, low-capacity binding site
50
might be missed or, at a higher drug concentration,
saturation of protein-binding sites might occur.
25
Relationship between Protein 0
Concentration and Drug Concentration 0 0.05 0.5 5
Protein concentration
in Drug–Protein Binding (mg/100 mL)
The drug concentration, the protein concentration, FIGURE 1120 Effect of protein concentration on the
and the association (affinity) constant, Ka, influence percentage of drug bound. A, B, and C represent hypothetical
the fraction of drug bound (Equation 11.24). With a drugs with respective decreasing binding affinity.
constant concentration of protein, only a certain
number of binding sites are available for a drug. At
have important effects on the fraction of drug bound.
low drug concentrations, most of the drug may be
Any factors that suddenly increase the fraction of
bound to the protein, whereas at high drug concen-
free drug concentration in the plasma will cause a
trations, the protein-binding sites may become satu-
change in the pharmacokinetics of the drug.
rated, with a consequent rapid increase in the free
Because protein binding is nonlinear in most
drug concentrations (Fig. 11-19).
cases, the percent of drug bound is dependent on the
To demonstrate the relationship of the drug con-
concentrations of both the drug and proteins in the
centration, protein concentration, and Ka, the follow-
plasma. In disease situations, the concentration of
ing expression can be derived from Equations 11.24
protein may change, thus affecting the percent of
and 11.25.
drug bound. As the protein concentration increases,
the percent of drug bound increases to a maximum.
1
β = (11.27) The shapes of the curves are determined by the asso-
1+ ([D]/n[PT ]) + (1/nKa [PT ]) ciation constant of the drug–protein complex and the
drug concentration. The effect of protein concentra-
From Equation 11.27, both the free drug concentra-
tion on drug binding is demonstrated in Fig. 11-20.
tion, [D], and the total protein concentration, [PT],
CLINICAL SIGNIFICANCE
OF DRUG–PROTEIN BINDING
Most drugs bind reversibly to plasma proteins to
some extent. When the clinical significance of the
fraction of drug bound is considered, it is important
to know whether the study was performed using
pharmacologic or therapeutic plasma drug concen-
trations. As mentioned previously, the fraction of
drug bound can change with plasma drug concentra-
tion and dose of drug administered. In addition, the
Drug concentration patient’s plasma protein concentration should be
FIGURE 1119 Fraction of drug bound versus drug considered. If a patient has a low plasma protein
concentration at constant protein concentration. concentration, then, for any given dose of drug, the
Fraction of drug bound (DB/DT)
Drug bound (percent)
Physiologic Drug Distribution and Protein Binding 291
TABLE 1112 Factors That Decrease Plasma in free warfarin level was responsible for an increase
Protein Concentration in bleeding when warfarin was coadministered
with phenylbutazone, which competes for the same
Mechanism Disease State
protein-binding site (O’Reilly, 1973; Udall, 1970;
Decreased protein synthesis Liver disease Sellers and Koch-Weser, 1971). Recently, studies
Increased protein catabolism Trauma, surgery and reviews have shown that the clinical significance
of warfarin protein binding and its impact on bleed-
Distribution of albumin into Burns
ing are less prominent, adding other factors and
extravascular space
explanations (Sands et al, 2002; Chan, 1995; Benet
Excessive elimination of protein Renal disease and Hoener, 2002). Since protein binding and metab-
olism both occur in vivo and can both influence the
rate of metabolism in a patient, it is not always clear
concentration of free (unbound) bioactive drug may whether to attribute the cause of a change in metabo-
be higher than anticipated. The plasma protein con- lism based on kinetic observations alone. Change in
centration is controlled by a number of variables, CYP enzymes may occur in genetic polymorphism
including (1) protein synthesis, (2) protein catabo- and at the same time change in protein may occur
lism, (3) distribution of the protein between intravas- due to a number of causes. Van Steeg et al (2009)
cular and extravascular space, and (4) excessive recently reviewed the effect of protein binding on
elimination of plasma protein, particularly albumin. drug pharmacokinetics and pharmacodynamics. The
A number of diseases, age, trauma, and related cir- authors discussed many important aspects of protein
cumstances affect the plasma protein concentration binding and drug disposition using beta-blocker as
(Tables 11-12–11-14). examples. Schmidt et al (2010) reviewed many
For example, liver disease results in a decrease examples of drug–protein binding and concluded
in plasma albumin concentration due to decreased that appropriate analysis requires careful consider-
protein synthesis. In nephrotic syndrome, an accu- ation of both pharmacokinetic and pharmacodynamic
mulation of waste metabolites, such as urea and uric processes, as they both contribute to the safety and
acid, as well as an accumulation of drug metabolites, efficacy of drugs. Ideally, the free drug concentra-
may alter protein binding of drugs. Severe burns may tions at the receptor site should be used for making
cause an increased distribution of albumin into the inferences about a drug’s pharmacological activity.
extracellular fluid, resulting in a smaller plasma Albumin has two known binding sites that share
albumin concentration. In certain genetic diseases, the binding of many drugs (MacKichan, 1992).
the quality of the protein that is synthesized in the Binding site I is shared by phenylbutazone, sulfon-
plasma may be altered due to a change in the amino amides, phenytoin, and valproic acid. Binding site II
acid sequence. Both chronic liver disease and renal is shared by the semisynthetic penicillins, proben-
disease, such as uremia, may cause an alteration in ecid, medium-chain fatty acids, and the benzodiaz-
the quality of plasma protein synthesized. An altera- epines. Some drugs bind to both sites. Displacement
tion in the protein quality may be demonstrated by occurs when a second drug is taken that competes
an alteration in the association constant or affinity of for the same binding site in the protein as the ini-
the drug for the protein. tial drug.
Although it is generally assumed that binding
sites are preformed, there is some evidence pointing
Drug Interactions—Competition to the allosteric nature of protein binding. This
for Binding Sites means that the binding of a drug modifies the con-
When a highly protein-bound drug is displaced from formation of protein in such a way that the drug
binding by a second drug or agent, a sharp increase binding influences the nature of binding of further
in the free drug concentration in the plasma may molecules of the drug. The binding of oxygen to
occur, leading to toxicity. For example, an increase hemoglobin is a well-studied biochemical example
292 Chapter 11
TABLE 1113 Physiologic and Pathologic Conditions Altering Protein Concentrations in Plasmaa
Albumin `1-Glycoprotein Lipoprotein
Decreasing Age (geriatric, neonate) Fetal concentrations Hyperthyroidism
Bacterial pneumonia Nephrotic syndrome Injury
Burns Oral contraceptives Liver disease?
Cirrhosis of liver Trauma
Cystic fibrosis
Gl disease
Histoplasmosis
Leprosy
Liver abscess
Malignant neoplasms
Malnutrition (severe)
Multiple myeloma
Nephrotic syndrome
Pancreatitis (acute)
Pregnancy
Renal failure
Surgery
Trauma
Increasing Benign tumor Age (geriatric) Diabetes
Exercise Celiac disease Hypothyroidism
Hypothyroidism Crohn’s disease Liver disease?
Neurological disease? Injury Nephrotic syndrome
Neurosis Myocardial infarction
Paranoia Renal failure
Psychosis Rheumatoid arthritis
Schizophrenia Stress
Surgery
Trauma
aIn the conditions listed, the protein concentrations are altered, on average, by 30% or more, and in some cases by more than 100%.
Data compiled from Jusko WJ, Gretch M: Plasma and tissue protein binding of drugs in pharmacokinetics, Drug Metab Rev 5:43–10, 1976, and
Friedman RB, et al: Effects of diseases on clinical laboratory tests, Clin Chem 26, 1980.
Physiologic Drug Distribution and Protein Binding 293
TABLE 1114 Protein Binding in Normal (Norm) Renal Function, End-Stage Renal Disease (ESRD),
during Hemodialysis (HD), and in Nephrotic Syndrome (NS)
Norm (% Bound) ESRD (% Bound) HD (% Bound) NS (% Bound)
Azlocillin 28 25
Bilirubin Decreased
Captopril 24 18
Cefazolin 84 73 22
Cefoxitin 73 20
Chloramphenicol 53 45 30
Chlorpromazine 98 98
Clofibrate 96 89
Clonidine 30 30
Congo red Decreased
Dapsone Normal
Desipramine 80 Normal
N-Desmethyldiazepam 98 94
Desmethylimipramine 89 88
Diazepam 99 94
Diazoxide (30 mg/mL) 92 86 83
(300 mg/mL) 77 72
Dicloxacillin 96 91
Diflunisal 88 56 39
Digitoxin 97 96 90 96
Digoxin 25 22
Doxycycline 88 71
Erythromycin 75 77
Etomidate 75 57
Fluorescein 86 Decreased
Furosemid 96 94 93
Indomethacin Normal
Maprotiline 90 Normal
b-Methyldigoxin 30 19
Methyl orange Decreased
Methyl red Decreased
Morphine 35 31
Nafcillin 88 81
(Continued)
294 Chapter 11
TABLE 1114 Protein Binding in Normal (Norm) Renal Function, End-Stage Renal Disease (ESRD),
during Hemodialysis (HD), and in Nephrotic Syndrome (NS) (Continued)
Norm (% Bound) ESRD (% Bound) HD (% Bound) NS (% Bound)
Naproxen 75 21
Oxazepam 95 88
Papaverine 97 94
Penicillin G 72 36
Pentobarbital 66 59
Phenobarbital 55 Decreased
Phenol red Decreased
Phenylbutazone 97 88
Phenytoin 90 80 93 81
Pindolol 41 Normal
Prazosin 95 92
Prednisolone (50 mg) 74 65 64
(15 mg) 87 88 85
D-Propoxyphene 76 80
Propranolol 88 89 90
Quinidine 88 86 88
Salicylate 94 85
Sulfadiazine Decreased
Sulfamethoxazole 74 50
Sulfonamides Decreased
Strophantin 1 2
Theophylline 60 Decreased
Thiopental 72 44
Thyroxine Decreased
Triamterene 81 61
Trimethoprim 70 68 70
Tryptophan 75 Decreased
D-Tubocurarine 44 41
Valproic acid 85 Decreased
Verapamil 90 Normal
Warfarin 99 98
From Keller et al (1984), with permission.
Physiologic Drug Distribution and Protein Binding 295
in which the initial binding of other oxygen to the highly potent and has a narrow therapeutic window.
iron in the heme portion influences the binding of Protein–drug binding has the buffering effect of pre-
other oxygen molecules. venting an abrupt rise in free drug concentration in
the body. For orally administered drugs, the liver
provides a good protection against drug toxicity
Effect of Change in Protein Binding because of hepatic portal drug absorption and metab-
Most studies of the kinetics of drug–protein binding olism. For a highly extracted drug orally adminis-
consider binding to plasma proteins. However, cer- tered, an increase in fu (more free drug) causes
tain drugs may also bind specific tissue proteins or hepatic clearance to increase (ie, fuClint), thus reduc-
other macromolecules, such as melanin or DNA, ing total AUCoral but not changing free drug AUCu
oral
drug receptors or transiently to transport proteins. due to the compensatory effect of fu AUCoral (ie,
Most literature exclude drug binding to other macro- decrease in AUCoral is compensated by the same
molecules and are limited to discussing the effect of increase in free AUCu = fu AUCoral) (see derivation of
drug binding to plasma albumin and AAG only. Equation 11.34 based on Benet and Hoener [2002]
Since many drugs are eliminated by the liver, it is under Protein Binding and Drug Exposure).
relevant to discuss the effect of protein binding after The assumptions and derivation should be care-
oral drug administration or by parenteral administra- fully observed before applying the concept to indi-
tion, after which the drug bypasses first-pass hepatic vidual drugs. Most important of all, the model
elimination. assumes a simple well-stirred hepatic model and
After IV drug administration, displacement of excludes drugs involving transporters, which is now
drugs from plasma protein binding causing an known to be common. A recent review (Schmidt et
increase in fu or increased free drug concentration al, 2010) further discussed the issue of protein bind-
may potentially facilitate extravascular drug distribu- ing and its effect on pharmacokinetics and pharma-
tion and an increase in the apparent volume of distri- codynamics. The author discussed the effect of
bution. The increased distribution results in a smaller changing VD on the elimination half-life of drugs
plasma Cp due to wider distribution, making drug using Equation 11.14, which is shown by rearrang-
elimination more difficult (k = Cl/VD). This is analo- ing to be the same as Equation 11.28
gous to reducing the fraction of free drug presented
for elimination per unit time based on a one-compart- V V 0.693
t
ment model. Consequently, a longer elimination half- 1/2 = ln2 D = D 1 . 4
1
Cl
( 1 )
Cl
life is expected due to wider tissue drug distribution.
The relationship is expressed by Equation 11.28 in
order to assess the distribution effect due to protein Drug Distribution, Drug Binding,
binding. Displacement, and Pharmacodynamics
The relationship of reversible drug–protein binding in
the plasma and drug distribution and elimination is
0.693 V
Cl = D = kV (11.28) shown in Fig. 11-8. A decrease in protein binding that
t D
1/2 results in an increased free drug concentration will
allow more drug to cross cell membranes and distrib-
Drug clearance may remain unaffected or only ute into all tissues, as discussed above. More drug will
slightly changed if the decrease in the elimination therefore be available to interact at a receptor site to
rate constant is not compensated by an increase in V produce a more intense pharmacologic effect, at least
D
as shown by Equation 11.28. The mean steady-state temporarily. The increased free concentration also may
total drug concentration will remain unchanged cause an increased rate of metabolism and decreased
based on no change in Cl or kVD. Whether the change half-life which then may produce a lower total steady-
in plasma drug–protein binding has pharmacody- state drug concentration but similar steady-state free
namic significance depends on whether the drug is drug concentration (see additional discussion below).
296 Chapter 11
Clinically, the pharmacodynamic response is
LEGEND:
influenced by both the distribution of the drug and Free
the concentration of the unbound drug fraction. The 1000 Total
drug dose and the dosage form must be chosen to 10-sec injection
100-sec injection
provide sufficiently high unbound drug concentra-
tions so that an adequate amount of drug reaches the
100
site of drug action (receptor). The onset of drug
action depends on the rate of the free (unbound) drug
that reaches the receptor and provides a minimum
effective concentration (MEC) to produce a pharma- 10
codynamic response (see Chapters 1 and 21). The
onset time is often dependent on the rate of drug
uptake and distribution to the receptor site. The inten-
sity of a drug action depends on the total drug con- 1
centration of the receptor site and the number of
receptors occupied by drug. To achieve a pharmaco- 0
dynamic response with the initial (priming) dose, the 0 8 16 24 32 40
Seconds
amount (mass) of drug when dissolved in the volume
of distribution must give a drug concentration ≥ MEC FIGURE 1121 Calculated time course of total and free
at the receptor site. Subsequent drug doses maintain diazoxide concentrations in arterioles. (From Sellers and Koch-
the pharmacodynamic effect by sustaining the drug Weser, 1973, with permission.)
concentration at the receptor site. Subsequent doses
are given at a dose rate (eg, 250 mg every 6 hours)
drug dose injected was the same. Although most
that replaces drug loss from the receptor site, usu-
drugs have linear binding at their therapeutic doses,
ally by elimination. However, redistributional fac-
in some patients, free drug concentration can increase
tors may also contribute to the loss of drug from the
rapidly with rising drug concentration as binding
receptor site.
sites become saturated. An example is illustrated in
A less understood aspect of protein binding is
Fig. 11-22 for lidocaine (MacKichan, 1992).
the effect of binding on the intensity and pharmaco-
dynamics of the drug after intravenous administra-
tion. Rapid IV injection may increase the free drug
concentration of some highly protein-bound drugs 1.00 Disopyramide
and therefore increase its intensity of action. Sellers
and Koch-Weser (1973) reported a dramatic increase 0.80
in hypotensive effect when diazoxide was injected
0.60
rapidly IV in 10 seconds versus a slower injection of Lidocaine
100 seconds. Diazoxide was 9.1% and 20.6% free
0.40
when the serum levels were 20 and 100 mg/mL,
respectively. Figure 11-21 shows a transient high free
0.20
diazoxide concentration that resulted after a rapid IV Carbamazeprine
injection, causing maximum arterial dilation and
0.00
hypotensive effect due to initial saturation of the 1 x 108 1 x 107 1 x 106 1 x 105 1 x 104 1 x 103
protein-binding sites. In contrast, when diazoxide Unbound concentration, M
was injected slowly over 100 seconds, free diazoxide
FIGURE 1122 Simulation showing changes in fraction
serum level was low, due to binding and drug distri-
of free (unbound) drug over various molar drug concentrations
bution. The slower injection of diazoxide produced a for three drugs with protein binding. (From MacKichan, 1992,
smaller fall in blood pressure, even though the total with permission.)
Unbound fraction in plasma Plasma diazoxide (mg/L)
Physiologic Drug Distribution and Protein Binding 297
The nature of drug–drug and drug–metabolite
interactions is also important in drug–protein binding. this example is based on one drug displacing
In this case, one drug may displace a second bound another drug, nutrients, physiologic products, and
drug from the protein, causing a sudden increase in the waste products of metabolism may cause dis-
pharmacologic response due to an increase in free drug placement from binding in a similar manner.
concentration. As illustrated by this example, displacement
is most important with drugs that are more than
Frequently Asked Questions 95% bound and has a narrow therapeutic index.
Under normal circumstances, only a small pro-
»»What happens to the pharmacokinetic parameters
of a drug when a displacing agent is given? portion of the total drug is active. Consequently,
a small displacement of bound drug causes a dis-
»»What kind of drugs are most susceptible to clinically proportionate increase in the free drug concentra-
relevant changes in pharmacokinetics? Does the rate tion, which may cause drug intoxication.
of administration matter?
With drugs that are not as highly bound to
plasma proteins, a small displacement from the
protein causes a transient increase in the free
EXAMPLE »» » drug concentration, which may cause a transient
increase in pharmacologic activity. However, more
Compare the percent of change in free drug con- free drug is available for both renal excretion and
centration when two drugs, A (95% bound) and hepatic biotransformation, which may be demon-
B (50% bound), are displaced by 5% from their strated by a transient decreased elimination half-
respective binding sites by the administration of life. Drug displacement from protein by a second
another drug (Table 11-15). For a highly bound drug can occur by competition of the second drug
drug A, a displacement of 5% of free drug is actu- for similar binding sites. Moreover, any altera-
ally a 100% increase in free drug level. For a weakly tion of the protein structure may also change the
bound drug like drug B, a change of 5% in free con- capacity of the protein to bind drugs. For exam-
centration due to displacement would cause only ple, aspirin acetylates the lysine residue of albu-
a 10% increase in free drug level over the initially min, which changes the binding capacity of this
high (50%) free drug concentration. For a patient protein for certain other anti-inflammatory drugs,
medicated with drug B, a 10% increase in free drug such as phenylbutazone.
level would probably not affect the therapeutic The displacement of endogenous sub-
outcome. However, a 100% increase in active drug, stances from plasma proteins by drugs is usually
as occurs with drug A, might be toxic. Although of little consequence. Some hormones, such as
TABLE 1115 Comparison of Effects of 5% Displacement from Binding on Two Hypothetical Drugs
Before Displacement After Displacement Percent Increase in Free Drug
Drug A
Percent drug bound 95 90
Percent drug free 5 10 +100
Drug B
Percent drug bound 50 45
Percent drug free 50 55 +10
298 Chapter 11
Protein Binding and Drug Exposure
thyroid and cortisol, are normally bound to spe-
The impact of protein binding on clinical drug effi-
cific plasma proteins. A small displacement of
cacy and safety has long been recognized (Koch-
these hormones rarely causes problems because
Weser and Sellers, 1976; Greenblatt et al, 1982) but
physiologic feedback control mechanisms take
has received renewed literature discussion recently
over. However, in infants, the displacement of bili-
(Sands et al, 2002; Chan, 1995; Benet and Hoener,
rubin by drugs can cause mental retardation and
2002, van Steeg et al, 2009, Schmidt et al, 2010).
even death, due to the difficulty of bilirubin elimi-
Free plasma drug concentration or free drug concen-
nation in newborns.
tration at the site of action is generally considered to
Finally, the binding of drugs to proteins can
be more relevant than total plasma drug concentra-
affect the duration of action of the drug. A drug
tion. When considering drug safety, how high and
that is extensively but reversibly bound to protein
how long the free plasma drug level will be sustained
may have a long duration of action due to a depot
are also important to a toxicokineticist. This is often
effect of the drug–protein complex.
measured by the AUC for the free plasma drug
While a change in free drug concentration
concentration.
due to changing protein binding can potentially
Based on the well-stirred venous equilibration
change the pharmacologic response of a drug,
model incorporating protein binding (Benet and
many drugs with a change in protein binding did
Hoener, 2002), organ clearance for a drug (Cl) is
not show a significant change in clinical effect
expressed as
(Benet and Hoener, 2002), as discussed in the next
section. The important question to ask is: Will the Qorgan fuClint
Cl =
increase in free drug concentration due to reduced Qorgan + (11.29)
fuClint
binding elicit a rapid pharmacologic response
For a low-extraction drug, where Q is blood flow, fu before the temporary increase in free drug is
is fraction of drug unchanged and Clint is intrinsic
diluted by a rapid distribution and/or elimination
clearance, Q
due to a greater fraction of free drug? Kruger and organ >> fuClint, the equation simplifies to
Figg (2001) observed that the angiogenesis activ- Cl = fuClint (11.30)
ity of suramin, an inhibitor of blood vessel prolif-
eration, is greatly altered by protein binding. In Clearance depends on fu and intrinsic clearance.
biological assays with aorta rings of rats, the effect Intrinsic clearance is flow independent; whereas
was measured ex vivo at the site directly, and the hepatic clearance, ClH, is flow dependent for a high
degree of protein binding was reported to be extraction drug.
important. In the body, the pathways to reach the Hepatic bioavailability of a drug, FH, is
receptor, distribution, and elimination are factors expressed as
that complicate the effect of a rise in free drug due
to displacement from binding. In general, the out- Q
F = H
H
come of a change in protein binding in vivo may QH + (11.31)
fuClint
be harder to measure depending on where the
Let Fabs be the fraction of drug absorbed to the
site of action is located. The onset of a drug, and its
gut wall and FG be the fraction that gets through the
distribution half-life to the site of action, may need
gut wall unchanged (ie, Foral = Fabs FG FH). The sys-
to be considered. In the next section, this subject
temic AUC after an oral dose is
is further discussed based on the recent concept
of drug exposure. The concept of drug exposure FabsFGDose
AUC
is important because adverse reactions in many oral = (11.32)
fuClint
organs are related to their exposure to plasma
drug concentration. For an unbound drug, AUCu
oral = [ f ]AUC
u oral
(11.33)
Physiologic Drug Distribution and Protein Binding 299
When substituted for AUCoral using Equation 11.32
into Equation 11.33, fu cancels out, and the equation Frequently Asked Questions
becomes »»Do all drugs that bind proteins lead to clinically
significant interactions?
F F Dose
AUCu = abs G
oral (11.34) »»What macromolecules participate in drug–protein
Clint binding?
Equation 11.34 above shows that for low-extraction »»How does drug–protein binding affect drug
elimination?
drugs, unbound drug exposure as measured by
unbound plasma drug area under the curve (AUCu
oral) »»What are the factors to consider when adjusting
is independent of f the drug dose for a patient whose plasma protein
u.
For a low-extraction drug, both IV and oral, concentration decreases to half that of normal?
changes in protein binding are generally not impor- »»fu is used to represent the fraction of free drug in the
tant. For a high-extraction drug after IV administra- plasma (Equations 11.30 and 11.33). Is fu always a
tion, changes in protein binding are clinically constant?
important whether metabolism is hepatic or nonhe-
»»Can a protein-bound drug be metabolized?
patic. For a drug that is administered IV and is
highly extracted by the liver (Qorgan << fu Clint),
AUCu
IV or unbound drug systemic exposure is
expressed by
CLINICAL EXAMPLE
f
uDose
AUCu
IV = fuAUCIV ≈ (11.35)
QH Protein concentration may change during some acute
disease states. For example, plasma AAG levels in
In this case, changes in binding may be clinically patients may increase due to the host’s acute-phase
important, as shown by the change of fu in response to infection, trauma, inflammatory pro-
Equation 11.35. cesses, and some malignant diseases. The acute-
The derivation of Equation 11.33 into phase response is a change in various plasma
Equation 11.34 is dependent on the fact that fu is proteins that is observed within hours or days fol-
constant as a function of t. If unbound drug con- lowing the onset of infection or injury. The acute-
centration Cu is changing at various Cp, that is, phase changes may be also indicative of chronic
concentration-dependent binding, then Cu = F(t) is disease (Kremer et al, 1988).
time dependent, and in fact, AUC will be nonlinear As many basic drugs bind to AAG, a change in
with dose and Equation 11.34 will be different for AAG protein concentration can contribute to more
different doses (see Chapter 10). Within therapeutic fluctuation in free drug concentrations among
drug concentrations, the effect of changes in fu is patients during various stages of infection or dis-
apparently not sufficient to change the efficacy of ease. Amprenavir (Agenerase), a protease inhibitor
most drugs and therefore is not of clinical concern. of human immunodeficiency virus type 1 (HIV-1), is
However, as more potent drugs with short elimina- highly bound to human plasma proteins, mostly to
tion half-lives are used, plasma drug concentrations AAG (approximately 90%). AAG levels are known
may potentially fall several fold and fu may change to vary with infection, including HIV disease.
significantly at various plasma concentrations. An Sadler et al (2001) showed a significant inverse lin-
anatomic-physiologic approach to evaluate drug ear relationship between AAG levels and amprenavir
concentrations (Mather, 2001) may be helpful in clearance as estimated by Cl/F. Unbound, or free,
understanding how drug efficacy and safety change amprenavir concentrations were not affected by
in protein binding and clearances in local tissues AAG concentrations even though the apparent total
(see Chapter 13). drug clearance was increased. The intrinsic clearance
300 Chapter 11
of the drug was not changed. The authors cautioned therapeutic free drug level through re-equilibration
that incorrect conclusions could be drawn about is difficult in such a case.
the pharmacokinetics of highly protein-bound The understanding of the molecular interactions
drugs if AAG concentration is not included in the of drug binding to proteins is essential to explain the
analysis. clinical pharmacology and toxicology in the body.
In addition, race, age, and weight were also Drug–protein binding is generally assumed to be
found to affect AAG levels. African American sub- reversible as modeled in later sections of this chap-
jects had significantly lower AAG concentrations ter. Taheri et al (2003) studied the binding and dis-
than Caucasian subjects. AAG in African-Americans placement of several local anesthetics, such as
was 77.2 ± 13.8 mg/dL versus 90 ± 20.2 mg/dL in lidocaine, mepivacaine, and bupivacaine with human
Caucasians (p < 0.0001). Pharmacokinetic analy- a1-acid glycoprotein (AAG). These investigators
sis showed that AAG correlated significantly with used a special molecular probe to see how local
age and race and was a significant predictor of anesthetics behave during equilibrium-competitive
amprenavir Cl/F. Interestingly, in spite of a statis- displacement from AAG. The change in recovery of
tically significant difference in total plasma AAG’s fluorescence as the quenching probe was
amprenavir level, a dose adjustment for racial dif- displaced from its high-affinity site was used to
ferences was not indicated, because the investiga- observe change in dissociation constants for the vari-
tors found the unbound amprenavir concentrations ous local anesthetics. The study demonstrated that
to be similar. the AAG-binding site has a strong positive correla-
Protein binding can lead to nonlinear or dose- tion between hydrophobicity of the local anesthetics
dependent kinetics. It was interesting to note that and their free energies of dissociation. The effect of
amprenavir Cl/F was dose dependent in the analy- pH and electrostatic forces on binding was also
sis without AAG data, but that no dose dependence explored. Studies by other investigators of these
was observed when AAG concentration was consid- molecular factors’ influence on binding were done
ered in the analysis. The higher doses of amprena- previously with albumin binding to different agents.
vir, which produce the greatest antiviral activity, More sophisticated models may be needed as the
resulted in the largest decrease in AAG concentra- understanding of molecular interactions of a drug
tion, which led to the greatest changes in total drug with a substrate protein improves. Theoretically, a
concentration. change in molecular conformation or allosteric bind-
In evaluating change in protein binding and its ing may change the activity of a drug but requires
impact on free plasma drug, it is important to real- clinical demonstration.
ize that protein changes or displacement often
results in changes in free plasma drug concentra-
tion. Nonetheless, the free drug is not necessarily CLINICAL EXAMPLE
increasingly eliminated unless the change in free
drug concentration facilitates metabolism, accom- A drug–drug interaction derived from the displace-
panied by a change in Clint (Clint measures the ment of lidocaine from tissue binding sites by mexi-
inherent capacity to metabolize the drug; see letine that resulted in the increased plasma lidocaine
Chapter 12). For some drugs, the change in protein concentrations was reported by Maeda et al (2002).
binding may be sufficiently compensated by a A case of an unexpected increase in plasma lido-
redistribution of the drug from one tissue to another caine concentration accompanied with severe side
within the body. In contrast, a change in drug pro- effects was observed when mexiletine was adminis-
tein binding accompanied by metabolism (Clint) tered to a patient with dilated cardiomyopathy.
will invariably result in an increased amount of Maeda et al (2002) further studied this observation
drug needed to maintain a steady-state level because in rabbits and in vitro. Mexiletine significantly
the total drug concentration is continuously being reduced the tissue distribution of lidocaine to the
eliminated. The maintenance of an adequate kidneys and lungs. Lidocaine plasma levels were
Physiologic Drug Distribution and Protein Binding 301
higher. Mexiletine had a strong displacing effect of Arterial and Venous Differences
lidocaine binding to the membrane component in Drug Concentrations
phosphatidylserine. Most pharmacokinetic studies are modeled based on
• Should loading doses of lidocaine be used in the blood samples drawn from various venous sites after
concurrent therapy of lidocaine and mexiletine? either IV or oral dosing. Physiologists have long recog-
• Would you consider the lung and kidney to be nized the unique difference between arterial and venous
“well equilibrated” tissues based on blood ow? blood. For example, arterial tension (pressure) of oxygen
drives the distribution of oxygen to vital organs. Chiou
(1989) and Mather (2001) have discussed the pharmaco-
kinetic issues when differences in drug concentrations Cp
MODELING DRUG DISTRIBUTION in arterial and venous are observed. They question the
validity of the assumption of the well-stirred condition or
Drug distribution may change in many disease and rapid mixing within the blood or plasma pool when there
physiologic states, making it difficult to predict the is gradual permeation into tissues in which the drug may
concentration of drug that reaches the site of drug then be metabolized. Indeed, some drug markers have
action (receptor). Pharmacokinetic models can be shown that rapid mixing may not be typical, except
used to predict these pharmacokinetic changes due when the drug is essentially confined to the blood pool
to changes in physiologic states. The model should due to protein binding.
consider free and bound drug equilibration and Differences in arterial and venous blood levels
metabolism at the apparent site of action, and tran- ranging as high as several hundred fold for griseofulvin
sient changes due to disease state (eg, pH change or have been reported. Forty compounds have been shown
impaired perfusion). to exhibit marked site dependence in plasma or blood
In pharmacokinetics, perfusion and rapid equili- concentration after dosing in both humans and animals.
bration within a region form the basis for the well- In some cases, differences are due mostly to large
stirred models that are used in many classical extraction of drug in poorly perfused local tissues, such
compartment models as well as some physiologic as with nitroglycerin (3.8-fold arteriovenous difference)
pharmacokinetic models. The concept of body or and procainamde (234% arteriovenous difference,
organ drug clearance assumes that uniform drug venous being higher). The classical assumption in phar-
concentration is rapidly established within a given macokinetics of rapid mixing within minutes in the
biological region (Corgan or Cplasma) at a given time entire blood circulation therefore may not be applicable
point. The model also allows: (1) the mass of drug to some drugs. Would the observed sampling differ-
present in the region can be calculated by multiply- ences result in significant difference in the AUCs
ing the concentration with its volume at a given time; between arterial and venous blood, or in prediction of
and (2) the rate of drug elimination from the site can toxicity or adverse effects of drugs? No such differences
be calculated by the product of clearance times drug were observed in the reviews by Chiou and Mather,
concentration. although the significance of these differences on drug
Model simplicity using the well-stirred approach therapy and toxicity has not been fully explored.
has advanced the concept of drug clearance and
allowed practical drug concentration to be estimated
based on body clearance and drug dose. The approach Frequently Asked Questions
has generally provided more accurate dosing for »»Why are most of the plasma drug concentration
many drugs for which drug action is determined data reported without indicating the sampling site
mostly by steady-state concentration, and a transient when there is a substantial difference in arterial and
change in concentration of short duration is not criti- venous blood drug concentrations for many drugs?
cal. However, caution should be exercised in inter- »»Does the drug concentration in the terminal phase of
preting model-predicted concentration to drug the curve show less dependency on site of sampling?
concentration at a given site in the body.
302 Chapter 11
CHAPTER SUMMARY
The processes by which drugs transverse capillary to the unbound drug in the liver for metabolism or in
membranes include passive diffusion and hydrostatic the kidney for excretion. These drugs are observed to
pressure. Passive diffusion is generally governed by have an ER >> fu.
Fick’s law of diffusion. Hydrostatic pressure repre- The pathophysiologic condition of the patient
sents the pressure gradient between the arterial end can affect drug–protein binding. Drug–protein bind-
of the capillaries entering the tissue and the venous ing may be reduced in uremic patients and in patients
capillaries leaving the tissue. Not all tissues have the with hepatic disease. During infection, stress, trauma,
same drug permeability. In addition, permeability of and severe burn, AAG levels may change and affect
tissues may change under various disease states, drug disposition.
such as inflammation. Lipophilic (hydrophobic) drugs may accumu-
Drug distribution can be perfusion/flow limited or late in adipose or other tissues which have a good
diffusion/permeability limited depending on the nature affinity for the drug.
of the drug. Drug distribution into cells is also con- The equation Vapp = Vp + Vt(fu/fut) defines Vapp
trolled by efflux and influx transporters for some drugs. which is related to plasma volume, tissue volume,
The factors that determine the distribution constant, kd, and fraction of free plasma and tissue drug in the
of a drug into an organ are related to the blood flow to body. The term Vapp allows the amount of drug in the
the organ, the volume of the organ, and the partitioning body to be calculated.
of the drug into the organ tissue, that is, kd = Q/VR. When a drug is tightly bound to a protein, only
The distribution half-life is inversely related to kd. the unbound drug is assumed to be metabolized;
The equation t1/2 = 0.693(VD /Cl) relates the elim- drugs belonging to this category are described as
ination half-life to the apparent volume of distribution restrictively eliminated. Some drugs may be elimi-
and clearance. A large apparent volume of distribu- nated even when they are protein bound and are
tion leads to low plasma drug concentrations making described as nonrestrictively eliminated.
it harder to remove the drug by the kidney or liver. The extent of drug binding to protein may be
Mechanistically, a low plasma drug concentration determined by two common in vitro methods, ultra-
may be due to (1) extensive distribution into tissues filtration and equilibrium dialysis. The number of
due to favorable lipophilicity, (2) extensive distribution binding sites and the binding constant can be deter-
into tissues due to protein binding in peripheral tis- mined using a graphic technique called the Scatchard
sues, or (3) lack of drug plasma protein binding. The plot. A drug tightly bound to protein has a large
equation is the basis for considering that Cl and VD association binding constant which is derived based
are both independent variables in contrast to Cl = kVD on the law of mass action.
which depicts Cl as proportional to VD with a con- Based on a “well-stirred venous equilibration”
stant, k, specific for the drug. model and hepatic clearance during absorption, many
Protein binding of a drug generally serves to orally given drugs do not result in clinically signifi-
retain the drug intravascularly, whereas tissue bind- cant changes in drug exposure when protein binding
ing generally pulls the drug away from the vascular (ie, fu) changes. The drug elimination rate increases
compartment. The two main proteins in the plasma in the liver when fu (free drug fraction) is increased
that are involved in drug–protein binding are albu- for many drugs given orally at doses below satura-
min and a1-acid glycoprotein, AAG. AAG tends to tion. In contrast, drugs administered by IV injection
bind mostly basic drugs. Protein-bound drugs are and a few orally administered drugs can have signifi-
generally not considered to be pharmacodynami- cant changes in free drug concentration when protein
cally active. Protein-bound drugs are slower to dif- binding changes. The clinical significance of changes
fuse and are not eliminated easily. For highly in protein binding must be considered on individual
extractable drugs, the bound drug may be dissociated drug basis and cannot be over generalized.
Physiologic Drug Distribution and Protein Binding 303
An important consideration regarding the effect of penetration to the site of action is important. Recent
change in drug–protein binding is the pharmacody- reviews indicate that simple hepatic flow/intrinsic
namics (PD) of the individual drug involved, that is, clearance-based analysis may sometimes be inadequate
how and where the drug exerts its action because drug to predict drug effect due to protein-binding changes.
LEARNING QUESTIONS
1. Why is the zone of inhibition in an antibiotic
Drug Percent Drug Bound
disc assay larger for the same drug concentra-
tion (10 mg/mL) in water than in serum? See Tetracycline 53
Fig. 11-23. Gentamycin 70
2. Determine the number of binding sites (n) and
Phenytoin 93
the association constant (Ka) from the following
data using the Scatchard equation. Morphine 38
r (D ë 10−4 M) r/D Which drug listed above might be predicted to
cause an adverse response due to the concur-
0.40 0.33
rent administration of a second drug such as
0.80 0.89 sulfisoxazole (Gantrisin)? Why?
1.20 2.00 5. What are the main factors that determine the
uptake and accumulation of a drug into tissues?
1.60 5.33
Which tissues would have the most rapid drug
uptake? Explain your answer.
Can n and Ka have fractional values? Why? 6. As a result of edema, fluid may leave the capil-
3. Discuss the clinical significance of drug–protein lary into the extracellular space. What effect
binding on the following: does edema have on osmotic pressure in the
a. Drug elimination blood and on drug diffusion into extracellular
b. Drug–drug interactions space?
c. “Percent of drug-bound” data 7. Explain the effects of plasma drug–protein
d. Liver disease binding and tissue drug–protein binding on
e. Kidney disease (a) the apparent volume of distribution and
4. Vallner (1977) reviewed the binding of drugs to (b) drug elimination.
albumin or plasma proteins. The following data 8. Naproxen (Naprosyn, Syntex) is a nonsteroidal
were reported: anti-inflammatory drug (NSAID) that is highly
bound to plasma proteins, >99%. Explain why
the plasma concentration of free (unbound)
naproxen increases in patients with chronic
alcoholic liver disease and probably other
forms of cirrhosis, whereas the total plasma
drug concentration decreases.
9. Most literature references give an average
value for the percentage of drug bound to
A B
plasma proteins.
FIGURE 1123 Antibiotic disc assay. A. Antibiotic in a. What factors influence the percentage of
water (10 mg/mL). B. Antibiotic in serum (10 mg/mL). drug bound?
304 Chapter 11
b. How does renal disease affect the protein 11. When a drug is 99% bound, it means that there
binding of drugs? is a potential risk of saturation. True or false?
c. How does hepatic disease affect the protein 12. Adenosine is a drug used for termination of tachy-
binding of drugs? cardia. The t1/2 after IV dose is only 20 to 30 sec-
10. It is often assumed that linear binding occurs at onds according to product information. Suggest
therapeutic dose. What are the potential risks a reason for such a short half-life based on your
of this assumption? knowledge of drug distribution and elimination.
ANSWERS
Frequently Asked Questions • The answer is False. The free drug concentrations
How does a physical property, such as partition in the tissue and plasma are the same after equili-
coefficient, affect drug distribution? bration, but the total drug concentration in the tissue
is not the same as the total drug concentration in
• Partitioning refers to the relative distribution of a the plasma. The bound drug concentration may
drug in the lipid and aqueous phases. Generally, vary depending on local tissue binding or the lipid
a high partition coefficient (Poil/water) favors tissue solubility of the drug. Many drugs have a long dis-
distribution and leads to a larger volume of dis- tributive phase due to tissue drug binding or lipid
tribution. Partitioning is a major factor that, along solubility. Drugs may equilibrate slowly into these
with protein binding of a drug, determines drug tissues and then be slowly eliminated. Drugs with
distribution. limited tissue affinity are easily equilibrated. Some
What are the causes of a long distribution half- examples of drugs with a long distributive phase
life for a body organ if blood flow to the tissue is are discussed in relation to the two-compartment
rapid? model (see Chapter 5).
• Generally, the long distribution half-life is caused What is the parameter that tells when half of the
by a tissue/organ that has a high drug concentra- protein-binding sites are occupied?
tion, due to either intracellular drug binding or • The ratio, r, is defined as the ratio of the number
high affinity for tissue distribution. Alternatively, of moles of drug bound to the number of moles
the drug may be metabolized slowly within the of protein in the system. For a simple case of one
tissue or the organ may be large and have a high binding site, r reflects the proportion of binding
capacity for organ uptake. sites occupied; r is affected by (1) the association
How long does it take for a tissue organ to be fully binding constant, (2) the free drug concentration,
equilibrated with the plasma? How long for a tissue and (3) the number of binding sites per mole of
organ to be half-equilibrated? protein. When [D], or free drug concentration, is
equal to 1 (or the dissociation constant K), the pro-
• The distribution half-life determines the time it
tein is 50% occupied for a drug with 1:1 binding
takes for a tissue organ to be equilibrated. It takes
according to Equation 11.19. (This can be veri-
4.32 distribution half-lives for the tissue organ to
fied easily by substituting for [D] into the right
be 95% equilibrated and one distribution half-life
side of the equation and determining r.) For a
for the drug to be 50% equilibrated. The concept
drug with n similar binding sites, binding occurs
is analogous to reaching steady state during drug
at the extent of 1:2 of bound drug:protein when
infusion (see Chapter 5).
[D] = 1/[Ka(2n − 1)]. This equation, however,
When a body organ is equilibrated with drug from the reflects binding in vitro when drug concentration
plasma, the drug concentration in that organ should is not changing; therefore, its conclusions are
be the same as that of the plasma. True or false? somewhat limited.
Physiologic Drug Distribution and Protein Binding 305
Do all drugs that bind proteins lead to clinically with a long elimination half-life. The elimination
significant interactions? phase is generally more gradual, since some drug
may be returned to the blood from the tissues as
• No. For some drugs, protein binding does not affect
drug is eliminated from the body.
the overall distribution of other drugs. Typically,
if a drug is highly bound, there is an increased Learning Questions
chance of a significant change in the fraction of
free drug when binding is altered. 1. The zone of inhibition for the antibiotic in
serum is smaller due to drug–protein binding.
Which macromolecules participate in drug–protein 2. Calculate r/(D) versus r; then graph the results
binding? on rectangular coordinates.
• Albumin, a1-acid glycoprotein, and lipoprotein. r r/(D × 104)
For some drugs and hormones, there may be a spe- 0.4 1.21
cific binding protein. 0.8 0.90
How does drug–protein binding affect drug 1.2 0.60
elimination? 1.6 0.30
The y intercept = nK = 1.5 × 104
• .
Most drugs are assumed to be restrictively bound, a
and binding reduces drug clearance and elimina- The x intercept = n = 2.
tion. However, some nonrestrictively bound drugs Therefore,
may be cleared easily. Changes in binding do not
affect the rate of elimination of these drugs. Some Ka = 1.5 × 104/2 = 0.75 × 104
drugs, such as some semisynthetic penicillins Ka may also be found from the slope.
that are bound to plasma protein, may be actively
8. The liver is important for the synthesis of
secreted in the kidney. The elimination rates of plasma proteins. In chronic alcoholic liver
these drugs are not affected by protein binding. disease or cirrhosis, fewer plasma proteins are
What are the factors to consider when adjusting the synthesized in the liver, resulting in a lower
drug dose for a patient whose plasma protein con- plasma protein concentration. Thus, for a
centration decreases to half that of normal? given dose of naproxen, less drug is bound to
the plasma proteins, and the total plasma drug
• It is important to examine why the albumin level is concentration is smaller.
reduced in the patient. For example, is the reduced 10. Protein binding may become saturated at any
albumin level due to uremia or hepatic dysfunc- drug concentration in patients with defective
tion? In general, reduced protein binding will proteins or when binding sites are occupied by
increase free drug concentration. Any change in metabolic wastes generated during disease states
drug clearance should be considered before reduc- (eg, renal disease). Diazoxide is an example of
ing the dose, since the volume of distribution may nonlinear binding at therapeutic dose.
be increased, partially offsetting the increase in 11. The answer is False. The percent bound refers
free drug concentration. to the percent of total drug that is bound. The
How does one distinguish between the distribution percent bound may be ≥99% for some drugs.
phase and the elimination phase after an IV injection Saturation may be better estimated using the
of a drug? Scatchard plot approach and by examining “r,”
which is the number of moles of drug bound
• In general, the early phase after an IV bolus dose divided by the number of moles of protein.
is the distributive phase. The elimination phase When r is 0.99, most of the binding sites are
occurs in the later phase, although distribution occupied. The fb, or fraction of bound drug, is
may continue for some drugs, especially for a drug useful for determining fu, fu = 1 − fb.
306 Chapter 11
12. Adenosine is extensively taken up by cells by deamination and/or is used as AMP in phos-
including the blood elements and the vascular phorylation. Consequently, adenosine has a short
endothelium. Adenosine is rapidly metabolized elimination half-life.
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Drug Elimination and
12 Hepatic Clearance
He Sun and Hong Zhao
Chapter Objectives ROUTE OF DRUG ADMINISTRATION AND
»» Describe the pathways for drug EXTRAHEPATIC DRUG METABOLISM
elimination in the body.
The decline from peak plasma concentrations after drug adminis-
»» Compare the clinical tration results from drug elimination or removal by the body. The
implications of hepatic and renal elimination of most drugs from the body involves the processes
disease on drug therapy. of both metabolism (biotransformation) and renal excretion
»» Describe the role of hepatic (see Chapter 7). For many drugs, the principal site of metabolism
blood flow, drug protein is the liver. However, other tissues or organs, especially those tissues
binding, and intrinsic clearance associated with portals of drug entry into the body, may also be
on hepatic clearance. involved in drug metabolism. These sites include the lung, skin,
gastrointestinal mucosal cells, microbiological flora in the distal
»» Explain how the rate of drug
portion of the ileum, and large intestine. The kidney may also be
elimination may change from
involved in certain drug metabolism reactions.
first-order elimination to zero-
Whether a change in drug elimination is more likely to be
order elimination and the clinical
affected by renal disease, hepatic disease, or a drug–drug interac-
implications of this occurrence.
tion may be predicted by measuring the fraction of the drug that is
»» Describe the biotransformation eliminated by either metabolism or excretion. Drugs that are
of drugs in the liver and which highly metabolized (such as phenytoin, theophylline, and lido-
enzymatic processes are caine) often demonstrate large intersubject variability in elimina-
considered “phase I reactions” tion half-lives and are dependent on the intrinsic activity of the
and “phase II reactions.” biotransformation enzymes, which may vary by genetic and envi-
ronmental factors. Intersubject variability in elimination half-lives
»» List the organs involved in drug
is less for drugs that are eliminated primarily by renal drug excre-
elimination and the significance
tion. Renal drug excretion is highly dependent on the glomerular
of each.
filtration rate (GFR) and blood flow to the kidney. Since GFR is
»» Discuss the relationship relatively constant among individuals with normal renal function,
between metabolic pathways the elimination of drugs that are primarily excreted unchanged in
and enzyme polymorphisms the urine is also less variable.
on intrasubject variability and
drug–drug interactions. First-Order Elimination
»» Describe how the exposure The rate constant of elimination (k) is the sum of the first-order
of a drug is changed when rate constant for metabolism (km) and the first-order rate constant
coadministered with another for excretion (ke):
drug that shares the same
metabolic pathway. k = ke + km (12.1)
309
310 Chapter 12
»» Define Michaelis–Menton In practice, the excretion rate constant (ke) is easily evaluated
kinetics and capacity-mediated for drugs that are primarily renally excreted. Nonrenal drug elimi-
metabolism. nation is usually assumed to be due for the most part to hepatic
metabolism, though metabolism or degradation can occur in any
»» Calculate drug and metabolite
organ or tissue that contains metabolic enzymes or is in a degrada-
concentrations for drugs that
tive condition. Therefore, the rate constant for metabolism (km) is
undergo both hepatic and
difficult to measure directly and is usually obtained from the dif-
biliary elimination.
ference between k and ke.
»» Define first-pass metabolism
and describe the relationship km = k − ke
between first-pass metabolism
and oral drug bioavailability. A drug may be biotransformed to several metabolites (metab-
»» Use urine data to calculate olite A, metabolite B, metabolite C, etc); thus, the metabolism rate
fraction of drug excreted and constant (km) is the sum of the rate constants for the formation of
metabolized. each metabolite:
»» Explain how Michaelis–Menton
k
kinetics can be used to determine m = kmA + kmB + kmC ++ kmI (12.2)
the mechanism of enzyme
inhibition and transporter The relationship in this equation assumes that the process of
inhibition. metabolism is first order and that the substrate (drug) concentra-
tion is very low. Drug concentrations at therapeutic plasma
»» Describe biliary drug excretion
levels for most drugs are much lower than the Michaelis–Menten
and define enterohepatic drug
constant, KM, and do not saturate the enzymes involved in
elimination.
metabolism. Nonlinear Michaelis–Menten kinetics must be used
»» Discuss the reasons why when drug concentrations saturate metabolic enzymes (see also
bioavailability is variable and Chapter 21).
can be less than 100%. Because these rates of elimination at low drug concentration
are considered first-order processes, the percentage of total drug
»» Describe BDDCS—Biological
Drug Disposition Classification metabolized may be obtained by the following expression:
System.
k
% drug metabolized m
= ×100 (12.3)
k
Fraction of Drug Excreted Unchanged (fe) and Fraction
of Drug Metabolized (1 – fe)
For most drugs, the fraction of dose eliminated unchanged (fe) and
the fraction of dose eliminated as metabolites can be determined.
For example, consider a drug that has two major metabolites and
is also eliminated by renal excretion (Fig. 12-1). Assume that 100 mg
of the drug was given to a patient and the drug was completely
absorbed (bioavailability factor F = 1). A complete (cumulative)
urine collection was obtained, and the quantities in parentheses in
Fig. 12-1 indicate the amounts of each metabolite and unchanged
drug that were recovered. The overall elimination half-life (t1/2) for
this drug was 2.0 hours (k = 0.347 h−1).
Drug Elimination and Hepatic Clearance 311
k elimination half-life of the drug is 2 hours and fe is
mA Metabolite A
(10 mg) 0.7, then ke is estimated by Equation 12.5.
k
e = fek (12.5)
Drug kmB Metabolite B
(100 mg) (20 mg) Because t1/2 is 2 hours, k is 0.693/2 h = 0.347 h−1, and
ke is
ke Unchanged drug ke = (0.7) (0.347) = 0.243 h−1
in urine (70 mg)
FIGURE 121 Model of a drug that has two major PRACTICAL FOCUS
metabolites and is also eliminated by renal excretion.
The percentages of drug excreted and metabolised
are clinically useful information. If the renal excre-
tion pathway becomes impaired, as in certain kidney
To determine the renal excretion rate constant, disorders, then less drug will be excreted renally and
the following relationship is used: hepatic metabolism may become the primary drug
elimination route. The reverse is true if liver function
ke total dose excreted in urine D∞
u
= = (12.4) declines. For example, if in the above situation renal
k total dose absorbed FD0 excretion becomes totally impaired (ke ≈ 0), the
elimination t1/2 can be determined as follows:
where D∞
u is the total amount of unchanged drug
recovered in the urine. In this example, ke is found by k = km + ke
proper substitution into Equation 12.4:
but
70
k = (0.347) = 0.243 h−1
e
100 ke ≈ 0
Therefore,
To find the percent of drug eliminated by renal
excretion, the following approach may be used: k ≈ km ≈ 0.104 h−1
ke 0.243
% drug excretion = ×100 = ×100 = 70% The new t1/2 (assuming complete renal shutdown) is
k 0.347
0.693
t1/2 = = 6.7 h
Alternatively, because 70 mg of unchanged drug was 0.104
recovered from a total dose of 100 mg, the percent of In this example, renal impairment caused the drug
drug excretion may be obtained by elimination t1/2 to be prolonged from 2 to 6.7 hours.
Clinically, the dosage of this drug must be lowered to
70
% drug excretion = × 100 = 70% prevent the accumulation of toxic drug levels. Methods
100 for adjusting the dose for renal impairment are dis-
cussed in Chapter 24.
Therefore, the percent of drug metabolized is
100%−70%, or 30%.
For many drugs, the literature has approximate HEPATIC CLEARANCE
values for the fraction of drug (fe) excreted unchanged
in the urine. In this example, the value of ke may be The clearance concept may be applied to any organ
estimated from the literature values for the elimina- and is used as a measure of drug elimination by the
tion half-life of the drug and fe. Assuming that the organ (see Chapter 7). Hepatic clearance may be
312 Chapter 12
defined as the volume of blood that perfuses the liver
which is cleared of drug per unit of time. As dis- In this example, the metabolites are recov-
cussed in Chapter 7, total body clearance is com- ered completely and hepatic clearance may be
posed of all the clearances in the body: calculated as total body clearance times the per-
cent of dose recovered as metabolites. Often,
ClT = Clnr + Clr (12.6) the metabolites are not completely recovered,
thus precluding the accuracy of this approach.
where ClT is total body clearance, Clnr is nonrenal In this case, hepatic clearance is estimated as the
clearance (often equated with hepatic clearance, Clh), difference between body clearance and renal
and Clr is renal clearance. Hepatic clearance (Clh) is clearance.
also equal to total body clearance (ClT) minus renal
clearance (ClR) assuming no other organ metabolism,
as shown by rearranging Equation 12.6 to
Extrahepatic Metabolism
Clh = ClT − ClR (12.6a)
A few drugs (eg, nitroglycerin) are metabolized
extensively outside the liver. This is known as extra-
EXAMPLES »» » hepatic metabolism. A simple way to assess extrahe-
patic metabolism is to calculate hepatic (metabolic)
1. The total body clearance for a drug is 15 mL/ and renal clearance of the drug and compare these
min/kg. Renal clearance accounts for 10 mL/ clearances to total body clearance.
min/kg. What is the hepatic clearance for the
drug?
Solution EXAMPLES »» »
Hepatic clearance = 15 – 10 = 5 mL/min/kg
1. Morphine clearance, ClT, for a 75-kg male
Sometimes the renal clearance is not known, patient is 1800 mL/min. After an oral dose,
in which case hepatic clearance and renal clear- 4% of the drug is excreted unchanged in the
ance may be calculated from the percent of intact urine (fe = 0.04). The fraction of drug absorbed
drug recovered in the urine. after an oral dose of morphine sulfate is
2. The total body clearance of a drug is 10 mL/ 24% (F = 0.24). Hepatic blood flow is about
min/kg. The renal clearance is not known. From 1500 mL/min. Does morphine have any extra-
a urinary drug excretion study, 60% of the drug hepatic metabolism?
is recovered intact and 40% is recovered as
Solution
metabolites. What is the hepatic clearance for
the drug, assuming that metabolism occurs in Since fe = 0.04, renal clearance Clr = 0.04 ClT and
the liver? nonrenal clearance Clnr = (1 – 0.04) ClT = 0.96 ClT.
Therefore, Clnr = 0.96 × 1800 mL/min = 1728 mL/
Solution
min. Since hepatic blood flow is about 1500 mL/
Hepatic clearance = total body clearance × (1 – fe) min, the drug appears to be metabolized faster
than the rate of hepatic blood flow. Thus, at least
(12.7)
some of the drug must be metabolized outside
where fe = fraction of intact drug recovered in the liver. The low fraction of drug absorbed after
the urine. an oral dose indicates that much of the drug
is metabolized before reaching the systemic
Hepatic clearance = 10 × (1 – 0.6) = 4 mL/min/kg
circulation.
Drug Elimination and Hepatic Clearance 313
ENZYME KINETICS—MICHAELIS–
2. Flutamide (Eulexin®, Schering), used to treat
prostate cancer, is rapidly metabolized in humans MENTEN EQUATION
to an active metabolite, a-hydroxyflutamide. The process of biotransformation or metabolism is
The steady-state level is 51 ng/mL (range the enzymatic conversion of a drug to a metabolite.
24–78 ng/mL) after oral multiple doses of 250 mg In the body, the metabolic enzyme concentration is
of flutamide given 3 times daily or every constant at a given site, and the drug (substrate) con-
8 hours (maufacturer’s approved label)∗. Calcu- centration may vary. When the drug concentration is
late the total body clearance and hepatic clear- low relative to the enzyme concentration, there are
ance assuming that flutamide is 90% metabo- abundant enzymes to catalyze the reaction, and the
lized, and is completely (100%) absorbed. rate of metabolism is a first-order process. Saturation
Solution of the enzyme usually occurs when the plasma drug
concentration is relatively high, all the enzyme
From Chapters 7 and 9, total body clearance, ClT, molecules become complexed with drug, and the
can be calculated by reaction rate is at a maximum rate; the rate process
FD then becomes a zero-order process (Fig. 12-2). The
Cl 0
=
T C∞ maximum reaction rate is known as Vmax, and the
τ
av
substrate or drug concentration at which the reaction
occurs at half the maximum rate corresponds to a com-
250 × 1, 000, 000
ClT = posite parameter KM. These two parameters determine
51 × 8
the profile of a simple enzyme reaction rate at various
= 6.127 × 105 mL/h drug concentrations. The relationship of these param-
= 10,200 mL/min eters is described by the Michaelis–Menten equation
(see Chapter 13).
Clnr = 10,200 mL/min × 0.9 Enzyme kinetics generally considers that 1 mole
= 9180 mL/min of drug interacts with 1 mole of enzyme to form an
enzyme–drug (ie, enzyme–substrate) intermediate.
The Clnr of flutamide is far greater than the rate The enzyme–drug intermediate further reacts to yield
of hepatic blood flow (about 1500 mL/min), a reaction product or a drug metabolite (Fig. 12-3).
indicating extensive extrahepatic clearance. The rate process for drug metabolism is described
by the Michaelis–Menten equation which assumes
that the rate of an enzymatic reaction is dependent on
Frequently Asked Questions
»»How does the route of drug administration affect
drug elimination? Vmax
»»Why does the rate of drug elimination for some drugs
change from first-order elimination to zero-order 0.5 Vmax
elimination?
»»What organs are involved in drug elimination?
KM
»»How is zero- or first-order elimination pro- Substrate concentration [S]
cesses related to either linear or nonlinear drug
metabolism? FIGURE 122 Michaelis–Menten enzyme kinetics.
The hyperbolic relationship between enzymatic reaction
velocity and the drug substrate concentration is described by
Michaelis–Menten enzyme kinetics. The KM is the substrate
∗Drugs@FDA, http://www.accessdata.fda.gov/scripts/cder/drugsatfda/ concentration when the velocity of the reaction is at 0.5Vmax.
Velocity (u)
314 Chapter 12
k
1 k k1[Et][D] = [ED](k1[D] + (k2 + k3)) (12.12)
3
E + D ED P + E
k
2 k + k
[Et ][D]= [ED][D] 2 3
+
k (12.13)
FIGURE 123 [D] = drug; [E] = enzyme; [ED] = drug– 1
enzyme intermediate; [P] = metabolite or product; k1, k2, and
Let
k3 = first-order rate constants. Brackets denote concentration.
k + k
2 3
K = (12.14)
M k
1
the concentrations of both the enzyme and the drug
and that an energetically favored drug–enzyme inter-
[Et][D] = [ED]([D] + KM) (12.15)
mediate is initially formed, followed by the forma-
tion of the product and regeneration of the enzyme.
Solving for [ED],
Each rate constant in Fig. 12-3 is a first-order
reaction rate constant. The following rates may be [D][E ]
denoted: [ED] t
= (12.16)
[D]+KM
Rate of intermediate [ED] formation = k1[E] [D] Multiplying by k3 on both sides,
Rate of intermediate [ED] decomposition = k2[ED] k
3[Et ][D] = k [ED]
+ k3[ED] [D] K 3 (12.17)
+ M
d[ED] The velocity or rate (v) of the reaction is the rate
= k [ ][ ]− [ ]− [ D]
dt 1 E D k2 ED k3 E for the formation of the product (metabolite) of the
(12.8)
d[ED] reaction, which is also the forward rate of decom-
= k1[E][D]− (k2 + k )[ED position of the enzyme–drug [ED] intermediate
dt 3 ]
(see Fig. 12-3).
By mass balance, the total enzyme concentration [Et] u = k3[ED] (12.18)
is the sum of the free enzyme concentration [E] and
the enzyme–drug intermediate concentration [ED]: When all the enzyme is saturated (ie, all the enzyme
is in the form of the ED intermediate due to the large
[Et] = [E] + [ED] (12.9) drug concentration), the reaction rate is dependent
on the availability of free enzyme, and the reaction
Rearranging, rate proceeds at zero-order maximum velocity, Vmax.
Vmax = k3 [Et] (12.19)
[E] = [Et] − [ED] (12.10)
Therefore, the velocity of metabolism is given by the
Substituting for [E] in Equation 12.8, equation
V [D]
v max
d[ED] = (12.20)
[D]+K
= k1([Et ]− [ED])[D]− (k + k ED 2 1
d 2 3)[ ] (1 . 1) M
t
Equation 12.20 describes the rate of metabolite
At steady state, the concentration [ED] is constant formation, or the Michaelis–Menten equation. The
with respect to time, because the rate of formation of maximum velocity (Vmax) corresponds to the rate when
the drug–enzyme intermediate equals the rate of all available enzymes are in the form of the drug–
decomposition of the drug–enzyme intermediate. enzyme (ED) intermediate. At Vmax, the drug (substrate)
Thus, d[ED]/dt = 0, and concentration is in excess, and the forward reaction,
Drug Elimination and Hepatic Clearance 315
k3[ED], is dependent on the availability of more free Kinetics of Enzyme Inhibition
enzyme molecules. The Michaelis constant, KM, is Many compounds (eg, cimetidine) may inhibit the
defined as the substrate concentration when the veloc- enzymes that metabolize other drugs in the body. An
ity (v) of the reaction is equal to one-half the maximum inhibitor may decrease the rate of drug metabolism
velocity, or 0.5Vmax (see Fig. 12-2). The KM is a useful by several different mechanisms. The inhibitor may
parameter that reveals the concentration of the substrate combine with a cofactor such as NADPH2 needed
at which the reaction occurs at half Vmax. In general, for for enzyme activity, interact with the drug or sub-
a drug with a large KM, a higher concentration will be strate, or interact directly with the enzyme. Enzyme
necessary before saturation is reached. inhibition may be reversible or irreversible. The
The Michaelis–Menten equation assumes that one mechanism of enzyme inhibition is usually classified
drug molecule is catalyzed sequentially by one enzyme by enzyme kinetic studies and observing changes in
at a time. However, enzymes may catalyze more than the KM and Vmax (see Fig. 12-4).
one drug molecule (multiple sites) at a time, which
may be demonstrated in vitro. In the body, drug may A
be eliminated by enzymatic reactions (metabolism) to Competitive enzyme inhibition
one or more metabolites and by the excretion of the
unchanged drug via the kidney. In Chapter 13, the Inhibitor
Michaelis–Menton equation is used for modeling drug
conversion in the body. Control
The relationship of the rate of metabolism to the
drug concentration is a nonlinear, hyperbolic curve
(see Fig. 12-2). To estimate the parameters Vmax and 0
KM, the reciprocal of the Michaelis–Menten equation 1/[S]
is used to obtain a linear relationship. Noncompetitive enzyme inhibition
1 KM 1 1 Inhibitor
= + (12.21)
v Vmax [D] Vmax
Control
Equation 12.21 is known as the Lineweaver–Burk
equation, in which KM and Vmax may be estimated
from a plot of 1/v versus 1/[D] (Fig. 12-4). Although 0
the Lineweaver–Burk equation is widely used, other 1/[S]
rearrangements of the Michaelis–Menten equation Uncompetitive enzyme inhibition
have been used to obtain more accurate estimates of
Vmax and KM. In Chapter 13, drug concentration [D] Inhibitor
is replaced by C, which represents drug concentra-
Control
tion in the body.
0
Frequently Asked Questions 1/[S]
»»How does one determine whether a drug follows FIGURE 124 Relationship of substrate concentration
Michaelis–Menton kinetics? alone or in the presence of an inhibitor. Lineweaver–Burk plots.
»»When does the rate of drug metabolism approach The Lineweaver–Burk equation, which is the reciprocal of the
Michaelis–Menten equation, is used to obtain estimates of V
V max
max?
and KM and to distinguish between various types of enzyme
»»What is the difference between v and Vmax? inhibition. [S] is the substrate concentration equal to [D] or
drug concentration.
1/u 1/u 1/u
316 Chapter 12
B C
Substrate
Substrate alone
alone
Substrate +
competitive antagonist
Substrate +
noncompetitive antagonist
C C’ = C (1 + [1]/Ki) EC50
Substrate concentration Substrate concentration
FIGURE 124 (Continued )
In the case of competitive enzyme inhibition, the cannot be reversed by increasing the drug concentra-
inhibitor and drug–substrate compete for the same tion, because the inhibitor will interact strongly with
active site on the enzyme. The drug and the inhibitor the enzyme and will not be displaced by the drug.
may have similar chemical structures. An increase in The reaction velocity in the presence of a noncom-
the drug (substrate) concentration may displace the petitive inhibitor is given by Equation 12.23
inhibitor from the enzyme and partially or fully For a Noncompetitive reaction,
reverse the inhibition. Competitive enzyme inhibi-
tion is usually observed by a change in the KM, but Vmax[D]
the Vmax remains the same. Vi = (12.23)
(1+ [I] /K i )([D]+ KM )
The equation for competitive inhibition is, in
the presence of an inhibitor, the reaction velocity VI
given by Equation 12.22.
k
1 k
V 3
max[D] VI = (12.22) E + D + I ED ED
[D]+ KM (1+ [I]/K i ) k
2
where [I] is the inhibitor concentration and is the k k
i –i
dissociation constant of the inhibitor which can be
determined experimentally. For a competitive reac-
tion as shown in Fig. 12-5, Ki is EI
k–I/k+I.
In noncompetitive enzyme inhibition, the inhibi-
tor may inhibit the enzyme by combining at a site on FIGURE 125 Diagram showing competitive inhibi-
the enzyme that is different from the active site tion of an enzyme [E] or a macromolecule (eg, a transport
(ie, an allosteric site). In this case, enzyme inhibi- protein) with an inhibitor [I], respectively, Ki = k–i/ki, or [D]
refers to the substrate concentration (ie, [D]). In the case of an
tion depends only on the inhibitor concentration. In
interaction with a macromolecule, [D] is referred to as ligand
noncompetitive enzyme inhibition, KM is not altered, concentration [E] would correspond to the macromolecule
but Vmax is lower. Noncompetitive enzyme inhibition concentration.
Substrate effect (E)
Substrate effect (E)
Drug Elimination and Hepatic Clearance 317
Equation (12.23b) relates Ki to [D], KM and [I] for a • How does cyclosporine change the pharmacoki-
general competitive reaction. Vi and V are the reac- netics of pravastatin?
tion velocity with and without inhibitor present. • Is pravastatin uptake involved?
[I]
K
i = (12.23a)
[D] V
+ Solution
1 −
1
K
M Vi Pravastatin and other statins have variable inter- and
intraindividual pharmacokinetics after oral dosing
Experimentally, IC50 is determined at 50% inhibition. due to a large first-pass effect. A drug that is metabo-
Vi and V are the velocity with and without inhibitor, lized and also subject to the efflux effect of hepatic
ie, Vi/V = 2/1. Substituting into Equation (12.23a) for transporters can affect overall plasma drug concen-
Vi/V = 2/1 yields the familiar Chang–Prusoff equation trations and liver drug concentrations. It is important
in the next section. to examine the drug dose used in the patient and
IC carefully assess if the dose range is adequately docu-
K = 50
i (12.23b)
mented by clinical data in a similar patient popula-
[D]
+1 tion, especially if an inhibitor is involved. Finally, it
KM is important to understand the pharmacokinetics,
pharmacodynamics, and risk-benefit involved for the
Other types of enzyme inhibition, such as mixed drug. Plasma drug concentrations are NOT the only
enzyme inhibition and enzyme uncompetitive inhibi- consideration. An oversimplification is often assumed
tion, have been described by observing changes in by considering only AUC and Cmax (ie, drug bioavail-
KM and Vmax. ability). In this example, the site of action is in the
liver. The therapeutic goal should always be to opti-
CLINICAL EXAMPLE mize drug concentrations at the site of action and to
avoid or minimize drug exposure at unintended sites
Pravastatin sodium (Pravachol®) is an HMG-CoA where adverse effects occur. In this case, adverse drug
reductase inhibitor (“statin”) which reduces choles- reaction, ADR, occurs at the heart (eg, myopathy)∗.
terol biosynthesis, thereby reducing cholesterol. The Whenever possible, a critical drug–drug interaction,
FDA-approved label states, “The risk of myopathy DDI, should be avoided or minimized with a wash-
during treatment with another HMG-CoA reductase out period during drug coadministration. Alternative
inhibitor is increased with concurrent therapy with therapeutic agents with less liability for DDI may be
either erythromycin, cyclosporine, niacin, or fibrates.” recommended to clinicians if feasible. A very useful
However, neither myopathy nor significant increases in integrated approach and model was recently published
CPK levels have been observed in three reports involv- about hepatic drug level of pravastatin. Watanabe et al
ing a total of 100 post-transplant patients (24 renal (2009) discussed the simulated plasma concentrations
and 76 cardiac) treated for up to 2 years concurrently of pravastatin with a detailed physiological model in
with pravastatin 10–40 mg and cyclosporine.” human and animals. Sensitivity analyses showed that
Pravastatin, like other HMG-CoA reductase inhibi- changes in the hepatic uptake ability altered the plasma
tors, has variable bioavailability. The coefficient of concentration of pravastatin markedly but had a
variation (CV), based on between-subject variability, minimal effect on the liver concentration, whereas
was 50% to 60% for AUC. Based on urinary recovery changes in canalicular efflux altered the liver con-
of radiolabeled drug, the average oral absorption of centration of pravastatin markedly but had a small
pravastatin is 34% and absolute bioavailability is 17%.
Pravastatin undergoes extensive first-pass extraction
∗Myopathy is not necessarily limited to the heart. In medicine,
in the liver (extraction ratio 0.66), which is its primary
a myopathy is a muscular disease in which the muscle bers do
site of action, and the primary site of cholesterol syn- not function for any one of many reasons, resulting in muscular
thesis and of LDL-C clearance. weakness.
318 Chapter 12
effect on the plasma concentration. In conclusion, Whereas the IC50 value for a compound may vary
the model allowed the prediction of the disposition between experiments depending on experimental con-
of pravastatin in humans. ditions, the Ki is an absolute value. Ki is the inhibition
This study suggested that changes in the OATP1B1 constant of the inhibitor; the concentration of com-
(transporter) activities may have a small impact on peting ligand in a competition assay which would
the therapeutic efficacy and a large impact on the occupy 50% of the enzyme if no ligand was present.
side effect (myopathy) of pravastatin, respectively, Pharmacologists often use this relationship to deter-
whereas changes in MRP2 activities may have oppo- mine the Ki of a competitive inhibitor on an enzyme
site impacts (ie, large effect on efficacy and small or a macromolecule such as a transporter. Since there
impact on side effect). are many drug inhibition interactions, it is important
to consider the ratio of inhibition concentration (eg,
Kinetics of Enzymatic Inhibition or steady-state plasma concentration in vivo to the IC50).
Macromolecule-Binding Inhibition In Vitro In general, if [I]/IC50 > 0.1, the interaction involved
should be investigated during early drug development
When an interaction involves competitive inhibition
in order to understand the important interaction issue
of an enzyme [E] or a macromolecule (eg, a transport
and assess how significant the potential interaction
protein with an inhibitor [I] as shown in Fig. 12-5),
might be clinically. Information on how to study
in vitro screening assays are commonly used to evaluate
drug metabolism inhibition/induction during devel-
potential inhibitors of enzymatic activity or macromole-
opment is available on the FDA web. Sub-class of
cule-ligand binding. IC50 is the total inhibitor concentra-
CYP enzymes and transporters are also updated for
tion that reduces enzymatic or macromolecule-ligand
DDI information (see FDA reference).
binding activities by 50% (IC50). However, measured
IC50 values depend on concentrations of the enzyme
(or target macromolecule), the inhibitor, and the sub- Metabolite Pharmacokinetics for Drugs That
strate (or ligand) along with other experimental condi- Follow a One-Compartment Model
tions. An accurate determination of the Ki value The one-compartment model may be used to esti-
requires an intrinsic, thermodynamic quantity that is mate simultaneously both metabolite formation and
independent of the substrate (ligand) but depends on drug decline in the plasma. For example, a drug is
the enzyme and inhibitor. The relationship for various given by intravenous bolus injection and then metab-
types of drug binding may be complex. Cer et al olized by parallel pathways (Fig. 12-6). Assume that
(2009) developed a software for computation of Ki for both metabolite formation and metabolite and parent
various types of inhibitions from IC50 measurements. drug elimination follow linear (first-order) pharma-
cokinetics at therapeutic concentrations. The elimi-
IC50 and Affinity nation rate constant and the volume of distribution
The relationship between the 50% inhibition concen- for each metabolite and the parent drug are obtained
tration and the inhibition constant is given by the from curve fitting of the plasma drug concentration–
Cheng–Prusoff equation below: time and each metabolite concentration–time curve.
If purified metabolites are available, each metabolite
IC
K = 50
i (12.23b)
[D]
+1 k k
fA
K Metabolite A emA
M
(10 mg)
Drug
where Ki shows the binding affinity of the inhibitor, k k
ke fB
IC Metabolite B emB
50 is the functional strength of the inhibitor, [D] is
(20 mg)
substrate (drug) concentration. Equation 12.23b was
published by Cheng and Prusoff in 1973. From FIGURE 126 Parallel pathway for the metabolism of a
Equation 12.23b, when [D] is << KM, Ki = IC50. When drug to metabolite A and metabolite B. Each metabolite may
[D] = KM, Ki = IC50/2. be excreted and/or further metabolized.
Drug Elimination and Hepatic Clearance 319
should be administered IV separately, to verify the PRACTICE PROBLEM
pharmacokinetic parameters independently.
The rate of elimination of the metabolite may be A drug is eliminated primarily by biotransformation
faster or slower than the rate of formation of the (metabolism) to a glucuronide conjugate and a sulfate
metabolite from the drug. Generally, metabolites conjugate. A single dose (100 mg) of the drug is given
such as glucuronide, sulfate, or glycine conjugates by IV bolus injection, and all elimination processes of
are more polar or more water soluble than the parent the drug follow first-order kinetics. The VD is 10 L and
the elimination rate constant for the drug is 0.9 h−1
drug and will be eliminated more rapidly than the .
parent drug. Therefore, the rate of elimination of The rate constant (kf) for the formation of the glucuro-
each of these metabolites is relatively more rapid nide conjugate is 0.6 h−1, and the rate constant for the
formation of the sulfate conjugate is 0.2 h−1
than the rate of formation. In contrast, if the drug is .
acetylated or metabolized to a less polar or less a. Predict the drug concentration 1 hour after the
water-soluble metabolite, then the rate of elimination dose.
of the metabolite is relatively slower than the rate of b. Predict the concentration of glucuronide and
formation of the metabolite. In this case, metabolite sulfate metabolites 1 hour after the dose, if the
accumulation will occur. Vm for both metabolites is the same as for the
Compartment modeling of drug and metabolites parent drug and the kem for both metabolites
is relatively simple and practical. The major short- is 0.4 h−1. (Note: Vm and kem usually differ
coming of compartment modeling is the lack of real- between metabolites and parent drug.) In this
istic physiologic information when compared to more example, Vm and kem are assumed to be the
sophisticated models that take into account spatial same for both metabolites, so that the concen-
location of enzymes and flow dynamics. However, tration of the two metabolites may be compared
compartment models are useful for predicting drug by examining the formation constants.
and metabolite plasma levels.
For a drug given by IV bolus injection, the metab-
Solution
olite concentration exhibiting linear pharmacokinetics
may be predicted from the following equation: The plasma drug concentration 1 hour after the dose
may be estimated using the following equation for a
k D
= − − one-compartment model, IV bolus administration:
C f 0 (e−kemt e−kf t
m ) (12.24)
Vm (kf kem )
D
C C0e−kt 0 e−kt
p = p =
where Cm is the metabolite concentration in plasma, VD
kem is the metabolite elimination rate constant, kf is
the metabolite formation rate constant, Vm is the 100
C = e−(0.9)(1)
p = 4.1 mg/L
metabolite volume of distribution, D0 is the dose of 10
drug, and VD is the apparent volume of distribution
of drug. All rate constants are first order. The plasma concentrations for the glucuronide and
sulfate metabolites 1 hour postdose are estimated after
substitution into Equation 12.24.
Frequently Asked Questions
»»Which first-order rate constants will be affected by (0.6)(100)
Glucuronide: ( (0.4
m = − ) (1) − −(0.6) (1)
C − e e )
the addition of an enzyme inhibitor? 10(0.6 0.4)
»»Will Vm (metabolite) differ from VD (parent drug)? Cm = 3.6 mg/L
If so, why?
(0.2)(100)
»»What is the relationship, if any, between k, k Sulfate: = ( −(0.4)(1)
m − −(0.2)(1)
C − e e )
em, km,
and kf?
10(0.2 0.4)
Cm = 1.5 mg/L
320 Chapter 12
Cephalothin Desacetylcephalothin
10
Urine Urine
8 Drug ke ku
kf
6 Cp Vp Cm Vm
Metabolite 1
k
4 12 k21
Ct Vt
2 Metabolite 2
0 FIGURE 128 Pharmacokinetic model of cephalothin and
0 1 2 3 4 desacetylcephalothin (metabolite) after an IV bolus dose.
Time
FIGURE 127 Simulation showing an IV bolus with
formation of two metabolites. After a single IV bolus dose of cephalothin (20 mg/kg)
to a rabbit, cephalothin declines as a result of
excretion and metabolism to desacetylcephalothin.
After an IV bolus dose of a drug, the equation The plasma levels of both cephalothin and desace-
describing metabolite concentration formation and tylcephalothin may be calculated using equations
elimination by first-order processes is kinetically based on a model with linear metabolism and
analogous to drug absorption after oral administration excretion.
(see Chapter 8). Simulated plasma concentration– The equations for cephalothin plasma and tissue
time curves were generated using Equation 12.24 for levels are the same as those derived in Chapter 5 for
the glucuronide and sulfate metabolites, respectively a simple two-compartment model, except that the
(Fig. 12-7). The rate constant for the formation of elimination constant k for the drug now consists of
the glucuronide is faster than the rate constant for the ke + kf, representing the rate constants for parent
formation of the sulfate. Therefore, the time for peak drug excretion and metabolite formation constant,
plasma glucuronide concentrations is shorter com- respectively.
pared to the time for peak plasma sulfate conjugate
concentrations. Equation 12.24 cannot be used if
k
drug metabolism is nonlinear because of enzyme 21 − a − k − b
C = D e at + 21 e−bt (12
p 0
Vp (b − a) Vp (a − b) .25)
saturation (ie, if metabolism follows Michaelis–
Menten kinetics).
k
C = D 12 − k
e at + 12 −
0 e bt
t Vt (b − a) Vt (a − b)
(12.26)
Metabolite Pharmacokinetics for Drugs That
Follow a Two-Compartment Model
a + b = k + k12 + k21 (12.27)
Cephalothin is an antibiotic drug that is metabolized
rapidly by hydrolysis in both humans and rabbits.
The metabolite desacetylcephalothin has less anti- ab = kk21 (12.28)
biotic activity than the parent drug. In urine, 18% to
33% of the drug was recovered as desacetylcepha- k = kf + ke (12.29)
lothin metabolite in a human. The time course of
both the drug and the metabolite may be predicted The equation for metabolite plasma concentra-
after a given dose from the distribution kinetics of tion, Cm, is triexponential, with three preexponential
both the drug and the metabolite. Cephalothin follows coefficients (C5, C6, and C7) calculated from the vari-
a two-compartment model after IV bolus injection in ous kinetic constants, Vm, and the dose of the drug.
a rabbit, whereas the desacetylcephalothin metabo-
C =C e−kut +C e−at
lite follows a one-compartment model (Fig. 12-8). +C e−bt (12.30)
m 5 6 7
Plasma concentration
Drug Elimination and Hepatic Clearance 321
TABLE 121 Distribution of Cytochrome
P-450 and Glutathione S-Transferase in the Rat
Tissue CYT P-450a GSH Transferaseb
Desacetylcephalothin
Liver 0.73 599
Lung 0.046 61
Kidney 0.135 88
Small intestine 0.042 103
Cephalothin
Colon 0.016 —c
Time (minutes)
Skin 0.12 —c
FIGURE 129 Formation of desacetylcephalothin from
Adrenal gland 0.5 308
cephalothin in the rabbit after an IV bolus dose of cephalothin.
aCytochrome P-450, nmole/mg microsome protein.
bGlutathione S-transferase, nmole conjugate formed/min/mg cytosolic
protein.
k
fD0k − k D k
C = 21 f 0 u cValues not available.
5 (12.31)
Vm (b − ku )(a − ku ) Data from Wolf (1984).
kfD0k2 − kfD a
C = 1 0
6 (12.32)
Vm (b − a)(ku − a)
tissues to a lesser degree depending on drug properties
kfD0k21 − k
C = fD0b and route of drug administration.
7 − (1
Vm (ku b)(a − 2.33)
b) The liver is both a synthesizing and an excreting
organ. The basic anatomical unit of the liver is the
For example, after the IV administration of cepha- liver lobule, which contains parenchymal cells in a
lothin to a rabbit, both metabolite and plasma cephalo- network of interconnected lymph and blood vessels.
thin concentration may be fitted to Equations 12.25 and The liver consists of large right and left lobes that
12.30 simultaneously (Fig. 12-9), with the following merge in the middle. The liver is perfused by blood
parameters obtained using a regression computer pro- from the hepatic artery; in addition, the large hepatic
gram (all rate constants in min−1). portal vein that collects blood from various segments
of the GI tract also perfuses the liver (Fig. 12-10).
The hepatic artery carries oxygen to the liver and
k12 = 0.052 k21 = 0.009 Vm = 285 mL/kg
accounts for about 25% of the liver blood supply.
ku = 0.079 k = 0.067 D0 = 20 mg/kg The hepatic portal vein carries nutrients to the liver
and accounts for about 75% of liver blood flow. The
kf = 0.045 Vp = 548 mL/kg ke = 0.022
terminal branches of the hepatic artery and portal
vein fuse within the liver and mix with the large
vascular capillaries known as sinusoids (Fig. 12-11).
ANATOMY AND PHYSIOLOGY Blood leaves the liver via the hepatic vein, which
empties into the vena cava (see Fig. 12-10). The
OF THE LIVER
liver also secretes bile acids within the liver lobes,
The liver is the major organ responsible for drug which flow through a network of channels and even-
metabolism. However, intestinal tissues, lung, kidney, tually empty into the common bile duct (Figs. 12-11
and skin also contain appreciable amounts of bio- and 12-12). The common bile duct drains bile and
transformation enzymes, as reflected by animal data biliary excretion products from both lobes into the
(Table 12-1). Metabolism may also occur in other gallbladder.
Concentration (mg/mL)
322 Chapter 12
Inferior vena cava Aortic artery
Esophagus
Hepatic veins
Cardiac sphincter
Liver Spleen
Hepatic artery
Stomach
Fundus
Antrum
Gallbladder
Pylorus
Hepatic portal vein
Common bile duct Pancreas
Pancreatic duct
Duodenum
Jejunum
Mesenteric vein
Ileum
Colon
Rectum
FIGURE 1210 The large hepatic portal vein that collects blood from various segments of the GI tract also perfuses the liver.
Interlobular
septum
Central vein
Sinusoids
Hepatic artery
Hepatocytes
Hepatic portal
vein
Bile ductule
Bile canaliculi
Portal area
FIGURE 1211 Intrahepatic distribution of the hepatic and portal veins.
Drug Elimination and Hepatic Clearance 323
Right hepatic
duct
Right hepatic Left hepatic duct
artery Left hepatic
Common artery
hepatic duct
Cystic duct Round
ligament
Common
hepatic
Gallbladder artery
FIGURE 1212 Intrahepatic distribution of the hepatic artery, portal vein, and biliary ducts. (From Lindner HH. Clinical Anatomy.
Norwalk, CT, Appleton & Lange, 1989, with permission.)
Although the principal sites of liver metabolism the heterogenicity of the liver, the hydrodynamics of
are the hepatocytes, drug transporters are also pres- hepatic blood flow, the nonlinear kinetics of drug
ent in the hepatocyte besides CYP isoenzymes. metabolism, and any unusual or pathologic condition
Transporters can efflux drug either in or out of the of the subject. Most models in practical use are sim-
hepatocytes, thus influencing the rate of metabolism. ple or incomplete models, however, because insuffi-
In addition, drug transporters are also present in the cient information is available about an individual
bile canaliculi which can eliminate drug by efflux. patient. For example, the average hepatic blood flow
Sinusoids are blood vessels that form a large is usually cited as 1.3–1.5 L/min. Hepatic arterial
reservoir of blood, facilitating drug and nutrient blood flow and hepatic venous (portal) blood enter
removal before the blood enters the general circula- the liver at different flow rates, and their drug con-
tion. The sinusoids are lined with endothelial cells, centrations are different. It is possible that a toxic
or Kupffer cells. Kupffer cells are phagocytic tissue metabolite may be transiently higher in some liver
macrophages that are part of the reticuloendothelial tissues and not in others. The pharmacokinetic chal-
system (RES). Kupffer cells engulf worn-out red lenge is to build models that predict regional (organ)
blood cells and foreign material. changes from easily accessible data, such as plasma
Drug metabolism in the liver has been shown to drug concentration.
be flow and site dependent. Some enzymes are
reached only when blood flow travels from a given
direction. The quantity of enzyme involved in metab- HEPATIC ENZYMES INVOLVED
olizing drug is not uniform throughout the liver.
Consequently, changes in blood flow can greatly IN THE BIOTRANSFORMATION
affect the fraction of drug metabolized. Clinically, OF DRUGS
hepatic diseases, such as cirrhosis, can cause tissue
fibrosis, necrosis, and hepatic shunt, resulting in Mixed-Function Oxidases
changing blood flow and changing bioavailability of The liver is the major site of drug metabolism, and the
drugs (see Chapter 24). For this reason, and in part type of metabolism is based on the reaction involved.
because of genetic differences in enzyme levels Oxidation, reduction, hydrolysis, and conjugation are
among different subjects and environmental factors, the most common reactions, as discussed under phase I
the half-lives of drugs eliminated by drug metabo- and phase II reactions in the next two sections. The
lism are generally very variable. enzymes responsible for oxidation and reduction of
A pharmacokinetic model simulating hepatic drugs (xenobiotics) and certain natural metabolites,
metabolism should involve several elements, including such as steroids, are monoxygenase enzymes known as
324 Chapter 12
mixed-function oxidases (MFOs). The hepatic paren- bind to cytochrome P-450, resulting in oxidation
chymal cells contain MFOs in association with the (or reduction) of the drugs. Cytochrome P-450 con-
endoplasmic reticulum, a network of lipoprotein sists of closely related isoenzymes (isozymes) that
membranes within the cytoplasm and continuous with differ somewhat in amino acid sequence and drug
the cellular and nuclear membranes. If hepatic paren- specificity (see Chapter 13). A general scheme for
chymal cells are fragmented and differentially centri- MFO drug oxidation is described in Fig. 12-13.
fuged in an ultracentrifuge, a microsomal fraction, or In addition to the metabolism of drugs, the CYP
microsome, is obtained from the postmitochondrial monooxygenase enzyme system catalyzes the bio-
supernatant. The microsomal fraction contains frag- transformation of various endogenous compounds
ments of the endoplasmic reticulum. such as steroids. The CYP monooxygenase enzyme
The mixed-function oxidase enzymes are struc- system is also located in other tissues such as kidney,
tural enzymes that constitute an electron-transport GI tract, skin, and lungs.
system that requires reduced NADPH (NADPH2), A few enzymatic oxidation reactions involved in
molecular oxygen, cytochrome P-450, NADPH– biotransformation do not include the CYP monooxy-
cytochrome P-450 reductase, and phospholipid. The genase enzyme system. These include monoamine oxi-
phospholipid is involved in the binding of the drug dase (MAO) that deaminates endogenous substrates
molecule to the cytochrome P-450 and coupling the including neurotransmitters (dopamine, serotonin, nor-
NADPH–cytochrome P-450 reductase to the cyto- epinephrine, epinephrine, and various drugs with a simi-
chrome P-450. Cytochrome P-450 is a heme protein lar structure); alcohol and aldehyde dehydrogenase in
with iron protoporphyrin IX as the prosthetic group. the soluble fraction of liver are involved in the metabo-
Cytochrome P-450 is the terminal component of an lism of ethanol and xanthine oxidase which converts
electron-transfer system in the endoplasmic reticu- hypoxanthine to xanthine and then to uric acid. Drug
lum and acts as both an oxygen- and a substrate- substrates for xanthine oxidase include theophylline and
binding locus for drugs and endogenous substrates in 6-mercaptopurine. Allopurinol is a substrate and inhibi-
conjunction with a flavoprotein reductase, NADPH– tor of xanthine oxidase and also delays metabolism of
cytochrome P-450 reductase. Many lipid-soluble drugs other substrates used in the treatment of gout.
NADP– Reduced avoprotein Cyt P450 (Fe3+)
drug (RH) complex Drug (R)
Cyt P450 reductase
e–
NADPH Oxidized avoprotein Cyt P450 (Fe3+)
RH Oxidized drug
CO
Cyt P450 Cyt P450 (Fe2+)
hu
CO RH Cyt P450 (Fe3+)
ROH
O2
RH
e–
H2O
Cyt P450 (Fe2+)
O +
2 2H
FIGURE 1213 Electron flow pathway in the microsomal drug-oxidizing system. (From Alvares and Pratt, 1990, with permission.)
Drug Elimination and Hepatic Clearance 325
DRUG BIOTRANSFORMATION Both the nature of the drug and the route of
administration may influence the type of drug
REACTIONS
metabolite formed. For example, isoproterenol
The hepatic biotransformation enzymes play an impor- given orally forms a sulfate conjugate in the gastro-
tant role in the inactivation and subsequent elimination intestinal mucosal cells, whereas after IV adminis-
of drugs that are not easily cleared through the kidney. tration, it forms the 3-O-methylated metabolite via
For these drugs—theophylline, phenytoin, acetamino- S-adenosylmethionine and catechol-O-methyltrans-
phen, and others—there is a direct relationship between ferase. Azo drugs such as sulfasalazine are poorly
the rate of drug metabolism (biotransformation) and absorbed after oral administration. However, the
the elimination half-life for the drug. azo group of sulfasalazine is cleaved by the intesti-
For most biotransformation reactions, the metabo- nal microflora, producing 5-aminosalicylic acid
lite of the drug is more polar than the parent compound. and sulfapyridine, which is absorbed in the lower
The conversion of a drug to a more polar metabolite bowel.
enables the drug to be eliminated more quickly than if The biotransformation of drugs may be classi-
the drug remained lipid soluble. A lipid-soluble drug fied according to the pharmacologic activity of the
crosses cell membranes and is easily reabsorbed by the metabolite or according to the biochemical mecha-
renal tubular cells, exhibiting a consequent tendency to nism for each biotransformation reaction. For most
remain in the body. In contrast, the more polar metabo- drugs, biotransformation results in the formation of
lite does not cross cell membranes easily, is filtered a more polar metabolite(s) that is pharmacologically
through the glomerulus, is not readily reabsorbed, and inactive and is eliminated more rapidly than the par-
is more rapidly excreted in the urine. ent drug (Table 12-2).
TABLE 122 Biotransformation Reactions and Pharmacologic Activity of the Metabolite
Reaction Example
Active Drug to Inactive Metabolite
Amphetamine Deamination Phenylacetone
→
Phenobarbital Hydroxylation Hydroxyphenobarbital
→
Active Drug to Active Metabolite
Codeine Demethylation Morphine
→
Procainamide Acetylation N-acetylprocainamide
→
Phenylbutazone Hydroxylation Oxyphenbutazone
→
Inactive Drug to Active Metabolite
Hetacillin Hydrolysis Ampicillin
→
Sulfasalazine Azoreduction Sulfapyridine + 5-aminosalicylic acid
→
Active Drug to Reactive Intermediate
Acetaminophen Aromatic Reactive metabolite (hepatic necrosis)
→
Hydroxylation
Benzo[a]pyrene Aromatic Reactive metabolite (carcinogenic)
→
Hydroxylation
326 Chapter 12
For some drugs the metabolite may be pharmaco- TABLE 123 Some Common Drug
logically active or produce toxic effects. Prodrugs are Biotransformation Reactions
inactive and must be biotransformed in the body to
Phase I Reactions Phase II Reactions
metabolites that have pharmacologic activity. Initially,
prodrugs were discovered by serendipity, as in the Oxidation Glucuronide conjugation
case of prontosil, which is reduced to the antibacterial Aromatic hydroxylation Ether glucuronide
agent sulfanilamide. More recently, prodrugs have
Side chain hydroxylation Ester glucuronide
been intentionally designed to improve drug stability,
increase systemic drug absorption, or to prolong the N-, O-, and S-dealkylation Amide glucuronide
duration of activity. For example, the antiparkinsonian Deamination
agent levodopa crosses the blood–brain barrier and is
Sulfoxidation, N-oxidation Peptide conjugation
then decarboxylated in the brain to l-dopamine, an
active neurotransmitter. l-Dopamine does not easily N-hydroxylation
penetrate the blood–brain barrier into the brain and Reduction Glycine conjugation
therefore cannot be used as a therapeutic agent. (hippurate)
Azoreduction
Nitroreduction Methylation
PATHWAYS OF DRUG
Alcohol dehydrogenase N-methylation
BIOTRANSFORMATION
Hydrolysis O-methylation
Pathways of drug biotransformation may be divided
Ester hydrolysis
into two major groups of reactions, phase I and
phase II reactions. Phase I, or asynthetic reactions, Amide hydrolysis Acetylation
include oxidation, reduction, and hydrolysis. Phase II, Sulfate conjugation
or synthetic reactions, include conjugations. A par-
Mercapturic acid
tial list of these reactions is presented in Table 12-3.
synthesis
In addition, a number of drugs that resemble natural
biochemical molecules are able to utilize the meta-
bolic pathways for normal body compounds. For
benzo[a]pyrene, and other drugs containing aromatic
example, isoproterenol is methylated by catechol
rings, reactive intermediates, such as epoxides, are
O-methyl transferase (COMT), and amphetamine is
formed during the hydroxylation reaction. These aro-
deaminated by monamine oxidase (MAO). Both COMT
matic epoxides are highly reactive and will react with
and MAO are enzymes involved in the metabolism
macromolecules, possibly causing liver necrosis
of noradrenaline.
(acetaminophen) or cancer (benzo[a]pyrene). The
biotransformation of salicylic acid (Fig. 12-14) dem-
Phase I Reactions onstrates the variety of possible metabolites that may
be formed. It should be noted that salicylic acid is also
Usually, phase I biotransformation reactions occur
conjugated directly (phase II reaction) without a pre-
first and introduce or expose a functional group on the
ceding phase I reaction.
drug molecules. For example, oxygen is introduced
into the phenyl group on phenylbutazone by aromatic
hydroxylation to form oxyphenbutazone, a more polar Conjugation (Phase II) Reactions
metabolite. Codeine is demethylated to form mor- Once a polar constituent is revealed or placed into the
phine. In addition, the hydrolysis of esters, such as molecule, a phase II or conjugation reaction may occur.
aspirin or benzocaine, yields more polar products, such Common examples include the conjugation of salicy-
as salicylic acid and p-aminobenzoic acid, respec- clic acid with glycine to form salicyluric acid or gluc-
tively. For some compounds, such as acetaminophen, uronic acid to form salicylglucuronide (see Fig. 12-14).
Drug Elimination and Hepatic Clearance 327
O
NH CCH3 NH2 NH2
OH
OC2H5 OC2H5 OC2H5
Acetophenetidin p-phenetidin 2-hydroxyphenetidin
O
NH CCH3
O O
NH CCH3 NH CCH3 O SO3H
p-hydroxyacetanilid
sulfate
O
Acetanilid OH NH CCH3
p-hydroxyacetanilid
(acetaminophen)
NH2
O C6H9O6
p-hydroxyacetanilid
glucuronide
NH2
OH
p-aminophenol Conjugated products
NH2
Aniline
OH
o-aminophenol
NHOH N O
Phenylhydroxylamine Nitrosobenzene
FIGURE 1214 Biotransformation of salicylic acid. (From Hucker et al, 1980, with permission.)
328 Chapter 12
Conjugation reactions use conjugating reagents, Scheme A
which are derived from biochemical compounds Energy
Conjugating reagent Activated conjugating
involved in carbohydrate, fat, and protein metabo- reagent nucleotide
lism. These reactions may include an active, high- Drug transferase
Activated conjugating Conjugated drug
energy form of the conjugating agent, such as uridine reagent nucleotide
diphosphoglucuronic acid (UDPGA), acetyl CoA,
3′-phosphoadenosine-5′-phosphosulfate (PAPS), or Example:
S-adenosylmethionine (SAM), which, in the pres- UDPGA transferase
Morphine + UDPGA Morphine O’-glucuronide
ence of the appropriate transferase enzyme, com-
bines with the drug to form the conjugate. Conversely,
the drug may be activated to a high-energy com- Scheme B
pound that then reacts with the conjugating agent in Energy
the presence of a transferase enzyme (Fig. 12-15). Drug Activated drug
nucleotide
The major conjugation (phase II) reactions are listed Conjugating agent
Activated drug Conjugated drug
in Tables 12-3 and 12-4. nucleotide Transferase
Some of the conjugation reactions may have
limited capacity at high drug concentrations, leading Example:
to nonlinear drug metabolism. In most cases, enzyme Acetyl CoA
Benzoic acid Benzoyl CoA
activity follows first-order kinetics with low drug (R—CO—S—CoA)
(substrate) concentrations. At high doses, the drug Glycine transferase
Benzoyl CoA Hippuric acid
concentration may rise above the Michaelis–Menten
rate constant (KM), and the reaction rate approaches FIGURE 1215 General scheme for phase II reactions.
zero order (Vmax). Glucuronidation reactions have
a high capacity and may demonstrate nonlinear
(saturation) kinetics at very high drug concentra- conjugation pathways may be due to several factors,
tions. In contrast, glycine, sulfate, and glutathione including (1) limited amount of the conjugate trans-
conjugations show lesser capacity and demonstrate ferase, (2) limited ability to synthesize the active
nonlinear kinetics at therapeutic drug concentrations nucleotide intermediate, or (3) limited amount of
(Caldwell, 1980). The limited capacity of certain conjugating agent, such as glycine.
TABLE 124 Phase II Conjugation Reactions
High-Energy Functional Groups
Conjugation Reaction Conjugating Agent Intermediate Combined with
Glucuronidation Glucuronic acid UDPGAa —OH, —COOH,
—NH2, SH
Sulfation Sulfate PAPSb —OH, —NH2
Amino acid conjugation Glycinec Coenzyme A thioesters —COOH
Acetylation Acetyl CoA Acetyl CoA —OH, —NH2
Methylation CH3 from S-adenosylmethionine S-adenosylmethionine —OH, —NH2
Glutathione (mercapturine Glutathione Arene oxides, epoxides Aryl halides, epoxides,
acid conjugation) arene oxides
aUDPGA = uridine diphosphoglucuronic acid.
bPAPS = 3’-phosphoadenosine-5’-phosphosulfate.
cGlycine conjugates are also known as hippurates.
Drug Elimination and Hepatic Clearance 329
In addition, the N-acetylated conjugation reac- metabolites and is the main intracellular molecule
tion shows genetic polymorphism: for certain drugs, for protection of the cell against reactive electro-
the human population may be divided into fast and philic compounds. Through the nucleophilic sulfhy-
slow acetylators. Finally, some of these conjugation dryl group of the cysteine residue, GSH reacts
reactions may be diminished or defective in cases of nonenzymatically and enzymatically via the enzyme
inborn errors of metabolism. glutathione S-transferase, with reactive electrophilic
Glucuronidation and sulfate conjugation are oxygen intermediates of certain drugs, particularly
very common phase II reactions that result in water- aromatic hydrocarbons formed during oxidative bio-
soluble metabolites being rapidly excreted in bile transformation. The resulting GSH conjugates are
(for some high-molecular-weight glucuronides) and/or precursors for a group of drug conjugates known as
urine. Acetylation and mercapturic acid synthesis are mercapturic acid (N-acetylcysteine) derivatives. The
conjugation reactions that are often implicated in formation of a mercapturic acid conjugate is shown
the toxicity of the drug; they will now be discussed in Fig. 12-16.
more fully. The enzymatic formation of GSH conjugates is
saturable. High doses of drugs such as acetaminophen
Acetylation (APAP) may form electrophilic intermediates and
deplete GSH in the cell. The reactive intermediate
The acetylation reaction is an important conjugation
covalently bonds to hepatic cellular macromolecules,
reaction for several reasons. First, the acetylated prod-
resulting in cellular injury and necrosis. The sug-
uct is usually less polar than the parent drug. The
gested antidote for intoxication (overdose) of acet-
acetylation of such drugs as sulfanilamide, sulfadia-
aminophen is the administration of N-acetylcysteine
zine, and sulfisoxazole produces metabolites that are
(Mucomyst), a drug molecule that contains available
less water soluble and that in sufficient concentration
sulfhydryl (R–SH) groups.
precipitate in the kidney tubules, causing kidney dam-
age and crystaluria. In addition, a less polar metabo-
lite is reabsorbed in the renal tubule and has a longer Glutathione Gly
elimination half-life. For example, procainamide S-transferase
Drug + GSH Drug S Cys
(elimination half-life of 3 to 4 hours) has an acetylated
metabolite, N-acetylprocainamide, which is biologi- Gln
cally active and has an elimination half-life of 6 to
7 hours. Lastly, the N-acetyltransferase enzyme Gly Transpeptidase Gly
responsible for catalyzing the acetylation of isoniazid (Glutathionase)
Drug S Cys Drug S Cys
and other drugs demonstrates a genetic polymorphism.
Two distinct subpopulations have been observed to Gln NH2
inactivate isoniazid, including the “slow inactivators”
and the “rapid inactivators” (Evans, 1968). Therefore, Gly
the former group may demonstrate an adverse effect Peptidase
Drug S Cys Drug S Cys
of isoniazide, such as peripheral neuritis, due to
the longer elimination half-life and accumulation NH2 NH2
of the drug.
Glutathione and Mercapturic N-acetylase
Drug S Cys Drug S Cys
Acid Conjugation
NH2 NHCOCH
Glutathione (GSH) is a tripeptide of glutamyl-cysteine- 3
glycine that is involved in many important biochemi- Mercapturic acid
(N-acetylcysteine)
cal reactions. GSH is important in the detoxification
of reactive oxygen intermediates into nonreactive FIGURE 1216 Mercapturic acid conjugation.
330 Chapter 12
Metabolism of Enantiomers oral dose of 300 mg of the racemic or mixed form,
Many drugs are given as mixtures of stereoisomers. the plasma concentration of the S form in most sub-
Each isomeric form may have different pharmacologic jects was only about 25% of that of the R form. The
actions and different side effects. For example, the elimination half-life of the S form (2.13 hours) was
natural thyroid hormone is l-thyroxine, whereas the much faster than that of the R form (76 hours) in
synthetic d enantiomer, d-thyroxine, lowers choles- these subjects (Fig. 12-17A). The severity of the
terol but does not stimulate basal metabolic rate like sedative side effect of this drug was also less in sub-
the l form. Since enzymes as well as drug receptors jects with rapid metabolism. Hydroxylation reduces
demonstrate stereoselectivity, isomers of drugs may the lipophilicity of the metabolite and may reduce
show differences in biotransformation and pharmaco- the partition of the metabolite into the CNS.
kinetics (Tucker and Lennard, 1990). With improved Interestingly, some subjects do not metabolize the S
techniques for isolating mixtures of enantiomers, form of mephenytoin well, and the severity of seda-
many drugs are now available as pure enantiomers. tion in these subjects was increased. The plasma
The rate of drug metabolism and the extent of drug level of the S form was much higher in these subjects
protein binding are often different for each stereo- (Fig. 12-17B). The variation in metabolic rate was
isomer. For example, (S)-(+)disopyramide is more attributed to genetically controlled enzymatic differ-
highly bound in humans than (R)-(–)disopyramide. ences within the population.
Carprofen, a nonsteroidal anti-inflammatory drug,
also exists in both an S and an R configuration. The
Regioselectivity
predominate activity lies in the S configuration.
The clearance of the S-carprofen glucuronide In addition to stereoselectivity, biotransformation
through the kidney was found to be faster than that enzymes may also be regioselective. In this case, the
of the R form, 36 versus 26 mL/min (Iwakawa et al, enzymes catalyze a reaction that is specific for a
1989). A list of some common drugs with enantio- particular region in the drug molecule. For example,
mers is given in Table 12-5. A review (Ariens and isoproterenol is methylated via catechol-O-methyl-
Wuis, 1987) shows that of 475 semisynthetic drugs transferase and S-adenosylmethionine primarily in
derived from natural sources, 469 were enantio- the meta position, resulting in a 3-O-methylated metab-
mers, indicating that the biologic systems are very olite. Very little methylation occurs at the hydroxyl
stereospecific. group in the para position.
The anticonvulsant drug mephenytoin is another
example of a drug that exists as R and S enantio-
Species Differences in Hepatic
mers. Both enantiomers are metabolized by hydrox-
Biotransformation Enzymes
ylation in humans (Wilkinson et al, 1989). After an
The biotransformation activity of hepatic enzymes
can be affected by a variety of factors (Table 12-6).
During the early preclinical phase of drug develop-
TABLE 125 Common Drug Enantiomers ment, drug metabolism studies attempt to identify the
major metabolic pathways of a new drug through the
Atropine Brompheniramine Cocaine
use of animal models. For most drugs, different ani-
Disopyramide Doxylamine Ephedrine mal species may have different metabolic pathways.
Propranolol Nadolol Verapamil For example, amphetamine is mainly hydroxylated in
rats, whereas in humans and dogs it is largely deami-
Tocainide Propoxyphene Morphine
nated. In many cases, the rates of metabolism may
Warfarin Thyroxine Flecainide differ among different animal species even though the
Ibuprofen Atenolol Subutamol biotransformation pathways are the same. In other
cases, a specific pathway may be absent in a particular
Metoprolol Terbutaline
species. Generally, the researcher tries to find the best
Drug Elimination and Hepatic Clearance 331
A B
1200 1200
1000 1000
500 500
R-mephenytoin
R-mephenytoin
100 100
50 50 S-mephenytoin
S-mephenytoin
10 10
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
Time (days) Time (days)
FIGURE 1217 Plasma level of mephenytoin after 300-mg oral dose of the recemic drug. A. Efficient metabolizer. B. Poor
metabolizer. The plasma levels of the R and S form are different due to different rates of metabolism of the two isomers. (Adapted from
Wilkinson et al, 1989, with permission.)
animal model that will be predictive of the metabolic DRUG INTERACTION EXAMPLE
profile in humans.
In recent years, in vitro drug screening with Lovastatin (Mevacor®) is a cholesterol-lowering agent
human liver microsomes or with hepatocytes has and was found to be metabolized by human liver
helped confirm whether a given CYP isoenzyme is microsomes to two major metabolites: 6′b-hydroxy
important in human drug metabolism. Animal mod- (Michaelis-Menten constant [KM]: 7.8 ± 2.7 mM) and
els also provide some supportive evidence. 6′-exomethylene lovastatin (KM, 10.3 ± 2.6 mM).
6′b-Hydroxylovastatin formation in the liver was inhib-
ited by the specific CYP3A inhibitors cyclosporine
(Ki, 7.6 ± 2.3 mM), ketoconazole (Ki, 0.25 ± 0.2 mM),
TABLE 126 Sources of Variation in Intrinsic and troleandomycin (Ki, 26.6 ± 18.5 mM).
Clearance Hydroxylation of lovastatin is a phase I reaction
Genetic factors and catalyzed by a specific cytochrome P-450 enzyme
Genetic differences within population commonly referred to as CYP3A. Ketoconazole and
Racial differences among different populations cyclosporine are CYP3A inhibitors and therefore
Environmental factors and drug interactions affect lovastatin metabolism. Lovastatin is referred to
Enzyme induction as a substrate. Substrate concentrations are expressed
Enzyme inhibition as [S] ([D] in Fig. 12-4A), preferably in (mM). The
Physiologic conditions Michaelis–Menten constant (KM) of the enzyme is
Age expressed in micromoles (mM) because most new
Gender drugs have different MW, making it easier to compare
Diet/nutrition by expressing them in moles. Cyclosporine would be
Pathophysiology
expected to produce a significant drug–drug interac-
Drug dosage regimen tion in the body based on a review of the Ki values. In
Route of drug administration addition to inhibiting the cytochrome P-450 enzyme
Dose-dependent (nonlinear) pharmacokinetics
pathway, an efflux transporter can deplete the drug
Plasma concentration (mg/mL)
Plasma concentration (mg/mL)
332 Chapter 12
before significant biotransformaton occurs. Efflux Another example of genetic differences in drug
inhibition would have the opposite effect. Thus, loca- metabolism is glucose 6-phosphate-dehydrogenase
tion (time and place) issues are important when DDI deficiency, which is observed in approximately 10%
involves a CYP and a transporter. of African Americans. A well-documented example
A systems biology approach that takes into of genetic polymorphism with this enzyme was
account all aspects of ADME processes integrated observed with phenytoin (Wilkinson et al, 1989).
with pharmacogenetics is needed to properly address Two phenotypes, EM (efficient metabolizer) and PM
various pharmacokinetic, pharmacodynamic, and clin- (poor metabolizer), were identified in the study
ical issues of risk/benefit. The interplay among the population. The PM frequency in Caucasians was
various processes including influx and efflux trans- about 4% and in Japanese was about 16%. Variation
porters may sometimes overweigh any single process in metabolic rate was also observed with mephobar-
when complex drug–drug interactions are involved. bital. The incidence of side effects was higher in
For most drugs, metabolism has multiple pathways Japanese subjects, possibly due to a slower oxidative
which are inherently complicated. Many pharmaco- metabolism. Variations in propranolol metabolism
dynamic drug actions in patients encounter the issue of due to genetic difference among Chinese populations
responder and nonresponder, which may be genetically were also reported (Lai et al, 1995). Some variations
defined or totally obscured. in metabolism may also be related to geographic
Knowledge of drug transport of drug from one rather than racial differences (Bertilsson, 1995).
site can make the hepatic intrinsic clearance concept Besides genetic influence, the basal level of
obsolete in some simple physiological blood flow enzyme activity may be altered by environmental fac-
models. Macro models based on mass balance are tors and exposure to chemicals. Shorter theophylline
kinetically based and the amount of drug in the elimination half-life due to smoking was observed in
plasma pool can still be computed and properly smokers. Apparently, the aromatic hydrocarbons, such
tracked. A drug–drug interaction between lovastatin as benzpyrene, that are released during smoking stimu-
and cyclosporine occurs because cyclosporine is a late the enzymes involved in theophylline metabolism.
CYP3A and transport inhibitor in the liver. Young children are also known to eliminate theophyl-
line more quickly. Phenobarbital is a potent inducer of
a wider variety of hepatic enzymes. Polycyclic hydro-
Frequently Asked Questions
carbons such as 3-methylcholanthrene and benzpyrene
»»Why is a compartment referred to as a black box?
also induce hepatic enzyme formation. These com-
»»What are the problems about modeling a real system pounds are carcinogenic.
in drug therapy? Hepatic enzyme activity may also be inhibited
by a variety of agents including carbon monoxide,
heavy metals, and certain imidazole drugs such as
Variation of Biotransformation Enzymes cimetidine. Enzyme inhibition by cimetidine may
Variation in metabolism may be caused by a number of lead to higher plasma levels and longer elimination
biologic and environmental variables (see Table 12-6). of coadministered phenytoin or theophylline. The
Pharmacogenetics is the study of genetic differences physiologic condition of the host—including age,
in pharmacokinetics and pharmacodynamics, includ- gender, nutrition, diet, and pathophysiology—also
ing drug elimination (see Chapter 13). For example, affects the level of hepatic enzyme activities.
the N-acetylation of isoniazid is genetically deter-
mined, with at least two identifiable groups, includ-
Genetic Variation of Cytochrome
ing rapid and slow acetylators (Evans et al, 1968).
The difference is referred to as genetic polymor- P-450 (CYP) Isozymes
phism. Individuals with slow acetylation are prone to The most important enzymes accounting for varia-
isoniazid-induced neurotoxicity. Procainamide and tion in phase I metabolism of drugs is the cytochrome
hydralazine are other drugs that are acetylated and P-450 enzyme group, which exists in many forms
demonstrate genetic polymorphism. among individuals because of genetic differences
Drug Elimination and Hepatic Clearance 333
(May, 1994; Tucker, 1994; Parkinson, 1996; see also The substrate specificities of the P-450 enzymes
Chapter 13). Initially, the cytochrome P-450 enzymes appear to be due to the nature of the amino acid resi-
were identified according to the substrate that was dues, the size of the amino acid side chain, and the
biotransformed. More recently, the genes encoding polarity and charge of the amino acids (Negishi et al,
many of these enzymes have been identified. 1996). The individual gene is denoted by an Arabic
Multiforms of cytochrome P-450 are referred to as number (last number) after the subfamily. For exam-
isozymes, and are classified into families (originally ple, cytochrome P-450 1A2 (CYP1A2) is involved
denoted by Roman numerals: I, II, III, etc) and sub- in the oxidation of caffeine and CYP2D6 is involved in
families (denoted by A, B, C, etc) based on the simi- the oxidation of drugs, such as codeine, propranolol,
larity of the amino acid sequences of the isozymes. If and dextromethorphan. The well-known CYP2D6 is
an isozyme amino acid sequence is 60% similar or responsible for debrisoquine metabolism among
more, it is placed within a family. Within the family, individuals showing genetic polymorphism. The
isozymes with amino acid sequences of 70% or more vinca alkaloids used in cancer treatment have shown
similarity are placed into a subfamily, and an Arabic great inter- and intraindividual variabilities. CYP3A
number follows for further classification. Further enzymes are known to be involved in the metabolism
information on the CYP enzymes including drug of vindesine, vinblastine, and other vinca alkaloids
interactions, classification, table of substrates, inhibi- (Rahmani and Zhou, 1993). Failing to recognize varia-
tors, and inducers have been published by Nelson, tions in drug clearance in cancer chemotherapy may
(2009) and the US FDA. Nebert et al (1989) and result in greater toxicity or even therapeutic failure.
Hansch and Zhang (1993) have reviewed the nomen- There are now at least eight families of cyto-
clature of the P-450 family of enzymes. A new chrome isozymes known in humans and animals.
nomenclature starts with CYP as the root denoting CYP 1–3 are best known for metabolizing clinically
cytochrome P-450, and an Arabic number now useful drugs in humans. Variation in isozyme distri-
replaces the Roman numeral (Table 12-7). The bution and content in the hepatocytes may affect
CYP3A subfamily of CYP3 appears to be respon- intrinsic hepatic clearance of a drug. The levels and
sible for the metabolism of a large number of struc- activities of the cytochrome P-450 isozymes differ
turally diverse endogenous agents (eg, testosterone, among individuals as a result of genetic and environ-
cortisol, progesterone, estradiol) and xenobiotics mental factors. Clinically, it is important to look for
(eg, nifedipine, lovastatin, midazolam, terfenadine, evidence of unusual metabolic profiles in patients
erythromycin). before dosing. Pharmacokinetic experiments using
a “marker” drug such as the antipyrine or dextro-
methorphan may be used to determine if the intrinsic
TABLE 127 Comparison of P-450
hepatic clearance of the patient is significantly dif-
Nomenclatures Currently in Use
ferent from that of an average subject.
P-450 Gene The metabolism of debrisoquin is polymorphic
Family/Subfamily New Nomenclature in the population, with some individuals having
P-450I CYP1 extensive metabolism (EM) and other individuals
having poor metabolism (PM). Those individuals
P-450IIA CYP2A
who are PM lack functional CYP2D6 (P-450IID6).
P-450IIB CYP2B In EM individuals, quinidine will block CYP2D6 so
P-450IIC CYP2C that genotypic EM individuals appear to be pheno-
typic PM individuals (Caraco et al, 1996). Some
P-450IID CYP2D
drugs metabolized by CYP2D6 (P-450IID6) are
P-450IIE CYP2E codeine, flecainide, dextromethorphan, imipramine,
P-450III CYP3 and other cyclic antidepressants that undergo ring
hydroxylation. The inability to metabolize substrates
P-450IV CYP4
for CYP2D6 results in increased plasma concentra-
Sources: Nebert et al (1989) and Hansch and Zhang (1993). tions of the parent drug in PM individuals.
334 Chapter 12
Drug Interactions Involving coadministered psychotropic drugs. Fluoxetine causes
Drug Metabolism a ten-fold decrease in the clearance of imipramine and
The enzymes involved in the metabolism of drugs desipramine because of its inhibitory effect on hydrox-
may be altered by diet and the coadministration of ylation (Toney and Ereshefsky, 1995).
other drugs and chemicals. A few clinical examples of enzyme inhibitors and
Enzyme induction is a
drug- or chemical-stimulated increase in enzyme inducers are listed in Table 12-8. Diet also affects
activity, usually due to an increase in the amount of drug-metabolizing enzymes. For example, plasma
enzyme present. Enzyme induction usually requires theophylline concentrations and theophylline clear-
some onset time for the synthesis of enzyme protein. ance in patients on a high-protein diet are lower than in
For example, rifampin induction occurs within 2 days, subjects whose diets are high in carbohydrates. Sucrose
while phenobarbital induction takes about 1 week to or glucose plus fructose decrease the activity of mixed-
occur. Enzyme induction for carbmazepine begins function oxidases, an effect related to a slower metabo-
after 3 to 5 days and is not complete for approxi- lism rate and a prolongation in hexobarbital sleeping
mately 1 month or longer. Smoking can change the time in rats. Chronic administration of 5% glucose was
rate of metabolism of many cyclic antidepressant suggested to affect sleeping time in subjects receiving
drugs (CAD) through enzyme induction (Toney and barbiturates. A decreased intake of fatty acids may lead
Ereshefsky, 1995). Agents that induce enzymes include to decreased basal MFO activities (Campbell, 1977)
aromatic hydrocarbons (such as benzopyrene, found in and affect the rate of drug metabolism.
cigarette smoke), insecticides (such as chlordane), and The protease inhibitor saquinavir mesylate
drugs such as carbamazepine, rifampin, and phenobar- (Invirase®, Roche) has very low bioavailability—only
bital (see also Chapter 22). about 4%. In studies conducted by Hoffmann-La
Enzyme inhibition may be
due to substrate competition or due to direct inhibition Roche, the area under the curve (AUC) of saquinavir
of drug-metabolizing enzymes, particularly one of was increased to 150% when the volunteers took a
several of the cytochrome P-450 enzymes. Many 150-mL glass of grapefruit juice with the saquinavir,
widely prescribed antidepressants generally known as and then another 150-mL glass an hour later.
selective serotonin reuptake inhibitors (SSRIs) have Concentrated grapefruit juice increased the AUC up to
been reported to inhibit the CYP2D6 system, result- 220%. Naringin, a bioflavonoid in grapefruit juice,
ing in significantly elevated plasma concentration of was found to be at least partially responsible for the
TABLE 128 Examples of Drug Interactions Affecting Mixed Function Oxidase Enzymes
Inhibitors of Drug Metabolism Example Result
Acetaminophen Ethanol Increased hepatotoxicity in chronic alcoholics
Cimetidine Warfarin Prolongation of prothrombin time
Erythromycin Carbamazepine Decreased carbazepine clearance
Fluoxetine Imipramine (IMI) Decreased clearance of CAD
Fluoxetine Desipramine (DMI) Decreased clearance of CAD
Inducers of Drug Metabolism Example Result
Carbamazepine Acetaminophen Increased acetaminophen metabolism
Rifampin Methadone Increased methadone metabolism, may precipitate
opiate withdrawal
Phenobarbital Dexamethasone Decreased dexamethasone elimination half-life
Rifampin Prednisolone Increased elimination of prednisolone
Drug Elimination and Hepatic Clearance 335
TABLE 129 Change in Drug Availability Due metabolizes saquinavir, resulting in an increase in its
to Oral Coadministration of Grapefruit Juice AUC. Ketoconazole and ranitidine (Zantac®) may
also increase the AUC of saquinavir by inhibition of
Drug Study
the cytochrome P-450 enzymes. In contrast, rifampin
Triazolam Hukkinen et al, 1995 greatly reduces the AUC of saquinavir, apparently due
Midazolam Kupferschmidt et al, 1995 to enzymatic stimulation. Other drugs recently shown
to have increased bioavailability when taken with
Cyclosporine Yee et al, 1995
grapefruit juice include several sedatives and the anti-
Coumarin Merkel et al, 1994 coagulant coumarin (Table 12-9). Increases in drug
Nisoldipine Baily DG et al, 1993a levels may be dangerous, and the pharmacokinetics of
drugs with potential interactions should be closely
Felodipine Baily DG et al, 1993b
monitored. More complete tabulations of the cyto-
chrome P-450s are available (Flockhart, 2003;
inhibition of saquinavir metabolism by CYP3A4, Parkinson, 1996; Cupp and Tracy, 1998); some exam-
present in the liver and the intestinal wall, which ples are given in Table 12-10.
TABLE 1210 Cytochrome P450 Isoforms and Examples
CYP1A2 Substrates—amitriptyline, imipramine, theophylline (other enzymes also involved); induced by smoking
Fluvoxamine, some quinolones, and grapefruit juice are inhibitors
CYP2B6 Substrates—cyclophosphamide, methadone
CYP2C9 Metabolism of S-warfarin and tolbutamide by CYP2C9
Substrates—NSAIDs—ibuprofen, diclofenac
CYP2C19 Omeprazole, S-mephenytoin, and propranolol
Diazepam (mixed), and imipramine (mixed)
Inhibitors: cimetidine, fluoxetine, and ketoconazole
CYP2D6 Many antidepressants, b-blockers are metabolized by CYP2D6
SRIIs, cimetidine are inhibitors
Substrates—amitriptyline, imipramine, fluoxetine, antipsychotics (haloperidol, thioridazine)
Inhibitors—paroxetine, fluoxetine, sertraline, fluvoxamine, cimetidine, haloperidol
CYP2E1 Substrates—acetaminophen, ethanol, halothane
Induced by INH and disulfiram
CYP3A4, 5, 6 CYP3A subfamilies are the most abundant cytochrome enzymes in humans and include many key thera-
peutic and miscellaneous groups:
Ketoconazole, atorvastatin, lovastatin
Azithromycin, clarithromycins, amitriptyline
Benzodiazepines—alprazolam, triazolam, midazolam
Calcium blockers—verapamil, diltiazam
Protease inhibitors—ritonavir, saquinavir, indinavir
Examples based on Flockhart (2003), Cupp and Tracy (1998), and Desta et al (2002).
336 Chapter 12
Auto-Induction and Time-Dependent The key CYP450 enzymes are collected in the
Pharmacokinetics microsomal fraction. The CYP450 enzymes retain
Many drugs enhance the activity of cytochrome their activity for many years in microsomes or
P-450 (CYP) enzymes and thereby change their own whole liver stored at low temperature. Hepatic
metabolism (auto-induction) or the metabolism of microsomes can be obtained commercially, with or
other compounds. When assessing induction, the without prior phenotyping, for most important
enzyme activity is usually measured before and after CYP450 enzymes. The cDNAs for the common
a period of treatment with the inducing agent. Thus, CYP450s have been cloned, and the recombinant
the induction magnitude of various CYP enzymes is human enzymatic proteins have been expressed in a
well known for several inducing agents. variety of cells. These recombinant enzymes provide
The an excellent way to confirm results using micro-
time-dependent pharmacokinetics have
been described with a model where the production somes. Pharmacokinetic endpoints recommended for
rates of the affected enzymes were proportional to assessment of the substrate are (1) exposure measures
the amounts of the inducing agents and the time such as AUC, Cmax, time to Cmax (Tmax), and others as
course of the induction process was described by the appropriate; and (2) pharmacokinetic parameters
turnover model. An example of a drug with time- such as clearance, volumes of distribution, and half-
dependent pharmacokinetics is carbamazepine. lives (FDA Guidance for Industry, 1999). For metab-
For new drugs, the potential for drug metabolism/ olism induction studies, in vivo studies are more
interaction is studied relied upon because enzyme induction may not be
in vitro and/or in vivo by identi-
fying whether the drug is a substrate for the common well predicted from in vitro results. Considerations
CYP450 subfamilies (FDA Guidance for Industry, in drug-metabolizing/interaction studies include:
1999, 2006). An understanding of the mechanistic (1) acute or chronic use of the substrate and/or inter-
basis of metabolic drug–drug interactions enables the acting drug; (2) safety considerations, including
prediction of whether the coadministration of two or whether a drug is likely to be an NTR (narrow thera-
more drugs may have clinical consequences affecting peutic range) or non-NTR drug; (3) pharmacoki-
safety and efficacy. In practice, an investigational netic and pharmacodynamic characteristics of the
drug under development is coadministered with an substrate and interacting drugs; and (4) the need to
approved drug (interacting drug) which utilizes assess induction as well as inhibition. The inhibit-
similar CYP pathways. Examples of substrates ing/inducing drugs and the substrates should be
include (1) midazolam for CYP3A; (2) theophylline dosed so that the exposures of both drugs are rele-
for CYP1A2; (3) repaglinide for CYP2C8; (4) war- vant to their clinical use.
farin for CYP2C9 (with the evaluation of S-warfarin);
(5) omeprazole for CYP2C19; and (6) desipramine Transporter-Based Drug–Drug Interactions
for CYP2D6. Additional examples of substrates, along Transporter-based interactions have been increasingly
with inhibitors and inducers of specific CYP enzymes, documented. Examples include the inhibition or
are listed in Table A-2 in Appendix A in the FDA draft induction of transport proteins, such as P-glycoprotein
guidance (2006). Examples of substrates include, but (P-gp), organic anion transporter (OAT), organic
are not limited to, (1) midazolam, buspirone, felodip- anion transporting polypeptide (OATP), organic cation
ine, simvastatin, or lovastatin for CYP3A4; (2) theoph- transporter (OCT), multidrug resistance–associated
ylline for CYP1A2; (3) S-warfarin for CYP2C9; and proteins (MRP), and breast cancer–resistant protein
(4) desipramine for CYP2D6. (BCRP). Examples of transporter-based interactions
Since metabolism usually occurs in the liver include the interactions between digoxin and quinidine,
(some enzymes such as CYP3A4 are also important fexofenadine and ketoconazole (or erythromycin),
in gut metabolism), human liver microsomes pro- penicillin and probenecid, and dofetilide and cimeti-
vide a convenient way to study CYP450 metabo- dine. Of the various transporters, P-gp is the most
lism. Microsomes are a subcellular fraction of tissue well understood and may be appropriate to evaluate
obtained by differential high-speed centrifugation. during drug development. Table 12-11 lists some of
Drug Elimination and Hepatic Clearance 337
TABLE 1211 Major Human Transporters and Known Substrates, Inhibitors, and Inducers
Gene Aliases Tissue Drug Substrate Inhibitor Inducer
ABCB1 P-gp, Intestine, liver, Digoxin, fexofenadine, Ritonavir, cyclosporine, Rifampin,
MDR1 kidney, brain, indinavir, vincristine, verapamil, erythromycin, St John’s
placenta, adrenal, colchicine, topotecan, ketocoanzole, itraconazole, wort
testes paclitaxel quinidine, elacridar
(GF120918) LY335979
valspodar (PSC833)
ABCB4 MDR3 Liver Digoxin, paclitaxel,
vinblastine
ABCB11 BSEP Liver Vinblastine
ABCC1 MRP1 Intestine, liver, Adefovir, indinavir
kidney, brain
ABCC2 MRP2, Intestine, liver, Indinavir, cisplatin Cyclosporine
CMOAT kidney, brain
ABCC3 MRP3, Intestine, liver, Etoposide, methotrexate,
CMOAT2 kidney, placenta, tenoposide
adrenal
ABCC4 MRP4
ABCC5 MRP5
ABCC6 MRP6 Liver, kidney Cisplatin, daunorubicin
ABCG2 BCRP Intestine, liver, Daunorubicin, doxorubicin, Elacridar (GFl20918),
breast, placenta topotecan, rosuvastatin, gefitinib
sulfasalazine
SLCOIB1 OATP1B1, Liver Rifampin, rosuvastatin, Cyclosporine, rifampin
OATP-C, methotrexate, pravastatin,
OATP2 thyroxine
SLCOIB3 OATP1B3, Liver Digoxin, methotrexate,
OATP8 rifampin,
SLC02B1 SLC21A9, Intestine, liver, Pravastatin
OATP-B kidney, brain
SLC1OA1 NTCP Liver, pancreas Rosuvastatin
From FDA Guidance (draft) 2006.
the major human transporters and known substrates, polymorphism, (2) enzymatic induction or inhibition
inhibitors, and inducers. due to coadministered drugs, (3) modification of
In the simple hepatic clearance model, intrin- influx and efflux transporters in the liver and the bile
sic clearance is assumed to be constant within the canaliculi.
same subject. This model describes how clearance Some hepatic transporters in the liver include
can change in response to physiologic changes P-gp and OATPs (Huang et al, 2009). When a trans-
such as blood flow or enzymatic induction. Patient porter is known to play a major role in translocating
variability and changes in intrinsic clearance may be drug in and out of cells and organelles within the
due to (1) patient factors such as age and genetic liver, the simple hepatic clearance model may not
338 Chapter 12
adequately describe the pharmacokintics of the drug 2. Literature search shows that digoxin trans-
within the liver. Micro constants may be needed to port by P-gp occurs at the liver canaliculi and
describe how the drug moves kinetically in and out P-gp will interact with ritonavir or quinidine
within a group of cells or compartment. Canalicular with coadministration (both are inhibitors of
transporters are present for many drugs. Biliary MDR1). Inhibition of efflux will increase the
excretion should also be incorporated into the model plasma level of digoxin. Other effects may
as needed. For this reason, local drug concentration also occur since most transport inhibitors are
in the liver may be very high, leading to serious liver not 100% specific and may affect metabolism/
toxicity. Huang et al (2009) have discussed the impor- disposition in other ways.
tance of drug transporters, drug disposition, and how 3. The package insert should be consulted on drug
to study drug interaction in the new drugs. distribution and drug interaction. A pharmacist
Knowledge of drug transporters and CYPs can should realize that although either one of the
help predict whether many drug interactions have the two inhibitors can increase AUC of digoxin
clinical significance. Pharmacists should realize that (by 1.5–2 x) in this hypothetical case, in reality,
the combined effect of efflux and CYP inhibition can a comprehensive evaluation of pharmaco-
cause serious or even fatal adverse reaction due to kinetics and pharmacodynamics of the drug
severalfold increase in AUC or Cmax. Impairment of doses involved and the medical profile of the
bile flow, saturation of conjugation enzymes (phase II) patient is needed to determine if an interaction
such as glucoronide, and sulfate conjugate formation is clinically significant.
can lead to adverse toxicity.
CLINICAL EXAMPLE FIRST-PASS EFFECTS
Digoxin is an MDR1/P-gp substrate. For some drugs, the route of administration affects
the metabolic rate of the compound. For example, a
1. Which of the following sites is important to
drug given parenterally, transdermally, or by inhala-
influence on the plasma levels of digoxin after
tion may distribute within the body prior to metabo-
oral administration?
lism by the liver. In contrast, drugs given orally are
a. Hepatocyte (canalicular)
normally absorbed in the duodenal segment of the
b. Hepatocyte (sinusoidal)
small intestine and transported via the mesenteric
c. Intestinal enterocyte
vessels to the hepatic portal vein and then to the liver
2. Ritonavir and quinidine are examples of P-gp
before entering the systemic circulation. Drugs that
inhibitors. What changes in AUC or Cmax would
are highly metabolized by the liver or by the intesti-
you expect for digoxin when coadministered
nal mucosal cells demonstrate poor systemic avail-
with either one of these two inhibitors?
ability when given orally. This rapid metabolism of
3. Using your knowledge of drug transporters
an orally administered drug before reaching the
and their substrate inhibitors, can you deter-
general circulation is termed first-pass effect or pre-
mine whether the above change in digoxin
systemic elimination.
plasma level is due to a change in metabolism
or distribution?
Evidence of First-Pass Effects
Solution
First-pass effects may be suspected when there is rela-
1. According to Table 12-11, MDR1 is an efflux tively low concentrations of parent (or intact) drug
transporter for digoxin in the liver (canaliculi) in the systemic circulation after oral compared to
and enterocyte. Digoxin is also a substrate for IV administration. In such a case, the AUC for a drug
MDR3, SLCO1B1, and other transporters. given orally also is less than the AUC for the same
MDR1 is inhibited by quinidine and ritonavir. dose of drug given intravenously. From experimental
Drug Elimination and Hepatic Clearance 339
findings in animals, first-pass effects may be assumed If both the ER for the liver and the blood flow to the
if the intact drug appears in a cannulated hepatic por- liver are known, then hepatic clearance, Clh, may be
tal vein but not in general circulation. calculated by the following expression:
For an orally administered drug that is chemically
stable in the gastrointestinal tract and is 100% systemi- Q (C −C )
Cl a v
h = =Q×ER (12.36)
cally absorbed (F = 1), the area under the plasma drug Ca
concentration curve, AUC∞
0, oral , should be the same
when the same drug dose is given intravenously, where Q is the effective hepatic blood flow.
AUC∞
0, IV . Therefore, the absolute bioavailability (F)
may reveal evidence of drug being removed by the Relationship between Absolute
liver due to first-pass effects as follows: Bioavailability and Liver Extraction
Liver ER provides a measurement of liver extraction
[AUC]∞
0, oral /D0, oral of a drug orally administered. Unfortunately, sam-
F = (12.34)
[AUC]∞0, IV /D pling of drug from the hepatic portal vein and artery
0, IV
is difficult and performed mainly in animals. Animal
For drugs that undergo first-pass effects, ER values may be quite different from those in
AUC∞
0, oral is smaller than AUC∞
0, IV and F < 1. Drugs humans. The following relationship between bio-
such as propranolol, morphine, and nitroglycerin availability and liver extraction enables a rough
have F values less than 1 because these drugs estimate of the extent of liver extraction:
undergo significant first-pass effects.
F = 1 − ER − F″ (12.37)
Liver Extraction Ratio where F is the fraction of bioavailable drug, ER is
Because there are many other reasons for a drug to the drug fraction extracted by the liver, and F″ is the
have a reduced F value, the extent of first-pass fraction of drug removed by nonhepatic process
effects is not precisely measured from the F value. prior to reaching the circulation.
The liver extraction ratio (ER) provides a direct mea- If F″ is assumed to be negligible—that is, there
surement of drug removal from the liver after oral is no loss of drug due to chemical degradation, gut
administration of a drug. metabolism, and incomplete absorption—ER may
be estimated from
C −C
a v
ER = (12.35) F = 1 − ER (12.38)
C
a
After substitution of Equation 12.34 into
where Ca is the drug concentration in the blood Equation 12.38,
entering the liver and Cv is the drug concentration
leaving the liver. [AUC]∞ D
ER = − 0,oral / 0,oral
1 ∞ (12.39)
Because Ca is usually greater than Cv, ER is usu- [AUC]0,IV /D0,IV
ally less than 1. For example, for propranolol, ER or
[E] is about 0.7—that is, about 70% of the drug is ER is a rough estimation of liver extraction for
actually removed by the liver before it is available a drug. Many other factors may alter this estimation:
for general distribution to the body. By contrast, if the size of the dose, the formulation of the drug, and
the drug is injected intravenously, most of the drug the pathophysiologic condition of the patient all may
would be distributed before reaching the liver, and affect the ER value obtained.
less of the drug would be metabolized the first time Liver ER provides valuable information in
the drug reaches the liver. determining the oral dose of a drug when the intra-
The ER may vary from 0 to 1.0. An ER of 0.25 venous dose is known. For example, propranolol
means that 25% of the drug is removed by the liver. requires a much higher oral dose compared to an
340 Chapter 12
IV dose to produce equivalent therapeutic blood TABLE 1212 Hepatic and Renal Extraction
levels, because of oral drug extraction by the liver. Ratios of Representative Drugs
Because liver extraction is affected by blood flow
Extraction Ratios
to the liver, dosing of drug with extensive liver
metabolism may produce erratic plasma drug levels. Intermediate
Low (<0.3) (0.3–0.7) High (>0.7)
Formulation of this drug into an oral dosage form
requires extensive, careful testing. HEPATIC EXTRACTION
Amobarbital Aspirin Arabinosyl-
Estimation of Reduced Bioavailability Due to cytosine
Liver Metabolism and Variable Blood Flow Antipyrine Quinidine Encainide
Blood flow to the liver plays an important role in the Chloramphenicol Desipramine Isoproterenol
amount of drug metabolized after oral administra-
Chlordiazepoxide Nortriptyline Meperidine
tion. Changes in blood flow to the liver may substan-
tially alter the percentage of drug metabolized and Diazepam Morphine
therefore alter the percentage of bioavailable drug. Digitoxin Nitroglycerin
The relationship between blood flow, hepatic clear-
Erythromycin Pentazocine
ance, and percent of drug bioavailable is
Isoniazid Propoxyphene
Cl
F h
′ = 1− = 1− ER (12.40)
Q Phenobarbital Propranolol
Phenylbutazone Salicylamide
where Clh is the hepatic clearance of the drug and Q
Phenytoin Tocainide
is the effective hepatic blood flow. F′ is the bioavail-
ability factor obtained from estimates of liver blood Procainamide Verapamil
flow and hepatic clearance, ER. Salicylic acid
This equation provides a reasonable approach
Theophylline
for evaluating the reduced bioavailability due to
first-pass effect. The usual effective hepatic blood Tolbutamide
flow is 1.5 L/min, but it may vary from 1 to 2 L/min
Warfarin
depending on diet, food intake, physical activity, or
drug intake (Rowland, 1973). For the drug propoxy- Data from Rowland (1978) and Brouwer et al (1992).
phene hydrochloride, F′ has been calculated from
hepatic clearance (990 mL/min) and an assumed
liver blood flow of 1.53 L/min:
In contrast, drugs with high extraction ratios have
0.99
F′ =1− = 0.35 poor bioavailability when given orally. Therefore, the
1.53
oral dose must be higher than the intravenous dose to
The results, showing that 35% of the drug is sys- achieve the same therapeutic response. In some cases,
temically absorbed after liver extraction, are rea- oral administration of a drug with high presystemic
sonable compared with the experimental values for elimination, such as nitroglycerin, may be impractical
propranolol. due to very poor oral bioavailability, and thus a sub-
Presystemic elimination or first-pass effect is a lingual, transdermal, or nasal route of administration
very important consideration for drugs that have a may be preferred.
high extraction ratio (Table 12-12). Drugs with low Furthermore, if an oral drug product has slow
extraction ratios, such as theophylline, have very little dissolution characteristics or release rate, then more
presystemic elimination, as demonstrated by com- of the drug will be subject to first-pass effect com-
plete systemic absorption after oral administration. pared to doses of drug given in a more bioavailable
Drug Elimination and Hepatic Clearance 341
form (such as a solution). In addition, drugs with
high presystemic elimination tend to demonstrate Solution
more variability in drug bioavailability between and The relative bioavailability of propranolol from the
within individuals. Finally, the quantity and quality tablet compared to the solution is 70% or 0.7. The
of the metabolites formed may vary according to the absolute bioailability, F, of propranolol from the tab-
route of drug administration, which may be clini- let compared to the IV dose is 21.6%, or F = 0.216.
cally important if one or more of the metabolites has From the table of ER values (Table 12-13), the ER for
pharmacologic or toxic activity. propranolol is 0.6 to 0.8. If the product is perfectly
To overcome first-pass effect, the route of admin- formulated, ie, the tablet dissolves completely and
istration of the drug may be changed. For example, all the drug is released from the tablet, the fraction
nitroglycerin may be given sublingually or topically, of drug absorbed after deducting for the fraction of
and xylocaine may be given parenterally to avoid the drug extracted by the liver is
first-pass effects. Another way to overcome first-pass
effects is to either enlarge the dose or change the drug F ′ = 1 − ER
product to a more rapidly absorbable dosage form. In F ′ = 1 − 0.7 (mean ER = 0.7)
either case, a large amount of drug is presented rap- F ′ = 0.3
idly to the liver, and some of the drug will reach the
general circulation in the intact state. Thus, under normal conditions, total systemic
Although Equation 12.40 seems to provide a absorption of propranolol from an oral tablet
convenient way of estimating the effect of liver would be about 30% (F = 0.3). The measurement
blood flow on bioavailability, this estimation is actu- of relative bioavailability for propranolol is always
ally more complicated. A change in liver blood flow performed against a reference standard given by
may alter hepatic clearance and F′. A large blood the same route of administration and can have a
flow may deliver enough drug to the liver to alter value greater than 100%.
the rate of metabolism. In contrast, a small blood The following shows a method for calculating
flow may decrease the delivery of drug to the liver the absolute bioavailability from the relative bio-
and become the rate-limiting step for metabolism availability provided the ER is accurately known.
(see below). The hepatic clearance of a drug is usu- Using the above example,
ally calculated from plasma drug data rather than
whole-blood data. Significant nonlinearity may be Absolute availability of the solution = 1 – ER =
the result of drug equilibration due to partitioning 1 – 0.7 = 0.3 = 30%
into the red blood cells. Relative availability of the solution = 100%
Absolute availability of the tablet = x%
Relative availability of the tablet = 70%
EXAMPLES »» »
30×70
x = =21%
1. A new propranolol 5-mg tablet was developed 100
and tested in volunteers. The bioavailabil- Therefore, this product has a theoretical absolute
ity of propranolol from the tablet was 70%, bioavailability of 21%. The small difference of cal-
compared to an oral solution of propranolol, culated and actual (the difference between 21.6%
and 21.6%, compared to an intravenous dose and 21%) absolute bioavailability is due largely to
of propranolol. Calculate the relative and liver extraction fluctuation. All calculations are per-
absolute bioavailability of the propranolol formed with the assumption of linear pharmaco-
tablet. Comment on the feasibility of further kinetics, which is generally a good approximation.
improving the absolute bioavailability of the ER may deviate significantly with changes in blood
propranolol tablet. flow or other factors.
342 Chapter 12
TABLE 1213 Pharmacokinetic Classification
of Drugs Eliminated Primarily by Hepatic 2. Fluvastatin sodium (Lescol®, Novartis) is a drug
Metabolism used to lower cholesterol. The absolute bioavail-
ability after an oral dose is reported to be 19% to
Extraction
29%. The drug is rapidly and completely absorbed
Ratio
(manufacturer’s product information). What are
Drug Class (Approx.) Percent Bound
the reasons for the low oral bioavailability in spite
Flow Limited of reportedly good absorption? What is the extrac-
Lidocaine 0.83 45–80a tion ratio of fluvastatin? (The absolute bioavail-
ability, F, is 46%, according to values reported in
Propranolol 0.6–0.8 93 the literature.)
Pethidine 0.60–0.95 60
(meperidine) Solution
Pentazocine 0.8 — Assuming the drug to be completely absorbed as
reported, using Equation 12.38,
Propoxyphene 0.95 —
ER = 1 – 0.46 = 0.54
Nortriptyline 0.5 95
Morphine 0.5–0.75 35 Thus, 54% of the drug is lost due to first-pass
effect because of a relatively large extraction ratio.
Capacity Limited, Binding Sensitive Since bioavailability is only 19% to 29%, there is
Phenytoin 0.03 90 probably some nonhepatic loss according to
Equation 12.37. Fluvastatin sodium was reported
Diazepam 0.03 98 to be extensively metabolized, with some drug
Tolbutamide 0.02 98 excreted in feces.
Warfarin 0.003 99
Chlorpromazine 0.22 91–99
Relationship between Blood Flow, Intrinsic
Clindamycin 0.23 94 Clearance, and Hepatic Clearance
Quinidine 0.27 82 Although Equation 12.40 seems to provide a conve-
nient way of estimating the effect of liver blood flow
Digitoxin 0.005 97
on bioavailability, this estimation is actually more
Capacity Limited, Binding Insensitive complicated. For example, factors that affect the
hepatic clearance of a drug include (1) blood flow to
Theophylline 0.09 59
the liver, (2) intrinsic clearance, and (3) the fraction
Hexobarbital 0.16 — of drug bound to protein.
A change in liver blood flow may alter hepatic
Amobarbital 0.03 61
clearance and F′. A large blood flow may deliver
Antipyrine 0.07 10 enough drug to the liver to alter the rate of metabo-
lism. In contrast, a small blood flow may decrease
Chloramphenicol 0.28 60–80
the delivery of drug to the liver and become the rate-
Thiopental 0.28 72 limiting step for metabolism. The hepatic clearance
of a drug is usually calculated from plasma drug data
Acetaminophen 0.43 5a
rather than whole-blood data. Significant nonlinearity
aConcentration dependent in part. may be the result of drug equilibration due to parti-
From Blaschke (1977), with permission. tioning into the red blood cells.
Drug Elimination and Hepatic Clearance 343
High-Extraction Ratio Drugs
ER
For some drugs (such as isoproterenol, lidocaine, 2.5 1.0
and nitroglycerin), the extraction ratio is high (>0.7),
and the drug is removed by the liver almost as rap- 0.9
2.0
idly as the organ is perfused by blood in which the
drug is contained. For drugs with very high extrac- 0.8
tion ratios, the rate of drug metabolism is sensitive to 15 0.7
changes in hepatic blood flow. Thus, an increase in
0.6
blood flow to the liver will increase the rate of drug
1.0
removal by the organ. Propranolol, a b-adrenergic 0.5
blocking agent, decreases hepatic blood flow by 0.4
decreasing cardiac output. In such a case, the drug 0.5 0.3
0.2
decreases its own clearance through the liver when
0.1
given orally. Many drugs that demonstrate first-pass 0
effects are drugs that have high extraction ratios with 0 0.5 1.0 1.5 2.0 2.5
respect to the liver. Liver blood
ow (L/min)
Intrinsic clearance (Clint) is used to describe the FIGURE 1218 The relationship between liver blood flow
total ability of the liver to metabolize a drug in the and total hepatic clearance for drugs with varying extraction
absence of flow limitations, reflecting the inherent rates (ER).
activities of the mixed-function oxidases and all
other enzymes. Intrinsic clearance is a distinct char-
acteristic of a particular drug, and as such, it reflects terms of all the factors in a physiologic model allows
the inherent ability of the liver to metabolize the drug clearance to be estimated when physiologic or
drug. Intrinsic clearance may be shown to be analo- disease conditions cause changes in blood flow or
gous to the ratio Vmax/KM for a drug that follows intrinsic enzyme activity. Smoking, for example, can
Michaelis–Menten kinetics. Hepatic clearance is a increase the intrinsic clearance for the metabolism of
concept that characterizes drug elimination based on many drugs.
both blood flow and the intrinsic clearance of the Changes or alterations in mixed-function oxi-
liver, as shown in Equation 12.41. dase activity or biliary secretion can affect the intrin-
sic clearance and thus the rate of drug removal by the
Cl
Clh= Q int (12.41) liver. Drugs that show low extraction ratios and are
Q+Clint eliminated primarily by metabolism demonstrate
marked variation in overall elimination half-lives
Low-Extraction Ratio Drugs within a given population. For example, the elimina-
tion half-life of theophylline varies from 3 to 9 hours.
When the blood flow to the liver is constant, hepatic
This variation in t1/2 is thought to be due to genetic
clearance is equal to the product of blood flow (Q)
differences in intrinsic hepatic enzyme activity.
and the extraction ratio (ER) (Equation 12.36).
Moreover, the elimination half-lives of these same
However, the hepatic clearance of a drug is not con-
drugs are also affected by enzyme induction, enzyme
stant. Hepatic clearance changes with blood flow
inhibition, age of the individual, nutritional, and
(Fig. 12-18) and the intrinsic clearance of the drug
pathologic factors.
are described in Equation 12.41. For drugs with low
Clearance may also be expressed as the rate of
extraction ratios (eg, theophylline, phenylbutazone,
drug removal divided by plasma drug concentration:
and procainamide), the hepatic clearance is less
affected by hepatic blood flow. Instead, these drugs
are more affected by the intrinsic activity of the rate of drug removed by the liver
Cl = (12.42)
mixed-function oxidases. Describing clearance in h Ca
Hepatic clearance (L/min)
344 Chapter 12
Because the rate of drug removal by the liver is usu- For a drug with restrictive clearance, the rela-
ally the rate of drug metabolism, Equation 12.42 tionship of blood flow, intrinsic clearance, and pro-
may be expressed in terms of hepatic clearance and tein binding is
drug concentration entering the liver (Ca):
f Cl′
Clh =Q u int (12.44)
Rate of liver drug metabolism = ClhCa (12.43) Q+ fuCli′nt
where fu is the fraction of drug unbound in the blood
and Cl′ is the intrinsic clearance of free drug.
int
HEPATIC CLEARANCE Equation 12.44 is derived by substituting fuCl′ for
int
OF A PROTEIN-BOUND Clint in Equation 12.41.
DRUG: RESTRICTIVE AND From Equation 12.44, when Cl′ is very small
int
in comparison to hepatic blood flow (ie, Q ≥ Cl′ ),
int
NONRESTRICTIVE CLEARANCE then Equation 12.45 reduces to Equation 12.46.
FROM BINDING
Qf
uCli′Cl nt
h = (12.45)
It is generally assumed that protein-bound drugs are Q
not easily metabolized (restrictive clearance), while
free (unbound) drugs are subject to metabolism. Clh = fuCl′ (12.46)
int
Protein-bound drugs do not easily diffuse through cell
membranes, while free drugs can reach the site of the As shown in Equation 12.46, a change in Cl′ or f
int u
mixed-function oxidase enzymes easily. Therefore, an will cause a proportional change in Clh for drugs
increase in the unbound drug concentration in the with protein binding.
blood will make more drug available for hepatic In the case where Cl′ for a drug is very large
int
extraction. The concept is discussed under restric- in comparison to flow (Cl′ >> Q), Equation 12.47
int
tive and nonrestrictive clearance (Gillette, 1973) of reduces to Equation 12.48.
protein-bound drugs (see Chapter 11).
Most drugs are restrictively cleared—for example, Q fuCl′ Cl int
h = (12.47)
diazepam, quinidine, tolbutamide, and warfarin. The fuCli′nt
clearance of these drugs is proportional to the frac-
tion of unbound drug (fu). However, some drugs, Clh ≈ Q (12.48)
such as propranolol, morphine, and verapamil, are
nonrestrictively extracted by the liver regardless of Thus, for drugs with a very high Cl′ , Cl is depen-
int h
drug bound to protein or free. Kinetically, a drug is dent on hepatic blood flow and independent of pro-
nonrestrictively cleared if its hepatic extraction ratio tein binding.
(ER) is greater than the fraction of free drug (fu), and For restrictively cleared drugs, change in bind-
the rate of drug clearance is unchanged when the ing generally alters drug clearance. For a drug with
drug is displaced from binding. Mechanistically, the low hepatic extraction ratio and low plasma binding,
protein binding of a drug is a reversible process and clearance will increase, but not significantly, when
for a nonrestrictively bound drug, the free drug gets the drug is displaced from binding. For a drug
“stripped” from the protein relatively easily com- highly bound to plasma proteins (more than 90%), a
pared to a restrictively bound drug during the pro- displacement from these binding sites will signifi-
cess of drug metabolism. The elimination half-life of cantly increase the free concentration of the drug,
a nonrestrictively cleared drug is not significantly and clearance (both hepatic and renal clearance)
affected by a change in the degree of protein bind- will increase (see Chapter 11). There are some
ing. This is an analogous situation to a protein-bound drugs that are exceptional and show a paradoxical
drug that is actively secreted by the kidney. increase in hepatic clearance despite an increase in
Drug Elimination and Hepatic Clearance 345
protein binding. In one case, increased binding to elimination half-life of a drug with a high extraction
AAG (a acid glycoprotein) was found to concen- ratio is not markedly affected by an increase in
trate drug in the liver, leading to an increased rate of hepatic enzyme activity because enzyme activity is
metabolism because the drug was nonrestrictively already quite high. In both cases, an orally adminis-
cleared in the liver. tered drug with a higher extraction ratio results in a
greater first-pass effect as shown by an increase in
Effect of Changing Intrinsic Clearance hepatic clearance.
and/or Blood Flow on Hepatic Extraction
and Elimination Half-Life after IV and Effect of Changing Blood Flow on Drugs
Oral Dosing with High or Low Extraction Ratio
The effects of altered hepatic intrinsic clearance and Drug clearance and elimination half-life are both
liver blood flow on the blood level–time curve have affected by changing blood flow to the liver. For
been described by Wilkinson and Shand (1975) after drugs with low extraction (E = 0.1), a decrease in
both IV and oral dosing. These illustrations show hepatic blood flow from normal (1.5 L/min) to one-
how changes in intrinsic clearance and blood flow half decreases clearance only slightly, and blood
affect the elimination half-life, first-pass effects, and level is slightly higher. In contrast, for a drug with
bioavailability of the drug as represented by the area high extraction ratio (E = 0.9), decreasing the blood
under the curve. flow to one-half of normal greatly decreases clear-
ance, and the blood level is much higher.
Effect of Theoretical Change in Clint and F Alterations in hepatic blood flow significantly
on Drug Clearance affect the elimination of drugs with high extraction
The relationship between blood flow (F), intrinsic ratios (eg, propranolol) and have very little effect on
clearance, and hepatic clearance was simulated with the elimination of drugs with low extraction ratios
hypothetic examples by Wilkinson and Shand (eg, theophylline). For drugs with low extraction
(1975). However, due to the prevalence of transport- ratios, any concentration of drug in the blood that
ers, the relationship may only apply unless all model perfuses the liver is more than the liver can eliminate.
assumptions are met. Consequently, small changes in hepatic blood flow
For drugs with low ER, the effect of doubling do not affect the removal rate of such drugs. In con-
Cl trast, drugs with high extraction ratios are removed
int from 0.167 to 0.334 L/min increases both the
extraction ratio (ER) and clearance (Cl) of the drug, from the blood as rapidly as they are presented to the
leading to a much shorter t1/2. The elimination half- liver. If the blood flow to the liver decreases, then the
life decreases about 50% due to the increase in elimination of these drugs is prolonged. Therefore,
intrinsic clearance. Simulation shows the change in drugs with high extraction ratios are considered to be
drug concentrations after oral administration when flow dependent. A number of drugs have been inves-
Cl tigated and classified according to their extraction by
int doubles. In this case, there is a decrease in both
AUC and t the liver.
1/2 (dashed line) due to the increase in
clearance of the drug.
For drugs with high ER, the effect of doubling
Clint from 13.7 to 27.0 L/min increases both the Effect of Changing Protein Binding
extraction ratio and clearance only. The elimination on Hepatic Clearance
half-life decreases only marginally. After oral admin- The effect of protein binding on hepatic clearance is
istration, when simulated, some decrease in AUC is often difficult to quantitate precisely, because it is
observed and the t1/2 is shortened moderately. not always known whether the bound drug is restric-
The elimination half-life of a drug with a low tively or nonrestrictively cleared. For example, ani-
extraction ratio is decreased significantly by an mal tissue levels of imipramine, a nonrestrictively
increase in hepatic enzyme activity. In contrast, the cleared drug, were shown to change as the degree of
346 Chapter 12
plasma protein binding changes (see Chapter 11). BILIARY EXCRETION OF DRUGS
As discussed, drug protein binding is not a factor in
hepatic clearance for drugs that have high extraction The biliary system of the liver is an important system
ratios. These drugs are considered to be flow limited. for the secretion of bile and the excretion of drugs.
In contrast, drugs that have low extraction ratios Anatomically, the intrahepatic bile ducts join outside
may be affected by plasma protein binding, depend- the liver to form the common hepatic duct (Fig. 12-20).
ing on the fraction of drug bound. For a drug that The bile that enters the gallbladder becomes highly
has a low extraction ratio and is less than 75% to concentrated. The hepatic duct, containing hepatic
80% bound, small changes in protein binding will bile, joins the cystic duct that drains the gallbladder
not produce significant changes in hepatic clear- to form the common bile duct. The common bile
ance. These drugs are considered capacity-limited, duct then empties into the duodenum. Bile consists
binding-insensitive drugs (Blaschke, 1977) and are primarily of water, bile salts, bile pigments, electro-
listed in Table 12-13. Drugs that are highly bound to lytes, and, to a lesser extent, cholesterol and fatty
plasma protein but with low extraction ratios are con- acids. The hepatic cells lining the bile canaliculi are
sidered capacity limited and binding sensitive, responsible for the production of bile. The produc-
because a small displacement in the protein binding tion of bile appears to be an active secretion process.
of these drugs will cause a very large increase in the Separate active biliary secretion processes have been
free drug concentration. These drugs are good exam- reported for organic anions, organic cations, and for
ples of restrictively cleared drugs. A large increase in polar, uncharged molecules.
free drug concentration will cause an increase in the Drugs that are excreted mainly in the bile have
rate of drug metabolism, resulting in an overall molecular weights in excess of 500. Drugs with
increase in hepatic clearance. Figure 12-19 illus- molecular weights between 300 and 500 are excreted
trates the relationship of protein binding, blood flow, both in urine and in bile. For these drugs, a decrease
and extraction. in one excretory route results in a compensatory
Flow-limited
0.8
0.6
0.4
0.2
Capacity-limited Capacity-limited
binding binding
insensitive sensitive
0 20 50 80 100
Drug bound to plasma proteins (percent)
FIGURE 1219 This diagram illustrates the way in which two pharmacokinetic parameters (hepatic extraction ratio and per-
cent plasma protein binding) are used to assign a drug into one of three classes of hepatic clearance (flow limited; capacity limited,
binding sensitive; and capacity limited, binding insensitive). Any drug metabolized by the liver can be plotted on the triangular
graph, but the classification is important only for those eliminated primarily by hepatic processes. The closer a drug falls to a corner
of the triangle (shaded areas), the more likely it is to have the characteristic changes in disposition in liver disease as described for
the three drug classes in the text. (From Blaschke, 1977, with permission.)
Extraction ratio
Drug Elimination and Hepatic Clearance 347
TABLE 1214 Examples of Drugs Undergoing
Enterohepatic Circulation and Biliary
BILE ACIDS Excretion
Common duct
Enterohepatic Circulation
20–30 g/d
recirculate Imipramine
Gut Indomethacin
Portal vein Morphine
Pregnenolone
Biliary Excretion (intact or as metabolites)
Cefamandole Fluvastatin
Approx. 0.8 g/d Cefoperazone Lovastatin
in feces
Chloramphenicol Moxalactam
FIGURE 1220 Enterohepatic recirculation of bile acids
and drug. (From Dow, 1963.) Diazepam Practolol
Digoxin Spironolactone
Doxorubicin Testosterone
increase in excretion via the other route. Compounds
Doxycycline Tetracycline
with molecular weights of less than 300 are excreted
almost exclusively via the kidneys into urine. Estradiol Vincristine
In addition to relatively high molecular weight,
drugs excreted into bile usually require a strongly
polar group. Many drugs excreted into bile are metab- Estimation of Biliary Clearance
olites, very often glucuronide conjugates. Most metab- In animals, bile duct cannulation allows both the vol-
olites are more polar than the parent drug. In addition, ume of the bile and the concentration of drug in the
the formation of a glucuronide increases the molecular bile to be measured directly using a special intubation
weight of the compound by nearly 200, as well as technique that blocks off a segment of the gut with an
increasing the polarity. inflating balloon. The rate of drug elimination may
Drugs excreted into the bile include the digitalis then be measured by monitoring the amount of drug
glycosides, bile salts, cholesterol, steroids, and indo- secreted into the GI perfusate.
methacin (Table 12-14). Compounds that enhance Assuming an average bile flow of 0.5 to 0.8 mL/
bile production stimulate the biliary excretion of min in humans, biliary clearance can be calculated if
drugs normally eliminated by this route. Furthermore, the bile concentration, Cbile, is known.
phenobarbital, which induces many mixed-function
oxidase activities, may stimulate the biliary excre- bile flow×Cbile
Cl (12.49)
biliary =
tion of drugs by two mechanisms: by an increase in Cp
the formation of the glucuronide metabolite and by
an increase in bile flow. In contrast, compounds that Alternatively, using the perfusion technique, the
decrease bile flow or pathophysiologic conditions amount of drug eliminated in bile is determined from
that cause cholestasis decrease biliary drug excre- the GI perfusate, and Clbiliary may be calculated with-
tion. The route of administration may also influence out the bile flow rate, as follows:
the amount of the drug excreted into bile. For example,
amount of drug secreted from bile per minute
drugs given orally may be extracted by the liver into Cl
biliary =
C
the bile to a greater extent than the same drugs given p
intravenously. (12.50)
348 Chapter 12
To avoid any complication of unabsorbed drug secondary peak then emerges as biliary-excreted
in the feces, the drug should be given by parenteral drug is reabsorbed. In experimental studies involv-
administration (eg, IV) during biliary determination ing animals, bile duct cannulation provides a means
experiments. The amount of drug in the GI perfusate of estimating the amount of drug excreted through
recovered periodically may be determined. The extent the bile. In humans, a less accurate estimation of
of biliary elimination of digoxin has been determined biliary excretion may be made from the recovery of
in humans using this approach. drug excreted through the feces. However, if the
drug was given orally, some of the fecal drug excre-
Enterohepatic Circulation tion could represent unabsorbed drug.
A drug or its metabolite is secreted into bile and
upon contraction of the gallbladder is excreted into CLINICAL EXAMPLE
the duodenum via the common bile duct.
Leflunomide, an immunomodulator for rheumatoid
Subsequently, the drug or its metabolite may be
arthritis, is metabolized to a major active metabolite
excreted into the feces or the drug may be reab-
and several minor metabolites. Approximately 48%
sorbed and become systemically available. The cycle
of the dose is eliminated in the feces due to high
in which the drug is absorbed, excreted into the bile,
biliary excretion. The active metabolite is slowly
and reabsorbed is known as enterohepatic circula-
eliminated from the plasma. In the case of serious
tion. Some drugs excreted as a glucuronide conju-
adverse toxicity, the manufacturer recommends giv-
gate become hydrolyzed in the gut back to the parent
ing cholestyramine or activated charcoal orally to
drug by the action of a b-glucuronidase enzyme
bind the active metabolite in the GI tract to prevent
present in the intestinal bacteria. In this case, the par-
drug reabsorption and to facilitate drug elimination.
ent drug becomes available for reabsorption.
The use of cholestyramine or activated charcoal
reduces the plasma levels of the active metabolite by
Significance of Biliary Excretion approximately 40% in 24 hours and by about 50%
When a drug appears in the feces after oral administra- in 48 hours.
tion, it is difficult to determine whether this presence
of drug is due to biliary excretion or incomplete Frequently Asked Questions
absorption. If the drug is given parenterally and then
»»Why do we use the term hepatic drug clearance to
observed in the feces, one can conclude that some of describe drug metabolism in the liver?
the drug was excreted in the bile. Because drug secre-
tion into bile is an active process, this process can be »»Please explain why many drugs with significant
saturated with high drug concentrations. Moreover, metabolism often have variable bioavailability.
other drugs may compete for the same carrier system. »»The metabolism of some drugs is affected more than
Enterohepatic circulation after a single dose of others when there is a change in protein binding. Why?
drug is not as important as after multiple doses or a
»»Give some examples that explain why the meta-
very high dose of drug. With a large dose or multiple bolic pharmacokinetics of drugs are important in
doses, a larger amount of drug is secreted in the bile, patient care.
from which drug may then be reabsorbed. This reab-
sorption process may affect the absorption and
elimination rate constants. Furthermore, the biliary ROLE OF TRANSPORTERS
secretion process may become saturated, thus alter- ON HEPATIC CLEARANCE
ing the plasma level–time curve. AND BIOAVAILABILITY
Drugs that undergo enterohepatic circulation
sometimes show a small secondary peak in the In the simple hepatic clearance model, intrinsic
plasma drug–concentration curve. The first peak clearance is assumed to be constant within the same
occurs as the drug in the GI tract is depleted; a small subject. This model describes how clearance can
Drug Elimination and Hepatic Clearance 349
change in response to physiologic changes such as High Solubility Low Solubility
blood flow or enzymatic induction. Patient variabil- Class 1 Class 2
ity and changes in intrinsic clearance may be due to Transporter Efux transporter
effects effects
(1) patient factors such as age and genetic polymor- minimal predominate
phism, (2) enzymatic induction or inhibition due to
coadministered drugs, and (3) modification of influx
Class 3 Class 4
and efflux transporters in the liver and the bile cana- Absorptive Absorptive and
liculi. When a transporter is known to play a major transporter efux transporter
role in translocating drug in and out of cells and effects effects could be
predominate important
organelles within the liver, the simple hepatic clear-
ance model may not adequately describe the phar-
High Solubility Low Solubility
macokinetics of the drug within the liver. Micro
constants may be needed to describe how the drug Class 1 Class 2
Metabolism Metabolism
moves kinetically in and out within a group of cells
or compartment. Biliary excretion should also be
incorporated into the model as needed. Since the
development of the hepatic model based on intrinsic Class 3 Class 4
clearance, much more information is now known Renal and/or Renal and/or
biliary elimination biliary elimination
about the interplay between transporters and strate- of unchanged of unchanged
gically located CYP isoenzymes in the GI, the hepa- drug drug
tocytes in various parts of the liver (see Figs. 12-11
and 12-12). More elaborate models are now avail- FIGURE 1221 Classification of Drugs Based on
able to relate transporters to drug disposition. Huang Biopharmaceutics Drug Disposition Classification System
(BDDCS). Data from Wu and Benet (2009).
et al (2009) has discussed the importance of drug
transporters, drug disposition, and how to study drug
interaction of the new drugs. The interplay between on post-absorption systemic levels following oral and
transporters, drug permeability in GI, and hepatic intravenous dosing.
drug extraction are important to the bioavailability Figure 12-21 provides a good summary of how
and the extent of drug metabolism. various physiologic and physiochemical factors influ-
It appears that drugs may be classified in several ence drug disposition. For example, Class 1 drugs are
classes to facilitate prediction of drug disposition. A not so much affected by transporters because absorp-
drug substance is considered to be “highly permeable” tion is generally good already due to high solubility
when the extent of the absorption (parent drug plus and permeability. Class 2 drugs are very much affected
metabolites) in humans is determined to be 90% of an by efflux transporters because of low solubility and
administered dose based on a mass balance determina- high permiability. The limited amount of drug solubi-
tion or in comparison to an intravenous reference dose. lized and absorbed could efflux back into the GI
Drugs may be classified into four BCS (biopharma- lumen due to efflux transporters, thus resulting in low
ceutical classification system) classes. With respect to plasma level. Further, efflux transporter may pump
oral bioavailability, Wu and Benet (2005) proposed drug into bile if located in the liver canaliculi.
categorizing drugs into the four classes based on solu-
bility and permeability as criteria may provide signifi-
cant new insights to predicting routes of elimination, Frequently Asked Questions
effects of efflux, and absorptive transporters on oral »»What are the effects of metabolism on Class 1 and 2
absorption, when transporter–enzyme interplay will drugs?
yield clinically significant effects such as low bioavail- »»What are the effects of transporters on Class 3 and 4
ability and drug–drug interactions (DDI), the direction drugs?
and importance of food effects, and transporter effects
Low High Low High
Permeability Permeability Permeability Permeability
350 Chapter 12
CHAPTER SUMMARY
The elimination of most drugs from the body involves be altered by genetic and environmental factors. Phase 2
the processes of both metabolism (biotransformation) reactions are generally conjugation reactions such as
and renal excretion. Drugs that are highly metabolized the formation of glucuronide and sulfate conjugations.
often demonstrate large intersubject variability in Cytochrome-mediated and acetylation reactions dem-
elimination half-lives and are dependent on the intrin- onstrate polymorphic variability in humans.
sic activity of the biotransformation enzymes. Renal First-pass effects or presystemic elimination
drug excretion is highly dependent on the glomerular may occur after oral drug administration in which
filtration rate (GFR) and blood flow to the kidney. some of the drugs may be metabolized or not
Hepatic clearance is influenced by hepatic blood absorbed prior to reaching the general circulation.
flow, drug–protein binding, and intrinsic clearance. The Alternate routes of drug administration are often
liver extraction ratio (ER) provides a direct measure- used to circumnavigate presystemic elimination.
ment of drug removal from the liver after oral adminis- Large-molecular-weight, polar drugs may be elimi-
tration of a drug. Drugs that are metabolized by the nated by biliary drug excretion. Enterohepatic drug
liver enzymes follow Michaelis–Menton kinetics. At elimination occurs when the drug is secreted into the
low drug concentrations the rate of metabolism is first GI tract and then reabsorbed.
order, whereas at very high drug concentrations, the The role of transporters on hepatic clearance and
rate of drug metabolism may approach zero-order phar- bioavailability in addition to hepatic drug metabolism
macokinetics. Phase 1 reactions are generally oxidation are important considerations when considering drug–
and reduction reactions and involve the mixed function drug interactions and oral drug absorption.
oxidases or cytochrome enzymes. These enzymes may
LEARNING QUESTIONS
1. A drug fitting a one-compartment model was 2. A new broad-spectrum antibiotic was adminis-
found to be eliminated from the plasma by the tered by rapid intravenous injection to a 50-kg
following pathways with the corresponding woman at a dose of 3 mg/kg. The apparent vol-
elimination rate constants. ume of distribution of this drug was equivalent
Metabolism: km = 0.200 h−1 to 5% of body weight. The elimination half-life
Kidney excretion: ke = 0.250 h−1 for this drug is 2 hours.
Biliary excretion: kb = 0.150 h−1 a. If 90% of the unchanged drug was recovered
a. What is the elimination half-life of this in the urine, what is the renal excretion rate
drug? constant?
b. What would be the half-life of this b. Which is more important for the elimination
drug if biliary secretion was completely of the drugs, renal excretion or biotransfor-
blocked? mation? Why?
c. What would be the half-life of this drug if 3. Explain briefly:
drug excretion through the kidney was com- a. Why does a drug that has a high extraction
pletely impaired? ratio (eg, propranolol) demonstrate greater
d. If drug-metabolizing enzymes were induced differences between individuals after
so that the rate of metabolism of this drug oral administration than after intravenous
doubled, what would be the new elimination administration?
half-life?
Drug Elimination and Hepatic Clearance 351
b. Why does a drug with a low hepatic extrac- 8. A new drug demonstrates high presystemic
tion ratio (eg, theophylline) demonstrate elimination when taken orally. From which of
greater differences between individuals after the following drug products would the drug be
hepatic enzyme induction than a drug with a most bioavailable? Why?
high hepatic extraction ratio? a. Aqueous solution
4. A drug is being screened for antihypertensive b. Suspension
activity. After oral administration, the onset c. Capsule (hard gelatin)
time is 0.5 to 1 hour. However, after intravenous d. Tablet
administration, the onset time is 6 to 8 hours. e. Sustained release
a. What reasons would you give for the differ- 9. For a drug that demonstrated presystemic
ences in the onset times for oral and intrave- elimination, would you expect qualitative
nous drug administration? and/or quantitative differences in the forma-
b. Devise an experiment that would prove the tion of metabolites from this drug given orally
validity of your reasoning. compared to intravenous injection? Why?
5. Calculate the hepatic clearance for a drug with an 10. The bioavailability of propranolol is 26%. Pro-
intrinsic clearance of 40 mL/min in a normal adult pranolol is 87% bound to plasma proteins and
patient whose hepatic blood flow is 1.5 L/min. has an elimination half-life of 3.9 hours. The
a. If the patient develops congestive heart apparent volume of distribution of propranolol
failure that reduces hepatic blood flow to is 4.3 L/kg. Less than 0.5% of the unchanged
1.0 L/min but does not affect the intrinsic drug is excreted in the urine.
clearance, what is the hepatic drug clearance a. Calculate the hepatic clearance for proprano-
in this patient? lol in an adult male patient (43 years old,
b. If the patient is concurrently receiving 80 kg).
medication, such as phenobarbital, which b. Assuming the hepatic blood flow is
increases the Clint to 90 mL/min but does 1500 mL/min, estimate the hepatic extrac-
not alter the hepatic blood flow (1.5 L/min), tion ratio for propranolol.
what is the hepatic clearance for the drug in c. Explain why hepatic clearance is more
this patient? important than renal clearance for the elimi-
6. Calculate the hepatic clearance for a drug with an nation of propranolol.
intrinsic clearance of 12 L/min in a normal adult d. What would be the effect of hepatic disease
patient whose hepatic blood flow is 1.5 L/min. such as cirrhosis on the (1) bioavailability
If this same patient develops congestive heart of propranolol and (2) hepatic clearance of
failure that reduces his hepatic blood flow to propranolol?
1.0 L/min but does not affect intrinsic clearance, e. Explain how a change in (1) hepatic blood
what is the hepatic drug clearance in this patient? flow, (2) intrinsic clearance, or (3) plasma
a. Calculate the extraction ratio for the liver in protein binding would affect hepatic clear-
this patient before and after congestive heart ance of propranolol.
failure develops. f. What is meant by first-pass effects? From
b. From the above information, estimate the the data above, why is propranolol a drug
fraction of bioavailable drug, assuming with first-pass effects?
the drug is given orally and absorption is 11. The following pharmacokinetic information
complete. for erythromycin was reported by Gilman et al
7. Why do elimination half-lives of drugs elimi- (1990, p. 1679):
nated primarily by hepatic biotransformation Bioavailability: 35%
demonstrate greater intersubject variability Urinary excretion: 12%
than those drugs eliminated primarily by glo- Bound in plasma: 84%
merular filtration? Volume of distribution: 0.78 L/kg
352 Chapter 12
Elimination half-life: 1.6 hours c. KM is 4 mm for this drug.
An adult male patient (41 years old, 81 kg) 15. Which of the following statements is/are true
was prescribed 250 mg of erythromycin base regarding the pharmacokinetics of diazepam
every 6 hours for 10 days. From the given data, (98% protein bound) and propranolol
calculate the following: (87% protein bound)?
a. Total body clearance a. Diazepam has a long elimination half-life
b. Renal clearance due to its lack of metabolism and its exten-
c. Hepatic clearance sive plasma protein binding.
12. Why would you expect hepatic clearance b. Propranolol is a drug with high protein bind-
of theophylline in identical twins to be less ing but unrestricted (unaffected) metabolic
variable compared to hepatic clearance in clearance.
fraternal twins? c. Diazepam exhibits low hepatic extraction.
13. Which of the following statements describe(s) 16. The hepatic intrinsic clearance of two drugs
correctly the properties of a drug that follows are as follows:
nonlinear or capacity-limited pharmacokinetics? Drug A: 1300 mL/min
a. The elimination half-life will remain con- Drug B: 26 mL/min
stant when the dose changes. Which drug is likely to show the greatest
b. The area under the plasma curve (AUC) increase in hepatic clearance when hepatic
will increase proportionately with an blood flow is increased from 1 L/min to
increase in dose. 1.5 mL/min? Which drug will likely be blood-
c. The rate of drug elimination = Cp × KM. flow limited?
d. At maximum saturation of the enzyme by 17. Pravastatin is a statin drug commonly pre-
the substrate, the reaction velocity is at Vmax. scribed. The package insert (approved labeling)
e. At very low substrate concentrations, the states that, “The risk of myopathy during
reaction rate approximates a zero-order rate. treatment with another HMG-CoA reductase
14. The Vmax for metabolizing a drug is 10 mm/h. inhibitor is increased with concurrent therapy
The rate of metabolism (v) is 5 mm/h when with either erythromycin or cyclosporine.”
drug concentration is 4 mm. Which of the fol- How does cyclosporine change the phar-
lowing statements is/are true? macokinetics of pravastatin? Is pravastatin
a. KM is 5 mm for this drug. uptake involved? Pravastatin is 18% oral
b. KM cannot be determined from the informa- bioavailability and 17% urinary excreted.
tion given.
ANSWERS
Frequently Asked Questions in determining the maintenance dose of a drug.
Hepatic drug clearance is often considered nonre-
Why do we use the term hepatic drug clearance to nal clearance when it is measured as the difference
describe drug metabolism in the liver? between total clearance and renal clearance.
• Hepatic drug clearance describes drug metabo-
Please explain why many drugs with significant metab-
lism in the liver and accounts for both the effect
olism often have variable bioavailability.
of blood flow and the intrinsic ability of the liver
to metabolize a drug. Hepatic drug clearance is • Most orally administered drugs pass through the
added to renal clearance and other clearances to liver prior to systemic absorption. The rate of
obtain total (body) clearance, which is important blood flow can greatly affect the extent of drug
Drug Elimination and Hepatic Clearance 353
that reaches the systemic circulation. Also, intrin- 2. a. k = 0.347 h–1
sic metabolism may differ among individuals and
may be genetically determined. These factors may k –1
e = (0.9)(0.347) = 0.312 h
cause drug levels to be more erratic for drugs that
b. Renal excretion, 90% of the drug is excreted
undergo extensive metabolism compared to drugs
unchanged.
that are excreted renally.
5. Normal hepatic clearance, ClH:
The metabolism of some drugs is affected more than Cl
others when there is a change in protein binding. Why? Cl =Q int
H
Q+Clint
• Protein synthesis may be altered by liver dysfunction.
In general, when drug–protein binding is reduced, Q =1.5 L/min Clint = 0.040 L/min
the free drug may be metabolized more easily. How- 0.040
ever, some drugs may be metabolized regardless of ClH =1.5 = 0.03
1.5+ 9 L/min
0.040
whether the drug is bound or free (for discussion
of nonrestrictive binding, see Chapter 11). In such a. Congestive heart failure:
cases, there is little change in pharmacodynamic
activity due to changes in drug–protein binding. 0.040
ClH =1.0 =
+ 0.0381 L/min
1.0 0.040
Give some examples that explain why the meta-
bolic pharmacokinetics of drugs are important in b. Enzyme induction:
patient care.
0.090
• ClH =1.5 = 0.085 L/min
Erythromycin, morphine, propranolol, various ste- 1.5+ 0.090
roids, and other drugs have large metabolic clear-
ance. In hepatic disease, highly potent drugs that Note: A change in blood flow, Q, did not
have a narrow therapeutic index should be moni- markedly affect ClH for a drug with low Clint.
tored carefully. Troglitazone (Rezulin), for exam- 6. Normal hepatic clearance:
ple, is a drug that can cause severe side effects in 12
patients with liver dysfunction; liver transaminase ClH =1.5 + = 1.33 L/min
1.5 12
should be monitored in diabetic patients.
Congestive heart failure (CHF):
Learning Questions
12
ClH =1.0 = 0.923 L/min
1. a. k = km + ke + kb = 0.20+ 0.25+ 0.15 1.0+12
= 0.60 h−1 Cl
a. Cl =Q (ER) =Q int
H Q+
Cl
0.693 0.693 int
t1/2 = = =1.16 h
k 0.60 Cl
ER = int
b. k = km + k = 0.45 h–1 Q+Cl
e int
t 12
1/2 =1.54 h Normal ER = 0.89 L/min
1.5+ =
12
c. k = 0.35 h–1
12
CHR ER =
t + = 0.92 L/min
1.0 12
1/2 =1.98 h
d. k = 0.80 h–1 b. F =1– ER =1– 0.89
t1/2 = 0.87 h F = 0.11or 11%
354 Chapter 12
10. a. Because <0.5% of the unchanged drug 0.693
is excreted in the urine, hepatic clearance 11. a. ClT = kVD (0.78)(81) = 27.4 L/h
1.6
nearly approximates total body
clearance. ClR = keVD
0.693
0.693 k = = = 1
Cl e 0.12k 0.12 0.052 h−
1.6
H ≈ ClT = kVD = (4.3)(80)
3.9
b. ClR = (0.052)(0.78)(81) = 3.29 L/h
= 61.1 L/h
Alternatively,
b. ClH =Q(ER) ClR = feClT
Q = (1.5 L/min)(60 min) = 90 L/h ClR = 0.12ClT = (0.12)(27.4) = 3.29 L/h
ER = 61.1/90 = 0.68 c. ClH =ClT –ClR = 27.4 – 3.29 = 24.11 L/h
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Pharmacogenetics
13 and Drug Metabolism
Thomas Abraham and Michael Adams
Chapter Objectives Variable response to a drug in the general population is thought to
follow a normal or Gaussian distribution about a mean or average
»» Define pharmacogenetics and
dose, ED50 (Fig. 13-1). Patients who fall within region A of the
pharmacogenomics.
curve may be described as hyper-responders while those in region B
»» Define genetic polymorphism may be characterized as poor or hypo-responders. While pharma-
and explain the difference cokinetic and pharmacodynamic differences are thought to be
between genotype and primarily responsible for this Gaussian variation in drug response,
phenotype. the extremes in drug response may be due to unique interindi-
»» Explain with relevant examples vidual genetic variability. Modern genetic methods have identi-
how genetic variability fied alterations in drug-metabolizing enzymes, drug transporters,
influences drug response, and drug receptors that, at least in part, explain many of these
pharmacokinetics, and dosing extremes in drug response. This has given birth to the field of
regimen design. pharmacogenetics, which seeks to characterize inter-individual drug-
response variability at the genetic level (Mancinelli et al, 2000).
»» Describe the relevance of CYP A related term, pharmacogenomics, is often used interchange-
enzymes and their genetic ably but includes the study of the genetic basis of disease and
variability to pharmacokinetics the pharmacological impact of drugs on the disease process
and dosing. (Mancinelli et al, 2000).
»» List the major drug transporters Advances in pharmacogenetics have been enabled by high-
and describe how their throughput technology that allows for the screening of tens of
genetic variability can impact thousands of genes rapidly and simultaneously. For example, the
pharmacokinetics. DNA chip is a microchip that uses hybridization technology to
concurrently detect the presence of tens of thousands of sequences
»» Discuss the main issues in
in a small sample. The probes (of known sequence) are spotted
applying genomic data to
onto discreet locations on the chip, so that complementary DNA
patient care, for example,
hybridization from the patient’s sample to a probe residing in a
clinical interpretation of data
defined location indicates the presence of a specific sequence
from various laboratories and
(Mancinelli et al, 2000; Dodgan et al, 2013). Other rapid and low-
accuracy of record keeping of
cost sequencing technologies such as ULCS (ultra-low-cost
large amounts of genomic data.
sequencing) or cyclic array technologies will also permit rapid and
high-volume sequencing and/or sequencing of individual genomes.
These technologies usually rely on some combination of miniatur-
ization, multiplex or parallel assays, analyte amplification and/or
concentration, and detection signal amplification.
Application of pharmacogenetics to pharmacokinetics and
pharmacodynamics helps in development of models that may pre-
dict an individual’s risk to an adverse drug event and therapeutic
357
358 Chapter 13
18
ED50
10
5
A
B
0
1 2 3 4 5
Dose (mg/kg)
FIGURE 131 Simulated Gaussian distribution of population response to a hypothetical drug. The ED50 indicates the mean
dose producing a therapeutic outcome while regions A and B highlight patients who are hyper- or hyporesponders to the drug
effect, respectively.
response (Fernandez-Rozadilla et al, 2013; Meyer form of genetic variability is the single nucleotide
et al, 2013). The promise of such modeling efforts polymorphism (SNP, often called “snip”), resulting
is that more individualized dosing regimens may from a change in a single nucleotide base pair within
be developed resulting in more “personalized the gene sequence (Ahles and Engelhardt, 2014).
medicine” with fewer adverse events and better Synonymous SNPs in the coding region of a gene
therapeutic outcomes (Phillips et al, 2001). This generally result in no change in the amino acid
chapter will focus on variations in pharmacoki- sequence of the eventual protein product. Non-
netic components due to pharmacogenetic factors. synonymous SNPs in the coding region will result in
Variations in drug response due to genetic varia- a change in the amino acid sequence of the protein.
tions in the drug’s receptor or downstream pro- In some cases, this alteration may have little effect
cesses can also be identified using pharmacogenetic on the protein’s structure and function, for example,
principles and screening; however, that is beyond if one acidic amino acid is replaced by another.
the scope of this chapter. However, non-synonymous SNPs have the potential
to drastically alter the function of protein (Ahles and
GENETIC POLYMORPHISMS Engelhardt, 2014). An example of such an effect
occurs if nucleotide position 2935 of the CYP2D6
Historically, population variability in drug metabo- gene has a C instead of an A (c.2935A>C). During
lism or therapeutic response was described in terms translation this results in the insertion of a proline
of the observed phenotype, for example, slow metab- instead of histidine at amino acid position 324 gen-
olizers or sensitive responders. With our understand- erating the CYP2D6*7 allele, with no drug metabo-
ing of genetics, we are often able to ascribe specific lizing activity (The Human Cytochrome P450 Allele
alterations in gene sequence, or genotype, to explain Nomenclature Database, 2014). Genetic variants
such observed effects. Genetic polymorphisms are that result from the insertion or deletion of a nucleo-
variations in gene sequences that occur in at least 1% tide in the coding region are also classified as
of the general population, resulting in multiple SNPs. Since the mRNAs from genes are translated
alleles or variants of a gene sequence. Polymorphisms to protein in 3-nucleotide codons, such insertions
are distinct from mutations that occur in less than or deletions can have a significant effect on the
1% of the population. The most commonly occurring eventual protein product. An example of such a
Percent responding
Pharmacogenetics and Drug Metabolism 359
polymorphism is the CYP2D6*3 allele where a sin- relative contributions to drug metabolism are high-
gle nucleotide deletion (A2637) results in a frame shift lighted in Fig. 13-2. Phase I enzymes perform oxi-
in translation that produces an enzyme with no cata- dation, reduction, and hydrolysis reactions while
lytic activity (The Human Cytochrome P450 Allele phase II enzymes perform conjugation reactions.
Nomenclature Database, 2014). Each variant of a gene Polymorphisms have been reported in both phases of
is represented by the star designation (*) followed by a drug-metabolizing enzymes and can affect the phar-
number, and each gene could potentially contain mul- macokinetic profile of a drug for a given patient.
tiple variants. A grouping of select variants is called a Understanding a patient’s genetic determinants of
haplotype and results in unique combinations of poly- drug metabolism and the consequences of these
morphisms with potentially novel phenotypes. polymorphisms could be used to design optimum,
Single nucleotide polymorphisms outside the personalized dosing regimens in the clinic that
coding region of the gene can result in altered levels would avoid adverse reactions or treatment failures
of protein activity as well. Polymorphisms in the due to subtherapeutic doses. While this may appear
promoter sequence of a gene can influence gene perfectly logical, the redundancy of drug metabo-
transcription rates resulting in greater or lesser lism and potential contribution from numerous
amounts of mRNA, and consequently protein expres- other factors (such as diet, other drugs, age, weight,
sion. Alternatively, SNPs in a splicing control region etc) make it difficult to translate enzyme status data
of the gene can result in the production of a unique to a clinical decision. For example, warfarin ther-
protein often missing one or more exons and result- apy is complicated by a combination of metabolic
ing in a unique (often truncated or inactive) protein. (CYP2C9 polymorphisms contribute 2%–10%),
In some cases, multiple copies of a gene on a chro- pharmacodynamic (VKORC1 polymorphisms con-
mosome can result in increased levels of protein tribute 10%–25%), and environmental factors
being expressed, and once again the CYP2D6 gene (20%–25% contribution). Several algorithms that
serves as a relevant example. The CYP2D6xN vari- take into account genetic information have been
ant (where N = 2–12 copies) results in very high developed for warfarin dosing and some are avail-
expression of the functional enzyme in patients who able online (Warfarin Dosing, 2009; Pharmacogenetics
are considered ultrarapid metabolizers of certain Knowledge Base, 2014). While these appear to be
drugs (The Human Cytochrome P450 Allele useful tools to account for genetic differences, the
Nomenclature Database, 2014; see below). reported effectiveness of achieving an optimal anti-
Polymorphic induction of gene expression is distinct coagulant dose of warfarin using algorithms is vari-
from that induced by drugs such as phenytoin, barbi- able (Caraco et al, 2008; Wang et al, 2012; Kimmel
turates, etc. However, it isn’t difficult to see that a et al, 2013). These confounding results demonstrate
mixed form of CYP gene expression due to genetics the need for more investigation into the factors
and drug induction could increase metabolic activity (including pharmacokinetic and pharmacodynamic
to an even greater extent. Deletion or inversion of factors) that contribute to variable responses, as well
entire genes on the chromosome would obviously as robust clinical investigations to validate these
have the opposite effect on enzyme activity and drug observations. There are 70 drugs that include phar-
metabolism. macogenetic information related to polymorphisms
in drug-metabolizing enzymes that contribute to
variable drug response (Pharmacogenetics Knowledge
Genetic Polymorphism in Drug Metabolism Base, 2014). Drugs that are thought to be affected by
As discussed in Chapter 12, drug metabolism is the polymorphisms, the consequence, and label
responsible for the chemical modification of drugs information are included in Table 13-1 (Evans, 1999;
or other xenobiotics that usually results in increased Pharmacogenetics Knowledge Base, 2014). Further
polarity to enhance elimination from the body. The examples of polymorphism affecting drugs among
enzymes that perform drug metabolism are classi- different race and special subject groups are shown
fied as either phase I or phase II enzymes and their in Table 13-2.
360 Chapter 13
TABLE 131 Clinically Important Genetic Polymorphisms of Drug Metabolism and Transporters
That Influence Drug Response
FDA Label Information^
(Pharmacogenetics
Enzyme Drug Drug Effect/Side Effect Knowledge Base, 2014)
CYP2C9 Warfarin Hemorrhage Actionable
Tolbutamide Hypoglycemia –
Phenytoin Phenytoin toxicity –
Glipizide Hypoglycemia –
Losartan Decreased antihypertensive effect –
CYP2D6 Antiarrhythmics Proarrhythmic and other toxic effects –
in poor metabolizers
Antidepressants Inefficacy in ultrarapid metabolizers Actionable/Information∗
Antipsychotics Tardive dyskinesia Actionable/Information∗
Eliglustat Inefficacy in ultrarapid metabolizers Testing recommended
Opioids Inefficacy of codeine as analgesic, Actionable
narcotic side effects, dependence
Pimozide Toxicity with high dose in poor Testing recommended
metabolizers
Tetrabenazine Toxicity with high dose in poor Testing recommended
metabolizers or inefficacy in ultrar-
apid metabolizers
Warfarin Higher risk of hemorrhage –
β-Adrenoceptor Increased blockade Actionable/Information∗
antagonists
CYP2C19 Omeprazole Higher cure rates when given with Information
clarithromycin
Diazepam Prolonged sedation Actionable
Clopidogrel Inefficacy in poor metabolizers Testing recommended
Dihydropyrimidine Fluorouracil Myelotoxicity, neurotoxicity Actionable
dehydrogenase
Plasma pseudo-cholinesterase Succinylcholine Prolonged apnea –
N-acetyltransferase Sulfonamides Hypersensitivity –
Amonafide Myelotoxicity –
Procainamide Drug-induced lupus erythematosus –
Hydralazine Drug-induced lupus erythematosus Information
Isoniazid Drug-induced lupus erythematosus Information
(Continued)
Pharmacogenetics and Drug Metabolism 361
TABLE 131 Clinically Important Genetic Polymorphisms of Drug Metabolism and Transporters
That Influence Drug Response (Continued)
FDA Label Information^
(Pharmacogenetics
Enzyme Drug Drug Effect/Side Effect Knowledge Base, 2014)
Thiopurine methyltransferase Mercaptopurine Myelotoxicity Testing recommended
Thioguanine Myelotoxicity Actionable
Azathioprine Myelotoxicity Testing recommended
UDP-Glucuronosyltransferase Irinotecan Diarrhea, Myelotoxicity Actionable
Multidrug-resistance gene Digoxin Increased concentrations of digoxin –
(MDR1) in plasma
Organic anion transporter Simvastatin Myopathy –
protein (SLCO1B1)
^Information: Drug label contains information on gene or protein responsible for drug metabolism but does not include evidence of variations in drug
response.
Actionable: Drug label contains information about changes in efficacy, dosage, or toxicity of a drug due to gene variants but does not discuss genetic
or other testing.
Testing recommended: Drug label recommends testing or states testing should be performed for specific gene or protein variants prior to use,
sometimes in a specific population.
∗Depends upon the specific drug agent.
From Evans and Relling (1999)
CYTOCHROME P-450 ISOZYMES antidepressants, antiarrhythmics, beta-adrenergic
antagonists, and opioids, which frequently have nar-
Cytochrome P-450 (CYP450) isozymes are the pri- row therapeutic indices. While we now have more
mary phase I oxidative enzymes that are found in detailed information on the genotypes, the pheno-
many species with functionality in the metabolism of typic differences in CYP2D6 were originally
xenobiotics and endogenous biochemical process. observed with debrisoquine, resulting in the more
The CYP450s are divided into families identified general descriptions of poor metabolizer (PM),
with numbers (CYP1, CYP2, CYP3, etc) and sub- extensive metabolizer (EM), and ultrarapid metabo-
families identified with letters (CYP2A, CYP2B, etc) lizer (UM) (Mahgoub et al, 1977; Idle et al, 1978).
based on amino acid similarities. The major drug- It is estimated that approximately 10% of the
metabolizing CYP450 families are CYP1, CYP2, and Caucasian population, 1% of the Asian population,
CYP3 (see Fig. 13-2) and those will be the focus of and between 0% and 19% of the African population
this section. have a PM phenotype of CYP2D6 (McGraw and
Waller, 2012), resulting in increased plasma concen-
CYP2D6 tration of the parent drug due to decreased metabolic
CYP2D6 is the most highly polymorphic CYP with clearance. In the case of debrisoquine, the increased
more than 70 allelic variants reported (The Human plasma concentration results in an exaggerated hypo-
Cytochrome P450 Allele Nomenclature Database, tensive response. When a patient with a PM pheno-
2014). Many of these allelic variants are clinically type is administered a tricyclic antidepressant, the
important because although CYP2D6 only makes up increased plasma concentration increases the poten-
about 5% of hepatic CYP activity, it is responsible tial for CNS depression. If metabolism is required
for the metabolism of as much as 25% of commonly for a drug to have activity, the patient with a PM
prescribed drugs (Fig. 13-2). These drugs include phenotype is more likely to have a treatment failure
362 Chapter 13
TABLE 132 Examples of Polymorphisms Affecting Drug Receptors and Enzymes Showing
Frequency of Occurrence
Frequency of
Enzyme/Receptor Polymorphism Drug Drug Effect/Side Effect
CYP2C9 14%–28% Warfarin Hemorrhage
(heterozygotes)
Tolbutamide Hypoglycemia
0.2%–1% Phenytoin Phenytoin toxicity
(homozygotes)
Glipizide Hypoglycemia
Losartan Decreased antihypertensive effect
CYP2D6 5%–10% Antiarrhythmics Proarrhythmic and other toxic
(poor metabolizers) effects
Toxicity in poor metabolizers
1%–10% (ultrarapid Antidepressants Inefficacy in ultrarapid
metabolizers) metabolizers
Antipsychotics Tardive dyskinesia
Opioids Inefficacy of codeine as analgesic,
narcotic side effects, dependence
Warfarin Higher risk of hemorrhage
β-Adrenoceptor antagonists Increased—blockade
CYP2C19 3%–6% (whites) Omeprazole Higher cure rates when given with
clarithromycin
8%–23% (Asians) Diazepam Prolonged sedation
Dihydropyrimidine 0.1% Fluorouracil Myelotoxicity, Neurotoxicity
dehydrogenase
Plasma pseudo-cholinesterase 1.5% Succinylcholine Prolonged apnea
N-acetyltransferase 40%–70% (whites) Sulphonamides Hypersensitivity
10%–20% (Asians) Amonafide Myelotoxicity (rapid acetylators)
Procainamide, hydralazine, Drug-induced lupus
isoniazid erythematosus
Thiopurine methyltransferase 0.3% Mercaptopurine, Myelotoxicity
thioguanine, azothioprine
UDP-glucuronosyltransferase 10%–15% Irinotecan Diarrhea, myelosuppression
ACE Enalapril, lisinapril captopril Renoprotective effect, cardiac
indexes, blood pressure
Potassium channels Quinidine Drug-induced QT syndrome
HERG Cisapride Drug-induced torsade de pointes
KvLQT1 Terfenadine disopyramide Drug-induced long-QT syndrome
VKORC Warfarin Over-anticoagulation
Epidermal growth factor Gefitinib Certain polymorphs susceptible
receptor (EGFR)
HKCNE2 Meflaquine clarithromycin Drug-induced arrhythmia
From Meyer (2000) with permission, and from Evans and Relling (1999) as well as Limdi and Veenstra (2010).
Pharmacogenetics and Drug Metabolism 363
Phase I Phase II
CYP1A1/2
CYP1B1
Epoxide CYP2A6
hydrolase
Others NAT1 NAT2
DPD Esterases CYP2B6
CYP2C8
NQO1 GST-M
GST-T
Others GST-P
CYP2C9
ALDH ADH
CYP2C19 GST-A
CYP2D6 STs
CYP3A4/5/7 UGTs
CYP2E1 HMT
COMT
TPMT
FIGURE 132 Drug-metabolizing enzymes that exhibit clinically relevant genetic polymorphisms. Essentially all of the major
human enzymes responsible for modification of functional groups (classified as phase I reactions [left]) or conjugation with endog-
enous substituents (classified as phase II reactions [right]) exhibit common polymorphisms at the genomic level; those enzyme
polymorphisms that have already been associated with changes in drug effects are separated from the corresponding pie charts.
The percentage of phase I and phase II metabolism of drugs that each enzyme contributes is estimated by the relative size of each
section of the corresponding chart. ADH, alcohol dehydrogenase; ALDH, aldehyde dehydrogenase; CYP, cytochrome P-450; DPD,
dihydropyrimidine dehydrogenase; NQO1, NADPH, quinone oxidoreductase or DT diaphorase; COMT, catechol O-methyltransferase;
GST, glutathione S-transferase; HMT, histamine methyltransferase; NAT, N-acetyltransferase; STs, sulfotransferases; TPMT, thiopurine
methyltransferase; UGTs, uridine 5′-triphosphate glucuronosyltransferases. (From Evans and Relling, 1999, with permission.)
than an adverse event. This has been reported with doses to achieve therapeutic activity when the patient
the breast cancer agent tamoxifen (Rolla et al, 2012). is a UM. On the other hand, drugs that require metab-
Tamoxifen has an active metabolite (endoxifen) pro- olism to an active metabolite are extremely active,
duced by CYP2D6 that is thought to be responsible with potentially serious consequences. Codeine is
for much of its antiestrogenic activities. The patient converted to morphine by a CYP2D6 O-demethylation
with the PM phenotype would not metabolize reaction to provide analgesic effects, and morphine-
tamoxifen to the active metabolite and, therefore, associated toxicity has been reported after codeine
does not benefit from clinically relevant endoxifen administration in patients who are UM (Gasche et al,
concentrations (Rolla et al, 2012). Genotypically, 2004). The FDA label for codeine-containing prod-
PM have two null alleles, which do not code for ucts includes a black box warning to highlight the
functional CYP2D6 due to a frame shift (CYP2D6*3 risk of death in children with CYP2D6 UM pheno-
and *6), a splicing defect (CYP2D6*4), or a gene types. The UM phenotype is the result of multiple
deletion (CYP2D6*5). copies (up to 12 copies) of either the wild-type
The UM have very high rates of CYP2D6 enzy- CYP2D6*1 or the *2 gene on a single chromosome
matic activity resulting in low plasma concentrations resulting in greatly enhanced functional CYP2D6
of drugs with consequent lower efficacy. Active activity (The Human Cytochrome P450 Allele
drugs like the tricyclic antidepressant amitriptyline Nomenclature Database, 2013). The UM phenotype
may require doses several-fold higher than standard is found in Caucasian populations (1%–10%), but is
364 Chapter 13
more common in others such as Saudi Arabians metabolism of the narrow therapeutic index blood
(20%) and Ethiopians (29%) (Samer et al, 2013). thinner warfarin. When a patient has one of these two
CYP2D6 EM phenotype includes 60%–85% of polymorphisms, the dose of warfarin needed for
the Caucasian population and has normal enzymatic clinically relevant anticoagulation is generally much
activity (CYP2D6*1). In addition to PM, EM, and less since drug clearance is reduced. If the dose of
UM, an intermediate metabolizer (IM) phenotype has warfarin is not appropriately lowered, then there is an
also been identified. The IM phenotype is a result of increased risk of bleeding. There are several other
either one null allele or two deficient alleles and is drugs affected by the polymorphisms of CYP2C9,
prevalent in up to 50% of Asians, 30% of Africans, including many nonsteroidal anti-inflammatory
and around 10%–15% of Caucasians (Samer et al, drugs, sulfonylureas, angiotensin II receptor antago-
2013). The deficient alleles include CYP2D6*2, *10, nists, and phenytoin. For each of these, the CYP2C9*2
and *17, each of which has enzymatic activity that is and *3 polymorphisms result in higher plasma concen-
less than the wild-type enzyme (CYP2D6*1). trations but, because of their high therapeutic indices
Understanding this complex interplay between (except phenytoin), do not usually result in adverse
all the different alleles of CYP2D6 and the many effects. In the case of phenytoin, the polymorphisms
drugs that it metabolizes provides a great opportu- result in drug accumulation and require dose reduction
nity for accurate genotyping to provide for sound to prevent toxicity (ie, dizziness, nystagmus, ataxia).
clinical decisions to prevent adverse events and pre-
vent therapeutic failures.
CYP2C19
CYP1A2 CYP2C19 is a highly polymorphic drug-metabolizing
enzyme with at least 30 variants reported (The Human
CYP1A2 activity varies widely with genetic poly-
Cytochrome P450 Allele Nomenclature Database,
morphisms contributing to observed differences in
2013). Polymorphisms in CYP2C19 result in vari-
levels of gene expression. CYP1A2 is responsible
able drug response to clopidogrel and several antide-
for the metabolism of about 5% of marketed drugs
pressants. The PM phenotype is often the result of two
including fluvoxamine, clozapine, olanzapine, and
null alleles, CYP2C19*2, and *3. Both alleles pro-
theophylline. Approximately 15% of the Japanese,
duce truncated, nonfunctional CYP2C19 through
5% of the Chinese, and 5% of the Australian popula-
the introduction of a stop codon. The stop codon in
tions are classified as CYP1A2 poor metabolizers.
the CYP2C19*2 allele is the result of a splicing
The most frequent allelic variant is CYP1A2*1F,
defect that introduces a frame shift while in the
which results in an increased expression caused by
CYP2C19*3 allele, an SNP introduces the early stop
an SNP in the upstream promoter region. Enhanced
codon (de Morais et al, 1994). The allelic frequency of
enzyme levels are thought to cause faster substrate
CYP2C19*2 has been shown to be 15% in Africans,
clearance, which has been associated with treatment
29%–35% in Asians, 12%–15% in Caucasians, and
failures for clozapine in smokers with the *1F allele
61% in Oceanians. CYP2C19*3 is mainly found in
(Eap et al, 2004). CYP1A2*1C is also an SNP in the
Asians (5%–9%) with very low frequency in
upstream promoter region that results in decreased
Caucasians (0.5%) (Samer et al, 2013).
enzyme expression and has a prevalence up to 25%
The CYP2C19 PM phenotype results in a lack
in Asian populations (McGraw and Waller, 2012).
of efficacy for the antiplatelet prodrug clopidogrel.
For activation, clopidogrel requires a two-step
CYP2C9 metabolism by several different CYP450 with
CYP2C9 has at least 30 different allelic variants with CYP2C19 being a significant contributor. Studies
the two most common being CYP2C9*2 and *3. have demonstrated, and the FDA has added to the
Both of these variants result in reduced CYP2C9 label, that deficiencies in CYP2C19 activity may
activity and are carried by about 35% of the Caucasian result in the increased risk of adverse cardiovascular
population. CYP2C9 is a major contributor to the outcomes because the PM does not activate clopidogrel
Pharmacogenetics and Drug Metabolism 365
sufficiently (Scott et al, 2011). With omeprazole the but not for testosterone 6β-hydroxylation (Sata et al,
opposite occurs since metabolism inactivates the 2000). The effects of the polymorphisms in CYP3A4
drug. The PM phenotype results in higher plasma are still under investigation but currently there are no
concentrations, larger AUC values, and greater effi- null phenotypes.
cacy in lowering gastric pH than extensive metaboliz-
ers with CYP2C19*1 alleles (Ogawaa and Echizen,
Other Phase I Enzymes
2010). The higher plasma concentration of omepra-
zole is particularly useful in the multiple-drug treat- While the CYP450s are the most abundant and exten-
ment of Helicobacter pylori. In the PM patients sively studied phase I drug-metabolizing enzymes,
treated with omeprazole, the H. pylori eradication others have polymorphisms that have an effect on the
rate is higher when they have one or more of the null clearance (or activation) of drugs and, therefore, affect
alleles (Shi and Klotz, 2008). the clinical outcomes of patients secondary to, at least
The CYP2C19*17 allele results in a gain of partially, changes in pharmacokinetics.
function and, therefore, has more metabolic capacity
Plasma pseudocholinesterase or serum
than the wild-type enzyme, CYP2C19*1, because of
an SNP in the upstream noncoding region that butyrylcholinesterase
induces transcription (Sim et al, 2006). Patients that Plasma pseudocholinesterase is responsible for the
have this UM phenotype are either heterozygous or inactivation through ester hydrolysis of the neuro-
homozygous for CYP2C19*17. Carriers of this muscular blockers succinylcholine and mivacurium.
allele are associated with higher risk for bleeding While mivacurium is no longer marketed in the US
due to the increased metabolism of clopidogrel to the market, succinylcholine is used to provide skeletal
active metabolite (Sibbing et al, 2010). These exam- muscle relaxation or paralysis for surgery or mechan-
ples demonstrate that both loss and gain of function ical ventilation. There are at least 65 allelic variants
alleles can have significant effects on patient out- of pseudocholinesterase that have been identified in
comes depending upon the blood levels and activity approximately 1.5% of the population that result in
of the parent drug and the metabolite. various levels of pseudocholinesterase deficiencies
(Soliday et al, 2010). These allelic variants include
non-synonymous point mutations or frame shift
CYP3A4 mutations that result in a PM phenotype for succi-
CYP3A4 is the most abundant CYP450 in the liver nylcholine. Patients with slowed metabolism of suc-
and metabolizes over 50% of the clinically used cinylcholine have elevated blood levels, prolonged
drugs (Fig. 13-2). In addition, the liver expression of duration of action, and prolonged apnea compared to
CYP3A4 is variable between individuals. To date, patients with fully functional pseudocholinesterase.
over 20 allelic variants of CYP3A4 have been iden-
tified (The Human Cytochrome P450 Allele Dihydropyrimidine dehydrogenase (DPD)
Nomenclature Database, 2013). Despite the large DPD is the first reduction and rate-limited step in
number of variants, there is limited data demonstrat- breakdown of the pyrimidine nucleic acids and their
ing any clinical significance for CYP3A4 substrates. analogs. Polymorphisms in DPD result in a loss of
Some of the variability may be caused by allelic vari- enzymatic activity leading to the accumulation of the
ants that influence the upstream noncoding region of chemotherapeutic agent 5-flourouracil (5-FU), which
the gene, specifically in CYP3A4*1B allele, which leads to significant toxicity including leukopenia,
may influence gene expression, although the exact thrombocytopenia, and stomatitis. It is estimated that
transcription factor binding site has not been identi- approximately 3%–5% of population has low or defi-
fied (Sata et al, 2000). The CYP3A4*2 allele has a cient DPD activity (Lu et al, 1993; Etienne et al,
non-synonymous SNP that is found in about 2.7% of 1994). There are three alleles, each with low fre-
the Caucasian population and has some decreased quency, that appear to account for the majority of the
clearance for the calcium channel blocker nifedipine deficient DPD activity observed and more than 20%
366 Chapter 13
of the serious toxicity observed with 5-FU adminis- accumulation of MP leading to an increased risk for
tration. DPYD*2A is the most common allelic vari- adverse effects like leukopenia (Ameyaw et al, 1999;
ant, although the exact frequency is not clear. This Schaeffeler et al, 2008). Although not well under-
variant results in a nonfunctional enzyme due to a stood, variations in the promoter region for TPMT
point mutation that creates an exon skipping splice can also account for some of the observed differ-
variant. DPYD*13 and c.2846A>T variants are non- ences in expression and susceptibility for adverse
synonymous SNPs that decrease the activity of the effects. The remaining variability may be accounted
DPD produced. There are many other allelic variants for with numerous other factors including some
that have been identified to date but have only been genetic and some environmental.
found in very small numbers or have unknown clini-
cal consequences.
Uridine Diphosphate (UDP)-
glucuronosyltransferase
PHASE II ENZYMES UDP-glucuronosyltransferase (UGT) is a super-
family of phase II drug-metabolizing enzymes that
As discussed in the previous chapter (drug metabo-
produce glucuronidation metabolites through conju-
lism), phase II drug-metabolizing enzymes are com-
gation reactions (see Chapter 12). Like the CYP450s,
monly referred to as transferases and perform
the UGTs are divided into families identified with
conjugation reactions that add a biochemical com-
numbers (UGT1, UGT2, etc) and subfamilies identi-
pound to a xenobiotic to facilitate its elimination.
fied with letters (UGT1A, UGT2B, etc) based on
Just like the phase I reactions, there are genetic
amino acid similarities. Drug metabolism is cata-
variations in the several phase II enzymes that influ-
lyzed almost exclusively by UGT1 and UGT2
ence the pharmacokinetics of drugs.
(Meech et al, 2012). At least 200 alleles for UGT1
and UGT2 gene families have been reported causing
Thiopurine S-methyltransferase changes in enzymatic activity or expression levels
Thiopurine drugs including 6-mercaptopurine (MP) that may contribute to individual variations in drug
and azathioprine are used for their anticancer and response (UGT Alleles Nomenclature Home Page,
immunosuppressive properties but can have signifi- June 2005). One of the most frequently studied
cant adverse effects including myelosuppression. genetic variations in Caucasians is the UGT1A1*28
The phase II metabolizing enzyme thiopurine allele (32%) (Stingl et al, 2014) due to changes in the
S-methyltransferase (TPMT) is involved in the deg- promoter region that decrease the expression of
radation of thiopurine drugs and TPMT polymor- UGT1A1 (Beutler et al, 1998). The UGT1A1*6
phisms account for about one-third of the variable allele is found most frequently in the Asian popula-
responses to MP and azathioprine (Colombel et al, tion (18%) and contains a non-synonymous SNP in
2000; Ansari et al, 2002). While TPMT alone only the coding region that results in decreased UGT1A1
explains one-third of the variability, other factors are activity (Stingl et al, 2014).
known to contribute, which highlights the challenge The potential effect of variable activity of UGT
and multifactorial nature of personalized medicine to is dependent on the relationship between parent drug
account for intraindividual differences. At least and metabolite. While most UGT metabolites are
twenty-eight allelic variants in the coding and splic- inactive, there are examples of activation including
ing region of TPMT have been identified with most morphine metabolism to the active 6-glucuronide
of the null phenotypes being associated with metabolite and various carboxylic acids metabolism
TPMT*2, TPMT*3A, and TPMT*3B alleles result- to reactive, potentially toxic, acylglucuronides
ing in non-synonymous mutations that lead to the (Stingl et al, 2014). The potential effects of these
production of an unstable enzyme and reduced activ- changes have been reported for over 22 different
ity overall. The loss of TPMT function is present in drugs with various changes to pharmacokinetic pro-
about 5% of the Caucasian population and results in files including AUC and clearance (Stingl et al, 2014).
Pharmacogenetics and Drug Metabolism 367
A summary of the pharmacogenetics for all 22 drugs slow metabolizers are associated with an increased
is beyond the scope of this chapter, but one example risk of lupus erythematosus (Chen et al, 2007). With
of a drug that includes FDA labeling related to UGT fast metabolizers, there can also be an increased
polymorphisms, irinotecan, will be briefly discussed. toxicity of the topoisomerase II inhibitor, amonafide,
Irinotecan is a prodrug topisomerase-1 inhibitor which is associated with a higher incidence of
that is approved to treat metastatic colon or rectal myelosuppression (Innocenti et al, 2001).
cancer. The active metabolite of irinotecan, SN-38,
is produced by ester hydrolysis and is primarily
cleared through biliary excretion after inactivation TRANSPORTERS
by UGT (Rothenberg, 1998). The accumulation of
Several membrane transporter proteins are involved
SN-38 is associated with dose- and treatment-limit-
in drug absorption from the intestinal tract and distri-
ing adverse effects including bone marrow toxicity
bution through the body. An increased appreciation
and diarrhea. The FDA-approved label for irinotecan
of the influence of these transporters on the uptake
recommends a dosage reduction in patients that are
and efflux of drugs into or out of tissues has enhanced
homozygous for UGT1A1*28 due to an increased
interest in the pharmacogenetics of these transporters.
risk of neutropenia (Food and Drug Administration,
It is likely that significant issues in oral drug bioavail-
2014). In Asian populations, the UGT1A1*6 allele is
ability and variable pharmacokinetics result from
associated with increased irinotecan toxicity and
genetic polymorphisms in transporters. Unlike many
decreased clearance compared to the UGT1A1*1
of the drug-metabolizing enzymes discussed above,
(wild-type) allele (Han et al, 2009). Other UGT
our current understanding of transporter pharmaco-
alleles including UGT1A7*3 and UGT1A9*22 may
genetics is not as well developed and the conse-
contribute to irinotecan toxicity by metabolizing
quences of the SNPs are not so clear.
SN-38 but the consequences of these variations are
not so clear.
MDR1 (P-Glycoprotein)
The MDR1 or ABCB1 gene codes for the efflux
N-Acetyltransferase protein P-glycoprotein (P-gp) that is frequently asso-
N-acetyltransferase (NAT) was identified as a poly- ciated with drug resistance to antineoplastic agents
morphic enzyme through phenotypic observations of including vincristine and doxorubicin. In cancers
fast or slow acetylators of the anti-tuberculosis drug, that express PGP, the drug is transported out of the
isoniazid (Evans and White, 1964). There are two cells, keeping the drug concentrations inside the
different human genes, NAT1 and NAT2, that code target cell low. In addition to this resistance function,
for functional NAT activity. While both NAT1 and expression of PGP also contributes to the efflux of
NAT2 are polymorphic, the fast and slow acetylator some drugs from various tissues that affect the pharma-
phenotype is associated with the NAT2 gene. The cokinetics of these compounds. There are many PGP
slow acetylator phenotype is found in about 50% of substrates and inhibitors as outlined in Chapter 11.
Caucasians, 90% of Arabs, and 10% of Japanese At least 66 SNPs in the ABCB1 gene have been
populations (Green et al, 2000). Several NAT2 reported, and the three most studied SNPs include
alleles, *5, *6, *7, *10, *14, and *17, are either null two synonymous and one non-synonymous variants
genes or encode of defective enzymes that contribute (Brambila-Tapia, 2013). The synonymous SNPs are
to the slow phenotype (Pharmacogenetics Knowledge reported to result in decreased expression of PGP
Base, 2014). Patients that are slow metabolizers of due to decreased mRNA expression, unstable
isoniazid exhibit increased blood levels of the drug, mRNA, or alterations in protein folding (Sissung et
which results in an increased incidence of neurotox- al, 2012). The effects of these SNPs on drug serum
icity (Pharmacogenetics Knowledge Base, 2014). The levels have been examined in multiple studies with
metabolism of both procainamide and hydralazine is substrates including digoxin and docetaxel. The
also dependent upon the activity of NAT2 such that reported results on the pharmacokinetic profile of
368 Chapter 13
these two drugs have been inconsistent with studies information on the variable responses or adverse
showing increased blood levels or no change com- effects of drugs.
pared to the wild-type gene (Sissung et al, 2012).
These results highlight the dependency on the indi-
vidual substrate, the complexity, and the effect of Solute Carrier Transporters
specific tissue transporter expression, which contrib-
Another important class of drug transporters is the
utes to the pharmacokinetic profile of each drug.
solute carriers (SLCs) such as the organic anion
Additionally, there are also known inhibitors to PGP
transporter protein (OATP) and organic cation trans-
that complicate the prediction of the pharmacoki-
porter (OCT). These transporters are located
netic profile in patients that are administered multi-
throughout the body and have various roles in the
ple drugs.
transport of many different drugs. OATP1B1 (coded
by the SLCO1B1 gene) is a hepatic influx trans-
ABC Transporters porter with at least 40 non-synonymous SNPs identi-
The multidrug resistance-associated proteins (MRPs) fied that result in either an altered expression or
are members of the ATP-binding cassette (ABC) activity of OATP1B1 (Sissung et al, 2012). While
superfamily with six members currently, of which the clinical consequences of all of these SNPs are
MRP1 (ABCC1), MRP2 (ABCC2), and MRP3 unknown, one SNP (c.521T>C) has been associated
(ABCC3) are commonly known to effect drug dispo- with an increased risk of simvastatin-induced myop-
sition. Like MDR, these transporters can also be athy (Ramesy et al, 2014). This non-synonymous
expressed in cancer cells, which confer resistance to SNP is associated with a lower plasma clearance of
the chemotherapeutic agent tamoxifen. It appears simvastatin and is found in the SLCLO1B1*5, *15,
that polymorphisms in this family are rare and occur and *17 alleles (Ramesy et al, 2014). These alleles
at different frequencies among different populations. are present in most populations with a frequency
Despite numerous studies, the functional importance between 5% and 20% and warrant the avoidance of
of these polymorphisms remains unclear (Sissung et high-dose simvastatin (>40 mg) or treatment with
al, 2012). Future studies with specific substrates and another statin to decrease the risk of simvastatin-
polymorphisms may ultimately provide additional induced myopathies (Sissung et al, 2012).
CHAPTER SUMMARY
The overarching theme for the effects of polymor- where daily dosing is guided by CYP2D6 phenotypes
phisms in drug-metabolizing enzymes and transport- to prevent adverse events and achieve therapeutic effi-
ers is that they have the potential to modify the cacy. A second instance is genotyping for polymor-
pharmacokinetic profile by influencing drug clear- phisms in CYP2C19, which is responsible for the
ance or activation, secondary to metabolism. While bioactivation of clopidogrel, an antiplatelet agent. In
the pharmacogenetics of these pharmacokinetic either case the clinician’s decision to order a genetic
determinants can account for some of this variability, test prior to drug therapy may be predicated on multi-
it is not able to explain all therapeutic or adverse ple factors such as whether there are alternative drug
event variations. So currently the FDA only recom- choices; whether the test results can be obtained in an
mends pharmacogenetic testing, due to pharmacoki- appropriate time frame; and whether the insurance or
netic factors, in a limited number of drug therapy patient is willing to pay for the test. In the two exam-
regimens (see Table 13-1). One instance where ples above, a genetic test may be ordered prior to
genetic testing is strongly suggested (based on phar- tetrabenazine (since good alternatives are not avail-
macokinetic parameters) is in the use of tetrabena- able), while prasugrel or ticagrelor may be selected
zine for the treatment of Huntington’s disease chorea, instead of clopidogrel as they are not affected by
Pharmacogenetics and Drug Metabolism 369
CYP2C19 variants. Genetic polymorphisms that many other factors including concomitant medications
affect pharmacodynamic interactions also contribute that may act as metabolism inducers or inhibitors,
to the variability of drug response, and genetic testing disease states, and age that cannot be accounted for by
is required in multiple instances where such variations genetics alone. It is these observations that temper the
alter the response to drug therapy, for example, imi- excitement of personalized medicine in preventing all
tanib for c-KIT-positive tumors. Additionally, there are adverse effects and therapeutic failures.
GLOSSARY
Allele: An alternative form of a gene at a given locus. the term “pharmacogenetics” is interchangeable with
Minor allele: A less common allele at a polymor- “pharmacogenomics.”
phic locus. Pharmacogenomic test: An assay intended to study
Biological marker (biomarker): A characteristic interindividual variations in whole-genome or candi-
that is objectively measured and evaluated as an date gene, single-nucleotide polymorphism (SNP)
indicator of normal biologic processes, pathogenic maps, haplotype markers, or alterations in gene
processes, or pharmacologic responses to a thera- expression or inactivation that may be correlated
peutic intervention. with pharmacological function and therapeutic
Genetic polymorphism: Minor allele frequency of response. In some cases, the pattern or profile of
≥1% in the population. change is the relevant biomarker, rather than changes
Genome: The complete DNA sequence of an in individual markers.
organism. Pharmacogenomics: Genome-wide analysis of the
Genotype: The alleles at a specific locus an indi- genetic determinants of drug efficacy and toxicity.
vidual carries. Pharmacogenetics focuses on a single gene while
Haplotype: A group of alleles from two or more loci pharmacogenomics studies multiple genes.
on a chromosome, inherited as a unit. Phenotype: Observable expression of a particular
Pharmacogenetic test: An assay intended to deter- gene or genes.
mine interindividual variations in DNA sequence Promoter: A segment of DNA sequence that con-
related to drug absorption and disposition (pharma- trols initiation of transcription of the gene and is
cokinetics) or drug action (pharmacodynamics), usually located upstream of the gene.
including polymorphic variation in the genes that Single-nucleotide polymorphism: A DNA sequence
encode the functions of transporters, metabolizing variation occurring when a single nucleotide—A, T,
enzymes, receptors, and other proteins. C, or G—in the gene (or other shared sequence) is
Pharmacogenetics: A study of genetic causes of altered.
individual variations in drug response. In this chapter,
ABBREVIATIONS
ABC transporters: ATP-binding cassette transporters P-gp: P-glycoprotein, MDR1, ABCB1
CYP: Cytochrome P450 PGt: Pharmacogenetics
EM: Extensive metabolizer PM: Poor metabolizer
IM: Intermediate metabolizer SLC: Solute carrier transporter
NAT: N-acetyltransferase SNP: Single-nucleotide polymorphism
OATP: Organic anion transporter protein UM: Ultrarapid metabolizer
OCT: Organic cation transporter
370 Chapter 13
Frequently Asked Questions
»»What are the differences between pharmacogenetics »»What types of genes are important to drug therapy?
and pharmacogenomics? How are PGx and PGt used How would variability in these genes impact drug
to improve healthcare? therapy?
»»How common and clinically relevant are metabolic
»»What is the difference between a mutation, poly-
morphism, SNP, and haplotype? Why are these polymorphisms?
distinctions important for individualizing drug »»How can genetic information be used to improve drug
therapy? therapy for individuals and/or groups of patients?
REFERENCES
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Physiologic Factors Related
14 to Drug Absorption
Phillip M. Gerk, Andrew B. C. Yu, and
Leon Shargel
Chapter Objectives DRUG ABSORPTION AND DESIGN
»» Define passive and active drug OF A DRUG PRODUCT
absorption.
Major considerations in the design of a drug product include the
»» Explain how Fick’s law of therapeutic objective, the application site, and systemic drug
diffusion relates to passive drug absorption from the application site. If the drug is intended for
absorption. systemic activity, the drug should ideally be completely and con-
»» Calculate the percent of drug sistently absorbed from the application site. In contrast, if the drug
nonionized and ionized for is intended for local activity, then systemic absorption from the
a weak acid or weak-base application should be minimal to prevent systemic drug exposure
drug using the Henderson– and possible systemic side effects. For extended-release drug prod-
Hasselbalch equation, and ucts, the drug product should remain at or near the application site
explain how this may affect drug and then slowly release the drug for the desired period of time. The
absorption. systemic absorption of a drug is dependent on (1) the physico-
chemical properties of the drug, (2) the nature of the drug product,
»» Define transcellular and and (3) the anatomy and physiology of the drug absorption site.
paracellular drug absorption In order to develop a drug product that elicits the desired
and explain using drug therapeutic objective, the pharmaceutical scientist must have a
examples. thorough understanding of the biopharmaceutic properties of the
»» Describe the anatomy and drug and drug product and the physiologic and pathologic factors
physiology of the GI tract and affecting drug absorption from the application site. A general
explain how stomach emptying description of drug absorption, distribution, and elimination is
time and GI transit time can shown in Fig. 14-1. Pharmacists must also understand the relation-
alter the rate and extent of drug ship of drug dosage to therapeutic efficacy and adverse reactions
absorption. and the potential for drug–drug and drug–nutrient interactions.
This chapter will focus on the anatomic and physiologic consider-
»» Explain the effect of food on
ations for the systemic absorption of a drug, whereas Chapters 15
gastrointestinal physiology and
to 18 will focus on the biopharmaceutic aspects of the drug and
systemic drug absorption.
drug-product design including considerations in manufacturing
»» Describe the various and performance tests. Since the major route of drug administra-
transporters and how they tion is the oral route, major emphasis in the chapter will be on
influence the pharmacokinetics gastrointestinal drug absorption.
of drug disposition in the GI
tract.
373
374 Chapter 14
»» Explain the pH-partition ROUTE OF DRUG ADMINISTRATION
hypothesis and how
gastrointestinal pH and the pKa Drugs may be given by parenteral, enteral, inhalation, intranasal,
of a drug may influence systemic transdermal (percutaneous), or intranasal route for systemic
drug absorption. Describe how absorption. Each route of drug administration has certain advan-
drug absorption may be affected tages and disadvantages. Some characteristics of the more com-
by a disease that causes changes mon routes of drug administration are listed in Table 14-1. The
in intestinal blood flow and/or systemic availability and onset of drug action are affected by blood
motility. flow at the administration site, the physicochemical characteristics
of the drug and the drug product, and any pathophysiologic condi-
»» List the major factors that tion at the absorption site. After a drug is systemically absorbed,
affect drug absorption from drug distribution and clearance follow normal physiological condi-
oral and nonoral routes of drug tions of the body. Drug distribution and clearance are not usually
administration. altered by the drug formulation but may be altered by pathology,
»» Describe various methods genetic polymorphism, and drug–drug interactions, as discussed in
that may be used to study other chapters.
oral drug absorption from the Many drugs are not administered orally because of insuffi-
gastrointestinal transit. cient systemic absorption from the GI tract. The diminished oral
drug absorption may be due to drug instability in the gastrointesti-
nal tract, drug degradation by the digestive enzymes in the intes-
tine, high hepatic clearance (first-pass effect), and efflux
transporters such as P-glycoprotein resulting in poor and/or erratic
systemic drug availability. Some orally administered drugs, such
as cholestyramine and others (Table 14-2), are not intended for
systemic absorption but may be given orally for local activity in
the gastrointestinal tract. However, some oral drugs such as mesa-
lamine and balsalazide that are intended for local activity in the GI
tract may also have a significant amount of systemic drug
absorption. Small, highly lipid-soluble drugs such as nitroglycerin
and fentanyl that are subject to high first-pass effects if swallowed
but may be given by buccal or sublingual routes to bypass degrada-
tion in the GI tract and/or first-pass effects. Insulin is an example
of protein peptide drug generally not given orally due to degrada-
tion and inadequate absorption in the GI tract.
Biotechnology-derived drugs (see Chapter 20) are usually
given by the parenteral route because they are too labile in the GI
tract to be administered orally. For example, erythropoietin and
human growth hormone (somatrophin) are administered intramus-
cularly, and insulin is given subcutaneously or intramuscularly.
Subcutaneous injection results in relatively slow absorption from
the site of administration compared to intravenous injection, which
provides immediate delivery to the plasma. Pathophysiologic con-
ditions such as burns will increase the permeability of drugs across
the skin compared with normal intact skin. Currently, pharmaceu-
tical research is being directed to devise approaches for the oral
absorption of various protein drugs such as insulin (Dhawan et al,
2009). Recently, inhaled insulin was approved for use by the FDA
Physiologic Factors Related to Drug Absorption 375
TISSUE RESERVOIRS
bound ⇔ free
THERAPEUTIC UNWANTED SITE
SITE OF ACTION OF ACTION
“Receptors”
bound ⇔ free CENTRAL bound ⇔ free
COMPARTMENT
ABSORPTION
DRUG CLEARANCE
[FREE DRUG]
DOSE
LIBERATION EXCRETION
Protein bound Metabolites
drug
BIOTRANSFORMATION
FIGURE 141 The interrelationship of the absorption, distribution, binding, metabolism, and excretion of a drug and its con-
centration at its sites of action. (From Buxton and Benet, 2011.)
TABLE 141 Common Routes of Drug Administration
Route Bioavailability Advantages Disadvantages
Parenteral Routes
Intravenous bolus Complete (100%) systemic Drug is given for immediate Increased chance for adverse
(IV) drug absorption. effect. reaction.
Rate of bioavailability Possible anaphylaxis.
considered instantaneous.
Intravenous Complete (100%) systemic Plasma drug levels more Requires skill in insertion of infusion
infusion (IV inf ) drug absorption. precisely controlled. set.
Rate of drug absorption May inject large fluid volumes. Tissue damage at site of injection
controlled by infusion rate. May use drugs with poor (infiltration, necrosis, or sterile
lipid solubility and/or abscess).
irritating drugs.
Subcutaneous Prompt from aqueous solution. Generally, used for insulin Rate of drug absorption depends on
injection (SC) Slow absorption from injection. blood flow and injection volume.
repository formulations. Insulin formulaton can vary from
short to intermediate and long acting.
Intradermal Drug injected into surface area Often used for allergy and Some discomfort at site of injection.
injection (dermal) of skin. other diagnostic tests, such
as tuberculosis.
Intramuscular Rapid from aqueous solution. Easier to inject than Irritating drugs may be very
injection (IM) Slow absorption from intravenous injection. painful. Different rates of absorp-
nonaqueous (oil) solutions. Larger volumes may be used tion depending on muscle group
compared to subcutaneous injected and blood flow.
solutions.
Intra-arterial 100% of solution is absorbed. Used in chemotherapy to Drug may also distribute to other
injection target drug to organ. tissues and organs in the body.
Intrathecal 100% of solution is absorbed. Drug is directly injected into
Injection cerebrospinal fluid (CSF) for
uptake into brain.
(Continued)
376 Chapter 14
TABLE 141 Common Routes of Drug Administration (Continued)
Route Bioavailability Advantages Disadvantages
Intraperitoneal In laboratory animals, (eg, rat) Used more in small labora- Drug absorption via mesenteric
injection drug absorption resembles tory animals. Less common veins to liver, may have some
oral absorption. injection in humans. Used hepatic clearance prior to systemic
for renally impaired patients absorption.
on peritoneal dialysis who
develop peritonitis.
Enteral Routes
Buccal or Rapid absorption from No “first-pass” effects. Buccal Some drugs may be swallowed.
sublingual (SL) lipidsoluble drugs. route may be formulated for Not for most drugs or drugs with
local prolonged action. high doses.
Eg, adhere to the buccal
mucosa with some antifungal.
Buccal is different from
sublingual which is usually
placed “under tongue.”
Oral (PO) Absorption may vary. Safest and easiest route of Some drugs may have erratic
Generally, slower absorption drug administration. absorption, be unstable in
rate compared to IV bolus or May use immediate-release the gastointestinal tract, or be
IM injection. and modified-release drug metabolized by liver prior to
products. systemic absorption.
Enteral Routes
Rectal (PR) Absorption may vary from Useful when patient cannot Absorption may be erratic.
suppository. swallow medication. Suppository may migrate to
More reliable absorption from Used for local and systemic different position.
enema (solution). effects. Some patient discomfort.
Other Routes
Transdermal Slow absorption, rate may Transdermal delivery system Some irritation by patch or drug.
vary. (patch) is easy to use. Permeability of skin variable with
Increased absorption with Used for lipid-soluble drugs condition, anatomic site, age, and
occlusive dressing. with low dose and low MW gender.
(molecular weight). Type of cream or ointment base
affects drug release and absorption.
Inhalation and Rapid absorption. May be used for local or Particle size of drug determines
intranasal Total dose absorbed is systemic effects. anatomic placement in respiratory
variable. tract.
May stimulate cough reflex.
Some drug may be swallowed.
but the product was fairly quickly discontinued by inhalation, rectal), the drug must first be absorbed into
the manufacturer because of poor patient and physi- the systemic circulation and then diffuse or be trans-
cian acceptance of this new route of administration. ported to the site of action before eliciting biological
Biotechnology-derived drugs are discussed more and therapeutic activity. The general principles and
fully in Chapter 20. kinetics of absorption from these extravascular sites
When a drug is administered by an extravascular follow the same principles as oral dosing, although
route of administration (eg, oral, topical, intranasal, the physiology of the site of administration differs.
Physiologic Factors Related to Drug Absorption 377
TABLE 142 Drugs Given Orally for Local Drug Activity in the Gastrointestinal Tract
Drug Example Comment
Cholestyramine Questran Cholestyramine resin is the chloride salt of a basic anion exchange resin, a cholesterol-
lowering agent. Cholestyramine resin is hydrophilic, but insoluble in water and not
absorbed from the digestive tract.
Balsalazide Colazal Balsalazide disodium is a prodrug that is enzymatically cleaved in the colon to produce
disodium mesalamine, an anti-inflammatory drug. Balsalazide disodium is intended for local action
in the treatment of mildly to moderately active ulcerative colitis. Balsalazide disodium and
its metabolites are absorbed from the lower intestinal tract and colon.
Mesalaminea Asacol HD Asacol HD delayed-release tablets have an outer protective coat and an inner coat which
delayed-release tablet dissolves at pH 7 or greater, releasing mesalamine in the terminal ileum for topical antiin-
tablet flammatory action in the colon.
Mesalamine Pentasa Pentasa capsule is an ethylcellulose-coated, controlled-release capsule formulation of
controlled-release capsule mesalamine designed to release therapeutic quantities of mesalamine throughout the
capsule gastrointestinal tract.
aMesalamine (also referred to as 5-aminosalicylic acid or 5-ASA). Although mesalamine is indicated for local anti-inflammatory activity in the lower GI
tract, mesalamine is systemically absorbed from the GI tract.
NATURE OF CELL MEMBRANES Membranes are major structures in cells, sur-
rounding the entire cell (plasma membrane) and
Many drugs administered by extravascular routes are acting as a boundary between the cell and the inter-
intended for local effect. Other drugs are designed to stitial fluid. In addition, membranes enclose most of
be absorbed from the site of administration into the the cell organelles (eg, the mitochondrion mem-
systemic circulation. For systemic drug absorption, brane). Functionally, cell membranes are semiper-
the drug may cross cellular membranes. After oral meable partitions that act as selective barriers to the
administration, drug molecules must cross the intes- passage of molecules. Water, some selected small
tinal epithelium by going either through or between molecules, and lipid-soluble molecules pass through
the epithelial cells to reach the systemic circulation. such membranes, whereas highly charged molecules
The permeability of a drug at the absorption site into and large molecules, such as proteins and protein-
the systemic circulation is intimately related to the bound drugs, do not.
molecular structure and properties of the drug and to The transmembrane movement of drugs is influ-
the physical and biochemical properties of the cell enced by the composition and structure of the
membranes. Once in the plasma, the drug may act plasma membranes. Cell membranes are generally
directly or have to cross biological membranes to thin, approximately 70–100 Å in thickness. Cell
reach the site of action. Therefore, biological mem- membranes are composed primarily of phospholip-
branes potentially pose a significant barrier to drug ids in the form of a bilayer interdispersed with car-
delivery. bohydrates and protein groups. There are several
Transcellular absorption is the process of drug theories as to the structure of the cell membrane. The
movement across a cell. Some polar molecules may not lipid bilayer or unit membrane theory, originally
be able to traverse the cell membrane but, instead, go proposed by Davson and Danielli (1952), considers
through gaps or tight junctions between cells, a process the plasma membrane to be composed of two layers
known as paracellular drug diffusion. Figure 14-2 of phospholipid between two surface layers of pro-
shows the difference between the two processes. teins, with the hydrophilic “head” groups of the
Some drugs are probably absorbed by a mixed mech- phospholipids facing the protein layers and the
anism involving one or more processes. hydrophobic “tail” groups of the phospholipids
378 Chapter 14
structure does not account for the diffusion of water,
Transcellular transport small-molecular-weight molecules such as urea, and
Paracellular transport certain charged ions.
Intestinal epithelial cell The fluid mosaic model, proposed by Singer and
Nicolson (1972), explains the transcellular diffusion
of polar molecules (Lodish, 1979). According to this
Brush-border Basolateral
membrane membrane model, the cell membrane consists of globular pro-
N teins embedded in a dynamic fluid, lipid bilayer
Na+ a+/
/Amino acid
Amino acid matrix (Fig. 14-3). These proteins provide a pathway
Amino acid Amino acid
for the selective transfer of certain polar molecules
EAAC1 Na+, Cl–/β-Amino acid and charged ions through the lipid barrier. As shown
H+/Oligopeptide H+/
PEPT1 ?
Oligopeptide in Fig. 14-3, transmembrane proteins are interdis-
persed throughout the membrane. Two types of pores
SGLT1 Na+/D-Glucose
of about 10 nm and 50–70 nm were inferred to be
GLUT5 D-Fructose GLUT2 Hexose
H+ present in membranes based on capillary membrane
/
MCT1? H+/Lactic acid MCT1?
Lactic acid transport studies (Pratt and Taylor, 1990). These
small pores provide a channel through which water,
H+/SCFA
ions, and dissolved solutes such as urea may move
HCO –
3 /
Monocarboxylic acid across the membrane.
+ Membrane proteins embedded in the bilayer serve
Na+/Phosphate Na /
Phosphate special purposes. These membrane proteins function
Na+/Bile acid as structural anchors, receptors, ion channels, or trans-
H+/Nicotinic acid porters to transduce electrical or chemical signaling
pathways that facilitate or prevent selective actions. In
HCO –
3 /Nicotinic acid contrast to simple bilayer structure, membranes are
OH–/Folic acid Folic acid highly ordered and compartmented (Brunton, 2011).
Choline Indeed many early experiments on drug absorption or
permeability using isolated gut studies were proven
ATP
MDR1 P-Glycoprotein not valid because the membrane proteins and electrical
ADP AT
Na+P properties of the membrane were compromised in
Na+/H+ K+ many epithelial cell membranes, including those of the
Antiporter ADP
gastrointestinal tract.
pH = 5.5–6.8 pH = 7.0 pH = 7.4
[Na+] = 140 mM [Na+] = 10–20 mM [Na+] = 140 mM
FIGURE 142 Summary of intestinal epithelial transport-
ers. Transporters shown by square and oval shapes demon- PASSAGE OF DRUGS ACROSS
strate active and facilitated transporters, respectively. Names
of cloned transporters are shown with square or oval shapes. CELL MEMBRANES
In the case of active transporters, arrows in the same direction
represent symport of substance and the driving force. Arrows Passive Diffusion
going in the reverse direction mean the antiport. (From Tsuji Theoretically, a lipophilic drug may pass through the
and Tamai, 1996, with permission.) Note that BCRP and MRP2 cell or go around it. If the drug has a low molecular
are positioned similarly to MDR1 (P-glycoprotein).
weight and is lipophilic, the lipid cell membrane is
not a barrier to drug diffusion and absorption.
aligned in the interior. The lipid bilayer theory Passive diffusion is the process by which molecules
explains the observation that lipid-soluble drugs spontaneously diffuse from a region of higher con-
tend to penetrate cell membranes more easily than centration to a region of lower concentration. This
polar molecules. However, the bilayer cell membrane process is passive because no external energy is
Physiologic Factors Related to Drug Absorption 379
Carbohydrate
Integral protein
Integral
protein Lipid
bilayer
Peripheral
protein
Cytoplasm
FIGURE 143 Model of the plasma membrane including proteins and carbohydrates as well as lipids. Integral proteins are
embedded in the lipid bilayer; peripheral proteins are merely associated with the membrane surface. The carbohydrate consists
of monosaccharides, or simple sugars, strung together in chains attached to proteins (forming glycoproteins) or to lipids (forming
glycolipids). The asymmetry of the membrane is manifested in several ways. Carbohydrates are always on the exterior surface and
peripheral proteins are almost always on the cytoplasmic, or inner, surface. The two lipid monolayers include different proportions
of the various kinds of lipid molecules. Most important, each species of integral protein has a definite orientation, which is the same
for every molecule of that species. (©George V. Kelvin.)
expended. In Fig. 14-4, drug molecules move for- will be higher than the number of backward-moving
ward and back across a membrane. If the two sides molecules; the net result will be a transfer of mole-
have the same drug concentration, forward-moving cules to the alternate side downstream from the
drug molecules are balanced by molecules moving concentration gradient, as indicated in the figure by
back, resulting in no net transfer of drug. When one the big arrow. The rate of transfer is called flux, and
side is higher in drug concentration at any given is represented by a vector to show its direction in
time, the number of forward-moving drug molecules space. The tendency of molecules to move in all
directions is natural, because molecules possess
kinetic energy and constantly collide with one
Membrane another in space. Only left and right molecule move-
FLUX J
ments are shown in Fig. 14-4, because movement of
Low molecules in other directions will not result in con-
concentration
High centration changes because of the limitation of the
concentration container wall.
FIGURE 144 Passive diffusion of molecules. Molecules in Passive diffusion is the major absorption process
solution diffuse randomly in all directions. As molecules diffuse for most drugs. The driving force for passive diffusion
from left to right and vice versa (small arrows), a net diffusion
is higher drug concentrations, typically on the muco-
from the high-concentration side to the low-concentration
side results. This results in a net flux (J) to the right side. Flux is sal side compared to the blood as in the case of oral
measured in mass per unit time (eg, ng/min). drug absorption. According to Fick’s law of diffusion,
380 Chapter 14
drug molecules diffuse from a region of high drug drug diffuses slowly into the brain as if a thick lipid
concentration to a region of low drug concentration. membrane exists. The term blood–brain barrier is
used to describe the poor diffusion of water-soluble
dQ DAK
= (C ( 4
d GI −Cp) 1 .1) molecules across capillary plasma membranes into
t h the brain. However, in certain disease states such as
where dQ/dt = rate of diffusion, D = diffusion co- meningitis these membranes may be disrupted or
efficient, A = surface area of membrane, K = lipid– become more permeable to drug diffusion.
water partition coefficient of drug in the biologic The diffusion coefficient, D, is a constant for
membrane that controls drug permeation, h = mem- each drug and is defined as the amount of a drug that
brane thickness, and CGI − Cp = difference between diffuses across a membrane of a given unit area per
the concentrations of drug in the gastrointestinal unit time when the concentration gradient is unity.
tract and in the plasma. The dimensions of D are area per unit time—for
Because the drug distributes rapidly into a large example, cm2/sec.
volume after entering the blood, the concentration of Because D, A, K, and h are constants under
drug in the blood initially will be quite low with usual conditions for absorption, a combined constant
respect to the concentration at the site of drug P or permeability coefficient may be defined.
absorption. For example, a drug is usually given in
milligram doses, whereas plasma concentrations are DAK
P = (14.2)
often in the microgram-per-milliliter or nanogram- h
per-milliliter range. If the drug is given orally, then
CGI >> Cp and a large concentration gradient is main- Furthermore, in Equation 14.1 the drug concentra-
tained until most of the drug is absorbed, thus driv- tion in the plasma, Cp, is extremely small compared
ing drug molecules into the plasma from the to the drug concentration in the gastrointestinal tract,
gastrointestinal tract. CGI. If Cp is negligible and P is substituted into
Given Fick’s law of diffusion, several other fac- Equation 14.1, the following relationship for Fick’s
tors can be seen to influence the rate of passive dif- law is obtained:
fusion of drugs. For example, the degree of lipid dQ
solubility of the drug influences the rate of drug = P(C ) (14.3
dt GI )
absorption. The partition coefficient, K, represents
the lipid–water partitioning of a drug across the Equation 14.3 is an expression for a first-order pro-
hypothetical membrane in the mucosa. Drugs that cess. In practice, the extravascular absorption of
are more lipid soluble have a larger value of K. The most drugs tends to be a first-order absorption pro-
surface area, A, of the membrane also influences the cess. Moreover, because of the large concentration
rate of absorption. Drugs may be absorbed from gradient between CGI and Cp, the rate of drug absorp-
most areas of the gastrointestinal tract. However, the tion is usually more rapid than the rate of drug
duodenal area of the small intestine shows the most elimination.
rapid drug absorption, due to such anatomic features Many drugs have both lipophilic and hydrophilic
as villi and microvilli, which provide a large surface chemical substituents. Those drugs that are more
area. These villi are less abundant in other areas of lipid soluble tend to traverse cell membranes more
the gastrointestinal tract. easily than less lipid-soluble or more water-soluble
The thickness of the hypothetical model mem- molecules. For drugs that act as weak electrolytes,
brane, h, is a constant for any particular absorption such as weak acids and bases, the extent of ionization
site. Drugs usually diffuse very rapidly through cap- influences the drug’s diffusional permeability. The
illary plasma membranes in the vascular compart- ionized species of the drug contains a charge and is
ments, in contrast to diffusion through plasma more water soluble than the nonionized species of the
membranes of capillaries in the brain. In the brain, drug, which is more lipid soluble. The extent of ion-
the capillaries are densely lined with glial cells, so a ization of a weak electrolyte will depend on both the
Physiologic Factors Related to Drug Absorption 381
pKa of the drug and the pH of the medium in which Gastric juice (pH 1.2) Plasma (pH 7.4)
the drug is dissolved. Henderson and Hasselbalch
R COOH R COOH
used the following expressions pertaining to weak
acids and weak bases to describe the relationship
between pKa and pH: – + – +
R COO + H O R COO + H O
3 3
For weak acids, FIGURE 145 Model for the distribution of an orally
administered weak electrolyte drug such as salicylic acid.
[Salt] [A− ]
Ratio = = 10(pH−pKa )
= (14.4)
[Acid] [HA]
In the plasma, at pH 7.4
For weak bases, (RCOO− )
Ratio = = 2.51×104
(RCOOH)
[Base] [RNH2 ] Ratio −
= = = 10(pH pKa ) (14.5)
[Salt] [RNH+
3 ] In gastric juice, at pH 1.2
With Equations 14.4 and 14.5, the proportion of free (RCOO− )
Ratio = = 10(1.2−3.0) = 1.58×10−2
acid or free base existing as the nonionized species
(RCOOH)
may be determined at any given pH, assuming the
pKa for the drug is known. For example, at a plasma The total drug concentration on either side of the
pH of 7.4, salicylic acid (pKa = 3.0) exists mostly in membrane is determined as shown in Table 14-3.
its ionized or water-soluble form, as shown below: Thus, the pH affects distribution of salicylic acid
(RCOOH) and its salt (RCOO−) across cell mem-
[Salt]
Ratio 10(7.4−3.0) branes. It is assumed that the acid, RCOOH, is freely
= =
[Acid] permeable and the salt, RCOO−, is not permeable
[Salt] across the cell membrane. In this example the total
log = 7.4 − 3.0 = 4.4
[Acid] concentration of salicylic acid at equilibrium is approx-
imately 25,000 times greater in the plasma than in the
[Salt]
2.51 104 stomach (see Table 14-3). These calculations can also
= ×
[Acid] be applied to weak bases, using Equation 14.5.
According to the pH-partition hypothesis, if
In a simple system, the total drug concentration on the pH on one side of a cell membrane differs from
either side of a membrane should be the same at the pH on the other side of the membrane, then (1) the
equilibrium, assuming Fick’s law of diffusion is the drug (weak acid or base) will ionize to different
only distribution factor involved. For diffusible degrees on respective sides of the membrane; (2) the
drugs, such as nonelectrolyte drugs or drugs that do total drug concentrations (ionized plus nonionized
not ionize, the drug concentrations on either side of
the membrane are the same at equilibrium. However,
for electrolyte drugs or drugs that ionize, the total TABLE 143 Relative Concentrations of
drug concentrations on either side of the membrane Salicylic Acid as Affected by pH
are not equal at equilibrium if the pH of the medium
differs on respective sides of the membrane. For Gastric Juice
example, consider the concentration of salicylic acid Drug (pH 1.2) Plasma (pH 7.4)
(pKa = 3.0) in the stomach (pH 1.2) as opposed to its RCOOH 1.0000 1
concentration in the plasma (pH 7.4) (Fig. 14-5).
RCOO– 0.0158 25,100
According to the Henderson–Hasselbalch equation
(Equation 14.4) for weak acids, at pH 7.4 and at pH 1.2, Total drug 1.0158 25,101
salicylic acid exists in the ratios that follow. concentration
382 Chapter 14
drug) on either side of the membrane will be role in determining the rate and extent of drug
unequal; and (3) the compartment in which the drug absorption. Uptake transporters move drug molecules
is more highly ionized will contain the greater total into the blood and increase plasma drug concentra-
drug concentration. For these reasons, a weak acid tion, whereas efflux transporters move drug mole-
(such as salicylic acid) will be rapidly absorbed cules back into the gut lumen and reduce systemic
from the stomach (pH 1.2), whereas a weak base drug absorption. These cells also express some drug-
(such as quinidine) will be poorly absorbed from metabolizing enzymes, and can contribute to presys-
the stomach. temic drug metabolism (Doherty, 2002).
Another factor that can influence drug concentra- Theoretically, a lipophilic drug may either pass
tions on either side of a membrane is a particular through the cell or go around it. If the drug has a low
affinity of the drug for a tissue component, which molecular weight and is lipophilic, the lipid cell
prevents the drug from moving freely back across the membrane is not a barrier to drug diffusion and
cell membrane. For example, a drug such as dicuma- absorption. In the intestine, drugs and other mole-
rol binds to plasma protein, and digoxin binds to tis- cules can go through the intestinal epithelial cells by
sue protein. In each case, the protein-bound drug does either diffusion or a carrier-mediated mechanism.
not move freely across the cell membrane. Drugs such Numerous specialized carrier-mediated transport
as chlordane are very lipid soluble and will partition systems are present in the body, especially in the
into adipose (fat) tissue. In addition, a drug such as intestine for the absorption of ions and nutrients
tetracycline might form a complex with calcium in the required by the body.
bones and teeth. Finally, a drug may concentrate in a
tissue due to a specific uptake or active transport pro-
Active Transport
cess. Such processes have been demonstrated for
iodide in thyroid tissue, potassium in the intracellular Active transport is a carrier-mediated transmem-
water, and certain catecholamines into adrenergic brane process that plays an important role in the
storage sites. Such drugs may have a higher total drug gastrointestinal absorption and in renal and biliary
concentration on the side where binding occurs, yet secretion of many drugs and metabolites. A few
the free drug concentration that diffuses across cell lipid-insoluble drugs that resemble natural physio-
membranes will be the same on both sides of the logic metabolites (such as 5-fluorouracil) are
membrane. absorbed from the gastrointestinal tract by this pro-
Instead of diffusing into the cell, drugs can also cess. Active transport is characterized by the ability
diffuse into the spaces around the cell as an absorp- to transport drug against a concentration gradient—
tion mechanism. In paracellular drug absorption, that is, from regions of low drug concentrations to
drug molecules smaller than 500 MW diffuse through regions of high drug concentrations. Therefore, this
the tight junctions, or spaces between intestinal epi- is an energy-consuming system. In addition, active
thelial cells. Generally, paracellular drug absorp- transport is a specialized process requiring a carrier
tion is very slow, being limited by tight junctions that binds the drug to form a carrier–drug complex
between cells. For example, if mannitol is dosed that shuttles the drug across the membrane and then
orally, it would be absorbed minimally and only dissociates the drug on the other side of the mem-
through this route; mannitol has very, very low oral brane (Fig. 14-6).
bioavailability.
GI lumen Intestinal epithelial cell Blood
Carrier-Mediated Transport
Carrier Carrier
Enterocytes are simple columnar epithelial cells that Drug + Drug–carrier Drug
Drug complex
line the intestinal walls in the small intestine and colon.
They express various drug transporters, are con- FIGURE 146 Hypothetical carrier-mediated transport
nected by tight junctions, and often play an important process.
Physiologic Factors Related to Drug Absorption 383
rate of drug absorption increases with drug concen-
A tration until the carrier molecules are completely
saturated. At higher drug concentrations, the rate of
B drug absorption remains constant, or zero order.
Several transport proteins are expressed in the
intestinal epithelial cells (Suzuki and Sugiyama et al,
2000; Takano et al, 2006) (Fig. 14-8). Although some
transporters facilitate absorption, other transporters
such as P-gp may effectively inhibit drug absorption.
P-gp (also known as MDR1), an energy-dependent,
membrane-bound protein, is an efflux transporter
Concentration of drug
that mediates the secretion of compounds from inside
FIGURE 147 Comparison of the rates of drug absorp- the cell back out into the intestinal lumen, thereby
tion of a drug absorbed by passive diffusion (line A) and a drug
absorbed by a carrier-mediated system (line B). limiting overall absorption (see Chapter 13). Thus,
drug absorption may be reduced or increased by the
presence or absence of efflux proteins. The role of
The carrier molecule may be highly selective for efflux proteins is generally believed to be a defense
the drug molecule. If the drug structurally resembles mechanism for the body to excrete and reduce drug
a natural substrate that is actively transported, then it accumulation.
is likely to be actively transported by the same car- P-gp is expressed also in other tissues such as the
rier mechanism. Therefore, drugs of similar structure blood–brain barrier, liver, and kidney, where it limits
may compete for sites of adsorption on the carrier. drug penetration into the brain, mediates biliary drug
Furthermore, because only a fixed number of carrier secretion, and mediates renal tubular drug secretion,
molecules are available, all the binding sites on the respectively. Efflux pumps are present throughout the
carrier may become saturated if the drug concentra- body and are involved in transport of a diverse group
tion gets very high. A comparison between the rate of hydrophobic drugs, natural products, and peptides.
of drug absorption and the concentration of drug at Many drugs and chemotherapeutic agents, such as
the absorption site is shown in Fig. 14-7. Notice that cyclosporin A, verapamil, terfenadine, fexofenadine,
for a drug absorbed by passive diffusion, the rate of and most HIV-1 protease inhibitors, are substrates of
absorption increases in a linear relationship to drug P-gp (see Chapter 13). In addition, individual genetic
concentration (first-order rate). In contrast, for drugs differences in intestinal absorption may be the result
that are absorbed by a carrier-mediated process, the of genetic differences in P-gp and other transporters.
Intestinal lumen (mucosal side)
Apical
(brush-border)
membrane PEPT1 P-gp BCRP MRP2
Epithelial cell
Basolateral
membrane MRP3
Blood (serosal side)
FIGURE 148 Localization of efflux transporters and PEPT1 in intestinal epithelial cell. (From Takano et al, 2006, with permission.)
Rate of drug absorption
384 Chapter 14
Facilitated Diffusion Uptake transporters. For convenience, influx
Facilitated diffusion is also a carrier-mediated transport transporters were referred to as those that enhance
system, differing from active transport in that the drug absorption as uptake transporters and those that
moves along a concentration gradient (ie, moves from cause drug outflow as efflux transporters. However,
a region of high drug concentration to a region of low this concept is too simple and inadequate to describe
drug concentration). Therefore, this system does not the roles of many transporters that have bidirectional
require energy input. However, because this system is efflux and other functions related to their location in
carrier mediated, it is saturable and structurally selec- the membrane. Recent progress has been made in
tive for the drug and shows competition kinetics for understanding the genetic role of membrane
drugs of similar structure. In terms of drug absorption, transporters in drug safety and efficacy. In particular,
facilitated diffusion seems to play a very minor role. more than 400 membrane transporters in two major
superfamilies—ATP-binding cassette (ABC) and
solute carrier (SLC)—have been annotated in the
Transporters and Carrier-Mediated human genome. Many of these transporters have been
Intestinal Absorption cloned, characterized, and localized in the human
Various carrier-mediated systems (transporters) are body including the GI tract. The subject was reviewed
present at the intestinal brush border and basolateral recently by The International Transporter Consortium
membrane for the absorption of specific ions and (ITC) (Giacomini, 2010).
nutrients essential for the body (Tsuji and Tamai, Many drugs are absorbed by carrier systems
1996). Both influx and efflux transporters are present because of the structural similarity to natural sub-
in the brush border and basolateral membrane that strates or simply because they encounter the transport-
will increase drug absorption (influx transporter) or ers located in specific part of the GI tract (Table 14-4).
decrease drug absorption (efflux transporter). The small intestine expresses a variety of uptake
TABLE 144 Intestine Transporters and Examples of Drugs Transported
Transporter Examples
Amino acid transporter Gabapentin D-Cycloserine
Methyldopa Baclofen
L-dopa
Oligopeptide transporter Cefadroxil Cephradine
Cefixime Ceftibuten
Cephalexin Captopril
Lisinopril Thrombin inhibitor
Phosphate transporter Fostomycin Foscarnet
Bile acid transporter S3744
Glucose transporter p-Nitrophenyl-β-d-glucopyranoside
P-glycoprotein efflux Etoposide Vinblastine
Cyclosporin A
Monocarboxylic acid transporter Salicylic acid Benzoic acid
Pravastatin
Data from Tsuji and Tamai (1996).
Physiologic Factors Related to Drug Absorption 385
transporters (see Fig. 14-2) for amino acids, peptides, be related to its defensive role in effluxing drugs and
hexoses, organic anions, organic cations, nucleosides, other xenobiotics out of different cells and vital body
and other nutrients (Tsuji and Tamai, 1996; Giacomini, organs. This transporter is sometimes called an
2010). Among these uptake (absorptive) transporters efflux transporter while others are better described
are the intestinal oligopeptide transporter, or di-/ as “influx” proteins. P-gp has the remarkable ability
tripeptide transporter, PepT1 has potential for enhanc- to efflux drug out of many types of cells including
ing intestinal absorption of peptide drugs. The expres- endothelial lumens of capillaries. The expression of
sion and function of PepT1 (gene symbol SLC15A1) P-gp is often triggered in many cancer cells making
are now well analyzed for this application. Proteins them drug resistant due to drug efflux.
given orally are digested in the gastrointestinal tract to For many GI transporters, the transport of a drug is
produce a variety of short-chain peptides; these di- often bidirectional (Fig. 14-9), and whether the trans-
and tripeptides could be taken up by enterocytes and porter causes drug absorption or exsorption depends on
the proton/peptide cotransporter (PepT1) localized which direction the flux dominates with regard to a
on the brush-border membrane. These uptake trans- particular drug at a given site. An example of how P-gp
porters are located at the brush border as well as in the affects drug absorption can be seen with the drug
basolateral membrane to allow efficient absorption of digoxin. P-gp is present in the liver and the GI tract. In
essential nutrients into the body. Uptake transporters Caco-2 cells and other model systems, P-gp is known
such as those for hexoses and amino acids also favor to efflux drug out of the enterocyte. Digoxin was previ-
absorption (see arrows as shown in Fig. 14-7). ously known to have erratic/incomplete absorption or
bioavailability problems. While reported bioavailability
Efflux transporters. Many of the efflux transporters issues were attributed to formulation or other factors, it
in the GI tract are membrane proteins located is also now known that knocking out the P-gp gene in
strategically in membranes to protect the body from mice increases bioavailability of the drug. In addition,
influx of undesirable compounds. A common example human P-gp genetic polymorphisms occur. Hoffmeyer
is MDR1 or P-gp (alias), which has the gene symbol et al (2000) demonstrated that a polymorphism in exon
ABCB1. P-gp is an example of the ABC subfamily. 26 (C3435T) resulted in reduced intestinal P-gp, lead-
MDR1 is one of the many proteins known as multidrug- ing to increased oral bioavailability of digoxin in the
resistance associated protein. It is important in pumping subject involved. However, direct determination of
drugs out of cells and causing treatment resistance in P-gp substrate in vivo is not always readily possible.
some cell lines (see Chapter 13). Most early determinations are done using in vitro cell
P-gp has been identified in the intestine and assay methods, or in vivo studies involving a cloned
reduces apparent intestinal epithelial cell permea- animal with the gene knocked out such as the P-gp, a
bility from lumen to blood for various lipophilic or KO (knock-out) mouse, for example, P-gp (−/−), which
cytotoxic drugs. P-gp is highly expressed on the api- is the most sensitive method to identify P-gp substrates.
cal surface of superficial columnar epithelial cells
of the ileum and colon, and expression decreases
proximally into the jejunum, duodenum, and stomach.
Takano et al (2006) reported that P-gp is present Enterocytes
in various human tissues and ranked as follows:
(1) adrenal medulla (relative level to that in KB-3-1
cells, > 500-fold); (2) adrenal (160-fold); (3) kidney Blood
medulla (75-fold); (4) kidney (50-fold); (5) colon
(31-fold); (6) liver (25-fold); (7) lung, jejunum, and
Gut lumen
rectum (20-fold); (8) brain (12-fold); (9) prostate
(8-fold); and so on, including skin, esophagus, stom-
ach, ovary, muscle, heart, and kidney cortex. The FIGURE 149 Diagram showing possible directional
widespread presence of P-gp in the body appears to movement of a substrate drug by a transporter.
Apical
Basolateral
386 Chapter 14
Changes in the expression of P-gp may be triggered by absorbed through amino acid transporters. Cefazolin,
diseases or other drugs, contributing to variability in a parenteral-only cephalosporin, is not available
P-gp activity and variable plasma drug concentrations orally because it cannot be absorbed to a significant
after a given dose is administered. Results from in vitro degree through this mechanism.
and preclinical (animal) studies may need to be verified
with by clinical drug–drug interaction studies to estab- Frequently Asked Questions
lish the role of P-gp in the oral bioavailability of a drug.
»»The bioavailability of an antitumor drug is provided in
The breast cancer resistance protein (BCRP; the package insert. Why is it important to know whether
gene symbol ABCG2) is like P-gp in that it is also the drug is an efflux transporter substrate or not?
found in many important fluid barrier layers, includ-
ing the intestine, liver, kidney, and brain. BCRP also »»Can the expression of efflux transporter in a cell
change as the disease progresses?
transports many drugs out of cells, working (like
P-gp) to keep various compounds out of the body (by »»Why is blockade of efflux transporter efflux of a drug,
decreasing their absorption) or helping to eliminate its glucuronide, or sulfate metabolite into the bile
them. Drugs transported by BCRP include many clinically important?
anticancer drugs (methotrexate, irinotecan, mitoxan-
trone), statins (rosuvastatin), as well as nitrofurantoin
and various sulfated metabolites of drugs and endog- Clinical Examples of Transporter Impact
enous compounds. The FDA requires all investiga- Multidrug resistance (MDR) to cancer cells has been
tional new drugs to be tested for their potential linked to efflux transporter proteins such as P-gp that
activity as substrates of both P-gp and BCRP, and can efflux or pump out chemotherapeutic agents from
also recommends determining if they are inhibitors the cells (Sauna et al, 2001). Paclitaxel (Taxol) is an
(Huang and Zhang, 2012). example of coordinated metabolism, efflux, and trig-
gering of hormone nuclear receptor to induce efflux
Frequently Asked Questions protein (Fig. 14-10). P-gp (see MDR1 in Fig. 14-2) is
responsible for 85% of paclitaxel excretion back into
»»What is the effect of intestinal P-gp on the blood
level of the substrate drug digoxin when a substrate the GI tract (Synold et al, 2001). Paclitaxel activates
inhibitor (ketoconazole) is present? the pregnane X receptor (also known as PXR, or alter-
natively as steroid X receptor [SXR]), which in turn
»»According to the diagram in Fig. 14-9, in which induces MDR1 transcription and P-gp expression,
direction is P-gp pumping the drug? Is P-gp acting resulting in even further excretion of paclitaxel into
as an efflux transporter in this diagram?
the intestinal fluid. Paclitaxel also induces CYP3A4
»»Why is it too simple to classify transporters based on and CYP2C8 transcription, resulting in increased
an “absorption” and “exsorption” concept? paclitaxel metabolism. Thus, in response to a xenobi-
»»Would a drug transport process involving ABC trans- otic challenge, PXR can induce both a first line of
porter be considered a passive or active transport defense (intestinal excretion) and a backup system
process? (hepatic drug inactivation) that limits exposure to
potentially toxic compounds. In contrast to paclitaxel,
»»How does a transporter influence the level of drug
docetaxel is a closely related antineoplastic agent that
within the cell?
does not activate PXR but has a much better absorp-
tion profile.
P-gp affects the bioavailability of many sub- Mutations of other transporters, particularly
strate drugs listed in Table 14-5. P-gp inhibitors those involved in reuptake of serotonin, dopamine,
should be carefully evaluated before coadministra- and gamma-aminobutyric acid (GABA), are pres-
tion with a P-gp substrate drug. Other transporters ently being studied with regard to clinically relevant
are also present in the intestines (Tsuji and Tamai, changes in drug response. Pharmacogenetic variabil-
1996). For example, many oral cephalosporins are ity in these transporters is an important consideration
Physiologic Factors Related to Drug Absorption 387
TABLE 145 Reported Substrates of P-gp—A Member of ATP-Binding Cassette (ABC) Transporters
Acebutolol, acetaminophen, actinomycin d, h-acetyldigoxin, amitriptyline, amprenavir, apafant, asimadoline, atenolol,
atorvastatin, azidopine, azidoprocainamide methoiodide, azithromycin
Benzo(a)pyrene, betamethasone, bisantrene, bromocriptine, bunitrolol, calcein-AM
Camptothecin, carbamazepine, carvedilol, celiprolol, cepharanthin, cerivastatin, chloroquine, chlorpromazine, chlorothiazide,
Clarithromycin, colchicine, corticosterone, cortisol, cyclosporin A
Daunorubicin (daunomycin), debrisoquine, desoxycorticoster one, dexamethasone, digitoxin,
Digoxin, diltiazem, dipyridamole, docetaxel, dolastatin 10, domperidone, doxorubicin (adriamycin)
Eletriptan, emetine, endosulFan, erythromycin, estradiol, estradiol-17h-d-glucuronide, etoposide (VP-16)
Fexofenadine, gf120918, grepafloxacin
Hoechst 33342, hydroxyrubicin, imatinib, indinavir, ivermectin
Levofloxacin, loperamide, losartan, lovastatin
Methadone, methotrexate, methylprednisolone, metoprolol, mitoxantrone, monensin
Morphine, 99mtc-sestamibi
N-desmethyltamoxifen, nadolol, nelfinavir, nicardipine, nifedipine, nitrendipine, norverapamil
Olanzapine, omeprazole
PSC-833 (valspodar), perphenazine, prazosin, prednisone, pristinamycin IA, puromycin
Quetiapine, quinidine, quinine
Ranitidine, reserpine
Rhodamine 123, risperidone, ritonavir, roxithromycin
Saquinavir, sirolimus, sparfloxacin, sumatriptan,
Tacrolimus, talinolol, tamoxifen, Taxol (paclitaxel), telithromycin, terfenadine, timolol, toremifene
Tributylmethylammonium, trimethoprim
Valinomycin, vecuronium, verapamil, vinblastine
Vincristine, vindoline, vinorelbine
Adapted from Takano et al (2006), with permission.
in patient dosing. When therapeutic failures occur, specific macromolecules into and out of a cell,
the following questions should be asked: (1) Is the respectively.
drug a substrate for P-gp and/or CYP3A4? (2) Is the During pinocytosis, phagocytosis, or transcyto-
drug being coadministered with anything that inhibits sis, the cell membrane invaginates to surround the
P-gp and/or CYP3A4? For example, grapefruit juice material and then engulfs the material, incorporat-
and many drugs can affect drug metabolism and oral ing it inside the cell (Fig. 14-11). Subsequently, the
absorption. cell membrane containing the material forms a ves-
icle or vacuole within the cell. Transcytosis is the
Vesicular Transport process by which various macromolecules are trans-
Vesicular transport is the process of engulfing parti- ported across the interior of a cell. In transcytosis,
cles or dissolved materials by the cell. Pinocytosis and the vesicle fuses with the plasma membrane to
phagocytosis are forms of vesicular transport that dif- release the encapsulated material to another side of
fer by the type of material ingested. Pinocytosis refers the cell. Vesicles are employed to intake the macro-
to the engulfment of small solutes or fluid, whereas molecules on one side of the cell, draw them across
phagocytosis refers to the engulfment of larger par- the cell, and eject them on the other side. Transcytosis
ticles or macromolecules, generally by macrophages. (sometimes referred to as vesicular transport) is
Endocytosis and exocytosis are the processes of moving the proposed process for the absorption of orally
388 Chapter 14
administered Sabin polio vaccine and various large
SXR
+ proteins.
Inactive
Paclitaxel Pinocytosis is a cellular process that permits the
Metabolites
active transport of fluid from outside the cell through
the membrane surrounding the cell into the inside of
the cell. In pinocytosis, tiny incuppings called caveolae
(little caves) in the surface of the cell close and then
pinch off to form pinosomes, little fluid-filled bubbles,
that are free within the cytoplasm of the cell.
An example of exocytosis is the transport of a
protein such as insulin from insulin-producing cells
of the pancreas into the extracellular space. The
insulin molecules are first packaged into intracellu-
SXR lar vesicles, which then fuse with the plasma mem-
+
Paclitaxel brane to release the insulin outside the cell.
MDR1
Excretion Pore (Convective) Transport
Very small molecules (such as urea, water, and sugars)
are able to cross cell membranes rapidly, as if the
FIGURE 1410 Mechanism of coordinated efflux and membrane contained channels or pores. Although
metabolism of paclitaxel by PXR (SXR). (From Synold et al, 2001, such pores have never been directly observed by
with permission.) microscopy, the model of drug permeation through
aqueous pores is used to explain renal excretion of
drugs and the uptake of drugs into the liver.
A certain type of protein called a transport protein
may form an open channel across the lipid membrane
of the cell (see Fig. 14-2). Small molecules including
Exocytosis drugs move through the channel by diffusion more
rapidly than at other parts of the membrane.
Ion-Pair Formation
Cytoplasm Strong electrolyte drugs are highly ionized or charged
molecules, such as quaternary nitrogen compounds
Endocytosis with extreme pKa values. Strong electrolyte drugs
maintain their charge at all physiologic pH values
and penetrate membranes poorly. When the ionized
drug is linked with an oppositely charged ion, an ion
pair is formed in which the overall charge of the pair
is neutral. This neutral drug complex diffuses more
easily across the membrane. For example, the forma-
tion of ion pairs to facilitate drug absorption has been
demonstrated for propranolol, a basic drug that forms
an ion pair with oleic acid, and quinine, which forms
ion pairs with hexylsalicylate (Nienbert, 1989).
FIGURE 1411 Diagram showing exocytosis and endo- An interesting application of ion pairs is the
cytosis. (From Alberts et al, 1989, with permission.) complexation of amphotericin B and DSPG
Physiologic Factors Related to Drug Absorption 389
(distearoylphosphatidylglycerol) in some amphotericin active metabolite. Coadministration of clopidogrel
B/liposome products. Ion pairing may transiently alter with omeprazole, an inhibitor of CYP2C19, reduces
distribution, reduce high plasma free drug concentra- the pharmacological activity of clopidogrel if given
tion, and reduce renal toxicity. either concomitantly or 12 hours apart.
The dual effect of a CYP isoenzyme and a trans-
porter on drug absorption is not always easy to deter-
DRUG INTERACTIONS IN THE mine or predict based on pharmacokinetic studies
GASTROINTESTINAL TRACT alone. A well-studied example is the drug digoxin.
Digoxin is minimally metabolized (CYP3A4), orally
Many agents (drug or chemical substances) may absorbed (Suzuki and Sugiyama, 2000), and a sub-
have dual roles as substrate and/or inhibitor between strate for P-gp based on:
CYP3A4 and P-glycoprotein, P-gp. Simultaneous
1. Human polymorphism single-nucleotide poly-
administration of these agents results in an increase
morphism (SNP) in exon 26 (C3435T) results
in the oral drug bioavailability of one or both of the
in a reduced intestinal expression level of P-gp,
drugs. Various drug–drug and drug–nutrient interac-
along with increased oral bioavailability of
tions involving oral bioavailability have been
digoxin.
reported in human subjects (Thummel and Wilkinson,
2. Ketoconazole increases the oral bioavailability
1998; Di Marco et al, 2002; von Richter et al, 2004).
and shortens mean absorption time from 1.1
Many commonly used medications (eg, dextro-
to 0.3 hour. Ketoconazole is a substrate and
methorphan hydrobromide) and certain food groups
inhibitor of P-gp; P-gp can subsequently influ-
(eg, grapefruit juice) are substrates both for the
ence bioavailability. The influence of P-gp is
efflux transporter, P-gp, and for the CYP3A enzymes
not always easily detected unless studies are
involved in biotransformation of drugs (see Chapter 12).
designed to investigate its presence.
Grapefruit juice also affects drug transport in the
intestinal wall. Certain components of grapefruit juice For this analysis, a drug is given orally and intra-
(such as naringin and bergamottin) are responsible for venously before and after administration of an inhibitor
the inhibition of P-gp and CYP3A. Di Marco et al drug. The AUC of the drug is calculated for each case.
(2002) demonstrated the inhibitory effect of grapefruit For example, ketoconazole causes an increase in the
and Seville orange juice on the pharmacokinetics of oral bioavailability of the immunosuppressant tacroli-
dextromethorphan. Using dextromethorphan as the mus from 0.14 to 0.30, without affecting hepatic bio-
substrate, these investigators showed that grapefruit availability (0.96–0.97) (Suzuki and Sugiyama, 2000).
juice inhibits both CYP3A activity as well as P-gp Since hepatic bioavailability is similar, the increase in
resulting in an increased bioavailability of dextro- bioavailability from 0.14 to 0.30 is the result of keto-
methorphan. Grapefruit juice has been shown to conazole suppression on P-gp.
increase the oral bioavailability of many drugs, such Mouly and Paine (2003) reported P-gp expres-
as cyclosporine or saquinavir, by inhibiting intestinal sion determined by Western blotting along the
metabolism. entire length of the human small intestine. They
Esomeprazole (Nexium) and omeprazole (Prilosec) found that relative P-gp levels increased progres-
are proton pump inhibitors that inhibit gastric acid sively from the proximal to the distal region. von
secretion, resulting an increased stomach pH. Richter et al (2004) measured P-gp as well as
Esomeprazole and omeprazole may interfere with the CYP3A4 in paired human small intestine and liver
absorption of drugs where gastric pH is an important specimens obtained from 15 patients. They reported
determinant of bioavailability (eg, ketoconazole, iron that much higher levels of both P-gp (about seven
salts, and digoxin). Both esomeprazole and omepra- times) and CYP3A4 (about three times) were found
zole are extensively metabolized in the liver by in the intestine than in the liver, suggesting the
CYP2C19 and CYP3A4. The prodrug clopidogrel critical participation of intestinal P-gp in limiting
(Plavix) inhibits platelet aggregation entirely due to an oral drug bioavailability.
390 Chapter 14
The concept of drug–drug interactions has
received increased attention in recent years, as they
may be responsible for many drug therapy-induced
medical problems (Johnson et al, 1999).
Frequently Asked Questions
»»Animal studies are not definitive when extrapo-
lated to humans. Why are animal studies or in vitro
transport studies in human cells often performed to Esophagus
decide whether a drug is a P-gp substrate?
»»How would you demonstrate that digoxin metabo-
lism is solely due to hepatic extraction and not due to
intestinal extraction since both CYP3A4 and P-gp are Diaphragm
present in the intestine in larger amounts? Stomach
Liver
Pylorus
Gallbladder
Duodenum Antrum
ORAL DRUG ABSORPTION Transverse Pancreas
colon Jejunum
Ascending
The oral route of administration is the most common Ileum
colon
and popular route of drug dosing. The oral dosage Cecum Descending
form must be designed to account for extreme pH Appendix colon
ranges, the presence or absence of food, degradative Rectum
enzymes, varying drug permeability in the different
regions of the intestine, and motility of the gastroin-
testinal tract. In this chapter we will discuss intesti- FIGURE 1412 Gastrointestinal tract.
nal variables that affect absorption; dosage-form
considerations are discussed in Chapters 15–18.
involved in the digestion of carbohydrates and pro-
Anatomic and Physiologic Considerations teins. Other secretions, such as mucus, protect the
The normal physiologic processes of the alimentary linings of the lumen of the GI tract. Digestion is the
canal may be affected by diet, contents of the gastro- breakdown of food constituents into smaller struc-
intestinal (GI) tract, hormones, the visceral nervous tures in preparation for absorption. Food constituents
system, disease, and drugs. Thus, drugs given by the are mostly absorbed in the proximal area (duodenum)
enteral route for systemic absorption may be affected of the small intestine. The process of absorption is
by the anatomy, physiologic functions, and contents the entry of constituents from the lumen of the gut
of the alimentary tract. Moreover, the physical, chem- into the body. Absorption may be considered the net
ical, and pharmacologic properties of the drug and the result of both lumen-to-blood and blood-to-lumen
formulation of the drug product will also affect sys- transport movements.
temic drug absorption from the alimentary canal. Drugs administered orally pass through various
The enteral system consists of the alimentary parts of the enteral canal, including the oral cavity,
canal from the mouth to the anus (Fig. 14-12). The esophagus, and various parts of the gastrointestinal
major physiologic processes that occur in the GI sys- tract. Residues eventually exit the body through the
tem are secretion, digestion, and absorption. Secretion anus. The total transit time, including gastric emptying,
includes the transport of fluid, electrolytes, peptides, small intestinal transit, and colonic transit, ranges
and proteins into the lumen of the alimentary canal. from 0.4 to 5 days (Kirwan and Smith, 1974). The
Enzymes in saliva and pancreatic secretions are also small intestine, particularly the duodenum area, is
Physiologic Factors Related to Drug Absorption 391
the most important site for drug absorption. Small local irritation. Very little drug dissolution occurs in
intestine transit time (SITT) ranges from 3 to 4 hours the esophagus.
for most healthy subjects. If absorption is not com-
pleted by the time a drug leaves the small intestine, Stomach
absorption may be erratic or incomplete. The stomach is innervated by the vagus nerve.
The small intestine is normally filled with diges- However, local nerve plexus, hormones, mechanore-
tive juices and liquids, keeping the lumen contents ceptors sensitive to the stretch of the GI wall, and
fluid. In contrast, the fluid in the colon is reabsorbed, chemoreceptors control the regulation of gastric
and the lumenal content in the colon is either semi- secretions, including acid and stomach emptying.
solid or solid, making further drug dissolution and The fasting pH of the stomach is about 2–6. In the
absorption erratic and difficult. The lack of the solu- presence of food, the stomach pH is about 1.5–2, due
bilizing effect of the chyme and digestive fluid con- to hydrochloric acid secreted by parietal cells.
tributes to a less favorable environment for drug Stomach acid secretion is stimulated by gastrin and
absorption. histamine. Gastrin is released from G cells, mainly
in the antral mucosa and also in the duodenum.
Oral Cavity Gastrin release is regulated by stomach distention
(swelling) and the presence of peptides and amino
Saliva is the main secretion of the oral cavity, and it
acids. A substance known as intrinsic factor enhances
has a pH of about 7. Saliva contains ptyalin (salivary
vitamin B-12 (cyanocobalamin) absorption. Various
amylase), which digests starches. Mucin, a glyco-
gastric enzymes, such as pepsin, which initiates pro-
protein that lubricates food, is also secreted and may
tein digestion, are secreted into the gastric lumen to
interact with drugs. About 1500 mL of saliva is secreted
initiate digestion.
per day.
Basic drugs are solubilized rapidly in the pres-
The oral cavity can be used for the buccal
ence of stomach acid. Mixing is intense and pressur-
absorption of lipid-soluble drugs such as fentanyl
ized in the antral part of the stomach, a process of
citrate (Actiq®) and nitroglycerin, also formulated
breaking down large food particles described as
for sublingual routes. Recently, orally disintegrating
antral milling. Food and liquid are emptied by open-
tablets, ODTs, have become available. These ODTs,
ing the pyloric sphincter into the duodenum. Stomach
such as aripiprazole (Abilify Discmelt®), rapidly
emptying is influenced by the food content and
disintegrate in the oral cavity in the presence of
osmolality. Fatty acids and mono- and diglycerides
saliva. The resulting fragments, which are suspended
delay gastric emptying (Hunt and Knox, 1968).
in the saliva, are swallowed and the drug is then
High-density foods generally are emptied from the
absorbed from the gastrointestinal tract. A major
stomach more slowly. The relation of gastric empty-
advantage for ODTs is that the drug may be taken
ing time to drug absorption is discussed more fully
without water. In the case of the antipsychotic drug,
in the next section.
aripiprazole, a nurse may give the drug in the form
Stomach pH may be increased due to the pres-
of an ODT (Abilify Discmelt) to a schizophrenic
ence of food and certain drugs such as omeprazole,
patient. The nurse can easily ascertain that the drug
a proton pump inhibitor used in gastroesophageal
was taken and swallowed.
reflux disease (GERD). Increased stomach pH may
cause a drug interaction with enteric-coated drug
Esophagus products (eg, diclofenac enteric-coated tablets,
The esophagus connects the pharynx and the cardiac Voltaren). Such drug products require acid pH in the
orifice of the stomach. The pH of the fluids in the stomach to delay drug release from the dosage form
esophagus is between 5 and 6. The lower part of the until it reaches the higher pH of the intestine. If the
esophagus ends with the esophageal sphincter, stomach pH is too high, the enteric-coated drug
which prevents acid reflux from the stomach. product may release the drug in the stomach, thus
Tablets or capsules may lodge in this area, causing causing irritation to the stomach.
392 Chapter 14
A few fat-soluble, acid-stable drugs may be as 8. Due to the presence of bicarbonate secretion, acid
absorbed from the stomach by passive diffusion. drugs will dissolve in the ileum. Bile secretion helps
Ethanol is completely miscible with water, easily dissolve fats and hydrophobic drugs. The ileocecal
crosses cell membranes, and is efficiently absorbed valve separates the small intestine from the colon.
from the stomach. Ethanol is more rapidly absorbed
from the stomach in the fasting state compared to the Colon
fed state (Levitt et al, 1997). The colon lacks villi and has limited drug absorption
due to lack of large surface area, blood flow, and the
Duodenum more viscous and semisolid nature of the lumen con-
A common duct from both the pancreas and the gall- tents. The colon is lined with mucin that functions as
bladder enters into the duodenum. The duodenal pH lubricant and protectant. The pH in this region is
is about 6–6.5, because of the presence of bicarbon- 5.5–7 (Shareef et al, 2003). A few drugs, such as
ate that neutralizes the acidic chyme emptied from theophylline and metoprolol, are absorbed in this
the stomach. The pH is optimum for enzymatic region. Drugs that are absorbed well in this region
digestion of protein and peptide-containing food. are good candidates for an oral sustained-release
Pancreatic juice containing enzymes is secreted into dosage form. The colon contains both aerobic and
the duodenum from the bile duct. Trypsin, chymo- anaerobic microorganisms that may metabolize
trypsin, and carboxypeptidase are involved in the some drugs. For example, l-dopa and lactulose are
hydrolysis of proteins into amino acids. Amylase is metabolized by enteric bacteria. Crohn’s disease
involved in the digestion of carbohydrates. Pancreatic affects the colon and thickens the bowel wall. The
lipase secretion hydrolyzes fats into fatty acid. The microflora also become more anaerobic. Absorption
complex fluid medium in the duodenum helps dis- of clindamycin and propranolol is increased, whereas
solve many drugs with limited aqueous solubility. other drugs have reduced absorption with this dis-
The duodenum is the major site for passive drug ease (Rubinstein et al, 1988). A few delayed-release
absorption due to both its anatomy, which creates a drug products such as mesalamine (Asacol tablets,
high surface area, and high blood flow. The duode- Pentasa capsules) have a pH-sensitive coating that
num is a site where many ester prodrugs are hydro- dissolves in the higher pH of the lower bowel, releas-
lyzed during absorption. Proteolytic enzymes in the ing the mesalamine to act locally in Crohn’s disease.
duodenum degrade many protein drugs preventing Balsalazide disodium capsules (Colazal), also used
adequate absorption of the intact protein drug. in Crohn’s disease, is a prodrug containing an azo
group that is cleaved by anaerobic bacteria in the
Jejunum lower bowel to produce mesalamine (5-aminosali-
The jejunum is the middle portion of the small intes- cylic acid or 5-ASA), an anti-inflammatory drug.
tine, between the duodenum and the ileum. Digestion
of protein and carbohydrates continues after addition Rectum
of pancreatic juice and bile in the duodenum. This The rectum is about 15 cm long, ending at the anus.
portion of the small intestine generally has fewer In the absence of fecal material, the rectum has a
contractions than the duodenum and is preferred for small amount of fluid (approximately 2 mL) with a
in vivo drug absorption studies. pH of about 7. The rectum is perfused by the superior,
middle, and inferior hemorrhoidal veins. The inferior
Ileum hemorrhoidal vein (closest to the anal sphincter) and
The ileum is the terminal part of the small intestine. the middle hemorrhoidal vein feed into the vena cava
This site also has fewer contractions than the duode- and back to the heart, thus bypassing the liver and
num and may be blocked off by catheters with an avoiding hepatic first-pass effect. The superior hemor-
inflatable balloon and perfused for drug absorption rhoidal vein joins the mesenteric circulation, which
studies. The pH is about 7, with the distal part as high feeds into the hepatic portal vein and then to the liver.
Physiologic Factors Related to Drug Absorption 393
The small amount of fluid present in the rectum Factors Affecting Drug Absorption in the
has virtually no buffer capacity; as a consequence, Gastrointestinal Tract
the dissolving drug(s) or even excipients can have a Drugs may be absorbed by passive diffusion from all
determining effect on the existing pH in the anorec- parts of the alimentary canal including sublingual,
tal area. Drug absorption after rectal administration buccal, GI, and rectal absorption. For most drugs, the
may be variable, depending on the placement of the optimum site for drug absorption after oral adminis-
suppository or drug solution within the rectum. A tration is the upper portion of the small intestine or
portion of the drug dose may be absorbed via the duodenum region. The unique anatomy of the duode-
lower hemorrhoidal veins, from which the drug num provides an immense surface area for the drug
feeds directly into the systemic circulation; some to diffuse passively (Fig. 14-13). The large surface
drugs may be absorbed via the superior hemor- area of the duodenum is due to the presence of valve-
rhoidal vein, which feeds into the mesenteric veins like folds in the mucous membrane on which are
to the hepatic portal vein to the liver, and be metabo- small projections known as villi. These villi contain
lized before systemic absorption. Thus some of the even smaller projections known as microvilli, form-
variability in drug absorption following rectal ing a brush border. In addition, the duodenal region is
administration may occur due to variation in the site highly perfused with a network of capillaries, which
of absorption within the rectum.
STRUCTURE INCREASE IN SURFACE AREA
SURFACE AREA (sq cm)
(relative to cylinder)
280 cm
Area of 1 3300
simple cylinder
Folds of Kerckring 3 10,000
(valvulae conniventes)
Villi 30 100,000
Microvilli 600 2,000,000
FIGURE 1413 Three mechanisms for increasing surface area of the small intestine. The increase in surface area is due to folds
of Kerkring, villi, and microvilli. (From Wilson, 1962, with permission.)
4 cm
394 Chapter 14
helps maintain a concentration gradient from the (Table 14-6). The pylorus and ileocecal valves pre-
intestinal lumen and plasma circulation. vent regurgitation or movement of food from the
distal to the proximal direction.
Gastrointestinal Motility
Once a drug is given orally, the exact location and/or Gastric Emptying Time
environment of the drug product within the GI tract is Anatomically, a swallowed drug rapidly reaches the
difficult to discern. GI motility tends to move the stomach. Eventually, the stomach empties its con-
drug through the alimentary canal, so the drug may tents into the small intestine. Because the duodenum
not stay at the absorption site. For drugs given orally, has the greatest capacity for the absorption of drugs
an anatomic absorption window may exist within the from the GI tract, a delay in the gastric emptying
GI tract in which the drug is efficiently absorbed. time for the drug to reach the duodenum will slow the
Drugs contained in a nonbiodegradable controlled- rate and possibly the extent of drug absorption,
release dosage form should be completely released thereby prolonging the onset time for the drug. Some
into this absorption window to be absorbed before the drugs, such as penicillin, are unstable in acid and
movement of the dosage form into the large bowel. decompose if stomach emptying is delayed. Other
The transit time of the drug in the GI tract drugs, such as aspirin, may irritate the gastric mucosa
depends on the physicochemical and pharmacologic during prolonged contact.
properties of the drug, the type of dosage form, and A number of factors affect gastric emptying
various physiologic factors. Movement of the drug time. Some factors that tend to delay gastric empty-
within the GI tract depends on whether the alimen- ing include consumption of meals high in fat, cold
tary canal contains recently ingested food (digestive beverages, and anticholinergic drugs (Burks et al,
or fed state) or is in the fasted or interdigestive state 1985; Rubinstein et al, 1988). Liquids and small
(Fig. 14-14). During the fasted or interdigestive state, particles less than 1 mm are generally not retained in
alternating cycles of activity known as the migrating the stomach. These small particles are believed to be
motor complex (MMC) act as a propulsive movement emptied due to a slightly higher basal pressure in the
that empties the upper GI tract to the cecum. Initially, stomach over the duodenum. Different constituents
the alimentary canal is quiescent. Then, irregular of a meal empty from the stomach at different rates.
contractions followed by regular contractions with Feldman et al (1984) observed that 10 oz of liquid
high amplitude (housekeeper waves) push any resid- soft drink, scrambled egg (digestible solid), and a
ual contents distally or farther down the alimentary radio-opaque marker (undigestible solid) were 50%
canal. In the fed state, the migrating motor complex emptied from the stomach in 30 minutes, 154 minutes,
is replaced by irregular contractions, which have the and 3–4 hours, respectively. Thus, liquids are generally
effect of mixing intestinal contents and advancing the emptied faster than digested solids from the stomach
intestinal stream toward the colon in short segments (Fig. 14-15).
Bile Mucus
secretion discharge
Phase I II III IV
Feeding
Force of
contractions
Duration
(minutes) 30–60 20–40 10–20 0–5
Interdigestive (fasted) state Digestive (fed) state
FIGURE 1414 A pictorial representation of the typical motility patterns in the interdigestive (fasted) and digestive (fed) state.
(From Rubinstein et al, 1988, with permission.)
Physiologic Factors Related to Drug Absorption 395
TABLE 146 Characteristics of the Motility Patterns in the Fasted Dog
Phase Duration Characteristics
Fasted State
I 30–60 min Quiescence.
II 20–40 min • Irregular contractions
• Medium amplitude but can be as high as phase III
• Bile secretion begins
• Onset of gastric discharge of administered fluid of small volume usually
occurs before that of particle discharge
• Onset of particle and mucus discharge may occur during the latter part
of phase II
III 5–15 min • Regular contractions (4–5 contractions/min) with high amplitude
• Mucus discharge continues
• Particle discharge continues
IV 0–5 min • Irregular contractions
• Medium descending amplitude
• Sometimes absent
Fed State
One phase only As long as food is present in • Regular, frequent contractions.
the stomach • Amplitude is lower than phase III
• 4–5 contractions/min
From Rubinstein et al (1988), with permission.
Large particles, including tablets and capsules, presence of food in the stomach. Indigestible solids
are delayed from emptying for 3–6 hours by the empty very slowly, probably during the interdiges-
tive phase, a phase in which food is not present and
the stomach is less motile but periodically empties
its content due to housekeeper wave contraction
100 (Fig. 14-16).
Solid
80
60 Motor activities during fasting
(interdigestive phases)
40 1
Liquid 2
20
3
0 4
0 20 40 60 80 100 120
Time after meal (minutes) 1 minute
FIGURE 1415 Gastric emptying of a group of normal FIGURE 1416 Motor activity responsible for gastric
subjects using the dual-isotope method. The mean and 1 SE of emptying of indigestible solids. Migrating myoelectric com-
the fraction of isotope remaining in the stomach are depicted at plex (MMC), usually initiated at proximal stomach or lower
various time intervals after ingestion of the meal. Note the expo- esophageal sphincter, and contractions during phase 3 sweep
nential nature of liquid emptying and the linear process of solid indigestible solids through open pylorus. (From Minami and
emptying. (From Minami and McCallum, 1984, with permission.) McCallum, 1984, with permission.)
Isotope in stomach (percent)
Phase
396 Chapter 14
Intestinal Motility favoring absorption. Once the drug is absorbed from
Normal peristaltic movements mix the contents of the small intestine, it enters via the mesenteric vessels
the duodenum, bringing the drug particles into inti- to the hepatic-portal vein and goes to the liver prior
mate contact with the intestinal mucosal cells. The to reaching the systemic circulation. Any decrease in
drug must have a sufficient time (residence time) at mesenteric blood flow, as in the case of congestive
the absorption site for optimum absorption. In the heart failure, will decrease the rate of drug removal
case of high motility in the intestinal tract, as in diar- from the intestinal tract, thereby reducing the rate of
rhea, the drug has a very brief residence time and drug bioavailability (Benet et al, 1976).
less opportunity for adequate absorption.
The average normal SITT was about 7 hours as Absorption through the Lymphatic System
measured in early studies using indirect methods The role of the lymphatic circulation in drug absorp-
based on the detection of hydrogen after an oral dose tion is well established. Lipophilic drugs may be
of lactulose (fermentation of lactulose by colon bac- absorbed through the lacteal or lymphatic vessels
teria yields hydrogen in the breath). Newer studies under the microvilli. Absorption of drugs through
using gamma scintigraphy have shown SITT to be the lymphatic system bypasses the liver and avoids
about 3–4 hours. Thus a drug may take about 4–8 hours the first-pass effect due to liver metabolism, because the
to pass through the stomach and small intestine dur- lymphatic vessels drain into the vena cava rather
ing the fasting state. During the fed state, SITT may than the hepatic-portal vein. The lymphatics are
take 8–12 hours. For modified-release or controlled- important in the absorption of dietary lipids and may
dosage forms, which slowly release the drug over an be partially responsible for the absorption of some
extended period of time, the dosage form must stay lipophilic drugs. Many poorly water-soluble drugs
within a certain segment of the intestinal tract so that are soluble in oil and lipids, which may dissolve in
the drug contents are released and absorbed before loss chylomicrons and be absorbed systemically via the
of the dosage form in the feces. Intestinal transit is lymphatic system. Bleomycin or aclarubicin were
discussed further in relation to the design of sustained- prepared in chylomicrons to improve oral absorption
release products in Chapter 19. through the lymphatic system (Yoshikawa et al, 1983,
In one study reported by Shareef et al (2003), 1989). Other drugs that can be significantly absorbed
utilizing a radio-opaque marker, mean mouth-to- through the lymphatic system include halofantrine,
anus transit time was 53.3 hours. The mean colon certain testosterone derivatives, temarotene, ontazo-
transit time was 35 hours, with 11.3 hours for the last, vitamin D-3, and the pesticide DDT. Notably, as
right (ascending transverse portion), 11.4 hours for the trend in drug development is to produce more
the left (descending and portion of the transverse), highly potent lipophilic drugs, targeting of the lym-
and 12.4 hours for the recto sigmoid colon. Dietary phatic system is receiving increased attention. In
fiber has the greatest effect on colonic transit. such efforts, the formulation of lipid excipients plays
Dietary fiber increases fecal weight, partly by retain- a very dramatic role in the success of lymphatic tar-
ing water and partly by increasing bacterial mass geting (Yanez et al, 2011).
(Shareef et al, 2003).
Effect of Food on Gastrointestinal
Perfusion of the Gastrointestinal Tract Drug Absorption
The blood flow to the GI tract is important in carry- The presence of food in the GI tract can affect the
ing absorbed drug to the systemic circulation. A large bioavailability of the drug from an oral drug product
network of capillaries and lymphatic vessels perfuse (Table 14-7). Digested foods contain amino acids,
the duodenal region and peritoneum. The splanchnic fatty acids, and many nutrients that may affect intes-
circulation receives about 28% of the cardiac output tinal pH and solubility of drugs. The effects of food
and is increased after meals. This high degree of per- are not always predictable and can have clinically
fusion helps to maintain a concentration gradient significant consequences. Some effects of food on
Physiologic Factors Related to Drug Absorption 397
TABLE 147 The Affect of Food on the Bioavailability of Selected Drugs
Drug Food Affect
Decreased bioavailability with food
Doxycycline The mean Cmax and AUC0-∞ of doxycycline are 24% and 13% lower, respectively, following single dose
Hyclate Delayed- administration with a high-fat meal (including milk) compared to fasted conditions.
Release Tablets
Atorvastatin Food decreases the rate and extent of drug absorption by approximately 25% and 9%, respectively,
calcium tablets as assessed by Cmax and AUC.
Clopidogrel Clopidogrel is a prodrug and is metabolized to a pharmacologically active metabolite and inactive
bisulfate tablets metabolites. The active metabolite AUC0-24 was unchanged in the presence of food, while there was a
57% decrease in active metabolite Cmax
Naproxen delayed- Naproxen delayed-release tablets are enteric coated tablets with a pH-sensitive coating. The presence of
release tablets food prolonged the time the tablets remained in the stomach. Tmax is delayed but peak naproxen levels,
Cmax was not affected.
Alendronate Bioavailability was decreased by approximately 40% when 10 mg alendronate was administered either
sodium tablets 0.5 or 1 hour before a standardized breakfast. Alendronate must be taken at least one-half hour before
the first food, beverage, or medication of the day with plain water only. Other beverages (including
mineral water), food, and some medications are likely to reduce drug absorption.
Tamsulosin HCl Taking tamsulosin capsules under fasted conditions results in a 30% increase in bioavailability (AUC) and
capsules 40% to 70% increase in peak concentrations (Cmax) compared to fed conditions.
Increased bioavailability with food
Oxycodone HCl CR Food has no significant effect on the extent of absorption of oxycodone from OxyContin. However,
tablets the peak plasma concentration of oxycodone increased by 25% when a OxyContin 160 mg tablet was
administered with a high-fat meal.
Metaxalone A high-fat meal increased Cmax by 177.5% and increased AUC (AUC0-t, AUC∞) by 123.5% and 115.4%,
Tablets respectively. Tmax was delayed (4.3 h versus 3.3 h) and terminal t1/2 was decreased (2.4 h versus 9.0 h).
Spironolactone Food increased the bioavailability of unmetabolized spironolactone by almost 100%. The clinical
tablets importance of this finding is not known
Food has very little affect on bioavailability
Gabapentin Food has only a slight effect on the rate and extent of absorption of gabapentin (14% increase in AUC
capsules and Cmax).
Tramadol HCl Oral administration of Tramadol hydrochloride tablets with food does not significantly affect its rate or
tablets extent of absorption.
Digoxin tablets When digoxin tablets are taken after meals, the rate of absorption is slowed, but the total amount of
digoxin absorbed is usually unchanged. When taken with meals high in bran fiber, however, the amount
absorbed from an oral dose may be reduced.
Bupropion HCl ER Food did not affect the Cmax or AUC of bupropion.
tablets
Methylphenidate In patients, there were no differences in either the pharmacokinetics or the pharmacodynamic performance
HCl ER tablets of Concerta® when administered after a high fat breakfast. There is no evidence of dose dumping in the
(Concerta®) presence or absence of food.
Fluoxetine HCl Food does not appear to affect the 846 systemic bioavailability of fluoxetine, although it may delay its
capsules absorption by 1 to 2 hours, which is probably not clinically significant.
Dutasteride soft Food reduces the Cmax by 10% to 15%. This reduction is of no clinical significance.
gelatin capsules
Food can affect bioavailability of the drug by affecting the rate and/or extent of drug absorption. In some cases, food may delay the Tmax for enteric coated
drugs due to a delay in stomach emptying time. For each drug, the clinical importance of the change in bioavailability due to food must be assessed.
398 Chapter 14
the bioavailability of a drug from a drug product
include (US Food and Drug Administration, Guidance
3.0 1-g oral doses
for Industry, December 2002):
High fat
• Delay in gastric emptying 2.5
• Stimulation of bile flow
• A change in the pH of the GI tract 2.0
Oleomargarine
• An increase in splanchnic blood flow 60 g
• A change in luminal metabolism of the drug substance 1.5
Oleomargarine
• Physical or chemical interaction of the meal with 30 g
1.0
the drug product or drug substance High protein,
no fat
Food effects on bioavailability are generally great- 0.5 Fasting
est when the drug product is administered shortly High fat
No griseofulvin
after a meal is ingested. The nutrient and caloric 0
0 4 8
contents of the meal, the meal volume, and the meal Hours
temperature can cause physiologic changes in the
FIGURE 1417 A comparison of the effects of different
GI tract in a way that affects drug product transit types of food intake on the serum griseofulvin levels following
time, luminal dissolution, drug permeability, and a 1.0-g oral dose. (From Crounse, 1961, with permission.)
systemic availability. In general, meals that are high
in total calories and fat content are more likely to
affect GI physiology and thereby result in a larger ensure that drugs will wash down the esophagus and
effect on the bioavailability of a drug substance or be more available for absorption. Generally, the bio-
drug product. The FDA recommends the use of availability of drugs is better in patients in the fasted
high-calorie and high-fat meals to study the effect state and with a large volume of water (Fig. 14-18).
of food on the bioavailability and bioequivalence of The solubility of many drugs is limited, and suffi-
drug products (FDA Guidance for Industry, 2002; cient fluid is necessary for dissolution of the drug.
see also Chapter 16). Some patients may be on several drugs that are
The absorption of some antibiotics, such as dosed frequently for months. These patients are
penicillin and tetracycline and certain hydrophilic often nauseous and are reluctant to take a lot of fluid.
drugs, is decreased with food, whereas other drugs, For example, HIV patients with active viral counts
particularly lipid-soluble drugs such as griseofulvin, may be on an AZT or DDI combination with one or
metaxalone, and metazalone, are better absorbed more of the protease inhibitors, Invirase
when given with food containing a high-fat content (Hoffmann-La Roche), Crixivan (Merck), or Norvir
(Fig. 14-17). The presence of food in the GI lumen (Abbott). These HIV treatments appear to be better
stimulates the flow of bile. Bile contains bile acids, than any previous treatments but depend on patient
which are surfactants involved in the digestion and compliance in taking up to 12–15 pills daily for
solubilization of fats, and also increases the solubil- weeks. Any complications affecting drug absorption
ity of fat-soluble drugs through micelle formation. can influence the outcome of these therapies. With
For some basic drugs (eg, cinnarizine) with limited antibiotics, unabsorbed drug may influence the GI
aqueous solubility, the presence of food in the stom- flora. For drugs that cause GI disturbances, residual
ach stimulates hydrochloric acid secretion, which drug dose in the GI tract can potentially aggravate
lowers the pH, causing more rapid dissolution of the the incidence of diarrhea.
drug and better absorption. Absorption of this basic Some drugs, such as erythromycin, iron salts,
drug is reduced when gastric acid secretion is aspirin, and nonsteroidal anti-inflammatory agents
reduced (Ogata et al, 1986). (NSAIDs), are irritating to the GI mucosa and are
Most drugs should be taken with a full glass given with food to reduce this irritation. For these
(approximately 8 fluid oz or 250 mL) of water to drugs, the rate of absorption may be reduced in the
mg/mL
Physiologic Factors Related to Drug Absorption 399
A
Carbohydrate B
2.5 Fat 9
Protein Carbohydrate
Fasting, 20 mL Fat
2.0 Fasting, 250 mL Protein
7 Fasting, 25 mL
Fasting, 250 mL
1.5
5
1.0
3
0.5
1
0 0
0 5 10 0 2 4 6
Time (hours) Time (hours)
FIGURE 1418 Effect of water volume and meal on the bioavailability of erythromycin and aspirin (ASA). (A) From Welling PG,
et al: Bioavailability of erythromycin state: influence of food and fluid volume. J Pharm Sci 67(6):764–766, June 1978, with permission.
(B) From Koch PA, et al: Influence of food and fluid ingestion on aspirin bioavailability. J Pharm Sci 67(11):1533–1535, November 1978,
with permission.
presence of food, but the extent of absorption may be rapid when given to a subject in the fed rather than
the same and the efficacy of the drug is retained. fasted state because of dosage form failures, known
The GI transit time for enteric-coated and non- as dose-dumping (Fig.14-19).
disintegrating drug products may also be affected by
the presence of food. Enteric-coated tablets may stay
in the stomach for a longer period of time because
food delays stomach emptying. Thus, the enteric- 35
Subject VA
coated tablet does not reach the duodenum rapidly, 30
Nausea, vomiting,
delaying drug release and systemic drug absorption.
25 headache
The presence of food may delay stomach emptying
of enteric-coated tablets or nondisintegrating dosage 20
forms for several hours. In contrast, since enteric- 15
coated beads or microparticles disperse in the
stomach, stomach emptying of the particles is less 10 After breakfast
Fasting
affected by food, and these preparations demonstrate 5
more consistent drug absorption from the duode-
0
num. Fine granules (smaller than 1–2 mm in size) 0 8 16 24 32 40 48 56 60
and tablets that disintegrate are not significantly Time (hours)
delayed from emptying from the stomach in the FIGURE 1419 Theophylline serum concentrations in
presence of food. an individual subject after a single 1500-mg dose of Theo-24
Food can also affect the integrity of the dosage taken during fasting and after breakfast. The shaded area indi-
form, causing an alteration in the release rate of the cates the period during which this patient experienced nausea,
repeated vomiting, or severe throbbing headache. The pattern
drug. For example, theophylline bioavailability from of drug release during the food regimen is consistent with
Theo-24 controlled-release tablets is much more “dose-dumping.” (From Hendeles et al, 1985, with permission.)
Serum level (mg/mL)
Plasma level (mg/mL)
Serum theophylline concentration (mg/mL)
400 Chapter 14
Food may enhance the absorption of a drug of nutrients with high caloric content supersedes that
beyond 2 hours after meals. For example, the timing faster rate and delays stomach emptying time.
of a fatty meal on the absorption of cefpodoxime Reduction in drug absorption may be caused by sev-
proxetil was studied in 20 healthy adults (Borin et al, eral other factors. For example, tetracycline hydro-
1995). The area under the plasma concentration–time chloride absorption is reduced by milk and food that
curve and peak drug concentration was significantly contains calcium, due to tetracycline chelation.
higher after administration of cefpodoxime proxetil However, significant reduction in absorption may
tablets with a meal and 2 hours after a meal relative simply be the result of reduced dissolution due to
to dosing under fasted conditions or 1 hour before a increased pH. Coadministration of sodium bicarbon-
meal. The time to peak concentration was not affected ate raises the stomach pH and reduces tetracycline
by food, which suggests that food increased the dissolution and absorption (Barr et al, 1971).
extent but not the rate of drug absorption. These Ticlopidine (Ticlid®) is an antiplatelet agent that
results indicate that absorption of cefpodoxime prox- is commonly used to prevent thromboembolic disor-
etil is enhanced with food or if the drug is taken ders. Ticlopidine has enhanced absorption after a
closely after a heavy meal. meal. The absorption of ticlopidine was compared in
Timing of drug administration in relation to subjects who received either an antacid or food or
meals is often important. Pharmacists regularly were in a control group (fasting). Subjects who
advise patients to take a medication either 1 hour received ticlopidine 30 minutes after a fatty meal had
before or 2 hours after meals to avoid any delay in an average increase of 20% in plasma concentrations
drug absorption. over fasting subjects, whereas antacid reduced
Alendronate sodium (Fosamax®) is a bisphos- ticlopidine plasma concentrations by approximately
phonate that acts as a specific inhibitor of osteoclast- the same amount. There was a higher incidence of
mediated bone resorption used to prevent osteoporosis. gastrointestinal complaint in the fasting group. Many
Bisphosphonates are very soluble in water and their other drugs have reduced gastrointestinal side effects
systemic oral absorption is greatly reduced in the when taken with food. The decreased gastrointestinal
presence of food. The approved labeling for alendro- side effects associated with food consumption may
nate sodium states that (Fosamax) “must be taken at greatly improve tolerance and compliance in patients.
least one-half hour before the first food, beverage, or
medication of the day with plain water only.” Double-Peak Phenomenon
Since fatty foods may delay stomach emptying Some drugs, such as ranitidine, cimetidine, and
time beyond 2 hours, patients who have just eaten a dipyridamole, after oral administration produce a
heavy, fatty meal should take these drugs 3 hours or blood concentration curve consisting of two peaks
more after the meal, whenever possible. Products (Fig. 14-20). This double-peak phenomenon is gen-
that are used to curb stomach acid secretion are usu- erally observed after the administration of a single
ally taken before meals, in anticipation of acid secre- dose to fasted patients. The rationale for the double-
tion stimulated by food. Famotidine (Pepcid) and peak phenomenon has been attributed to variability
cimetidine (Tagamet) are taken before meals to curb in stomach emptying, variable intestinal motility, pres-
excessive acid production. In some cases, drugs are ence of food, enterohepatic recycling, or failure of a
taken directly after a meal or with meals to increase tablet dosage form.
the systemic absorption of the drug (eg, itraconazole, The double-peak phenomenon observed for
metaxalone) or with food to decrease gastric irrita- cimetidine (Oberle and Amidon, 1987) may be due to
tion of the drug (eg, ibuprofen). Many lipophilic variability in stomach emptying and intestinal flow
drugs have increased bioavailability with food pos- rates during the entire absorption process after a sin-
sibly due to formation of micelles in the GI tract and gle dose. For many drugs, very little absorption occurs
some lymphatic absorption. in the stomach. For a drug with high water solubility,
Fluid volume tends to distend the stomach and dissolution of the drug occurs in the stomach, and
speed up stomach emptying; however, a large volume partial emptying of the drug into the duodenum will
Physiologic Factors Related to Drug Absorption 401
1.0 showed that a tablet that does not disintegrate or
A
incompletely disintegrates may have delayed gastric
emptying, resulting in a second absorption peak.
0.5
0
0 1 2 3 4 5 6
ORAL DRUG ABSORPTION DURING
1.5 B DRUG PRODUCT DEVELOPMENT
1.0 Prediction of Oral Drug Absorption
During the screening of new chemical entities for
0.5 possible therapeutic efficacy, some drugs might
not be discovered due to lack of systemic absorp-
0 tion after oral administration. Lipinski et al (2001)
0 1 2 3 4 5 6 reviewed the chemical structure of many orally
1.5 C administered drugs and published the Rule of Five.
During drug screening, “Rule of Five” predicts that
1.0 poor drug absorption or permeation is more likely
when there are more than five H-bond (hydrogen-
bond) donors. For 10 H-bond acceptors, the molecu-
0.5
lar weight (MWT) is greater than 500, and the
calculated log P (Clog P) is greater than 5 (or Mlog
0
0 1 2 3 4 5 6 P > 4.15). The rule is based on molecular computa-
Time (hours) tion and simulation and the effect of hydrophobicity,
FIGURE 1420 Serum concentrations of dipyridamole in hydrogen bond, molecular size, and other relevant
three groups of four volunteers each. (A) After taking 25 mg as factors in assessing absorption using computational
tablet intact. (B) As crushed tablet. (C) As tablet intact 2 hours methods. The method is not applicable to drugs
before lunch. (From Mellinger TJ, Bohorfoush JG: Blood levels whose absorption involves transporters. These rules
of dipyridamole (Persantin) in humans. Arch Int Pharmacodynam
were developed to avoid types of chemical structures
Ther 163:471–480, 1966, with permission.)
during early drug development that are unlikely to
have adequate bioavailability. These rules have been
result in the first absorption peak. A delay in stomach modified by others (Takano et al, 2006). Rules for
emptying results in a second absorption peak as the drug molecules that would improve the chance for
remainder of the dose is emptied into the duodenum. oral absorption would include:
In contrast, ranitidine (Miller, 1984) produces a
• Molecular weight ≤500 Da
double peak after both oral or parenteral (IV bolus)
• Not more than five H-bond donors (nitrogen or
administration. Ranitidine is apparently concen-
oxygen atoms with one or more hydrogen atoms)
trated in the bile within the gallbladder from the
(O−H or N−H group)
general circulation after IV administration. When
• Not more than 10 H-bond acceptors (nitrogen or
stimulated by food, the gallbladder contracts and
oxygen atoms)
bile-containing drug is released into the small intes-
• An octanol–water partition coefcient, log P ≤ 5.0
tine. The drug is then reabsorbed and recycled
(enterohepatic recycling). These rules only help predict adequate drug absorp-
Tablet integrity may also be a factor in the pro- tion and do not predict adequate pharmacodynamic
duction of a double-peak phenomenon. Mellinger activity. Moreover, some chemical structures do not
and Bohorfoush (1966) compared a whole tablet or follow the above rules, but may have good therapeu-
a crushed tablet of dipyridamole in volunteers and tic properties.
Dipyridamole serum (mg/mL)
402 Chapter 14
Burton et al (2002) reviewed the difficulty in the stomach or the GI tract is monitored using a
predicting drug absorption based only on physico- gamma camera. Simultaneously, blood levels or uri-
chemical activity of drug molecules and discussed nary excretion of the drug may be measured. This
other factors that can affect oral drug absorption. study can be used to correlate residence time of the
Burton et al state that drug absorption is a complex drug in a given region after capsule breakup to drug
process dependent upon drug properties such as absorption. The same technique is used to study drug
solubility and permeability, formulation factors, and absorption mechanisms in different regions of the GI
physiological variables, including regional permea- tract before a drug is formulated for extended
bility differences, pH, mucosal enzymology, and release.
intestinal motility, among others. These investigators Gamma scintigraphy has been used to study the
point out that intestinal drug absorption, permeabil- effect of transit time on the absorption of theophyl-
ity, fraction absorbed, and, in some cases, even bio- line (Sournac et al, 1988). In vitro drug release char-
availability are not equivalent properties and cannot acteristics were correlated with total gastrointestinal
be used interchangeably. Often these properties are transit time. The results showed a significant correla-
influenced by the nature of the drug product and tion between the in vitro release of theophylline and
physical and chemical characteristics of the drug. the percent of the total amount of theophylline
Software programs, such as GastroPlustm, have absorbed in vivo. This study illustrates the impor-
recently been developed to predict oral drug absorp- tance of gamma scintigraphy for the development of
tion, pharmacokinetics, and pharmacodynamic drugs specialized drug dosage forms.
in human and preclinical species. Simulation pro-
grams may use physicochemical data, such as molec-
ular weight, pKa, solubility at various pH, log P/log D, Markers to Study Effect of Gastric and GI
type of dosage form, in vitro inputs such as dissolution, Transit Time on Absorption
permeability/Caco-2, CYP metabolism (gut/liver), Many useful agents are available that may be used as
transporter rates, and in vivo inputs such as drug tools to study absorption and understand the mecha-
clearance and volume of distribution. nism of the absorptive process. For example, man-
nitol has a concentration-dependent effect on small
intestinal transit. Adkin et al (1995) showed that
METHODS FOR STUDYING FACTORS small concentrations of mannitol included in a phar-
THAT AFFECT DRUG ABSORPTION maceutical formulation could lead to reduced uptake
of many drugs absorbed exclusively from the small
Gamma Scintigraphy to Study Site intestine. No significant differences between the
of Drug Release gastric emptying times of the four solutions of dif-
Gamma scintigraphy is a technique commonly used ferent concentrations tested were observed.
to track drug dosage form movement from one Similarly, Hebden et al (1999) demonstrated
region to another within the GI tract after oral that codeine slowed GI transit, decreased stool water
administration. Gamma scintigraphy also has many content, and diminished drug absorption when com-
research applications and is widely used for formula- pared to controls. The results indicated that stool
tion studies, such as the mechanism of drug release water content may be an important determinant in
from a hydrophilic matrix tablet (Abrahamsson et al, colonic drug absorption. In contrast, the sugar lactu-
1998). Generally a nonabsorbable radionuclide that lose accelerated GI transit, increased stool water
emits gamma rays is included as marker in the for- content, and enhanced drug absorption from the
mulation. In some studies, two radiolabels may be distal gut. Quinine absorption was greater when
used for simultaneous detection of liquid and solid given with lactulose compared to no lactulose.
phases. One approach is to use labeled technetium Riley et al (1992) studied the effects of gas-
(Tc99m) in a capsule matrix to study how a drug is tric emptying and GI transit on the absorption of
absorbed. The image of the capsule breaking up in several drug solutions (furosemide, atenolol,
Physiologic Factors Related to Drug Absorption 403
hydrochlorothiazide, and salicylic acid) in healthy in different parts of the GI tract because the rate of
subjects. These drugs may potentially be absorbed drug release is constant (zero order) and generally
differently at various sites in the GI system. not altered by the environment of the gastrointestinal
Subjects were given 20 mg oral metoclopramide or tract. The constant rate of drug release provides rela-
60 mg oral codeine phosphate to slow gastric emp- tively constant blood concentrations.
tying. The study showed that gastric emptying time
affects the absorption of salicylic acid, but not that In Vivo GI Perfusion Studies
of furosemide, hydrochlorothiazide, or atenolol. In the past, segments of guinea pig or rat ileums
In vivo experiments are needed to determine the were cut and used to study drug absorption; how-
effect of changing transit time on drug absorption. ever, we now know that many of the isolated prepa-
rations were not viable shortly after removal, making
Remote Drug Delivery Capsules (RDDCs) the absorption data collected either invalid or diffi-
cult to evaluate. In addition, the differences among
Drug absorption in vivo may be studied either directly species make it difficult to extrapolate animal data to
by an intubation technique that directly takes samples humans.
from the GI tract or remotely with a special device,
GI perfusion is an in vivo method used to study
such as the Heidelberg capsule. The Heidelberg cap- absorption and permeability of a drug in various seg-
sule (Barrie, 1999) is a device used to determine the ments of the GI tract. A tube is inserted from the
pH of the stomach. The capsule contains a pH sensor mouth or anus and placed in a specific section of the
and a miniature radio transmitter (invented by H. G. GI tract. A drug solution is infused from the tube at
Noeller and used at Heidelberg University in Germany a fixed rate, resulting in drug perfusion of the desired
decades ago). The capsule is about 2 cm × 0.8 cm and GI region. The jejunal site is peristaltically less
can transmit data to outside after the device is swal- active than the duodenum, making it easier to intu-
lowed and tethered to the stomach. Other, newer bate, and therefore, it is often chosen for perfusion
telemetric methods may be used to take pictures of studies. Perfusion studies in other sites such as the
various regions of the GI tract. duodenum, ileum, and even the colon have also been
An interesting remote drug delivery capsule performed by gastroenterologists and pharmaceuti-
(RDDC) with electronic controls for noninvasive cal scientists.
regional drug absorption study was reported by Parr Lennernas et al (1992, 1995) have applied per-
et al (1999). This device was used to study absorp- fusion techniques in humans to study permeability in
tion of ranitidine hydrochloride solution in 12 healthy the small intestine and the rectum. These methods
male volunteers. Mean gastric emptying of the yield direct absorption information in various seg-
RDDC was 1.50 hours, and total small intestine tran- ments of the GI tract. The regional jejunal perfusion
sit was 4.79 hours. The capsule was retrieved from method was reported to have great potential for
the feces at 30.25 hours. The onset of ranitidine serum mechanistic evaluations of drug absorption.
levels depended on the time of capsule activation and Buch and Barr (1998) evaluated propranolol
the site of drug release. HCl in the proximal and distal intestine in humans
(n = 7 subjects) using direct intubation. Propranolol
Osmotic Pump Systems HCl is a beta blocker that has high inter- and intrasu-
The osmotic pump system is a drug product that bject variability in absorption and metabolism. These
contains a small hole from which dissolved drug is investigators showed that propranolol was better
released (pumped out) at a rate determined by the absorbed from a solution in the distal region of the
rate of entrance of water from the GI tract across a intestine. This study is difficult to relate to the pro-
semipermeable membrane due to osmotic pressure pranolol extended-release oral products for which
(see Chapter 18). The drug is either mixed with an differences in drug release rates and GI transit time
osmotic agent or located in a reservoir. Osmotic may also influence inter- and intrasubject variability
pump systems may be used to study drug absorption in bioavailability.
404 Chapter 14
More recently, balloon-isolated jejunal drug is a human colon adenocarcinoma cell line that dif-
administration has been used to determine the ferentiates in culture and resembles the epithelial
absorption characteristics of (-)epicatechin, vitamin lining of the human small intestine. The permeabil-
E, and vitamin E acetate (Actis-Goretta et al, 2013). ity of the cellular monolayer may vary with the stage
The current efforts to determine intestinal regional of cell growth and the cultivation method used.
drug absorption have been recently reviewed, and However, using monolayers of Caco-2 cells under
data generated from these studies will be useful to controlled conditions, the permeability of a drug
refine models for predicting drug absorption may be determined. Caco-2 cells can also be used to
(Lennernas, 2014). study interactions of drugs with the transporter P-gp
discussed below.
Drug permeability using the Caco-2 cell line has
Intestinal Permeability to Drugs
been suggested as an in vitro method for passively
Drugs that are completely absorbed (F > 90%) after transported drugs. In some cases, the drug permea-
oral administration generally demonstrate high per- bility may appear to be low due to efflux of drugs via
meability in in vitro models. Previously, poor drug membrane transporters such as P-gp. Permeability
absorption was mostly attributed to poor dissolution, studies using the Caco-2 cell line have been sug-
slow diffusion, degradation, or poor intestinal per- gested as a method for classifying the permeability
meation. Modern technology has shown that poor or of a drug according to the Biopharmaceutics
variable oral drug bioavailability among individuals Classification System, BCS (Tolle-Sander and Polli,
is also the result of individual genetic differences in 2002; US Food and Drug Administration, Guidance
intestinal absorption (see Chapter 13). Interindividual 2003, August 2002; Sun and Pang, 2007). The main
differences in membrane proteins, ion channels, purpose of the BCS is to identify a drug as having
uptake transporters, and efflux pumps (such as high or low permeability as a predictor of systemic
P-glycoprotein, P-gp) that mediate directional trans- drug absorption from the GI tract (see Chapter 16).
port of drugs and their metabolites across biological
membranes can change the extent of drug absorp-
Drug Transporters
tion, or even transport to the site of action elsewhere
in the body. It is now clear that the behavior of drugs Many methods are available to study the actions of
in the body is the result of an intricate interplay drug transporters in the GI tract. In addition to
between these receptors, drug transporters, and the Caco-2 cells, there are several commercially avail-
drug-metabolizing systems. This insight provides able expression systems to study various transport-
another explanation for erratic drug absorption ers, including those required by the FDA in drug
beyond poor formulation and first-pass metabolism. development. These systems include transporters
Alternative methods to study intestinal drug recombinantly expressed in insect, frog, or mamma-
permeability include in vivo or in situ intestinal per- lian cells. Also, the plasma membranes of some of
fusion in a suitable animal model (eg, rats), and/or these expression systems can also be isolated, pro-
in vitro permeability methods using excised intesti- viding membrane vesicle preparations that are
nal tissues, or monolayers of suitable epithelial cells devoid of drug-metabolizing activity.
such as Caco-2 cells. In addition, the physicochemi-
cal characterization of a drug substance (eg, oil–water Determinations of Artificial Membrane
partition coefficient) provides useful information to Permeability
predict a drug’s permeability. To accelerate early determinations of factors involved
in drug absorption, permeability and solubility of a
Caco-2 Cells for In Vitro Permeability Studies novel drug candidate are determined early in the drug
Although in vivo studies yield much definitive infor- development process. Permeability of drug candidates
mation about drug permeability in humans, they are may be determined using high-throughput screening
tedious and costly to perform. The Caco-2 cell line techniques, such as the parallel artificial membrane
Physiologic Factors Related to Drug Absorption 405
permeability assay (PAMPA). In this technique, artifi- because the free base readily precipitates out due to
cial lipid membranes are supported on a filter between the weak basicity.
two fluid compartments, one of which contains the Dapsone, itraconazole, and ketoconazole may
drug candidate. The rate of appearance into the oppo- also be less well absorbed in the presence of achlor-
site compartment is then measured to determine the hydria. In patients with acid reflux disorders, proton
permeability of the compound. Several models and pump inhibitors, such as omeprazole, render the
variations of this approach are available, and investi- stomach achlorhydric, which may also affect drug
gators should pay attention particularly to the lipid absorption. Coadministering orange juice, colas, or
composition of the artificial membranes as well as other acidic beverages can facilitate the absorption of
other experimental details. Notably, the PAMPA can some medications requiring an acidic environment.
only predict simple diffusional permeability, which HIV–AIDS patients are prone to a number of
does not involve uptake or efflux transporters (Avdeef gastrointestinal (GI) disturbances, such as decreased
et al, 2007). gastric transit time, diarrhea, and achlorhydria.
Rapid gastric transit time and diarrhea can alter the
absorption of orally administered drugs. Achlorhydria
EFFECT OF DISEASE STATES ON may or may not decrease absorption, depending on
DRUG ABSORPTION the acidity needed for absorption of a specific drug.
Indinavir, for example, requires a normal acidic
Drug absorption may be affected by any disease environment for absorption. The therapeutic win-
that causes changes in (1) intestinal blood flow, dow of indinavir is extremely narrow, so optimal
(2) gastrointestinal motility, (3) changes in stom- serum concentrations are critical for this drug to be
ach emptying time, (4) gastric pH that affects drug efficacious.
solubility, (5) intestinal pH that affects the extent Congestive heart failure (CHF) patients with
of ionization, (6) the permeability of the gut wall, persistent edema have reduced splanchnic blood flow
(7) bile secretion, (8) digestive enzyme secretion, and develop edema in the bowel wall. In addition,
or (9) alteration of normal GI flora. Some factors intestinal motility is slowed. The reduced blood flow
may dominate, while other factors sometimes can- to the intestine and reduced intestinal motility results
cel the effects of one another. Pharmacokinetic in a decrease in drug absorption. For example, furo-
studies comparing subjects with and without the semide (Lasix), a commonly used loop diuretic, has
disease are generally necessary to establish the erratic and reduced oral absorption in patients with
effect of the disease on drug absorption. Patients in CHF and a delay in the onset of action.
an advanced stage of Parkinson’s disease may have As discussed above, Crohn’s disease is an
difficulty swallowing and greatly diminished gas- inflammatory disease of the distal small intestine
trointestinal motility. and colon. The disease is accompanied by regions of
Patients on tricyclic antidepressants (imiprimine, thickening of the bowel wall, overgrowth of anaero-
amitriptyline, and nortriptyline) and antipsychotic bic bacteria, and sometimes obstruction and deterio-
drugs (phenothiazines) with anticholinergic side ration of the bowel. The effect on drug absorption is
effects may have reduced gastrointestinal motility or unpredictable, although impaired absorption may
even intestinal obstructions. Delays in drug absorption, potentially occur because of reduced surface area
especially with slow-release products, have occurred. and thicker gut wall for diffusion. For example,
Achlorhydric patients may not have adequate higher plasma propranolol concentration has been
production of acids in the stomach; stomach HCl is observed in patients with Crohn’s disease after oral
essential for solubilizing insoluble free bases. Many administration of propranolol. Serum a-1-acid gly-
weak-base drugs that cannot form soluble salts will coprotein levels are increased in Crohn’s disease
remain undissolved in the stomach when there is no patients and may affect the protein binding and dis-
hydrochloric acid present and are therefore unab- tribution of propranolol in the body and result in
sorbed. Salt forms of these drugs cannot be prepared higher plasma concentrations.
406 Chapter 14
Celiac disease is an inflammatory disease Antacids containing aluminum, calcium, or magne-
affecting mostly the proximal small intestine. Celiac sium may complex with drugs such as tetracycline,
disease is caused by sensitization to gluten, a viscous ciprofloxacin, and indinavir, resulting in a decrease
protein found in cereals and grains. Patients with in drug absorption. To avoid this interaction, antac-
celiac disease generally have an increased rate of ids should be taken 2 hours before or 6 hours after
stomach emptying and increased permeability of the drug administration.
small intestine. Cephalexin absorption appears to be Proton pump inhibitors such as omeprazole
increased in celiac disease, although it is not possi- (Prilosec®), lansoprazole (Prevacid®), pantoprazole
ble to make general predictions about these patients. (Protonix®), and others decrease gastric acid produc-
Other intestinal conditions that may potentially tion, thereby raising gastric pH. These drugs may
affect drug absorption include corrective surgery interfere with drugs for which gastric pH affects bio-
involving peptic ulcer, antrectomy with gastroduode- availability (eg, ketoconazole, iron salts, ampicillin
nostomy, and selective vagotomy. esters, and digoxin) and enteric-coated drug products
Recently, hypoxemia and hypovolemia have been (eg, aspirin, diclofenac) in which the pH-dependent
shown to have adverse effects on the intestinal micro- enteric coating may dissolve in the higher gastric pH
villi (Harrois et al, 2013). Since the microvilli are and release drug prematurely (“dose-dumping”).
important for many aspects of drug absorption, patients Cholestyramine is a nonabsorbable ion-
with significant blood loss, hypoxemia, or intestinal exchange resin for the treatment of hyperlipidemia.
ischemia may be reasonably expected to have altered Cholestyramine binds warfarin, thyroxine, and loper-
drug oral absorption. Caregivers may need to consider amide, similar to activated charcoal, thereby reducing
non-enteral routes of drug administration. absorption of these drugs.
Drugs That Affect Absorption of Other Drugs Nutrients That Interfere with Drug
Anticholinergic drugs in general may reduce stom- Absorption
ach acid secretion. Propantheline bromide is an Many nutrients substantially interfere with the
anticholinergic drug that may also slow stomach absorption or metabolism of drugs in the body
emptying and motility of the small intestine. Tricyclic (Anderson, 1988; Kirk, 1995). The effect of food on
antidepressants and phenothiazines also have anti- bioavailability was discussed earlier. Oral drug–
cholinergic side effects that may cause slower peri- nutrient interactions are often drug specific and can
stalsis in the GI tract. Slower stomach emptying may result in either an increase or a decrease in drug
cause delay in drug absorption. absorption.
Metoclopramide is a drug that stimulates stom- Absorption of calcium in the duodenum is an
ach contraction, relaxes the pyloric sphincter, and, in active process facilitated by vitamin D, with calcium
general, increases intestinal peristalsis, which may absorption as much as four times more than that
reduce the effective time for the absorption of some in vitamin D deficiency states. It is believed that
drugs and thereby decrease the peak drug concentra- a calcium-binding protein, which increases after
tion and the time to reach peak drug concentration. vitamin D administration, binds calcium in the intes-
For example, digoxin absorption from a tablet is tinal cell and transfers it out of the base of the cell to
reduced by metoclopramide but increased by an anti- the blood circulation.
cholinergic drug, such as propantheline bromide. Grapefruit juice often increases bioavailability,
Allowing more time in the stomach for the tablet to as observed by an increase in plasma levels of many
dissolve generally helps with the dissolution and drugs that are substrates for cytochrome P-450 (CYP)
absorption of a poorly soluble drug, but would not be 3A4 (see Chapter 12). Grapefruit juice contains vari-
helpful for a drug that is not soluble in stomach acid. ous flavonoids such as naringin and furanocoumarins
Antacids should not be given with cimetidine, such as bergamottin, which inhibit certain cyto-
because antacids may reduce drug absorption. chrome P-450 enzymes involved in drug metabolism
Physiologic Factors Related to Drug Absorption 407
(especially CYP3A4). In this case, the observed increase nasal membranes must also be considered. In gen-
in the plasma drug–blood levels is due to decreased eral, a drug must be sufficiently lipophilic to cross
presystemic elimination in the GI tract and/or liver. the membranes of the nasal epithelium in order to be
Indirectly, the amount of drug absorbed systemically absorbed. Small molecules with balanced lipophilic
from the drug product is increased. Grapefruit juice and hydrophilic properties tend to be absorbed more
can also block drug efflux by inhibiting P-gp for easily. This observation poses a challenge for nasal
some drugs. delivery of larger molecules such as proteins and
peptides, which would benefit from delivery routes
that avoid the degradative environment of the intes-
MISCELLANEOUS ROUTES OF DRUG tine. Dosage forms intended for nasal drug delivery
ADMINISTRATION include nasal drops, nasal sprays, aerosols, and neb-
ulizers (Su and Campanale, 1985).
For systemic drug absorption, the oral route is the Depending on the metabolic absorption, and
easiest, safest, and most popular route of drug chemical profile of the drug, some drugs are rapidly
administration. Alternate routes of drug administra- absorbed through the nasal membrane and can
tion have been used successfully to improve sys- deliver rapid therapeutic effect. Various hormones
temic drug absorption or to localize drug effects in and insulin have been tested for intranasal delivery.
order to minimize systemic drug exposure and In some cases the objective is to improve availability,
adverse events. Furthermore, enteral drug adminis- and in other cases it is to reduce side effects.
tration (through nasogastric tubes and the like) may Vasopressin and oxytocin are older examples of
be necessary in patients incapable of swallowing drugs marketed as intranasal products. In addition,
medications but requiring chronic dosing. In such many opioids are known to be rapidly absorbed from
cases, oral liquid (solutions, suspensions, or emul- the nasal passages and can deliver systemic levels of
sions) may be administered; some of these may the drug almost as rapidly as an intravenous injection
require extemporaneous compounding. Increasingly (Dale et al, 2002). A common problem with nasal
popular nonparenteral alternatives to oral drug deliv- drug delivery is the challenge of developing a formu-
ery for systemic drug absorption include nasal, inhala- lation with nonirritating ingredients. Many surfac-
tion, and transdermal drug delivery. Nasal, inhalation, tants that facilitate absorption tend to be moderately
and topical drug delivery may also be used for local or very irritating to the nasal mucosa.
drug action (Mathias et al, 2010). Intranasal corticosteroids for treatment of allergic
and perennial rhinitis have become more popular since
Nasal Drug Delivery intranasal delivery is believed to reduce the total dose
Nasal drug delivery may be used for either local or of corticosteroid required. A lower dose also leads to
systemic effects. Because the nasal region is richly minimization of side effects such as growth suppres-
supplied with blood vessels, nasal administration is sion. This logic has led to many second-generation
also useful for systemic drug delivery. However, the corticosteroids such as beclomethasone dipropio-
total surface area in the nasal cavity is relatively nate, budesonide, flunisolide, fluticasone propionate,
small, retention time in the nasal cavity is generally mometasone furoate, and triamcinolone acetonide that
short, and some drug may be swallowed. The swal- are being considered or developed for intranasal
lowed fraction of the dose would have all the disad- delivery (Szefler, 2002). However, the potential for
vantages of oral route, including low oral growth suppression in children varies. In one study,
bioavailability and undesirable taste, as seen with beclomethasone dipropionate reduced growth in
sumatriptan nasal spray (Imitrex). These factors may children, but mometasone furoate nasal spray used
limit the nose’s capacity for systemic delivery of for 1 year showed no signs of growth suppression.
drugs requiring large doses. Surfactants are often Overall, the second-generation corticosteroids are
used to increase systemic penetration, although the given by nasal delivery to cause minimal systemic
effect of chronic drug exposure on the integrity of side effects (Szefler, 2002).
408 Chapter 14
Inhalation Drug Delivery Topical and Transdermal Drug Delivery
Inhalation drug delivery may also be used for local Topical drug delivery is generally used for local drug
or systemic drug effects. The lung has a potential effects at the site of application. Dosing is dependent
absorption surface of some 70 m2, a much larger upon the concentration of the drug in the topical
surface than the small intestine or nasal passages. product (eg, cream, ointment) and the total surface
When a substance is inhaled, it is exposed to mem- area applied. Drug may be applied as an ointment or
branes of the mouth or nose, pharynx, trachea, bron- cream to the skin or various mucous membranes
chi, bronchioles, alveolar sacs, and alveoli. The such as intravaginally. Even though the objective is
lungs and their associated airways are designed to to obtain a local drug effect, some of the drug may
remove foreign matter from the highly absorptive be absorbed systemically.
peripheral lung surfaces via mucociliary clearance. Transdermal products are generally used for
However, if compounds such as aerosolized drug can systemic drug absorption. For transdermal drug
reach the peripheral region of the lung, absorption delivery the drug is incorporated into a transdermal
can be very efficient. therapeutic system or patch, but it may be incorpo-
Particle (droplet) size and velocity of application rated into an ointment as well (see Chapter 15). The
control the extent to which inhaled substances pene- advantages of transdermal delivery include continu-
trate into airway spaces. Optimum size for deep air- ous release of drug over a period of time, low presys-
way penetration of drug particles is 3–5 mm. Large temic clearance, and good patient compliance.
particles tend to deposit in upper airways, whereas Other routes of drug administration are discussed
very small molecules (<3 mm) are exhaled before elsewhere and in Chapter 15.
absorption can occur. Most inhalation devices deliver
approximately 10% of the administered dose to the Frequently Asked Questions
lower respiratory tract. A number of devices such as »»What is an “absorption window”?
spacers (to reduce turbulence and improve deep inha-
lation) have been developed to increase lung delivery. »»Why are some drugs orally absorbed better with
An in vitro device useful to measure the particle size food, whereas the oral absorption of other drugs are
slowed or decreased by food?
emitted from an aerosol or a mechanically produced
fine mist is the cascade impacter. »»What type of food is expected to have the greatest
Recently, recombinant human insulin for inhala- effect on gastrointestinal pH and gastrointestinal
tion (Exubera®) was approved by the FDA, demon- transit time?
strating the viability of this delivery route even for »»Are drugs that are administered as an oral solution
large biological drugs. Insulin inhalation was with- completely absorbed from the gastrointestinal tract?
drawn from the US market in 2007 due to lack of
»»What factors influence drug absorption?
consumer demand for the product.
CHAPTER SUMMARY
Oral systemic drug absorption is a complex process as described by Fick’s law of diffusion according to
dependent upon many biopharmaceutic factors the pH-partition hypothesis, which may be a first-
including (1) the physicochemical properties of the order process depending on permeability and how
drug, (2) the nature of the drug product, (3) the much drug is dissolved at the absorption site. Orally
anatomy and physiology of the drug absorption site, administered drugs may not be absorbed all along
and (4) the type and amount of food or other drugs the gastrointestinal tract. The duodenum affords the
present in the gut. Most drugs are passively absorbed optimum area for absorption due to the high surface
Physiologic Factors Related to Drug Absorption 409
area and blood flow. Several substrate-specific trans- and drug dosage form factors jointly influence sys-
porters may be the dominant factor responsible for temic drug absorption.
bioavailability of some drugs. These drugs are Biopharmaceutic factors such as drug aqueous
absorbed by active transport, which is a carrier- solubility, permeability of cell membranes, the
mediated process that requires energy and transports degree of ionization, molecular size, particle size,
the drug against a concentration gradient. Active and nature of the dosage form will also affect sys-
drug absorption may be saturable depending on the temic drug absorption. The prediction of drug
carrier protein involved and is often site specific. absorption based on physicochemical activity of
Influx and efflux transporters in the gastrointestinal drug molecules and other factors have been attempted
tract influence systemic drug absorption. A well- during drug screening and discovery. Often these
known class of transporters in the GI tract is known properties are influenced by biopharmaceutic factors
as the ABC family. MDR1 (alias P-gp) is an exam- such as formulation, physiological variables, pH,
ple. P-gp reduces drug absorption by effluxing the intestinal regional permeability differences, lumenal
drug out of the enterocytes and back into the gut contents, transporters, and intestinal motility. Drug
lumen. When the absorption process becomes satu- absorption is greatly dependent on routes of admin-
rated, the rate of drug absorption no longer follows a istration. Parenteral, inhalation, transdermal, and
first-order process. Many efflux transporters in the intranasal routes all present physiologic and bio-
GI and other parts of the body are now recognized, pharmaceutic issues that must be understood in
and their presence and quantity are genetically order to develop an optimum formulation that is
expressed and may be activated by certain diseases, consistently absorbed systemically. Various meth-
such as cancer. P-glycoprotein is a common efflux ods are used to study drug absorption depended on
transporter in the GI tract, which may be inhibited by the route involved. Gamma scintigraphy and marker
coadministered drugs and nutrients leading to methods are used to study stomach emptying time
enhanced systemic absorption. In addition to normal and GI transit time. GI perfusion methods are used
gastrointestinal and physiologic factors such as stom- to determine the influence of transporters and the
ach emptying time, small intestine transit time, local effect of presystemic clearance and regional drug
pH, content of the GI tract, presystemic metabolism, absorption.
LEARNING QUESTIONS
1. A recent bioavailability study in adult human a. Give the drug as a suspension and recom-
volunteers demonstrated that after the adminis- mend that the suspension be taken on an
tration of a single enteric-coated aspirin granule empty stomach.
product given with a meal, the plasma drug levels b. Give the drug as a hydrochloride salt.
resembled the kinetics of a sustained-release c. Give the drug with milk.
drug product. In contrast, when the product was d. Give the drug as a suppository.
given to fasted subjects, the plasma drug levels 3. What is the primary reason that protein drugs
resembled the kinetics of an immediate-release such as insulin are not given orally for sys-
drug product. Give a plausible explanation for temic absorption?
this observation. 4. Which of the following statements is true
2. The aqueous solubility of a weak-base drug regarding an acidic drug with a pKa of 4?
is poor. In an intubation (intestinal perfusion) a. The drug is more soluble in the stomach
study, the drug was not absorbed beyond the when food is present.
jejunum. Which of the following would be the b. The drug is more soluble in the duodenum
correct strategy to improve drug absorption than in the stomach.
from the intestinal tract? c. The drug is more soluble when dissociated.
410 Chapter 14
5. Which region of the gastrointestinal tract is What is the effect of antacid and high-fat
most populated by bacteria? What types of breakfast on the bioavailability of misoprostol?
drugs might affect the gastrointestinal flora? Comment on how these factors affect the rate
6. Discuss methods by which the first-pass effect and extent of systemic drug absorption.
(presystemic absorption) may be circumvented. 8. Explain why the following occur.
7. Misoprostol (Cytotec, GD Searle) is a synthetic a. Drug A is given by IV bolus injection and
prostaglandin E1 analog. According to the the onset of the pharmacodynamic effect is
manufacturer, the following information was immediate. When Drug A is given orally in
obtained when misoprostol was taken with an the same dose, the onset of the pharmacody-
antacid or high-fat breakfast: namic effect is delayed and the intensity of
the pharmacodynamic effect is less than the
drug given by IV bolus injection.
Cmax AUC0–24 hour tmax
Condition (pg/mL) (pg·h/mL) (minutes) b. Drug B is given by IV bolus injection and
the onset of the pharmacodynamic effect is
Fasting 811 ± 317a 417 ± 135 14 ± 8 delayed. When Drug B is given orally in the
With antacid 689 ± 315 349 ± 108b 20 ± 14 same dose to fasted subjects, the onset of
the pharmacodynamic effect is shorter and
With high- 303 ± 176b 373 ± 111 64 ± 79b
fat breakfast the pharmacodynamic effect is more intense
after IV bolus injection.
aResults are expressed as the mean ± SD (standard deviation).
bComparisons with fasting results statistically significant, p < 0.05.
ANSWERS TO QUESTIONS
Frequently Asked Questions Are drugs that are administered as an oral solution
What is an “absorption window”? completely absorbed from the gastrointestinal tract?
• An absorption window refers to the segment of • After oral administration, the drug in solution may
the gastrointestinal tract from which the drug is precipitate in the gastrointestinal tract. The pre-
well absorbed and beyond which the drug is either cipitated drug needs to redissolve before it can be
poorly absorbed or not absorbed at all. After oral absorbed. Some drug solutions are prepared with
administration, most drugs are well absorbed in the a co-solvent, such as alcohol or glycerin, and form
duodenum and to a lesser extent in the jejunum. coarse crystals on precipitation that dissolve slowly,
A small amount of drug absorption may occur from whereas other drugs precipitate into fine crystals that
the ileum. redissolve rapidly. The type of precipitate is influ-
enced by the solvent, by the degree of agitation, and
Why are some drugs absorbed better with food by the physical environment. In vitro mixing and
whereas the oral absorption of other drugs is slowed dilution of the drug solution in artificial gastric juice,
or decreased by food? artificial intestinal juice, or other pH buffers may
• Food, particularly food with a high fat content, predict the type of drug precipitate that is formed.
stimulates the production of bile, which is released In addition, drugs dissolved in a highly viscous
into the duodenum. The bile helps to solubilize a solution (eg, simple syrup) may have slower absorp-
lipid-soluble drug, thereby increasing drug absorp- tion because of the viscosity of the solution. Fur-
tion. Fatty food also slows gastrointestinal motil- thermore, drugs that are readily absorbed across the
ity, resulting in a longer residence time for the drug gastrointestinal membrane may not be completely
to be absorbed from the small intestine. bioavailable (ie, 100% systemic absorption) due to
Physiologic Factors Related to Drug Absorption 411
first-pass effects (discussed in Chapter 12). Finally, given parenterally. Other routes of administra-
drugs that are absorbed by saturable mechanisms tion, such as intranasal and rectal administration,
may have concentrations exceeding the capacity have had some success or are under current
of the intestine to absorb all the drug within the investigation for the systemic absorption of
absorption window. protein drugs.
4. The answer is c. Raising the pH of an acid
What factors contribute to a delay in drug absorption?
drug above its pKa will increase the dissocia-
• The major biologic factor that delays gastrointes- tion of the drug, thereby increasing its aqueous
tinal drug absorption is a delay in gastric empty- solubility.
ing time. Any factor that delays stomach empty- 5. The large intestine is most heavily populated
ing time, such as fatty food, will delay the drug by bacteria, yeasts, and other microflora. Some
entering into the duodenum from the stomach and, drugs that are not well absorbed in the small
thereby, delay drug absorption. intestine are metabolized by the microflora to
products that are absorbed in the large bowel.
Learning Questions For example, drugs with an azo link (eg, sul-
1. In the presence of food, undissolved aspirin fasalazine) are cleaved by bacteria in the bowel
granules larger than 1 mm are retained up to and the cleaved products (eg, 5-aminosalicylic
several hours longer in the stomach. In the acid and sulfapyridine) are absorbed. Other
absence of food, aspirin granules are emptied drugs, such as antibiotics (eg, tetracyclines),
from the stomach within 1–2 hours. When may destroy the bacteria in the large intestine,
the aspirin granules empty into the duodenum resulting in an overgrowth of yeast (eg, Can-
slowly, drug absorption will be as slow as dida albicans) and leading to a yeast infection.
with a sustained-release drug product. Enteric- Destruction of the microflora in the lower
coated aspirin granules taken with an evening bowel can also lead to cramps and diarrhea.
meal may provide relief of pain for arthritic 6. First-pass effects are discussed more fully in
patients late into the night. Chapter 12. Alternative routes of drug admin-
2. The answer is b. A basic drug formulated as a istration such as buccal, inhalation, sublin-
suspension will depend on stomach acid for dis- gual, intranasal, and parenteral will bypass
solution as the basic drug forms a hydrochloric the first-pass effects observed after oral drug
acid (HCl) salt. If the drug is poorly soluble, administration.
adding milk may neutralize some acid so that the 7. Although antacid statistically decreased the
drug may not be completely dissolved. Making extent of systemic drug absorption (p < .05)
an HCl salt rather than a suspension of the base as shown by an AUC0−4 h of 349 ± 108 pg·h/mL,
ensures that the drug is soluble without being compared to the control (fasting) AUC0−4 h
dependent on stomach HCl for dissolution. value of 417 ± 135 pg·h/mL, the effect of antacid
3. Protein drugs are generally digested by pro- is not clinically significant. A high-fat diet
teolytic enzymes present in the GI tract and, decreased the rate of systemic drug absorption,
therefore, are not adequately absorbed by the as shown by a longer tmax value (64 minutes)
oral route. Protein drugs are most commonly and lower Cmax value (303 pg/mL).
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Part 1. Administration in fasting state. J Controll Release
7:139–146, 1988.
414 Chapter 14
BIBLIOGRAPHY
Berge S, Bighley L, Monkhouse D: Pharmaceutical salts. J Pharm Martonosi AN (ed): Membranes and Transport, Vol 1. New York,
Sci 66:1–19, 1977. Plenum, 1982.
Blanchard J: Gastrointestinal absorption, II. Formulation factors McElnay JC: Buccal absorption of drugs. In Swarbick J, Boylan
affecting bioavailability. Am J Pharm 150:132–151, 1978. JC (eds). Encyclopedia of Pharmaceutical Technology, Vol 2.
Davenport HW: Physiology of the Digestive Tract, 5th ed. Chicago, New York, Marcel Dekker, 1990, pp 189–211.
Year Book Medical, 1982. Palin K: Lipids and oral drug delivery. Pharm Int 272–275,
Evans DF, Pye G, Bramley R, et al: Measurement of gastro- November 1985.
intestinal pH profiles in normal ambulant human subjects. Gut Palin K, Whalley D, Wilson C, et al: Determination of gastric-
29:1035–1041, 1988. emptying profiles in the rat: Influence of oil structure and
Eye IS: A review of the physiology of the gastrointestinal tract in volume. Int J Pharm 12:315–322, 1982.
relation to radiation doses from radioactive materials. Health Pisal DS, Koslowski MP, Balu-Iyer SV: Delivery of therapeutic
Phys 12:131–161, 1966. proteins. J Pharm Sci 99(5):2557–2575, 2010.
Houston JB, Wood SG: Gastrointestinal absorption of drugs Welling PG: Interactions affecting drug absorption. Clin Pharmaco-
and other xenobiotics. In Bridges JW, Chasseaud LF (eds). kinet 9:404–434, 1984.
Progress in Drug Metabolism, Vol 4. London, Wiley, 1980, Welling PG: Dosage route, bioavailability and clinical efficacy.
Chap 2. In Welling PW, Tse FLS (eds). Pharmacokinetics: Regulatory,
Leesman GD, Sinko PJ, Amidon GL: Stimulation of oral drug Industry, Academic Perspectives. New York, Marcel Dekker,
absorption: Gastric emptying and gastrointestinal motility. 1988, Chap 3.
In Welling PW, Tse FLS (eds). Pharmacokinetics: Regulatory, Welling PG: Absorption of drugs. In Swarbrick J, Boylan JC (eds).
Industry, Academic Perspectives. New York, Marcel Dekker, Encyclopedia of Pharmaceutical Technology. New York,
1988, Chap 6. Marcel Dekker, 2002, pp 8–22.
Mackowiak PA: The normal microbial flora. N Engl J Med 307: Wilson TH: Intestinal Absorption. Philadelphia, Saunders, 1962.
83–93, 1982.
Biopharmaceutic
15 Considerations in Drug
Product Design and In Vitro
Drug Product Performance
Sandra Suarez, Patrick J. Marroum, and
Minerva Hughes
Chapter Objectives Biopharmaceutics is the study of the physicochemical properties of
the drug and the drug product, in vitro, as it relates to the bioavail-
»» Describe the biopharmaceutic
ability of the drug, in vivo, and its desired therapeutic effect.
factors affecting drug design.
Biopharmaceutics thus links the physical and chemical properties of
»» Define the term “rate-limiting the drug and the drug product to their clinical performance, in vivo.
step” and discuss how the Consequently, a primary concern in biopharmaceutics is the bio-
rate-limiting step relates to the availability of drugs. Bioavailability refers to the measurement of
bioavailability of a drug. the rate and extent of active drug that becomes available at the site
»» Differentiate between the terms of action. For the majority of orally administered drugs, the site of
solubility and dissolution. action is within the systemic circulation and the drug must be
absorbed to achieve a pharmacological response. Oral drug absorp-
»» Differentiate between the tion involves at least three distinct steps: drug release or dissolution
concept of drug absorption and from the drug product in the body’s fluids, permeation of the drug
bioavailability. across the gastrointestinal (GI) linings into the systemic circulation,
»» Describe the various in vitro and and drug disposition during GI transit (eg, GI stability, motility,
in vivo tests commonly used to metabolism, etc). Additional drug disposition may occur in the
evaluate drug products. systemic circulation and thus reduce the concentration of drug
available to the target tissues. However, because the systemic blood
»» Describe the statistical methods
circulation ultimately delivers therapeutically active drug to the tis-
for comparing two dissolution
sues and to the drug’s site of action, changes in oral bioavailability
profiles for similarity.
affect changes in the pharmacodynamics and toxicity of a drug.
»» List the USP dissolution A drug product may also be designed to deliver the drug
apparatus and provide examples directly to the site of action before reaching the systemic circula-
of drug products for which the tion, which is often termed locally acting drug. Some examples of
dissolution apparatus might be products in this class include ophthalmic, pulmonary, and nasal
appropriate. drug products. Similar to systemic bioavailability, local drug bio-
»» Define sink conditions and availability is strongly influenced by physicochemical properties
explain why dissolution medium of the drug and drug product, the rate and extent of drug release
must maintain sink conditions. from the drug product, and permeation at the target site (eg, skin
physiology compared with that in the cornea). Regardless of the
»» Define in vitro–in vivo correlation intended site of drug action, biopharmaceutics aims to balance the
(IVIVC) and explain why a amount and extent of drug delivered from the drug product to
Level A correlation is the most achieve optimal therapeutic efficacy and safety for the patient.
important correlation for IVIVC.
415
416 Chapter 15
»» Define clinically relevant BIOPHARMACEUTIC FACTORS AND
drug product specifications
RATIONALE FOR DRUG PRODUCT DESIGN
and describe the methods to
establish them. In broad terms, the factors affecting drug bioavailability may be
related to the formulation of the drug product or the biological
»» Explain the biopharmaceutic
constraints of the patient.
classification system and
Drugs are not usually given as pure chemical drug sub-
how solubility, dissolution,
stances, but are formulated into finished dosage forms (ie, drug
and permeation apply to BCS
products). These drug products include the active drug substance
classification.
combined with selected additional ingredients (excipients) that
»» Provide a description of some make up the dosage form. Although excipients are considered
common oral drug products and inert with respect to pharmacodynamic activity, excipients are
explain how biopharmaceutic important in the manufacture of the drug product and provide
principles may be used to functionality to the drug product with respect to drug release and
formulate a product that will dissolution (see also Chapter 18).
extend the duration of activity of Some common drug products include liquids, tablets, capsules,
the active drug. injectables, suppositories, transdermal systems, and topical creams
and ointments. These finished dosage forms or drug products are
then given to patients to achieve a specific therapeutic objective.
The design of the dosage form, the formulation of the drug product,
and the manufacturing process require a thorough understanding of
the biopharmaceutic principles of drug delivery. Considerations in
the design of a drug product to deliver the active drug with the
desired bioavailability characteristics and therapeutic objectives
include (1) the physicochemical properties of the drug molecule,
(2) the finished dosage form (eg, tablet, capsule, etc), (3) the nature
of the excipients in the drug product, (4) the method of manufactur-
ing, and (5) the route of drug administration.
Biopharmaceutics allows for the rational design of drug prod-
ucts and is based on:
• The physical and chemical properties of the drug substance
• The route of drug administration, including the anatomic and
physiologic nature of the application site (eg, oral, topical, inject-
able, implant, transdermal patch, etc)
• Desired pharmacodynamic effect (eg, immediate or prolonged
activity)
• Toxicologic properties of the drug
• Safety of excipients
• Effect of excipients and dosage form on drug product performance
• Manufacturing processes
As mentioned above, some drugs are intended for topical or local
therapeutic action at the site of administration. Drugs intended for
local activity are designed to have a direct pharmacodynamic
action without affecting other body organs, and systemic drug
absorption is often undesirable. Locally acting drugs may be
administered orally (eg, local GI effect) or applied topically to the
Biopharmaceutic Considerations in Drug Product Design and In Vitro Drug Product Performance 417
skin, nose, eye, mucous membranes, buccal cavity, size and its distribution, the spray pattern, and plume
throat, or rectum. A drug intended for local activity geometry of the emitted dose, which may affect its
may also be given intravaginally, into the urethral in vivo performance. Also, drug-polymer coating
tract, or intranasally; inhaled into the lungs; and may be applied to a cardiac stent for local delivery of
applied into the ear or on the eye. Examples of drugs antiproliferative drugs directly to diseased tissue
used for local action include anti-infectives, antifun- during percutaneous coronary intervention to treat a
gals, local anesthetics, antacids, astringents, vaso- blocked artery.
constrictors, antihistamines, bronchodilators, and By choosing the route of drug administration
corticosteroids. Though systemic absorption is unde- carefully and properly designing the drug product,
sired, it may occur with locally acting drugs and the bioavailability of the active drug can be varied
modifying the drug product design may help to miti- from rapid and complete absorption to a slow, sus-
gate systemic effects. tained rate of absorption or even virtually no absorp-
Each route of drug administration presents spe- tion, depending on the therapeutic objective. Once
cial biopharmaceutic considerations in drug product the drug is systemically absorbed, normal physio-
design. For example, the design of a vaginal tablet logic processes for drug distribution and elimination
formulation for the treatment of a fungal infection occur. These intrinsic factors may also be influenced
must use ingredients compatible with vaginal anat- by the specific formulation of the drug (eg, encapsu-
omy and physiology. An eye medication requires lated drug in liposome or microspheres may change
special considerations for formulation pH, isotonicity, the drug distribution and systemic clearance). The
sterility, the need to minimize local irritation to the rate of drug release from the product and the rate and
cornea, potential for drug loss from draining by tears, extent of drug absorption are important in determin-
and residual systemic drug absorption. For a drug ing the onset, intensity, and duration of drug action.
administered by an extravascular route (eg, intramus- Biopharmaceutic considerations often deter-
cular injection), local irritation, drug dissolution at mine the ultimate dose and dosage form of a drug
the application site, and drug absorption from the product. For example, the dosage form for a locally
intramuscular site are some of the factors that must acting drug such as a topical drug product (eg, oint-
be considered. Systemic absorption after extravascu- ment) is often expressed in concentration or as a
lar administration is influenced by the anatomic and percentage of the active drug in the formulation
physiologic properties of the site and the physico- (eg, 0.5% hydrocortisone ointment). The amount of
chemical properties of the drug and the drug product. drug applied is not specified because the concentra-
On the other hand, if the drug is given by an intravas- tion of the drug at the active site relates to the phar-
cular route (eg, IV administration), systemic drug macodynamic action. However, biopharmaceutic
absorption is considered complete or 100% bioavail- studies must be performed to ensure that the drug
able, because the drug is placed directly into the product does not irritate, cause an allergic response,
general circulation. However, drug disposition can be or allow significant systemic drug absorption. In
altered by modifying the composition of the drug contrast, the dosage form for a systemically acting
product (eg, addition on mannitol may change the drug is expressed in terms of mass, such as milli-
renal clearance of the drug). grams or grams. In this case, the dose is based on
A drug product may also be designed as a com- the amount of drug that is absorbed systemically
bination drug/device product to allow the drug for- and dissolved in an apparent volume of distribution
mulation to be used in conjunction with a specialized to produce a desired drug concentration at the target
medical device or packaging component. For exam- site. The therapeutic dose may also be adjusted
ple, a drug solution or suspension may be formulated based on the weight or surface area of the patient, to
to work with a nebulizer or metered-dose inhaler for account for the differences in the apparent volume
administration into the lungs. Both the physical of distribution, which is expressed as mass per unit
characteristics of the nebulizer and the formulation of body weight (mg/kg) or mass per unit of body
of the drug product can influence the droplet particle surface area (mg/m2). For many commercial drug
418 Chapter 15
Disintegration and
Dissolution Absorption
Drug in drug release Solid drug Drug in Drug in
drug product particles solution body
FIGURE 151 Rate processes of drug bioavailability.
products, the dose is determined based on average where dissolution of the drug is the rate-limiting step
body weights and may be available in several dose in the appearance in the systemic circulation, with a
strengths, such as 10-mg, 5-mg, and 2.5-mg tablets, discriminating dissolution method, the probability of
to accommodate differences in body weight and establishing a predictive in vitro–in vivo correlation
possibly to titrate the dose in the patient. (IVIVC) is higher.
Frequently Asked Questions Disintegration
»»How do excipients improve the manufacturing of an For immediate-release, solid oral dosage forms, the
oral drug product? drug product must disintegrate into small particles
and release the drug. To monitor uniform tablet disin-
»»If excipients do not have pharmacodynamic activity,
tegration, the United States Pharmacopeia (USP) has
how do excipients affect the performance of the
drug product? established an official disintegration test (Fig. 15-2).
Solid drug products exempted from disintegration
tests include troches, tablets that are intended to be
RATE-LIMITING STEPS IN DRUG chewed, and drug products intended for sustained
release or prolonged or repeat action as well as liquid-
ABSORPTION
filled soft gelatin capsules.
Systemic drug absorption from a drug product con-
sists of a succession of rate processes (Fig. 15-1).
For solid oral, immediate-release drug products (eg,
tablets, capsules), the rate processes include (1) dis-
integration of the drug product and subsequent 5.5-cm stroke,
release of the drug, (2) dissolution of the drug in an 30/min
aqueous environment, and (3) absorption across cell
membranes into the systemic circulation. In the pro-
cess of drug disintegration, dissolution, and absorp-
tion, the rate at which drug reaches the circulatory
Media 37°C
system is determined by the slowest step in the
sequence. The slowest step in a series of kinetic pro- 1000-mL Beaker
cesses is called the rate-limiting step. For drugs that
have very poor aqueous solubility, the rate at which 6 Glass tubes,
1-inch diameter
the drug dissolves (dissolution) is often the slowest
step and therefore exerts a rate-limiting effect on
drug bioavailability. In contrast, for a drug that has a Plastic disks
(when specied)
high aqueous solubility, the dissolution rate is rapid,
Tablet
and the rate at which the drug crosses or permeates
cell membranes is the slowest or rate-limiting step. 10-Mesh screen
In general, for drug products that slowly release the
drug from the formulation such as extended- or FIGURE 152 USP disintegration testing apparatus.
controlled-release formulations or for drug products (Hanson and Gray, 2004, with permission.)
Biopharmaceutic Considerations in Drug Product Design and In Vitro Drug Product Performance 419
The process of disintegration does not imply medium is an important prior condition for predicting
complete dissolution of the tablet and/or the drug. systemic drug absorption. The rate at which drugs with
Complete disintegration is defined by the USP-NF poor aqueous solubility dissolve from an intact or dis-
(National Formulary) as “that state in which any integrated solid dosage form in the gastrointestinal
residues of the tablet, except fragments of insoluble tract often controls the rate of systemic absorption of
coating, remaining on the screen of the test appara- the drug. Thus, dissolution tests may be used to predict
tus in the soft mass have no palpably firm core.” The bioavailability and may be used to discriminate formu-
official apparatus for the disintegration test and pro- lation factors that affect drug bioavailability. As per 21
cedure is described in the USP-NF. Separate specifi- CFR (Code of Federal Regulations), dissolution test-
cations are given for drug products that are designed ing is required for US Food and Drug Administration
not to disintegrate. These products include troches, (FDA)-approved solid oral drug products.
chewable tablets, and modified-release (MR) drug Noyes and Whitney (1897) and other investiga-
products. tors studied the rate of dissolution of solid drugs.
Although disintegration tests allow for mea- According to their observations, the steps in dissolu-
surement of the formation of fragments, granules, tion include the process of drug dissolution at the
or aggregates from solid dosage forms, no infor- surface of the solid particle, thus forming a saturated
mation is obtained from these tests on the rate of solution around the particle. The dissolved drug in
dissolution of the active drug. However, there has the saturated solution, known as the stagnant layer,
been some interest in using only the disintegration diffuses to the bulk of the solvent from regions of
test and no dissolution test for drug products that high drug concentration to regions of low drug con-
meet the Biopharmaceutical Classification System centration (Fig. 15-3).
(BCS) for highly soluble and highly permeable The overall rate of drug dissolution may be
drugs (Chapter 16). In general, the disintegration described by the Noyes–Whitney equation
test serves as a component in the overall quality (Equation 15.1):
control of tablet manufacture. Disintegration testing
dC DA
can be used in lieu of dissolution testing, provided = (C −C) (15.1)
dt h s
the following ICH Q6A guidelines are met: (1) The
product under consideration is rapidly dissolving where dC/dt = rate of drug dissolution at time t, D =
(dissolution >80% in 15 minutes at pH 1.2, 4.0, and diffusion rate constant, A = surface area of the particle,
6.8); (2) the drug product contains drugs that are Cs = concentration of drug (equal to solubility of drug)
highly soluble throughout the physiological range in the stagnant layer, C = concentration of drug in the
(dose/solubility volume <250 mL from pH 1.2 to bulk solvent, and h = thickness of the stagnant layer.
6.8); and (3) a relationship to dissolution has been
established or when disintegration is shown to be
more discriminating than dissolution and dissolu-
tion characteristics do not change on stability.
Solid drug Stagnant
particle layer
Dissolution and Solubility
Dissolution is the process by which a solid drug sub-
stance becomes dissolved in a solvent over time. Cs
Solubility is the mass of solute that dissolves in a
C
specific mass or volume of solvent at a given tempera-
ture (eg, 1 g of NaCl dissolves in 2.786 mL of water Bulk solvent
at 25°C). Solubility by definition is an equilibrium FIGURE 153 Dissolution of a solid drug particle in a
property, whereas dissolution is a dynamic property. solvent. (Cs = concentration of drug in the stagnant layer,
In biologic systems, drug dissolution in an aqueous C = concentration of drug in the bulk solvent.)
420 Chapter 15
The rate of dissolution, dC/dt, is the rate of drug dis- increase the diffusion constant, D. Moreover, an
solved per time expressed as concentration change in increase in agitation of the solvent medium will
the dissolution fluid. reduce the thickness, h, of the stagnant layer, allow-
The Noyes–Whitney equation shows that dis- ing for more rapid drug dissolution.
solution in a flask may be influenced by the physico- Factors that affect drug dissolution of a solid
chemical characteristics of the drug, the formulation, oral dosage form include (1) the physical and chemi-
and the solvent. The dissolution of drug in the body, cal nature of the active drug substance, (2) the nature
particularly in the gastrointestinal tract, is consid- of the excipients, (3) the method of manufacture, and
ered to be dissolving in an aqueous environment. (4) the dissolution test conditions.
Permeation of drug across the gut wall (a model lipid
membrane) is affected by the ability of the drug to Frequently Asked Questions
diffuse (D) and to partition between the lipid mem- »»What is meant by the rate-limiting step in drug
branes. A favorable partition coefficient (K bioavailability from a solid oral drug product?
oil/water)
will facilitate drug absorption (see Chapter 14). »»What is the usual rate-limiting step for a poorly
In addition to these factors, the temperature of soluble and highly permeable drug (BCS 2)?
the medium and the agitation rate also affect the rate
»»How could the manufacturing process affect drug
of drug dissolution. In vivo, body temperature is
product performance?
maintained at a constant 37°C, and the agitation
(primarily peristaltic movements in the gastrointesti-
nal tract) is reasonably constant. In contrast, in vitro PHYSICOCHEMICAL PROPERTIES
studies of dissolution kinetics require maintenance OF THE DRUG
of constant temperature and agitation. Temperature
is generally kept at 37°C, and the agitation or stirring In addition to their effect on dissolution kinetics, the
rate is held to a specified agitation rate such as 75 rpm physical and chemical properties of the drug sub-
(revolutions per minute). An increase in temperature stance as well as the excipients are important consid-
will increase the kinetic energy of the molecules and erations in the design of a drug product (Table 15-1).
TABLE 151 Physicochemical Properties for Consideration in Drug Product Design
pKa and pH profile Necessary for optimum stability and solubility of the final product.
Particle size May affect the particle surface of the drug and therefore the dissolution rate of the product.
Polymorphism The ability of a drug to exist in various crystal forms may change the solubility of the drug. Also, the
stability of each form is important, because polymorphs may convert from one form to another.
Hygroscopicity Moisture absorption may affect the physical structure as well as stability of the product.
Partition coefficient May give some indication of the relative affinity of the drug for oil and water. A drug that has high
affinity for oil may have poor release and dissolution from the drug product.
Excipient interaction The compatibility of the excipients with the drug and sometimes trace elements in excipients may
affect the stability of the product. It is important to have specifications of all raw materials.
pH stability profile The stability of solutions is often affected by the pH of the vehicle; furthermore, because the pH
in the stomach and gut is different, knowledge of the stability profile would help avoid or prevent
degradation of the product during storage or after administration.
Impurity profile The presence of impurities may depend upon the synthetic route for the active drug and subse-
quent purification. Impurities need to be “qualified” or tested for safety. Changes in the synthetic
method may change the impurity profile.
Chirality The presence of chirality may show that the isomers have differences in pharmacodynamic activity.
Biopharmaceutic Considerations in Drug Product Design and In Vitro Drug Product Performance 421
For example, intravenous solutions are difficult to considered by the formulator during development.
prepare with drugs that have poor aqueous solubility. Also, the potential for converting from the salt form
Drugs that are physically or chemically unstable may to the unionized drug form during drug product
require special excipients, coatings, or manufacturing manufacturing must be considered for optimal drug
processes to protect the drug from degradation. product design.
Drugs with a potent pharmacodynamic response,
such as estrogens and other hormones, penicillin Stability, pH, and Drug Absorption
antibiotics, cancer chemotherapeutic agents, and
The stability–pH profile is a plot of the reaction rate
others, may cause adverse reactions to personnel
constant for drug degradation versus pH. If drug
who are exposed to these drugs during manufacture
decomposition occurs by acid or base catalysis, some
and also present a problem for manufacturing.
prediction of degradation of the drug in the gastro-
intestinal tract may be made. For example, erythro-
Solubility, pH, and Drug Absorption mycin has a pH-dependent stability profile. In acidic
medium, as in the stomach, erythromycin decompo-
The solubility–pH profile is a plot of the solubility of
sition occurs rapidly, whereas in neutral or alkaline
the drug at various physiologic pH values. In design-
pH, the drug is relatively stable. Consequently, eryth-
ing oral dosage forms, the formulator must consider
romycin tablets are coated with an acid-resistant film,
that the natural pH environment of the gastrointesti-
which is referred to as enteric coating, to protect
nal tract varies from acidic in the stomach to slightly
against acid degradation in the stomach. The knowl-
alkaline in the small intestine. A basic drug is more
edge of erythromycin stability subsequently led to
soluble in an acidic medium, forming a soluble salt.
the preparation of a less water-soluble erythromycin
Conversely, an acid drug is more soluble in the intes-
salt that is more stable in the stomach. The dissolu-
tine, forming a soluble salt in the more alkaline pH
tion rate of erythromycin drug substance powder,
environment found there. The solubility–pH profile
without excipients, varied from 100% dissolved in
gives a rough estimation of the completeness of dis-
1 hour for the water-soluble version to less than 40%
solution for a dose of a drug in the stomach or in the
dissolved in 1 hour for the less water-soluble version.
small intestine.
The slow-dissolving erythromycin drug substance
Solubility may be improved with the addition of
also resulted in slow-dissolving drug products formu-
an acidic or basic excipient. Solubilization of aspi-
lated with the modified drug. Thus, in the erythromy-
rin, for example, may be increased by the addition of
cin case, the dissolution rate of the powdered drug
an alkaline buffer. In the formulation of controlled-
substance was a very useful in vitro tool for predict-
release drugs, buffering agents may be added to slow
ing bioavailability problems of the resulting erythro-
or modify the release rate of a fast-dissolving drug.
mycin product in the body.
Typically, the controlled-release drug product of this
type is a nondisintegrating. The buffering agent is
released slowly rather than rapidly, so that the drug Particle Size and Drug Absorption
does not dissolve immediately in the surrounding Dissolution kinetics is also affected by particle size.
gastrointestinal fluid. As previously described in the Noyes–Whitney dis-
In addition to considering the potential for in situ solution model, the dissolution rate is proportional to
salt formation at different pH values for ionizable the surface area of the drug. Dissolution takes place
drug substances, direct salt formation of the drug is at the surface of the solute (drug), and thus, the
a common approach for tailoring the dissolution greater the surface area, the better the water satura-
rate, and consequently, drug absorption for many tion, and the more rapid the rate of drug dissolution.
ionizable drugs. Salt formation may change the The effective surface area of a drug is increased enor-
drug’s physicochemical properties in many aspects, mously by a reduction in the particle size (ie, more
including its solubility, chemical stability, polymor- particles for a given volume). The geometric shape of
phism, and manufacturability, all of which must be the particle also affects the surface area, and, during
422 Chapter 15
dissolution, the surface is constantly changing. For noncrystalline forms, solvates are forms that contain
dissolution calculations using the various models, a solvent (solvate) or water (hydrate), and desolvated
however, the solute particle is usually assumed to solvates are forms that are made by removing the
have retained its geometric shape. solvent from the solvate. Many drugs exist in an
Particle size and particle size distribution stud- anhydrous state (no water of hydration) or in a
ies are important for drugs that have low water solu- hydrous state.
bility, particularly class II drugs according to the Polymorphs have the same chemical structure
Biopharmaceutical Classification System (BCS) (see but different physical properties, such as different
Chapter 16) where dissolution is often rate limiting solubility, hygroscopicity, density, hardness, and
for absorption. Consequently, there are many drugs compression characteristics. Some polymorphic
that are very active when administered intravenously crystals have much lower aqueous solubility than the
but are not very effective when given orally because amorphous forms, causing a product to be incom-
of poor oral absorption owing to the drug’s poor pletely absorbed.
aqueous solubility. Griseofulvin, nitrofurantoin, and Chloramphenicol, for example, has several crys-
many steroids are drugs with low aqueous solubility; tal forms, and when given orally as a suspension, the
reduction of the particle size by milling to a micron- drug concentration in the body was found to be
ized form has improved the oral absorption of these dependent on the percent of b-polymorph in the sus-
drugs. A disintegrant may also be added to the for- pension. The b form is more soluble and better
mulation to ensure rapid disintegration of the tablet absorbed (Fig. 15-4). In general, the crystal form
and release of the particles. The addition of surface- that has the lowest free energy is the most stable
active agents may increase wetting as well as solu- polymorph. A drug that exists as an amorphous form
bility of these drugs. (noncrystalline form) generally dissolves more rap-
Sometimes micronization and varying the idly than the same drug in a more structurally rigid
choice of excipient are not sufficient to overcome crystalline form. Some polymorphs are metastable
solubility-related bioavailability problems. In these and may convert to a more stable form over time.
cases, so-called nanosizing, or producing even A change in crystal form may cause problems in
smaller drug substance particles, may be beneficial. manufacturing the product. For example, a change
As compared with micronization, nanosized parti-
cles may be formulated for injection drug products
(eg, nano-suspension) in addition to traditional oral 24
dosage forms. 100%
It is possible that nanosized drug particles may 20
not dissolve readily after IV administration and end
16 75%
up sequestered by the reticuloendothelial system
(RES). However, the nanoparticles will eventually 12 50%
dissolve, permeate into the cytoplasm, and contrib-
25%
ute to overall systemic drug exposure in a pseudo 8
extended-release pharmacokinetic profile.
4 0%
0
Polymorphism, Solvates, and Drug 0 2 4 6 8 10 12 14 22 24
Absorption After dosing (hours)
Polymorphism refers to the arrangement of a drug FIGURE 154 Comparison of mean blood serum levels
substance in various crystal forms or polymorphs. In obtained with chloramphenicol palmitate suspensions con-
taining varying ratios of a- and b-polymorphs, following single
recent years, the term polymorph has been used fre-
oral dose equivalent to 1.5 g chloramphenicol. Percentage
quently to describe polymorphs, solvates, amorphous polymorph b in the suspension. (From Aguiar et al, 1967, with
forms, and desolvated solvates. Amorphous forms are permission.)
Chloramphenicol (mg/mL)
Biopharmaceutic Considerations in Drug Product Design and In Vitro Drug Product Performance 423
absorption from the absorption site, increase drug
Dihydrate bioavailability, etc. Some of the excipients used in
100 the manufacture of solid and liquid drug products are
listed in Tables 15-2 and 15-3.
80 Excipients in the drug product may also affect
the dissolution kinetics of the drug, either by altering
60 the medium in which the drug is dissolving or by
Monohydrate reacting with the drug itself. Some of the more com-
40 mon manufacturing problems that affect dissolution
are listed in Table 15-4. Other excipients include
20 Anhydrate suspending agents that increase the viscosity of the
drug vehicle and thereby diminish the rate of drug
0
0 10 20 30 40 50 60 dissolution from suspensions. Tablet lubricants, such
Time (minutes) as magnesium stearate, may repel water and reduce
dissolution when used in large quantities. Coatings,
FIGURE 155 Dissolution behavior of erythromycin
dihydrate, monohydrate, and anhydrate in phosphate buffer particularly shellac, will crosslink upon aging and
(pH 7.5) at 37°C. (From Allen et al, 1978, with permission.) decrease the dissolution rate.
in the crystal structure of the drug may cause crack-
ing in a tablet or even prevent a granulation from
TABLE 152 Common Excipients Used in Solid
being compressed into a tablet. Re-formulation of a
Drug Products
product may be necessary if a new crystal form of
a drug is used. Property in Dosage
Some drugs interact with solvent during the Excipient Form
manufacturing process to form a crystal called a Lactose Diluent
solvate. Water may form special crystals with drugs
Dibasic calcium phosphate Diluent
called hydrates; for example, erythromycin hydrates
have quite different solubility compared to the anhy- Starch Disintegrant, diluent
drous form of the drug (Fig. 15-5). Ampicillin trihy- Microcrystalline cellulose Disintegrant, diluent
drate, on the other hand, was reported to be less
Magnesium stearate Lubricant
absorbed than the anhydrous form of ampicillin
because of faster dissolution of the latter. Stearic acid Lubricant
Hydrogenated vegetable oil Lubricant
Talc Lubricant
FORMULATION FACTORS
Sucrose (solution) Granulating agent
AFFECTING DRUG PRODUCT
Polyvinyl pyrrolidone Granulating agent
PERFORMANCE (solution)
Excipients are added to a formulation to provide Hydroxypropylmethyl- Tablet-coating agent
certain functional properties to the drug and dosage cellulose
form; excipients also affect drug product perfor- Titinium dioxide Combined with dye as
mance, in vivo (Amidon et al, 2007; Chapter 18). colored coating
Some of these functional properties of the excipients
Methylcellulose Coating or granulating
are used to improve the manufacturability of the dos- agent
age form, stabilize the drug against degradation,
Cellulose acetate phthalate Enteric-coating agent
decrease gastric irritation, control the rate of drug
Dissolved (percent)
424 Chapter 15
TABLE 153 Common Excipients Used in Oral increase the rate of drug dissolution, whereas higher
Liquid Drug Products surfactant concentrations tend to form micelles with
the drug and thus decrease the dissolution rate. Large
Excipient Property in Dosage Form
drug particles have a smaller surface area and dissolve
Sodium carboxy- Suspending agent more slowly than smaller particles. Poor disintegration
methyl cellulose of a compressed tablet may be due to high compres-
Tragacanth Suspending agent sion of tablets without sufficient disintegrant.
Sodium alginate Suspending agent Some excipients, such as sodium bicarbonate,
may change the pH of the medium surrounding the
Xanthan gum Thixotropic suspending agent
active drug substance. Aspirin, a weak acid when
Veegum Thixotropic suspending agent formulated with sodium bicarbonate, will form a
Sorbitol Sweetener water-soluble salt in an alkaline medium, in which
the drug rapidly dissolves. The term for this process
Alcohol Solubilizing agent, preservative
is dissolution in a reactive medium. The solid drug
Propylene glycol Solubilizing agent dissolves rapidly in the reactive solvent surrounding
Methyl, propylparaben Preservative the solid particle. However, as the dissolved drug
molecules diffuse outward into the bulk solvent, the
Sucrose Sweetener
drug may precipitate out of solution with a very fine
Polysorbates Surfactant particle size. These small particles have enormous
Sesame oil For emulsion vehicle collective surface area, dispersing and redissolving
readily for more rapid absorption upon contact with
Corn oil For emulsion vehicle
the mucosal surface.
Excipients in a formulation may interact directly
Surfactants, on the other hand, may affect drug with the drug to form a water-soluble or water-
dissolution in an unpredictable fashion. Low concen- insoluble complex. For example, if tetracycline is for-
trations of surfactants decrease the surface tension and mulated with calcium carbonate, an insoluble complex
TABLE 154 Effect of Excipients on the Pharmacokinetic Parameters of Oral Drug Productsa
Excipients Example ka tmax AUC
Disintegrants Avicel, Explotab ↑ ↓ ↑/−
Lubricants Talc, hydrogenated ↓ ↑ ↓/−
vegetable oil
Coating agent Hydroxypropylmethyl – – –
cellulose
Enteric coat Cellulose acetate ↓ ↑ ↓/−
phthalate
Sustained-release Methylcellulose, ↓ ↑ ↓/−
agents ethylcellulose
Sustained-release Castorwax, Carbowax ↓ ↑ ↓/−
agents (waxy agents)
Sustained-release Veegum, Keltrol ↓ ↑ ↓/−
agents (gum/viscous)
aThis may be concentration and drug dependent. ↑ = Increase, ↓ = decrease, − = no effect, ka = absorption rate constant, tmax = time for peak drug
concentration in plasma, AUC = area under the plasma drug concentration–time curve.
Biopharmaceutic Considerations in Drug Product Design and In Vitro Drug Product Performance 425
of calcium tetracycline is formed that has a slow rate
of dissolution and poor absorption. 80
70 0.5%
Excipients may be added intentionally to the
formulation to enhance the rate and extent of drug 60
absorption or to delay or slow the rate of drug 50 1.0%
absorption (see Table 15-4). For example, excipients 40
that increase the aqueous solubility of the drug gen- 30 5.0%
erally increase the rate of dissolution and drug 20
absorption. Excipients may increase the retention
10
time of the drug in the gastrointestinal tract and
0
therefore increase the total amount of drug absorbed. 0 2 4 6 8 10 12 14
Excipients may also act as carriers to increase drug Time (hours)
diffusion across the intestinal wall. In contrast, cer- FIGURE 157 Effect of lubricant on drug absorption.
tain excipients may create a barrier between the drug Percentage of magnesium stearate in formulation. Incomplete
and body fluids that retard drug dissolution and thus drug absorption occurs for formulation with 5% magnesium
stearate.
reduce the rate or extent of drug absorption.
Common excipients found in oral drug products
are listed in Tables 15-2 and 15-3. Excipients should
be pharmacodynamically inert. However, excipients the formulation may retard drug dissolution and slow
may change the functionality (performance) of the the rate of drug absorption. The total amount of drug
drug substance and the bioavailability of the drug absorbed may also be reduced (Fig. 15-7). To prevent
from the dosage form. For solid oral dosage forms this problem, the lubricant level should be decreased
such as compressed tablets, excipients may include or a different lubricant selected. Sometimes, increas-
(1) a diluent (eg, lactose), (2) a disintegrant (eg, ing the amount of disintegrant may overcome the
starch), (3) a lubricant (eg, magnesium stearate), and retarding effect of lubricants on dissolution. However,
(4) other components such as binding and stabilizing with some poorly soluble drugs an increase in disin-
agents. If used improperly in a formulation, the rate tegrant level has little or no effect on drug dissolution
and extent of drug absorption may be affected. For because the fine drug particles are not wetted. The
example, Fig. 15-6 shows that an excessive quantity influence of some common ingredients on drug
of magnesium stearate (a hydrophobic lubricant) in absorption parameters is summarized in Table 15-4.
These are general trends for typical preparations.
100
0.5% DRUG PRODUCT PERFORMANCE,
90
80 IN VITRO: DISSOLUTION AND DRUG
1.0%
70 RELEASE TESTING
60
Dissolution and drug release tests are in vitro tests
50
that measure the rate and extent of dissolution or
40
5.0% release of the drug substance from a drug product,
30
usually in an aqueous medium under specified con-
20
ditions. In vitro dissolution testing provides useful
10
information throughout the drug development pro-
0
0 10 20 30 40 50 60 cess (Table 15-5).
Time (minutes) The dissolution test is an important quality control
FIGURE 156 Effect of lubricant on drug dissolution. procedure used to confirm batch-to-batch reproduc-
Percentage of magnesium stearate in formulation. ibility and to show typical variability in composition
Dissolved (percent)
Plasma drug level (mm/mL)
426 Chapter 15
TABLE 155 Purpose of Dissolution and Drug should be able to reflect changes in the formulation,
Release Tests manufacturing process, and physical and chemical
characteristics of the drug, such as particle size,
Formulation development and selection
Confirmation of batch-to-batch reproducibility polymorphs, and surface area (Gray et al, 2001).
Establish drug product stability The dissolution test is typically a requirement
Demonstrate that the product performs consistently for routine batch testing and qualification of certain
throughout its use period or shelflife scale-up and postapproval changes (SUPAC) for
Establish in vivo–in vitro correlations (IVIVC)
many marketed drug products (see Chapter 18).
Evaluate the biopharmaceutic implications of a product
change, rather than to require a bioequivalence study After a change is made to a formulation, the manu-
(SUPAC—scale-up and postapproval changes) facturer needs to assess the potential effect of the
change on the drug’s bioavailability. If the changes
are deemed minor, the impact on its in vivo perfor-
mance can be assessed by comparing the pre- and
and manufacturing parameters. Dissolution and drug postchange product dissolution profile using the
release tests are also used as a measure of drug prod- approved dissolution method or under different pH
uct performance, in vitro when linked to product conditions. If differences exist between the dissolu-
performance in vivo. The dissolution test should tion profiles, an in vivo bioequivalence study may be
reflect relevant changes in the drug product formula- performed to determine whether the observed differ-
tion or changes in the manufacturing process that ence in vitro translates into different pharmacokinetics
might affect drug release characteristics and conse- in vivo, which could affect the safety and efficacy pro-
quently in vivo performance. Ideally, the dissolution file of the drug product. Major postapproval manu-
method used for a particular drug product in vitro facturing changes require a bioequivalence study to
should mimic the release characteristics of the drug support approval of the change, but this bioequivalence
product in vivo and should potentially be able to dif- study may be waived in the presence of an acceptable
ferentiate among formulations with different release in vitro–in vivo correlation (see Chapter 16).
characteristics.
In vitro drug dissolution studies are often used
for monitoring drug product stability and manufac- Development and Validation of Dissolution
turing process control. In this case, the dissolution and Drug Release Tests
test provides evidence that the product will perform The USP dissolution test is an in vitro performance test
consistently throughout its use period or shelf life. applicable to many dosage forms such as tablets, cap-
The dissolution test is not only useful for the sules, transdermals, suppositories, suspensions, etc.
quality control of finished product, but can provide The development and validation of dissolution tests is
valuable information during formulation develop- discussed in several USP general information chapters
ment (ie, salt form selection, excipient selection, (eg, USP <711>, USP <1092>, USP <724>). The dis-
etc). A suitable dissolution method may uncover a solution procedure requires a dissolution apparatus,
formulation problem with the drug product that dissolution medium, and test conditions that provide a
could result in a bioavailability problem. method that is discriminating yet sufficiently rugged
Each dissolution method is specific for the drug and reproducible for day-to-day operation and capable
product and its formulation. When developing opti- of being transferred between laboratories.
mal dissolution parameters, a variety of conditions The choice of apparatus and dissolution medium
(ie, apparatus, media pH, etc) should be explored. is based on the physicochemical characteristics of
The ultimate goal is to identify a dissolution test that the drug (including solubility, stability) and the type
is capable of distinguishing between acceptable and of formulation (such as immediate release, enteric
unacceptable drug formulations as observed by dif- coated, extended release, rapidly dissolving, etc).
ferent drug dissolution rates under the same experi- The development of an appropriate dissolution
mental conditions. Overall, a suitable dissolution test test requires the investigator to explore different
Biopharmaceutic Considerations in Drug Product Design and In Vitro Drug Product Performance 427
TABLE 156 Conditions That May Affect Drug forms, USP Apparatus 1 and Apparatus 2 are used
Dissolution and Release most frequently. The dissolution test conditions should
be able to discriminate a change in formulation that
Drug substance
Particle size might affect drug product performance. In addition,
Polymorph the dissolution test should be sufficiently rugged and
Surface area reproducible for day-to-day operation and capable of
Chemical stability in dissolution media being transferred between laboratories. The current
Formulation of drug product
USP-NF lists officially recognized dissolution appa-
Excipients (lubricants, suspending agents, etc)
Medium ratus (Table 15-7). Once a suitable dissolution test is
Volume obtained, acceptable dissolution criteria (specifica-
pH tions) are developed for the drug product. For exam-
Molarity ple, Philip and Daly (1983) devised a method using
Co-solvents, added enzymes/surfactants
pH 6.6 phosphate buffer as the dissolution medium
Temperature of medium
Apparatus instead of 0.1 N HCl to avoid instability of the anti-
Hydrodynamics biotic drug erythromycin. Using the USP paddle
Agitation rate method at 50 rpm and a temperature of 22°C, the
Shape of dissolution vessel dissolution of the various erythromycin tablets was
Placement of tablet in vessel
shown to vary with the source of the bulk active drug
Sinkers (for floating products and products that stick to
side of vessel) (Table 15-8 and Fig. 15-8).
Visual observations of the dissolution and disin-
tegration behavior of the drug product are important
agitation rates, different media (including volume and should be recorded. Dissolution and disintegra-
and pH of medium), and different kinds of dissolu- tion patterns can indicate manufacturing variables.
tion apparatus (Table 15-6). For solid oral dosage These observations are particularly useful during
TABLE 157 USP-NF and Non-USP-NF Dissolution Apparatus
Apparatusa Name Agitation Method Drug Product
Apparatus 1 Rotating basket Rotating stirrer Tablets, capsules
Apparatus 2 Paddle Rotating stirrer Tablets, capsules, modified
drug products, suspensions
Apparatus 3 Reciprocating cylinder Reciprocation Extended-release drug
products
Apparatus 4 Flow cell Fluid movement Drug products containing
low water-soluble drugs
Apparatus 5 Paddle over disk Rotating stirrer Transdermal drug products
Apparatus 6 Cylinder Rotating stirrer Transdermal drug products
Apparatus 7 Reciprocating disk Reciprocation Extended-release drug
products
Rotating bottle (Non-USP-NF) Extended-release drug
products (beads)
Diffusion cell (Franz) (Non-USP-NF) Ointments, creams, trans-
dermal drug products
aUSP-NF dissolution apparatus and non-USP-NF dissolution apparatus.
428 Chapter 15
TABLE 158 Dissolution of Erythromycin position in different experiments. The usual medium
Stearate Bulk Drug and Corresponding Tablets volume is 500–1000 mL. Drugs that are poorly water
soluble may require use of a very large-capacity ves-
Percent Dissolution after 1.0 h
sel (up to 2000 mL) to observe significant dissolution.
500-mg 250-mg In some cases, a surfactant (eg, sodium lauryl sulfate,
Curve No. Bulk Drug Tablet Tablet Triton X-100, etc) may be added to the dissolution
4 49 44 medium for water-insoluble drugs. Sink conditions
is a term referring to an excess volume of medium
6 72 70
(at least 3×) that allows the solid drug to dissolve
7 75 70 continuously. If the drug solution becomes saturated,
– 78 – 80 no further net drug dissolution will take place.
According to the USP-NF, “the quantity of medium
8 82 75
used should not be less than 3 times that needed to
9 92 85 form a saturated solution of the drug substance.”
The amount of agitation and the nature of the
From Philip and Daly (1983), with permission.
stirrer affect hydrodynamics of the system, thereby
affecting the dissolution rate. Stirring rates must be
dissolution method development and formulation controlled, and criteria differ among drug prod-
optimization. ucts. Low stirring rates (50–75 rpm) are more dis-
The size and shape of the dissolution vessel may criminating of formulation factors affecting
affect the rate and extent of dissolution. For exam- dissolution than higher stirring rates. However, a
ple, dissolution vessels range in size from several higher dissolution rate may be needed for some
milliliters to several liters. The shape may be round- special formulations in order to obtain reproduc-
bottomed or flat, so the tablet might lie in a different ible dissolution rates. Suspensions that contain
viscous or thickening agents may settle into a dif-
fusion-controlled “cone-shape” region in the flask
10 when stirring rate is too slow. The temperature of
100 9 the dissolution medium must be controlled, and
8 variations in temperature must be avoided. Most
6
dissolution tests are performed at 37°C. However,
80 7
5 for transdermal drug products, the recommended
4 temperature is 32°C.
The nature of the dissolution medium will also
60 3 affect the dissolution test. The solubility of the drug
1 must be considered, as well as the total amount of
2 drug in the dosage form. The dissolution medium
40 should not be saturated by the drug (ie, sink condi-
tions are maintained). Usually, a volume of medium
larger than the amount of solvent needed to com-
20 pletely dissolve the drug is used in the dissolution
test. Which medium is best is determined through
careful investigative studies. The dissolution
0
0 0.50 1.00 1.50 2.00 medium in many USP dissolution tests is deaerated
Time (hours) water or, if substantiated by the solubility character-
FIGURE 158 istics of the drug or formulation, a buffered aqueous
Dissolution profile of various lots of eryth-
romycin stearate as a function of time (0.05 M, pH 6.6 phos- solution (typically pH 4–8) or dilute HCl may be
phate buffer). (From Philip and Daly, 1983, with permission.) used. The significance of deaeration of the medium
Erythromycin in solution (percent)
Biopharmaceutic Considerations in Drug Product Design and In Vitro Drug Product Performance 429
should be determined. Various investigators have the USP-NF monograph for a particular drug product
used 0.1 N HCl, phosphate buffer, simulated gastric or may be recommended by the FDA.1 The USP-NF
fluid, water, and simulated intestinal fluid, depend- sets standards for dissolution and drug release tests of
ing on the nature of the drug product and the loca- most drug products listed in USP monographs.
tion in the gastrointestinal tract where the drug is Alternative dissolution methods, particularly the use
expected to dissolve. of comparative dissolution rate profiles under various
The design of the dissolution apparatus, along conditions, are often used during drug develop-
with the other factors previously described, has a ment to better understand the relationship of the
marked effect on the outcome of the dissolution test. formulation components and manufacturing pro-
No single apparatus and test can be used for all drug cess on drug release.
products. Each drug product must be considered The USP dissolution apparatus and the type of
individually with the dissolution test (method and drug products that is often used with the apparatus are
limit(s)) that best correlates to in vivo bioavailability listed in Table 15-7. For USP Apparatus 1 (basket)
to the extent feasible. and 2 (paddle), low rotational speeds affect the repro-
Usually, the dissolution test will state that a ducibility of the hydrodynamics, whereas at high
certain percentage of the labeled amount of drug rotational speeds, turbulence may occur. Dissolution
product must dissolve within a specified period of profiles that show the drug dissolving too slowly or
time. In practice, the absolute amount of drug in the too rapidly may justify increasing or decreasing
drug product may vary from tablet to tablet. the rotational speed (Gray et al, 2001). The choice
Therefore, a prescribed number of tablets from each of apparatus for solid oral dosage forms is often
lot are usually considered to get a representative dis- Apparatus 1 (rotating basket) or Apparatus 2 (paddle)
solution rate for the product. due to the ease of use, availability of the apparatus,
and availability of automated methods.
Frequently Asked Questions Apparatus 1: Rotating Basket
»»Drug absorption involves at least three distinct
The rotating basket apparatus (Apparatus 1) consists
steps: dissolution, permeation, and disposition
during transit in GI (an additional step of drug of a cylindrical basket held by a motor shaft. The
disposition in the body is involved as well for basket holds the sample and rotates in a round flask
bioavailability). How are these processes validated containing the dissolution medium. The entire flask
in vitro when the in vivo requirement for drug is immersed in a constant-temperature bath set at
bioavailability is waived? 37°C. Agitation is provided by rotating the basket.
The rotating speed and the position of the basket
»»What are the risk mitigating steps taken above if
some manufacturing processes cannot be validated must meet specific requirements set forth in the cur-
in vitro? rent USP. The most common rotating speed for the
basket method is 100–150 rpm. A disadvantage of
»»Why is it important to maintain sink conditions?
the rotating basket is that the formulation may clog
to the 40-mesh screen.
COMPENDIAL METHODS OF
Apparatus 2: Paddle Method
DISSOLUTION
The paddle apparatus (Apparatus 2) consists of a spe-
The USP-NF describes the official dissolution appa- cial, coated paddle that minimizes turbulence due to
ratus and includes information for performing disso- stirring (Fig. 15-9). The paddle is attached vertically
lution tests on a variety of drug products including
tablets, capsules, and other special products such as
1The FDA provides recommendations for many drug products
transdermal preparations. The selection of a particu- on its website, www.accessdata.fda.gov/scripts/cder/dissolution
lar dissolution method for a drug may be specified in /index.cfm.
430 Chapter 15
Speed control
module RPM control knob
RPM readout
Power on/off switch
RPM
Stainless steel
support posts
Drive motor
Locking collars for
repositioning
Fixed drive plate
Height adjustment
ring
Isolated
Circular bubble level heater/circulator
Plastic or glass
dissolution vessels
Free-standing
Adjustable mounts heater/circulator
holder
Acrylic water bath Heavy-duty base plate
(vessel support plate)
FIGURE 159 Typical setup for performing the USP dissolution test with the Distek 2000. The system is equipped with a height
adjustment ring for easy adjustment of paddle height. (Drawing courtesy of Distek Inc, Somerset, NJ.)
to a variable-speed motor that rotates at a controlled tablets. A sinker, such as a few turns of platinum wire,
speed. The tablet or capsule is placed into the round- may be used to prevent a capsule or tablet from float-
bottom dissolution flask, which minimizes turbulence ing. A sinker may also be used for film-coated tablets
of the dissolution medium. The apparatus is housed in that stick to the vessel walls or to help position the
a constant-temperature water bath maintained at tablet or capsule under the paddle (Gray et al, 2001).
37°C, similar to the rotating-basket method. The posi- The sinker should not alter the dissolution character-
tion and alignment of the paddle are specified in the istics of the dosage form.
USP. The paddle method is very sensitive to tilting.
Improper alignment may drastically affect the disso-
lution results with some drug products. The most Apparatus 3: Reciprocating Cylinder
common operating speeds for Apparatus 2 are 50 or The reciprocating cylinder apparatus (Apparatus 3)
75 rpm for solid oral dosage forms and 25 rpm for oral consists of a set of cylindrical, flat-bottomed glass
suspensions. Apparatus 2 is generally preferred for vessels equipped with reciprocating cylinders for
Biopharmaceutic Considerations in Drug Product Design and In Vitro Drug Product Performance 431
dissolution testing of extended-release products, addition of a stainless steel disk assembly designed
particularly bead-type modified-release dosage for holding the transdermal system at the bottom of
forms. Reciprocating agitation moves the dosage the vessel. The entire preparation is placed in a dis-
form up and down in the media. The agitation rate is solution flask filled with specified medium main-
generally 5–30 dpm (dips per minute). The recipro- tained at 32°C. The paddle is placed directly over the
cating cylinder can be programmed for dissolution in disk assembly. Samples are drawn midway between
various media for various times. The media can be the surface of the dissolution medium and the top of
changed easily. This apparatus may be used during the paddle blade at specified times. Matrix transder-
drug product development to attempt to mirror pH mal patches can be cut to size of the disk assembly.
changes and transit times in the GI tract such as
starting at pH 1 and then pH 4.5 and then at pH 6.8. Apparatus 6: Cylinder
The cylinder method (Apparatus 6) for testing trans-
Apparatus 4: Flow-through-Cell dermal preparation is modified from the basket
The flow-through-cell apparatus (Apparatus 4) con- method (Apparatus 1). In place of the basket, a
sists of a reservoir for the dissolution medium and a stainless steel cylinder is used to hold the sample.
pump that forces dissolution medium through the The sample is mounted onto cuprophan (an inert
cell holding the test sample. The media may be a porous cellulosic material) and the entire system
non-recirculating, continuous flow solution, or recir- adheres to the cylinder. Testing is maintained at
culating solution. The flow rate is critical. Flow rate 32°C. Apparatus 6 may be used for reservoir trans-
ranges from 4 to 32 mL/min. Apparatus 4 may be dermal patches that cannot be cut smaller. Samples
used for modified-release dosage forms that contain are drawn midway between the surface of the disso-
active ingredients having very limited solubility. The lution medium and the top of the rotating cylinder
high volume provides “infinite” sink conditions. for analysis.
There are many variations of this method.
Essentially, the sample is held in a fixed position Apparatus 7: Reciprocating Disk
while the dissolution medium is pumped through the
The reciprocating disk method for testing transdermal
sample holder, thus dissolving the drug. Laminar
products uses a motor drive assembly (Apparatus 7)
flow of the medium is achieved by using a pulseless
that reciprocates vertically. The samples are placed on
pump. Peristaltic or centrifugal pumps are not rec-
disk-shaped holders using cuprophan supports. The
ommended. The flow rate is usually maintained
test is also carried out at 32°C, and reciprocating fre-
between 10 and 100 mL/min. The dissolution medium
quency is about 30 cycles per minute.
may be fresh or recirculated. In the case of fresh
medium, the dissolution rate at any moment may be
obtained, whereas in the official paddle or basket ALTERNATIVE METHODS OF
method, cumulative dissolution rates are monitored.
A major advantage of the flow-through method is the DISSOLUTION TESTING
easy maintenance of a sink condition for dissolution. Rotating Bottle Method
A large volume of dissolution medium may also be
The rotating bottle method was suggested in
used, and the mode of operation is easily adapted to
NF-XIII (National Formulary) but has become less
automated equipment.
popular since. The rotating bottle method was used
mainly for controlled-release beads. For this pur-
Apparatus 5: Paddle-over-Disk pose the dissolution medium may be easily changed,
The USP-NF also lists a paddle-over-disk method such as from artificial gastric juice to artificial
for testing the release of drugs from transdermal intestinal juice. The equipment consists of a rotat-
products. The apparatus (Apparatus 5) uses the pad- ing rack that holds the sample drug products in
dle and vessel assembly from Apparatus 2 with the bottles. The bottles are capped tightly and rotated in
432 Chapter 15
a 37°C temperature bath. At various times, the sam- Dosage Glass disk
donor area
ples are removed from the bottle, decanted through a
40-mesh screen, and the residues are assayed. An Membrane Dosage water
equal volume of fresh medium is added to the remain-
ing drug residues within the bottles and the dissolu-
Sampling port
tion test is continued. A dissolution test with pH 1.2 Receptor solution
medium for 1 hour, pH 2.5 medium for the next
1 hour, followed by pH 4.5 medium for 1.5 hours, Water jacket 32°C
pH 7.0 medium for 1.5 hours, and pH 7.5 medium
for 2 hours was recommended to simulate the condi- Helix mixer Replace port
tion of the gastrointestinal tract. The main disadvan- & magnetic stirrer with bubble trap
tage is that this procedure is manual and tedious. FIGURE 1510 The Franz diffusion cell. (Courtesy of
Hanson Research Corporation [www.hansonresearch.com
/vert_diffusion_cell.htm], with permission.)
Intrinsic Dissolution Method
Most methods for dissolution deal with a finished drug
product. Sometimes a new drug or substance may be The source of skin may be human cadaver skin or
tested for dissolution without the effect of excipients or animal skin (eg, hairless mouse skin). Anatomically,
the fabrication effect of processing. The dissolution of each skin site (eg, abdomen, arm) has different drug
a drug powder by maintaining a constant surface area permeation qualities. The skin is mounted on the Franz
is called intrinsic dissolution. Intrinsic dissolution is diffusion cell system. The drug product (eg, ointment)
usually expressed as mg/cm2/min. In one method, the is placed on the skin surface and the drug permeates
basket method is adapted to test dissolution of powder across the skin into a receptor fluid compartment that
by placing the powder in a disk attached with a clipper may be sampled at various times. The Franz diffusion
to the bottom of the basket. cell system is useful for comparing in vitro drug
release profiles and skin permeation characteristics to
aid in selecting an appropriate formulation that has
Peristalsis Method optimum drug delivery.
The peristalsis method attempts to simulate the
hydrodynamic conditions of the gastrointestinal tract Dissolution Testing of Enteric-Coated
in an in vitro dissolution device. The apparatus con- Products
sists of a rigid plastic cylindrical tubing fitted with a
septum and rubber stoppers at both ends. The disso- USP-NF lists two methods (Method A and Method B)
lution chamber consists of a space between the sep- for testing enteric-coated products. The latest revi-
tum and the lower stopper. The apparatus is placed in sion of the USP-NF should be consulted for com-
a beaker containing the dissolution medium. The plete details of the methods.
dissolution medium is pumped with peristaltic action Both methods require that the dissolution test be
through the dosage form. performed in the apparatus specified in the drug
monograph (usually Apparatus 2 or Apparatus 1).
The product is first studied with 0.1 N HCl for 2 hours
Diffusion Cells and then the medium is changed to pH 6.8 buffer
Static and flow-through diffusion cells are commer- medium. The buffer stage generally runs for 45 minutes
cially available to characterize in vitro drug release or for the time specified in the monograph. The
and drug permeation kinetics from topically applied objective is that no significant dissolution occurs in
dosage form (eg, ointment, cream) or transdermal the acid phase (less than 10% for any sample unit),
drug product. The Franz diffusion cell is a static and a specified percentage of drug is released in
diffusion system that is used for characterizing the buffer phase. Dissolution acceptance criteria
drug permeation through a skin model (Fig. 15-10). are defined in the individual drug monographs for
Biopharmaceutic Considerations in Drug Product Design and In Vitro Drug Product Performance 433
commercial products. Appropriate criteria will need considers mechanical specifications of the instrument
to be established for novel drugs formulated as design and its manufacture (FDA Guidance for
enteric-coated drug products. Industry, January 2010). Instead of using a calibrator
tablet, a pharmaceutical manufacturer can use an
Dissolution Approaches for Novel/Special appropriately rigorous method of mechanical calibra-
Dosage Forms tion for dissolution Apparatus 1 and 2.
New or specialized dosage forms are being devel-
oped for improving patient compliance, to enhance Frequently Asked Questions
therapeutic response and for marketing exclusivity.
»»Which dissolution apparatus are most often used for
Some of these dosage forms include osmotic cap- tablets and capsules?
sules, orally disintegrating tablets, medicated chew-
ing gums, soft gelatin capsules containing drug »»What is meant by “sink” conditions?
dissolved in oil, nanomaterial, liposomal drug prod- »»How is the discriminating ability of the method
ucts, implants, intrauterine devices, and drug-eluting assessed?
stents. While conventional apparatus may be used to
»»Can the discriminating ability of the dissolution
evaluate the dissolution kinetics of nonconventional method be improved by tightening the dissolution
dosage forms, specialized or modified systems may acceptance criteria?
be needed for others. For example, medicated chew-
ing gum and extended-release parenteral products
may need a specialized dissolution apparatus or a Discriminating Dissolution Test
modified dissolution apparatus (Siewart et al, 2003).
The value of in vitro dissolution testing is its ability to
characterize drug products and assist in decision mak-
USP Performance Verification Test and ing including (1) ensuring quality control through a
Mechanical Calibration linkage to batches used in pivotal clinical studies;
Dissolution is a complex system that mainly consists (2) information on batch-to-batch consistency; and
of three components: (1) the analyst, (2) the dissolu- (3) guide in formulation development. Dissolution
tion apparatus, and (3) the analytical procedure/ testing is the only product test that truly measures the
instrument. In order for the dissolution test to be effect of formulation and physical properties of the
performed properly, and give meaningful results, active pharmaceutical ingredient (API) on the rate of
these three components must interact together opti- drug solubilization. In addition, under certain circum-
mally, or the results can be misleading. The USP stances (eg, presence of an adequate IVIVC) in vitro
general chapter for dissolution includes performance dissolution testing can serve as a surrogate for bio-
verification test (PVT), to assure the suitability of equivalence studies to assess the impact of some pre-
Apparatus 1 and 2 when used for testing drug prod- and postapproval changes. The dissolution testing
ucts. PVT requires chemical calibration with calibra- procedure should be discriminating to ensure its value.
tor tablets that may be obtained from USP-NF. The A discriminating method is the one that is
calibration tablets, either prednisone tablets for dis- appropriately sensitive to manufacturing changes. A
solution tests requiring disintegrating tablets or sali- discriminating method is able to differentiate drug
cylic acid as a standard for nondisintegrating tablets, products manufactured under target conditions ver-
are used to qualify USP dissolution Apparatus 1 and sus drug products that are intentionally manufac-
Apparatus 2. PVT is also useful to compare perfor- tured with meaningful variations (ie, ±10%–20%
mance of different dissolution apparatus used in dif- change) to the specification ranges of the most rele-
ferent laboratories. vant material attributes and manufacturing variables
Mechanical calibration is a critical component of (eg, drug substance particle size, polymorphism,
the qualification of the dissolution apparatus. The FDA compression force, tablet hardness, etc). The choice
has introduced a mechanical calibration approach that of experimental design to evaluate the most relevant
434 Chapter 15
variables will depend on the design of the dosage
form, the manufacturing process, and intrinsic prop- 90
erties of the API (Brown et al, 2004).
80
Developing a discriminating method is crucial
when setting drug product specifications (eg, disso-
70
lution acceptance criterion) because the value of this
specification depends on the discriminating ability
60
of the method. If the method is over-discriminating,
batches with adequate performance will be rejected
50
creating a burden for the pharmaceutical companies.
If it is under-discriminating, batches with an inade- 40 Form A 100 microns
quate performance will be accepted, which may put Clinical trial form: 40 microns
Form B 30 microns
the patient to risk. However, unless an in vitro–in 30 Form C 65 microns
vivo relationship (IVIVR) or correlation (IVIVC)
has been established between dissolution and in vivo 0 10 20 30 40 50 60
Time (min)
data (eg, plasma concentrations), the biorelevancy of
the method (ability of the method to reject for FIGURE 1511 Effect of particle size and drug release
batches with inadequate in vivo performance) cannot rate—Importance of selecting the right specification-sampling
time point and specification value to establish a discriminating
be determined.
dissolution method.
Ideally, dissolution (or release) method and
acceptance criterion should be further evaluated
using in vivo bioavailability or bioequivalence stud- to Q = 80% at 45 minutes may not be appropriate
ies with product variants manufactured during the because it would be accepting a batch that does not
course of pharmaceutical development, including have the same performance as that for the clinical
batches used in clinical trials. A dissolution method batch. Selecting the wrong acceptance criterion
and acceptance criterion should be modified if (eg, overly permissive criterion), despite the meth-
they are found to be over-discriminating or under- od’s intrinsic discriminating ability, renders the
discriminating when compared with the results of method not discriminating.
in vivo studies.
One should note that the discriminating ability is DISSOLUTION PROFILE
determined not only by the dissolution method settings COMPARISONS
but also by the selected specification-sampling time
point and specification value. Figure 15-11 illustrates Dissolution profile comparisons are used to assess
the importance of selecting the right specification- the similarity of the dissolution characteristics of two
sampling time point and specification value to estab- formulation or different strengths of the same formu-
lish a discriminating method. Batches A through C are lation to decide whether in vivo bioavailability/
commercial batches. The fast release batch corre- bioequivalence studies are needed. The SUPAC-IR
sponds to a pivotal Phase 3 clinical batch. What can and SUPAC-MR (FDA guidances for immediate-
we say about the discriminating ability of the dissolu- release and modified-release oral formulations,
tion method? The method seems sensitive to particle respectively) provide recommendations to firms who
size changes; however, because batch A failed simi- intend, during the postapproval period, to change
larity testing (eg, f2 statistical testing), then the dis- (a) the components or compositions; (b) the site of
solution acceptance criterion should be selected in a manufacture; (c) the scale-up/scale-down of manufac-
way that rejects this batch, increasing in this way the ture; and/or (d) the manufacturing (process and equip-
method’s discriminating ability. Selecting a criterion ment) of the drug product. For each type of change,
of Q = 80% at 30 minutes fulfills this purpose. these guidances list documentation (eg, dissolution
Note that setting a dissolution acceptance criterion testing, bioequivalence, etc) that should be normally
% Drug dissolved
Biopharmaceutic Considerations in Drug Product Design and In Vitro Drug Product Performance 435
provided to support the change depending on the 120
level of complexity of the proposed change (Levels 1,
100
2, and 3). Note that the principles listed in these guid-
ances can also be applicable for manufacturing changes 80
occurring during product development. 60
For minor changes and some major changes (eg,
manufacturing site change for an immediate-release 40 Rt
T
formulation) for which in vivo bioequivalence is not t
20
warranted, dissolution profile comparisons either in
0
the proposed media or in multimedia can be submit- 0 2 4 6 8 10 12 14
ted to support the change. Time (hours)
Dissolution profiles may be considered similar by FIGURE 1512 Dissolution of test and reference ER
virtue of overall profile similarity and/or similarity at tablets. Rt = reference and Tt = text.
every dissolution sample time point. The FDA guid-
ance on dissolution testing (FDA Guidance for Industry,
1997a) describes three statistical methods for the evalu-
ation of similarity: (1) model-independent approach The similarity factor (f2) is determined by
using a similarity factor; (2) model-independent multi- comparing the dissolution profiles of 6–12 units
variate confidence region procedure; and (3) model- each of the test and reference products (Fig. 15-12).
dependent approach. The first approach is described Using the mean dissolution values from both pro-
below. Refer to the dissolution testing guidance for files at each time interval, the similarity factor (f2)
details on the other two approaches. is calculated. For this calculation, three to four or
A model-independent approach uses a differ- more dissolution time points should be available.
ence factor (f1) and a similarity factor (f2) to compare The dissolution measurements of the test and refer-
dissolution profiles. The difference factor (f1) calcu- ence batches should be performed under exactly
lates the percent (%) difference between the two the same conditions, and only one measurement
curves at each time point and is a measurement of should be considered after 85% dissolution of both
the relative error between the two curves. products. The dissolution time points for both pro-
files should be the same (eg, 15, 30, 45, and
n n
f 60 minutes). f2 values greater than 50 mean that
1 = ∑ | Rt − T R
t | / ∑ t ×
100
t=1 t=1 there is less than 10% difference between the two dis-
solution profiles. f2 values greater than 50 (50–100)
where n is the number of time points, R is the dis- ensure sameness or equivalence of the two curves
solution value of the reference batch at time t, and T and, thus, of the performance of the test (postchange)
is the dissolution value of the test batch at time t. and reference (prechange) products. Note that to
The similarity factor (f2) is a logarithmic recipro- allow use of mean data, the percent coefficient of
cal square root transformation of the sum of squared variation at the earlier time points (eg, 15 minutes)
error and is a measurement of the similarity in the should not be more than 20%, and at other time
percent (%) dissolution between the two curves. points should not be more than 10%. If these crite-
−0.5 ria are not met, then other approaches such as
n
f2 = 50 × log 1+ (1/n)∑ (R T 2
t − t ) ×
t=
100 multivariate approaches (refer to the dissolution
1 guidance for details on these approaches) should
be used to determine similarity. In addition, dis-
where n is the number of time points, R is the dis- solution profile comparisons are not applicable
solution value of the reference (prechange) batch at from statistical perspective when the release char-
time t, and T is the dissolution value of the test (post- acteristics are very fast achieving greater than 85%
change) batch at time t. in 15 minutes.
Percent dissolved
436 Chapter 15
MEETING DISSOLUTION the release of any lots with dissolution profiles
outside those that were studied clinically.
REQUIREMENTS
The term Q means the amount of drug dissolved
According to the Code of Federal Regulations (CFR),
within a given time period established in the drug
a drug product application should include the specifi-
product specification table and is expressed as a per-
cations necessary to ensure the identity, strength,
centage of label content. For example, a value of
quality, purity, potency, and bioavailability of the
Q = 80% at 30 minutes means that the mean percent
drug product, including, and acceptance criteria relat-
dissolved of 12 units individually tested is at least
ing to, dissolution rate in the case of solid dosage
80% at the selected time point of 30 minutes. Note
forms. For the selection of the dissolution acceptance
that when implementing dissolution as a quality con-
criteria, the following points should be considered:
trol tool for batch release and stability analysis, the
1. The dissolution profile data from the pivotal testing should follow the recommendations listed in
clinical batches and primary (registration) the USP method <711> for immediate-release dos-
stability batches should be used for the setting age forms and <724> for modified-release dosage
of the dissolution acceptance criteria of your forms. For example, for Stage 1, which considers the
product (ie, specification-sampling time point testing of 6 units, each unit must meet the criterion
and specification value). A significant trend in of not less than 85% at 30 minutes for a drug product
the change in dissolution profile during stabil- whose acceptance criterion was set to Q = 80% at
ity should be justified with dissolution profile 30 minutes. Testing should continue through the
comparisons and in vivo data in those instances three stages (S1, S2, S3) unless the results conform at
where the similarity testing fails. either Stage 1 or Stage 2 (Table 15-9).
2. Specifications should be established based on
average in vitro dissolution data for each lot
under study, equivalent to USP Stage 2 testing TABLE 159 Theophylline Extended-Release
(n = 12). Capsules, USP
3. For immediate-release formulations, the last
Test 1
time point should be the time point where at
least 80% of drug has been released. If the max- Time (h) Amount Dissolved
imum amount released is less than 80%, the last
1 Between 10% and 30%
time point should be the time when the plateau
of the release profile has been reached. Percent 2 Between 30% and 55%
release of less than 80% should be justified with 4 Between 55% and 80%
data (eg, sink conditions information).
8 Not less than 80%
4. For extended-release formulations, a minimum
of three time points is recommended to set the Test 2
specifications. These time points should cover
Time (h) Amount Dissolved
the early, middle, and late stages of the release
profile. The last time point should be the time 1 Between 3% and 15%
point where at least 80% of drug has been 2 Between 20% and 40%
released. If the maximum amount released is
4 Between 50% and 75%
less than 80%, the last time point should be the
time when the plateau of the release profile has 6 Between 65% and 100%
been reached. 8 Not less than 80%
5. The dissolution acceptance criterion should be
Both of these theophylline ER capsule products are for products
set in a way to ensure consistent performance labeled for dosing every 12 h. These products are bioequivalent in vivo
from lot to lot, and this criterion should not allow and are approved by FDA as therapeutic equivalents.
Biopharmaceutic Considerations in Drug Product Design and In Vitro Drug Product Performance 437
The USP-NF monographs may have multiple air bubbles on the surface of the dosage form unit
dissolution tests for generic drug products that are and can affect dissolution in both the basket and
approved by the FDA as therapeutic equivalents. paddle methods.
Although both the brand and approved generic drug Several published articles are available describ-
products are bioequivalent, their in vitro dissolution ing high variability in dissolution results, due to
profiles may be different. Ideally, both methods hydrodynamic effects, unpredictability, and random-
should have very similar discriminating ability; how- ness of observed results even for dissolution appara-
ever, this can only be determined when an IVIVR or tus calibrator tablets (Bocanegra et al, 1990; Gray
an IVIVC has been established for the drug products and Hubert, 1994; Achanta et al, 1995; Qureshi and
rending the method not only discriminating but also McGilveray, 1999). Small variations in the location
predictive of in vivo performance. of the tablet on the vessel bottom caused by the ran-
domness of the tablet descent through the liquid are
likely to result in significantly different velocities and
PROBLEMS OF VARIABLE CONTROL velocity gradients near the tablet (Armenante and
IN DISSOLUTION TESTING Muzzio, 2005). Experiments were conducted using
USP paddle apparatus by placing (aligned to the
As described above, various equipment and operating walls) a metal strip (1.7 mm thick × 6.4 mm wide) to
variables are associated with dissolution testing. evaluate the effect of variable mixing/stirring and
Understating the effects of operating conditions, the flow pattern in a drug dissolution vessel. The major-
hydrodynamics and the geometric variables on the ity of products evaluated gave significantly higher
velocity distribution in the dissolution system are criti- dissolution results with vessels containing metal strip
cal to enhance the reliability of dissolution testing and than without. The extent of increased dissolution
to avoid product recalls. with the metal strip varied from products indicating
Dissolution testing is a complex process involv- that, employing the current apparatuses, products
ing various steps such as solid–liquid mass transfer, may provide lower-than-anticipated results that may
particle erosion, possible particle disintegration, not be reflective of the product drug release charac-
particle suspension, and particle–liquid interactions. teristics (Qureshi and Shabnam, 2001).
However, this process is further complicated by
other factors such as shear stress distribution as a
function of tablet location within the apparatus,
and the location of the tablet upon its release inside PERFORMANCE OF DRUG
the apparatus. PRODUCTS: IN VITRO–IN VIVO
Depending on the particular dosage form CORRELATION
involved, the variables may or may not exert a pro-
nounced effect on the rate of dissolution of the drug For controlled-release or extended-release formula-
or drug product. Variations may occur with the same tion, since dissolution or release of the drug from the
type of equipment and procedure. The centering and formulation is the rate-limiting step in the appear-
alignment of the paddle is critical in the paddle ance of the drug into the systemic circulation, it is
method. Turbulence can create increased agitation, possible to establish a relationship between the
resulting in a higher dissolution rate. Wobbling and release of the drug in vitro and its release in vivo or
tilting due to worn equipment should be avoided. its absorption into the systemic circulation. If such
The basket method is less sensitive to the tilting correlation exists, then one is able to predict the
effect. However, the basket method is more sensitive plasma concentration time profile of a drug from its
to clogging due to gummy materials. Pieces of small in vitro dissolution. Usually such a correlation is
particles can also clog up the basket screen and cre- developed with two or more formulations with dif-
ate a local nonsink condition for dissolution. ferent release characteristics. It is recommended that
Furthermore, dissolved gas in the medium may form a correlation be established with three or more
438 Chapter 15
formulations. However, if the dissolution of the drug other by more than 20% (US IVIVC guidance for
is independent of the dissolution conditions (such as industry; EMA, August 2012).
apparatus agitation rate, pH, etc), then it is possible to
establish such a correlation with only one formula-
Categories of In Vitro–In Vivo Correlations
tion. The establishment of a predictive IVIVC not
only provides you with a better understanding of the Level A Correlation
release properties of the drug product but also enables Level A correlation is the highest level of correlation
one to decrease the number of in vivo studies needed and represents a point-to-point (1:1) relationship
to approve and maintain a drug product on the market between an in vitro dissolution and the in vivo input
resulting in an economic benefit as well as a decreased rate of the drug from the dosage form. Level A correla-
regulatory burden. It also enables one to set clinically tion compares the percent (%) drug released versus
meaningful dissolution specifications based on the percent (%) drug absorbed. Generally, the percentage
predicted plasma concentration time profile. of drug absorbed may be calculated by the Wagner–
A meaningful and predictive IVIVC is a correla- Nelson or Loo–Riegelman procedures (see Chapter 8)
tion that is able to predict the Cmax and AUC within or by direct mathematical deconvolution, a process
20% (FDA guidance for industry, 1997b). There are of mathematical resolution of blood level into an
two ways in evaluating the predictability of the cor- input (absorption) and an output (disposition) com-
relation: (1) Internal predictability refers to the abil- ponent (Fig. 15-13).
ity to predict the pharmacokinetic profile of the The major advantage of a Level A correlation is
formulations that were used to develop the correla- that a point-to-point correlation is developed. All
tion; (2) external predictability refers to the ability to in vitro dissolution data and all in vivo plasma drug
detect the profile of a lot or formulation that was not concentration–time profile data are used. Once a
used to develop the IVIVC. In the United States and Level A correlation is established, an in vitro disso-
in Europe, a bioequivalence study can be waived lution profile can serve as a surrogate for in vivo
based on the IVIVC if the predicted mean AUC and performance. A change in manufacturing site,
Cmax of the test and reference do not differ from each method of manufacture, raw material supplies, minor
A. Plasma drug concentration versus time B. Fraction of drug absorbed versus time
70.0
60.0
50.0 1.2
40.0 Deconvolution 1
30.0 0.8
0.6
20.0 0.4
10.0 0.2
0.0 0
0 10 20 30 40 0 2 4 6
Time (hours) Time (hours)
C. Percent drug dissolved D. Percent drug dissolved versus
percent drug absorbed
100 100
80 80
60 Percent drug absorbed 60
40 40
20 20
0 0
0 10 20 30 0 20 40 60 80 100
Time (hours) Percent dissolved
FIGURE 1513 Deconvolution of plasma drug concentration–time curve.
Percent drug dissolved Drug concentration (ng/mL)
Percent dissolved Fraction of
drug absorbed
Biopharmaceutic Considerations in Drug Product Design and In Vitro Drug Product Performance 439
formulation modification, and even product strength The absorption rate is usually more difficult to
using the same formulation can be justified without determine than peak absorption time. Therefore, the
the need for additional human studies. Level A cor- absorption time may be used in correlating dis-
relation enables the in vitro dissolution test to solution data to absorption data. In the analysis of
become meaningful and clinically relevant quality in vitro–in vivo drug correlation, rapid drug dissolu-
control test that can predict in vivo drug product tion may be distinguished from the slower drug
performance. absorption by observation of the absorption time for
the preparation. The absorption time refers to the
Level B Correlation time for a constant amount of drug to be absorbed.
Level B correlation utilizes the principle of statisti- In one study involving three sustained-release aspi-
cal moment (see Chapter 25) in which the mean rin products (Levy et al, 1965), the dissolution times
in vitro dissolution time is compared to either the for the preparations were linearly correlated to the
mean residence time (MRT)2 or the mean in vivo dis- absorption times (Fig. 15-14). The results from this
solution time (MDT). Level B correlation uses all of study demonstrated that aspirin was rapidly absorbed
the in vitro and in vivo data, but is not a point-to- and was very much dependent on the dissolution rate
point correlation. Different profiles can give the for absorption.
same parameter values. The Level B correlation
alone cannot justify formulation modification, man- Percent of drug dissolved versus percent of
ufacturing site change, excipient source change, drug absorbed. If a drug is absorbed completely
batch-to-batch quality, etc. after dissolution, a linear correlation may be
obtained by comparing the percentage of drug
Level C Correlation absorbed to the percentage of drug dissolved. In
A Level C correlation is not a point-to-point correla- choosing the dissolution method, one must consider
tion. A Level C correlation establishes a single-point the appropriate dissolution medium and use a slow
relationship between a dissolution parameter such as dissolution stirring rate so that in vivo dissolution is
percent dissolved at a given time and a pharmacoki- approximated.
netic parameter of interest such as AUC and C Aspirin is absorbed rapidly, and a slight change
max.
Level C correlation is useful for formulation selec- in formulation may be reflected in a change in the
tion and development but has limited application.
Multiple Level C correlation relates one or several
pharmacokinetic parameters of interest to the amount 2.0
of drug dissolved at several time points of the disso-
lution profile. In general, if one is able to develop a
1.5
multiple Level C correlation, then it may be feasible
to develop a Level A correlation. Several examples of
Level C correlation are given below. 1.0
Dissolution rate versus absorption rate. If
0.5
dissolution of the drug is rate limiting, a faster
dissolution rate may result in a faster rate of
appearance of the drug in the plasma. It may be 0
0 2 4 6 8
possible to establish a correlation between rate of Absorption time (hours)
dissolution and rate of absorption of the drug. FIGURE 1514 An example of correlation between time
required for a given amount of drug to be absorbed and time
required for the same amount of drug to be dissolved in vitro
2MRT is the mean (average) time that the drug molecules stay in for three sustained-release aspirin products. (From Wood, 1966,
the body, whereas the MDT is the mean time for drug dissolution. with permission.)
Dissolution time (hours)
440 Chapter 15
100
1.50 C
E H
B K
80 1.25
F
A
1.00
60 G J
0.75
E C
40 H
B K
1.25
F
20 A
1.00
G J
0 0.75
0 20 40 60 80 0 20 40 60 80 100
Dissolved at time t (percent) ( T – lag time
t = ) Dissolved (percent)
2
FIGURE 1516 In vitro–in vivo correlation between Cmax
FIGURE 1515 An example of continuous in vivo–in vitro and percent drug dissolved. A, 30 min (slope = 0.06, r = 0.902,
correlation of aspirin. (From Levy et al, 1965, with permission.) p < 0.001). B, 60 min (slope = 0.10, r = 0.940, p < 0.001). (Letters
on graph indicate different products.) (From Shah et al, 1983,
with permission.)
amount and rate of drug absorption during the period
of observation (see Figs. 15-14 and 15-15). If the
drug is absorbed slowly, which occurs when absorp- dissolution rate was product C, for which about
tion is the rate-limiting step, a difference in dissolu- 100% of the labeled contents dissolved in the test
tion rate of the product may not be observed. In this (Fig. 15-17). Interestingly, these products also show
case, the drug would be absorbed very slowly inde- the shortest time to reach peak concentration (tmax).
pendent of the dissolution rate. The tmax is dependent on the absorption rate constant.
Maximum plasma concentrations versus
percent of drug dissolved in vitro. When
different drug formulations are studied for dissolution, 6 A
G J
a poorly formulated drug may not be completely
dissolved and released, resulting in lower plasma drug F
5
concentrations. The percentage of drug released at any
time interval will be greater for the more bioavailable E
drug product. When such drug products are studied in 4 B
K
vivo, the peak drug serum concentration will be higher
for the drug product that shows the highest percent H
3
of drug dissolved. An example of in vitro–in vivo
C
correlation for 100-mg phenytoin sodium capsules
is shown in Fig. 15-16. Several products were tested 0
0 20 40 60 80 100
(Shah et al, 1983). A linear correlation was observed
Dissolved (percent)
between the maximum drug concentration in the body
and the percent of drug dissolved in vitro. FIGURE 1517 In vitro–in vivo correlation between tmax
and percent drug dissolved in 30 minutes by basket method.
The dissolution study on the phenytoin sodium Letters on graph indicate different products. (From Shah et al,
products (Shah et al, 1983) showed that the fastest 1983, with permission.)
Absorbed at time T (percent)
Time to peak (hours) Maximum concentration (mg/mL)
Biopharmaceutic Considerations in Drug Product Design and In Vitro Drug Product Performance 441
In this case, the fastest absorption would also result BCS Class I drugs. A BCS Class I drug product con-
in the shortest tmax. tains a highly soluble drug substance that is highly
permeable and from which the drug rapidly dis-
Serum drug concentration versus percent of solves from the drug product over the physiologic
drug dissolved. In a study on aspirin absorption, pH range of 1–7.4. Highly permeable drugs are
the serum concentration of aspirin was correlated drugs whose absolute bioavailability is greater than
to the percent of drug dissolved using an in vitro 90%. It is to be noted that the BCS only applies to
dissolution method (Wood, 1966). The dissolution oral immediate-release formulations and cannot be
medium was simulated gastric juice. Because aspirin applied to modified-release formulations or for buc-
is rapidly absorbed from the stomach, the dissolution cally absorbed drug products (FDA Guidance for
of the drug is the rate-limiting step, and various Industry, August 2000).
formulations with different dissolution rates will cause
differences in the serum concentration of aspirin by
minutes (Fig. 15-18). APPROACHES TO ESTABLISH
CLINICALLY RELEVANT DRUG
Biopharmaceutic Drug Classification System PRODUCT SPECIFICATIONS
The biopharmaceutic drug classification system,
BCS, discussed more fully in Chapter 16, is a predic- Establishing the appropriate product specifications is
tive approach to relate certain physicochemical char- critical in assuring that the manufacture of the dos-
acteristics of a drug substance and drug product to in age form is consistent and successful throughout the
vivo bioavailability. The BCS is not a direct in vitro– product’s life cycle. Product specifications are typi-
in vivo correlation. For example, the drug substance cally considered as those limits that define adequate
from an immediate-release (IR) oral drug product quality and that support the in vitro determinations
would tend to be rapidly and mostly absorbed if the of identity, purity, potency, and strength of the drug
drug substance and drug product meet the criteria for product. On the other hand, clinically relevant speci-
fications are those specifications that, in addition,
take into consideration the clinical impact assuring
48 consistent safety and efficacy profile. In this case,
the choice of acceptance criteria is no longer made
40 based on the in vitro results but on predetermined
clinical acceptable outcomes. Understanding the
relationship between the in vitro measures and the
32
clinical outcomes may provide flexibility in setting
specifications.
24 How are clinically relevant specifications set?
The ideal approach would be to adopt the quality by
16 design (QbD) approach in the drug development pro-
cess. This approach should include the understanding
of the critical quality attributes (CQA) and interac-
8
tions and the impact that these may have on the quality
target product profile (QTPP). Under the QbD para-
digm it is assumed that all the batches manufactured
0 20 40 60 80 100
Dissolved (percent) within the design space (DS) have the same in vivo
performance, in such a way that once the DS is veri-
FIGURE 1518 Example of in vivo–in vitro two-point cor-
fied, no studies are needed for movements within the
relation between 10-minute serum level and percent dissolved
at 1.2 minutes (°) and the 20-minute serum level and percent DS. The key question arises as: How do we achieve
dissolved at 4.2 minutes (•). (From Wood, 1966, with permission.) the goal of demonstrating that all the batches within
Serum level (mg/mL)
442 Chapter 15
the DS have the same in vivo performance? In based on the mean dissolution values of batches
answering this question the use of biopharmaceutic tested in pivotal clinical trials. Any major changes
tools such as dissolution and BA/BE studies become implemented to a pivotal clinical trial formulation
relevant because it would be rather impractical to need to be supported by additional BA/BE studies
determine the clinical relevance of movements within since dissolution can only support the implementation
the DS through clinical efficacy and safety trials. of minor changes.
As such, one approach to establishing clinically It is widely accepted that minor changes can be
relevant drug product specifications may be to man- evaluated by dissolution profile comparisons and
ufacture several product variants with different dis- they would have no or minimal effect on the bio-
solution characteristics resulting in markedly availability and consequently the safety and effi-
different plasma concentration versus time profiles. cacy profile; however, there may be the case when
In so doing, one can also (a) assess the impact of certain minor apparent changes may have an in vivo
changes in various product attributes or process impact and the assessment of the impact on clinical
parameters on in vitro dissolution and in vivo perfor- performance depends on the discriminating ability
mance, (b) explore relationship between in vitro dis- of the method (ie, established using data from
solution and in vivo bioavailability, and (c) determine DOE studies). These limitations make this approach
relative bioavailability or bioequivalence among less desirable.
product variants, using clinical trial material as a
reference. Consequently, this approach not only Approach B: Data linking in vitro and in vivo
facilitates the identification of the critical material performance ARE available. In this case, studies
attributes (CMA) and critical process parameters have been carried out to determine whether changing
(CPP) but also facilitates establishing clinically rel- the CMAs or CPPs have an effect on dissolution and
evant drug product specifications. This understand- systemic exposure. The in vitro–in vivo assessment
ing helps in defining and verifying the DS limits, (IVIVA) process often involves the following
which links the important in vitro performance of the steps: (a) Prepare product variants using critical
drug product to the desired clinical performance. formulation and/or manufacturing variables to study
Due to the critical role that dissolution plays in their in vitro dissolution characteristics, (b) develop
defining the bioavailability of the drug, in vitro dissolu- a discriminating dissolution method, (c) conduct
tion, if identified as a CQA, can serve as a relevant in vivo pharmacokinetic study(ies) in appropriate
predictor of the in vivo performance of the drug prod- groups of human subjects to test these product
uct. In this case, clinically meaningful dissolution variants along with a reference standard (ie, the
method and specifications will minimize the variability formulation used in pivotal Phase 3 clinical trials),
to the patient and therefore will optimize drug therapy. (d) identify the products exhibiting the fastest and
There are several general approaches that can be slowest dissolution characteristics, and (e) evaluate
used for determining clinically relevant dissolution relative bioavailability and/or bioequivalence of
specifications, depending on whether in vivo data the product variants and determine if an IVIVC or
(ie, systemic exposure) are available (Suarez-Sharp, an IVIVR (eg, established by determining whether
2011a, 2011b, 2012). the drug product variants with extreme dissolution
profiles are bioequivalent) can be established for the
Approach A: Data linking in vitro and drug products under study. In general, data analysis
in vivo performance are NOT available. In this from these approaches will result in one of the
approach, although there is PK and efficacy and safety following outcomes:
data for the relevant phases of product development,
no relationship has been established linking variations Sub-Approach B1: An IVIVR Has Been Estab-
on the CMAs, and CPPs, and dissolution on clinical lished. In those cases where an IVIVC has been
performance. Therefore, drug product specifications attempted but cannot be established, an IVIVR
(ie, dissolution acceptance criterion) are established should be investigated as this would provide some
Biopharmaceutic Considerations in Drug Product Design and In Vitro Drug Product Performance 443
leeway and support for further drug product for- Q = 80% at 20 minutes. Setting a wider dissolution
mulation refinement. While an IVIVR is not as acceptance criterion based on in vivo data allows for
robust as an IVIVC, it can be an important tool the setting of wider particle size specifications deter-
in the QbD approach to formulation development mined in this particular case, on the slowest releasing
and justification. For example, verification of the batch that is BE to the clinical batch.
DS and the clinical relevancy of the specifications A small variation to this approach as described
for material attributes and process parameters can above would be to use data from an in vivo BA/BE
still be determined in the absence of an IVIVC; study where at least two formulation variants have
however, clinical relevancy can only be assured been evaluated and determine whether the dissolution
for those changes whose dissolution profiles fall method and acceptance criterion are able to reject for
within the extremes of dissolution profiles for batches that are not bioequivalent. As explained
batches that were bioequivalent to the clinical trial above, when this happens the method and acceptance
formulation. criteria may be considered clinically relevant.
Figure 15-19 illustrates the advantage of this Sub-Approach B2: An IVIVC Has Been Estab-
approach over approach A. This figure shows the lished. This is the most desirable approach for
relationship between drug substance particle size, setting clinically relevant product specifications,
dissolution, and BE. Under approach A with batch D including dissolution acceptance criteria. It may be
failing similarity testing (ie, f2 testing) and in the challenging to develop an IVIVC for IR products as
absence of BA/BE data, the appropriate specification compared to extended-release dosage forms. Since
was set at Q = 80% at 15 minutes in order to reject the mechanisms for release of drug from IR dos-
batch D. However, for this particle case there was age forms is simpler than that for modified-release
actually a BE study showing that all the batches con- dosage forms, one might expect that an IVIVC
sidered were BE to the clinical batch. Under these would be easier to develop with IR formulations.
conditions, one can then set an acceptance criterion However, mainly Level C correlation for IR prod-
that does not reject this batch, which in this case is ucts have been successful and useful in guiding
Batches A, B, C, D, and clinical were BE
90
Lower bound Clinical batch
80
Approach A:
60 Upper bound Q = 205 at 15 min.
40
20 Batch A Sub-approach B1
Clinical batch Q = 80% at 20 min
Batch B
Batch C
0.0 Batch D
0 5 10 15 20 60
Time (min)
FIGURE 1519 Setting clinically relevant dissolution acceptance criterion. The advantage of approach A versus sub-approach B1.
Drug dissolved (%)
444 Chapter 15
drug product development and the identification of verified by conducting a similarity test. A failed
critical process parameters and material attributes similarity test is an indication of a significant
affecting product performance such as dissolu- difference in the in vitro release rate.
tion (see IVIVC section on how to set appropriate 2. Lack of a rank order correlation.
dissolution specifications for these dosage forms 3. Gut wall metabolism that can affect the bio-
using an IVIVC). availability of the drug.
4. Instability of the drug in the GI tract.
A properly validated IVIVC enhances drug
5. The IVIVC should be developed in the fasted
product understanding and provides justification of
state and only in fed conditions when the drug
manufacturing changes during drug product devel-
is not tolerated.
opment. It enhances the significance of the in vitro
6. The use of mean-based deconvolution instead
testing leading to drug product specifications’ (eg,
of individual-based deconvolution in the case of
dissolution acceptance criteria) setting based on tar-
a two-stage approach correlation.
geted clinically relevant plasma concentrations. In
7. The IVIVC was over-parameterized and not
addition, it allows for the prediction of the clinical
fully mechanistic.
impact of movements within the DS without the
8. Complex absorption processes were not
need for additional in vivo studies.
captured by the model.
9. The use of different scaling factors for the
Failure of Correlation of In Vitro Dissolution formulations.
to In Vivo Absorption 10. When it comes to the applicability of the
A robust IVIVC should demonstrate its ability to IVIVC (eg, postapproval changes, support of
predict the in vivo performance of a drug product wider dissolution acceptance criteria), simi-
from its in vitro dissolution characteristics over the larity test (eg, f2 testing) is often used instead
range of in vitro release rates evaluated during the of IVIVC predictions. It should be noted that
construction and validation of the correlation. Well- IVIVC supersedes similarly testing in such a
defined IVIVCs have been reported for modified- way that when an IVIVC is approved, the data
release drug products (see Chapter 19) but have been that should be included to support the change
more difficult to predict for IR drug products. The should be the difference in predicted means for
success for establishing a robust IVIVC depends on Cmax and AUC.
several factors including (1) the selection of a dis-
As noted above, the problem of no correlation
criminating dissolution method that mimics the drug
between systemic exposure and dissolution may be
product’s in vivo performance; (2) the number of
due to the complexity of drug absorption and the
formulations used in the construction of the correla-
weakness of the dissolution method. The use of the
tion; (3) inclusion of formulation with significant
so-called “physiologically relevant in vitro release
different release characteristics as demonstrated by
approaches” can be used to understand the effects of
dissolution similarity test; (4) design of the in vivo
formulation factors on release (dispersion, dissolu-
BA/BE study (eg, fast vs. feed conditions); (5) mod-
tion, drug precipitation, and stability), and the inter-
eling approach (mechanistic vs. not mechanistic), etc.
actions between active pharmaceutical ingredients,
The following is a list of the most common reasons
dosage form, excipients, and the in vivo environ-
(besides not meeting the validation requirements) for
ment. These “physiologically relevant dissolution
a lack of successful IVIVCs (Suarez-Sharp, 2012):
approaches” may increase the likelihood for the
1. Failing to meet the criteria for in vitro and in development of successful IVIVCs.
vivo experimentation in terms of the number of “Physiologically relevant approaches” can range
in vitro release characteristics of the formula- from using physiologically relevant media in stan-
tions used in the construction of the IVIVC. dard dissolution apparatus as stated in the guidance
Differences in in vitro release rate may be for industry documents (FDA Guidance for Industry,
Biopharmaceutic Considerations in Drug Product Design and In Vitro Drug Product Performance 445
A. Water B. Acid
100 100
Product BE
80 80
60 60
40 Product BO-1 40
20 20
0 0
0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8
Time (hours) Time (hours)
C. Acid and pH 7.4 D. pH 5.4 phosphate buffer
phosphate buffer
100 100
80 80
60 60
40 40
20 20
0 0
0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8
Time (hours) Time (hours)
FIGURE 1520 Dissolution profile of two quinidine gluconate sustained-release products in different dissolution media. Each
data point is the mean of 12 tablets. f(• = product BE, ° = product BO-1.) (Data from Prasad et al, 1983.)
1997a) to more complicated media to mimic in vivo dissolution test be carefully researched before being
conditions such as food effects and alcohol dose adopted as a method for predicting drug absorption.
dumping (Klein, 2010). Note, however, that success-
ful IVIVCs have been possible when simple dissolu-
tion methods are used (Suarez-Sharp, 2012). DRUG PRODUCT STABILITY
An excellent example of the importance of dis-
solution design is shown in Fig. 15-20. Dissolution The long-term stability of any drug product is a criti-
tests using four different dissolution media were cal attribute of overall product quality, given that it
performed for two quinidine gluconate sustained- defines the time period for which product quality,
release tablets (Prasad et al, 1983). Brand BE was safety, and effectiveness are assured. Product stability
known to be bioavailable, whereas product BO-1 was is usually determined by testing a variety of stability
known to be incompletely absorbed. It is interesting indicating attributes such as drug potency, impuri-
to see that using acid medium as well as acid fol- ties, dissolution, and other relevant physicochemical
lowed by pH 7.4 buffer did not distinguish the two measures of performance as necessary.
products well, whereas using water or pH 5.4 buffer Stability studies are generally performed under
as dissolution medium clearly distinguished the well-controlled storage and testing conditions and
“good” product from the one that was not completely provide evidence on how the quality of a drug prod-
available. In this case, the use of an acid medium is uct varies with time under the influence of a variety
consistent with the physiologic condition in the stom- of environmental factors such as temperature, humid-
ach, but this procedure would be misleading as a ity, oxygen, and light. The time period during which
quality control tool. It is important that any new a drug product is expected to remain within the
Dissolved (percent) Dissolved (percent)
Dissolved (percent) Dissolved (percent)
446 Chapter 15
established product quality specification under the The drug product must effectively deliver the
labeled storage conditions is generally termed “shelf- active drug at an appropriate rate and amount to the
life”; however, this term is often used interchange- target receptor site so that the intended therapeutic
ably with expiration period, expiry date, or expiration effect is achieved. To achieve this goal, the drug
date. must traverse the required biological membrane bar-
riers, escape widespread distribution to unwanted
areas, endure metabolic attack, and cause an altera-
CONSIDERATIONS IN THE DESIGN tion of cellular function. The finished dosage form
OF A DRUG PRODUCT should not produce any additional side effects or
discomfort due to the drug and/or excipients. Ideally,
Biopharmaceutic Considerations all excipients in the drug product should be pharma-
As mentioned above, biopharmaceutics is the study cologically inactive ingredients alone or in combina-
of the manufacturing factors and physicochemical tion in the final dosage form.
properties influencing the rate and extent of drug The finished drug product is a compromise of
absorption from the site of administration of a drug various factors, including therapeutic objectives, phar-
and the use of this information to (1) anticipate macokinetics, physical and chemical properties, man-
potential clinical problems arising from poor absorp- ufacturing, cost, and patient acceptance. Most
tion of a candidate drug and (2) optimize bioavail- important, the finished drug product should meet the
ability of newly developed compounds. Some of the therapeutic objective by delivering the drug with maxi-
major biopharmaceutic considerations in the design mum bioavailability and minimum adverse effects.
of a drug product are given in Table 15-10.
The essential elements of the biopharmaceutical
considerations in drug product design include (Kaplan, Pharmacodynamic Considerations
1972) (1) studies done to decide the physicochemical Pharmacodynamics is the study of the effect of a
nature of the drug to be used, for example, salt and drug in the body and its mechanism of action.
particle size; (2) the timing of these studies in relation Therapeutic considerations include the desired phar-
to the preclinical studies with the drug; (3) the deter- macodynamic and pharmacologic properties of the
mination of the solubility and dissolution characteris- drug, including the desired therapeutic response and
tics; (4) the evaluation of drug absorption and the type and frequency of adverse reactions to the
physiological disposition studies; and (4) the design drug. The therapeutic objective influences the design
and evaluation of the final drug formulation. of the drug product, route of drug administration,
dose, dosage regimen, and manufacturing process.
An oral drug used to treat an acute illness is gener-
TABLE 1510 Dissolution Acceptance ally formulated to release the drug rapidly, allowing
for quick absorption and rapid onset. If more rapid
Number
drug absorption is desired (or if oral absorption is
Stage Tested Acceptance Criteria
not feasible for chemical, metabolic, or tolerability
S1 6 Each unit is not less than Q + 5% reasons), then an injectable drug formulation might
S2 6 Average of 12 units (S1 + S be formulated. In the case of nitroglycerin, which is
2) is
equal to or greater than Q, and no highly metabolized if swallowed, a sublingual tablet
unit is less than Q – 15% formulation allows for rapid absorption of the drug
S3 12 Average of 24 units (S1 + S2 + S3) from the buccal area of the mouth for the treatment
is equal to or greater than Q, not of angina pectoris.
more than 2 units are less than In order to reduce unwanted systemic side effects,
Q – 15%, and no unit is less than locally acting drugs such as inhaled drugs have been
Q – 25%
developed. The advantage of inhaled therapy for local
Adapted with permission from United States Pharmacopeia, 2004. action is that it is possible to deliver the drug directly
Biopharmaceutic Considerations in Drug Product Design and In Vitro Drug Product Performance 447
into the lungs, reducing the amount needed to reach a of the pharmacokinetic properties, namely absorption,
therapeutic effect at the site of action and thereby distribution, metabolism, and excretion (ADME), of
reducing systemic side effects resulting in an improved the molecules being investigated as potential drug
benefit:risk ratio. candidates. The data obtained from these studies
For the treatment of certain diseases, such as allow the development of a dose(s) and dosage regi-
hypertension, chronic pain, etc, an extended- or men that are age appropriate including avoidance of
controlled-release dosage form is preferred. The drug–drug interactions, food effect interactions, and
extended-release dosage form releases the drug achieving an appropriate drug release rate that will
slowly, thereby controlling the rate of drug absorption maintain a desired drug level in the body. Clinical
and allowing for more constant plasma drug concen- failures of about 50% of the Investigational New
trations. In some cases, an immediate-drug-release Drug (IND) filings are attributed to their inadequate
component is included in the extended-release dosage ADME attributes. It is, therefore, not surprising that
form to allow for both rapid onset followed by a the pharmaceutical industry is searching for ever
slower sustained release of the drug, for example, more effective means to minimize this problem.
zolpidem tartrate extended-release tablets (Ambien® Building mathematical models (known as in
CR tablets). Controlled-release and modified-release silico screens) to reliably predict ADME attributes
dosage forms are discussed in Chapter 19. solely from molecular structure is at the heart of
this effort in reducing costs as well as development
Drug Substance Considerations cycle times (Gombar et al, 2003). Also, the integra-
tion of PK and PD allows for the characterization of
The physicochemical properties of the drug sub-
the onset, intensity, and duration of the pharmaco-
stance (see Table 15-1) are major factors that are
logical effect of a drug and its interaction to the
controlled or modified by the formulator. Important
mechanism of action. In understanding the interre-
physicochemical properties include solubility, stabil-
lationship of these two disciplines, light can be
ity, chirality, polymorphs, solvate, hydrate, salt form,
shed on situations where one or the other needs to
ionizable behavior, and impurity profile. These
be optimized in drug development. As such PK/PD
physicochemical properties influence the type of
modeling and simulation provides quantitative
dosage form, the formulation, and the manufacturing
assessment of dose/exposure-response relation-
process. Physical properties of the drug—such as
ships with extensive applications at the early and
intrinsic dissolution rate, particle size, and crystal-
late-stage drug development as well as during deci-
line form—are influenced by methods of processing
sion making.
and manufacturing. If the drug has low aqueous
Until recently, it is well known that there is a
solubility and an intravenous injection is desired, a
great degree of individual variation, called polymor-
soluble salt of the drug may be prepared. Chemical
phism in the genes coding for drug-metabolizing
instability or chemical interactions with certain
enzymes. The degree of polymorphism can signifi-
excipients will also affect the type of drug product
cantly affect the drug metabolism and, therefore, the
and its method of fabrication. There are many cre-
pharmacokinetics and the clinical outcome of the
ative approaches to improve the product; only a few
drug. Thus, variations in oxidation of some drugs
are discussed in this chapter.
have been attributed to genetic differences in certain
CYP enzymes. Genetic polymorphisms of CYP2D6
Pharmacokinetics of the Drug and CYP2C19 enzymes are well characterized, and
Drug development is a laborious process that can be human populations of “extensive metabolizers” and
roughly grouped into the following five stages: “poor metabolizers” have been identified. Applying
(1) disease target identification, (2) target validation, pharmacogenomics (eg, genomic biomarkers) into
(3) high-throughput identification of drug leads, (4) lead the drug development and clinical trial evaluation
optimization, and (5) preclinical and clinical evalua- allows for the selection of an optimal group of
tion. Stages 3–5 mainly involve the characterization patients to be enrolled into trials and reduce the
448 Chapter 15
number of adverse events. This will lead to more absorbed drugs and drugs with highly variable bio-
successful clinical trials and decrease the time to availability have a risk that, under unusual conditions
market for compounds. (eg, change in diet or disease condition, drug–drug
interaction), excessive drug bioavailability can occur
leading to more intense pharmacodynamic activity
Bioavailability of the Drug and possible adverse events. If the drug is not
Bioavailability is a pharmacokinetic term that absorbed after the oral route or a higher dose
describes the rate and extent to which the active drug causes toxicity, then the drug must be given by an
ingredient is absorbed from a drug product and alternative route of administration, and a different
becomes available at the site of drug action. As such, dosage form such as a parenteral drug product
bioavailability is concerned with how quickly (eg, might be needed.
when rapid onset of action is needed) and how much
of a drug (since this represent the “effective dose”)
appears in the blood after a specific dose is adminis- Dose Considerations
tered. Given that the pharmacologic response is Some patients experience unique differences from
generally related to the concentration of drug at its the regular adult population in pharmacokinetic
site of action, the availability of a drug from a dosage parameters due to differences in metabolic back-
form is a critical element of a drug product’s clinical ground, renal clearance, weight, volume of distribu-
efficacy. However, most bioavailability studies tion, age, and disease stage (eg, liver impairment,
involve the determination of drug concentration renal impairment) and, consequently, require indi-
mainly in the plasma since it is rather difficult to vidualized dosing. Therefore, the drug product must
measure the concentration at the site of action. usually be available in several dose strengths to
Before a systemically acting drug reaches the allow for individualized dosing and possibly dose
systemic circulation, the drug must be absorbed; how- titration. Some tablets are also scored for breaking,
ever, before the drug is absorbed, the drug product to potentially allow (as supported by appropriate
must disintegrate and the drug substance must be dis- data) the administration of fractional tablet doses.
solved and transferred across the gastrointestinal tract The absence of an available pediatric dosage
membrane into the systemic circulation. Therefore, form for some medications increases the potential
any factors affecting these three processes such as for dosing errors and may produce serious complica-
psychochemical properties of the drug, formulation tions in this patient population. Congress enacted the
and manufacturing variables, physiological factors, Pediatric Research Equity Act (PREA) and other
drug–drug interactions, and food effect interactions laws requiring drug companies to study their prod-
will also affect bioavailability. ucts in children under certain circumstances. When
The stability of the drug in the gastrointestinal pediatric studies are necessary, they must be con-
tract, including the stomach and intestine, is another ducted with the same drug and for the same use for
consideration. Some drugs, such as penicillin G, are which they were approved in adults. Thus, specific
unstable in the acidic medium of the stomach. The dosing guidelines and useful dosage forms for pedi-
addition of buffering in the formulation or the use of atric patients are being developed in order to opti-
an enteric coating on the dosage form will protect mize therapeutic efficacy and limit, or prevent
the drug from degradation at a low pH. serious adverse side effects.
Some drugs have poor bioavailability because of In the presence of renal or liver impairment, the
first-pass effects (presystemic elimination). If oral drug metabolism or excretion process may be altered
drug bioavailability is poor due to metabolism by requiring smaller dose. For example, in case of renal
enzymes in the gastrointestinal tract or in the liver, insufficiency, phenobarbitone, which is mainly
then a higher dose may be needed, as in the case of excreted by the kidneys, should be given in smaller
propranolol, or an alternative route of drug adminis- dose, and in case of patients with liver impairment,
tration, as in the case of nitroglycerin. Incompletely morphine should be given in smaller dose.
Biopharmaceutic Considerations in Drug Product Design and In Vitro Drug Product Performance 449
The size and the shape of a solid oral drug prod- be given more frequently or given in an extended-
uct are designed for easy swallowing. The total size release drug product. Simplifying the medication
of a drug product is determined by the dose of the dosing frequency could improve compliance mark-
drug and any additional excipients needed to manu- edly (Jin et al, 2008). Thus to minimize fluctuating
facture the desired dosage form. For oral dosage plasma drug concentrations and improve patient
forms, if the recommended dose is large (1 g or compliance, an extended-release drug product may
more), then the patient may have difficulty in swal- be preferred.
lowing the drug product. For example, many patients
may find a capsule-shaped tablet (caplet) easier to
swallow than a large round tablet. Large or oddly Patient Considerations
shaped tablets, which may become lodged in the The drug product and therapeutic regimen must be
esophageal sphincter during swallowing, are gener- acceptable to the patient. Poor patient compliance
ally not manufactured. Some esophageal injuries due may result from poor product attributes, such as dif-
to irritating drug lodged in the esophagus have been ficulty in swallowing, disagreeable odor, bitter medi-
reported with potassium chloride tablets and other cine taste, or two frequent and/or unusual dosage
drugs. Older patients may have more difficulties in requirements.
swallowing large tablets and capsules. Most of these In recent years, creative packaging has allowed
swallowing difficulties may be overcome by taking the patient to remove one tablet each day from a spe-
the product with a large amount of fluid. cially designed package so that the daily doses are not
missed. Orally disintegrating tablets and chewable
tablets allow the patient to typically take the medica-
Dosing Frequency tion without water. These innovations improve com-
Both the dose and the dosing frequency including pliance. Of course, pharmacodynamic factors, such as
the total daily dose should be considered when side effects of the drug or an allergic reaction, also
developing a therapeutic dosage regimen for a influence patient compliance.
patient (see Chapter 22). The dose is the amount of Transmucosal (nasal) administration of anti-
drug taken at any one time. This can be expressed as epileptic drugs may be more convenient, easier to
the weight of drug (eg, 100 mg), volume of drug use, just as safe, and is more socially acceptable
solution (eg, 5 mL, 5 drops), or some other quantity than rectal administration.
(eg, 2 puffs). The dosage regimen is the frequency at
which the drug doses are given. Examples include
two puffs twice a day, one capsule two times a day, Route of Drug Administration
etc. The total daily dose is calculated from the dose The route of drug administration (see Chapter 14)
and the number of times per day the dose is taken. affects the rate and extent (bioavailability) of the drug,
The dosing frequency is in part determined by thereby affecting the onset, duration, and intensity of
the clearance of the drug and the target plasma drug the pharmacologic effect (efficacy and safety). For
concentration. When the dosing frequency or interval intravenous (IV) delivery, the total dose of drug
is less than the half-life, (t1/2), greater accumulation reaches the systemic circulation. However, drug deliv-
occurs, that is, steady-state levels are higher and there ery by other routes may result in only partial absorp-
is less fluctuation. If the dosing interval is much tion, resulting in lower bioavailability. For example,
greater than the half-life of the drug, then minimum following oral administration, a drug dissolves in the
concentration, Cp min, approaches zero. Under these GI and then gets absorbed through the epithelial
conditions, no accumulation will occur and the plasma cells of the intestinal mucosa; however, this process
concentration–time profile will be the result of may be affected by factors such as presence of food.
administration of a series of single doses. In the design of a drug dosage form, the pharmaceu-
As such if the drug has a short elimination half- tical manufacturer must consider (1) the intended
life or rapid clearance from the body, the drug must route of administration; (2) the size of the dose;
450 Chapter 15
(3) the anatomic and physiologic characteristics of DRUG PRODUCT CONSIDERATIONS
the administration site, such as membrane permeabil-
ity and blood flow; (4) the physicochemical properties Pharmaceutical development companies are looking at
of the site, such as pH, osmotic pressure, and presence new approaches to deliver drugs safely and improve
of physiologic fluids; and (5) the interaction of the efficacy and patient compliance. Noninvasive systemic
drug and dosage form at the administration site, drug delivery such as oral, inhalation, intranasal, trans-
including alteration of the administration site due to dermal, etc are much more preferred compared to
the drug and/or dosage form. invasive drug delivery such as intramuscular, intrave-
Although the pharmacodynamic activity of the nous, and subcutaneous (Mathias and Hussain, 2010).
drug at the receptor site is similar with different Although the oral route of drug administration is pre-
routes of administration, severe differences in the ferred and is the most popular route of drug adminis-
intensity of the pharmacodynamic response and the tration, alternate noninvasive systemic drug delivery is
occurrence of adverse events may be observed. For being considered for biotechnology-derived drugs
example, isoproterenol has a thousandfold difference (proteins), ease of self-administration (orally disinte-
in activity when given orally or by IV injection. grating tablets), or prolonged drug delivery (transder-
Figure 15-21 shows the change in heart rate due to mal patch). The discussion below briefly describes
isoproterenol with different routes of administration. some of the more popular drug products.
Studies have shown that isoproterenol is metabolized
in the gut and during passage through the liver (pre-
systemic elimination or first-pass effects). The rate Oral Drug Products
and types of metabolite formed are different depend- Oral administration of drug products is the most com-
ing on the routes of administration. mon, convenient, and economic route. The major
The use of novel drug delivery methods could advantages of oral drug products are the convenience
enhance the efficacy and reduce the toxicity of anti- of administration, safety, and the elimination of dis-
epileptic drugs (AEDs). As such, slow-release oral comforts involved with injections. The hazard of rapid
forms of medication or depot drugs such as skin intravenous administration causing toxic high concen-
patches might improve compliance and, therefore, tration of drug in the blood is avoided. The main dis-
seizure control. In emergency situations, administra- advantages of oral drug products are the potential
tion via rectal, nasal, or buccal mucosa can deliver issues of reduced, erratic, or incomplete bioavailabil-
the drug more quickly than can oral administration ity due to solubility, permeability, and/or stability
(Fisher and Ho, 2002). problems. Unabsorbed drug may also alter the con-
tents and microbiologic flora of the gastrointestinal
tract. Some orally administered drugs may irritate the
gastrointestinal linings causing nausea or gastrointes-
160 tinal discomfort. Bioavailability may be altered by
Intravenous drug and food interactions and any pathology of the
120 GI tract such as ulcerative colitis (see Chapter 14).
Tracheal
The oral route is nevertheless problematic because of
80 the unpredictable nature of gastrointestinal drug
Rectal absorption due to factors such as the presence of food
40 Intestinal that may alter the gastrointestinal tract pH, gastric
motility, and emptying time, as well as the rate and
0
0.1 10 100 1000 extent of drug absorption.
Dose (mg/kg) Highly ionized drug molecules are not absorbed
FIGURE 1521 Dose–response curve to isoproterenol by easily. The ganglion-blocking drugs hexametho-
various routes in dogs. (From Gillette and Mitchell, 1975, with nium, pentolinium, and bretylium are ionized at
permission.) intestinal pH. Therefore, they are not sufficiently
Increase in heart rate (percent)
Biopharmaceutic Considerations in Drug Product Design and In Vitro Drug Product Performance 451
absorbed orally to be effective systemically. Neomycin, hydrophobic, but have some solubility in aqueous
gentamicin, and cefamandole are not well absorbed solutions. This is one reason why many successfully
orally. Drugs with large molecular weights may not developed drugs are weak acids or weak bases to
be well absorbed when given orally. The antibiotics begin with.
neomycin and vancomycin are not absorbed after The most significant issue to consider when
oral administration and are used for local antibacte- formulating poorly water-soluble drugs is the risk of
rial effect in the gastrointestinal tract. Some large precipitation in the lumen of the gastrointestinal
molecules are absorbed when administered in solu- tract. The lipid formulation classification system
tion with a surface-active agent. For example, cyclo- (LFCS) provides a simple framework that can be
sporine has been given orally with good absorption used, in combination with appropriate in vitro tests,
when formulated with a surfactant in oil. A possible to predict how the fate of a drug is likely to be
role of the oil is to stimulate the flow of lymph as affected by formulation, and to optimize the choice
well as to delay retention of the drug. Oily vehicles of lipid formulation for a particular drug (Puoton,
have been used to lengthen the gastrointestinal tran- 2006). Poorly water-soluble drug candidates present
sit time of oral preparations. considerable formulation challenges. These drugs
Delivering proteins and peptides by the oral can be successfully formulated for oral administra-
route has been a big challenge, given the lack of tion. Some options available involve either reduction
stability such as enzymatic degradation in the diges- of particle size (of crystalline drug) or formulation of
tive system prior to absorption. Considerable prog- the drug in solution, as an amorphous system or lipid
ress has been made over past few years in developing formulation (Puoton, 2006).
innovative technologies for promoting absorption Lipophilic drugs are more soluble in lipids or
across GI and numbers of these approaches are dem- oily vehicles. Lipid-soluble drugs given with fatty
onstrating potential in clinical studies. In developing excipients mix with digested fatty acids, which are
oral protein delivery systems with high bioavailability, emulsified by bile in the small intestine. The emulsi-
three practical approaches might be most helpful fied drug is then absorbed through the GI mucosa or
(Morishita and Peppas, 2006): (1) modification of through the lymphatic system. A normal digestive
the physicochemical properties of macromolecules; function of the small intestine is the digestion and
(2) addition of novel function to macromolecules; or absorption of fats such as triglycerides. These fats
(3) use of improved delivery carriers. Chemical are first hydrolyzed into monoglycerides and fatty
modification and use of mucoadhesive polymeric acids by pancreatic lipase. The fatty acids then react
system for site-specific drug delivery seem to be with carrier lipoproteins to form chylomicrons,
promising candidates for protein and peptide drug which are absorbed through the lymph. The chylo-
delivery (Shaji and Patole, 2008). Also, nanoparti- microns eventually release the fatty acids, and any
cles with peptidic ligands are especially worthy of lipophilic drugs incorporated in the oil phase. Fat
notice because they can be used for specific targeting substances trigger receptors in the stomach to delay
in the gastrointestinal tract. stomach emptying and reduce GI transit rates.
Prolonged transit time allows more contact time for
increased drug absorption.
Absorption of Lipid-Soluble Drugs When griseofulvin or phenytoin was given orally
Lipid solubility of drugs is a major factor affecting in corn oil suspensions, an increase in drug absorp-
the extent of drug distribution, particularly to the tion was demonstrated (Bates and Equeira, 1975).
brain, where the blood–brain barrier restricts the pen- The increase in absorption was attributed to the for-
etration of polar and ionized molecules. Inconsistently, mation of mixed micelles with bile secretions, which
drugs that are highly hydrophobic are also poorly aid drug dissolution. Hydrophobic drugs such as
absorbed, because they are poorly soluble in aqueous griseofulvin and metaxalone have greater bioavail-
fluid and, therefore, cannot get to the surface of cells. ability when given with a high-fat meal. A meal high
For a drug to be readily absorbed, it must be mainly in lipids will delay stomach emptying depending on
452 Chapter 15
the volume and nature of the oil. For example, the It has been shown that acute aspirin-induced
bioavailability of a water-insoluble antimalarial drug damage to the gastric mucosa can be reduced by
was increased in dogs when oleic acid was incorpo- chemically associating aspiring with the phospho-
rated as part of a vehicle into a soft gelatin capsule lipid, phosphatidylcholine (PC) and that the mecha-
(Stella et al, 1978). Calcium carbonate, a source of nism of mucosal protection provided by this compound
calcium for the body, was only about 30% available is not related to any alteration in the ability of aspirin to
in a solid dosage form, but was almost 60% bioavail- inhibit mucosal COX activity (Bhupinderjit et al, 1999).
able when dispersed in a special vehicle as a soft gela- Also, certain drugs have been formulated into soft
tin capsule (Fordtran et al, 1986). Bleomycin, an gelatin capsules to improve drug bioavailability and
anticancer drug (MW 1500), is poorly absorbed orally reduce gastrointestinal side effects. If the drug is for-
and therefore was formulated for absorption through mulated in the soft gelatin capsule as a solution, the
the lymphatic system. The lymphotropic carrier was drug may disperse and dissolve more rapidly, leaving
dextran sulfate. Bleomycin was linked by ionic bonds less residual drug in the gut and causing less irritation.
to the carrier to form a complex. The carrier dextran This approach may be useful for a drug that causes
(MW 500,000) was too large to be absorbed through local irritation but will be ineffective if the drug is
the membrane and pass into the lymphatic vessels inherently ulcerogenic. Indomethacin, for example,
(Yoshikawa et al, 1989). may cause ulceration in animals even when adminis-
tered parenterally.
There are many options available to the formula-
Gastrointestinal Side Effects tor to improve the tolerance of the drug and minimize
Many orally administered drugs such as aspirin are gastric irritation. The nature of excipients and the
irritating to the stomach. These drugs may cause nau- physical state of the drugs are important and must
sea or stomach pain due to local irritation when taken be carefully assessed before a drug product is formu-
on an empty stomach. In some cases, food or antacids lated. Some excipients may improve the solubility of
may be given together with the drug to reduce stom- the drug and facilitate absorption, whereas others
ach irritation. Alternatively, the drug may be enteric may physically adsorb the drug to reduce irritation.
coated to reduce gastric irritation. Buffered aspirin Often, a great number of formulations must be con-
tablets, enteric-coated aspirin tablets, and rapidly dis- sidered before an acceptable one is chosen.
solving effervescent tablets and granules are available
to minimize local gastric irritation. However, enteric
coating may sometimes delay or reduce the amount of Immediate-Release and Modified-Release
drug absorbed. Furthermore, enteric coating may not Drug Products
abolish gastric irritation completely, because the drug The USP differentiates between an immediate-
may occasionally be regurgitated back to the stomach release (IR) drug product and a modified-release
after the coating dissolves in the intestine. Enteric- (MR) drug product. For the IR drug product, no
coated tablets may be greatly affected by the presence deliberate effort has been made to modify the drug
of food in the stomach. The drug may not be released release rate. IR drug products disintegrate rapidly
from the stomach for several hours when stomach after administration. IR dosage forms release the
emptying is delayed by food. active drug(s) within short time (eg, 80% of drug
Buffering material or antacid ingredients have also after 60 min). Applying particular formulation and
been used with aspirin to reduce stomach irritation. process technologies, even faster drug release can be
When a large amount of antacid or buffering material is achieved. The basic approach used in development
included in the formulation, dissolution of aspirin may of tablets is the use of superdisintegrants like cross-
occur quickly, leading to reduced irritation to the stom- linked crospovidone, sodium starch glycolate, car-
ach. However, many buffered aspirin formulations do boxymethylcellulose, etc. These superdisintegrants
not contain sufficient buffering material to make a dif- provide instantaneous disintegration of tablets fol-
ference in dissolution in the stomach. lowing oral administration.
Biopharmaceutic Considerations in Drug Product Design and In Vitro Drug Product Performance 453
For MR drug products, the pattern of drug release and the lack of a stratum corneum epidermis. This
from the dosage form has been deliberately changed minimal barrier to drug transport results in a rapid
from that of a conventional (immediate-release) form rise in blood concentrations. Sublingual and buccal
of the drug. Types of MR drug products include medications are compounded in the form of small,
delayed release (eg, enteric coated) and extended quick-dissolving tablets, sprays, lozenges, or liquid
release (ER). ER formulations are designed to reduce suspensions. A buccal tablet may be designed to
dosing frequency for drugs with a short elimination release drug slowly for a prolonged effect. This form
half-life and duration of effect. These forms reduce of drug product administration is very effective as it
the fluctuation in plasma drug concentration, pro- avoids first-pass metabolism by the liver before gen-
viding a more uniform therapeutic effect while mini- eral distribution. Consequently, for a drug with sig-
mizing adverse effects. Absorption rate is slowed by nificant first-pass effect, buccal/sublingual absorption
different methods including coating drug particles may provide better bioavailability than oral adminis-
with wax or other water-insoluble material, by embed- tration and rapid unset of action as it may be absorbed
ding the drug in a matrix that releases it slowly during in the blood stream in minutes.
transit through the GI tract, or by complexing the drug For example, Sorbitrate sublingual tablet,
with ion-exchange resins. Sorbitrate chewable tablet, and Sorbitrate oral tablet
An ER oral dosage form should meet the follow- (Zeneca) are three different dosage forms of isosor-
ing characteristics: (1) The BA profile established for bide dinitrate for the relief and prevention of angina
the drug product rules out the occurrence of any dose pectoris. The sublingual tablet is a lactose formula-
dumping; (2) the drug product’s steady-state perfor- tion that dissolves rapidly under the tongue and is
mance is comparable (eg, degree of fluctuation is then absorbed. The chewable tablet is chewed, and
similar or lower) to a currently marketed noncon- some drug is absorbed in the buccal cavity; the oral
trolled release or controlled-release drug product that tablet is simply a conventional product for GI absorp-
contains the same active drug ingredient or therapeu- tion. The chewable tablet contains flavor, confec-
tic moiety and that is subject to an approved full NDA; tioner’s sugar, and mannitol, which are absent in both
(3) the drug product’s formulation provides consistent the oral and sublingual tablets. The sublingual tablet
pharmacokinetic performance between individual dos- contains lactose and starch for rapid dissolution. The
age units; and (4) the drug product has a less frequent onset of sublingual nitroglycerin is rapid, much faster
dosing interval compared to a currently marketed non- than when nitroglycerin is taken orally or absorbed
controlled release drug product. Chapter 19 discusses through the skin. The duration of action, however, is
MR drug products in more detail. shorter than with the other two routes. Some peptide
drugs have been reported to be absorbed by the buc-
cal route, which provides a route of administration
Buccal and Sublingual Tablets without the drug being destroyed by enzymes in the
A drug that diffuses and penetrates rapidly across GI tract.
mucosal membranes may be placed under the tongue A newer approach to drug absorption from the
and be rapidly absorbed. A tablet designed for oral cavity has been the development of a translingual
release under the tongue is called a sublingual tablet. nitroglycerin spray (Nitrolinqual Pumpspray). The
Nitroglycerin, isoproterenol, erythrityl tetranitrate, spray, containing 0.4 mg per metered dose, is given
and isosorbide dinitrate are common examples. A by spraying one or two metered doses onto the oral
tablet designed for release and absorption of the drug mucosa at the onset of an acute angina attack.
in the buccal (cheek) pouch is called a buccal tablet. Fentanyl citrate is a potent, lipid-soluble opioid
The buccal cavity is the space between the mandibu- agonist that crosses mucosal membranes rapidly.
lar arch and the oral mucosa, an area well supplied Fentanyl has been formulated as a transdermal drug
with blood vessels for efficient drug absorption. product (Durapress®) and as an oral lozenge on a
Oral transmucosal absorption is generally rapid handle (Actiq®) containing fentanyl citrate for oral
because of the rich vascular supply to the mucosa transmucosal delivery. According to the manufacturer,
454 Chapter 15
fentanyl bioavailability from Actiq is about 50%, rep- 500 distinct species of bacteria as resident flora.
resenting a combination of rapid absorption across the Within the cecum and colon, anaerobic species
oral mucosa and slower absorption through swallow- dominate and bacterial counts of 1012/mL have been
ing and transport across the gastrointestinal mucosa. reported. Among the reactions carried out by these
gut flora are azoreduction and enzymatic cleavage,
that is, glycosides. These metabolic processes may
Colonic Drug Delivery be responsible for the metabolism of many drugs and
Drugs that are destroyed following oral administra- may also be applied to colon-targeted delivery of
tion by the acidic environment of the stomach or peptide-based macromolecules such as insulin by
metabolized by enzymes may only be slightly oral administration (Philip and Philip, 2010).
affected in the colon. Oral drug products for colonic Drugs such as the beta-blockers, oxprenolol and
drug delivery have been studied not only for the metoprolol, and isosorbide-5-mononitrate, nonsteroi-
delivery of drugs for the treatment of local diseases dal anti-inflammatory drugs (NSAIDs), steroids, pep-
associated with the lower bowel and colon (eg, Crohn’s tides, and vaccines are well absorbed in the colon,
disease) but also for their potential for the delivery of similar to absorption in the small intestine. Thus, these
proteins and therapeutic peptides (eg, insulin) for sys- drugs are suitable candidates for colonic delivery. The
temic absorption (Chourasia and Jain, 2003; Shareef, NSAID naproxen has been formed into a prodrug
et. al, 2003). Targeting drug delivery to the colon has naproxen–dextran that survives intestinal enzyme and
several therapeutic advantages. Crohn’s disease or intestinal absorption. The prodrug reaches the colon,
chronic inflammatory colitis may be more effec- where it is enzymatically decomposed into naproxen
tively treated by direct drug delivery to the colon. and dextran (Harboe et al, 1989).
For example, mesalamine (5-aminosalicylic acid,
Asacol®) is available in a delayed-release tablet
coated with an acrylic-based resin that delays the Rectal and Vaginal Drug Delivery
release of the drug until it reaches the distal ileum Products for rectal or vaginal drug delivery may be
and beyond. Other approaches include prodrugs (sul- administered in either solid or liquid dosage forms.
fasalazine and balsalazine) to deliver 5-aminosali- Rectal drug administration can be used for either
cylic acid (5-ASA) for localized chemotherapy of local or systemic drug delivery. Rectal drug delivery
inflammatory bowel disease (IBD). Drugs contain- for systemic absorption is preferred for drugs that
ing an azo bond (balsalazide) and azo cross-linked cannot be tolerated orally (eg, when a drug causes
polymers used as a coating are degraded by anaero- nausea) or in situations where the drug cannot be
bic microbes in the lower bowel. given orally (eg, during an epileptic attack). Rectal
Protein drugs are generally unstable in the acidic route offers potential advantages for drug delivery
environment of the stomach and are also degraded by such as rapid absorption of many low-molecular-
proteolytic enzymes present in the stomach and small weight drugs, partial avoidance of first-pass metabo-
intestine. Researchers are investigating the oral deliv- lism, potential for absorption into the lymphatic
ery of protein and peptide drugs by protecting them system, retention of large volumes, rate-controlled
against enzymatic degradation for later release in drug delivery, and absorption enhancement (Lakshmi
the colon. et al, 2012). However, this route also has some disad-
Drug delivery to the colon is highly influenced vantages as many drugs are poorly or erratically
by several factors including high bacterial level, the absorbed across the rectal mucosa, dissolution prob-
physiology of the colonic environment, level of lems, and drug metabolism in microorganisms among
fluid, and transit time. Thus availability of most other factors. Thus to overcome these, various absorp-
drugs to the absorptive membrane is low because of tion-enhancing adjuvants, surfactants, mixed micelle,
the high water absorption capacity of the colon, the and cyclodextrins have been investigated.
colonic contents are considerably viscous, and their The rate of absorption from this route can be
mixing is not efficient. The human colon has over affected by several factors including formulation,
Biopharmaceutic Considerations in Drug Product Design and In Vitro Drug Product Performance 455
concentration of drug, pH of the rectal content, pres- Parenteral Drug Products
ence of stools, volume of fluid, etc. A sustained- The parenteral route of administration refers to all
release preparation may be prepared for rectal forms of drugs administered via a syringe, needle, or
administration. The rate of release of the drug from catheter into body tissues or fluids such as intrave-
this preparation is dependent on the nature of the base nous, intra-arterial, intraosseous, intramuscular, sub-
composition and on the solubility of the drug involved. cutaneous, and intrathecal routes.
Release of drug from a suppository depends on In general, intravenous (IV) bolus administration
the composition of the suppository base. A water- of a drug provides the most rapid onset of drug
soluble base, such as polyethylene glycol and glyc- action. After IV bolus injection, the drug is distrib-
erin, generally dissolves and releases the drug; on uted via the circulation to all parts of the body within
the other hand, an oleaginous base with a low melt- a few minutes. After intramuscular (IM) injection,
ing point may melt at body temperature and release drug is absorbed from the injection site into the
the drug. Some suppositories contain an emulsifying bloodstream (Fig. 15-22). Plasma drug input after
agent that keeps the fatty oil emulsified and the drug oral and IM administration involves an absorption
dissolved in it. phase in which the drug concentration rises slowly to
Vaginal drug delivery offers a valuable route for a peak and then declines according to the elimination
drug delivery through the use of specifically designed half-life of the drug. (Note that the systemic elimina-
carrier systems for both local and systemic applica- tion of all products is essentially similar; only the rate
tions. A range of drug delivery platforms suitable for and extent of absorption may be modified by formu-
intravaginal administration have been developed lation.) The plasma drug level peaks instantaneously
such as intravaginal rings, vaginal tablets, creams, after an IV bolus injection, so a peak is usually not
hydrogels, suppositories, and particulate systems. visible. After 3 hours, however, the plasma level of
For example, progesterone vaginal supposito- the drug after intravenous administration has declined
ries have been evaluated for the treatment of premen-
strual symptoms of anxiety and irritability. Antifungal
agents are often formulated into suppositories for
treating vaginal infections. Fluconazole, a triazole 100
antifungal agent, has been formulated to treat vulvo-
vaginal candidiasis. The result of oral doses is com- 90 Intravenous
parable to that of a clotrimazole vaginal suppository.
80
Many vaginal preparations are used for the delivery
of antifungal agents. 70 Intramuscular
The rate and extent of drug absorption after
intravaginal administration may vary depending on 60
formulation factors, age of the patient, vaginal physi-
50
ology, and menstrual cycle. As such exhaustive
efforts have been made recently to evaluate the 40 Oral
vagina as a potential route for the delivery of mole-
cules, such as proteins, peptides, small interfering 30
RNAs, oligonucleotides, antigens, vaccines, and 20
hormones. However, successful delivery of drugs
through the vagina remains a challenge, primarily 10
due to the poor absorption across the vaginal epithe-
0
lium, cultural sensitivity, hygiene, personal, gender 0 2 4 6 8 10 12 14
specificity, local irritation, and other factors that Time (hours)
need to be addressed during the design of a vaginal FIGURE 1522 Plasma concentration of a drug after the
formulation (Ashok et al, 2012). same dose is administered by three different routes.
mg/mL
456 Chapter 15
to a lower level than after the oral and intramuscular CLINICAL EXAMPLE
administration. In this example (see Fig. 15-22), the
areas under the plasma curves are all approximately Hyperlipidemia is the medical term for high levels of
equal, indicating that the oral and intramuscular cholesterol and triglycerides in the blood. Individuals
preparations are both well formulated and 100% with hyperlipidemia are predisposed to clogged blood
available. Frequently, because of incomplete absorp- vessels, or atherosclerosis, which puts them at a high
tion or metabolism, oral preparations may have a risk for heart disease and stroke. Fenofibrate is the
lower area under the curve. dimethyl ester prodrug of fenofibric acid, a lipid-
Drug absorption after an intramuscular injection modulating agent commonly used to treat hyperlip-
may be faster or slower than after oral drug adminis- idemia. Fenofibrate is practically insoluble in water
tration. Intramuscular preparations are generally and it has the lowest and most variable bioavailabil-
injected into a muscle mass such as in the buttocks ity within the class of lipid-modulating fibrates
(gluteus muscle) or in the deltoid muscle. Drug (Najib, 2002). The drug is marketed in capsule or
absorption occurs as the drug diffuses from the mus- tablet dosage forms, and dissolution is most likely
cle into the surrounding tissue fluid and then into the the rate-limiting step for oral absorption. Consequently,
blood. Different muscle tissues have different blood drug product design focused heavily on biopharma-
flow. For example, blood flow to the deltoid muscle ceutic principles to improve the reliability and pre-
is higher than blood flow to the gluteus muscle. dictability of drug absorption from the initial 100-mg
Intramuscular injections may be formulated to have capsule formulation, previously marketed under the
a faster or slower drug release by changing the trade name Lipidil®. The bioavailability of the origi-
vehicle of the injection preparation. Aqueous solu- nal 100-mg capsule formulation was first enhanced
tions release drug more rapidly, and the drug is through micronization, or particle size reduction.
more rapidly absorbed from the injection site, Based on relative bioavailability studies, a 100-mg
whereas a viscous, oily, or suspension vehicle may fenofibrate original capsule is bioequivalent to a
result in a slow drug release and consequently slow 67-mg micronized fenofibrate capsule, Tricor®
and sustained drug absorption. Viscous vehicles (fenofibrate capsules, micronized).
generally slow down drug diffusion and distribu- However, despite improved oral bioavailability,
tion. A drug in an oily vehicle must partition into an the Tricor micronized fenofibrate capsule formula-
aqueous phase before systemic absorption. A drug tion still demonstrated increased drug exposure when
that is very soluble in oil and relatively insoluble in taken with food, up to 35%. Further particle size
water may have a relatively long and sustained reduction through NanoCrystal® colloidal dispersion
release from the absorption site because of slow technology, and optimizing tableting excipients, led
partitioning. to a new reduced dose tablet that could be adminis-
Modified-release parenteral dosage forms have tered without regards to food, Tricor fenofibrate tab-
been developed in which the drug is entrapped or let. A 145-mg nanosized Tricor fenofibrate tablet is
encapsulated into inert polymeric or lipophilic bioequivalent to the 200-mg micronized Tricor feno-
matrices that slowly release the drug in vivo over a fibrate capsule (Tricor Package Insert, 2004).
week or up to several years (Patil and Burgess, A second formulation of fenofibric acid, the cho-
2010). The polymers or lipophilic carriers used to line salt, was tailored based on the different physico-
deliver the drugs in MR parenterals are either biode- chemical properties between the salt and free acid,
gradable in vivo or are nonbiodegradable. Nonerodible, and effects of modified-release excipients, to address
nonbiodegradable systems are removed at the end of the food effect and drug solubility challenges, Trilipix®
therapy. Drugs, including peptides and proteins, have fenofibric acid delayed-release capsules. Compared
also been formulated as emulsions, suspensions, lipo- with fenofibrate, the choline salt form is freely water
somes, and nanoparticles for parenteral injection. A soluble and readily absorbed. Thus, through biophar-
change in a parenteral drug product from a solution to maceutic design considerations, researchers were able
an emulsion, liposome, etc will alter the drug’s distri- to develop a 135-mg fenofibric acid salt product with
bution and pharmacokinetic profile. equivalent exposures to the 200-mg Tricor micronized
Biopharmaceutic Considerations in Drug Product Design and In Vitro Drug Product Performance 457
capsule product that could be taken without regard to Nasal devices have progressively evolved from
food (Trilipix Package Insert, 2008). the pipettes and the droppers through to spraying
devices such as squeeze bottles, toward, a nasal gel
Nasal Drug Products pump, pressurized metered dose inhalers (MDIs),
and dry-powder inhalers (Djupesland, 2013). Drug
The nasal route of administration has been used for the
development in the near future should not only rely
delivery of drug products for both topical and systemic
on innovative new compounds and sophisticated
actions. A variety of different drug products such as
formulations but also rely on the efficiency, safety,
antihistamines, corticosteroids, anticholinergics, and
and comfort of the dispensing systems. The ideal
vasoconstrictors are currently being marketed for the
nasal drug delivery system should have optimum
local treatment of congestion, rhinitis, sinusitis, and
performance (accurate and reproducible dose, nar-
related allergic or chronic conditions. Recently,
row droplet/particle size distribution, in particular)
increasing investigations of the nasal route have
and support patient compliance, thus contributing to
focused especially on nasal application for systemic
the reduction in global health expenditure.
drug delivery. The intranasal delivery of drugs for sys-
Certain studies should be performed to charac-
temic action is aimed at optimizing drug bioavailabil-
terize the performance properties of the nasal drug
ity, given its large surface area, porous endothelial
product and to provide support in defining the opti-
membrane, high total blood flow, and the avoidance of
mal labeling statements regarding use. Delivery sys-
first-pass metabolism. Thus, peptides such as calcito-
tems for nasal administration can vary in both design
nin and pituitary hormones have been successfully
and mode of operation, and these characteristics may
delivered through the nasal route. Intranasal delivery is
be unique to a particular drug product. Regardless of
also currently being marketed for treatments for
the design, the most crucial attributes are the repro-
migraine, smoking cessation, acute pain relief, osteo-
ducibility of the dose, the spray plume, and the par-
porosis, and vitamin B12 deficiency. In addition,
ticle/droplet size distribution, since these parameters
MedImmune Inc. and Wyeth marketed the first intra-
can affect the delivery of the drug substance to the
nasal vaccine in the United States: FluMist®.
intended biological target. Studies to define these
Recently, the nasal route of administration has
characteristics will help facilitate correct use and
gained increasing consideration for obtaining sys-
maintenance of the drug product and contribute to
temic absorption or brain uptake of drugs. The deliv-
patient compliance. For the most part, these should
ery of drugs to the CNS from the nasal route may
be one-time studies, preferably performed on multi-
occur via olfactory neuroepithelium. Drug delivery
ple batches (eg, two or three) of drug product repre-
through nasal route into CNS has been reported for
sentative of the product intended for distribution
Alzheimer’s disease, brain tumors, epilepsy, pain,
(FDA Guidance for Industry, 2002).
and sleep disorders (Pavan et al, 2008).
The concept of classical bioequivalence and bio-
There are various factors that affect the systemic
availability may not be applicable for all nasal drug
bioavailability of drugs that are administered through
products specially those for local action. In addition,
the nasal route (Kumari et al, 2013). These factors
the doses administered are typically so small that
can be classified as follows:
blood or serum concentrations may not be detectable
1. Physiochemical properties of the drugs: lipophilic– by routine analytical procedures. Therefore, for
hydrophilic balance, chemical form, polymor- locally acting drug product, major manufacturing
phism, enzymatic degradation in nasal cavity, changes may require the need for clinical trials.
molecular size, solubility, and dissolution rate
2. Delivery effect: formulation (concentration, pH,
osmolarity), droplet/particle size distribution, Inhalation Drug Products
viscosity Localized drug delivery to the lungs is an impor-
3. Nasal effect: mucociliary clearance, cold, rhini- tant and effective therapeutic method for treating a
tis, membrane permeability, environmental pH, variety of pulmonary disorders including asthma,
the anatomical and physiological bronchitis, and cystic fibrosis. The advantages of
458 Chapter 15
inhalation therapy for the treatment of lung disorders TABLE 1511 Failure of In Vitro–In Vivo
are the following: (1) Relatively small doses are Correlation (IVIVC)
needed for effective therapy, reducing exposure of
Biorelevant dissolution method needed
drug to the systemic circulation, and potentially
Immediate-release drug product containing a rapidly dis-
minimizes adverse effects; (2) wide surface area for solving and rapidly absorbed drug (BCS1)
absorption and relatively low metabolic activity of Dissolution media may not reflect physiological conditions
the lungs; (3) the lungs provide substantially greater in the GI tract
bioavailability for macromolecules than any other GI transit time
port of entry to the systemic circulation. pH in different regions of GI tract
The therapeutic effect for locally acting inhaled Contents of GI tract
drugs and the duration of this effect are determined Fed or fasted state
mainly by the dose deposited at the site of action and Normal digestive enzymes
its pulmonary clearance. In turn, drug distribution Flora of GI tract
and deposition along the respiratory tract (RT) Other factors affecting systemic drug absorption
depend on several factors such as (1) characteristics In vitro dissolution is a closed system, whereas in vivo
of the inhaled formulation (particle size distribution, drug absorption is an open system
shape, electrical charge, density, and hygroscopicity) Pre-systemic drug elimination (first-pass effects)
and (2) breathing patterns such as frequency, depth, Enterohepatic circulation
and flow rate. An ideal inhalation aerosol for local
delivery may be one with a relatively slow rate of
pulmonary absorption and clearance. It has been possible to deliver larger drug doses (milligram com-
shown that increasing the lipophilicity (Derendorf pared with microgram dosing) to the airways and
et al, 2006) and optimization of particle size (MMAD achieve greater deposition efficiency than the older
<5 mm) (Labiris and Dolovich, 2003; Gonda 1987) devices (>50% lung deposition vs. ≤20% with older
and release rate (Gonda, 1987; Suarez et al, 1998), it devices) (Dolovich, 1999).
is possible to increase the lung residence time of the The development of drugs for pulmonary drug
drug. Currently, there are more than 65 different delivery has focused mainly on the optimization of
inhaled products of more than 20 active ingredients particle or device technologies to improve the aerosol
marketed to treat respiratory diseases (Labiris and generation and pulmonary deposition of inhaled
Dolovich, 2003). Inhaled glucocorticoids (eg, fluti- drugs. Although substantial progress has been made
casone propionate, budesonide, triamcinolone ace- in these areas, no significant advances have been
tonide, mometasone furoate, etc) are some drugs made that would lead pulmonary drug delivery beyond
usually prescribed for the treatment of local pulmo- the treatment of some respiratory diseases. One main
nary diseases. The modification of the physicochem- reason for this stagnation is the poor knowledge about
ical (eg, side chains added to the D-ring of the (1) details on the fate of inhaled drug or carrier parti-
structure to slow the dissolution of the drug in the cles after deposition in the lungs; (2) how much drug
aqueous bronchial fluid) and biopharmaceutical (total amount) reaches the lungs and validated method
properties (eg, low oral bioavailability) of these to demonstrate this; and (3) differential assessment on
drugs made possible to increase its targeting (high the region of drug deposition (eg, central portion vs.
benefit:risk ratio) to the site of action, the lungs. periphery lung deposition). Inhalation products are
Inhalation therapy for local action is generated by complex drug–device combination products, bearing
different devices that aim to deliver the drug to the quite distinctive performance characteristics and
lower airways. Inhalation devices can be classified into patient instructions for use and handling. Thus, bio-
three different categories: MDIs, dry-powder inhalers availability/bioequivalence studies alone may not be
(eg, Aerolizer®, Diskus®, Flexaler®, Turbohaler®, etc), sufficient for documentation of the locally acting
and nebulizer inhalers. Some examples of inhalation drug products (FDA Guidance for Industry, 1989a;
and intranasal products are shown in Table 15-11. The FDA, 2013), following major manufacturing changes
recent development of new inhalation devices makes it or for approval of generics because for delivery to
Biopharmaceutic Considerations in Drug Product Design and In Vitro Drug Product Performance 459
the target sites these drugs do not depend upon sys- circulation for systemic activity. Scopolamine®
temic circulation. Following administration of the (Transderm Scop) delivers drug through the skin of
locally acting drug product, drug moieties detected the ear for relief of motion sickness. Transdermal
in the systemic circulation (i) appear subsequent to administration may release the drug over an extended
its delivery to and absorption from the local site, and period of several hours or days (eg, estrogen replace-
(ii) contain drug absorbed from multiple sites. ment therapy) without the discomforts of gastrointes-
Despite these arguments, some experts (Adams et al, tinal side effects or first-pass effects. Many transdermal
2010; O’Connor et al, 2011) believe that pharmaco- products deliver drug at a constant rate to the body,
kinetic studies might be able to provide some key similar to a zero-order infusion process. As a result, a
information (how much drug is deposited, where is stable, plateau level of the drug may be maintained.
it deposited, how long does it stay in the lung) Many therapeutic categories of drugs are now avail-
needed for demonstration of bioequivalence of inha- able as transdermal products (Table 15-12).
lation drugs for local action. Transdermal products vary in design (Gonzalez
The role of aerosol therapy is emerging beyond and Cleary, 2010). In general, the patch contains
the initial focus. This expansion has been driven by several parts: (1) a backing or support layer; (2) a
the Montreal protocol and the need to eliminate chlo- drug layer (reservoir containing the dose); (3) a
rofluorocarbons (CFCs) from traditional metered- release-controlling layer (usually a semipermeable
dose inhalers, by the need for delivery devices and film), (4) a pressure-sensitive adhesive (PSA); and
formulations that can efficiently and reproducibly (5) a protective strip, which must be removed prior
target the systemic circulation for the delivery of pro- to application (see Chapter 19, Fig. 19-14). The
teins and peptides, and by developments in medicine release-controlling membrane may be a polymeric
that have made it possible to consider curing lung
diseases with aerosolized gene therapy and preventing
epidemics of influenza and measles with aerosolized TABLE 1512 Biopharmaceutic Consider-
vaccines. The rate of absorption from the periphery of ations in Drug Product Design
the lung has been shown to be twice as fast as that
Pharmacodynamic considerations
taking place from the central portions, owing to the
Therapeutic objective
variable thickness of the epithelial cells versus alveo-
Toxic effects
lar cells (Brown and Schanker, 1983). Therefore, to
Adverse reactions
achieve maximum bioavailability of drugs aimed for
Drug considerations
systemic delivery, attention should be paid on deliver-
Chemical and physical properties of drug
ing the drug to the periphery of the lungs.
Drug product considerations
The continued expansion of the role of aerosol
Pharmacokinetics of drug
therapy will probably depend on several factors such
Bioavailability of drug
as the demonstration of the safety of this route of
Route of drug administration
administration for drugs that have their targets out-
Desired drug dosage form
side the lung and are administered long term (eg,
Desired dose of drug
insulin aerosol) (Laube, 2005).
Patient considerations
Compliance and acceptability of drug product
Transdermal Drug Products
Cost
Transdermal drug products, sometimes referred to as Manufacturing considerations
transdermal delivery systems or “patches,”3 are placed Cost
on the skin to deliver drug into the patient’s systemic Availability of raw materials
Stability
3Several “patches” are available for local activity on the skin. Quality control
Examples include lidocaine patch for local anesthetic activity Method of manufacturing
due to pain from shingles and diclofenac sodium patch, a topical
Patents
nonsteroidal anti-inammatory drug (NSAID).
460 Chapter 15
film such as ethylvinyl copolymer, which controls Scale-Up and Postapproval
the release rate of the dose and its duration of Changes (SUPAC)
action. The PSA layer is important for maintaining Any change in a drug product after it has been approved
uninterrupted skin contact for drug diffusion for marketing by the FDA is known as a postapproval
through the skin. In some cases, the drug is blended change. Postapproval changes may include formulation
directly into an adhesive, such as acrylate or sili- (component and composition), equipment, manufactur-
cone; performing the dual functions of release ing process, site, and scale-up in a drug product after it
control and adhesion, this product is known as has been approved for marketing by the FDA (FDA
“drug in adhesive.” In other products, the drug dose Guidance for Industry, November 1999). A major
may be placed in a separate insoluble matrix layer, concern of industry and the FDA is that if a pharma-
which helps control the release rate. This is gener- ceutical manufacturer makes any such, whether these
ally known as a “matrix patch,” and provides a little changes will affect the identity, strength, purity, quality,
more control of the release rate as compared to the bioavailability safety, or efficacy of the approved
simple “reservoir” type of patch. Multilayers of drug product. In addition, any changes in raw mate-
drugs may be involved in other transdermal prod- rial (ie, material used for preparing active pharmaceu-
ucts using a “laminate” design. In many cases, drug tical ingredient), excipients, or packaging (including
permeation through the skin is the slowest step in container closure system) should also be shown not to
the transdermal delivery of drug into the body. See affect the quality of the drug product. There are three
Chapter 19 for a discussion of modified-release levels of manufacturing changes.
drug products. Level 1 changes are defined as changes that are
unlikely to have any detectable impact on formula-
tion quality and performance and are usually reported
Absorption Enhancers
in the annual report.
A variety of excipients known as absorption enhanc- Level 2 changes could have a significant impact
ers or permeation enhancers have been incorporated in formation quality and performance and are usu-
into the drug product to promote systemic drug ally reported in a change being affected supplement.
absorption from the application site. For oral drug Level 2 changes usually require dissolution profile
products that contain poorly absorbed hydrophobic comparisons in multiple media.
drugs, surfactants have been added to the formula- Level 3 changes are likely to have a significant
tion to help solubilize the drug by making the drug impact on quality and performance and are usually
more miscible in water. The stratum corneum is the reported in a prior approval supplement. Level 3
major barrier to systemic drug absorption from changes usually require the conduct of a bioequiv-
transdermal drug products. The addition of excipi- alence study unless a predictive IVIVC is present.
ents or the use of physical approaches has been used
to enhance drug permeation from transdermal prod-
ucts. For example, Estraderm®, a estradiol transder- Frequently Asked Questions
mal system, contains ethanol, which promotes drug »»What physical or chemical properties of a drug sub-
delivery through the stratum corneum of the skin. The stance are important in designing a drug for (a) oral
use of ultrasound (phonophoresis or sonophoresis) has administration or (b) parenteral administration?
been used by physical therapists to enhance percutane- »»For a lipid-soluble drug that has very poor aqueous
ous absorption of hydrocortisone ointments and solubility, what strategies could be used to make this
creams from intact skin. Iontophoresis is a technique drug more bioavailable after oral administration?
using a small electric charge to deliver drug containing
»»For a weak ester drug that is unstable in highly
an ionic charge through the stratum corneum. Most of acidic or alkaline solutions, what strategies could be
these absorption enhancement approaches attempt to used to make this drug more bioavailable after oral
disrupt the cellular barriers to drug transport and allow administration?
the drug to permeate better.
Biopharmaceutic Considerations in Drug Product Design and In Vitro Drug Product Performance 461
CHAPTER SUMMARY
Biopharmaceutics is the study of the physicochemical successful throughout the product’s life cycle.
properties of the drug and the drug product and links Clinically relevant specifications are those specifica-
these properties to drug product quality and drug tions that, in addition, take into consideration the
product performance. Biopharmaceutics has a crucial clinical impact assuring consistent safety and effi-
role in establishing a link between the in vivo product cacy profile. In this case, clinically meaningful dis-
performance such as bioavailability, onset of action, solution method and specifications will minimize the
safety, and efficacy to the drug product critical process variability to the patient and, therefore, will optimize
parameters and material attributes. Both in vitro drug therapy. Due to the critical role that dissolution
(eg, dissolution) and in vivo methods (bioavailability) plays in defining the bioavailability of the drug,
are applied to evaluate drug product quality and drug in vitro dissolution, if identified as CQA, can serve
product performance. Thus, the selection of a suitable as a relevant predictor of the in vivo performance of
salt form of the drug that has improved stability, aque- the drug product.
ous solubility, and bioavailability is based on the An in vitro–in vivo correlation (IVIVC) estab-
drug’s physicochemical properties. Polymorphism lishes a relationship between a biological property
refers to the arrangement of a drug substance in vari- of the drug (such as pharmacodynamic effect or
ous crystalline forms. The selection of a suitable crys- plasma drug concentration) and a physicochemical
tal, solvate, or hydrates may be crucial to improve the property of the drug product containing the drug
solubility and dissolution of a drug, and therefore its substance, such as dissolution rate. A properly vali-
bioavailability. The particle size distribution of the dated IVIVC enhances drug product understanding
drug is an important property for insoluble, hydropho- and provides justification of manufacturing changes
bic drugs. Decreasing the particle size for some low- during drug product development. It enhances the
solubility drugs may result in improved bioavailability. significance of the in vitro testing leading to drug
Systemic drug absorption from a drug product con- product specifications’ (eg, dissolution acceptance
sists of a succession of rate processes including (1) criteria) setting based on targeted clinically relevant
disintegration of the drug product and subsequent plasma concentrations. In addition, it allows for the
release of the drug, (2) dissolution of the drug in an prediction of the clinical impact of movements
aqueous environment, and (3) absorption of the drug within the design space without the need for addi-
across cell membranes into the systemic circulation. tional in vivo studies.
The slowest step in a series of kinetic processes is The use of biopharmaceutic tools such as dis-
called the rate-limiting step. Dissolution is a dynamic solution and BA/BE studies become very relevant in
process by which a solid drug substance becomes dis- setting clinically relevant drug product specifica-
solved in a dissolution medium. Developing a discrimi- tions because it would be rather impractical to deter-
nating dissolution method and setting the appropriate mine the clinical relevance of movements within the
product specifications is critical in assuring that the design space through clinical efficacy and safety
manufacture of the dosage form is consistent and trials.
462 Chapter 15
LEARNING QUESTIONS
1. What are the two rate-limiting steps possible 5. What effect does the oral administration of an
in the oral absorption of a solid drug product? anticholinergic drug, such as atropine sulfate,
Which one would apply to a soluble drug? have on the bioavailability of aspirin from an
Which one could be altered by the pharmacist? enteric-coated tablet? (Hint: Atropine sulfate
Give examples. decreases gastrointestinal absorption.)
2. What is the physiologic transport mechanism 6. Drug formulations of erythromycin, including
for the absorption of most drugs from the gas- its esters and salts, have significant differences
trointestinal tract? What area of the gastrointes- in bioavailability. Erythromycin is unstable
tinal tract is most favorable for the absorption in an acidic medium. Suggest a method for
of drugs? Why? preventing a potential bioavailability problem
3. Explain why the absorption rate of a soluble for this drug.
drug tends to be greater than the elimination 7. Why can two generic drug products have dif-
rate of the drug. ferent dissolution profiles in vitro and still be
4. What type of oral dosage form generally bioequivalent in vivo?
yields the greatest amount of systemically
available drug in the least amount of time?
(Assume that the drug can be prepared in any
form.) Why?
ANSWERS
Frequently Asked Questions For a lipid-soluble drug that has very poor aqueous
solubility, what strategies could be used to make this
What physical or chemical properties of a drug sub- drug more bioavailable after oral administration?
stance are important in designing a drug for (a) oral
administration or (b) parenteral administration? • A lipid-soluble drug may be prepared in an oil-in-
water (o/w) emulsion or dissolved in a nonaqueous
• For optimal drug absorption after oral administra- solution in a soft gelatin capsule. A co-solvent may
tion, the drug should be water soluble and highly improve the solubility and dissolution of the drug.
permeable so that it can be absorbed throughout
the gastrointestinal tract. Ideally, the drug should For a weak ester drug that is unstable in highly
not change into a polymorphic form that could acidic or alkaline solutions, what strategies could be
affect its solubility. The drug should be stable used to make this drug more bioavailable after oral
in both gastric and intestinal pH and preferably administration?
should not be hygroscopic. • The rate of hydrolysis (decomposition) of the ester
For parenteral administration, the drug should drug may be reduced by formulating the drug in
be water soluble and stable in solution, preferably a co-solvent solution. A reduction in the percent
at autoclave temperature. The drug should be non- of the aqueous vehicle will decrease the rate of
hydroscopic and preferably should not change into hydrolysis. In addition, the drug should be formu-
another polymorphic form. lated at the pH in which the drug is most stable.
Biopharmaceutic Considerations in Drug Product Design and In Vitro Drug Product Performance 463
Learning Questions the drug dose, which is great initially. Even if
1. The rate-limiting steps in the oral absorption ka < k, the initial drug absorption rate may be
of a solid drug product are the rate of drug dis- greater than the drug elimination rate. After
solution within the gastrointestinal tract and the the drug is absorbed from the absorption site,
rate of permeation of the drug molecules across dDA/dt ≤ dDE/dt.
the intestinal mucosal cells. Generally, disinte- 4. A drug prepared as an oral aqueous drug
gration of the drug product is rapid and not rate solution is generally the most bioavailable.
limiting. Water-soluble drugs dissolve rapidly However, the same drug prepared as a well-
in the aqueous environment of the gastrointes- designed immediate-release tablet or capsule
tinal tract, so the permeation of the intestinal may have similar bioavailability. In the case of
mucosal cells may be the rate-limiting step. The an oral drug solution, there is no dissolution
drug absorption rate may be altered by a variety step; the drug molecules come into contact with
of methods, all of which depend on knowledge intestinal membrane, and the drug is rapidly
of the biopharmaceutic properties of the drug absorbed. As a result of first-pass effects (dis-
and the drug product and on the physiology cussed in Chapter 12), a drug given in an oral
of the gastrointestinal tract. Drug examples drug solution may not be 100% bioavailable.
are described in detail in this chapter and in If the drug solution is formulated with a high
Chapter 14. solute concentration—such as sorbitol solution,
2. Most drugs are absorbed by passive diffusion. which yields a high osmotic pressure—gastric
The duodenum area provides a large surface motility may be slowed, thus slowing the rate
area and blood supply that maintains a large of drug absorption.
drug concentration gradient favorable for drug 5. Anticholinergic drugs prolong gastric empty-
absorption from the duodenum into the sys- ing, which will delay the absorption of an
temic circulation. enteric-coated drug product.
3. If the initial drug absorption rate, dD 6. Erythromycin may be formulated as enteric-
A/dt,
was slower than the drug elimination rate, coated granules to protect the drug from degrada-
dDE/dt, then therapeutic drug concentrations tion at the stomach pH. Enteric-coated granules
in the body would not be achieved. It should are less affected by gastric emptying and food
be noted that the rate of absorption is gener- (which delays gastric emptying) compared to
ally first order, dDA/dt = D0ka, where D0 is enteric-coated tablets.
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Drug Product Performance,
16 In Vivo: Bioavailability and
Bioequivalence
Barbara Davit, Dale Conner, and Leon Shargel
Chapter Objectives DRUG PRODUCT PERFORMANCE
»» Define bioavailability, Drug product performance,1 in vivo, may be defined as the release
bioequivalence, and drug of the drug substance from the drug product leading to bioavail-
product performance. ability of the drug substance. The assessment of drug product
»» Explain why certain drugs performance is important since bioavailability is related both to the
and drug products have low pharmacodynamic response and to adverse events. Thus, perfor-
bioavailability. mance tests relate the quality of a drug product to clinical safety
and efficacy. Bioavailability studies are drug product performance
»» Explain why first-pass effect as
studies used to define the effect of changes in the physicochemical
well as chemical instability of a
properties of the drug substance, the formulation of the drug, and
drug can result in low relative
the manufacture process of the drug product (dosage form). Drug
bioavailability.
product performance studies are used in the development of new
»» Distinguish between and generic drug products.
bioavailability and Bioavailability is one aspect of drug product quality that links
bioequivalence. the in vivo performance of a new drug product to the original for-
»» Explain why relative mulation that was used in clinical safety and efficacy studies.
bioavailability may have values Bioequivalence studies are drug product performance tests that
greater than 100%. compare the bioavailability of the same active pharmaceutical
ingredient from one drug product (test) to a second drug product
»» Explain why bioequivalence (reference). Bioavailability and bioequivalence can be considered
may be considered as a measure as measures of the drug product performance in vivo.
of drug product performance.
»» Describe various methods Bioequivalence Studies in New Drug Development (NDA)
for measuring bioavailability During drug development, bioequivalence studies are used to com-
and the advantages and pare (a) early and late clinical trial formulations; (b) formulations
disadvantages of each. used in clinical trials and stability studies, if different; (c) clinical
»» Describe the statistical criteria trial formulations and to-be-marketed drug products, if different;
for bioequivalence and 90% and (d) product strength equivalence, as appropriate. Bioequivalence
confidence intervals. study designs are used to support new formulations of previously
approved products, such as a new fixed-dose combination version
of two products approved for coadministration, or modified-release
versions of immediate-release products. Postapproval, in vivo
1A glossary of important terms appears at the end of this chapter.
469
470 Chapter 16
»» Explain the conditions Clinical efcacy
Clinical and safety studies
under which a generic drug Active pharmaceutical
drug
product manufacturer may ingredient (drug substance)
product
PK/BA studies
request a waiver (biowaiver)
for performing an in vivo
bioequivalence study. Marketed drug product Dissolution proles and/or
(brand) bioequivalence studies
»» Define therapeutic equivalence
and explain why bioequivalence
is only one component of the
regulatory requirements for Dissolution proles and/or
Postapproval changes
bioequivalence studies
therapeutic equivalence.
FIGURE 161 Drug product performance and new drug product devel-
opment for NDAs. Drug product performance may be determined in vivo by
bioequivalence studies or in vitro by comparative drug dissolution studies.
BA = bioavailability.
bioequivalence studies may be needed to support regulatory
approval of major changes in formulation, manufacturing, or site,
in comparison to reference formulation (usually the prechange
formulation) (Fig. 16-1).
The initial safety and clinical efficacy studies during new
drug development may use a simple formulation such as a hard
gelatin capsule containing only the active ingredient diluted with
lactose. If the new drug demonstrates appropriate human efficacy
and safety, a to-be-marketed drug product (eg, compressed tablet)
may be developed. Since the initial safety and efficacy studies
were performed using a different formulation (ie, hard gelatin
capsule), the pharmaceutical manufacturer must demonstrate that
the to-be-marketed drug product demonstrates equivalent drug
product performance to the original formulation (Fig. 16-1).
Equivalent drug product performance is generally demonstrated
by an in vivo bioequivalence study in normal healthy volunteers.
Under certain conditions, equivalent drug product performance
may be demonstrated in vitro using comparative dissolution pro-
files (see Chapter 15).
As stated above, the marketed drug product that is approved
by the US Food and Drug Administration (FDA) may not be the
same formulation that was used in the original safety and clinical
efficacy studies. After the drug product is approved by the FDA
and marketed, the manufacturer may perform changes to the for-
mulation. These changes to the marketed drug product are known
as postapproval changes (see also Chapter 17). These postapproval
changes, often termed SUPAC (scale-up and postapproval change
based on several FDA guidance documents), could include a
change in the supplier of the active ingredient, a change in the
formulation, a change in the manufacturing process, and/or a
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 471
Comparative dissolution
Generic
Active pharmaceutical proles and/or
drug
ingredient (drug substance) bioequivalence studies
product
to approved RLD
Dissolution proles plus
Postapproval changes bioequivalence studies,
if required
FIGURE 162 Drug product performance and generic drug product development. Drug product performance may be deter-
mined in vivo by bioequivalence studies or in vitro by comparative drug/release dissolution studies.
change in the manufacturing site. In each case, the in vivo bioequivalence studies in normal healthy adult
manufacturer must demonstrate that drug product subjects under fasted and fed conditions. Drug product
performance did not change and is the same for the performance comparisons in vitro may also include
drug product manufactured before and after the comparative drug dissolution/release profiles. Similar
SUPAC change. As shown in Fig. 16-1, drug product to the brand-name drug product manufacturer, the
performance may be determined by in vivo bioequiv- generic drug manufacturer may make changes after
alence studies or by in vitro comparative drug release FDA approval in the formulation, in the source of the
or dissolution profiles. active pharmaceutical ingredient, manufacturing pro-
cess, or other changes. For any postapproval change,
Bioequivalence Studies in Generic Drug the manufacturer must demonstrate that the change
Development (ANDA) did not alter the performance of the drug product.
Comparative drug product performance studies are
important in the development of generic drug prod-
PURPOSE OF BIOAVAILABILITY
ucts (Fig. 16-2). A generic drug product is a multi-
source drug product2 that has been approved by the AND BIOEQUIVALENCE STUDIES
FDA as a therapeutic equivalent to the reference
Bioavailability and bioequivalence studies are impor-
listed drug product3 (usually the brand or innovator
tant in the process of approving pharmaceutical prod-
drug product) and has proven equivalent drug product
ucts for marketing. Bioavailability is defined as the
performance. Clinical safety and efficacy studies are
rate and extent to which the active ingredient or active
not generally performed on generic drug products.
moiety is absorbed from a drug product and becomes
Since the formulation and method of manufacture of
available at the site of action (US-FDA, CDER,
a drug product can affect the bioavailability and sta-
2014a). Bioavailability data provide an estimate of the
bility of the drug, the generic drug manufacturer must
fraction of drug absorbed from the formulation, and
demonstrate that the generic drug product is pharma-
provide information about the pharmacokinetics of the
ceutically equivalent, bioequivalent, and therapeuti-
drug. Relative bioavailability studies compare two
cally equivalent to the comparator brand-name drug
drug product formulations. A bioequivalence study is
product. Drug product performance comparison for
a specialized type of relative bioavailability study.
oral generic drug products is usually measured by
Bioequivalence is defined as the absence of a signifi-
cant difference in the rate and extent to which the
active ingredient or active moiety becomes available at
2Multisource drug products are drug products that contain the same
active drug substance in the same dosage form and are marketed by the site of drug action when administered at the same
more than one pharmaceutical manufacturer. molar dose under similar conditions in an appropri-
3 ately designed study.
Reference listed drugs corresponding to proposed generic versions
are listed by the US-FDA in its publication Approved Drug Products Bioavailability and bioequivalence data play piv-
with Therapeutic Equivalence Evaluations (Orange Book). otal roles in regulatory submissions for marketing
472 Chapter 16
approval of new and generic drugs throughout the A drug product’s bioavailability provides an estimate
world. Each regulatory agency has developed its own of the relative fraction of the administered dose that
unique system of guidelines advising new and generic is absorbed into the systemic circulation (US-FDA,
drug applicants on how to conduct acceptable bioavail- CDER, 2014c). Determining the fraction (f) of
ability and bioequivalence studies to support marketing administered dose absorbed involves comparing the
approval. A recent survey of international bioequiva- drug product’s systemic exposure (represented by
lence guidelines showed that there are more similarities the concentration-versus-time or pharmacokinetic
than differences among approaches used by various profile) with that of a suitable reference product. For
international jurisdictions (Davit et al, 2013). In this systemically available drug products, bioavailability
chapter, discussion of the relationship between bio- is most often assessed by determining the area under
availability, bioequivalence, and drug approval require- the drug plasma concentration-versus-time profile
ments will focus on the perspective of the FDA. Where (AUC). The AUC is considered the most reliable
appropriate, the reader will be directed to references measure of a drug’s bioavailability, as it is directly
covering international jurisdictions for further reading. proportional to the total amount of unchanged drug
In summary, clinical studies are used to determine that reaches the systemic circulation (Le, 2014).
the safety and efficacy of drug products. Bioavailability Figure 16-3 shows how the drug concentration-ver-
studies are drug product performance studies used to sus-time profile is used to identify the pharmacoki-
define the effect of changes in the physicochemical netic parameters that form the basis of bioavailability
properties of the drug substance, the formulation of the and bioequivalence comparisons.
drug, and manufacture process of the drug product
(dosage form). Bioequivalence studies are used to com- Absolute Bioavailability
pare the bioavailability of the same drug (same salt or
Absolute bioavailability compares the bioavailability
ester) from various drug products. Bioavailability and
of the active drug in the systemic circulation fol-
bioequivalence can be considered as performance mea-
lowing extravascular administration with the bio-
sures of the drug product in vivo. If the drug products
availability of the same drug following intravenous
are pharmaceutically equivalent, bioequivalent, and
administration (Fig. 16-4). Intravenous drug adminis-
therapeutically equivalent (as defined by the regulatory
tration is considered 100% absorbed. The route of
agency such as the FDA), then the clinical efficacy and
extravascular administration can be inhaled, intra-
the safety profile of these drug products are assumed to
muscular, oral, rectal, subcutaneous, sublingual, topi-
be similar and may be substituted for each other.
cal, transdermal, etc. The absolute bioavailability is
the dose-corrected AUC of the extravascularly admin-
Frequently Asked Questions istered drug product divided by the AUC of the drug
»»Why are bioequivalence studies considered as drug product given intravenously. Thus, for an oral formu-
product performance studies? lation, the absolute bioavailability is calculated as
»»What are the differences between a safety/efficacy follows:
study and an in vivo bioequivalence study? How do
the study objectives differ? AUCpo ⋅Div
Fabs =
AUC
»»What’s the difference between drug product iv ⋅Dpo
performance and bioequivalence?
where
Fabs is the fraction of the dose absorbed, expressed as
RELATIVE AND ABSOLUTE a percentage;
AVAILABILITY AUCpo is the AUC following oral administration;
Div is the dose administered intravenously;
Regulatory agencies such as the FDA require sub- AUCiv is the AUC following intravenous administra-
mission of bioavailability data in applications to tion; and
market new drug products (US-FDA, CDER, 2014b). Dpo is the dose administered orally.
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 473
350
300 Cmax
250
200
150
100
50
t AUC
max
0
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48
Time (hours)
FIGURE 163 Plasma drug concentration–time curve after oral drug administration.
Absolute availability, Fabs, may be expressed as Relative Bioavailability
a fraction or as a percent by multiplying Fabs × 100. Another type of comparative bioavailability assess-
A drug given by the intravenous route will have an ment is provided by a relative bioavailability study.
absolute bioavailability of 100% (f = 1). A drug In a relative bioavailability study, the systemic expo-
given by an extravascular route may have an Fabs = 0 sure of a drug in a designated formulation (generally
(no systemic absorption) and Fabs = 1.0 (100% sys- referred to as treatment A or reference formulation)
temic absorption). is compared with that of the same drug administered
100
IV
90
Oral
80
70
60
50
40
30
20
10
0
0 2 4 6 8 10 12 14 16 18 20 22 24
Time (hours)
FIGURE 164 Relationship between plasma drug concentration-versus-time profiles for an intravenously administered
formulation versus an orally administered formulation. In an absolute bioavailability study, the systemic exposure profile of a drug
administered by the oral route (black curve) is compared with that of the drug administered by the intravenous route (green curve).
Plasma drug concentration (ng/mL)
Drug plasma concentration
474 Chapter 16
in a reference formulation (generally referred to as fixed-dose combination doublet) or concurrently
treatment B or test formulation). In a relative bio- according to an approved combination regimen
availability study, the AUCs of the two formulations (ie, two treatments). Relative bioavailability study
are compared as follows: designs are also commonly used for bridging formu-
lations during drug development, for example, to
AUC ⋅D
Frel = 100 ⋅ A B evaluate how drug systemic availability from a new
AUCB ⋅D premarket formulation compares with that from an
A
existing premarket formulation.
where
Frel is the relative bioavailability of treatment (formu- PRACTICE PROBLEM
lation) A, expressed as a percentage;
AUCA is the AUC following administration of treat- The bioavailability of a new investigational drug was
ment (formulation) A; studied in 12 volunteers. Each volunteer received
DA is the dose of formulation A; either a single oral tablet containing 200 mg of the
AUCB is the AUC of formulation B; and drug, 5 mL of a pure aqueous solution containing
DB is the dose of formulation B. 200 mg of the drug, or a single IV bolus injection
containing 50 mg of the drug. Plasma samples were
Relative bioavailability studies are frequently obtained periodically up to 48 hours after the dose
included in regulatory submissions. For example, the and assayed for drug concentration. The average AUC
FDA recommends that new drug developers rou- values (0–48 hours) are given in the table below.
tinely use an oral solution as the reference for a new From these data, calculate (a) the relative bioavail-
oral formulation, for the purpose of assessing how ability of the drug from the tablet compared to the
formulation impacts bioavailability. Other types of oral solution and (b) the absolute bioavailability of
relative bioavailability studies used in drug develop- the drug from the tablet.
ment include studies to characterize food effects and
drug–drug interactions. In a food-effect bioavail-
Dose AUC Standard
ability study, oral bioavailability of the drug product Drug Product (mg) (mg · h/mL) Deviation
given with food (usually a high-fat, high-calorie
meal) is compared to oral bioavailability of the drug Oral tablet 200 89.5 19.7
product given under fasting conditions. The drug Oral solution 200 86.1 18.1
product given under fasting conditions is treated as
IV bolus 50 37.8 5.7
the reference treatment. The goal of a drug–drug injection
interaction study is to determine whether there is an
increase or decrease in bioavailability in the pres-
Solution
ence of the interacting drug. As such, the general
drug–drug interaction study design compares drug The relative bioavailability of the drug from the tab-
relative bioavailability with and without (reference let is estimated in the equation below. No adjustment
treatment) the interacting drug. Relative bioavail- for the dose is necessary since the nominal doses are
ability studies are used in developing new formula- the same.
tions of existing immediate-release drug products,
89.5
such as new modified-release versions or new fixed- Relative bioavailability = = 1.04 or 104%
86.1
dose combination formulations. In the case of a new
modified-release version, the reference product is The relative bioavailability of the drug from the tab-
the approved immediate-release product. In the case let is 1.04, or 104%, compared to the solution. In this
of a new fixed-dose combination, the reference prod- study, the difference in drug bioavailability between
uct can be the single-entity drug products adminis- tablet and solution would need to be analyzed statis-
tered either separately (ie, three treatments for a tically to determine whether the difference in drug
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 475
bioavailability is statistically significant. It is possible absorption, as determined by comparison of mea-
for the relative bioavailability to be greater than 100%. sured parameters. The FDA’s regulations (US-FDA,
In this case, the tablet formulation may have some CDER, 2014a) list the following approaches to
property or excipient that increases bioavailability. determining bioequivalence, in descending order of
The absolute drug bioavailability from the tablet accuracy, sensitivity, and reproducibility:
is calculated and adjusted for the dose.
• In vivo measurement of active moiety or moieties
89.5/200 in biological fluid (ie, a pharmacokinetic study)
F = absolute bioavailability =
37.5/50 • In vivo pharmacodynamic (PD) comparison
• In vivo limited clinical comparison
= 0.592 or 59.2% • In vitro comparison
• Any other approach deemed acceptable (by the
Because F, the fraction of dose absorbed from the
FDA)
tablet, is less than 1, the drug from the oral tablet is
not completely absorbed systemically, as a result of For drug products that are not intended to be
either poor oral absorption of the drug itself, formu- absorbed into the bloodstream, bioavailability may
lation effects that reduce oral bioavailability, or metab- be assessed by measurements intended to reflect the
olism by first-pass effect (presystemic elimination). rate and extent to which the active ingredient or
The relative bioavailability of the drug from the active moiety becomes available at the site of action.
tablet is approximately 100% when compared to the The design of the bioavailability study depends on
oral solution. the objectives of the study, the ability to analyze the
The comparison between oral solution (little to drug (and metabolites) in biological fluids, the phar-
no formulation effect) and IV administration gives macodynamics of the drug substance, the route of
information on the absorption of the drug itself when drug administration, and the nature of the drug prod-
formulation effects are virtually nonexistent. With uct. For all systemically active drugs, with a few
this knowledge, one can interpret the absolute bio- exceptions, bioequivalence should be demonstrated
availability from the tablet and know if there is an by an in vivo study based on pharmacokinetic (PK)
effect of that formulation to change bioavailability or endpoints, as this is the most sensitive, accurate, and
relative bioavailability is the same whether the tablet reproducible approach. The other approaches—PD,
formulation wasn’t even there. clinical, or in vitro—may be more appropriate for
Results from bioequivalence studies may show locally acting drugs that are not systemically absorbed,
that the relative bioavailability of the test oral product such as those administered topically or those that act
is greater than, equal to, or less than 100% compared locally within the gastrointestinal (GI) tract. These
to the reference oral drug product. However, the results latter BE approaches are considered on a case-by-case
from these bioequivalence studies should not be misin- basis (Table 16-1). Detailed examples to illustrate when
terpreted to imply that the absolute bioavailability of PD, clinical, or in vitro approaches are most suitable
the drug from the oral drug products is also 100% for establishing BE are presented below.
unless the oral formulation was compared to an intra-
venous injection (completely bioavailable) of the drug.
IN VIVO MEASUREMENT OF
ACTIVE MOIETY OR MOIETIES
METHODS FOR ASSESSING IN BIOLOGICAL FLUIDS
BIOAVAILABILITY AND
Plasma Drug Concentration
BIOEQUIVALENCE
Measurement of drug concentrations in blood,
Direct and indirect methods may be used to assess plasma, or serum after drug administration is the
drug bioavailability. Bioequivalence of a drug prod- most direct and objective way to determine systemic
uct is demonstrated by the rate and extent of drug drug bioavailability. By appropriate blood sampling,
476 Chapter 16
TABLE 161 Methods for Assessing For many systemically absorbed drugs, small differ-
Bioavailability and Bioequivalence ences in tmax may have little clinical effect on overall
drug product performance. However, for some drugs,
In vivo measurement of active moiety or moieties in
biological fluids such as delayed action drug products, large differ-
ences in tmax may have clinical impact.
Plasma drug concentration
Time for peak plasma (blood) concentration (tmax)
Peak plasma drug concentration (C Cmax: The peak plasma drug concentration,
max)
Area under the plasma drug concentration–time curve Cmax, represents the maximum plasma drug concen-
(AUC) tration obtained after oral administration of drug. For
Urinary drug excretion many drugs, a relationship is found between the
Cumulative amount of drug excreted in the urine (D pharmacodynamic drug effect and the plasma drug
u)
Rate of drug excretion in the urine (dDu/dt) concentration. Cmax provides indications that the
Time for maximum urinary excretion (t) drug is sufficiently systemically absorbed to provide
In vivo pharmacodynamic (PD) comparison a therapeutic response. In addition, Cmax provides
Maximum pharmacodynamic effect (Emax) warning of possibly toxic levels of drug. The units of
Time for maximum pharmacodynamic effect Cmax are concentration units (eg, mg/mL, ng/mL).
Area under the pharmacodynamic effect–time curve
Although not a unit for rate, Cmax is often used in
Onset time for pharmacodynamic effect
bioequivalence studies as a surrogate measure for the
Clinical endpoint study rate of drug bioavailability. So, the expectation is
Limited, comparative, parallel clinical study using prede-
that as the rate of drug absorption goes up, the peak
termined clinical endpoint(s) and performed in patients
or Cmax will also be larger. If the rate of drug absorp-
In vitro studies tion goes down, then the peak or Cmax is smaller.
Comparative drug dissolution, f2 similarity factor
In vitro binding studies
Examples: Cholestyramine resin—In vitro equilibrium AUC: The area under the plasma level–time
and kinetic binding studies curve, AUC, is a measurement of the extent of drug
bioavailability (see Fig. 16-3). The AUC reflects the
Any other approach deemed acceptable (by the FDA)
total amount of active drug that reaches the systemic
circulation. The AUC is the area under the drug
plasma level–time curve from t = 0 to t = ∞, and is
an accurate description of the plasma drug concen- equal to the amount of unchanged drug reaching the
tration–time profile of the therapeutically active drug general circulation divided by the clearance.
substance(s) can be obtained using a validated drug
assay. ∞
[AUC]∞0 = ∫ C (1 .1)
0 pdt 6
tmax: The time of peak plasma concentration,
tmax, corresponds to the time required to reach maxi- FD FD
[AUC]∞ = 0 0
0 = (16.2)
mum drug concentration after drug administration. clearance kVD
At tmax, peak drug absorption occurs and the rate of
drug absorption exactly equals the rate of drug elimi- where F = fraction of dose absorbed, D0 = dose,
nation (Fig. 16-3). Drug absorption still continues k = elimination rate constant, and VD = volume of
after tmax is reached, but at a slower rate. When com- distribution. The AUC is independent of the route
paring drug products, tmax can be used as an approxi- of administration and processes of drug elimination
mate indication of drug absorption rate. The value as long as the elimination processes do not change.
for tmax will become smaller (indicating less time The AUC can be determined by a numerical inte-
required to reach peak plasma concentration) as the gration procedure, such as the trapezoidal rule
absorption rate for the drug becomes more rapid. method. The units for AUC are concentration × time
Units for tmax are units of time (eg, hours, minutes). (eg, mg·h/mL).
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 477
C
B
A
Dose (mg)
FIGURE 167 Relationship between AUC and dose when
Time metabolism (elimination) is saturable.
FIGURE 165 Plasma level–time curve following admin-
istration of single doses of (A) 250 mg, (B) 500 mg, and (C) When the AUC is not directly proportional to the
1000 mg of drug. dose, bioavailability of the drug is difficult to evalu-
ate because drug kinetics may be dose dependent.
For many drugs, the AUC is directly propor- Conversely, absorption may also become saturated
tional to dose. For example, if a single dose of a drug resulting in lower-than-expected changes in AUC.
is increased from 250 to 1000 mg, the AUC will also
show a fourfold increase (Figs. 16-5 and 16-6). Urinary Drug Excretion Data
In some cases, the AUC is not directly proportional Urinary drug excretion data is an indirect method for
to the administered dose for all dosage levels. For estimating bioavailability. The drug must be excreted
example, as the dosage of drug is increased, one of the in significant quantities as unchanged drug in the
pathways for drug elimination may become saturated urine. In addition, timely urine samples must be col-
(Fig. 16-7). Drug elimination includes the processes of lected and the total amount of urinary drug excretion
metabolism and excretion. Drug metabolism is an must be obtained (see Chapter 3).
enzyme-dependent process. For drugs such as salicylate
and phenytoin, continued increase of the dose causes ∞
D
u : The cumulative amount of drug excreted in
saturation of one of the enzyme pathways for drug the urine, D∞, is related directly to the total amount of
u
metabolism and consequent prolongation of the elimi- drug absorbed. Experimentally, urine samples are
nation half-life. The AUC thus increases disproportion- collected periodically after administration of a drug
ally to the increase in dose, because a smaller amount of product. Each urine specimen is analyzed for free
drug is being eliminated (ie, more drug is retained). drug using a specific assay. A graph is constructed
that relates the cumulative drug excreted to the col-
lection-time interval (Fig. 16-8).
0 250 500 750 1000 A B C
Dose (mg) Time
FIGURE 166 Linear relationship between AUC and dose FIGURE 168 Corresponding plots relating the plasma
(data from Fig. 16-5). level–time curve and the cumulative urinary drug excretion.
Plasma level (mg/mL)
Area under curve (AUC)
Cumulative amount
of drug in urine Area under curve (AUC)
478 Chapter 16
The relationship between the cumulative amount A
of drug excreted in the urine and the plasma level–
time curve is shown in Fig. 16-8. When the drug is
almost completely eliminated (point C), the plasma
concentration approaches zero and the maximum
amount of drug excreted in the urine, D∞, is obtained.
u
dDu/dt: The rate of drug excretion. Because most A B C
drugs are eliminated by a first-order rate process, the Time
rate of drug excretion is dependent on the first-order
B
elimination rate constant, k, and the concentration of
drug in the plasma, Cp. In Fig. 16-9, the maximum rate
of drug excretion, (dDu/dt)max, is at point B, whereas
the minimum rate of drug excretion is at points A and C.
Thus, a graph comparing the rate of drug excretion
with respect to time should be similar in shape to the
plasma level–time curve for that drug (Fig. 16-10).
A B C
Time
t∞: The total time for the drug to be excreted. In FIGURE 1610 Corresponding plots relating the plasma
Figs. 16-9 and 16-10, the slope of the curve segment level–time curve and the rate of urinary drug excretion.
A–B is related to the rate of drug absorption, whereas
point C is related to the total time required after drug
administration for the drug to be absorbed and com-
pletely excreted, t = ∞. The t∞ is a useful parameter BIOEQUIVALENCE STUDIES
in bioequivalence studies that compare several drug BASED ON PHARMACODYNAMIC
products.
ENDPOINTS—IN VIVO
A PHARMACODYNAMIC (PD)
COMPARISON
In some cases, the quantitative measurement of a
drug in plasma is not available or in vitro approaches
are not applicable. The following criteria for a PD
endpoint study are important:
A B C
Time • A dose–response relationship is demonstrated.
• The PD effect of the selected dose should be at the
B rising phase of the dose–response curve, as shown
in Fig. 16-11.
• Sufficient measurements should be taken to assure
an appropriate PD response profile.
• All PD measurement assays should be validated
for specicity, accuracy, sensitivity, and precision.
For locally acting, nonsystemically absorbed drug
A B C
Time products, such as topical corticosteroids, plasma
FIGURE 169 Corresponding plots relating the plasma drug concentrations may not reflect the bioavail-
level–time curve and the cumulative urinary drug excretion. ability of the drug at the site of action. An acute
Cumulative amount Plasma level
of drug in urine
Rate of drug Plasma level
excretion (dDu/dt)
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 479
Dose response 25
Peak effect
100
20
15
50 10
Area under
5 the peak effect-
versus-time
ED50 value curve
0
0 0 5 10 15 20 25 30
Log dose Time (hours)
Time for peak effect
Dose response FIGURE 1612 Acute pharmacodynamic effect–time
curve. It shows an acute pharmacologic effect that is measured
periodically after a single oral dose. The effect curve is similar
to Fig. 16-3.
The use of an acute pharmacodynamic effect to
determine bioavailability generally requires demon-
stration of a dose–response curve (Fig. 16-11 and
Chapter 21). Bioavailability is determined by char-
Dose (arithmetic scale) acterization of the dose–response curve. For bio-
FIGURE 1611 Dose–response curves. Dose–response equivalence determination, pharmacodynamic
curves for dose versus response graphed on a log or arithmetic parameters including the total area under the acute
scale. pharmacodynamic effect–time curve, peak pharma-
codynamic effect, and time for peak pharmacody-
namic effect are obtained from the pharmacodynamic
pharmacodynamic effect,4 such as an effect on forced effect–time curve (Fig. 16-12). The onset time and
expiratory volume, FEV1 (inhaled bronchodilators), duration of the pharmacokinetic effect may also be
or skin blanching (topical corticosteroids) can be included in the analysis of the data. The use of phar-
used as an index of drug bioavailability. In this case, macodynamic endpoints for the determination of
the acute pharmacodynamic effect is measured over a bioavailability and bioequivalence is much more
period of time after administration of the drug prod- variable than the measurement of plasma or urine
uct. Measurements of the pharmacodynamic effect drug concentrations. Some examples of drug prod-
should be made with sufficient frequency to permit a ucts for which bioequivalence PD endpoints are
reasonable estimate for a time period at least three recommended are listed on Table 16-2.
times the half-life of the drug (Gardner, 1977). This
approach may be particularly applicable to dosage
BIOEQUIVALENCE STUDIES BASED
forms that are not intended to deliver the active
moiety to the bloodstream for systemic distribution ON CLINICAL ENDPOINTS—
(Zou and Yu, 2014). CLINICAL ENDPOINT STUDY
The clinical endpoint study is the least accurate,
least sensitive to bioavailability differences, and
4A pharmacodynamic endpoint is an acute pharmacologic effect
that is directly related to the drug’s activity that can be measured most variable. A predetermined clinical endpoint is
quantitatively. used to evaluate comparative clinical effect in the
Intensity of response
Intensity of response
Effect
480 Chapter 16
TABLE 162 Examples of Drug Products for Which FDA Recommends That Bioequivalence Studies
Use Pharmacodynamic Endpoints
Drug Product Indication Mechanism of Action Endpoint
Acarbose tablet (if no Q1/Q2 Treatment of type 2 Inhibition of intestinal Reduction in blood glucose
sameness between test and diabetes a-glucosidase, thereby concentrations
reference) decreasing absorption of
starch and oligosaccharides
Lanthanum carbonate Reduction of serum Inhibits phosphate absorp- Reduction in urinary
tablet phosphate levels in patients tion by forming highly insol- phosphate excretion
with end-stage renal disease uble lanthanum phosphate
complexes in GI tract
Orlistat capsules Treatment of obesity Inhibition of intestinal Amount of fat excreted
lipase, thereby reducing in feces over 24 hours at
absorption of free fatty acids steady state
and monoacylglycerols
Fluticasone propionate Relief of skin itching and The application of cortico- Skin chromameter measure-
cream inflammation steroids causes blanching in ments through at least
the microvasculature of the 24 hours after application
skin (not the mechanism of
action, but quantitatively
measurable)
Albuterol sulfate metered Relaxes smooth muscle of A beta2-adrenergic agonist • Either a bronchoprovoca-
dose inhaler airways, thus protecting tion or bronchodilatation
against bronchoconstrictor assay is suitable
challenges • For bronchoprovocation,
measure the concentra-
tion or dose of methacho-
line required to decrease
FEV1 by 20%
• For bronchodilatation,
measure the AUEC0-4 h,
AUEC0-6 h, and maximum
FEV1 through 6 hours
post-dose
Fluticasone propionate/ Treatment of asthma • Fluticasone is an anti- Measure area under the
salmeterol xinafoate and chronic obstructive inflammatory cortico- FEV1-time curve at desig-
inhalation power pulmonary disease (COPD) steroid nated intervals on first day
• Salmeterol is a beta2- and last day of 4-week daily
adreneric agonist treatment period
Low-molecular-weight Anticoagulant Inactivation of Factor Xa • To assure pharmaceutical
heparins for IV and Factor IIa in coagulation equivalence of two formu-
administration cascade lations, measure anti-Xa
and anti-IIa activities
• Demonstration of in vivo
bioequivalence is waived
because product is a true
solution
Adapted from Zou and Yu (2014).
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 481
TABLE 163 Examples of Drug Products for Which FDA Recommends Bioequivalence Studies
with Clinical Endpoints
Product Study Patients Study Duration Endpoint(s)
Calcipotriene cream Plaque psoriasis 56 days Proportions of subjects in the PP population
with treatment success on PGA and clinical
success of PASI
Imiquimod cream Actinic keratosis 14 weeks Proportion of subjects in the PP population
with treatment success (100% clearance of
all AK lesions)
Ketoconazole Dandruff 28 days Proportion of subjects with treatment suc-
shampoo cess or cure, defined as a score of 0 or 1 on
the Global Evaluation Scale (erythema rating)
Miconazole nitrate Vulvovaginal candidiasis 21–30 days Proportion of patients with therapeutic cure,
vaginal cream defined as both mycological and clinical
cure, at the test-of-cure visit
Nitazoxanide tablets Diarrhea caused by Giardia 10 days Proportion of patients with a “well” clinical
lamblia response, defined as either (1) no symptoms,
no watery stool, and no more than 2 soft
stools with no hematochezia within the
past 24 hours or (2) no symptoms and no
unformed stools within the past 48 hours
Sucralfate tablets Active duodenal ulcer disease; 8 weeks Proportion of patients with ulcer healing at
patients must be Helicobacter week 8 by endoscopic examination; if more
pylori negative or continue to than one ulcer is observed at enrollment,
have the presence of an ulcer both must demonstrate healing at week 8
after appropriate H. pylori for success (“cure”)
treatment
chosen patient population. Highly variable clinical clinical studies have been used to establish bioequiv-
responses require the use of a large number of alence for topical antifungal drug products (eg, keto-
patient study subjects, which increases study costs conazole) and for topical acne preparations. For
and requires a longer time to complete compared to dosage forms intended to deliver the active moiety to
the other approaches for determination of bioequiva- the bloodstream for systemic distribution, this approach
lence. A placebo arm is usually included to demon- may be considered acceptable only when analytical
strate that the study is sufficiently sensitive to identify methods cannot be developed to permit use of one of
the clinical effect in the patient population enrolled in the other approaches. Some examples of drug prod-
the study. The FDA considers this approach only ucts where a clinical endpoint bioequivalence study
when analytical methods and pharmacodynamic is recommended (Davit and Conner, 2015) are listed
methods are not available to permit use of one of the in Table 16-3.
approaches described above. The clinical study is
usually a limited, comparative, parallel clinical study
IN VITRO STUDIES
using predetermined clinical endpoint(s).
Clinical endpoint BE studies are recommended Comparative drug release/dissolution studies under
for those products that have negligible systemic certain conditions may give an indication of drug bio-
uptake, for which there is no identified PD measure, availability and bioequivalence. Ideally, the in vitro
and for which the site of action is local. Comparative drug dissolution rate should correlate with in vivo
482 Chapter 16
drug bioavailability (see Chapter 15 on in vivo–in vitro recommended BE approaches consist of comparative
correlation, IVIVC). The test and reference products in vitro release testing and physicochemical charac-
for which in vitro release rates form the basis of the terization (US-FDA, CDER, 2012b).
bioequivalence usually demonstrate Q1/Q2 sameness
(qualitatively same inactive ingredients in the quanti-
tative same amounts). Comparative dissolution studies BIOEQUIVALENCE STUDIES BASED
are often performed on several test formulations of ON MULTIPLE ENDPOINTS
the same drug during drug development. Comparative
dissolution profiles may be considered similar if the The FDA may recommend two or more bioequiva-
similarity factor (f2) is greater than 50 (see Chapter 15). lence studies, each based on a different approach,
For drugs whose dissolution rate is related to the rate for some drug products with complex delivery sys-
of systemic absorption, the test formulation that dem- tems or mechanisms of action. Some examples of
onstrates the most rapid rate of drug dissolution in vitro drug products that FDA requires multiple bioequiv-
will generally have the most rapid rate of drug bio- alence studies (Davit and Conner, 2015) are listed in
availability in vivo. Under certain conditions, com- Table 16-4.
parative dissolution profiles of higher and lower dose
strengths of a solid oral drug product such as an
immediate-release tablet are used to obtain a waiver BIOEQUIVALENCE STUDIES
(biowaiver) of performing additional in vivo bioequiv-
Differences in the predicted clinical response or an
alence studies (see section on biowaivers).
adverse event may be due to differences in the phar-
macokinetic and/or pharmacodynamic behavior of
the drug among individuals or to differences in the
OTHER APPROACHES DEEMED
bioavailability of the drug from the drug product.
ACCEPTABLE (BY THE FDA) Bioequivalent drug products that have the same sys-
temic drug bioavailability will have the same predict-
The FDA may also use in vitro approaches other than
able drug response. However, variable clinical
comparative dissolution for establishing bioequiva-
responses among individuals that are unrelated to
lence. The use of in vitro biomarkers and in vitro
bioavailability may also be due to differences in the
binding studies has been proposed to establish bio-
pharmacodynamics of the drug. Differences in phar-
equivalence. For example, cholestyramine resin is a
macodynamics, that is, the relationship between the
basic quaternary ammonium anion-exchange resin
drug and the receptor site, may be due to differences
that is hydrophilic, insoluble in water, and not
in receptor sensitivity to the drug (see Chapter 21).
absorbed in the gastrointestinal tract. The bioequiva-
Various factors affecting pharmacodynamic drug
lence of cholestyramine resin is performed by equi-
behavior may include age, drug tolerance, drug inter-
librium and kinetic binding studies of the resin to bile
actions, and unknown pathophysiologic factors.
acid salts (US-FDA, CDER, 2012a). For calcium
acetate tablets, which exert the therapeutic response
by binding phosphate in the GI tract, the FDA recom- Bases for Determining Bioequivalence
mends a relatively simple in vitro binding assay Bioequivalence is established if the in vivo bioavail-
based on the test/reference binding ratio over a range ability of a test drug product (usually the generic
of phosphate concentrations. Since this test is thought product) does not differ significantly (ie, statistically
to be highly reproducible, the BE acceptance crite- not significant) from that of the reference listed drug
rion is that the test/reference binding ratio should fall (usually the brand-name product approved through
within limits of 0.9–1.1 (US-FDA, CDER, 2011a). the NDA route) in the product’s rate and extent of
The FDA accepts various other in vitro approaches drug absorption. Bioequivalence is determined by
for BE assessment of proposed generic locally acting comparison of measured parameters (eg, concentra-
drug products. For the acyclovir topical ointment, tion of the active drug ingredient in the blood, urinary
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 483
TABLE 164 Drug Products for Which FDA Recommends Multiple Bioequivalence Approaches
Product Indicated to Treat Approach Endpoint
Diclofenac gel Osteoarthritis of the knee Clinical Pain score change from baseline
In vivo PK AUC, Cmax
Nitazoxanide oral Diarrhea caused by Giardia Clinical Proportion of patients with a “well” clinical response
lamblia
In vivo PK AUC, Cmax
Fluticasone Allergic rhinitis Clinical Total nasal symptom score (TNSS) change from
propionate nasal baseline
suspension
In vivo PK AUC, Cmax
In vitro Comparison of device performance with regard
to the amount of drug per actuation, droplet size
distribution, and plume shape
Mesalamine Ulcerative colitis In vivo PK AUC, pAUC, Cmax
DR and ER oral
formulations
In vitro Comparison of dissolution profiles in several different
media of varying pH values
Mesalamine rectal Distal ulcerative In vivo PK AUC, Cmax
enema colitis, proctitis, and
proctosigmoiditis
In vitro Dissolution profiles at pH 4.5, 6.8, 7.2 (Apparatus 2),
900 mL, 35, 50 rpm
Mesalamine Ulcerative proctitis In vivo PK AUC, Cmax
suppository
In vitro Comparison of physicochemical properties
Risperidone long- Bipolar I disorder and Steady-state AUCt , (Cmax)SS
acting injectable schizophrenia PK in patients
In vitro Comparison of the time for 50% of drug to be
released at two bracketing sampling times
Lansoprazole DR Gastroesophageal reflux In vivo PK AUC, Cmax
capsule disease
In vitro Comparison of sedimentation volume, granule
dispersion, recovery, and acid resistance, after
dispersing into apple juice and dispensing into
nasogastric tubes
Dexamethasone/ Prophylaxis against In vivo PK AUC, Cmax, in aqueous humor of cataract surgery
Tobramycin inflammation and infection patients
Ophthalmic during cataract surgery
Suspension
In vitro Microbial kill rates against specified microorganisms
484 Chapter 16
excretion rates, or pharmacodynamic effects), when parameters, pharmacodynamic parameters, clinical
administered at the same molar dose of the active observations, and/or in vitro studies may be used to
moiety under similar experimental conditions, either determine drug bioavailability from a drug product.
single dose or multiple dose. The design and evaluation of well-controlled bio-
In a few cases, a drug product that differs from equivalence studies require cooperative input from
the reference listed drug in its rate of absorption, but pharmacokineticists, statisticians, clinicians, bioanalyt-
not in its extent of absorption, may be considered ical chemists, and others. For some generic drugs, the
bioequivalent if the difference in the rate of absorption FDA offers general guidelines for conducting these
is intentional and appropriately reflected in the label- studies. For example, Statistical Procedures for
ing and/or the rate of absorption is not detrimental to Bioequivalence Studies Using a Standard Two-
the safety and effectiveness of the drug product. Treatment Crossover Design is available from the FDA
(US-FDA, CDER, 2000a); the publication addresses
three specific aspects, including (1) logarithmic trans-
DESIGN AND EVALUATION OF
formation of pharmacokinetic data, (2) sequence effect,
BIOEQUIVALENCE STUDIES and (3) outlier consideration. However, even with the
availability of such guidelines, the principal investiga-
Objective
tor should prepare a detailed protocol for the study.
All scientific studies should have clearly stated Some of the elements of a protocol for an in vivo bio-
objectives. The main objective for a bioequivalence availability study are listed in Table 16-5.
study is that the drug bioavailability from test and For bioequivalence studies, the test and refer-
reference products is not statistically different when ence drug formulations must contain the same drug
administered to patients or subjects at the same in the same dose strength and in similar dosage
molar dose from pharmaceutically equivalent drug forms (eg, immediate release or controlled release),
products through the same route of administration and must be given by the same route of administra-
under similar experimental conditions. tion. Before beginning the study, the Institutional
Review Board (IRB) of the clinical facility in which
Study Considerations the study is to be performed must approve the study.
The basic design for a bioequivalence study is deter- The IRB is composed of both professional and lay
mined by (1) the scientific questions and objectives to persons with diverse backgrounds who have clinical
be answered, (2) the nature of the reference material experience and expertise as well as sensitivity to
and the dosage form to be tested, (3) the availability of ethical issues and community attitudes. The IRB is
analytical methods, (4) the pharmacokinetics and responsible for all ethical issues including safe-
pharmacodynamics of the drug substance, (5) the route guarding the rights and welfare of human subjects.
of drug administration, and (6) benefit–risk and ethical The basic guiding principle in performing studies
considerations with regard to testing in humans. is do not do unnecessary human research. Generally,
Since bioequivalence studies are performed to the study is performed in normal, healthy male and
compare the bioavailability of the test or generic female volunteers who have given informed consent to
drug product to the reference or brand-name prod- be in the study. Critically ill patients are not included
uct, the statistical techniques should be of sufficient in an in vivo bioavailability study unless the attending
sensitivity to detect differences in rate and extent of physician determines that there is a potential benefit to
absorption that are not attributable to subject vari- the patient. The number of subjects in the study will
ability. Once bioequivalence is established, it is depend on the expected intersubject and intrasubject
likely that both the generic and brand-name dosage variability. Patient selection is made according to cer-
forms will produce the same therapeutic effect. The tain established criteria for inclusion in, or exclusion
FDA publishes guidances for bioequivalence studies from, the study. For example, the study might exclude
(US-FDA, CDER, 2010a). Sponsors may also any volunteers who have known allergies to the drug,
request a meeting with the FDA to review the study are overweight, or have taken any medication within a
design for a specific drug product. Pharmacokinetic specified period (often 1 week) prior to the study.
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 485
TABLE 165 Elements of a Bioavailability are compared. The FDA designates a single reference
Study Protocol listed drug5 as the standard drug product to which all
generic versions must be shown to be bioequivalent.
I. Title
A. Principal investigator (study director) The FDA hopes to avoid possible significant variations
B. Project/protocol number and date among generic drugs and their brand-name counter-
II. Study objective parts. Such variations could result if generic drugs
III. Study design were compared to different reference listed drugs.
A. Design
The reference drug product should be administered
B. Drug products
1. Test product(s) by the same route as the comparison formulations
2. Reference product unless an alternative route or additional route is needed
C. Dosage regimen to answer specific pharmacokinetic questions. For
D. Sample collection schedule example, if an active drug is poorly bioavailable after
E. Housing/confinement
oral administration, the drug may be compared to an
F. Fasting/meals schedule
G. Analytical methods oral solution or an intravenous injection. For bioequiva-
IV. Study population lence studies on a proposed generic drug product, the
A. Subjects reference standard is the reference listed drug (RLD),
B. Subject selection which is listed in the FDA’s Approved Drug Products
1. Medical history
with Therapeutic Equivalence Evaluations—the Orange
2. Physical examination
3. Laboratory tests Book (US-FDA, CDER, 2014d), and the proposed
C. Inclusion/exclusion criteria generic drug product is often referred to as the “test”
1. Inclusion criteria drug product. The RLD is generally a formulation cur-
2. Exclusion criteria rently marketed with a fully approved NDA for which
D. Restrictions/prohibitions
there are valid scientific safety and efficacy data. The
V. Clinical procedures
A. Dosage and drug administration RLD is usually the innovator’s or original manufactur-
B. Biological sampling schedule and handling er’s brand-name product and is administered according
procedures to the dosage recommendations in the labeling.
C. Activity of subjects Before beginning an in vivo bioequivalence study,
VI. Ethical considerations
the total content of the active drug substance in the
A. Basic principles
B. Institutional review board test product (generally the generic product) must be
C. Informed consent within 5% of that of the reference product. Moreover,
D. Indications for subject withdrawal in vitro comparative dissolution or drug-release studies
E. Adverse reactions and emergency procedures under various specified conditions are usually per-
VII. Facilities
formed for both test and reference products before
VIII. Data analysis
A. Analytical validation procedure performing the in vivo bioequivalence study.
B. Statistical treatment of data
IX. Drug accountability Regulatory Recommendations for
X. Appendix
Optimizing Bioavailability Study Design
The FDA lists a number of recommendations to con-
Moderate smokers may be included in these studies. sider in designing clinical relative bioavailability
The subjects generally fast for 10–12 hours (overnight) studies in drug development. These recommenda-
prior to drug administration and may continue to fast tions include the following:
for a 2- to 4-hour period after dosing. • Use of a randomized crossover design whenever
possible
Reference Listed Drug (RLD)
For bioequivalence studies of generic products, one 5The reference listed drug (RLD) is listed in the Orange Book,
formulation of the drug is chosen as a reference stan- Approved Drug Products with Therapeutic Equivalence Evaluations.
dard against which all other formulations of the drug http://www.accessdata.fda.gov/scripts/cder/ob/default.cfm.
486 Chapter 16
• Enrolling both male and female subjects whenever Factors Influencing Bioavailability and
possible Impact on Drug Development
• Administering single doses rather than multiple Various factors influence bioavailability (Table 16-6).
doses, as single-dose studies are more sensitive, Some of these factors are listed below with implica-
although multiple-dose studies may be more suit- tions for formulation development and optimization
able in some cases of dosing regimens.
• Conducting the studies under fasting and fed con- Physicochemical properties of the drug and
ditions6
formulation. Formulations can be designed to
• Measuring the parent drug rather than metabolites, improve the bioavailability of poorly soluble drugs,
unless the parent cannot be reliably measured. Pre- extend the absorption phase by slowing the rate of
systemically formed metabolites that contribute release of drugs (controlled-release formulations), or
meaningfully to safety and efcacy should also be prevent dissolution in the gastric lumen for drugs
measured that are destroyed by gastric acidity (enteric-coated
In addition, the FDA recommends that C formulations) (see also Chapter 15).
max and tmax
be measured to compare peak exposure and rate of An example of how formulation design can
absorption, and that AUC0-t (AUC to the last measur- improve bioavailability is shown by comparing the
able drug concentration) and AUC immunosuppressant drug cyclosporine systemic
0-∞ (AUC extrapo-
lated to infinity) be measured to compare total exposure exposures provided by the Neoral® microemulsion
or extent of drug absorption. Drug exposure parame- formulation to those provided by the Sandimmune®
ters should be log-transformed before statistical com- formulation. The Neoral label states that, in a rela-
parisons. Further detail about the statistical tests will tive bioavailability study in renal transplant, rheuma-
be provided later in the discussion on bioequivalence toid arthritis, and psoriasis patients, the mean
study designs. cyclosporine AUC was 20%–50% greater, and the
mean cyclosporine Cmax was 40%–106% greater,
compared to following administration with
Sandimmune. In addition, the dose-normalized AUC
Frequently Asked Questions in liver transplant patients administered Neoral for
»»What are the study protocol considerations for con- 28 days was 50% greater and Cmax was 90% greater
ducting a bioequivalence study? than in those patients administered Sandimmune.
»»What is the reference listed drug (RLD), and how is Drug stability and pH effects. Acid-labile drugs
the RLD selected?
potentially have low bioavailability, as they are sub-
»»How is a bioavailability study of a new molecular ject to acid-induced degradation in the low pH condi-
entity conducted? tions of the stomach. For such drugs to achieve
»»Why does the value for relative bioavailability some- therapeutic plasma concentrations, it is necessary to
times exceed 1.0, whereas the value for absolute deliver them by formulations that protect against acid-
bioavailability cannot exceed 1.0 7? induced degradation, such as buffered products or
enteric-coated products. Enteric-coated formulations
are used to deliver acid-labile drugs such as didano-
sine (Damle et al, 2002), a purine nucleoside analog
indicted to treat HIV disease, and omeprazole and
lansoprazole (Horn and Howden, 2005), which are
6In a food-effect bioavailability study, the reference treatment
is the oral formulation of the drug product given on an empty proton pump inhibitors indicated to treat acid reflux.
stomach, which is compared with the same oral formulation given
with food, usually a high-fat, high-calorie meal. Presystemic and first-pass metabolism. The effects
7F will appear to exceed 1.0, if the absolute bioavailability is near of presystemic metabolism on oral bioavailability
100% and variability yields a result slightly higher than 1.0. is (Jagdale et al, 2009) illustrated by propranolol, a
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 487
TABLE 166 Factors Influencing Bioavailability and Impacting Drug Development
• Physicochemical properties of the drug and formulation
£ The active drug ingredient has low solubility in water (eg, less than 5 mg/mL)
£ The dissolution rate of the product is slow (eg, <50% in 30 min when tested with a general method specified by the FDA)
£ The particle size and surface area of the active drug ingredient is critical in determining its bioavailability
£ Certain structural forms of the active drug ingredient (eg, polymorphic forms, solvates, complexes, and crystal modifications)
dissolve poorly, thus affecting bioavailability
• Drug product
£ Drug products that have a high ratio of excipients to active ingredients (eg, >5:1)
£ Specific inactive ingredients (eg, hydrophilic or hydrophobic excipients and lubricants) either may be required for absorption
of the active drug or may interfere with such absorption
• Drug stability
£ The drug (and drug product) has poor stability leading to short shelf life
£ The active drug ingredient or therapeutic moiety is unstable in specific portions of the GI tract and requires special coatings
or formulations (eg, buffers, enteric coatings, etc) to ensure adequate absorption
• pH effects (eg, pH within the gastrointestinal lumen)
• Surface of dosage form and time available for absorption
• Presystemic metabolism, including hepatic first-pass effect
• Food effects, for orally administered formulations
• The active drug ingredient or its precursor is absorbed mostly in a particular segment of the GI tract or is absorbed from a
localized site
• Drug–drug interactions
• Efflux transporters (such as P-glycoprotein)
• The drug product is subject to dose-dependent kinetics in or near the therapeutic range, and the rate and extent of absorption
are important in establishing bioequivalence
• Age
• Disease state
nonselective beta adrenergic receptor blocking agent Food effects. Food can either decrease drug bio-
used as an antihypertensive, antianginal, and anti- availability or increase bioavailability, or have no
arrhythmic, presystemic metabolism. Propranolol is effect on bioavailability (Davit and Conner, 2008;
almost completely absorbed after oral administra- Dehaven and Conner, 2014). Food can influence
tion, but due to extensive first-pass metabolism in the bioavailability in a number of ways, such as affect-
liver, only about 25% of the parent drug reaches the ing gastrointestinal pH, gastric emptying, intestinal
systemic circulation. transit, splanchnic blood flow, and first-pass metabo-
lism. Food can also affect bioavailability by physical
Prodrugs that undergo rapid presystemic metab- or chemical interactions. Most food effects on drug
olism can be used to improve bioavailability, as illus- bioavailability are not considered clinically signifi-
trated by valacyclovir, a prodrug of the nucleoside cant, and, consequentially, most drug products are
analog antiviral compound acyclovir. Valacyclovir labeled to be administered without regard to meals.
undergoes rapid presystemic conversion to acyclovir. If the food effects on drug bioavailability are clini-
Both valacyclovir and acyclovir are effective in treat- cally significant, then the drug product labeling will
ing herpes infections. However, because acyclovir provide instructions about how to achieve the opti-
bioavailability is greatly enhanced when delivered by mal dosing regimen—either to take the drug only on
its prodrug valacyclovir, for treating herpes zoster, it an empty stomach, or only with food, depending on
is only necessary to administer Valtrex® (valacyclovir) the nature of the bioavailability effect and clinical
tablets administered once daily, compared to 5 times consequences.
daily for Zovirax® (acyclovir) capsules.
488 Chapter 16
An example of food reducing bioavailability other drugs be defined during drug development
and the implications for drug product labeling is (US-FDA, CDER, 2012c). Two examples of drug–
illustrated by didanosine, discussed earlier. As food drug interactions, one of enzyme inhibition and the
prolongs gastric emptying, this increases the length second of enzyme induction, will show how the
of time that the acid-labile didanosine will be in ability of coadministered drugs to alter systemic
contact with a low pH environment. The Videx® EC bioavailability impacts both recommendations for
label states that food reduced the didanosine Cmax optimal dosing regimens and development of new
by 46% and its AUC by 19%. Consequently, the formulations to maximize bioavailability.
Videx EC label recommends that didanosine should An example of a drug–drug interaction that
be taken on an empty stomach in order to avoid the increases bioavailability is provided by ritonavir
possibility of exposing a patient to subtherapeutic (an HIV protease inhibitor indicated for treating
plasma levels. HIV disease), which is a potent inhibitor of cyto-
Food-induced increases in drug bioavailability chrome P450 3A (CYP3A). As such, ritonavir coad-
can be either desirable or undesirable. The food ministration increases systemic bioavailability of
effect on isotretinoin (indicated to treat severe recal- drugs that are metabolized by CYP3A. For drugs
citrant nodular acne) bioavailability is used to opti- such as sedative hypnotics, antiarrhythmic, and
mize the dosing regimen. The Accutane® label ergot alkaloid preparations, large increases in sys-
states that for isotretinoin capsules, both the Cmax temic bioavailability caused by ritonavir coadmin-
and AUC were more than doubled when the drug istration can result in potentially serious and/or
product was taken with a meal compared with fasted life-threatening adverse events; thus, ritonavir
conditions. Consequently, the label recommends coadministration with these drugs is contraindi-
that isotretinoin capsules should always be taken cated. For other coadministered CYP3A substrate
with food. By contrast, in some cases, food-induced drugs for which ritonavir increases bioavailability,
increases in oral bioavailability may be associated such as antidepressants, clarithromycin, immuno-
with safety concerns. This situation is illustrated by modulators, rifabutin, and trazadone, the Norvir®
the drug efavirenz, a non-nucleoside reverse tran- labeling recommends either dose-adjustment or
scriptase inhibitor indicated to treat HIV disease. additional monitoring of the coadministered drug to
The Sustiva® label describes how coadministration maintain systemic bioavailability levels associated
of a high-fat, high-calorie meal increased the efavi- with safety and efficacy.
renz AUC and Cmax by 22% and 39%, respectively, Because ritonavir can significantly increase the
and coadministration of a lower-fat, lower-calorie bioavailability of CYP3A substrates, it has been
meal increased the efavirenz AUC and Cmax by 17% developed as a “booster” to improve systemic expo-
and 51%, respectively. Due to concern that exposure sure of HIV therapies that are CYP3A substrates
to higher efavirenz systemic bioavailability could and that have low oral bioavailability due to exten-
result in increased serious adverse events, the sive hepatic clearance (de Mendoza et al, 2006).
Sustiva® label recommends that efavirenz capsules Notably, ritonavir is formulated together with the
and tablets be taken on an empty stomach, prefera- HIV-1 protease inhibitor lopinavir in the fixed-dose
bly at bedtime. combination product Kaletra®. Ritonavir in the
Kaletra formulation inhibits the CYP3A-mediated
Effects of drug–drug interactions. Changes in metabolism of lopinavir, thereby increasing lopina-
drug bioavailability due to drug–drug interactions vir systemic bioavailability to levels that achieve
can occur via a variety of mechanisms, such as inhi- antiviral activity.
bition of metabolizing enzymes, induction of metab- Enzyme inducers coadministered with drugs
olizing enzymes, inhibitor of transporters, and can potentially lower systemic bioavailability to sub-
induction of transporters. The FDA recommends that therapeutic levels. An example is the antibacterial
interactions between an investigational new drug and drug rifampin (used in treatment of tuberculosis),
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 489
which is a potent inducer of cytochrome P-450 The FDA recommends that sponsors developing pedi-
enzymes. Coadministration of rifampin with drugs atric formulations conduct pharmacokinetic studies in
metabolized by metabolic pathways induced by the pediatric population to determine how the dosing
rifampin can result in lower bioavailability due to regimen should be adjusted to achieve the same sys-
acceleration of metabolism. The Rifadin® label temic exposure that is safe and effective in adults
states that, to maintain optimum therapeutic bio- (Chapter 23).
availability, dosages of drugs metabolized by these Systemic bioavailability of drugs can change with
enzymes may require dose adjustment when starting aging (Klotz, 2009). Impairments in the functional
or stopping concomitantly administered rifampin. reserve of multiple organs can occur with advancing
Some examples of these drugs for which rifampin age, and such impairments might affect drug metabo-
lowers systemic bioavailability to the extent that lism and pharmacokinetics. Advancing age is associ-
dose adjustment is needed include anticonvulsants, ated with changes such as decreases in liver mass and
antiarrhythmics, beta-blockers, calcium channel perfusion, changes in body composition, and decreases
blockers, fluoroquinolones, oral hypoglycemic agents, in renal function. Many of these changes result in
transplant drugs, and tricyclic antidepressants. For increased drug bioavailability. As a result, it is recom-
some drugs, such as oral contraceptives, coadmin- mended that clinicians carefully monitor dosing regi-
istration with rifampin is contraindicated due to mens and drug action in geriatric patients.
concerns that rifampin coadministration can lower
oral contraceptive systemic bioavailability to sub- Disease state. The bioavailability of drugs
therapeutic levels. eliminated primarily through renal excretory
mechanisms is likely to increase in patients with
Efflux transporters. The cardiac glycoside digoxin impaired renal function (Chapter 24). The FDA
is a substrate for P-glycoprotein, at the level of recommends that, where appropriate, drug phar-
intestinal absorption, renal tubular secretion, and macokinetics be characterized in patients with
biliary-intestinal secretion (Hughes and Crowe, 2010). varying degrees of renal impairment. The results of
Therefore, drugs that induce or inhibit P-glycoprotein such studies are used to determine how doses can
have the potential to alter digoxin bioavailability. be adjusted in patients with renal impairment in
Examples of such drugs include amiodarone, propafe- order to achieve the same systemic drug bioavail-
none, quinidine, and verapamil. As digoxin is a narrow ability as in patients with normal renal function
therapeutic index drug, small changes in bioavail- (US-FDA, CDER, 2010b). Similarly, it may be
ability can potentially result in serious adverse events advisable to conduct pharmacokinetic studies of
due to loss of efficacy (bioavailability is lower than drugs that are primarily cleared by the liver in
the therapeutic range) or life-threatening toxicity patients with varying degrees of hepatic impair-
(bioavailability exceeds the therapeutic range). ment (US-FDA, CDER, 2003a). The results of
Digoxin oral solution USP labeling instructs the prac- pharmacokinetic studies in hepatic-impaired
titioner to measure serum digoxin concentrations patients can be useful in determining whether dose
before initiating concomitant drugs, reduce the digoxin adjustments are required in such patients to achieve
dose once concomitant therapy is initiated, and con- the same systemic drug bioavailability as in
tinue to monitor digoxin serum concentrations. patients with normal liver function.
The systemic bioavailability of a drug in patients
Age. The systemic bioavailability of a drug is can differ from that in healthy normal subjects.
controlled by its absorption, distribution, metabolism, Ordinarily, sponsors conduct single- and multiple-
and elimination (ADME). In pediatric patients, growth dose pharmacokinetic studies in both healthy normal
and developmental changes in factors influencing subjects and the target patient population in early
ADME lead to drug bioavailability that can differ stage development, to characterize similarities and
from that of adult patients (US-FDA, CDER, 2014e). differences in drug systemic bioavailability.
490 Chapter 16
Analytical Methods Fasting Study
Analytical methods used in an in vivo bioavailability, Bioequivalence studies are usually evaluated by a
bioequivalence, or pharmacodynamic studies must single-dose, two-period, two-treatment, two-sequence,
be validated for accuracy and sufficient sensitivity. open-label, randomized crossover design comparing
The actual concentration of the active drug ingredi- equal doses of the test and reference products in
ent or therapeutic moiety, or its active metabolite(s), fasted, adult, healthy subjects. This study is requested
must be measured with appropriate precision in body for all immediate-release and modified-release oral
fluids or excretory products. For bioavailability and dosage forms. Both male and female subjects may be
bioequivalence studies, both the parent drug and its used in the study. Blood sampling is performed just
major active metabolites are generally measured. For before (zero time) the dose and at appropriate inter-
bioequivalence studies, the parent drug is measured. vals after the dose to obtain an adequate description of
Measurement of the active metabolite is important the plasma drug concentration–time profile. The sub-
for very high-hepatic clearance (first-pass metabo- jects should be in the fasting state (overnight fast of at
lism) drugs when the parent drug concentrations are least 10 hours) before drug administration and should
too low to be reliable. continue to fast for up to 4 hours after dosing. No other
The analytical method for measurement of the medication is normally given to the subject for at least
drug must be validated for accuracy, precision, sen- 1 week prior to the study. In some cases, a parallel
sitivity, specificity, and robustness. The use of more design may be more appropriate for certain drug prod-
than one analytical method during a bioequivalence ucts, containing a drug with a very long elimination
study may not be valid, because different methods half-life. A replicate design may be used for a drug
may yield different values. Data should be pre- product containing a drug that has high intrasubject
sented in both tabulated and graphic form for evalu- variability.
ation. The plasma drug concentration–time curve
for each drug product and each subject should be
Food Intervention Study
available.
Coadministration of food with an oral drug product
may affect the bioavailability of the drug. Food inter-
STUDY DESIGNS vention or food effect studies are generally con-
ducted using meal conditions that are expected to
For many drug products, the FDA, Division of provide the greatest effects on GI physiology so that
Bioequivalence, Office of Generic Drugs, provides systemic drug availability is maximally affected.
guidance for the performance of in vitro dissolution Food effects on bioavailability are generally greatest
and in vivo bioequivalence studies (US-FDA, when the drug product is administered shortly after
CDER, 2010a). Generally, two bioequivalence stud- a meal is ingested. The nutrient and caloric contents
ies are required for solid oral dosage forms, includ- of the meal, the meal volume, and the meal tempera-
ing (1) a fasting study and (2) a food intervention ture can cause physiological changes in the GI tract
study. For extended-release capsules containing in a way that affects drug product transit time, lumi-
beads (pellets) that might be poured on a semisolid nal dissolution, drug permeability, and systemic
food such as applesauce, an additional “sprinkle” availability.
bioequivalence study is recommended. Other study Meals that are high in total calories and fat con-
designs such as parallel design, replicate design, tent are more likely to affect the GI physiology and
and multiple-dose (steady-state) bioequivalence thereby result in a larger effect on the bioavailability
studies have been proposed by the FDA. Proper of a drug substance or drug product (US-FDA,
study design and statistical evaluation are important CDER, 2003b). In addition, the high fat meal can
considerations for the determination of bioequiva- have a significant effect on certain modified-release
lence. Some of the designs listed above are summa- drug products causing them to dose dump. The test
rized here. meal is a high-fat (approximately 50% of total caloric
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 491
content of the meal) and high-calorie (approximately drug formulations (A, B, C, D), are described in
800–1000 calories) meal. A typical test meal is two eggs Tables 16-7 and 16-8. The Latin-square design plans
fried in butter, two strips of bacon, two slices of toast the clinical trial so that each subject receives each
with butter, 4 oz of brown potatoes, and 8 oz of milk. drug product only once, with adequate time between
This test meal derives approximately 150, 250, and medications for the elimination of the drug from the
500–600 calories from protein, carbohydrate, and fat, body. In this design, each subject is his own control,
respectively (www.fda.gov/cder/guidance/4613dft.pdf). and subject-to-subject variation is reduced. Moreover,
For bioequivalence studies for generic drugs, variations due to sequence, period, and treatment
drug bioavailability from both the test and reference (formulation) are reduced, so that all patients do not
products should be affected similarly by food. The receive the same drug product on the same day and in
usual study design uses a single-dose, randomized, the same order. The order in which the drug treat-
two-treatment, two-period, crossover study compar- ments are given should not stay the same in order to
ing equal doses of the test and reference products. prevent any bias in the data due to a residual effect
Following an overnight fast of at least 10 hours, from the previous treatment. Possible carryover
subjects are given the recommended meal 30 min- effects from any particular drug product are mini-
utes before dosing. The meal is consumed over 30 mized by changing the sequence or order in which
minutes, with administration of the drug product the drug products are given to the subject. Thus, drug
immediately after the meal. The drug product is product B may be followed by drug product A, D, or
given with 240 mL (8 fluid oz) of water. No food is C (Table 16-8). After each subject receives a drug
allowed for at least 4 hours postdose. This study is product, blood samples are collected at appropriate
requested for all modified-release dosage forms and time intervals so that a valid blood drug level–time
may be requested for immediate-release dosage curve is obtained. The time intervals should be
forms if the bioavailability of the active drug ingre- spaced so that the peak blood concentration, the total
dient is known to be affected by food (eg, ibuprofen, area under the curve, and the absorption and elimina-
naproxen). According to the labeling for certain tion phases of the curve may be well described.
extended-release capsules that contain coated beads, Period refers to the time period in which a study
the capsule contents can be sprinkled over soft foods is performed. A two-period study is a study that is
such as applesauce. This is taken by the fasted sub- performed on two different days (time periods) sepa-
ject and the bioavailability of the drug is then mea- rated by a washout period during which most of the
sured for the NDA. For generic drug products in drug is eliminated from the body—generally about
Abbreviated New Drug Applications (ANDAs), this
study is performed as a bioequivalence study to dem-
onstrate that both products, sprinkled on food, will TABLE 167 Latin-Square Crossover Design
have equivalent bioavailability. Bioavailability stud- for a Bioequivalence Study of Three Drug
ies might also examine the effects of other foods and Products in Six Human Volunteers
special vehicles such as apple juice. Drug Product
Study Study Study
CROSSOVER STUDY DESIGNS Subject Period 1 Period 2 Period 3
Subjects who meet the inclusion and exclusion study 1 A B C
criteria and have given informed consent are selected 2 B C A
at random. A complete crossover design is usually
3 C A B
employed, in which each subject receives the test
drug product and the reference product. Examples of 4 A C B
Latin-square crossover designs for a bioequivalence 5 C B A
study in human volunteers, comparing three differ-
6 B A C
ent drug formulations (A, B, C) or four different
492 Chapter 16
TABLE 168 Latin-Square Crossover Design the same drug product twice to the same subject, the
for a Bioequivalency Study of 4 Drug Products replicate design provides a measure for within-subject
in 16 Human Volunteers variability. Replicate design studies may be used for
highly variable drugs and for narrow therapeutic
Drug Product
index drugs. In the case of highly variable drugs
Study Study Study Study (%CV greater than 30), a large number of subjects
Subject Period 1 Period 2 Period 3 Period 4 (>80) would be needed to demonstrate bioequiva-
1 A B C D lence using the standard two-way crossover design.
Drugs with high within-subject variability gener-
2 B C D A
ally have a wide therapeutic window and despite
3 C D A B high variability, these products have been demon-
4 D A B C strated to be both safe and effective. Replicate
designs for highly variable drugs/products require a
5 A B D C
smaller number of subjects and, therefore, do not
6 B D C A unnecessarily expose a large number of healthy
7 D C A B subjects to a drug when this large number of sub-
jects is not needed for assurance of bioequivalence
8 C A B D
(Haidar et al, 2008).
9 A C B D Replicated crossover designs are used for the
10 C B D A determination of individual bioequivalence, to esti-
mate within-subject variance for both the test and
11 B D A C
reference drug products, and to provide an estimate
12 D A C B of the subject-by-formulation interaction variance. A
13 A C D B four-period, two-sequence, two-formulation design
is shown below:
14 C D B A
15 D B A C
Period 1 Period 2 Period 3 Period 4
16 B A C D
Sequence 1 T R T R
Sequence 2 R T R T
10 elimination half-lives. A sequence refers to the where R = reference and T = treatment.
number of different orders in the treatment groups in
a study. For example, a two-sequence, two-period In this design, the same reference and the same test
study would be designed as follows: are each given twice to the same subject. Other
sequences are possible. In this design, reference-
to-reference and test-to-test comparisons may also
Period 1 Period 2
be made.
Sequence 1 T R
Sequence 2 R T Narrow Therapeutic Index Drugs
where R Narrow therapeutic index (NTI) drugs, also referred
= reference and T = treatment.
to as critical dose drugs, are drugs in which small
changes in dose or concentration may lead to serious
Replicated Crossover Study Designs therapeutic failures or serious adverse drug reactions in
The standard bioequivalence criterion using the two- patients. Narrow therapeutic index drugs consistently
way crossover design does not give an estimate of display the following characteristics: (a) Subtherapeutic
within-subject (intrasubject) variability. By giving concentrations may lead to serious therapeutic failure;
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 493
(b) there is little separation between therapeutic and variable, provided that certain constraints are applied
toxic doses (or the associated plasma concentra- to this approach in order to maintain an acceptable
tions); (c) they are subject to therapeutic monitoring type I error rate and satisfy any public health con-
based on pharmacokinetic or pharmacodynamic cerns (Davit et al, 2012).
measures; (d) they possess low-to-moderate within-
subject variability (<30%); and (e) in clinical prac-
Period 1 Period 2 Period 3
tice, doses are generally adjusted in very small
increments (<20%). The FDA currently recommends Sequence 1 T R R
that bioequivalence studies of narrow therapeutic Sequence 2 R T R
index drugs should employ a four-way, fully repli-
Sequence 3 R R T
cated, crossover study design. The replicated study
design permits comparison of both test and reference
means and test and reference within-subject variabil- Under this design, if the test product has lower vari-
ity (Davit et al, 2013). ability than the reference product, the study will
An additional test recommended in bioequiva- need a smaller number of subjects to pass the bio-
lence studies of generic narrow therapeutic index equivalence criteria. Scaled average bioequivalence
drugs is a test for within-subject variability. The test is evaluated for both AUC and Cmax.
determines whether within-subject variability of the
test narrow therapeutic index drug does not differ Parallel Study Designs
significantly from that of the reference by evaluating A nonreplicate, parallel design is used for drug prod-
the test/reference ratio of the within-subject standard ucts that contain drugs that have a long elimination
deviation. The FDA currently recommends that all half-life or drug products such as depot injections in
bioequivalence studies on narrow therapeutic index which the drug is slowly released over weeks or
drugs must pass both the reference-scaled approach months. In this design, two separate groups of volun-
and the unscaled average bioequivalence limits of teers are used. One group will be given the test prod-
80.00%–125.00%. uct and the other group will be given the reference
product. It is important to balance the demographics
of both groups of volunteers. Blood sample collec-
Reference Scaled Average Bioequivalence
tion time should be adequate to ensure completion of
Recently a three-sequence, three-period, two-treatment gastrointestinal transit (approximately 2–3 days) of
partially replicated crossover design for bioequiva- the drug product and absorption of the drug sub-
lence studies of highly variable drugs has been recom- stance. Cmax and a suitably truncated AUC, generally
mended by the FDA (Haidar et al, 2008). The partially to 72 hours after dose administration, can be used to
replicated design allows the estimation of the within- characterize peak and total drug exposure, respec-
subject variance and subject-by-formulation interac- tively. For drugs that demonstrate low intrasubject
tion for the reference product. The time for completion variability in distribution and clearance, an AUC
of this study is shorter than the fully replicated four- truncated at 72 hours (AUC72
0 hours) can be used in
way crossover design. place of AUCt or AUC∞. This design is not recom-
0 0
This design is usually used for highly variable mended for drugs that have high intrasubject vari-
drugs with within-subject variability ≥30%. Large ability in distribution and clearance.
numbers of subjects may be needed in bioequiva-
lence studies of highly variable drugs; the FDA
implemented the reference-scaled average bioequiv- Multiple-Dose (Steady-State) Study Design
alence approach to ease regulatory burden and A bioequivalence study may be performed using a
reduce unnecessary human testing. Using this multiple-dose study design. Multiple doses of the
approach, the implied BE limits can widen to be same drug are given consecutively to reach steady-
larger than 80%–125% for drugs that are highly state plasma drug levels. The multiple-dose study is
494 Chapter 16
designed as a steady-state, randomized, two-treat- Determination of bioavailability using multiple
ment, two-way, crossover study comparing equal doses reveals changes that are normally not detected
doses of the test and reference products in healthy in a single-dose study. For example, nonlinear phar-
adult subjects. Each subject receives either the test or macokinetics may occur after multiple drug doses
the reference product separated by a “washout” due to the higher plasma drug concentrations saturat-
period, which is the time needed for the drug to be ing an enzyme system involved in absorption or
completely eliminated from the body. elimination of the drug. Nonlinear pharmacokinetics
To ascertain that the subjects are at steady state, after multiple-dose studies may be observed by ris-
three consecutive trough concentrations (Cmin) are ing Cmin drug concentrations and AUCt after each
determined. The last morning dose is given to the sub- dosing interval. With some drugs, a drug-induced
ject after an overnight fast, with continual fasting for at malabsorption syndrome can also alter the percent-
least 2 hours following dose administration. Blood age of drug absorbed. In this case, drug bioavailabil-
sampling is then performed over one dosing interval. ity may decrease after repeated doses if the fraction
The area under the curve during a dosing interval at of the dose absorbed (F) decreases or if the total
steady state should be the same as the area under the body clearance (kVD) increases. It should be noted
curve extrapolated to infinite time after a single dose. that nonlinear PK can also be observed by high sin-
Pharmacokinetic analyses for multiple-dose gle doses of the drug.
studies include calculation of the following parame- There are several disadvantages of using the
ters for each subject: multiple-dose crossover method for the determina-
tion of bioequivalence. (1) The study takes more time
AUC0-tau—Area under the curve during a dosing
to perform, because steady-state conditions must be
interval
reached. A longer time for completion of a study
tmax—Time to Cmax during a dosing interval
leads to greater clinical costs and the possibility of a
Cmax—Maximum drug concentration during dos-
subject dropping out and not completing the study.
ing interval
(2) More plasma samples must be obtained from the
Cmin—Drug concentration at the end of a dosing
subject to ascertain that steady state has been reached
interval
and to describe the plasma level–time curve accu-
Cav—The average drug concentration during a
rately. (3) Because C∞ depends primarily on the dose
dosing interval av
of the drug and the time interval between doses, the
Degree of fluctuation = (Cmax− Cmin)/Cmax extent of drug systemically available is more impor-
Swing = (Cmax− Cmin)/Cmin tant than the rate of drug availability. Small differ-
The data are analyzed statistically using analysis of ences in the rate of drug absorption may not be
variance (ANOVA) on the log-transformed AUC and observed with steady-state study comparisons
Cmax. To establish bioequivalence, both AUC and
Cmax for the test (generic) product should be within
80%–125% of the reference product using a 90% Clinical Endpoint Bioequivalence Study
confidence interval. Estimation of the absorption Study design for a clinical endpoint study generally
rate constant during multiple dosing is difficult, consists of a randomized, double-blind, placebo-
because the residual drug from the previous dose controlled, parallel-designed study comparing test
superimposes on the dose that follows. However, the product, reference product, and placebo product in
data obtained in multiple doses are useful in calcu- patients. A placebo arm is usually included to dem-
lating a steady-state plasma level. onstrate that the treatments are active (above the
The extent of bioavailability, measured by no-effect part of the effect versus dose curve, see
assuming the [AUC]∞0 , is dependent on clearance: Fig. 16-11) and the study is sufficiently sensitive to
identify the clinical effect in the patient population
FD enrolled in the study. In some cases, the use of a
[AUC]∞ 0
0 =
ClT placebo may not be included for safety reasons.
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 495
The primary analysis for bioequivalence is deter- period is used between drug treatments. Therefore,
mined by evaluating the difference between the pro- the patient is maintained on his or her previous dose
portion of patients in the test and reference treatment of medication or an equal dose of the test product, and
groups who are considered a “therapeutic cure” at blood sampling is performed during a dosage interval
the end of study. The superiority of the test and refer- (Fig. 16-13, reference product A). Once blood sam-
ence products against the placebo is also tested using pling is accomplished, the patient takes equal oral
the same dichotomous endpoint of “therapeutic cure.” doses of the other drug product (test or reference) and
the previous drug product is discontinued. Drug dos-
ing with each drug product continues until attainment
Determination of Bioequivalence of Drug
of steady state. When steady state is reached, the
Products in Patients Maintained on a plasma level–time curve for a dosage interval with the
Therapeutic Drug Regimen second drug product is described (Fig. 16-13, drug
A bioequivalence study may be performed in patients product B). Using the same plasma measures as
already maintained on the reference (brand-name) before, the bioequivalence or lack of bioequivalence
drug. Due to safety concerns, certain drugs such as may be determined. The patient then continues with
clozapine, a dibenzodiazepine derivative with potent his or her therapy with the original drug product.
antipsychotic properties, should not be given to nor- Products are given in random order: A then B, B
mal healthy subjects (US-FDA, CDER, 2011b). then A. Failure to do this might lead to a sequence
Instead, bioequivalence studies on clozapine should effect. The reference product that is tested is pro-
be performed in patients who have been stabilized on vided by the investigator from a known lot (not the
the highest strength (eg, 100 mg) using a multiple- patient’s own prescription).
dose bioequivalence study design. Patients on these Since the patients are being treated with the
or other drugs such as antipsychotics (US-FDA, reference (brand) product A, the drug concentrations
CDER, 2013a) or cancer chemotherapeutic drugs are at steady state prior to the start of the study and
(Kaur et al, 2013) would be at risk if a washout the accumulation phase is not observed. The test
60
Reference product A Test product B
50
40
30
20
10
0
24 34 44 54 64 74
Time (hours)
FIGURE 1613 Multiple-dose bioequivalence study in patients. Bioequivalence is determined by comparison of the steady-
state plasma drug-versus-time profile after administration of the reference drug product A to the steady-state plasma drug–time
profile after administration of the test drug product B.
Plasma drug concentration (ng/mL)
496 Chapter 16
drug product B is started and the reference drug each blood sample was analyzed for total and free
product A is stopped. The total plasma drug concen- thyroxine (T4), total and free triiodothyronine (T3),
trations are maintained. Bioequivalence is deter- the major metabolite of T4, and thyrotropin (TSH).
mined by comparison of the steady-state plasma
a. Why were hypothyroid patients used in this
drug-versus-time profile after administration of the
study?
reference drug product A to the steady-state plasma
b. Why were the subjects dosed for 50 days with
drug–time profile after administration of the test
each thyroid product?
drug product B.
c. Why were blood samples obtained on days 48,
If the blood level–time curve of the second drug
49, and 50?
product is bioequivalent, as shown by AUCt and
d. Why was T3 measured?
Cmax, to that of the reference drug product, the sec-
e. Why was TSH measured?
ond product is considered to be bioequivalent. If the
second drug has less bioavailability (assuming that
only the extent of drug absorption is less than that of Solution
the reference drug), the resulting C∞ will be smaller
av a. Normal healthy euthyroid subjects would be at
than that obtained with the first drug. C∞ is not actu-
av risk if they were to take levothyroxine sodium
ally used as a direct measurement. Usually, the drug
for an extended period of time.
manufacturer will perform dissolution and content
b. The long (50-day) daily dosing for each prod-
uniformity tests before performing a bioequivalence
uct was required to obtain steady-state drug
study. These in vitro dissolution tests will help
levels because of the long elimination half-life
ensure that the C∞ obtained from each drug product
av of levothyroxine.
in vivo will not be largely different from each other.
c. Serum from blood samples was taken on
In contrast, if the extent of drug availability is greater in
days 48, 49, and 50 to obtain three consecutive
the second drug product, the C∞ will be higher.
av Cmin drug levels.
d. T3 is the active metabolite of T4.
CLINICAL EXAMPLE e. The serum TSH concentration is inversely
proportional to the free serum T4 concentrations
Levothyroxine Sodium Oral Tablets and gives an indication of the pharmacodynamic
A multiple dose relative bioavailability study8 of two activity of the active drug.
synthetic branded levothyroxine sodium oral tablets,
product A and product B, were evaluated in 20
CLINICAL EXAMPLE
euthyroid patients. The investigation was designed
as a two-way crossover study in which the patients Mercaptopurine (Purinethol) Oral Tablets
who had been diagnosed as hypothyroid by their Mercaptopurine (Purinethol) is a cytotoxic drug used
primary-care physician were given a single 100-mg to treat cancer and is available in a 50-mg oral tablet.
daily dose of either product A or product B levothy- The FDA recommends bioequivalence steady-state
roxine sodium tablets for 50 days and then switched studies (US-FDA, CDER, 2011c) in patients receiving
over immediately to the other treatment for 50 days. therapeutic oral doses (usually 100–200 mg/d in the
Predose blood samples were taken on days 1, 25, 48, average adult) or maintenance daily doses (usually
49, and 50 of each phase, and, on day 50, a complete 50–100 mg/d in the average adult).
blood sampling was performed. The serum from Patients should be on a stable regimen using the
same dosage unit (multiples of the same 50-mg
8For the FDA-recommended bioequivalence study for strength). Plasma drug concentration–time profiles
levothyroxine sodium tablets, see FDA Guidance for Industry:
are obtained in these patients at steady state with the
Levothyroxine Sodium Tablets—In Vivo Pharmacokinetic
and Bioavailability Studies, and In Vitro Dissolution Testing, brand product. The proposed generic drug product is
December 2000. then given to these patients at the same dosage
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 497
regimen until steady state is reached. Plasma drug metrics for the test and reference drug products
concentration–time profiles are obtained for the (US-FDA, CDER, 2000a).
generic drug product; then the patients return to the Many statistical approaches (parametric tests)
original brand medication. assume that the data are distributed according to
a normal distribution or “bell-shaped curve” (see
Frequently Asked Questions Appendix A). The pharmacokinetic parameters such
»»What do sequence, washout period, and period as Cmax and AUC may not be normally distributed,
mean in a crossover bioavailability study? and the true distribution is difficult to ascertain
because of the small number of subjects used in a
»»Why does the FDA request a food intervention
bioequivalence study. The distribution of data that
(food-effect) study for new and generic drug products
have been transformed to log values resembles more
before granting approval?
closely a normal distribution compared to the distri-
»»What type of bioequivalence studies are requested bution of non-log-transformed data.
for drugs that are not systemically absorbed or for
those drugs in which the Cmax and AUC cannot be Two One-Sided Tests Procedure
measured in the plasma?
The two one-sided tests procedure is also referred to as
»»How do inter- and intrasubject variability affect the the confidence interval approach (Schuirmann, 1987).
statistical demonstration of bioequivalence for a This statistical method is used to demonstrate if the
drug product? bioavailability of the drug from the test formulation is
too low or high in comparison to that of the reference
product. The objective of the approach is to determine
PHARMACOKINETIC EVALUATION if there are large differences (ie, greater than 20%)
between the mean parameters.
OF THE DATA The 90% confidence limits are estimated for the
For single-dose studies, including a fasting study or sample means. The interval estimate is based on
a food intervention study, the pharmacokinetic anal- Student’s t distribution of the data. In this test, pres-
yses include calculation for each subject of the area ently required by the FDA, a 90% confidence interval
under the curve to the last quantifiable concentration about the ratio of means of the two drug products
(AUCt
0 ) and to infinity (AUC∞
0 ), tmax, and Cmax. must be within ±20% for measurement of the rate and
Additionally, the elimination rate constant, k, the extent of drug bioavailability. For most drugs, up to a
elimination half-life, t1/2, and other parameters may 20% difference in AUC or Cmax between two formula-
be estimated. For multiple-dose studies, pharmaco- tions would have no clinical significance. The lower
kinetic analysis includes calculation for each subject 90% confidence interval for the ratio of means cannot
of the steady-state area under the curve, (AUCt
∞), be less than 0.80, and the upper 90% confidence inter-
t val for the ratio of the means cannot be greater than
max, Cmin, Cmax, and the percent fluctuation [100 ×
(Cmax − Cmin)/Cmin]. Proper statistical evaluation 1.20. When log-transformed data are used, the 90%
should be performed on the estimated pharmacoki- confidence interval is set at 80%–125%. These confi-
netic parameters. dence limits have also been termed the bioequivalence
interval (Midha et al, 1993). The 90% confidence
interval is a function of sample size and study vari-
Statistical Evaluation of the Data ability, including inter- and intrasubject variability.
Bioequivalence is generally determined using a com- For a single-dose, fasting or food intervention
parison of population averages of a bioequivalence bioequivalence study, an ANOVA is usually per-
metric, such as AUC and Cmax. This approach, termed formed on the log-transformed AUC and Cmax values.
average bioequivalence, involves the calculation of a There should be no statistical differences between the
90% confidence interval for the ratio of averages mean AUC and Cmax parameters for the test (generic)
(population geometric means) of the bioequivalence and reference drug products. In addition, the 90%
498 Chapter 16
TABLE 169 Statistical Analysis for Average each pharmacokinetic parameter, such as AUC, may be
Bioequivalence masked, and the investigator might erroneously con-
clude that the two drug products are bioequivalent.
• Based on log-transformed data
• Point estimates of the mean ratios A statistical difference between the pharmacoki-
Test/reference for AUC and Cmax are between 80% and netic parameters obtained from two or more drug
125% products is considered statistically significant if there
• AUC and Cmax is a probability of less than 1 in 20 times or 0.05 prob-
90% confidence intervals (CI) must fit between 80%
ability (p ≤ .05) that these results would have happened
and 125%
• Bioequivalence criteria on the basis of chance alone. The probability, p, is
Two one-sided tests procedure used to indicate the level of statistical significance. If
• Test (T) is not significantly less than reference p < .05, the differences between the two drug products
• Reference (R) is not significantly less than test are not considered statistically significant.
• Significant difference is 20% (a = 0.05 significance
To reduce the possibility of failing to detect
level)
T/R = 80/100 = 80% small differences between the test products, a power
R/T = 80% (all data expressed as T/R, so this test is performed to calculate the probability that the
becomes 100/80 = 125%) conclusion of the ANOVA is valid. The power of
• The statistical model typically includes factors accounting the test will depend on the sample size, variability of
for the following sources of variation: sequence, subjects
the data, and desired level of significance. Usually, the
nested in sequences, period, and treatment
power is set at 0.80 with a b = 0.2 and a level of
From US-FDA, CDER (2000). significance of 0.05. The higher the power, the test is
more sensitive and the greater the probability that the
conclusion of the ANOVA is valid.
confidence intervals about the ratio of the means for
AUC and Cmax values of the test drug product should
not be less than 0.80 (80%) nor greater than 1.25 THE PARTIAL AUC IN
(125%) of that of the reference product based on log- BIOEQUIVALENCE ANALYSIS
transformed data. Table 16-9 summarizes the statisti-
Several new drug delivery systems have a complex
cal analysis for average bioequivalence. Presently,
approach to drug release (eg, combinations of zero-
the FDA accepts only average bioequivalence esti-
order and first-order release) that produces an unusu-
mates used to establish bioequivalence of generic
ally shaped plasma drug concentration-versus-time
drug products.
profile. The shape of this plasma drug concentration-
versus-time profile is related to the pharmacodynam-
Analysis of Variance ics of the drug.
An analysis of variance (see ANOVA) is a statistical To evaluate a generic dosage form of these new
procedure (see Appendix A) used to test the data for drug delivery systems, the FDA recommends includ-
differences within and between treatment and con- ing the partial AUC (pAUC) as a pivotal BE metric.
trol groups. A bioequivalent product should produce The pAUC is defined as the area under the plasma
no significant difference in all pharmacokinetic concentration-versus-time profile over two specified
parameters tested. The parameters tested statistically time points. The choice of sampling time points for
usually include AUCt , AUC∞, and C
0 max obtained calculating the pAUC is based on the pharmacokinetic/
0
for each treatment or dosage form. Other metrics of pharmacodynamic or efficacy/safety data for the drug
bioavailability have also been used to compare the under examination.
bioequivalence of two or more formulations. The The FDA currently expects the pAUC to be ana-
ANOVA may evaluate variability in subjects, treat- lyzed statistically when determining bioequivalence
ment groups, study period, formulation, and other of multiphasic modified-release (MR) formulations
variables, depending on the study design. If the vari- designed to achieve a rapid therapeutic response fol-
ability in the data is large, the difference in means for lowed by a sustained response. Such products are
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 499
12
Cmax
10
8
6
4
2
0
T T t
0 max 10 20 30 40
Time (hours)
AUC0-T
FIGURE 1614 Partial AUC analysis in a bioequivalence study. The partial AUC (pAUC) refers to the AUC between two speci-
fied, clinically relevant, time points on the drug plasma concentration-versus-time profile. The sampling time T should be selected
based on the pharmacokinetic and pharmacodynamic properties of the active ingredient.
generally formulated with both an immediate-release biphasic absorption characteristics, which result in
component and a delayed- or extended-release com- rapid initial absorption from the gastrointestinal tract
ponent. Figure 16-14 illustrates how a pAUC analy- similar to zolpidem tartrate immediate release, and
sis, based on two partial AUCs, is applied. The two then provide extended plasma concentrations beyond
partial AUCs consist of an early pAUC measure AUC0-T 3 hours of administration. As a result, patients receiv-
to compare test and reference exposure responsible for ing Ambien CR experience both rapid onset of sleep
early onset of response, and a late pAUC measure and maintenance of sleep. To ensure that a test zolpi-
AUCT-t to compare test and reference exposure respon- dem tartrate extended-release tablet provides the
sible for sustained response. The early AUC0-T is mea- same pharmacodynamic response (timing of sleep
sured beginning at sampling time 0 to a truncation onset and maintenance) when switched with the ref-
time T. The late AUCT-t is measured from the trunca- erence product, the FDA expects that, in a bioequiva-
tion time T to the last sampling point with measur- lence study comparing the two, the parameters
able drug concentration. These two metrics replace AUC0-1.5h, AUC1.5h-t, AUC0-∞, and Cmax will all pass
AUC0-t in bioequivalence evaluation. The bioequiva- bioequivalence limits of 80.00%–125.00% (US-FDA,
lence determination is based on comparison of test CDER, 2011d). The sampling time for the early and
and reference Cmax, AUC0-∞, AUC0-T , and AUCT-t. late pAUCs for the zolpidem extended-release tablet
The partial AUC (pAUC) refers to the AUC were selected based on zolpidem pharmacokinetic–
between two specified, clinically relevant, time points pharmacodynamic relationships.
on the drug plasma concentration-versus-time pro- The FDA recently posted a draft guidance for
file. The sampling time T should be selected based on industry recommending the application of three
the pharmacokinetic and pharmacodynamic proper- pAUC metrics, for bioequivalence studies of generic
ties of the active ingredient. versions of the methylphenidate multiphasic MR
tablet (US-FDA, CDER, 2014f). The reference listed
Examples of Partial AUC Analyses drug for this product is Concerta®, indicated for the
treatment of attention deficit hyperactivity disorder.
The first product to which this approach was applied The product is labeled to be administered once in the
was the zolpidem extended-release formulation. The morning, before the start of the school day, for pedi-
reference for this product, Ambien CR®, exhibits atric patients. The three pAUC metrics are proposed
ng/mL
500 Chapter 16
to ensure that when patients for whom Concerta profiles following oral administration (US-FDA,
treatment is indicated switch formulations, they will CDER, 2013b). However, because the site of mesala-
experience equivalent therapeutic responses over the mine action is the colon and rectum, the FDA con-
course of the day. Thus, for an acceptable bioequiva- cluded that comparisons of AUC and Cmax alone in BE
lence study, the 90% confidence intervals of the studies would not distinguish between products with
geometric mean test/reference ratios Cmax, AUC0-T , materially different mesalamine release profiles at the
1
AUCT A C
1-T , U a d A
2 T
2-T , n UC∞ should fall within the sites of drug action (US-FDA, CDER, 2010c). Thus, the
3
limits of 80.00%–125.00%. The sampling time T1 for pAUC is used to analyze systemic mesalamine concen-
the first pAUC (AUC0-T ) is based on the time at trations over specified time intervals to determine
1
which 90%–95% of subjects are likely to achieve an whether mesalamine from test and reference products
early onset of response. The middle pAUC (AUCT )
1-T is available at the same rate and to the same extent at
2
comparison is to ensure similar drug exposures during the colon and rectum (Davit and Conner, 2015).
the remaining school hours (for pediatric patients)
after early onset of exposure. The late pAUC com- BIOEQUIVALENCE EXAMPLES
parison (AUCT2-T ) is to ensure equivalent methyl-
3
phenidate exposures during the latter part of the A simulated example of the results for a single-dose,
dosing interval, corresponding to the duration of the fasting study is shown in Table 16-11 and in Fig. 16-15.
sustained response. As shown by the ANOVA, no statistical differences
The pAUC is also used as a BE metric in studies for the pharmacokinetic parameters, AUCt , AUC∞,
0 0
comparing test and reference versions of mesalamine and Cmax, were observed between the test product and
orally administered MR formulations (Table 16-10). the brand-name product. The 90% confidence limits
Mesalamine is indicated to treat inflammatory dis- for the mean pharmacokinetic parameters of the test
eases of the colon and rectum, and is thought to act product were within 0.80–1.25 (80%–125%) of the
locally rather than systemically. Table 16-10 sum- reference product means based on log transforma-
marizes the mesalamine RLD oral MR formulations, tion of the data. The power test for the AUC mea-
associated indications, and Pauc metrics used in BE sures was above 99%, showing good precision of the
studies against each of these RLDs. Mesalamine is data. The power test for the Cmax values was 87.9%,
well absorbed, most likely throughout the small and showing that this parameter was more variable.
large intestines, with the result that it is possible to Table 16-12 shows the results for a hypothetical
measure plasma concentrations and determine PK bioavailability study in which three different tablet
TABLE 1610 Bioequivalence Metrics for In Vivo Studies of Mesalamine Modified-Release Oral
Dosage Forms
Formulation Reference Bioequivalence Metrics
Mesalamine delayed-release capsule Delzicol® For both fasting and fed studies: Cmax, AUC8-48 h, AUC0-t
Mesalamine delayed-release tablet Asacol®
Mesalamine delayed-release tablet Asacol HD®
Mesalamine delayed-release tablet Lialda®
Mesalamine extended-release capsule Pentasa® For fasting study: Cmax, AUC0-3 h, AUC3 h-t, AUC0-t
For fed study: Cmax and AUC0-t are pivotal; AUC0-3 h and AUC0-t
are supportive
Mesalamine extended-release capsule Apriso®
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 501
TABLE 1611 Bioavailability Comparison of a Generic (Test) and Brand-Name (Reference) Drug
Products (Log-Normal Transformed Data)
p Values
90% Confidence for
Interval (Lower Limit, Product Power of ANOVA
Variable Units Geometric Mean % Ratio Upper Limit) Effects ANOVA %CV
Test Reference
Cmax ng/mL 344.79 356.81 96.6 (89.5, 112) 0.3586 0.8791 17.90%
ng · h/mL 2659.12 2674.92 99.4 (95.1, 104) 0.8172 1.0000 12.60%
AUC∞ 2708.63 2718.52 99.6 (95.4, 103) 0.8865 1.0000 12.20%
tmax h 4.29 4.24 101
Kelim 1/h 0.0961 0.0980 98.1
t1/2 h 8.47 8.33 101.7
The results were obtained from a two-way, crossover, single-dose study in 36 fasted, healthy, adult male and female volunteers. No statistical differ-
ences were observed for the mean values between test and reference products.
formulations were compared to a solution of the confidence interval for the AUC showed that for
drug given in the same dose. As shown in the table, tablet A, the bioavailability was less than 80% (ie,
the bioavailability from all three tablet formulations 74%), compared to the solution at the low-range
was greater than 80% of that of the solution. estimate, and would not be considered bioequivalent
According to the ANOVA, the mean AUC values based on the AUC.
were not statistically different from one another, nor For illustrative purposes, consider a drug that has
different from that of the solution. However, the 90% been prepared at the same dosage level in three
350
300
250
200
150
100
50
0
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48
Time (hours)
A: Test B: Reference
FIGURE 1615 Bioequivalence of test and reference drug products: mean plasma drug concentrations.
Plasma drug concentration (ng/mL)
502 Chapter 16
TABLE 1612 Summary of the Results of a Bioavailability Studya
90% Confidence
Dosage Form Cmax (lg/mL) tmax (h) AUC0–24 (lg h/mL) Fb Interval for AUC
Solution 16.1 ± 2.5 1.5 ± 0.85 1835 ± 235
Tablet A 10.5 ± 3.2c 2.5 ± 1.0c 1523 ± 381 81 74%–90%
Tablet B 13.7 ± 4.1 2.1 ± 0.98 1707 ± 317 93 88%–98%
Tablet C 14.8 ± 3.6 1.8 ± 0.95 1762 ± 295 96 91%–103%
aThe bioavailability of a drug from four different formulations was studied in 24 healthy, adult male subjects using a four-way Latin-square crossover
design. The results represent the mean ± standard deviation.
bOral bioavailability relative to the solution.
cp ≤ .05.
formulations, A, B, and C. These formulations are rapid than that from formulation B, because the tmax for
given to a group of volunteers using a three-way, ran- formulation A is shorter. Because the AUC for formu-
domized crossover design. In this experimental design, lation A is identical to the AUC for formulation B, the
all subjects receive each formulation once. From each extent of bioavailability from both of these formula-
subject, plasma drug level and urinary drug excretion tions is the same. Note, however, the Cmax for A is
data are obtained. With these data we can observe the higher than that for B, because the rate of drug absorp-
relationship between plasma and urinary excretion tion is more rapid.
parameters and drug bioavailability (Fig. 16-16). The The Cmax is generally higher when the extent of
rate of drug absorption from formulation A is more drug bioavailability is greater. The rate of drug absorp-
tion from formulation C is the same as that from formu-
lation A, but the extent of drug available is less. The
A Cmax for formulation C is less than that for formula-
tion A. The decrease in Cmax for formulation C is
AUC
A = AUCB proportional to the decrease in AUC in comparison
AUCC = 0.5 AUCA
to the drug plasma level data for formulation A. The
A
B corresponding urinary excretion data confirm these
C observations. These relationships are summarized in
Table 16-13. The table illustrates how bioavailability
parameters for plasma and urine change when only the
Time extent and rate of bioavailability are changed, respec-
tively. Formulation changes in a drug product may
B
affect both the rate and extent of drug bioavailability.
STUDY SUBMISSION AND DRUG
A
REVIEW PROCESS
B
The contents of New Drug Applications (NDAs)
C
and Abbreviated New Drug Applications (ANDAs)
are similar in terms of the quality of manufacture
(Table 16-14). The submission for an NDA must
Time contain safety and efficacy studies as provided by
FIGURE 1616 Corresponding plots relating plasma animal toxicology studies, clinical efficacy studies,
concentration and urinary excretion data. and pharmacokinetic/bioavailability studies. For the
Cumulative amount of drug in urine Plasma level
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 503
TABLE 1613 Relationship of Plasma Level and Urinary Excretion Parameters to Drug Bioavailability
Extent of Drug Bioavailability Decreases Rate of Drug Bioavailability Decreases
Parameter Change Parameter Change
Plasma data
tmax Same tmax Increase
Cmax Decrease Cmax Decrease
AUC Decrease AUC Same
Urine data
t∞ Same t∞ Increase
[dD /dt ] Decrease
u maxa
[dD /dt ] Decrease
u maxa
D∞ Decrease D∞ Same
u u
aMaximum rate of urinary drug excretion.
generic drug manufacturer, the bioequivalence study These results, along with case reports and various
is the pivotal study in the ANDA that replaces the data supporting the validity of the analytical method,
animal, clinical, and pharmacokinetic studies. are included in the submission. The FDA reviews the
An outline for the submission of a completed study in detail according to the outline presented in
bioavailability to the FDA is shown in Table 16-15. Table 16-16. If necessary, an FDA investigator may
The investigator should be sure that the study has inspect both the clinical and analytical facilities used
been properly designed, the objectives are clearly in the study and audit the raw data used in support of
defined, and the method of analysis has been vali- the bioavailability study. For ANDA applications,
dated (ie, shown to measure precisely and accurately the FDA Office of Generic Drugs reviews the entire
the plasma drug concentration). The results are ana- ANDA as shown in Fig. 16-17. If the application is
lyzed both statistically and pharmacokinetically. incomplete, the FDA will not review the submission
and the sponsor will receive a Refusal to File letter.
TABLE 1614 NDA Versus ANDA Review
Process Frequently Asked Questions
»»What is the most appropriate bioequivalence design
Brand-Name Drug NDA Generic Drug ANDA
for a solid oral drug product containing a drug for
Requirements Requirements
systemic absorption?
1. Chemistry 1. Chemistry
»»What are some of the problems associated with
2. Manufacturing 2. Manufacturing clinical endpoint bioequivalence studies?
3. Controls 3. Controls
4. Labeling 4. Labeling WAIVERS OF IN VIVO
5. Testing 5. Testing BIOEQUIVALENCE STUDIES
6. Animal studies 6. Bioequivalence (BIOWAIVERS)
7. Clinical studies
In some cases, in vitro dissolution testing may be used
8. Bioavailability in lieu of in vivo bioequivalence studies. When the drug
Source: Center for Drug Evaluation & Research, US Food & Drug product is in the same dosage form but in different
Administration, http://www.fda.gov. strengths and is proportionally similar in active and
504 Chapter 16
TABLE 1615 Proposed Format and Contents of an In Vivo Bioequivalence Study Submission and
Accompanying In Vitro Data
Title page V. Pharmacokinetic Parameters and Tests
Study title Definition and calculations
Name of sponsor Statistical tests
Name and address of clinical laboratory Drug levels at each sampling time and pharmacokinetic
Name of principal investigator(s) parameters
Name of clinical investigator Figure of mean plasma concentration–time profile
Name of analytical laboratory Figures of individual subject plasma concentration–time
Dates of clinical study (start, completion) profiles
Signature of principal investigator (and date) Figure of mean cumulative urinary excretion
Signature of clinical investigator (and date) Figures of individual subject cumulative urinary
excretion
Table of contents
Figure of mean urinary excretion rates
I. Study Résumé
Fgures of individual subject urinary excretion rates
Product information
Tables of individual subject data arranged by drug,
Summary of bioequivalence study
drug/period, drug/sequence
Summary of bioequivalence data
Plasma VI. Statistical Analyses
Urinary excretion Statistical considerations
Figure of mean plasma concentration–time profile Summary of statistical significance
Figure of mean cumulative urinary excretion Summary of statistical parameters
Figure of mean urinary excretion rates Analysis of variance, least squares estimates, and least
squares means
II. Protocol and Approvals
Asessment of sequence, period, and treatment effects
Protocol
90% confidence intervals for the difference between
Letter of acceptance of protocol from FDA
test and reference products for the log-normal trans-
Informed consent form
formed parameters of AUC0–t, AUC0–∞, and Cmax should
Letter of approval of Institutional Review Board
be within 80% and 125%
List of members of Institutional Review Board
VII. Appendices
III. Clinical Study
Randomization schedule
Summary of the study
Sample identification codes
Details of the study
Analytical raw data
Demographic characteristics of the subjects
Chromatograms of at least 20% of subjects
Subject assignment in the study
Medical record and clinical reports
Mean physical characteristics of subjects arranged by
Clinical facilities description
sequence
Analytical facilities description
Details of clinical activity
Curricula vitae of the investigators
Deviations from protocol
Vital signs of subjects VIII. In Vitro Testing
Adverse reactions report Dissolution testing
Dissolution assay methodology
IV. Assay Methodology and Validation
Content uniformity testing
Assay method description
Potency determination
Validation procedure
Summary of validation IX. Batch Size and Formulation
Data on linearity of standard samples Batch record
Data on interday precision and accuracy Quantitative formulation
Data on intraday precision and accuracy
Figure for standard curve(s) for low/high ranges
Chromatograms of standard and quality control
samples
Sample calculation
Modified from Dighe and Adams (1991), with permission.
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 505
TABLE 1616 General Elements of a study on the highest strength. Ideally, if there is a strong
Biopharmaceutics Review correlation between dissolution of the drug and the
bioavailability of the drug, then the comparative disso-
Introduction Summary and
analysis of data lution tests comparing the test product to the reference
product should be sufficient to demonstrate bioequiva-
Study design Comments
lence. For most drug products, especially immediate-
Study objective(s) Deficiencies release tablets and capsules, no strong correlation
Assay description and validation Recommendation exists, and the FDA requires an in vivo bioequivalence
study. For oral solid dosage forms, an in vivo bioequiv-
alence study may be required to support at least one
inactive ingredients, an in vivo bioequivalence study of dose strength of the product. Usually, an in vivo bio-
one or more of the lower strengths can be waived based equivalence study is required for the highest dose
on the dissolution tests and an in vivo bioequivalence strength. If the lower-dose-strength test product is
Applicant
ANDA
Acceptable and No Refuse to File Letter
Complete? Issued
Yes
Review by OGD/CDER
Bioequivalence Review Chemistry/Micro
Review
Request for Plant
Labeling Review
Inspection
Bioequivalence Yes Chemistry/Micro/Label-
Review Acceptable? ing Review
No Acceptable? No
Bioequivalence Not Approvable
Def ciency Letter Letter
Preapproval
Inspection
Acceptable? No Approval Deferred
Pending
Satisfactory Results
Yes
ANDA APPROVED
FIGURE 1617 Generic drug review process. (Source: Office of Generic Drugs, Center for Drug Evaluation & Research, US Food
& Drug Administration.)
506 Chapter 16
substantially similar in active and inactive ingredients, • Acceptable in vitro dissolution should be demon-
then only a comparative in vitro dissolution between strated for the strength(s) for which the biowaiver
the test and brand-name formulations may be used. is sought.
For example, an immediate-release (IR) tablet is
The FDA does not grant biowaivers for generic
available in 200-mg, 100-mg, and 50-mg strengths.
modified-release products, but may deem non-
The 100- and 50-mg-strength tablets are made the
biostudy strength(s) BE to the corresponding biostudy
same way as the highest-strength tablet. A human
strength(s) subject to certain criteria. This policy
bioequivalence study is performed on the highest or
applies to all MR dosage forms, including but not
200-mg strength. Comparative in vitro dissolution
limited to delayed-release tablets and capsules,
studies are performed on the 100-mg and 50-mg
extended-release tablets, transdermal products, and
dose strengths. If these drug products have no known
long-acting injectables (Davit et al, 2013).
bioavailability problems, are well absorbed systemi-
cally, are well correlated with in vitro dissolution,
and have a large margin of safety, then arguments for Dissolution Profile Comparisons
not performing an in vivo bioavailability study may Comparative dissolution profiles are used as (1) the
be valid. Methods for correlation of in vitro dissolu- basis for formulation development of bioequivalent
tion of the drug with in vivo drug bioavailability are drug products and proceeding to the pivotal in vivo
discussed in Chapters 15 and 19. The manufacturer bioequivalence study (Chapter 15); (2) comparative
does not need to perform additional in vivo bio- dissolution profiles are used for demonstrating the
equivalence studies on the lower-strength products if equivalence of a change in the formulation of a drug
the products meet all in vitro criteria. product after the drug product has been approved for
marketing (see SUPAC in Chapter 17); and (3) the
Regulatory Perspective for Biowaiver basis of a biowaiver of a lower-strength drug product
The FDA permits the waiving of BE studies for that is dose proportional in active and inactive ingre-
products for which BE is self-evident. This includes dients to the higher-strength drug product.
solutions for parenteral, oral, or local use. There are A model-independent mathematical method
generally additional criteria to be met before a bio- was developed by Moore and Flanner (1996) to com-
waiver can be granted. Test and reference solutions pare dissolution profiles using two factors, f1 and f2.
intended for parenteral use should have the same The factor f2, known as the similarity factor, mea-
active and inactive ingredients in the same amounts. sures the closeness between the two profiles:
The FDA generally refers to this as qualitative (Q1)
−0.5
and quantitative (Q2) sameness. Generic drug prod-
1 n
f2 = 50 × log 1+ ∑(R 2
1 − T
1)
×100
uct solutions that are intended for oral or topical use n
t=1 can have different excipients than their correspond-
ing RLD products, but should not contain excipients
where n is the number of time points, R1 is the dissolu-
that could potentially cause differences in drug sub-
tion value of the reference product at time t, and T1 is
stance absorption.
the dissolution value of the test product batch at time t.
The FDA will consider granting biowaivers to
The reference may be the original drug product
non-biostudy strengths of a generic IR solid oral
before a formulation change (prechange) and the test
dosage form drug product line, provided that the fol-
may be the drug product after the formulation was
lowing three criteria are met:
changed (postchange). Alternatively, the reference
• An acceptable BE study is conducted on at least may be the higher-strength drug product and the test
one strength. may be the lower-strength drug product. The f2 com-
• The strength(s) for which the biowaiver is sought parison is the focus of several FDA guidances and is
should be proportionally similar to the strength on of regulatory interest in knowing the similarity of the
which BE was demonstrated. two dissolution curves. When the two profiles are
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 507
identical, f2 = 100. An average difference of 10% at According to the BCS, drug substances are clas-
all measured time points results in an f2 value of 50 sified as follows:
(Shah et al, 1998). The FDA has set a public stan-
• Class 1: high solubility–high permeability
dard for f2 value between 50 and 100 to indicate
• Class 2: low solubility–high permeability
similarity between two dissolution profiles (US-FDA,
• Class 3: high solubility–low permeability
CDER, 1997).
• Class 4: low solubility–low permeability
In some cases, two generic drug products may
have dissimilar dissolution profiles and still be bio- A theoretical basis for correlating in vitro drug
equivalent in vivo. For example, Polli et al (1997) dissolution with in vivo bioavailability was devel-
have shown that slow-, medium-, and fast-dissolving oped by Amidon et al (1995). This approach is based
formulations of metoprolol tartrate tablets were bio- on the aqueous solubility of the drug and the perme-
equivalent. Furthermore, bioequivalent modified- ation of the drug through the gastrointestinal tract.
release drug products may have different drug The classification system is based on Fick’s first law
release mechanisms and therefore different dissolu- applied to a membrane:
tion profiles. For example, for theophylline extended-
release capsules, the United States Pharmacopeia J = P C
w w w
(USP) lists 10 individual drug release tests for prod-
where Jw is the drug flux (mass/area/time) through
ucts labeled for dosing every 12 hours. However,
the intestinal wall at any position and time, Pw is the
only generic drug products that are FDA approved as
permeability of the membrane, and Cw is the drug
bioequivalent drug products and listed in the current
concentration at the intestinal membrane surface.
edition of the Orange Book may be substituted for
This approach assumes that no other compo-
each other.
nents in the formulation affect the membrane perme-
ability and/or intestinal transport. Using this approach,
Frequently Asked Questions Amidon et al (1995) studied the solubility and per-
meability characteristics of various representative
»»Why are preclinical animal toxicology studies and
clinical efficacy drug studies in human subjects drugs and obtained a biopharmaceutic drug classifi-
not required by the FDA to approve a generic cation for predicting the in vitro drug dissolution of
drug product as a therapeutic equivalent to the IR solid oral drug products with in vivo absorption.
brand-name drug product? The FDA may waive the requirement for per-
forming an in vivo bioavailability or bioequivalence
»»Are bioequivalence studies needed for each dose
study for certain IR solid oral drug products that
strength of an oral drug product? For example,
an oral drug product is commercially available in meet very specific criteria, namely, the permeability,
200-mg, 100-mg, and 50-mg dose strengths. solubility, and dissolution of the drug. These charac-
teristics include the in vitro dissolution of the drug
product in various media, drug permeability infor-
mation, and assuming ideal behavior of the drug
THE BIOPHARMACEUTICS
product, drug dissolution, and absorption in the GI
CLASSIFICATION SYSTEM (BCS) tract. For regulatory purposes, drugs are classified
according to the BCS in accordance with the solubility,
The BCS is a scientific framework for classifying
permeability, and dissolution characteristics of the
drug substances based on their aqueous solubility
drug (US-FDA, CDER, 2000b).
and intestinal permeability. When combined with the
dissolution of the drug product, the BCS takes into
account three major factors that govern the rate and Solubility
extent of drug absorption from IR solid oral dosage An objective of the BCS approach is to determine the
forms. These factors are dissolution, solubility, and equilibrium solubility of a drug under approximate
intestinal permeability. physiologic conditions. For this purpose, determination
508 Chapter 16
of pH–solubility profiles over a pH range of 1–8 is drug product is considered rapidly dissolving when not
suggested. The solubility class is determined by cal- less than 85% of the label amount of drug substance
culating what volume of an aqueous medium is suffi- dissolves within 30 minutes using USP Apparatus I
cient to dissolve the highest anticipated dose strength. (see Chapter 14) at 100 rpm or Apparatus II at 50 rpm
A drug substance is considered highly soluble when in a volume of 900 mL or less in each of the follow-
the highest dose strength is soluble in 250 mL or less of ing media: (1) acidic media such as 0.1 N HCl or
aqueous medium over the pH range 1–8. The volume simulated gastric fluid USP without enzymes, (2) a
estimate of 250 mL is derived from typical bioequiv- pH 4.5 buffer, and (3) a pH 6.8 buffer or simulated
alence study protocols that prescribe administration intestinal fluid USP without enzymes.
of a drug product to fasting human volunteers with a The FDA is in the process of revising the BCS
glass (8 oz) of water. guidance to permit biowaivers for generic formula-
tions of Class 3 drugs (Mehta, 2014). Table 16-17
Permeability summarizes the recently proposed FDA criteria to be
met for BCS biowaivers.
Studies of the extent of absorption in humans, or
intestinal permeability methods, can be used to deter-
mine the permeability class membership of a drug. Biopharmaceutics Drug Disposition
To be classified as highly permeable, a test drug Classification System
should have an extent of absorption >90% in humans.
The major aspects of BCS are the consideration of
Supportive information on permeability characteris-
solubility and permeation. According to BCS, perme-
tics of the drug substance should also be derived from
ability in vivo is considered high when the active drug
its physical–chemical properties (eg, octanol: water
is systemically absorbed ≥90%. Wu and Benet (2005)
partition coefficient).
and Benet et al (2008) have proposed modification of
Some methods to determine the permeability of a
the BCS system known as the Biopharmaceutics
drug from the gastrointestinal tract include (1) in vivo
Drug Disposition Classification System (BDDCS),
intestinal perfusion studies in humans; (2) in vivo
which takes into account drug metabolism (hepatic
or in situ intestinal perfusion studies in animals;
clearance) and transporters in the gastrointestinal
(3) in vitro permeation experiments using excised
tract for drugs that are orally administered. For BCS
human or animal intestinal tissues; and (4) in vitro
1 drugs (ie, high solubility and high permeability),
permeation experiments across a monolayer of cul-
transporter effects will be minimal. However, BCS 2
tured human intestinal cells. When using these meth-
drugs (low solubility and high permeability), trans-
ods, the experimental permeability data should
porter effects are more important. These investigators
correlate with the known extent-of-absorption data in
suggest that the BCS should be modified on the basis
humans.
of the extent of drug metabolism, overall drug dispo-
After oral drug administration, in vivo permea-
sition, including routes of drug elimination and the
bility can be affected by the effects of efflux and
effects of efflux, and absorptive transporters on oral
absorptive transporters in the gastrointestinal tract,
drug absorption.
by food, and possibly by the various excipients pres-
ent in the formulation.
Drug Products for Which Bioavailability or
Bioequivalence May Be Self-Evident
Dissolution The best measure of a drug product’s performance
The dissolution class is based on the in vitro dissolu- is to determine the in vivo bioavailability of the
tion rate of an IR drug product under specified test drug. For some well-characterized drug products
conditions and is intended to indicate rapid in vivo and for certain drug products in which bioavail-
dissolution in relation to the average rate of gastric ability is self-evident (eg, sterile solutions for
emptying in humans under fasting conditions. An IR injection), in vivo bioavailability studies may be
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 509
TABLE 1617 Criteria Proposed by FDA for Consideration of BCS-Based Biowaivers of Immediate-
Release Generic Drug Products
BCS Class 1
Highly Soluble Oral Bioavailability Dissolution Criteria on Excipients
Highest strength, over ≥85% • ≥85% in 30 minutes at pH 1.0, • Test and reference should be
range of pH 1.0–6.8 4.5, 6.8 (“rapidly dissolving”) pharmaceutical equivalents
• Volume = 500 mL • Test and reference should not
• Paddles at 50 rpm, or basket at differ in amounts of excipients
100 rpm known to affect bioavailability
BCS Class 3
Highly Soluble Oral Bioavailability Dissolution Criteria on Excipients
Highest strength, over <85% • ≥85% in 15 minutes at pH 1.0, • Test and reference should be
range of pH 1.0–6.8 4.5, 6.8 (“very rapidly dissolving) pharmaceutical equivalents
• Volume = 500 mL • Test and reference formulations
• Paddles at 50 rpm, or basket at should be Q1 and Q2 the same
100 rpm
unnecessary or unimportant to the achievement of 3. The drug product is in an oral dosage form that
the product’s intended purposes. The FDA will is not intended to be absorbed (eg, an antacid
waive the requirement for submission of in vivo or a radiopaque medium). Specific in vitro
evidence demonstrating the bioavailability of the bioequivalence studies may be required by
drug product if the product meets one of the follow- the FDA. For example, the bioequivalence of
ing criteria (US-FDA, CDER, 2014a). However, cholestyramine resin is demonstrated in vitro
there may be specific requirements for certain drug by the binding of bile acids to the resin.
products, and the appropriate FDA division should 4. The drug product meets both of the following
be consulted. conditions:
a. It is administered by inhalation as a gas or
1. The drug product (a) is a solution intended vapor (eg, as a medicinal or as an inhalation
solely for intravenous administration and anesthetic).
(b) contains an active drug ingredient or b. It contains an active drug ingredient or
therapeutic moiety combined with the same therapeutic moiety in the same dosage form
solvent and in the same concentration as in an as a drug product that is the subject of an
intravenous solution that is the subject of an approved, full NDA.
approved, full NDA. 5. The drug product meets all of the following
2. The drug product is a topically applied prepara- conditions:
tion (eg, a cream, ointment, or gel intended for a. It is an oral solution, elixir, syrup, tincture,
local therapeutic effect). The FDA has released or similar other solubilized form.
guidances for the performance of bioequiva- b. It contains an active drug ingredient or
lence studies on topical corticosteroids and therapeutic moiety in the same concentration
antifungal agents. The FDA is also considering as a drug product that is the subject of an
performing dermatopharmacokinetic (DPK) approved, full NDA.
studies on other topical drug products. In addi- c. It contains no inactive ingredient that is
tion, in vitro drug release and diffusion studies known to significantly affect absorption of the
may be required. active drug ingredient or therapeutic moiety.
510 Chapter 16
GENERIC BIOLOGICS product and the reference product should consider
all relevant characteristics of the protein product
(BIOSIMILAR DRUG PRODUCTS)
(eg, the primary, secondary, tertiary, and quater-
Biologics, or biotechnology-derived drugs, in contrast nary structure, post-translational modifications,
to drugs that are chemically synthesized, are derived and functional activity[ies]). The objective of this
from living sources such as humans, animals, or assessment is to maximize the potential for detect-
microorganisms. Many biologics are complex mix- ing differences in quality attributes between the
tures that are not easily identified or characterized and proposed biosimilar product and the reference
are manufactured using biotechnology or are purified product.
from natural sources. Other biological drugs, such as • Functional activities: Functional assays serve mul-
insulin and growth hormone, are proteins derived by tiple purposes in the characterization of protein
biotechnology and have been well characterized. products. These tests act to complement physico-
Advances in analytical sciences (both physicochemi- chemical analyses and are a quality measure of the
cal and biological) enable some protein products to be function of the protein product.
characterized extensively in terms of their physico- • Receptor binding and immunochemical proper-
chemical and biological properties. These analytical ties: When binding or immunochemical proper-
procedures have improved the ability to identify and ties are part of the activity attributed to the protein
characterize not only the desired product but also product, analytical tests should be performed to
product-related substances and product- and process- characterize the product in terms of these specific
related impurities. Advances in manufacturing science properties.
and production methods may enhance the likelihood • Impurities: The applicant should characterize,
that a product will be highly similar to another prod- identify, and quantify impurities (product and pro-
uct by better targeting the original product’s physio- cess related) in the proposed biosimilar product
chemical and functional properties. and the reference product.
The assessment of biosimilarity between a pro- • Reference product and reference standards: A
posed biosimilar product and its reference product thorough physicochemical and biological assess-
involves the robust characterization of the proposed ment of the reference product should provide a
biosimilar product, including comparative physico- base of information from which to develop the
chemical and functional studies. The FDA recom- proposed biosimilar product and justify reliance
mends the following factors that must be considered on certain existing scientific knowledge about the
in assessing whether products are highly similar reference product.
(US-FDA, CDER, 2014g). • Finished drug product: Product characterization
studies should be performed on the most down-
• Expression system: Therapeutic protein products
stream intermediate best suited for the analytical
can be produced by microbial cells (prokaryotic,
procedures used.
eukaryotic), cell lines of human or animal origin • Stability: An appropriate physicochemical and
(eg, mammalian, avian, insect), or tissues derived
functional comparison of the stability of the pro-
from animals or plants. It is expected that the ex-
posed biosimilar product with that of the reference
pression construct for a proposed biosimilar prod-
product should be initiated including accelerated
uct will encode the same primary amino acid se-
and stress stability studies, or forced degradation
quence as its reference product.
studies.
• Manufacturing process: A comprehensive under-
standing of all steps in the manufacturing process The foundation for an assessment of biosimilarity
for the proposed biosimilar product should be es- between a proposed biosimilar product and its refer-
tablished during product development. ence product involves the robust characterization of
• Assessment of physicochemical properties: Physi- the proposed biosimilar product, including compara-
cochemical assessment of the proposed biosimilar tive physicochemical and functional studies.
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 511
Biosimilarity Versus Interchangeability Biosimilars and interchangeable biotechnology-
The Patient Protection and Affordable Care Act of derived drugs will be considered on a case-by-case
2010 contains provisions that establish an abbrevi- basis. After FDA approval, the manufacturer must
ated regulatory approval pathway for generic ver- provide robust postmarketing safety monitoring as
sions of biological medicines (ie, biosimilars). The an important component in ensuring the safety and
new legislation establishes two distinct categories of effectiveness of biological products,
biosimilar products: (1) biological products that are
“biosimilar” to a reference biological product, and FDA Guidance Documents
(2) biological products that are “interchangeable” The legislation makes clear that the FDA will play a
with the reference product. central role in defining the specific criteria needed to
Biosimilar biological drug products are biologi- demonstrate biosimilarity for a given class of bio-
cal products that are highly similar to the reference logical. In deference to the FDA’s expertise in this
product notwithstanding minor differences in clini- area, the legislation specifically states that the FDA
cally inactive components. In addition, there are no can issue guidance documents with respect to the
clinically meaningful differences between the bio- approval of a biosimilar product. The guidance can
logical product and the reference product in terms of be general or specific in nature, and the public must
the safety, purity, and potency of the product. be provided with an opportunity to comment.
Interchangeable biological drug products are Advocates for the manufacture of generic bio-
biological products that are interchangeable with a logics argue that bioequivalent biotechnology-derived
reference biological product if (1) it meets the cri- drug products can be made on a case-by-case basis.
teria for being biosimilar to the reference product, Those opposed to the development of generic biolog-
(2) it can be expected to produce the same clinical ics or biosimilar drug products have claimed that
result as the reference product in any given patient, generic manufacturers do not have the ability to fully
and (3) the risk in terms of safety or diminished characterize the active ingredient(s), that immuno-
efficacy in alternating or switching between use of genicity-related impurities may be present in the
the biological and reference product is not greater product, and that the manufacture of a biologic drug
than the risk of using the reference product without product is process dependent. Several biosimilar drug
such alteration or switch. products have been approved in Europe. Currently,
FDA determination of biosimilar drug products there are several applications for biosimilar drug
is based on the totality of the evidence provided by a products under review by the FDA. In the United
sponsor to support a demonstration of biosimilarity. States, FDA regulatory approval is based on a step-
The FDA recommends that sponsors use a stepwise wise approach that includes a comparison of the
approach in their development of biosimilar prod- proposed product and the reference product with
ucts. FDA regulatory approval of a biosimilar drug respect to structure, function, animal toxicity, human
product is based on a stepwise approach includes a pharmacokinetics (PK) and pharmacodynamics (PD),
comparison of the proposed product and the refer- clinical immunogenicity, and clinical safety and
ence product including: effectiveness.
• Analytical studies that demonstrate that the bio-
logical product is highly similar to the reference
product notwithstanding minor differences in clin- CLINICAL SIGNIFICANCE OF
ically inactive components BIOEQUIVALENCE STUDIES
• Animal studies (including the assessment of toxicity)
• Clinical study or studies (including the assessment Bioequivalence of different formulations of the same
of immunogenicity and pharmacokinetics or phar- drug substance involves equivalence with respect to
macodynamics) that are sufcient to demonstrate the rate and extent of systemic drug absorption.
safety, purity, and potency Clinical interpretation is important in evaluating the
512 Chapter 16
results of a bioequivalence study. A small difference
EXAMPLE »» »
between drug products, even if statistically signifi-
cant, may produce very little difference in therapeutic
IMPACT OF EFFLUX TRANSPORTERS ON
response. Generally, two formulations whose rate and
BIOEQUIVALENCE STUDY
extent of absorption differ by 20% or less are consid-
Digoxin is a drug that may be absorbed differently
ered bioequivalent. The Report by the Bioequivalence
in individuals that expressed the efflux gene MDR1.
Task Force (1988) considered that differences of less
than 20% in AUC and Cmax between drug products are Questions
“unlikely to be clinically significant in patients.” The • What would be the impact of such an individual
Task Force further stated that “clinical studies of recruited into a bioavailability study?
effectiveness have difficulty detecting differences in • Would a protocol with the usual crossover design
doses of even 50%–100%.” Therefore, normal varia- be able to adequately evaluate the bioequiva-
tion is observed in medical practice and plasma drug lence of a generic digoxin product with a refer-
levels may vary among individuals greater than 20%. ence? Explain why or why not.
According to Westlake (1973), a small, statisti- Solution
cally significant difference in drug bioavailability Bioequivalence studies for generic drug prod-
from two or more dosage forms may be detected if ucts compare the bioavailability of the drug from
the study is well controlled and the number of sub- the test (generic) product to the bioavailability of
jects is sufficiently large. When the therapeutic the drug from the reference (brand) product. The
objectives of the drug are considered, an equivalent study design is a two-way, crossover design in
clinical response should be obtained from the com- which each subject takes each drug product. The
parison dosage forms if the plasma drug concentra- study design usually includes males and females
tions remain above the minimum effective with different ethnic backgrounds. In addition,
concentration (MEC) for an appropriate interval and some studies include both smokers and nonsmok-
do not reach the minimum toxic concentration ers. Although there may be large intersubject vari-
(MTC). Therefore, the investigator must consider ability due to gender, environmental, and genetic
whether any statistical difference in bioavailability factors, the crossover design minimizes intrasu-
would alter clinical efficiency. bject variability by comparing the bioavailability of
Special populations, such as the elderly or test and reference products in the same individual.
patients on drug therapy, are generally not used for Thus each individual subject should have similar
bioequivalence studies. Normal, healthy volunteers drug absorption characteristics after taking the
are preferred for bioequivalence studies, because test or reference drug products.9
these subjects are less at risk and may more easily
endure the discomforts of the study, such as blood
sampling. Furthermore, the objective of these studies
is to evaluate the bioavailability of the drug from the SPECIAL CONCERNS IN
dosage form, and use of healthy subjects should BIOAVAILABILITY AND
minimize both inter- and intrasubject variability. It is
theoretically possible that the excipients in one of BIOEQUIVALENCE STUDIES
the dosage forms tested may pose a problem in a The general bioequivalence study designs and
patient who uses the generic dosage form. evaluation, such as the comparison of AUC, Cmax,
For the manufacture of a dosage form, specifica- and tmax, may be used for systemically absorbed
tions are set to provide uniformity of dosage forms.
With proper specifications, quality control proce-
9For a few drug products, a high intrasubject variability (>30%
dures should minimize product-to-product variability
CV) may be observed for which the bioavailability response
by different manufacturers and lot-to-lot variability changes for the same drug product each time the drug is dosed in
with a single manufacturer (see Chapter 18). the same subject.
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 513
TABLE 1618 Issues in Establishing in analysis of variance coefficient of variation (Shah
Bioavailability and Bioequivalence et al, 1996). The number of subjects required to
demonstrate bioequivalence for these drug products
Drugs with high intrasubject variability
may be excessive, requiring more than 60 subjects
Drugs with long elimination half-life to meet current FDA bioequivalence criteria. The
Biotransformation of drugs intrasubject variability may be due to the drug itself
or to the drug formulation or to both. The FDA has
Stereoselective drug metabolism
held public forums to determine whether the cur-
Drugs with active metabolites rent bioequivalence guidelines need to be changed
Drugs with polymorphic metabolism for these highly variable drugs (Davit et al, 2012).
For drugs with very long elimination half-lives
Nonbioavailable drugs (drugs intended for local effect)
or a complex elimination phase, a complete plasma
Antacids drug concentration–time curve (ie, three elimination
Local anesthetics half-lives or an AUC representing 90% of the total
AUC) may be difficult to obtain for a bioequivalence
Anti-infectives
study using a crossover design. For these drugs, a
Anti-inflammatory steroids truncated (shortened) plasma drug concentration–
Dosage forms for nonoral administration time curve (0–72 hours) may be more practical. The
use of a truncated plasma drug concentration–time
Transdermal
curve allows for the measurement of peak absorption
Inhalation and decreases the time and cost for performing the
Ophthalmic bioequivalence study.
Many drugs are stereoisomers, and each isomer
Intranasal
may give a different pharmacodynamic response and
Bioavailable drugs that should not produce peak drug may have a different rate of biotransformation. The
levels
bioavailability of the individual isomers may be dif-
Potassium supplements ficult to measure because of problems in analysis.
Endogenous drug levels Some drugs have active metabolites, which should
be quantitated as well as the parent drug. Drugs such
Hormone replacement therapy
as thioridazine and selegilene have two active metab-
Biotechnology-derived drugs olites. The question for such drugs is whether bio-
Erythropoietin interferon equivalence should be proven by matching the
bioavailability of both metabolites and the parent
Protease inhibitors
drug. Assuming both biotransformation pathways
Complex drug substances follow first-order reaction kinetics, then the metabo-
Conjugated estrogens lites should be in constant ratio to the parent drug.
Genetic variation in metabolism may present a bio-
equivalence problem. For example, the acetylation
of procainamide to N-acetylprocainamide demon-
drugs and conventional oral dosage forms. However, strates genetic polymorphism, with two groups of
for certain drugs and dosage forms, systemic bio- subjects consisting of rapid acetylators and slow
availability and bioequivalence are difficult to acetylators. To decrease intersubject variability, a
ascertain (Table 16-18). Drugs and drug products bioequivalence study may be performed on only one
(eg, cyclosporine, chlorpromazine, verapamil, iso- phenotype, such as the rapid acetylators.
sorbide dinitrate, sulindac) are considered to be Some drugs (eg, benzocaine, hydrocortisone, anti-
highly variable if the intrasubject variability in infectives, antacids) are intended for local effect and
bioavailability parameters is greater than 30% by formulated as topical ointments, oral suspensions, or
514 Chapter 16
TABLE 1619 Possible Surrogate Markers for Bioequivalence Studies
Possible Surrogate Marker
Drug Product Drug for Bioequivalence
Metered-dose inhaler Albuterol Forced expiratory volume (FEV1)
Topical steroid Hydrocortisone Skin blanching
Anion-exchange resin Cholestyramine Binding to bile acids
Antacid Magnesium and aluminum hydroxide gel Neutralization of acid
Topical antifungal Ketoconazole Drug uptake into stratum corneum
rectal suppositories. These drugs should not have sig- more indirect methods must be used to ascertain bio-
nificant systemic bioavailability from the site of equivalence. For example, urinary potassium excretion
administration. The bioequivalence determination for parameters are more appropriate for the measurement
drugs that are not absorbed systemically from the site of bioavailability of potassium supplements. However,
of application can be difficult to assess. For these for certain hormonal replacement drugs (eg, levothy-
nonsystemic-absorbable drugs, a “surrogate” marker is roxine), the steady-state hormone concentration in
needed for bioequivalence determination (Table 16-19). hypothyroid individuals, the thyroidal-stimulating hor-
For example, the acid-neutralizing capacity of an oral mone level, and pharmacodynamic endpoints may also
antacid and the binding of bile acids to cholestyramine be appropriate to measure.
resin have been used as surrogate markers in lieu of in
vivo bioequivalence studies.
Various drug delivery systems and newer dosage
GENERIC SUBSTITUTION
forms are designed to deliver the drug by a nonoral
route, which may produce only partial systemic bio- Drug product selection and generic drug product
availability. For the treatment of asthma, inhalation of substitution are major responsibilities for physicians,
the drug (eg, albuterol, beclomethasone dipropionate) pharmacists, and others who prescribe, dispense, or
has been used to maximize drug in the respiratory purchase drugs. To facilitate such decisions, the
passages and to decrease systemic side effects. Drugs FDA publishes annually, in print and on the Internet,
such as nitroglycerin given transdermally may differ Approved Drug Products with Therapeutic Equivalence
in release rates, in the amount of drug in the trans- Evaluations, also known as the Orange Book (www
dermal delivery system, and in the surface area of .fda.gov/cder/ob/default.htm). The Orange Book
the skin to which the transdermal delivery system is identifies drug products approved on the basis of
applied. Thus, the determination of bioequivalence safety and effectiveness by the FDA and contains
among different manufacturers of transdermal deliv- therapeutic equivalence evaluations for approved mul-
ery systems for the same active drug is difficult. tisource prescription drug products. These evaluations
Dermatopharmacokinetic studies investigate drug serve as public information and advice to state health
uptake into skin layers after topical drug administra- agencies, prescribers, and pharmacists to promote
tion. The drug is applied topically, the skin is peeled public education in the area of drug product selection
at various time periods after the dose, using trans- and to foster containment of healthcare costs.
parent tape, and the drug concentrations in the skin To contain drug costs, most states have adopted
are measured. generic substitution laws to allow pharmacists to
Drugs such as potassium supplements are given dispense a generic drug product for a brand-name
orally and may not produce the usual bioavailability drug product that has been prescribed. Some states
parameters of AUC, Cmax, and tmax. For these drugs, have adopted a positive formulary, which lists
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 515
therapeutically equivalent or interchangeable drug are evaluated according to specific criteria. The
products that pharmacists may dispense. Other evaluation codes used for these drugs are listed in
states use a negative formulary, which lists drug Table 16-20. The drug products are divided into two
products that are not therapeutically equivalent, and/ major categories: “A” codes apply to drug products
or the interchange of which is prohibited. If the drug considered to be therapeutically equivalent to other
is not in the negative formulary, the unlisted generic pharmaceutically equivalent products, and “B” codes
drug products are assumed to be therapeutically apply to drug products that the FDA, at this time,
equivalent and may be interchanged. does not consider to be therapeutically equivalent to
other pharmaceutically equivalent products. A list of
therapeutic-equivalence-related terms and their defi-
Approved Drug Products with Therapeutic nitions is also given in the monograph. According to
Equivalence Evaluations (Orange Book) the FDA, evaluations do not mandate that drugs be
The Orange Book contains therapeutic equivalence purchased, prescribed, or dispensed, but provide
evaluations for approved drug products made by vari- public information and advice. The FDA evaluation
ous manufacturers. These marketed drug products of the drug products should be used as a guide only,
TABLE 1620 Therapeutic Equivalence Evaluation Codes
A Codes
Drug products considered to be therapeutically equivalent to other pharmaceutically equivalent products
AA Products in conventional dosage forms not presenting bioequivalence problems
AB Products meeting bioequivalence requirements
AN Solutions and powders for aerosolization
AO Injectable oil solutions
AP Injectable aqueous solutions
AT Topical products
B Codes
Drug products that the FDA does not consider to be therapeutically equivalent to other pharmaceutically equivalent products
B∗ Drug products requiring further FDA investigation and review to determine therapeutic equivalence
BC Extended-release tablets, extended-release capsules, and extended-release injectables
BD Active ingredients and dosage forms with documented bioequivalence problems
BE Delayed-release oral dosage forms
BN Products in aerosol–nebulizer drug delivery systems
BP Active ingredients and dosage forms with potential bioequivalence problems
BR Suppositories or enemas for systemic use
BS Products having drug standard deficiencies
BT Topical products with bioequivalence issues
BX Insufficient data
Adopted from Approved Drug Products with Therapeutic Equivalence Evaluations (Orange Book) (www.fda.cder/ob/default.htm), 2003.
516 Chapter 16
with the practitioner exercising professional care flavor. There may also be better stability of one
and judgment. product over another under adverse storage condi-
The concept of therapeutic equivalence as used tions or allergic reactions in rare cases due to a
to develop the Orange Book applies only to drug coloring or a preservative ingredient, as well as
products containing the same active ingredient(s) differences in cost to the patient.
and does not encompass a comparison of different FDA evaluation of therapeutic equivalence in no
therapeutic agents used for the same condition way relieves practitioners of their professional
(eg, propoxyphene hydrochloride versus pentazo- responsibilities in prescribing and dispensing such
cine hydrochloride for the treatment of pain). Any products with due care and with appropriate infor-
drug product in the Orange Book that is repack- mation to individual patients. In those circumstances
aged and/or distributed by other than the applica- where the characteristics of a specific product, other
tion holder is considered to be therapeutically than its active ingredient, are important in the ther-
equivalent to the application holder’s drug product apy of a particular patient, the physician’s specifica-
even if the application holder’s drug product is tion of that product is appropriate. Pharmacists must
single source or coded as nonequivalent (eg, BN). also be familiar with the expiration dates/times and
Also, distributors or repackagers of an application labeling directions for storage of the different prod-
holder’s drug product are considered to have the ucts, particularly for reconstituted products, to assure
same code as the application holder. Therapeutic that patients are properly advised when one product
equivalence determinations are not made for unap- is substituted for another.
proved, off-label indications. With this limitation,
however, the FDA believes that products classified
as therapeutically equivalent can be substituted with
the full expectation that the substituted product will EXAMPLE »» »
produce the same clinical effect and safety profile
INTERPRETATION OF THERAPEUTIC
as the prescribed product (www.fda.gov/cder/ob
EVALUATION CODE FOR NIFEDIPINE
/default.htm).
EXTENDEDRELEASE TABLETS
Professional care and judgment should be exer-
The FDA has approved a few drug products
cised in using the Orange Book. Evaluations of
containing the same active drug from different
therapeutic equivalence for prescription drugs are
pharmaceutical manufacturers, each of which
based on scientific and medical evaluations by the
has provided a separate New Drug Application
FDA. Products evaluated as therapeutically equiva-
(NDA) for its own product. Since no information
lent can be expected, in the judgment of the FDA,
is available to demonstrate whether the two
to have equivalent clinical effect and no difference
NDA-approved drug products are bioequivalent,
in their potential for adverse effects when used
each branded drug product becomes a separate
under the conditions of their labeling. However,
reference listed drug (Table 16-21). Generic drug
these products may differ in other characteristics
manufacturers must demonstrate to which RLD
such as shape, scoring configuration, release mech-
product is bioequivalent.
anisms, packaging, excipients (including colors,
flavors, preservatives), expiration date/time, and, in
some instances, labeling. If products with such dif-
ferences are substituted for each other, there is a
potential for patient confusion due to differences in In Table 16-21, AB1 products are bioequivalent
color or shape of tablets, inability to provide a to each other and can be substituted. AB2 products
given dose using a partial tablet if the proper scor- are bioequivalent to each other and can be substi-
ing configuration is not available, or decreased tuted. However, an AB1 product cannot be substi-
patient acceptance of certain products because of tuted for an AB2 product.
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 517
TABLE 1621 Nifedipine Extended-Release Oral Tablet
Active Dosage Form; Proprietary
TE Code RLD Ingredient Route Strength Name Applicant
AB1 Yes Nifedipine Extended 90 mg Adalat CC Bayer Healthcare
tablet release; oral
AB1 No Nifedipine Extended 90 mg Nifedipine Actavis
tablet release; oral
AB1 No Nifedipine Extended 90 mg Nifedipine Valeant Intl
tablet release; oral
AB2 Yes Nifedipine Extended 90 mg Procardia XL Pfizer
tablet release; oral
AB2 No Nifedipine Extended 90 mg Nifedipine Mylan
tablet release; oral
AB2 No Nifedipine Extended 90 mg Nifedipine Osmotica Pharm
tablet release; oral
TE = therapeutic equivalent.
Source: Approved Drug Products with Therapeutic Equivalence Evaluations (Orange Book), [www.accessdata.fda.gov/scripts/cder/ob/default.cfm].
GLOSSARY10 Bioequivalent drug products: This term describes
pharmaceutical equivalent or pharmaceutical alter-
Abbreviated New Drug Application (ANDA): Drug native products that display comparable bioavail-
manufacturers must file an ANDA for approval to mar- ability when studied under similar experimental
ket a generic drug product. The generic manufacturer conditions. For systemically absorbed drugs, the test
is not required to perform clinical efficacy studies or (generic) and reference listed drug (brand name)
nonclinical toxicology studies for the ANDA. shall be considered bioequivalent if (1) the rate and
Bioavailability: Bioavailability means the rate and extent of absorption of the test drug do not show a
extent to which the active ingredient or active moiety significant difference from the rate and extent of
is absorbed from a drug product and becomes avail- absorption of the reference drug when administered
able at the site of action. For drug products that are not at the same molar dose of the therapeutic ingredient
intended to be absorbed into the bloodstream, bioavail- under similar experimental conditions in either a
ability may be assessed by measurements intended to single dose or multiple doses or (2) the extent of
reflect the rate and extent to which the active ingredient absorption of the test drug does not show a signifi-
or active moiety becomes available at the site of action. cant difference from the extent of absorption of the
Bioequivalence requirement: A requirement imposed reference drug when administered at the same molar
by the FDA for in vitro and/or in vivo testing of speci- dose of the therapeutic ingredient under similar
fied drug products, which must be satisfied as a condi- experimental conditions in either a single dose or
tion for marketing. multiple doses and the difference from the reference
drug in the rate of absorption of the drug is inten-
tional, is reflected in its proposed labeling, is not
10The denitions are from Approved Drug Products with
essential to the attainment of effective body drug
Therapeutic Equivalence Evaluations (Orange Book). [www
.fda.gov/Drugs/InformationOnDrugs/ucm129662.htm], Code of concentrations on chronic use, and is considered
Federal Regulations, 21 CFR 320, and other sources. medically insignificant for the drug.
518 Chapter 16
When the above methods are not applicable (eg, Equivalence: Relationship in terms of bioavailabil-
for drug products that are not intended to be ity, therapeutic response, or a set of established
absorbed into the bloodstream), other in vivo or in standards of one drug product to another.
vitro test methods to demonstrate bioequivalence Generic name: The established, nonproprietary, or
may be appropriate. Bioequivalence may sometimes common name of the active drug in a drug product
be demonstrated using an in vitro bioequivalence (eg, acetaminophen).
standard, especially when such an in vitro test has Generic substitution: The process of dispensing a
been correlated with human in vivo bioavailability different brand or an unbranded drug product in
data. In other situations, bioequivalence may some- place of the prescribed drug product. The substituted
times be demonstrated through comparative clinical drug product contains the same active ingredient or
trials or pharmacodynamic studies. therapeutic moiety as the same salt or ester in the
Bioequivalent drug products may contain differ- same dosage form but is made by a different manu-
ent inactive ingredients, provided the manufacturer facturer. For example, a prescription for Motrin
identifies the differences and provides information brand of ibuprofen might be dispensed by the phar-
that the differences do not affect the safety or effi- macist as Advil brand of ibuprofen or as a non-
cacy of the product. branded generic ibuprofen if generic substitution is
Biosimilar or biosimilarity: The biological product permitted and desired by the physician.
is highly similar to the reference product notwith- Pharmaceutical alternatives: Drug products that
standing minor differences in clinically inactive contain the same therapeutic moiety but as different
components, and there are no clinically meaningful salts, esters, or complexes. For example, tetracycline
differences between the biological product and the phosphate and tetracycline hydrochloride equivalent
reference product in terms of the safety, purity, and to 250-mg tetracycline base are considered pharma-
potency of the product. ceutical alternatives. Different dosage forms and
Brand name: The trade name of the drug. This strengths within a product line by a single manufac-
name is privately owned by the manufacturer or dis- turer are pharmaceutical alternatives (eg, an extended-
tributor and is used to distinguish the specific drug release dosage form and a standard immediate-release
product from competitor’s products (eg, Tylenol, dosage form of the same active ingredient). The FDA
McNeil Laboratories). currently considers a tablet and capsule containing the
Chemical name: The name used by organic chem- same active ingredient in the same dosage strength as
ists to indicate the chemical structure of the drug pharmaceutical alternatives.
(eg, N-acetyl-p-aminophenol). Pharmaceutical equivalents: Drug products in
Drug product: The finished dosage form (eg, tablet, identical dosage forms that contain the same active
capsule, or solution) that contains the active drug ingredient(s), that is, the same salt or ester, are of the
ingredient, generally, but not necessarily, in associa- same dosage form, use the same route of administra-
tion with inactive ingredients. tion, and are identical in strength or concentration
Drug product performance: Drug product perfor- (eg, chlordiazepoxide hydrochloride, 5-mg cap-
mance, in vivo, may be defined as the release of the sules). Pharmaceutically equivalent drug products
drug substance from the drug product, leading to are formulated to contain the same amount of active
bioavailability of the drug substance and leading to a ingredient in the same dosage form and to meet the
pharmacodynamic response. Bioequivalence studies same or compendial or other applicable standards
are drug product performance tests. (ie, strength, quality, purity, and identity), but they
Drug product selection: The process of choosing or may differ in characteristics such as shape, scoring
selecting the drug product in a specified dosage form. configuration, release mechanisms, packaging,
Drug substance: A drug substance is the active excipients (including colors, flavors, preservatives),
pharmaceutical ingredient (API) or component in the expiration time, and, within certain limits, labeling.
drug product that furnishes the pharmacodynamic When applicable, pharmaceutical equivalents must
activity. meet the same content uniformity, disintegration
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 519
times, and/or dissolution rates. Modified-release as therapeutically equivalent those products that
dosage forms that require a reservoir or overage or meet the following general criteria: (1) they are
certain dosage forms such as prefilled syringes in approved as safe and effective; (2) they are pharma-
which residual volume may vary must deliver identi- ceutical equivalents in that they (a) contain identical
cal amounts of active drug ingredient over an identi- amounts of the same active drug ingredient in the
cal dosing period. same dosage form and route of administration, and
Pharmaceutical substitution: The process of dis- (b) meet compendial or other applicable standards of
pensing a pharmaceutical alternative for the prescribed strength, quality, purity, and identity; (3) they are
drug product. For example, ampicillin suspension is bioequivalent in that (a) they do not present a known
dispensed in place of ampicillin capsules, or tetracy- or potential bioequivalence problem, and they meet
cline hydrochloride is dispensed in place of tetracy- an acceptable in vitro standard, or (b) if they do pres-
cline phosphate. Pharmaceutical substitution generally ent such a known or potential problem, they are
requires the physician’s approval. shown to meet an appropriate bioequivalence stan-
Reference listed drug: The reference listed drug dard; (4) they are adequately labeled; and (5) they
(RLD) is identified by the FDA as the drug product are manufactured in compliance with Current
on which an applicant relies when seeking approval Good Manufacturing Practice regulations. The FDA
of an ANDA. The RLD is generally the brand-name believes that products classified as therapeutically
drug that has a full NDA. The FDA designates a equivalent can be substituted with the full expecta-
single RLD as the standard to which all generic ver- tion that the substituted product will produce the
sions must be shown to be bioequivalent. The FDA same clinical effect and safety profile as the pre-
hopes to avoid possible significant variations among scribed product.
generic drugs and their brand-name counterparts. Therapeutic substitution: The process of dispens-
Such variations could result if generic drugs were ing a therapeutic alternative in place of the pre-
compared to different RLDs. scribed drug product. For example, amoxicillin is
Therapeutic alternatives: Drug products contain- dispensed instead of ampicillin or ibuprofen is dis-
ing different active ingredients that are indicated for pensed instead of naproxen. Therapeutic substitution
the same therapeutic or clinical objectives. Active can also occur when one NDA-approved drug is
ingredients in therapeutic alternatives are from the substituted for the same drug that has been approved
same pharmacologic class and are expected to have by a different NDA, for example, the substitution of
the same therapeutic effect when administered to Nicoderm (nicotine transdermal system) for Nicotrol
patients for such condition of use. For example, ibu- (nicotine transdermal system).
profen is given instead of aspirin; cimetidine may be
given instead of ranitidine.
Therapeutic equivalents: Drug products are con- Frequently Asked Questions
sidered to be therapeutic equivalents only if they are »»Can pharmaceutic equivalent drug products that are
pharmaceutical equivalents and if they can be not bioequivalent have similar clinical efficacy?
expected to have the same clinical effect and safety
»»What is the difference between generic substitution
profile when administered to patients under the con- and therapeutic substitution?
ditions specified in the labeling. The FDA classifies
520 Chapter 16
CHAPTER SUMMARY
Drug product performance may be defined as the healthy volunteers. Bioequivalence is generally deter-
release of the drug substance from the drug product mined if the 90% confidence intervals for Cmax and
leading to bioavailability of the drug substance. AUC fall within 80%–125% of the reference listed
Bioequivalence is a measure of comparative drug drug based on log transformation of the data. Food
product performance and relates the quality of a drug intervention or food effect studies are generally con-
product to clinical safety and efficacy. The absolute ducted using meal conditions that are expected to
availability of drug is the systemic availability of a provide the greatest effects on GI physiology so that
drug after extravascular administration (eg, oral, rectal, systemic drug availability is maximally affected. The
transdermal, subcutaneous) compared to IV dosing, Biopharmaceutics Classification System (BCS) is
whereas relative bioavailability compares the bioavail- based on the solubility, permeability, and dissolution
ability of a drug from two or more drug products. The characteristics of the drug. However, systemic drug
most direct method to assess drug bioavailability is to bioavailability may also be affected by transporters in
determine the rate and extent of systemic drug absorp- the GI tract, hepatic clearance, GI transit and motility,
tion by measurement of the active drug concentrations and the contents of the GI tract.
in plasma. The main pharmacokinetic parameters, Drug product selection and generic substitution
Cmax and AUC, are used to determine bioequivalence. are important responsibilities of the pharmacist. A
However, other pharmacokinetic parameters such as listing of approved drug products of generic drug
tmax and elimination t½ should also be assessed. The products that may be safely substituted is available
most common statistical design for bioequivalence in Approved Drug Products with Therapeutic
studies is the two-way, crossover design in normal Equivalence Evaluations (Orange Book).
LEARNING QUESTIONS
1. An antibiotic was formulated into two different Each drug product was given in the same dose
oral dosage forms, A and B. Biopharmaceutic as the other. Explain how the various possible
studies revealed different antibiotic blood level formulation factors could have caused the dif-
curves for each drug product (Fig. 16-18). ferences in blood levels. Give examples where
possible. How would the corresponding urinary
drug excretion curves relate to the plasma
level–time curves?
2. Assume that you have just made a new for-
A mulation of acetaminophen. Design a proto-
col to compare your drug product against the
acetaminophen drug products on the market.
MEC What criteria would you use for proof of
bioequivalence for your new formulation?
B How would you determine if the acetamino-
phen was completely (100%) systemically
absorbed?
0 1 2 3 4 5 3. The data in Table 16-22 represent the average
Time findings in antibiotic plasma samples taken
FIGURE 1618 Blood level curves for two different oral from 10 humans (average weight 70 kg), tabu-
dosage forms of a hypothetical antibiotic. lated in a 4-way crossover design.
Blood level
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 521
TABLE 1622 Comparison of Plasma Concentrations of Antibiotic, as Related to Dosage Form
and Time
Plasma Concentration (lg/mL)
IV Solution Oral Solution Oral Tablet Oral Capsule
Time after Dose (h) (2 mg/kg) (10 mg/kg) (10 mg/kg) (10 mg/kg)
0.5 5.94 23.4 13.2 18.7
1.0 5.30 26.6 18.0 21.3
1.5 4.72 25.2 19.0 20.1
2.0 4.21 22.8 18.3 18.2
3.0 3.34 18.2 15.4 14.6
4.0 2.66 14.5 12.5 11.6
6.0 1.68 9.14 7.92 7.31
8.0 1.06 5.77 5.00 4.61
10.0 0.67 3.64 3.16 2.91
12.0 0.42 2.30 1.99 1.83
µg
AUC × h 9 0
2 . 1
mL
45.0 116.0 116.0
a. Which of the four drug products in one-compartment open model with first-order
Table 16-22 would be preferred as a refer- absorption and first-order elimination:
ence standard for the determination of rela- ka k
D →D V →
GI B D
tive bioavailability? Why?
b. From which oral drug product is the drug The drug was given in a single oral dose
absorbed more rapidly? of 250 mg to a group of college students
c. What is the absolute bioavailability of the 21–29 years of age. Mean body weight was
drug from the oral solution? 60 kg. Samples of blood were obtained at various
d. What is the relative bioavailability of the time intervals after the administration of the drug,
drug from the oral tablet compared to the and the plasma fractions were analyzed for active
reference standard? drug. The data are summarized in Table 16-23.
e. From the data in Table 16-15, determine: a. The minimum effective concentration of
(i) Apparent VD Aphrodisia in plasma is 2.3 mg/mL. What is
(ii) Elimination t1/2 the onset time of this drug?
(iii) First-order elimination rate constant k b. The minimum effective concentration of
(iv) Total body clearance Aphrodisia in plasma is 2.3 mg/mL. What is
f. From the data above, graph the cumulative the duration of activity of this drug?
urinary excretion curves that would correspond c. What is the elimination half-life of Aphrodi-
to the plasma concentration–time curves. sia in college students?
4. Aphrodisia is a new drug manufactured by the d. What is the time for peak drug concentration
Venus Drug Company. When tested in humans, (tmax) of Aphrodisia?
the pharmacokinetics of the drug assumes a e. What is the peak drug concentration (Cmax)?
522 Chapter 16
TABLE 1623 Data Summary of Active Drug a. What is the absolute bioavailability of the
Concentration in Plasma Fractions drug from the tablet?
b. What is the relative bioavailability of the
Time (h) Cp (lg/mL) Time (h) Cp (lg/mL)
capsule compared to the oral solution?
0 0 12 3.02 7. According to the prescribing information for
1 1.88 18 1.86 cimetidine (Tagamet®), following IV or IM
administration, 75% of the drug is recovered
2 3.05 24 1.12
from the urine after 24 hours as the parent com-
3 3.74 36 0.40 pound. Following a single oral dose, 48% of the
5 4.21 48 0.14 drug is recovered from the urine after 24 hours
as the parent compound. From this information,
7 4.08 60 0.05
determine what fraction of the drug is absorbed
9 3.70 72 0.02 systemically from an oral dose after 24 hours.
8. Define bioequivalence requirement. Why does
the FDA require a bioequivalence requirement
f. Assuming that the drug is 100% sys-
for the manufacture of a generic drug product?
temically available (ie, fraction of drug
9. Why can we use the time for peak drug
absorbed equals unity), what is the AUC for
concentration (t
Aphrodisia? max) in a bioequivalence study
for an estimate of the rate of drug absorption,
5. You wish to do a bioequivalence study on three
rather than calculating the ka?different formulations of the same active drug.
10. Ten male volunteers (18–26 years of age)
Lay out a Latin-square design for the proper
weighing an average of 73 kg were given either
sequencing of these drug products in six normal,
4 tablets each containing 250 mg of drug (drug
healthy volunteers. What is the main reason for
product A) or 1 tablet containing 1000 mg of
using a crossover design in a bioequivalence
drug (drug product B). Blood levels of the drug
study? What is meant by a “random” population?
were obtained and the data are summarized in
6. Four different drug products containing the
Table 16-25.
same antibiotic were given to 12 volunteer
a. State a possible reason for the difference in
adult males (age 19–28 years, average weight
the time for peak drug concentration (t
73 kg) in a 4-way crossover design. The vol- max,A)
after drug product A compared to the t
unteers fasted for 12 hours prior to taking the max,B
after drug product B. (Assume that all the
drug product. Urine samples were collected up
tablets were made from the same formula-
to 72 hours after the administration of the drug
tion—ie, the drug is in the same particle
to obtain the maximum urinary drug excretion,
size, same salt form, same excipients, and
D∞ . The data are presented in Table 16-24.
u same ratio of excipients to active drug.)
b. Draw a graph relating the cumulative
TABLE 1624 Urinary Drug Excretion Data amount of drug excreted in urine of patients
Summary given drug product A compared to the
cumulative drug excreted in urine after drug
Cumulative Urinary
Dose Drug Excretion product B. Label axes.
Drug Product (mg/kg) 0–72 h c. In a second study using the same 10 male
volunteers, a 125-mg dose of the drug was
IV solution 0.2 20
given by IV bolus and the AUC was com-
Oral solution 4 380 puted as 20 mg·h/mL. Calculate the fraction
Oral tablet 4 340 of drug systemically absorbed from drug
product B (1 × 1000-mg) tablet using the
Oral capsule 4 360 data in Table 16-25.
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 523
TABLE 1625 Blood Level Data Summary for Two Drug Products
Drug Product
A, 4 × 250-mg B, 1000-mg
Kinetic Variable Unit Tablet Tablet Statistic
Time for peak drug concentration (range) h 1.3 1.8 p < .05
(0.7–1.5) (1.5–2.2)
Peak concentration (range) mg/mL 53 47 p < .05
(46–58) (42–51)
AUC (range) mg · h/mL 118 103 NS
(98–125) (90–120)
t1/2 h 3.2 3.8 NS
(2.5–3.8) (2.9–4.3)
11. After performing a bioequivalence test com- 180 mL of water. Food intake was allowed at
paring a generic drug product to a brand-name 5 hours postdose. Blood samples (10 mL) were
drug product, it was observed that the generic taken just before the dose and periodically after
drug product had greater bioavailability than dosing. The serum fraction was separated from
the brand-name drug product. the blood and analyzed for tolazamide by high-
a. Would you approve marketing the generic pressure liquid chromatography.
drug product, claiming it was superior to the Data Analysis: Serum data were analyzed by
brand-name drug product? a digital computer program using a regression
b. Would you expect identical pharmacody- analysis and by the percent of drug unabsorbed
namic responses to both drug products? by the method of Wagner and Nelson (1963).
c. What therapeutic problem might arise in AUC was determined by the trapezoidal rule
using the generic drug product that might and an analysis of variance was determined by
not occur when using the brand-name drug Tukey’s method.
product? a. Why was a Latin-square crossover design
12. The following study is from Welling et al (1982): used in this study?
Tolazamide Formulations: Four tolazamide b. Why were the subjects fasted before being
tablet formulations were selected for this study. given the tolazamide tablets?
The tablet formulations were labeled A, B, C, c. Why did the authors use the Wagner–Nelson
and D. Disintegration and dissolution tests were method rather than the Loo–Riegelman method
performed by standard USP-23 procedures. for measuring the amount of drug absorbed?
Subjects: Twenty healthy adult male volunteers d. From the data in Table 16-26 only, from
between the ages of 18 and 38 years (mean, which tablet formulation would you expect
26 years) and weighing between 61.4 and the highest bioavailability? Why?
95.5 kg (mean, 74.5 kg) were selected for the e. From the data in Table 16-26, did the disin-
study. The subjects were randomly assigned tegration times correlate with the dissolution
to four groups of five each. The 4 treatments times? Why?
were administered according to 4 × 4 Latin- f. Do the data in Table 16-27 appear to corre-
square design. Each treatment was separated by late with the data in Table 16-26? Why?
1-week intervals. All subjects fasted overnight g. Draw the expected cumulative urinary excre-
before receiving the tolazamide tablet the tion–time curve for formulations A and B.
following morning. The tablet was given with Label axes and identify each curve.
524 Chapter 16
TABLE 1626 Disintegration Times and h. Assuming formulation A is the reference
Dissolution Rates of Tolazamide Tabletsa formulation, what is the relative bioavailabil-
ity of formulation D?
Mean Disinte-
gration Timeb Percent Dissolved i. Using the data in Table 16-27 for formula-
Tablet min (Range) in 30 minc (Range) tion A, calculate the elimination half-life
(t1/2) for tolazamide.
A 3.8 (3.0–4.0) 103.9 (100.5–106.3)
13. If in vitro drug dissolution and/or release stud-
B 2.2 (1.8–2.5) 10.9 (9.3–13.5) ies for an oral solid dosage form (eg, tablet)
C 2.3 (2.0–2.5) 31.6 (26.4–37.2) does not correlate with the bioavailability of
the drug in vivo, why should the pharmaceuti-
D 26.5 (22.5–30.5) 29.7 (20.8–38.4) cal manufacturer continue to perform in vitro
aN = 6. release studies for each production batch of the
bBy the method of USP-23. solid dosage form?
cDissolution rates in pH 7.6 buffer.
From Welling et al (1982), with permission.
TABLE 1627 Mean Tolazamide Concentrationsa in Serum
Treatment (lg/mL)
Time (h) A B C D Statisticb
0 10.8 ± 7.4 1.3 ± 1.4 1.8 ± 1.9 3.5 ± 2.6
ADCB
1 20.5 ± 7.3 2.8 ± 2.8 5.4 ± 4.8 13.5 ± 6.6
ADCB
3 23.9 ± 5.3 4.4 ± 4.3 9.8 ± 5.6 20.0 ± 6.4
ADCB
4 25.4 ± 5.2 5.7 ± 4.1 13.6 ± 5.3 22.0 ± 5.4
ADCB
5 24.1 ± 6.3 6.6 ± 4.0 15.1 ± 4.7 22.6 ± 5.0
ADCB
6 19.9 ± 5.9 6.8 ± 3.4 14.3 ± 3.9 19.7 ± 4.7
ADCB
8 15.2 ± 5.5 6.6 ± 3.2 12.8 ± 4.1 14.6 ± 4.2
ADCB
12 8.8 ± 4.8 5.5 ± 3.2 9.1 ± 4.0 8.5 ± 4.1
CADB
16 5.6 ± 3.8 4.6 ± 3.3 6.4 ± 3.9 5.4 ± 3.1
CADB
24 2.7 ± 2.4 3.1 ± 2.6 3.1 ± 3.3 2.4 ± 1.8
CBAD
Cmax, mg/mLc 27.8 ± 5.3 7.7 ± 4.1 16.4 ± 4.4 24.0 ± 4.5
ADCB
tmax, hd 3.3 ± 0.9 7.0 ± 2.2 5.4 ± 2.0 4.0 ± 0.9
BCDA
AUC0–24, mg h/mLe 260 ± 81 112 ± 63 193 ± 70 231 ± 67
ADCB
aConcentrations ± 1 SD, n = 20.
bFor explanation see text.
cMaximum concentration of tolazamide in serum.
dTime of maximum concentration.
eArea under the 0–24-h serum tolazamide concentration curve calculated by trapezoidal rule.
From Welling et al (1982), with permission.
Drug Product Performance, In Vivo: Bioavailability and Bioequivalence 525
14. Is it possible for two pharmaceutically equiva- acceptable for proving that two drug prod-
lent solid dosage forms containing different ucts are bioequivalent?
inactive ingredients (ie, excipients) to demon- b. Are pharmacokinetic models needed in the
strate bioequivalence in vivo even though these evaluation of bioequivalence?
drug products demonstrate differences in drug c. Is it necessary to use a pharmacokinetic
dissolution tests in vitro? model to completely describe the plasma
15. For bioequivalence studies, tmax, Cmax, and drug concentration–time curve for the deter-
AUC, along with an appropriate statistical mination of tmax, Cmax, and AUC?
analysis, are the parameters generally used to d. Why are log-transformed data used for the
demonstrate the bioequivalence of two similar statistical evaluation of bioequivalence?
drug products containing the same active drug. e. What is an add-on study?
a. Why are the parameters tmax, Cmax, and AUC
ANSWERS
Frequently Asked Questions example, for Period 1, half the subjects receive
treatment A, brand product, and the other half of the
Why are preclinical animal toxicology studies and subjects receive treatment B, generic product.
clinical efficacy drug studies in human subjects not
required by the FDA to approve a generic drug prod- Why does the FDA require a food intervention (food-
uct as a therapeutic equivalent to the brand-name effect) study for generic drug products before grant-
drug product? ing approval?
• Preclinical animal toxicology and clinical efficacy • Manufacturers are required to perform a food-in-
studies were performed on the marketed brand tervention bioavailability study on all drugs whose
drug product as part of the New Drug Application bioavailability is known to be affected by food. In
(NDA) prior to FDA approval. These studies do addition, a food-intervention bioavailability study
not have to be repeated for the generic bioequiva- is required on all modified-release products since
lent drug product. The manufacturer of the generic (1) the modified-release formulation (eg, enteric
drug product must submit an Abbreviated New coating, sustained-release coating) may be af-
Drug Application (ANDA) to the FDA, demon- fected by the presence of food and (2) modified-
strating that the generic drug product is a thera- release products have a greater potential to be af-
peutic equivalent (see definitions in Chapter 15) to fected by food due to their longer residence time
the brand drug product. in the gastrointestinal tract and changes in gastro-
intestinal motility.
What do sequence, washout period, and period mean
in a crossover bioavailability study? What type of bioequivalence studies are required for
• drugs that are not systemically absorbed or for those
The sequence is the order in which the drug prod-
drugs in which the Cmax and AUC cannot be measured
ucts (ie, treatments) are given (eg, brand product fol-
in the plasma?
lowed by generic product or vice versa). Sequence
is important to prevent any bias due to the order of • If the drug is not absorbed systemically from the
the treatments in the study. The term washout re- drug product, a surrogate marker must be used as a
fers to the time for total elimination of the dose. The measure of bioequivalence. This surrogate marker
time for washout is determined by the elimination may be a pharmacodynamic effect or, as in the
half-life of the drug. Period refers to the drug-dosing case of cholestyramine resin, the binding capacity
day on which the drug is given to the subjects. For for bile acids in vitro.
526 Chapter 16
Learning Questions c. 8.75 hours
d. 5 hours
3. a. Oral solution: The drug is in the most bio- e. 4.21 mg/mL
available form. f. 77.98 mg h/mL
b. Oral solution: Same reason as above.
c. Absolute bioavailability 5. Drug Product
[AUC]soln /dose
Subject Period 1 Period 2 Week 3
soln
=
[AUC]IV /dose IV 1 A B C
145/10 2 B C A
= = 1.0
29/2 3 C A B
4 A C B
d. Relative bioavailability
5 C B A
[AUC]tab /dosetab
= 6 B A C
[AUC]
soln /dosesoln
6. a. Absolute bioavailability
116/10
= = 0.80
145/10 D∞
= u,PO /dosePO 340/4
=
D∞ /dose 20/0.2
0 u,IV IV
e. (1) Cp = 6.67 µg/mL
= 0.85 or 85%
(by extrapolation of IV curve)
b. Relative bioavailability
2000 µg/kg
VD = µ = 300 mL/kg
6.67 g/mL D∞
ucap /dosecap 360/4
= =
(2) t1/2 = 3.01 h D∞ /dose 380/4
usoln sol
(3) k = 0.23 h−1
= 0.947 or 94.7%
(4) ClT = kVD = 69 m/kg·h
7. The fraction of drug absorbed systemically is
4. Plot the data on both rectangular and semi-
the absolute bioavailability.
log graph paper. The following answers were
obtained from estimates from the plotted Fraction of drug absorbed
plasma level–time curves. More exact answers % of dose excreted after PO
may be obtained mathematically by substitution =
% of dose excreted after IV
into the proper formulas.
a. 1.37 hours 48%
= = 0.64
b. 13.6 hours 75%
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Biopharmaceutical
17 Aspects of the Active
Pharmaceutical Ingredient
and Pharmaceutical
Equivalence
Changquan Calvin Sun, Leon Shargel, and
Andrew BC Yu
Chapter Objectives INTRODUCTION
»» Define active pharmaceutical In order to bring a new drug to the market, a company must submit
ingredient1 (API) and drug a new drug application (NDA) to the FDA for review and approval.
product (finished dosage form). Regulatory approval is based on evidence that establishes the
»» Define pharmaceutical safety and efficacy of the new drug product through one or more
equivalence (PE) and therapeutic clinical trials (FDA, cited June 5, 2014). The development of a
equivalence (TE). new drug, from discovery to entering the market, is a lengthy and
expensive process. These clinical studies are typically performed
»» Describe the physical and
by a large pharmaceutical company known as the innovator com-
biopharmaceutical properties of
pany. The innovator company patents the new drug and gives it a
API important in the design and
brand name. The brand drug product is available from only one
performance of drug products.
manufacturer until patent expiration. These drug products are also
»» Discuss why physical and known as single-source drugs, which are marketed at a high price,
biopharmaceutical properties a practice that allows the company to recover the costs in develop-
of the API and the drug product ment and to make a profit. The patents are critical for encouraging
are interrelated and important innovation that is needed for developing new drugs to effectively
in drug product design and treat diseases. Once the patent expires, other companies can make
performance. and market the generic versions of the brand drug product after
»» Describe the main methods gaining approval for marketing by a regulatory agency through an
used to test (PE) of the active Abbreviated New Drug Application (ANDA) process, which pres-
ingredient (API) or the dosage ents a substantially lower barrier than the NDA process (Fig. 17-1).
form (drug product). At that point, the drug becomes a multisource drug, provided the
generic drug products contain the same active pharmaceutical
»» Explain the relationship of ingredient (API) in the same dosage form and given by the same
PE, bioequivalence (BE), and route of administration (Chapter 16). Through market competition,
therapeutic equivalence (TE). the price of a multisource drug is significantly lower than the sin-
»» Explain whether a generic drug gle-source brand drug. It was estimated that the substitution of for
product that is not an exact PE brand-name drugs by generics saved buyers $8–10 billion dollars
can be TE.
1The active pharmaceutical ingredient (API) is also referred to as the drug substance.
Both drug substance and API will be used interchangeably in this chapter.
529
530 Chapter 17
»» Explain why a generic drug Drug product
product with identical PE BE Generic drug
may not lead to equivalent product (ANDA)
pharmacokinetic and PE BE studies
Innovator
pharmacodynamic performance. (NDA)
Brand drug
product (NDA)
clinical studies
Drug molecule
FIGURE 171 An illustration of the different barriers that must be over-
come to gain the approval of a new drug product through either New Drug
Application (NDA) or Abbreviated New Drug Application (ANDA) approval
processes. BE = bioequivalence, PE = pharmaceutical equivalence.
in the US in 1994 (Cook et al, 1998). This number is undoubtedly
much higher today. This makes the drug more readily affordable to
the general public. The competition of generic drug products
reduces global healthcare costs and motivates brand name compa-
nies to sustain their business through more innovations. Generic
drug products are especially important for countries where innova-
tor drug products are not available. Therefore, a balance must be
reached to both encourage innovation by brand name companies and
curb costs in drug purchasing through generic drugs competition.
The safety and efficacy of a generic drug product is established
by demonstrating that the generic drug product is a therapeutic
equivalent (TE) to the branded or innovator drug product (see
Chapter 16). Under the current ANDA process for approval of
generic drug products, TE of a generic drug product is assumed if
the following conditions are met:
• They are approved as safe and effective.
• They are pharmaceutical equivalents.
• They are bioequivalent in that (a) they do not present a known
or potential bioequivalence problem, and they meet an accept-
able in vitro standard, or (b) if they do present such a known or
potential problem, they are shown to meet an appropriate bio-
equivalence standard.
• They are adequately labeled.
• They are manufactured in compliance with Current Good Manu-
facturing Practice regulations.
Among the list of criteria, the requirements of pharmaceuti-
cally equivalent (PE) and bioequivalent (BE) to the innovator drug
product are most crucial for a generic drug product to be considered
as being therapeutically equivalent (TE) to the innovator drug prod-
uct (Fig. 17-2) (FDA Guidance for Industry, 2003). The substitution
of innovator drug products with TE generic drug products by a
Biopharmaceutical Aspects of the Active Pharmaceutical Ingredient and Pharmaceutical Equivalence 531
Pharmaceutical Bioequivalence Therapeutic
+ =
equivalence (PE) (BE) equivalence (TE)
FIGURE 172 The relationship between pharmaceutical equivalence, bioequivalence, and therapeutic equivalence in the cur-
rent regulatory framework.
pharmacist is allowed without the permission of the applicable (CFR Part 320, 2013). However, in the
prescriber. The FDA believes that products classified cases of modified-release dosage forms, such as a
as therapeutically equivalent can be substituted with transdermal drug delivery product, which require a
the full expectation that the substituted product will reservoir or overage, and prefilled syringes, which
produce the same clinical effect and safety profile as require residual volume, drug content may vary as
the prescribed product. long as the delivered amount of drug is identical to
Although the cost-saving advantage of generic the innovator drug product. Different salt forms or
substitution is obvious, the absence of direct clinical prodrugs of the same API do not qualify as being
studies in patients leads to a lingering concern about identical under this definition by the FDA. Therefore,
efficacy of generic drug products. Patients often ask, strict criteria on API in a drug product must be met in
“Are they [generic drugs] really as safe and effica- order to be qualified as a pharmaceutical equivalent.
cious as the innovator drug products?” To answer this Pharmaceutically equivalent drug products may
question, the concepts of PE and BE must be care- contain different inactive ingredients, or excipients, for
fully examined.2,3 example, colorant, flavor, and preservative. They may
contain different amounts of impurities within an
Frequently Asked Questions allowable range. This flexibility in compositions of the
»»If two APIs are pharmaceutical equivalents, can we drug product sometimes, though rarely, leads to unde-
assume that these two APIs are also identical? sirable consequences on the therapeutic performance
as we will discuss later. In addition, pharmaceutically
»»Can drug products that are not pharmaceutical equivalent drug products may differ in characteristics
equivalents be bioequivalent in patients?
such as shape, release mechanism, scoring (for tab-
lets), packaging, and even labeling to some extent.
Strictly speaking, only identical drug products
Pharmaceutical Equivalents
are truly bioequivalent and therapeutically equivalent.
For generic drug products to be pharmaceutical However, for practical reasons, two drug products are
equivalents, they must be identical dosage forms that generally viewed as bioequivalent (BE), under the
contain identical amounts of the chemically identical current FDA policies, when they do not significantly
API. Pharmaceutical equivalents deliver identical differ in the rate and extent of the API (or its active
amounts of the API over the identical dosing period. moiety) reaching the site of drug action when admin-
They must meet the identical compendial or other istered at the same molar dose and under similar
applicable standards on potency, content uniformity, conditions in an appropriately designed study (see
disintegration times, and dissolution rates where Chapter 16). If the rate of a product is purposely
modified, such as certain extended-release dosage
2As noted in Chapter 16, the currently marketed brand drug forms, but the change in rate does not significantly
product may not have the identical formulation as the original affect the extent of availability of the API to the site of
formulation used in the safety and efcacy studies in patients. drug action (ie, not medically significant for the drug
Brand and generic manufacturers may make changes in the to work), they may still be considered as bioequiva-
formulation after approval. Both brand and generic manufactures
lent, provided such change is reflected in the labeling
may use BE studies to demonstrate that the change in formulation
or manufacturing process did not change the BE of the product. and it does not affect the effective drug concentration
3Denitions appear both in Chapter 16 and at the end of this in body on chronic use. Some of the issues concerning
chapter. pharmaceutical equivalence are listed in Table 17-1.
532 Chapter 17
TABLE 171 Issues in Establishing Pharmaceutical Equivalence of the API and Drug Product
Active Pharmaceutical
Ingredient (API) Comments
Particle size Particle size differences can lead to differences in dissolution rates and differences in bulk density.
In solution, the API is PE. However, particle size is important in suspensions and can cause a prob-
lem in dissolution. In suspensions, PE can be problematic.
Polymorph Different crystalline forms and also amorphous API may have different dissolution rates. However,
in solution the API is PE. In the case of an IV solution made with an API containing a polymorphic
form impurity, after initial solubilization, the API may precipitate out during its product cycle.
Long-term stability of this solution may be a problem.
Hydrate/Anhydrous Although differences in the water of hydration, in solution the API is PE. There may be dissolu-
tion rate different between different hydrates and anhydrous forms of the API. Different water
contents in hydrates and anhydrous forms affect API potency.
Impurities PE may be synthesized using different synthetic pathways, leading to differences in impurities.
Different purification methods can also lead to residual solvents and different impurities that
need to be qualified depending on whether these are above or below threshold level.
Stability Crystal defects as a result of different methods of synthesis and purification may affect the shelf
life of the drug substance. Amorphous forms often degrade more rapidly for many APIs.
Thus, stability is a PE issue, which may lead to a change in efficacy of the API due to more rapid
decomposition.
Racemic/Chirality Racemic APIs may be PE if the ratio of isomers is the same in both products. However, omepra-
zole (Prilosec) may not be considered as a PE to esomeprazole (Nexium), the S-isomer of omepra-
zole, since different isomers may have different pharmacodynamic activity.
Biotechnology-derived Biotechnology-derived products include proteins and peptides that need to be both pharmaceu-
drugs tical equivalent to the innovator drug and have equivalent pharmacodynamic activity. Addition-
ally, differences in impurities may lead to immunogenicity problems (see Chapter 20).
Dosage Form
(Drug Product) Comments
Drug product delivery Transdermal systems and oral ER drug products may have different drug delivery systems but are
system considered PE to their respective brand drug product provided they meet the additional require-
ments for therapeutic equivalence.
Size, shape, and other Differences in physical characteristics (eg, size and shape of the tablet or capsule) are not strictly
physical attributes of a PE issue but may affect patient compliance and acceptability of medication regimens, could
generic tablets and lead to medication errors, and could have different GI transit times.
capsules
Excipients Generic and brand drug products may have different excipients and still be considered PE pro-
vided they meet the requirements for therapeutic equivalence.
Sterile solutions The ingredients in many sterile drug solutions (eg, ophthalmic solutions) must be the same, both
qualitative and quantitative.
Overage Overage is generally disallowed unless justified by data. Transdermal products using a reservoir
system may have an overage to maintain the desired bioavailability.
Liposomes and emulsions Liposomes and emulsions are dispersed systems with two or more liquid phases, generally
composed of lipid and aqueous phases. PE is difficult to establish for these drug products. For
example, there may be differences in drug concentration in the lipid phase and in the aqueous
phase.
(Continued)
Biopharmaceutical Aspects of the Active Pharmaceutical Ingredient and Pharmaceutical Equivalence 533
TABLE 171 Issues in Establishing Pharmaceutical Equivalence of the API and Drug Product
(Continued)
Active Pharmaceutical
Ingredient (API) Comments
Inhalation products Different designs in inhalation devices may deliver drugs with different particle size, plume
geometry, etc, which may produce different clinical efficacy. Certain inhalation products may be
considered PE provided they meet the requirements for therapeutic equivalence.
Manufacturing process The manufacturing process can affect drug product performance. For example, an increase in
compaction may produce a harder tablet that disintegrates more slowly, thereby releasing the
drug more slowly (see also Chapter 18).
PHARMACEUTICAL ALTERNATIVES that is otherwise pharmaceutically equivalent to the
innovator products. Cefuroxime is an antimicrobial
Drug products that contain the same therapeutic prophylaxis that is used as a single-dose IV injection
moiety or its precursor but differ in dosage form, in patients undergoing coronary artery bypass graft-
API amount, or chemical structure (different salt ing surgery in the operating room immediately
forms, prodrugs, complexes, etc) are considered before the induction of general anesthesia. When a
“pharmaceutical alternatives” by the FDA as long as brand name drug product was used, a single dose of
they meet applicable standards. Therefore, if the API 3 g of cefuroxime generally achieves and maintains
is identical, an 80-mg drug tablet is a pharmaceutical serum levels sufficient to prevent infections during
alternative to a 100-mg drug product. Tablet prod- the surgery. Occasionally, a 0.75 g dose is adminis-
ucts containing different chemical form of an API, tered 12 hours after the surgery to prevent infections.
for example, a prodrug or a different salt, are phar- However, when a generic cefuroxime was used to
maceutical alternatives regardless whether or not the substitute the brand drug for cost saving, an increased
molar dose is the same. In addition, the route of frequency of post-surgical infections occurred
administration should be the same for two products (Fujimura et al, 2011). Some patients had to be
to qualify as pharmaceutical alternatives. For exam- admitted to the surgical intensive care unit. When the
ple, an IV injectible drug product cannot be a phar- brand name drug product was again used, new cases
maceutical alternative to an oral tablet. Pharmaceutical of severe postoperative infection stopped. When the
alternatives may or may not be bioequivalent or generic drug product was reintroduced, higher inci-
therapeutically equivalent with the innovator drug dence of postoperative infections again occurred.
product. In addition, capsule and tablets containing Subsequent investigation confirmed that, although
the same API, for example, quinidine sulfate 200-mg both drug products are chemically identical, the
tablets versus quinidine sulfate 200-mg capsules are generic product hydrolyzed very quickly to render it
considered as pharmaceutical alternatives even if the less effective by the time it is administered (Fujimura
products are bioequivalent. et al, 2011). Although reasons that caused the poor
stability in the generic product were not given, it is
Stability-Related Therapeutic likely that the differences in formulation and/or
Nonequivalence manufacturing process are responsible.
Generic IV drug products are bioequivalent if they
are pharmaceutically equivalent because their bio- Excipients and Impurities-Related
availability is 100% by the nature of their route of Therapeutic Nonequivalence
administration. However, different drug products Drugs are rarely administered alone. Various excipi-
may have different stability, which can significantly ents, such as binder, solubilizer, stabilizer, preserva-
impact therapeutic performance of a drug product tives, lubricant, diluents, and colorants, are added to
534 Chapter 17
make the final drug product. Sometimes, impurities trihydrate drug substance is a pharmaceutic equivalent
and contaminants are present in the drug product. (PE) to the innovator’ API. A consultant stated further
Unfortunately, the focus of quality control has been that the proposed product has the same chemical for-
traditionally placed on the analysis of drug in the mula, antibacterial activity, potency, and excipients as
product. The recent safety problem with heparin due in the innovator’s drug product. The generic drug
to the contamination by over-sulfated chondroitin product will be marketed in a similar package. A bio-
sulfate, an impurity that is structurally similar to hepa- equivalence study was performed comparing the pro-
rin, is a wakeup call to the scientific community that posed generic drug product to the brand drug product.
impurities must also be considered to ensure thera- The rate and extent of the generic product was found
peutic equivalence or the sameness between two to be within the required BE requirements (see
products (Dodd and Besag, 2009; Vesga et al, 2010). Chapter 16). After submission to the FDA, the prod-
Similarly, although less dramatically, impurities con- uct was rejected by the FDA’s Office of Generic
tained in drugs and excipients, degradation during Drugs. Based on your understanding of the PE defini-
manufacturing and storage, interaction between drug tion, what could be the possible reasons for the FDA
and excipients may also have a negative impact on the not approving this product? (Hint: Consult Table 17-1
safety and efficacy of a drug product. They should be about the potential issues with PE, TE, and BE.)
considered when evaluating whether or not a generic
drug product is therapeutically equivalent to the inno- Solution
vator drug product. In addition, some adverse reac-
Per the definition of PE below, four attributes are
tions may not be evident in a single-dose BE study but
possible sources of failure in PE. The Code of
may show up during chronic use of the drug. Hence,
Federal Regulations (CFR) also defines some prod-
impurities in the drug and excipients must be con-
uct performance criteria, which must be met. PE
trolled to avoid unintended problems in safety and
should NOT be defined subjectively. For clarity, it is
efficacy of generic drug products. It should also be
useful to group the potential issues under those terms
pointed out that the absence of some critical func-
in this chapter with PE heading. Other product
tional excipients or the inappropriate amounts of them
design factors are discussed in Chapter 15.
in a drug product may lead to poor efficacy even if the
Pharmaceutical equivalents (PE) are drug prod-
drug itself is of high quality (Zuluaga et al, 2010).
ucts in identical dosage forms that contain identical
The potential problems mentioned above are true
amounts of the identical active drug ingredient and
for both innovator and generic drug products.
meet the identical compendial or other applicable
However, the innovator drug product has proven its
standard of identity, strength, quality, and purity,
safety and effectiveness through a well-controlled
including potency and, where applicable, content uni-
clinical study. Unless there are major changes in the
formity, disintegration times, and/or dissolution rates.
formulation, quality of drug and excipients, or manu-
Possible sources of pharmaceutical inequivalence:
facturing process, the potential problems related to
excipients and impurities are usually not a concern on 1. Stability is affected by various factors such
the clinical performance of innovator drug products. as residual solvent, reagents, and by-products
(impurities) that are the results of different
methods of chemical synthesis and purification.
PRACTICE PROBLEM 2. Drug substance suppliers may use different
starting materials (SM) during synthesis. The
A generic manufacturer wants to make an amoxicillin starting materials may also have different impu-
suspension, 250 mg/5 mL with identical excipients as rities, depending on the method of crystalliza-
in the brand product. The generic manufacturer pur- tion method used for purification. Generally,
chased the API from a drug supplier who imported impurity profiles are synthetic route dependent,
various grades of amoxicillin trihydrate from different and may not always be detected using the same
countries. The supplier reported that the amoxicillin analytical method as the innovator.
Biopharmaceutical Aspects of the Active Pharmaceutical Ingredient and Pharmaceutical Equivalence 535
3. The stability may not be detected with the BA/ 6. Chirality is important as the same chemical
BE test. However, the FDA requires clinical formula may be structurally different resulting
samples to be retained, and it is possible that in different solubility and/or activity. Note the
the retained samples may fail stability speci- reference to “identical active drug ingredients”
fication later. In addition, content uniformity in the definition. Therefore, d-thyroxine and
may be a quality issue for failure under PE l-thyroxine will not be considered as PE.
defined.
Comment 1: The CFR states that the purity and
identity criteria must be met. Although the CFR Polymorphic Form-Related Therapeutic
does not directly refer to the impurity profile
Nonequivalence
and all the detail drug substance properties,
the comprehensive statements clearly state that For poorly soluble drugs, a change in polymorph
the drug substance, which ends up in the drug form may impact bioavailability. In the FDA’s
product, must perform as intended. definition of pharmaceutical equivalence, poly-
Comment 2: A change in particle size, or morph is not considered. Hence, two products are
crystallinity, during product manufacturing still considered pharmaceutically equivalent even
can result in batch-to-batch or within-batch when different polymorph is used. For patent rea-
variability failure. When this occurs, even an sons, some generic manufacturers seek approval of
objective BE study will not preclude regulatory new products that contain a different polymorph
rejection or product failure. Another important than the brand name product. In that case, the
issue is the content uniformity in the context of potential phase change during manufacture and
the drug substance and the product in a multi- storage will need to be carefully evaluated and
drug source environment. The statistical nature controlled. The potential impact due to polymorph
of this is the recognition of an adequate design form difference can be masked by appropriate for-
for sampling, and the relevance of quality-by- mulation design. In some cases, even difference in
design (QbD) (see Chapter 18), which when drug crystal morphology may lead to different
properly implemented, minimizes the need for bioavailability (Modi et al, 2013). These factors
more testing of factors that affect PE. should be evaluated in the design of generic drug
4. Low level of an unsuspicious trace solvent may product to ensure bioequivalence and therapeutic
change the crystal form, solid state stability of a equivalence.
drug substance.
5. By-products in a drug substance from starting
materials may cause PE issues that affect qual- Particle Size-Related Therapeutic
ity. In some cases toxicity or even carcinoge- Nonequivalence
nicity issues must be considered when different For low-dose tablet products, content uniformity is a
drug sources are used. It is important to note challenge. Even for the brand name product, unin-
that as progress occurs, more efficient synthetic tended particle size variations have an impact on
methods may be discovered for generic drugs. content uniformity in tablet products, especially
The synthetic process may be quite different those manufactured using the direct compression
even though a higher yield may be achieved, process (Rohrs et al, 2006). It is possible that the
the impurity profile should be also acceptable. batch of generic tablets used for BE study meets the
Compendial standards such as the European content uniformity requirement and demonstrates
Pharmacopeia or USP-NF are helpful, but addi- BE with the brand name product. However, some
tional evaluation may be needed. Some of this subsequent batches of the generic tablets fail to meet
information may be in the DMF (drug master the content uniformity requirement and clinical out-
file, or also referred to as master file) provided comes unexpectedly vary. This problem is also faced
by the drug substance supplier. by the brand name drug manufacturers. It can be
536 Chapter 17
minimized if stringent quality control is imple- FORMULATION AND
mented, which is usually the case by the innovator
MANUFACTURING PROCESS
drug companies but not always so by all generic drug
manufacturers. In that case, the uncontrolled generic CHANGES
substitution may occasionally cause unintended
Even for innovator drug products, the marketed prod-
problems in therapeutic performance that negate any
uct may not have been used in the original clinical
cost saving by the generic substitution to the tax pay-
trials that establish its efficacy and safety. In addition,
ers. Besides the potential content uniformity issue,
changes to the formulation, suppliers of excipients,
variations in particle size can also potentially impact
manufacturing process, or manufacturing site may be
bioavailability of poorly soluble drugs because
necessary in order to smoothly manufacture the drug
smaller drug particles correspond to larger surface
product at large scale after the approval. The FDA
area for dissolution and potentially much higher
requires the manufacturer to demonstrate that drug
bioavailability (Jounela et al, 1975). Consequently,
product performance is not affected by these scale-up
the safety and effectiveness of a solid dosage form
and postapproval changes (SUPAC) (FDA, 1995,
drug product may be affected by variations in parti-
1997). It sometimes happens that changes in the for-
cle size of the drug. Therefore, inadequate particle
mulation and manufacturing process for a brand
size control may lead to non-bioequivalence and
name drug product are more than allowed by SUPAC.
poor consistency in clinical performance.
If so, a BE study is required. Compared to the materi-
als that require SUPAC, the differences between a
generic drug product and the products used in the
Bioequivalence of Drugs with clinical trials are likely much more due to different
Multiple Indications formulations and different manufacturing processes.
Hence, the requirement of a BE study for generic
Another interesting point to consider is the validity
products is perhaps a minimum by comparison.
of extrapolation TE in one indication of a drug to
another indication. A generic drug product might
have been clinically shown to be therapeutically SIZE, SHAPE, AND OTHER
equivalent to a brand name product in one indica- PHYSICAL ATTRIBUTES OF GENERIC
tion. In that case, can we conclude that the generic TABLETS AND CAPSULES
drug product is therapeutically equivalent for all
other indications of the drug? The demonstration of Although a generic drug product, such as a tablet or
TE in one population of patients plus the BE in capsule, is a pharmaceutical equivalent and bioequiva-
healthy volunteers is certainly a very strong evi- lent to the brand drug product, generic drug manufac-
dence suggesting TE in other indications. However, turers should consider physical attributes of these
a definitive answer can only be attained through a products to ensure therapeutic equivalence (FDA
clinical study for each indication because different Guidance for Industry, December 2003). There has
characteristics of the drug may be critical for suc- been an increasing concern that differences in physical
cessful clinical outcomes in different patient popu- characteristics (eg, size and shape of the tablet or cap-
lations. For example, a drug may dissolve quickly sule) may affect patient compliance and acceptability
and get absorbed completely in one patient popula- of medication regimens or could lead to medication
tion with a normal pH environment in their GI tract. errors. For example, difficulty in swallowing tablets or
Hence, variation in particle size and formulation capsules can be a problem for many individuals and
does not affect bioavailability. However, the bio- may lead to a variety of adverse events and patient
availability of the same two drug products in the noncompliance with treatment regimens. In addition to
same cancer patients may be very different because possible swallowing difficulty, larger tablets and cap-
of the much slower dissolution of the drug in their sules have been shown to prolong esophageal transit
GI tract, which has a higher pH. time. This can lead to disintegration of the product in
Biopharmaceutical Aspects of the Active Pharmaceutical Ingredient and Pharmaceutical Equivalence 537
the esophagus and/or cause injury to the esophagus, CHANGES TO AN APPROVED NDA
resulting in pain and localized esophagitis and the
OR ANDA
potential for serious sequelae including ulceration.
Studies in humans have also suggested that oval tablets After the approval of a new drug product or generic
may be easier to swallow and have faster esophageal drug product, the manufacturer may make a change
transit times than round tablets of the same weight. to the marketed product (FDA Guidance for
The weight of the tablet or capsule also may affect Industry, April 2004). These changes may include
transit time, with heavier tablets or capsules having changes in the API, changes in the manufacturing
faster transit times compared to similarly sized, lighter process, change in the formulation, scale-up or an
tablets or capsules. Surface area, disintegration time, increase in the batch size of the drug product,
and propensity for swelling when swallowed are addi- change in the manufacturing site, and change in the
tional parameters that can influence esophageal transit container closure system. In many cases, the manu-
time and have the potential to affect the performance facturer may make multiple changes to the drug
of the drug product for its intended use. Consequently, product. For any of these changes, it is important to
these physical attributes should also be considered for assess whether the change has a potential to have an
generic drug products intended to be swallowed intact. adverse effect on the identity, strength, quality,
purity, or potency of a drug product as these factors
may relate to the safety or effectiveness of the drug
Frequently Asked Question product (Table 17-2). The FDA must be notified
whenever a manufacturer makes a change to an
»»How would the shape or size of an oral drug product
affect compliance in an elderly patient? approved product. The reporting requirement for a
change is listed in Table 17-2. The manufacturer
TABLE 172. Changes to an Approved NDA or ANDA
Change Definition FDA Reporting Requirement Example
Major A change that has a substantial Prior Approval Supplement—requires the A move to a different
change potential to have an adverse effect on submission of a supplement and approval manufacturing site for
the identity, strength, quality, purity, by the FDA prior to distribution of the the manufacturer of an
or potency of a drug product as these drug product ER capsule
factors may relate to the safety or effec-
tiveness of the drug product
Moder- A change that has a moderate potential (1) Supplement—Changes Being Effected A change in the manu-
ate to have an adverse effect on the iden- in 30 Days—requires the submission of facturing process for an
change tity, strength, quality, purity, or potency a supplement to FDA at least 30 days IR tablet
of the drug product as these factors before the distribution of the drug prod-
may relate to the safety or effectiveness uct made using the change
of the drug product (2) Supplement—Changes Being
Effected—moderate changes for which
distribution can occur when FDA receives
the supplement
Minor A change that has minimal potential to Annual report—The applicant must A change in an existing
change have an adverse effect on the identity, describe minor changes in its next annual code imprint for a dos-
strength, quality, purity, or potency of report age form. For example,
the drug product as these factors may changing from a
relate to the safety or effectiveness of numeric to alphanu-
the drug product meric code
Source: FDA Guidance for Industry (April 2004). The essence of this guidance has been incorporated into 21 CFR 340.70.
538 Chapter 17
must assess the effects of the change before distribut- (Rodriguez et al, 2010). In this case, the brand name
ing a drug product made with a manufacturing change. oxacillin product was withdrawn from the countries
by its original manufacturer because of a lack of
profit due to the intense competition from generic
Frequently Asked Questions products. This left the patients in the entire region
»»Why do drug manufacturers make changes to an ap- who require oxacillin therapy to face a highly dan-
proved drug product that is currently on the market? gerous consequence in their health. Patients with
»»Should a bioequivalence study be performed every life-threatening infections might die due to ineffec-
time a drug manufacturer makes a change in the tive drug therapy unnoticed by the physician.
formulation of the drug product? Unfortunately, such dismaying situation is also
found in other drugs, such as gentamicin (Zuluaga et
»»Where can we find a list of US products with thera-
al, 2010), cefuroxime (Mastoraki et al, 2008), metro-
peutic equivalence and a discussion of evaluation
nidazole (Agudelo and Vesga 2012), vancomycin
criteria?
(Vesga et al, 2010). For drugs with narrow therapeu-
tical indices, such as some antiepileptic drugs, thera-
peutic nonequivalence have also been reported
How Prevalent Is the Therapeutic (Crawford et al, 2006). For antibiotic drugs, the use
Nonequivalence of a Generic Product? of substandard drug products may have contributed
The assumption of therapeutic equivalence by a to the drug resistance. Other concerns on therapeutic
generic drug product that meets BE requirement is nonequivalence of generic products have been dis-
rarely challenged. For the benefit of all, it is impor- cussed (Dettelbach, 1986; Lamy 1986). In any case,
tant to ask the following questions: “How often is a the assumption of therapeutic equivalence by a bio-
generic product not therapeutically equivalent to a equivalent generic product requires more careful
brand product?” and “If they occur frequently, why examination. The occurrence of therapeutic non-
the TE failures are rarely observed?” Insights useful equivalence of generic products may be much higher
to answering these questions may be gained from than what most people believe.
analyzing one example of nontherapeutic equivalent
vancomycin. A generic injectible vancomycin failed
to treat a liver transplant patient against infection. THE FUTURE OF PHARMACEUTICAL
However, switching to the innovator product led to EQUIVALENCE AND THERAPEUTIC
speedy recovery by the patient (Rodriguez et al, EQUIVALENCE
2009). Had this case been non-life-threatening, the
different bactericidal activities between the generic In light of the emerging evidences pointing out the
and innovator products may have been ignored. A potential difference in therapeutic nonequivalence of
patient that requires longer treatment may be simply generic drug products, suggestions have been made
attributed to differential individual response to a to require clinical evaluations on clinical efficacy of
therapy. The physician may simply switch to a dif- generic products with randomized double-blind com-
ferent kind of antibiotics. On the other hand, a death parative study for each major indication (Fujimura et
of the patient, in this case caused by ineffective al, 2011). Such a requirement, although scientifically
drug therapy, may be simply attributed to the sever- rigorous, effectively stifles the competition that is
ity of the disease where a death is not an unex- critical for bringing down the cost of prescription
pected outcome (Rodriguez et al, 2009). Either drugs. In absence of a predictive in vitro analytical
scenario will conceal the problem in the antibiotic method or a valid animal model, a sensible approach
failure. In another example, several generic oxacil- to this problem is to allow restricted substitution to
lin products do not show similar potency as that of the prescribed drugs, say no more than 50%, while
the innovator product, hence, not bioequivalent. closely monitoring the therapeutic performance by
Those products that do meet BE requirement, how- medical doctors and regulatory authority. Full substi-
ever, lack therapeutic equivalence in an animal model tution by a given generic product is allowed when
Biopharmaceutical Aspects of the Active Pharmaceutical Ingredient and Pharmaceutical Equivalence 539
confidence on its clinical efficacy and safety is estab- typically more complex structure of biological prod-
lished. This approach does not affect the approval ucts and the processes by which such products are
process and the entry of generic drug products to the manufactured. Most biological products are produced
market. However, it does slightly reduce the rate that in a living system such as a microorganism, or plant
generic products completely take over the market, or animal cells, whereas small-molecule drugs are
thus reducing the chance of therapeutic failure, typically manufactured through chemical synthesis
before their clinical safety and efficacy is firmly (FDA Guidance for Industry, 2012a, 2012b).
established. This approach avoids the catastrophic Biosimilar or biosimilarity means that the bio-
failures of substandard drug products while still tak- logical product is highly similar to the reference
ing advantage of the generic competition. product notwithstanding minor differences in clini-
A reason to the documented failures in thera- cally inactive components, and there are no clini-
peutic equivalence of generic products may be attrib- cally meaningful differences between the biological
uted to the empirical nature of drug product product and the reference product in terms of the
development. In absence of a clear understanding in safety, purity, and potency of the product.
the relationship among structure, property, and per- Interchangeable biosimilar drug products
formance (Sun, 2009), each product by a different include the following:
manufacture can be potentially very different.
• The biological product is biosimilar to the refer-
Therefore, a successful BE study may not assure the
ence product.
therapeutic equivalence. Having recognized the
• It can be expected to produce the same clinical
challenge, the way forward would be for the scien-
result as the reference product in any given patient.
tific community, pharmaceutical companies, drug
• For a product administered more than once, the
regulatory agencies (DRAs) worldwide to work
safety and reduced efcacy risks of alternating or
together to advance the science that enables the
switching are not greater than with repeated use of
design of high-quality and stable drug products in a
the reference product.
consistent way. In the short term, DRAs can appro-
priately tighten the BE requirement, at least for types Due to the complexity of these products, the
of products with known TE problems, to minimize FDA intends to consider the totality of the evidence
the occurrence of drug therapy failure due to sub- provided by a sponsor to support a demonstration of
standard generic drug products. In his 1986 editorial, biosimilarity. The FDA recommends that sponsors
Dr. Dettelbach stated, “However, until we institute a use a stepwise approach in their development of
system of evaluating generic drugs in patients, in biosimilar products. Evidence demonstrating bio-
whom therapeutic and pharmacodynamics differ- similarity can include a comparison of the proposed
ences can be of critical importance, we may be play- product and the reference product with respect to
ing a dangerous game” (Dettelbach, 1986). After so structure, function, animal toxicity, human pharma-
many years, his statement still remains largely true. cokinetics (PK) and pharmacodynamics (PD), clini-
cal immunogenicity, and clinical safety and
effectiveness. In addition, the FDA will consider the
BIOSIMILAR DRUG PRODUCTS biosimilar development program, including the man-
ufacturing process.
The Biologics Price Competition and Innovation Act
of 2009 (BPCI Act) amended the Public Health
Service Act (PHS Act) and other statutes to create an §320.1 Definitions (2014 Code of Federal
abbreviated licensure pathway in section 351(k) of Regulation, Title 21)
the PHS Act for biological products shown to be bio- (a) Bioavailability means the rate and extent to
similar to, or interchangeable with, an FDA-licensed which the active ingredient or active moiety is
biological reference product. Biological products can absorbed from a drug product and becomes available
present challenges given the scientific and technical at the site of action. For drug products that are not
complexities that are associated with the larger and intended to be absorbed into the bloodstream,
540 Chapter 17
bioavailability may be assessed by measurements difference in the rate at which the active ingredient
intended to reflect the rate and extent to which the or moiety becomes available at the site of drug
active ingredient or active moiety becomes available action is intentional and is reflected in the proposed
at the site of action. labeling, is not essential to the attainment of effec-
(b) Drug product means a finished dosage form, tive body drug concentrations on chronic use, and is
for example, tablet, capsule, or solution, that con- considered medically insignificant for the drug.
tains the active drug ingredient, generally, but not (f) Bioequivalence requirement means a require-
necessarily, in association with inactive ingredients. ment imposed by the Food and Drug Administration
(c) Pharmaceutical equivalents mean drug for in vitro and/or in vivo testing of specified drug
products in identical dosage forms that contain iden- products, which must be satisfied as a condition of
tical amounts of the identical active drug ingredient, marketing.
that is, the same salt or ester of the same therapeutic (g) Same drug product formulation means the
moiety, or, in the case of modified-release dosage formulation of the drug product submitted for
forms that require a reservoir or overage or such approval and any formulations that have minor dif-
forms as prefilled syringes where residual volume ferences in composition or method of manufacture
may vary, that deliver identical amounts of the active from the formulation submitted for approval, but are
drug ingredient over the identical dosing period; do similar enough to be relevant to the agency’s deter-
not necessarily contain the same inactive ingredi- mination of bioequivalence.
ents; and meet the identical compendial or other [42 FR 1634, Jan. 7, 1977, as amended at 42 FR
applicable standard of identity, strength, quality, and 1648, Jan. 7, 1977; 57 FR 17997, Apr. 28, 1992; 67
purity, including potency and, where applicable, FR 77672, Dec. 19, 2002; 74 FR 2861, Jan. 16,
content uniformity, disintegration times, and/or dis- 2009]. Explanations of related terms are found in the
solution rates. preface in the Orange book.
(d) Pharmaceutical alternatives mean drug
products that contain the identical therapeutic moi-
ety, or its precursor, but not necessarily in the same HISTORICAL PERSPECTIVE
amount or dosage form or as the same salt or ester.
Each such drug product individually meets either the In the last decade, many FDA guidances were devel-
identical or its own respective compendial or other oped to guide the control and manufacturing of API
applicable standard of identity, strength, quality, and that impact PE issues. Many of the guidances were
purity, including potency and, where applicable, withdrawn with the adoption of the ICH quality guid-
content uniformity, disintegration times and/or dis- ances by the EU, Japan, and the United States (Step
solution rates. 4, announced in CFR 2008). The quality (Q) guid-
(e) Bioequivalence means the absence of a sig- ance for API (referred to as drug substance in ICH) is
nificant difference in the rate and extent to which the well discussed in the preamble for Q3A, which fully
active ingredient or active moiety in pharmaceutical discuss API issues in the developed world: impuri-
equivalents or pharmaceutical alternatives becomes ties, by-products, enantiomers, crystallinity, and
available at the site of drug action when adminis- other quality attributes. The issue of degradation
tered at the same molar dose under similar condi- impurities that may still form due to processing in the
tions in an appropriately designed study. Where formulated product is discussed in Q3B (drug prod-
there is an intentional difference in rate (eg, in cer- uct guidance). A series of Q guidances (ich.org) are
tain extended-release dosage forms), certain phar- easily available. As the QbD and progress evolve, the
maceutical equivalents or alternatives may be present regulations of drug source supply will be
considered bioequivalent if there is no significant updated accordingly. Revision of compendial and
difference in the extent to which the active ingredi- compliance policy notification as well as CFRs
ent or moiety from each product becomes available announcement should be frequently consulted. For
at the site of drug action. This applies only if the example: Compliance Policy Guide Sec. 420.300
Biopharmaceutical Aspects of the Active Pharmaceutical Ingredient and Pharmaceutical Equivalence 541
Changes in Compendial Specifications and New Drug impurities that may not be controlled under the drug
Application Supplements; Withdrawal of Guidance. substance guidance. Therefore, in the new ICH guid-
https://www.federalregister.gov/articles/2012 ance (ICH Q3A, 2006), it advises in the preamble that
/08/30/2012-21415/compliance-policy-guide regardless of new or old molecules, any impurities
-sec-420300-changes-in-compendial-specifications- above defined thresholds must be identified; addition-
and-new-drug-application. ally, total impurities must be reported. If impurities are
A Notice by the Food and Drug Administration relatively high with respect to dose, they must be quali-
was posted on August 30, 2012. fied (ie, determined by toxicity studies to be within safe
A pharmacist should recognize that even a level). Consequently, most generic manufacturers tend
compendial grade drug source, manufactured by a to use historically known manufacturing methods with-
new process may potentially form new degradation out introducing new or unknown impurities.
CHAPTER SUMMARY
Pharmaceutical equivalence (PE), along with bio- characteristics such as shape, scoring configuration,
equivalence, is important for establishing therapeutic release mechanisms, packaging, and excipients
equivalence (TE) of generic drug products. PE is also (including colors, flavors, and preservatives). PE is
important for postapproval changes in both brand and more difficult to establish for complex APIs, complex
generic drug products. The determination of PE drug products, or multiple APIs within the drug prod-
depends upon the physical and chemical properties of uct (eg, combination drug product). Biotechnology-
the active pharmaceutical ingredient (API), as well as derived drugs, such as proteins and polypeptides, that
the design and manufacture of the finished dosage are proposed for biosimilar drug products have addi-
form (drug product). For the API, different synthetic tional issues with respect to structure, function, ani-
pathways and purification steps can lead to physical mal toxicity, human pharmacokinetics (PK) and
and chemical differences in the API, including parti- pharmacodynamics (PD), clinical immunogenicity,
cle size, degree of hydration, crystalline form, impu- and clinical safety and effectiveness.
rities, and stability. The drug product can differ in
LEARNING QUESTIONS
1. The reference listed drug marketed by a brand 4. For a generic drug product to be “pharmaceuti-
drug company has a patent on the crystalline cal equivalent” to the innovator drug (or refer-
form of the API. A generic drug manufacturer ence drug product), which of the following is
wants to make a therapeutic equivalent of the true? Explain your answer.
brand drug product using an amorphous form a. API in the generic product must be identical
of the API. Will the generic manufacturer be to the API in the reference drug product.
able to meet the requirements for pharmaceuti- b. It is desirable but not necessary for API to be
cal equivalence and therapeutic equivalence identical in the generic and reference drug
with the amorphous form of the API? products.
2. Why is it more difficult to determine PE for c. Many APIs used in generic products are
biosimilars, such as erythropoietin injection referenced by drug master files and meet
(Procrit) compared to small molecules, such as compendial standards. For these APIs, does
atorvastatin calcium tablets (Lipitor)? it mean generic products are always pharma-
3. Explain why a generic drug products can be a ceutically equivalent to the brand name drug?
pharmaceutical equivalent but not identical to 5. Under what circumstances is particle size distribu-
the brand drug product. tion of API critical for the product performance?
542 Chapter 17
6. Can a generic drug product containing a differ- the literature. This API is supplied by various
ent polymorph of an API be pharmaceutically suppliers with DMFs available. How would
equivalent to an innovator drug product? How a generic manufacturer planning to market a
about if a different salt or cocrystal is used in miconazole vaginal cream ensure that the API
the generic drug product? purchased is safe? Does supplier-designated
7. The drug miconazole may contain benzyl “EP or USP-NF” grade necessarily ensure that
chloride-related impurity/imtermediate that PE is met?
may be potentially genotoxic as reported in
ANSWERS
Frequently Asked Questions • There are many reasons that a manufacturer makes
If two active pharmaceutical ingredients are phar- a change in the formulation. For example, changed
maceutical equivalents, can we assume that these physical properties of API, due to the use of a
two APIs are also identical? more economical API synthesis process, necessi-
• No. The API can differ in particle size, crystal tate a change in the formulation to assure the same
structure, hydrate, impurities, and/or stability (see performance of drug product. A manufacturer may
Table 17-1.) want to enlarge the units manufactured (scale-up),
Can drug products that are not pharmaceutical use new manufacturing equipment, and/or change
equivalents be bioequivalent in patients? the manufacturing site.
• Yes. Capsules and tablets containing the same Should a bioequivalence study be performed
API can be bioequivalent. However, in the United every time a drug manufacturer makes a change in
States, capsules and tablets are pharmaceutical the formulation of the drug product?
alternatives. Extended-release tablets or capsules • If the change in formulation is minor, such as re-
that have different drug release processes can be moval of the color, and the manufacturer can show
bioequivalent in vivo. Tablets containing either the the likelihood that the change would not affect the
API or a salt of the API can be bioequivalent when bioequivalence of the formulation after the minor
absorption is not dissolution limited. change, no bioequivalence study would be needed.
How would the shape or size of an oral drug Where can we find a list of US products with
product affect compliance in an elderly patient? therapeutic equivalence and a discussion of evalua-
• Certain shape, size, or color may discourage the tion criteria?
patient from swallowing the tablet. For many pa- • The publication Approved Drug Products with
tients, tablets containing a 1000 mg of active drug Therapeutic Equivalence Evaluations (the List,
can be difficult to swallow. commonly known as the Orange Book. http://www
Why do drug manufacturers make changes to an .fda.gov/Drugs/DevelopmentApprovalProcess
approved drug product that is currently on the /ucm079068.htm). A discussion of PE, TE, and
market? other terms are found in the preface.
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Postapproval Changes: Chemistry, Manufacturing, and Controls, macol 26(5):309–316, 1986.
In Vitro Dissolution Testing, and In Vivo Bioequivalence Docu- Mastoraki E, et al: Incidence of postoperative infections in
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Center for Drug Evaluation and Research, Editor, 1995. receiving antimicrobial prophylaxis with original and generic
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Scale-Up and Postapproval Changes: Chemistry, Manufactur- Modi S.R., et al: Impact of crystal habit on biopharmaceutical per-
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Bioequivalence Documentation. FDA, US Department of Rodriguez CA, et al: Potential therapeutic failure of generic van-
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Impact of Biopharmaceutics
18 on Drug Product Quality
and Clinical Efficacy
Leon Shargel and Andrew Yu
Chapter Objectives RISKS FROM MEDICINES
»» Describe the types of safety and Side effects from the use of drugs are the major cause of drug-
efficacy risks that may occur related injuries, adverse events, and deaths. The FDA (FDA,
after taking a drug product and CDER, 2005, 2007) has summarized various types of safety and
various means for preventing efficacy risks from medicines (Fig. 18-1). Side effects are observed
these risks. in clinical trials or postmarketing surveillance and result in listing
»» Differentiate between drug of adverse events in the drug’s labeling. Some side effects are
product quality and drug avoidable, and others are unavoidable. Avoidable side effects may
product performance. include known drug–drug or drug–food interactions, contraindica-
tions, improper compliance, etc. In many cases, drug therapy
»» Differentiate between quality
requires an individualized drug treatment plan and careful patient
control and quality assurance.
monitoring. Known side effects occur with the best medical prac-
»» Explain how quality by design tice and even when the drug is used appropriately. Examples
(QbD) ensures the development include nausea from antibiotics or bone marrow suppression from
and manufacture of a drug chemotherapy. Medication errors include wrong drug, wrong dose,
product that will deliver or incorrect drug administration. Some side effects are unavoid-
consistent performance. able. These uncertainties include unexpected adverse events, side
»» Define quality target product effects due to long-term therapy, and unstudied uses and unstudied
profile (QTPP) and explain populations. For example, a rare adverse event occurring in fewer
how QTPP is different than than 1 in 10,000 persons would not be identified in normal premar-
conventional quality product ket testing. Chapters 13, 21, and 22 discuss how pharmacogenetics,
criteria. pharmacokinetics, pharmacodynamics, and clinical considerations
may improve drug efficacy and safety in many instances. Drug
»» Identify various formulation and product quality is another important consideration. Quality is rec-
manufacturing process factors ognized and defined in ICH (International Conference on
that affect product quality and Harmonisation,1 which provides for international standards of new
performance and the concept of drug product quality; see below) as the suitability of either a drug
QTPP. substance (Chapter 17) or drug product for its intended use. This
»» Describe the quality principles term includes such attributes as the identity, strength, and purity.
underlying basis for the Drug product quality defects are an important source of risk that
development, manufacture, and affects drug product performance and can affect patient safety and
quality assurance of the drug therapeutic efficacy. Product quality includes strength and purity
product throughout its life cycle
in QbD.
1International Conference on Harmonisation—Quality, http://www.fda.gov/Drugs
/GuidanceComplianceRegulatoryInformation/Guidances/ucm065005.htm.
545
546 Chapter 18
»» Describe how product Known side effects Medication Product quality
specifications relate to drug errors defects
Unavoidable Avoidable
product quality and the
relevance to quality assurance of
the drug product through QbD. Preventable
adverse
»» Describe a practical strategy events
to track risks in a drug product
development by drawing a Remaining
uncertainties
scientific roadmap for validating Injury Unexpected side effects
the overall process of material or death Unstudied uses
Unstudied populations
acquiring, manufacturing, and
distributional steps involved in FIGURE 181 Sources of risk from drug products (CDER report, FDA).
a drug product appropriately
labeled for medical use.
of the drug substance, the manufacturing process of the drug
»» Define critical quality attributes
product, and the monitoring of the manufacturing operations.2
and how these attributes relate
This chapter will focus on drug product quality and risks of prod-
to clinical safety and efficacy.
uct quality defects that affect drug product performance. To mini-
»» Explain how postapproval mize product quality defects, regulatory agencies such as the FDA
changes in a drug product must consider risk-based regulatory decisions supporting the drug
may affect drug quality and approval process. These decisions depend on the scientific under-
performance. standing of how formulation and manufacturing process factors
affect product quality and performance and are the underlying
»» List the major reasons that a
basis for the development, manufacture, and quality assurance of
drug product might be recalled
the drug product throughout its life cycle.3
due to quality defects.
RISK ASSESSMENT
Risk assessment is a valuable science-based process used in qual-
ity risk management that can aid in identifying which material
attributes and process parameters potentially have an effect on
product critical quality attributes (CQAs). Risk assessment is typi-
cally performed early in the pharmaceutical development process
and is repeated as more information becomes available and greater
knowledge is obtained. Risk assessment tools can be used to iden-
tify and rank parameters (eg, process, equipment, input materials)
with potential to have an impact on product quality, based on prior
knowledge and initial experimental data. Once the significant
parameters are identified, they can be further studied to achieve a
higher level of process understanding.
2Pharmaceutical manufacturers are required to follow current Good Manufacturing
Practices (cGMP) to ensure that the drug products are made consistently with
high quality.
3A glossary of terms appears at the end of the chapter.
Impact of Biopharmaceutics on Drug Product Quality and Clinical Efficacy 547
TABLE 181 Drug Product Quality and based on a sound understanding of the mechanistic
Performance Attributes activity of the drug substance and its optimal delivery
to achieve the desired therapeutic outcome. The inte-
Product quality
gration of biopharmaceutics and QbD optimizes drug
Chemistry, manufacturing, and controls (CMC)
product development and performance, which has
Microbiology
been described by a biopharmaceutics risk assessment
Information that pertains to the identity, strength,
quality, purity, and potency of the drug product roadmap (Fig. 18-2) (Selen et al, 2014).
Validation of manufacturing process and identification This manufacturing process is carefully designed
of critical quality attributes using scientific principles throughout and integrat-
ing assurance of product quality into the design
Product performance
of the manufacturing process (quality assurance).
In vivo
Information gained from pharmaceutical develop-
Bioavailability and bioequivalence
ment studies and from the manufacturing process
In vitro
provides scientific understanding to support the
Drug release/dissolution
establishment of the design space (see below), speci-
fications, and manufacturing controls that ensure
that each batch of the drug product will be produced
DRUG PRODUCT QUALITY AND with the same quality and performance. The infor-
DRUG PRODUCT PERFORMANCE mation from pharmaceutical development studies is
also the basis for quality risk management. Changes
Drug product quality relates to the biopharmaceutic in formulation and manufacturing processes during
and physicochemical properties of the drug sub- development and life cycle management after market
stance and the drug product to the in vivo perfor- approval provide additional knowledge and further
mance of the drug. The performance of each drug support the manufacture of the drug product. Every
product must be consistent and predictable to assure step that affects drug manufacture must also be tested
both clinical efficacy and safety. Drug product attri- to demonstrate that the desired physical and func-
butes and performance are critical factors that influ- tional outcomes are achieved (process validation).
ence product quality (Table 18-1). Each component Once the manufacturing process has been validated,
of the drug product and the method of manufacture every single lot produced by this method must meet
contribute to quality. Quality must be built into the the desired specifications (quality control).
product during research, development, and produc-
tion. Quality is maintained by implementing systems
and procedures that are followed during the develop-
Frequently Asked Questions
ment and manufacture of the drug product.
For convenience, drug product quality is listed in »»Explain how to “build in” drug quality to ensure that
“the performance of a drug product will be predict-
Table 18-2 separately from drug product perfor-
able to assure clinical efficacy and safety.”
mance. However, drug product quality must be main-
tained since drug product quality impacts directly on »»What do you use as a reference in evaluating perfor-
drug product performance. mance of a new product in a quality system?
PHARMACEUTICAL DEVELOPMENT Quality Risks in Drug Products
The pharmaceutical development process must design Various risks related to drug product quality and per-
a quality drug product (QbD, quality by design) using formance can impact patient medication. Most serious
a manufacturing process that provides consistent drug side effects of drugs are recognized and are described
product performance and achieves the desired thera- in the approved product label to prevent serious
peutic objective. The product development program is injury. Quality risks are occasionally very serious.
548 Chapter 18
TABLE 182 Approaches to Pharmaceutical Development
Aspect Minimal Approaches Enhanced, Quality-by-Design Approaches
Overall pharmaceutical • Mainly empirical • Systematic, relating mechanistic understanding of
development • Developmental research often material attributes and process parameters to drug
conducted one variable at a time product CQAs
• Multivariate experiments to understand product
and process
• Establishment of design space
• Process analytical technology (PAT) tools utilized
Manufacturing process • Fixed • Adjustable within design space
• Validation primarily based on initial • Life cycle approach to validation and, ideally,
full-scale batches continuous process verification
• Focus on optimization and • Focus on control strategy and robustness
reproducibility • Use of statistical process control methods
Process controls • In-process tests primarily for • PAT tools utilized with appropriate feed forward
go/no-go decisions and feedback controls
• Off-line analysis • Process operations tracked and trended to support
continual improvement efforts postapproval
Product specifications • Primary means of control • Part of the overall quality control strategy
• Based on batch data available at the • Based on desired product performance with
time of registration relevant supportive data
Control strategy • Drug product quality controlled pri- • Drug product quality ensured by risk-based control
marily by intermediates (in-process strategy for well-understood product and process
materials) and end-product testing • Quality controls shifted upstream, with the pos-
sibility of real-time release testing or reduced
end-product testing
Life cycle management • Reactive (ie, problem-solving and • Preventive action
corrective action) • Continual improvement facilitated
From FDA Guidance for Industry: Q8(R2) Pharmaceutical Development, November 2009.
Biopharmaceutics
risk assessment
roadmap:
Early discovery/ (1) Integrates
development: knowledge on the Clinical
patient’s needs, the
For understanding development:
therapeutic target,
the therapeutic Clinical safety and
and drug substance.
target, mechanism efcacy studies–
(2) Identies and leads
of action, binding for understanding
to timely conduct of
kinetics, and determining
key learn and
pharmacology, and endpoints and
conrm studies,
how the drug methods including
and to feasibility
substance can determination of
assessments.
elicit the intended dose, dosing, and
(3) Advances
therapeutic labeling.
development of a
response.
drug product with
therapy-driven and
optimized drug
delivery
characteristics.
FIGURE 182 Biopharmaceutics risk assessment roadmap as a connecting and translational tool for improving and enhancing
product quality. (From Selen et al, 2014.)
Impact of Biopharmaceutics on Drug Product Quality and Clinical Efficacy 549
Mostly, quality risks compromise the intended effect Quality risks may be tracked by following all
of medicine or produce unintended adverse reactions. operation steps involved from drug product
Recently, a biopharmaceutics risk assessment roadmap development throughout the manufacturing pro-
(BioRAM) has been developed for optimizing clinical cess, distribution, and patient utilization of the
drug product performance (Selen et al, 2009, 2014). drug product. Key operations in manufacturing
BioRAM uses biopharmaceutic tools to identify and and pharmaceutical development are listed in
address potential challenges to optimize the drug prod- Table 18-2. These operations and quality controls
uct for patient benefit (Fig. 18-3). As stated by Selen et are found in the many FDA references essential for
al (2014), “Understanding the mode of action of a drug proper operation of those steps (http://www.fda.gov
substance and its optimal delivery for generating the /Drugs/GuidanceComplianceRegulatoryInformation
desired therapeutic effect is the central tenet of BioRAM. /Guidances/ucm065005.htm).
Based on mechanistic knowledge gained about the drug Quality documents are important to ensure FDA
substance and how it elicits the intended response, compliance, which inspects manufacturing facilities
BioRAM can help to select the optimal drug.” and its operation. The development pharmaceutics
“Integrating Unfeasible
Product Development”
Specic learning studies/methods
Possibly/ are designed to develop formulation
probably (links to Scenario 1–4) 4
Conrmatory
studies
Feasible and methods
Prior knowledge and identied
preformulation studies: Feasibility assessment 6
API characteristics and supports development of the
“estimated” dose can lead selected scenario/
to selection of a delivery formulation
scenario (formulation 3 Yes
strategy) (links to Scenario
1–4) Yes
2 Unlikely “risk”>>>”benet”
Yes Clear and precise
understanding of patient
need and performance
Patient needs and “estimated” criteria for chosen
doses for the desired clinical “Clinical” formulation approach
effect based on mechanism of (QTPP)
action are known (QTPP)
1 5
Further clinical
No studies to conrm
Supportive exploratory Further clinical clinical benet of
Futher work is work (learning phase) learning studies to No drug and product
needed to determine includes modeling and further increase (registration
clinical effect prole simulation (links to methods). understanding of studies)
Focused on clinical clinical utility of
A understanding of impact of molecule (and E
molecule on disease formulation Further work is
B approach) needed to determine
C clinical effect prole
D
FIGURE 183 The biopharmaceutics risk assessment roadmap (BioRAM). (From Selen et al, 2014.)
550 Chapter 18
section can uncover product risks that are often an EXAMPLE OF QUALITY RISK
extension of poor formulation or poor product
design. Modern design concepts involve identifying Imported drugs—Quality of the active pharmaceu-
risk sources (variate) that take into account the fre- tical ingredient (API) from various sources is regu-
quency of occurrence and components (unit process) lated by different countries. These regulations involve
of the overall operation. The overall process involves common risks that are quite critical. It is important
many materials and operations. Hence a QbD approach that the API or product is properly reviewed to meet
is often multivariate by necessity. An understanding either component or FDA criteria.
of risk involves some probability and statistics. QbD Development pharmaceutics involves select-
is very much rooted in statistics. However, an under- ing appropriate excipients, the API source, and the
standing of the basic material science and interplay fabricating development concept to the drug product
of functional components should always override the (eg, oral tablet, eye product, transdermal patch, etc).
tools and mathematics that are used to implement Drug development risks are numerous and
them. These tools should be viewed as an aid to dis- vary with the product type. A risk in QbD may be
cover or add more choice to manufacturing through easily overlooked with an inadequate quality strategy.
QbD. The risks from drug product quality are some- For example, a tablet may be friable and soft due to
times described as product drug quality defects. poor formulation or the tablet blend may be exces-
Some of the quality elements important during prod- sively compressed. Too often, inadequate under-
uct development are listed in Table 18-3. standing of excipient functions or inclusion of
suitable binders (eg, or starch, macrocrystalline cel-
TABLE 183 Quality Elements of Pharmaceutical lulose) results in an incorrect QbD strategy, that is,
Development and Quality by Design testing friability and hardness at different hardness at
• Define quality target product quality profile (QTPP). inappropriate levels instead of using a suitable
• Design and develop formulations and manufacturing binder or increasing the proportion of excipients.
processes to ensure predefined product quality. The proper inclusion of suitable ingredients may
• Identify critical quality attributes (CQA), process param- result in a product that is so robust that hardness
eters, and sources of variability that are critical to quality
has little or no effect on disintegration while still
from the perspective of patients, and then translate them
into the attributes that the drug product should possess. maintaining friability. A well-designed QbD study
• Perform a risk assessment: linking material attributes on such a product would do away with need exten-
and process parameters to drug product CQAs. sive testing.
• Identify a design space for critical processing variables Method of preparation risks—Preparation
and formulation variables that impact in vivo product
broadly describes synthesis, manufacturing, and
performance.
• Establish how the critical process parameters can be packaging steps. API risks have been discussed in
varied to consistently produce a drug product with the the previous chapter. API material properties include
desired characteristics. particle size, crystal forms, and compression charac-
• Establish the relationships between formulation and teristics. However, these properties may be reduced
manufacturing process variables (including drug sub-
by the impact resulting from a poor API that has
stance and excipient attributes and process parameters);
identify desired product characteristics and sources of residual solvents (eg, chloroform, toluene), or sol-
variability. vents that may be classified as carcinogenic. With
• Implement a flexible and robust manufacturing process the adoption of recent FDA quality guidances,
that can adapt and produce a consistent product over time. residual solvents are generally well controlled with
• Develop process analytical technology (PAT) to integrate
generally recognized standards with FDA-approved
systems during drug product manufacture that provides
continuous real-time quality assurance. products.
• Control manufacturing processes to produce consistent Control of starting materials in API synthesis—
quality over time. Sources of impurities such as heavy metals, solvents,
• Apply product life cycle management and continual and impurities are risks that may impact quality in
improvement.
subsequent steps in unknown ways. For example,
Impact of Biopharmaceutics on Drug Product Quality and Clinical Efficacy 551
metallic impurities, even not harmful, may have an with predefined objectives and emphasizes the
impact on stability of some products, and low level understanding of product and processes and process
may alter the appearance of a product even not harm- control. Product and process performance character-
ful. Related impurities to an API may sometimes istics are scientifically designed to meet specific
have pharmacologic properties of their own. In gen- objectives (Yu, 2008). To achieve QbD objectives,
eral, the history or processes that precede starting product and process characteristics important to
materials is not documented. Starting materials may desired performance must be derived from a combi-
not be regulatory controlled or inspected. It is of nation of prior knowledge and experimental assess-
particularly importance to maintain a good quality ment during product development. Quality cannot be
practice by the vendor or supplier even though the tested in drug products. Quality should be built in the
starting materials are not strictly regulated. A chemi- design and confirmed by testing. With a greater
cal may be produced for chemical or industrial pur- understanding of the drug product and its manufac-
pose. For example, urea is produced as fertilizer turing process, regulatory agencies are working with
rather than for drug or excipient use. pharmaceutical manufacturers to use systematic
Control tests on the finished product are quality approaches to drug product development that will
tests that are specified, including stability, dissolution, achieve product quality and the desired drug product
and other special product tests. It is important to con- performance (FDA Guidance for Industry, 2009).
sider whether the tests will have impact on the perfor- The elements of QbD are listed in Table 18-3.
mance of the product. Most of the issues raised by this Quality target product profile (QTPP) is a pro-
question are addressed in the relevance of the product spective summary of the quality characteristics of a
attributes to clinical performance. Figures 18-2 and 18-3 drug product that ideally will be achieved to ensure
address these issues. Recently, the concept of product the desired quality, taking into account safety and
life cycle, learn and confirm using QbD versus the efficacy of the drug product. As part of the quality
convention concept of “set the specification and system, the concept QTPP was introduced in QbD.
maintain” is being debated and will impact on quite QTPP summarizes all the important product attri-
new and a both benefit and risk. butes that are targeted and designed by the manufac-
turer during design and manufacturing. QTPP helps
to maintain the quality throughout the life cycle of
Frequently Asked Questions the product.
»»Can a QbD strategy for testing hardness and disinte- The following steps are informative in under-
gration replace the need for a full dissolution profile standing various aspects of the overall scheme and
testing of all batches? its relevance:
»»Can a dissolution test of a tablet at the beginning 1. Quality target product profile (QTPP)-driven
and the end period of stability cycle replace dissolu- specifications
tion testing every 3 or 6 months during the stability 2. BioRAM (see Fig. 18-3)
cycle? 3. Advancing and leveraging science and tech-
»»Is sterility testing of an injection product at the initial nology including mechanistic understanding,
and the end of production batch adequate to justify in silico tools, statistical evaluations
the stability of a new product? 4. Knowledge sharing and collaborations based
on multidimensional collaborations and shared
database
Quality (by) Design (QbD) By the use of an integrated approach to QbD using
A major principle that drives manufacturing process biopharmaceutic principles, drug products can be
development is QbD. Quality by design is a system- manufactured with the assurance that product quality
atic, scientific, risk-based, holistic, and proactive and performance will be maintained throughout its
approach to pharmaceutical development that begins life cycle.
552 Chapter 18
Critical Manufacturing Attributes (CMAs) and Process Analytical Technology (PAT)
Critical Process Parameters (CPPs) Like design space, process analytical technology
In process development, the most important pro- (PAT) also uses critical processes and materials to
cesses and component properties should be identified improve the quality of the product, but in PAT the
in the manufacturing process. A CQA is a physical, emphasis is on monitoring these variables in a timely
chemical, biological, or microbiological property or manner. PAT is intended to support innovation and
characteristic that needs to be controlled (directly or efficiency in pharmaceutical development, manufac-
indirectly) to ensure product quality. The pharmaceu- turing, and quality assurance (FDA Guidance for
tical manufacturer should identify critical manufac- Industry, September 2004). Conventional pharmaceu-
turing attributes (CMAs), critical process parameters tical manufacturing is generally accomplished using
(CPPs), and sources of variability that ensure the batch processing with laboratory testing conducted on
quality of the finished dosage form. The CQAs samples collected during the manufacturing process
should be based on clinical relevance. Thus, the and after the drug product is made (finished dosage
manufacturer of the drug product designs and devel- form). These laboratory tests are used to evaluate
ops the formulations and manufacturing processes to quality of the drug product (see quality control and
ensure a predefined quality. quality assurance below). Newer methods based on
science and engineering principles now exist for
Design Space improving pharmaceutical development, manufac-
The interaction between critical processes and materi- turing, and quality assurance starting earlier in the
als should also be studied to optimize manufacturing development timeline through innovation in product
processes. A design space is defined for critical pro- and process development, analysis, and control.
cessing variables and formulation variables that impact PAT uses an integrated systems approach to regu-
in vivo product performance. There may be several lating pharmaceutical product quality. PAT assesses
variables that affect the product variability in vitro. mitigating risks related to poor product and process
It is important to identify which of these variables are quality, and then monitors and controls them. PAT is
actually relevant to drug product performance in vivo. characterized by the following:
ICH defines design space in Q8 as follows:
• Product quality and performance are ensured
• The multidimensional combination and interac- through the design of effective and efficient manu-
tion of input variables (eg, material attributes) and facturing processes.
process parameters that have been demonstrated to • Product and process specifications are based on
provide assurance of quality. a mechanistic understanding of how formulation
• Working within the design space is not consid- and process factors affect product performance.
ered a change. Movement out of the design space • Continuous real-time quality assurance.
is considered to be a change and would normally • Relevant regulatory policies and procedures are
initiate a regulatory postapproval change process. tailored to accommodate the most current level of
• Design space is proposed by the applicant and is scientific knowledge.
subject to regulatory assessment and approval. • Risk-based regulatory approaches recognize:
• The scientific understanding of how formulation
Design space is the geometrical region suitable
and manufacturing process factors affect prod-
for quality manufacturing when two or more process/
uct quality and performance.
material variables are plotted in a two-dimensional
• The capability of process control strategies to
or higher-dimensional space to show the combined
prevent or mitigate the risk of producing a poor
effects of the relevant processing variables during
quality product.
manufacturing. Some of these processing variables
may or may not be critical to drug product perfor- PAT enhances manufacturing efficiencies by improv-
mance. Thus, the manufacturer knows which process ing the manufacturing process, through scientific
variable is critical and must have stricter control. innovation and with better communication between
Impact of Biopharmaceutics on Drug Product Quality and Clinical Efficacy 553
manufacturers and the regulatory agencies. PAT may they have no pharmacodynamic activity of their
be considered a part of the overall QbD such that own. However, excipients have different functional
quality is built into the product during manufacture. purposes and influence the performance of the drug
An increased emphasis on building quality into drug product (Amidon et al, 2007; Shargel, 2010).
products allows more focus to be placed on relevant Compressed tablets may consist of the active ingre-
multifactorial relationships among material, manu- dient, a diluent (filler), a binder, buffering agents, a
facturing process, environmental variables, and their disintegrating agent, and one or more lubricant.
effects on quality. This enhanced focus provides a Approved FD&C and D&C dyes or lakes (dyes
basis for identifying and understanding relationships adsorbed onto insoluble aluminum hydroxide), fla-
among various critical formulation and process fac- vors, and sweetening agents may also be present.
tors and for developing effective risk mitigation strat- These excipients provide various functional pur-
egies (eg, product specifications, process controls, poses such as improving compression, improving
training). The data and information to help under- powder flow, stability of the active ingredient, and
stand these relationships can be leveraged through other properties (Table 18-4). For example, diluents
preformulation programs, development and scale-up such as lactose, starch, dibasic calcium phosphate,
studies, as well as from improved analysis of manu- and microcrystalline cellulose are added where the
facturing data collected over the life of a product. quantity of active ingredient is small and/or difficult
to compress.
The physical and chemical properties of the
EXCIPIENT EFFECT ON DRUG excipients, the physical and chemical properties of
PRODUCT PERFORMANCE the API, and the manufacturing process all play a
role in the performance of the finished dosage form.
Drug products are finished dosage forms that contain Each excipient must be evaluated to maintain consis-
the API along with suitable diluents and/or excipi- tent performance of the drug product throughout the
ents. Excipients are generally considered inert in that product’s life cycle.
TABLE 184 Common Excipients for Solid Oral Dosage Forms
Function in
Excipient Compressed Tablet Possible Effect on Drug Product Performance
Microcrystalline cellulose, Diluent Very low-dose drug (eg, 5 mg) may have high ratio of excipi-
lactose, calcium carbonate ents to active drug leading to a problem of homogeneous
blending and possible interaction of drug with excipients.
Copovidone, starch, Binder Binders give adhesiveness to the powder blend and can affect
methylcellulose tablet hardness. Harder tablets tend to disintegrate more
slowly.
Magnesium stearate Lubricant Lubricants are hydrophobic; over-lubrication can slow dissolu-
tion of API.
Starch Disintegrant Disintegrant allows for more rapid fragmentation of tablet in
vivo, reducing disintegration time and allowing for more rapid
dissolution.
FD&C colors and lakes Color
Various Coating Coatings may have very little effect (film coat) or have rate-
controlling effect on drug release and dissolution (eg, enteric
coat).
554 Chapter 18
PRACTICAL FOCUS formulated in a rapidly dissolving immediate-release
product.
BSE in Gelatin Excessive use of lubricant should be avoided.
Gelatin and other excipients may be produced from When new excipients or atypically large amounts
ruminant sources such as bones and hides obtained from of commonly used excipients are included in an
cattle. In the early 1990s, the FDA became concerned immediate-release solid dosage form, additional
about transmissible spongiform encephalopathies information documenting the absence of an impact on
(TSEs) in animals and Creutzfeldt–Jakob disease in bioavailability of the drug may be requested by the
humans. In 1993, the FDA recommended against the FDA. Such information can be provided with a relative
use of materials from cattle that had resided in, or bioavailability study using a simple aqueous solution
originated from, countries in which bovine spongi- as the reference product. Large quantities of certain
form encephalopathy (BSE, or “mad cow disease”) excipients, such as surfactants (eg, polysorbate 80)
had occurred. The FDA organized a Transmissible and sweeteners (eg, mannitol or sorbitol), may be
Spongiform Encephalopathies Advisory Committee problematic.
to help assess the safety of imported and domestic
gelatin and gelatin by-products in FDA-regulated
products with regard to the risk posed by BSE. The Frequently Asked Questions
FDA published a guidance to industry concerning the »»How does a change in drug product quality change
sourcing and processing of gelatin used in pharma- drug product performance?
ceutical products to ensure the safety of gelatin as it
»»What is the difference between critical manufactur-
relates to the potential risk posed by BSE (http://www
ing attribute (CMA), critical product attribute (CPA),
.fda.gov/opacom/morechoices/industry/guidance
and critical quality attribute (CQA)?
/gelguide.htm). In some cases, such as the magnesium
stearates, a vegetative source may be used to avoid »»How can a pharmaceutical manufacturer ensure
the BSE/TSE concern. that a drug product has the same drug product per-
formance before and after a change in the supplier
of the active pharmaceutical ingredient or a change
Gelatin Capsules Stability in the supplier of an excipient?
Soft and hard gelatin capsules show a decrease in the
dissolution rate as they age in simulated gastric fluid
(SGF) with and without pepsin or in simulated intes-
tinal fluid (SIF) without pancreatin. This has been QUALITY CONTROL
attributed to pellicle formation. When the dissolution AND QUALITY ASSURANCE
of aged or slower-releasing capsules was carried out
An independent quality assurance (QA) unit is a
in the presence of an enzyme (pepsin in SGF or pan-
vital part of drug development and manufacture. QA
creatin in SIF), a significant increase in dissolution
is responsible for ensuring that all the appropriate
was observed. In this setting, multiple dissolution
procedures have been followed and documented. QA
media may be necessary to assess product quality
provides a high probability that each dose or pack-
adequately.
age of a drug product will have predictable charac-
teristics and perform according to its labeled use.
Excipient Effects The quality control (QC) unit is responsible for the
Excipients can sometimes affect the rate and extent in-process tests beginning from receipt of raw mate-
of drug absorption. In general, using excipients that rials, throughout production, finished product, pack-
are currently in FDA-approved immediate-release aging, and distribution.
solid oral dosage forms within a suitable range will Principles of quality assurance include the fol-
not affect the rate or extent of absorption of a highly lowing: (1) Quality, safety, and effectiveness must be
soluble and highly permeable drug substance that is designed and built into the product; (2) quality cannot
Impact of Biopharmaceutics on Drug Product Quality and Clinical Efficacy 555
be inspected or tested into the finished product; and compression will not only increase tablet hardness
(3) each step of the manufacturing process must be but can also deform the controlled-release pellets.
controlled to maximize the probability that the finished The deformed pellets lose their controlled-release
product meets all quality and design specifications. characteristics and the active drug, metoprolol, dis-
QA/QC has the responsibility and authority to solves more quickly resulting in a faster-than-desired
approve or reject all components, drug product con- rate of systemic drug absorption. Inadequate amount
tainers, closures, in-process materials, packaging of lubricant or glidant can also aggravate or damage
material, labeling, and drug products, and the author- pellets during compression.
ity to review production records to ensure that no
errors have occurred or, if errors have occurred, that Good Manufacturing Practices
they have been fully investigated. QA/QC is respon-
Good Manufacturing Practices (GMPs) are FDA
sible for approving or rejecting drug products manu-
regulations that describe the methods, equipment,
factured, processed, packed, or held under contract
facilities, and controls required for producing human
by another company.
and veterinary products. GMPs define a quality sys-
tem that manufacturers use to build quality into their
PRACTICAL FOCUS products. For example, approved drug products
developed and produced according to GMPs are con-
Tablet compression may affect drug product perfor-
sidered safe, properly identified, of the correct
mance of either immediate-release or extended-
strength, pure, and of high quality. The US regula-
release drug products even between products
tions are called current Good Manufacturing Practices
containing the same active drug. Metoprolol is a
(cGMPs), to emphasize that the expectations are
beta 1-selective (cardioselective) adrenoceptor block-
dynamic. These regulations are minimum require-
ing agent that is available as an immediate-release
ments that may be exceeded by the manufacturer.
tablet (metoprolol tartrate tablets, USP—Lopressor®)
GMPs help prevent inadvertent use or release of
and an extended-release tablet (metoprolol succinate
unacceptable drug products into manufacturing and
extended-release tablets—Toprol-XL®). Metoprolol
distribution. GMP requirements include well-trained
is a highly soluble and highly permeable drug that
personnel and management, buildings and facilities,
meets the Biopharmaceutics Classification System,
and written and approved Standard Operating
BCS 1 (Chapter 16). Metoprolol is rapidly and com-
Procedures (SOPs), as listed in Table 18-5.
pletely absorbed from the immediate-release tablet.
Compression makes the powder blend more
compact and affects tablet hardness, especially when Guidances for Industry
inadequate amount of binder is added. Excessive The FDA publishes guidances for the industry to pro-
compression may cause the tablet to disintegrate more vide recommendations to pharmaceutical manufac-
slowly, resulting in a slower rate of dissolution and turers for the development and manufacture of drug
systemic drug absorption. Adequate use of binder and substances and drug products (http://www.fda.gov
lubricant during product design obviates the need to /drugs/guidancecomplianceregulatoryinformation
use excessive force during compression/compaction. /guidances/ucm121568.htm). The International
The metoprolol succinate extended-release tab- Conference on Harmonization of Technical
let (Toprol-XL) is a multiple-unit system containing Requirements for Registration of Pharmaceuticals for
metoprolol succinate in a multitude of controlled- Human Use (ICH) is composed of the regulatory
release pellets. Each pellet acts as a separate drug authorities of Europe, Japan, and the United States,
delivery unit and is designed to deliver metoprolol and experts from the pharmaceutical industry. The
continuously over the dosage interval (Toprol-XL ICH is interested in the global development and
approved label). The controlled-release pellets are availability of new medicines while maintaining safe-
mixed with excipients and compressed into tablets. guards on quality, safety and efficacy, and regulatory
If the tablet is compressed too strongly, the high obligations to protect public health (www.ich.org).*
556 Chapter 18
TABLE 185 Current Good Manufacturing Practice for Finished Pharmaceuticals
Subpart A—General Provisions
Scope, definitions
Subpart B—Organization and Personnel
Responsibilities of quality control unit, personnel qualifications, personnel responsibilities, consultants
Subpart C—Buildings and Facilities
Design and construction features, lighting, ventilation, air filtration, air heating and cooling, plumbing, sewage and refuse,
washing and toilet facilities, sanitation, maintenance
Subpart D—Equipment
Equipment design, size, and location, equipment construction, equipment cleaning and maintenance, automatic, mechanical,
and electronic equipment, filters
Subpart E—Control of Components and Drug Product Containers and Closures
General requirements, receipt and storage of untested components, drug product containers and closures; testing and
approval or rejection of components, drug product containers and closures; use of approved components, drug product
containers and closures; retesting of approved components, drug product containers and closures, rejected components,
drug product containers and closures, drug product containers and closures
Subpart F—Production and Process Controls
Written procedures; deviations, change of components, calculation of yield, equipment identification, sampling and testing
of in-process materials and drug products, time limitations on production, control of microbiological contamination,
reprocessing
Subpart G—Packaging and Labeling Controls
Materials examination and usage criteria, labeling issuance, packaging and labeling operations, tamper-resistant packaging
requirements for over-the-counter human drug products, drug product inspection, expiration dating
Subpart H—Holding and Distribution
Warehousing procedures, distribution procedures
Subpart I—Laboratory Controls
General requirements, testing and release for distribution, stability testing, special testing requirements, reserve samples,
laboratory animals, penicillin contamination
Subpart J—Records and Reports
General requirements; equipment cleaning and use log; component, drug product, container, closure, and labeling records;
master production and control records, batch production and control records, production record review, laboratory records,
distribution, complaint files
Subpart K—Returned and Salvaged Drug Products
Returned drug products, drug product salvaging
From: US Code of Federal Regulations.
Quality Standards may provide acceptance criteria, that is, numerical
Public standards are necessary to ensure that drug limits, ranges, or other criteria for the test for the
substances and drug products have consistent and drug substance or drug product. An impurity is
reproducible quality. The United States Pharmacopeia defined as any component of the drug substance that
National Formulary (USP-NF, www.usp.org) is is not the entity defined as the drug substance.
legally recognized by the US Food, Drug and Drugs with a USP or NF designation that do not
Cosmetic Act and sets public standards for drug conform to the USP monograph may be considered
products and drug substances. The USP-NF contains adulterated. Specifications are the standards a drug
monographs for drug substances and drug products product must meet to ensure conformance to prede-
that include standards for strength, quality, and termined criteria for consistent and reproducible
purity. In addition, the USP-NF contains general quality and performance.
chapters that describe specific procedures that sup- International Conference on Harmonization
port the monographs. The tests in the monographs (ICH) has published several guidances to regulate
Impact of Biopharmaceutics on Drug Product Quality and Clinical Efficacy 557
drug substance and drug product manufacturing. The TABLE 186 Guidelines for the Format and
main approach is to promote “better understanding Content of the Chemistry, Manufacturing, and
of manufacturing processes with quality (by) design.” Controls Section of an Application
QbD improves the quality of the product and makes
I. Drug Substance
it easier for regulatory agencies to evaluate postap- A. Description, including physical and chemical charac-
proval changes of a drug product. ICH guideline Q8 teristics and stability
describes pharmaceutical development and ICH guid- 1. Name(s)
ance Q10 discusses pharmaceutical quality systems. 2. Structural formula
3. Physical and chemical characteristics
Earlier guidances such as ICH Q6A provide more
4. Elucidation of structure
specific details on setting acceptance criteria and test 5. Stability
specification for new drug substances and new drug B. Manufacturer(s)
products. The ICH guidance Q6A has been recom- C. Method(s) of manufacturer and packaging
mended for adoption in the United States, the European 1. Process controls
2. Container-closure system
Union, and Japan. These regulations will be applied to
D. Specifications and analytical methods for the drug
new drug substances and drug products. substance
E. Solid-state drug substance forms and their relation-
ship to bioavailability
RISK MANAGEMENT II. Drug Product
A. Components
Regulatory and Scientific Considerations B. Composition
C. Specifications and analytical methods for inactive
The FDA develops rational, science-based regulatory
components
requirements for drug substances and finished drug D. Manufacturer(s)
products. The FDA establishes quality standards and E. Method(s) of manufacture and packaging
acceptance criteria for each component used in the 1. Process controls
manufacture of a drug product. Each component 2. Container closure system
must meet an appropriate quality and performance III. Methods validation package
objective.
IV. Environmental assessment
Drug Manufacturing Requirements FDA Guidance (1999).
Assurance of product quality is derived from care-
ful attention to a number of factors, including
produce a product meeting its predetermined spec-
selection of quality parts and materials, adequate
ifications and quality characteristics. Process vali-
product and process design, control of the process,
dation is a key element in ensuring that these
and in-process and end-product testing. Because of
quality assurance goals are met. Proof of valida-
the complexity of today’s medical products, routine
tion is obtained through collection and evaluation
end-product testing alone often is not sufficient to
of data, preferably beginning at the process devel-
ensure product quality. The chemistry, manufacturing,
opment phase and continuing through the produc-
and controls (CMC) section of a drug application
tion phase.
describes the composition, manufacture, and speci-
The product’s end use should be a determining
fications of the drug substance and drug product
factor in the development of product (and compo-
(Table 18-6).
nent) characteristics and specifications. All pertinent
aspects of the product that may affect safety and
Process Validation effectiveness should be considered. These aspects
Process validation is the process for establishing include performance, reliability, and stability.
documented evidence to provide a high degree of Acceptable ranges or limits should be established for
assurance that a specific process will consistently each characteristic to set up allowable variations.
558 Chapter 18
Specifications are the quality standards (ie, tests, TABLE 187 Major Reasons for Drug Recalls
analytical procedures, and acceptance criteria) that Failed USP dissolution test requirements
confirm the quality of drug substances, drug prod- Microbial contamination of nonsterile products
ucts, intermediates, raw material reagents, compo- Lack of efficacy
nents, in-process material, container closure systems, Impurities/degradation products
and other materials used in the production of the Lack of assurance of sterility
drug substance or drug product. The standards or Lack of product stability—Stability data failing to support
specifications that are critical to product quality are expiration date
considered CMAs or CPPs. Cross-contamination with other products
Through careful design and validation of both Deviations from good manufacturing practices
the process and process controls, a manufacturer can Failure or inability to validate manufacturing processes
establish with a high degree of confidence that all Failure or inability to validate drug analysis methods
manufactured units from successive lots will be Subpotency or superpotency
acceptable. Successfully validating a process may Labeling mix-ups including
reduce the dependence on intensive in-process and • Labeling: Label error on declared strength
finished product testing. In most cases, end-product • Labeling: Correctly labeled product in incorrect carton
testing plays a major role in ensuring that quality or package
assurance goals are met; that is, validation and end- Misbranded: Promotional literature with unapproved
product testing are not mutually exclusive. therapeutic claims
Marketed without a new or generic approval
Drug Recalls and Withdrawals Adapted from Center for Drug Evaluation and Research, CDER 2007
The FDA coordinates drug recall information and Update and other sources.
prepares health hazard evaluations to determine the
risk to public health from products being recalled.
The FDA classifies recall actions in accordance to the optimization of the manufacturing process, and
level of risk. The FDA and the manufacturer develop upgrade of the packaging system. A change within a
recall strategies based on the potential health hazard given parameter can have varied effect depending on
and other factors, including distribution patterns and the type of product. For example, a change in the
market availability. The FDA also determines the container closure/system of a solid oral dosage form
need for public warnings and assists the recalling may have little impact on an oral tablet dosage form
firm with public notification. Table 18-7 lists some of unless the primary packaging component is critical
the major reasons for drug recalls. to the shelf life of the finished product.
If a pharmaceutical manufacturer makes any
change in the drug formulation, scales up the formu-
SCALE-UP AND POSTAPPROVAL lation to a larger batch size, or changes the process,
equipment, or manufacturing site, the manufacturer
CHANGES (SUPAC)
should consider whether any of these changes will
A postapproval change is any change in a drug prod- affect the identity, strength, purity, quality, safety, and
uct after it has been approved for marketing by the efficacy of the approved drug product. Moreover, any
FDA. Postapproval manufacturing changes may changes in the raw material (ie, active pharmaceutical
adversely impact drug product quality. Since safety ingredient), excipients (including a change in grade
and efficacy are established using clinical batches, or supplier), or packaging (including container clo-
the same level of quality must be ensured in the fin- sure system) should also be shown not to affect the
ished drug product released to the public. A change quality of the drug product. The manufacturer should
to a marketed drug product can be initiated for a assess the effect of the change on the identity,
number of reasons, including a revised market fore- strength (eg, assay, content uniformity), quality (eg,
cast, change in an API source, change in excipients, physical, chemical, and biological properties), purity
Impact of Biopharmaceutics on Drug Product Quality and Clinical Efficacy 559
(eg, impurities and degradation products), or potency quantitative change in the excipients beyond an allow-
(eg, biological activity, bioavailability, bioequiva- able range, particularly for drug products containing a
lence) of a product as they may relate to the safety or narrow therapeutic window, might require an in vivo
effectiveness of the product. bioequivalence study to demonstrate that drug quality
The FDA has published several SUPAC guid- and performance were not altered by the change.
ances, including Changes to an Approved NDA or The SUPAC guidance is an early guidance that
ANDA for the pharmaceutical industry. These guid- assesses changes in manufacturing and its effect on
ances address the following issues: product quality. The basic concepts continue to be a
useful guide, and in many respects, QbD extends its
• Components and composition of the drug product
scope. With adequate QbD study, some changes in
• Manufacturing site change
manufacturing may require only an annual report
• Scale-up of drug product
instead of a prior approval supplements for regula-
• Manufacturing equipment
tory purposes. The ultimate question to ask is: Will
• Manufacturing process
the product quality be assured to be equivalent or
• Packaging
better and meet with prior information described in
• Active pharmaceutical ingredient
the application with QbD data?
These documents describe (1) the level of change,
(2) recommended CMC tests for each level of change, Assessment of the Effects of the Change
(3) in vitro dissolution tests and/or bioequivalence
Assessment of the effect of a change should include
tests for each level of change, and (4) documentation
a determination that the drug substance intermedi-
that should support the change. The level of change is
ates, drug substance, in-process materials, and/or
classified as to the likelihood that a change in the drug
drug product affected by the change conform to
product as listed above might affect the quality of the
the approved specifications. Acceptance criteria are
drug product. The levels of change as described by the
numerical limits, ranges, or other criteria for the tests
FDA are listed in Table 18-8.
described. Conformance to a specification means that
As noted in Table 18-8, a Level 1 change, which
the material, when tested according to the analytical
could be a small change in the excipient amount
procedures listed in the specification, will meet the
(eg, starch, lactose), would be unlikely to alter the
listed acceptance criteria. Additional testing may be
quality or performance of the drug product, whereas
needed to confirm that the material affected by manu-
a Level 3 change, which may be a qualitative or
facturing changes continues to meet its specification.
The assessment may include, as appropriate, evaluation
of any changes in the chemical, physical, microbiologi-
TABLE 188 FDA Definitions of Level of cal, biological, bioavailability, and/or stability profiles.
Changes That May Affect the Quality of an This additional assessment may involve testing of the
Approved Drug Product postchange drug product itself or, if appropriate, the
Change component directly affected by the change. The type of
Level Definition of Level additional testing depends on the type of manufacturing
change, the type of drug substance and/or drug product,
Level 1 Changes that are unlikely to have any
detectable impact on the formulation and the effect of the change on the quality of the prod-
quality and performance. uct. Examples of additional tests include:
Level 2 Changes that could have a significant • Evaluation of changes in the impurity or degradant
impact on formulation quality and profile
performance.
• Toxicology tests to qualify a new impurity or
Level 3 Changes that are likely to have a signifi- degradant or to qualify an impurity that is above a
cant impact on formulation quality and previously qualified level
performance. • Evaluation of the hardness or friability of a tablet
560 Chapter 18
• Assessment of the effect of a change on bioequiva- the drug product are then established so that future
lence (may include multipoint and/or multimedia production batches do not fall outside the bioequiva-
dissolution profiles and/or an in vivo bioequiva- lence of the marketed drug product.
lence study)
• Evaluation of extractables from new packaging Adverse Effect
components or moisture permeability of a new Sometimes manufacturing changes have an adverse
container closure system effect on the identity, strength, quality, purity, or
potency of the drug product. For example, a type of
process change could cause a new degradant to be
Equivalence
formed that requires qualification and/or quantifica-
The manufacturer usually assesses the extent to which tion. The manufacturer must show that the new
the manufacturing change has affected the identity, degradant will not affect the safety or efficacy of the
strength, quality, purity, or potency of the drug product product. Changes in the qualitative or quantitative
by comparing test results from pre- and postchange formulation, including inactive ingredients, are con-
material and then determining if the test results are sidered major changes and are likely to have a signifi-
equivalent. The drug product after any changes should cant impact on formulation quality and performance.
be equivalent to the product made before the change. However, the deletion or reduction of an ingredient
An exception to this general approach is that when intended to affect only the color of a product is con-
bioequivalence should be redocumented for certain sidered to be a minor change that is unlikely to affect
Abbreviated New Drug Application (ANDA) postap- the safety of the drug product.
proval changes, the comparator should be the refer-
ence listed drug. Equivalence does not necessarily Postapproval Changes of Drug Substance
mean identical. Equivalence may also relate to mainte-
nance of a quality characteristic (eg, stability) rather Manufacturing changes of the active pharmaceutical
than a single performance of a test. ingredient (API)—also known as the drug substance
or bulk active—may change its quality attributes.
These quality attributes include chemical purity, solid-
Critical Manufacturing Variables state properties, and residual solvents. Chemical purity
Critical manufacturing variables (CMVs, sometimes is dependent on the synthetic pathway and purification
referred to as critical manufacturing attributes, process. Solid-state properties include particle size,
CMAs) include items in the formulation, process, polymorphism, hydrate/solvate, and solubility. Small
equipment, materials, and methods for the drug prod- amounts of residual solvents such as dichloromethane
uct that can significantly affect in vitro dissolution. If may remain in the API after extraction and/or purifi-
possible, the manufacturer should determine whether cation. Changes in the solid-state properties of the
there is a relationship between CMV, in vitro dissolu- API may affect the manufacture of the dosage form
tion, and in vivo bioavailability.4 The goal is to or product performance. For example, a change in
develop product specifications that will ensure bio- particle size may affect API bulk density and tablet
equivalence of future batches prepared within limits hardness, whereas different polymorphs may affect
of acceptable dissolution specifications. One approach API solubility and stability. Changes in particle size
to obtaining this relationship is to compare the bio- and/or polymorph may affect the drug’s bioavailability
availability of test products with slowest and fastest in vivo. Moreover, the excipient(s) and vehicle func-
dissolution characteristics to the bioavailability of the tionality and possible pharmacologic properties may
marketed drug product. Dissolution specifications for affect product quality and performance.
Frequently Asked Question
4In vitro dissolution/drug release studies that relate to the in vivo »»Does a change in the manufacturing process
drug bioavailability may be considered a drug product perfor- require FDA approval?
mance test.
Impact of Biopharmaceutics on Drug Product Quality and Clinical Efficacy 561
PRACTICAL FOCUS increases 2.5% and microcrystalline cellulose
decreases by 2.5%) relative to the target dosage form
Quantitative Change in Excipients weight if it is to stay within the Level 1 range. The
A manufacturer would like to increase the amount of examples are for illustrations only and the latest offi-
starch by 2% (w/w) in an immediate-release drug cial guidance should be consulted for current views.
product. It should be noted that a small change in the
amount of excipients is less likely to affect the bio-
• Would you consider this change in an excipient to
availability of a highly soluble, highly permeable drug
be a Level 1, 2, or 3 change? Why?
in an immediate-release drug product compared to a
The FDA has determined that small changes in drug that has low solubility and low permeability.
certain excipients for immediate-release drug products
may be considered Level 1 changes. Table 18-9 lists Changes in Batch Size (Scale-Up/Scale-Down)
the changes in excipients, expressed as percentage
For commercial reasons, a manufacturer may increase
(w/w) of the total formulation, less than or equal to the
the batch size of a drug product from 100,000 units
following percent ranges that are considered Level 1
to 5 million units. Even though similar equipment is
changes. According to this table, a 2% increase in
used and the same Standard Operating Procedures
starch would be considered a Level 1 change.
(SOPs) are used, there may be problems in manufac-
The total additive effect of all excipient changes
turing a very large batch. This problem is similar to
should not be more than 5%. For example, in a drug
a chef’s problem of cooking the main entrée for two
product containing the active ingredient lactose,
persons versus cooking the same entrée for a ban-
mirocrystalline cellulose, and magnesium stearate,
quet of 200 persons using the same recipe. The FDA
the lactose and microcrystalline cellulose should not
has generally considered that a change in batch size
vary by more than an absolute total of 5% (eg, lactose
greater than tenfold is a Level 2 change and requires
the manufacturer to notify the FDA and provide
documentation for all testing before marketing this
TABLE 189 Level 1—Allowable Changes product.
in Excipients
Percent Excipient PRODUCT QUALITY PROBLEMS
(W/W) of Total Target
Excipient Dosage Form Weight The FDA and industry are working together to estab-
lish a set of quality attributes and acceptance criteria
Filler ±5
Disintegrant ±3 for certain approved drug substances and drug prod-
Starch ±1 ucts that would indicate less manufacturing risk.
Other Table 18-10 summarizes some of the quality attri-
Binder ±0.5 butes for these products. However, all approved drug
Lubricant ±0.25 products must be manufactured under current Good
Calcium stearate ±0.25 Manufacturing Practices.
Magnesium stearate ±1 Drug substances and drug products that have
Other
more quality risk are generally those products that
Glidant ±1 are more complex to synthesize or manufacture
Talc ±0.1 (Fig. 18-4). For example, biotechnology-derived drugs
Other
(eg, proteins) made by fermentation may have more
Film coat ±1 quality risk than chemically synthesized small mol-
These percentages are based on the assumption that the drug ecules. Extended-release and delayed-release drug
substance in the product is formulated to 100% of label/potency. products may also present a greater quality risk than
Source: FDA Guidance, 1995. an immediate-release drug product. Drug products
562 Chapter 18
TABLE 1810 Quality Attributes and Criteria for Certain Approved Drug Substances and Drug
Products
Drug Substances Drug Products
Attribute Criteria Attribute Criteria
Chemical structure Well characterized Dosage form Oral (immediate release),
simple solutions, others
Synthetic process Simple process
Quality No toxic impurities; adequate Manufacturing process Easy to manufacture (TBD)
specifications Quality Adequate specifications
Physical properties Polymorphic forms, particle Biopharmaceutic Highly permeable and highly
size are well controlled Classification soluble drugs
Systems (BCS)
Stability Stable drug substance Stability Stable drug product (TBD)
Manufacturing history TBD
Others TBD Manufacturing history TBD
Others TBD
TBD, to be defined.
Adapted from Chui, 2000.
that have a very small ratio of active drug substance POSTMARKETING SURVEILLANCE
to excipients are more difficult to blend uniformly
and thus may have a greater quality risk. Good Pharmaceutical manufacturers are required to file
Manufacturing Practices and control of the critical periodic postmarket reports for an approved
manufacturing operations help maintain the quality ANDA to the FDA through its Postmarketing
of the finished product. Complex operations can Surveillance Program. The main component of the
have consistent outcome quality as long as the manu- requirement is the reporting of adverse drug expe-
facturer maintains control of the process and builds riences. This is accomplished by reassessing drug
in quality during manufacturing operations. risks based on data learned after the drug is mar-
keted. In addition, labeling changes may occur
after market approval. For example, a new adverse
reaction discussed by postmarketing surveillance
is required for both branded and generic drug
High Risk products.
GLOSSARY
BioRAM: The biopharmaceutics risk assess-
Low Risk
ment roadmap (BioRAM) optimizes drug
Low Medium High product development and performance by using
Complexity therapy-driven target drug delivery profiles as a
FIGURE 184 General principles to define low-risk drugs. framework to achieve the desired therapeutic
(Adapted from Chui, 2002.) outcome.
Probability of Detection
Low Medium High
Impact of Biopharmaceutics on Drug Product Quality and Clinical Efficacy 563
Continuous process verification: An alternative Process robustness: Ability of a process to
approach to process validation in which manufac- tolerate variability of materials and changes in the
turing process performance is continuously moni- process and equipment without negative impact on
tored and evaluated. quality.
Critical quality attribute (CQA): A physical, Quality: The suitability of either a drug substance
chemical, biological, or microbiological property or or a drug product for its intended use. This term
characteristic that should be within an appropriate includes such attributes as the identity, strength,
limit, range, or distribution to ensure the desired and purity (from ICH Q6A specifications: test
product quality. procedures and acceptance criteria for new drug
Design space: The multidimensional combination substances and new drug products: chemical
and interaction of input variables (eg, material substances).
attributes) and process parameters that have been Quality by design (QbD): A systematic approach
demonstrated to provide quality assurance. Working to development that begins with predefined
within the design space is not considered a change. objectives and emphasizes product and process
Movement out of the design space is considered to understanding and process control, based on sound
be a change and would normally initiate a regula- science and quality risk management.
tory postapproval change process. Design space is Quality target product profile (QTPP): A
proposed by the applicant and is subject to regula- prospective summary of the quality characteristics
tory assessment and approval. of a drug product that ideally will be achieved to
Formal experimental design: A structured, ensure the desired quality, taking into account
organized method for determining the relationship safety and efficacy of the drug product.
between factors affecting a process and the output of Specified impurity: An identified or unidentified
that process. Also known as “design of experiments.” impurity that is selected for inclusion in the new
Life cycle: All phases in the life of a product from drug substance or new drug product specification
the initial development through marketing until the and is individually listed and limited in order to
product’s discontinuation. ensure the quality of the new drug substance or
Process analytical technology (PAT): A system for new drug product.
designing, analyzing, and controlling manufacturing Unidentified impurity: An impurity that is
through timely measurements (ie, during process- defined solely by qualitative analytical properties
ing) of critical quality and performance attributes of (eg, chromatographic retention time).
raw and in-process materials and processes with the
goal of ensuring final product quality.
CHAPTER SUMMARY
The pharmaceutical development process must product requires a systematic, scientific, risk-based,
design a quality drug product (QbD, quality by holistic, and proactive approach that begins with
design) using a manufacturing process that provides predefined objectives and emphasizes product and
consistent drug product performance and achieves processes understanding and process control (QbD).
the desired therapeutic objective. Drug product qual- Quality cannot be tested into drug products. Quality
ity and drug product performance are important for should be built in the design and confirmed by test-
patient safety and therapeutic efficacy. Drug product ing. Quality control (QC) and quality assurance
quality and drug product performance relate to the (QA) help ensure that drug products are manufac-
biopharmaceutic and physicochemical properties of tured with quality and have consistent performance
the drug substance and the drug product and to the throughout their life cycle. Manufacturers must
manufacturing process. The development of a drug demonstrate that any changes in the formulation
564 Chapter 18
after FDA approval (SUPAC) does not alter drug defects are controlled through Good Manufacturing
product quality and performance compared to the Practices, monitoring, and surveillance. The QTPP
initial formulation. Excipients that have no inherent approach is an approach commonly recommended for
pharmacodynamic activity may affect drug product drug development. The need for “learn and confirm”
performance. Drug products may be recalled due to is an important approach evaluating different quality
deficiencies in drug product quality. Product quality systems balancing risk and need for progress.
LEARNING QUESTIONS
1. Three batches of ibuprofen tablets, 200 mg, 4. For solid oral drug products, a change in the
are manufactured by the same manufac- concentration of which of the following excipi-
turer using the same equipment. Each batch ents is more likely to influence the bioavail-
meets the same specifications. Does meeting ability of a drug? Why?
specifications mean that each batch of drug Starch
product contains the identical amount of Magnesium stearate
ibuprofen? Microcrystalline cellulose
2. What should a manufacturer of a modified- Talc
release tablet consider when making a qualita- Lactose
tive or quantitative change in an excipient? 5. How does the polymorphic form of the active
3. Explain how a change in drug product quality drug substance influence the bioavailability
may affect drug product performance. Provide of a drug? Can two different polymorphs of
at least three examples. the same active drug substance have the same
bioavailability?
ANSWERS
Learning Questions batches meet a specification of ±5% and would be
considered to meet the label claim of 200 mg of
Three batches of ibuprofen tablets, 200 mg, are ibuprofen per tablet.
manufactured by the same manufacturer using the
same equipment. Each batch meets the same specifi- What should a manufacturer of a modified-release
cations. Does meeting specifications mean that each tablet consider when making a qualitative or quanti-
batch of drug product contains the identical amount tative change in an excipient?
of ibuprofen? • The manufacturer must consider whether the
excipient is critical or not critical to drug release.
• Specifications provide a quantitative limit (accep- If the excipient (eg, starch) is not critical to drug
tance criteria) to a test product (eg, the total drug release (ie, a non-release-controlling excipient),
content must be within ±5% or the amount of then small changes in the starch concentration,
impurities in the drug substance must not be more generally less than 3% of the total target dosage
than [NMT] 1%). Thus, one batch of nominally form weight, is unlikely to affect the formulation
200-mg ibuprofen tablets may contain an average quality and performance. A qualitative change
content of 198 mg, whereas the average content in the excipient may affect drug release and thus
for another batch of 200-mg ibuprofen tablets will have significant effect on the formulation
may have an average content of 202 mg. Both performance.
Impact of Biopharmaceutics on Drug Product Quality and Clinical Efficacy 565
REFERENCES
Amidon GE, Peck GE, Block LH, Moreton RC, Katdare A, International Conference on Harmonisation (ICH) Guidances:
Lafaver R, Sheehan C: Proposed new USP general informa- http://www.ich.org.
tion chapter, Excipient performance <1059>. Pharm Forum Lionberger RL: FDA critical path initiatives: Opportunities for
33(6):1311–1323, 2007. generic drug development. AAPS J 10(1):103–109, 2008.
Chui Y: Risk-Based CMC Review, An Update, Advisory Risk-Based CMC Review; Advisory Committee for Pharmaceutical
Committee for Pharmaceutical Sciences Meeting, FDA, Sciences, FDA, Oct 21, 2002.
October 21, 2002. Selen A: Office of New Drug Quality Assessment/CDER/FDA,
CMC initiative: Risk-Based CMC Reviews, PhRMA-Dialog, Oct 27, 32nd Annual Midwest Biopharmaceutical Statistics Workshop,
2000. The critical path initiative—Transforming the way Ball State University, Muncie, Indiana, May 18–20, 2009.
FDA-regulated products are developed, evaluated, manufac- Selen A, et al: The biopharmaceutics risk assessment roadmap
tured, and used. FDA, April 2009 (www.fda.gov/downloads for optimizing clinical drug product performance. J Pharm
/ScienceResearch/SpecialTopics/CriticalPathInitiative Sci 103(11):3377–3397, 2014. Also published online in
/UCM186110.pdf). Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002
FDA, CDER Report to the Nation: 2005. /jps.24162, August 22, 2014.
FDA, CDER 2007 Update. Shargel L: Drug product performance and interchangeability of
FDA Guidance: Immediate Release Solid Oral Dosage Forms: multisource drug substances and drug products. Pharm Forum
Scale-Up and Postapproval Changes, 1995. 35:744–749, 2010.
FDA Guidance for Industry: Changes to an Approved NDA or US Code of Federal Regulations (CFR), 21 CFR Part 211.
ANDA, April 2004 http://www.fda.gov/drugs/guidancecom- http://www.fda.gov/drugs/guidancecomplianceregulatory
plianceregulatoryinformation/guidances/ucm121568.htm. information/guidances/ucm121568.htm. Accessed August 10,
FDA Guidance for Industry: PAT—A Framework for Innovative 2011.
Pharmaceutical Development, Manufacturing, and Quality Yu LX: Pharmaceutical quality by design: Product and process
Assurance, September 2004. development, understanding, and control. Pharm Res 25:
FDA Guidance for Industry: Q8(R1) Pharmaceutical Development, 781–791, 2008.
June 2009.
FDA Quality Guidances for Industry, http://www.fda.gov/Drugs
/GuidanceComplianceRegulatoryInformation/Guidances
/ucm065005.htm.
BIBLIOGRAPHY
http://www.fda.gov/Drugs/GuidanceComplianceRegulatory Yu LX, Amidon G, Khan MA, Hoag SW, Polli J, Raju GK,
Information/Guidances/ucm065005.htm (source of regulatory Woodcock J: Understanding pharmaceutical quality by design.
documents for quality systems and QbD discussions). AAPS J 6(4):771–783, 2014.
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http://www.fda.gov/downloads/aboutfda/centersoffices Drugs, http://www.fda.gov/downloads/aboutfda/centersoffices
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Modified-Release Drug
19 Products and Drug Devices
Hong Ding
Chapter Objectives MODIFIED-RELEASE (MR) DRUG PRODUCTS
»» Define modified-release drug AND CONVENTIONAL (IMMEDIATE-RELEASE,
products. IR) DRUG PRODUCTS
»» Differentiate between
Most conventional (also named as immediate-release, IR) oral
conventional, immediate-
drug products, such as tablets and capsules, are formulated to
release, extended-release,
release the active pharmaceutical ingredient (API) immediately
delayed-release, and targeted
after oral administration. In the formulation of conventional drug
drug products.
products, no deliberate effort is made to modify the drug release
»» Explain the advantages and rate. Usually, immediate-release products generally result in rela-
disadvantages of extended- tively rapid drug absorption and onset of accompanying pharma-
release drug products. codynamic (PD) effects, but not always. In the case of conventional
»» Describe the kinetics of oral products containing prodrugs, the pharmacodynamic activity
extended-release drug products may be altered due to the time consumption with conversion from
compared to immediate-release prodrugs to the active drug by hepatic or intestinal metabolism or
drug products. by chemical hydrolysis. Alternatively, in the case of conventional
oral products containing poorly soluble (lipophilic drugs), drug
»» Explain when an extended- absorption may be gradual due to slow dissolution in or selective
release drug product should absorption across the GI tract, also resulting in a delayed onset
contain an immediate-release time.
drug dose. In order to achieve a desired therapeutic objective or better
»» Explain why extended-release patient compliance, the pattern of drug release from modified-
beads in capsule formulation release (MR) dosage forms is deliberately changed from that of a
may have a different conventional (immediate-release, IR) dosage formulation. MR
bioavailability profile compared drug products have always been more effective therapeutic alterna-
to an extended-release tablet tive to conventional or IR dosage forms. The objective of MR drug
formulation of the same drug. products for oral administration is to control the release of the
therapeutic agent and thus control drug absorption from gastroin-
»» Describe several approaches
testinal tract. Types of MR drug products include, but not limited
for the formulation of an oral
to, delayed-release (eg, enteric-coated), extended-release (ER),
extended-release drug product.
and orally disintegrating tablets (ODT).
»» Explain why a transdermal The term modified-release (MR) drug product is used to
drug product (patch) may be describe products that alter the timing and/or rate of release of the
considered an extended-release drug substance in the formulation. A modified-release dosage form
drug product. is a formulation in which the drug-release characteristics of time
course and/or location are chosen to accomplish therapeutic or
567
568 Chapter 19
»» Describe the components of convenience objectives, which is not offered by conventional dos-
a transdermal drug delivery age forms such as solutions, ointments, or promptly dissolving
system. dosage forms. Several types of modified-release oral drug products
are recognized:
»» Explain why an extended-release
formulation of a drug may 1. Extended-release drug products. A dosage form that allows
have a different efficacy profile at least a twofold reduction in dosage frequency as compared
compared to the same dose of to that drug presented as an immediate-release (conventional)
drug given in as a conventional, dosage form. Examples of extended-release dosage forms
immediate-release, oral dosage include controlled-release, sustained-release, and long-acting
form in multiple doses. drug products.
»» List the studies that might be 2. Delayed-release drug products. A dosage form that releases
required for the development a discrete portion/portions of drug at a time other than the
of an extended-release drug promptly release after administration. An initial portion may
product. be released promptly after administration. Enteric-coated
dosage forms are common delayed-release products (eg,
»» List the several achievements on enteric-coated aspirin and other NSAID products).
the drug devices based on the 3. Targeted-release drug products. A dosage form that releases
modified-release drug design. drug at or near the intended physiologic site of action (see
Chapter 20). Targeted-release dosage forms may have either
immediate- or extended-release characteristics.
4. Orally disintegrating tablets (ODTs). ODTs have been devel-
oped to disintegrate rapidly in the saliva after oral administra-
tion. ODTs may be used without the addition of water. The
drug is dispersed in saliva and swallowed with little or no
water.
The term controlled-release drug product was previously used to
describe various types of oral extended-release-rate dosage forms
on the action firm applied, including sustained-release, sustained-
action, prolonged-action, long-action, slow-release, and pro-
grammed drug delivery. Other terms, such as ER (extended-release),
SR (sustained-release), XL (another abbreviation for extended-
release), XR (extended-release), and CR (controlled-release), are
also used to indicate the mechanism of the extended-release drug
product employed. Retarded release is an older term for a slow-
release drug product. Many of these terms for modified-release
drug products were introduced by drug companies to reflect a spe-
cial design either for an extended-release drug product or for use in
marketing.
Modified-release drug products are designed for different
routes of administration based on the physicochemical, pharmaco-
dynamic (PD), and pharmacokinetic (PK) properties of the drug
and on the properties of the materials used in the dosage form
(Table 19-1). Several different terms are now defined to describe
the available types of modified-release drug products based on the
drug release characteristics of the products.
Modified-Release Drug Products and Drug Devices 569
TABLE 191 Modified Drug Delivery Products
Route of
Administration Drug Product Examples Comments
Oral drug products Extended release Diltiazem HCl extended Once-a-day dosing.
release
Delayed release Diclofenac sodium Enteric-coated tablet for drug delivery
delayed-release into small intestine.
Delayed (targeted) drug Mesalamine delayedrelease Coated for drug release in terminal
release ileum.
Oral mucosal drug Oral transmucosal fentanyl Fentanyl citrate is in the form of a
delivery citrate flavored sugar lozenge that dissolves
slowly in the mouth.
Oral soluble film Ondansetron The film is placed top of the tongue.
Film will dissolve in 4 to 20 seconds.
Orally disintegrating Aripiprazole ODT is placed on the tongue. Tablet
tablets (ODT) disintegration occurs rapidly in saliva.
Transdermal drug Transdermal therapeutic Clonidine transdermal Clonidine TTS is applied every 7 days
delivery systems system (TTS) therapeutic system to intact skin on the upper arm or
chest.
Iontophoretic drug Small electric current moves charged
delivery molecules across the skin.
Ophthalmic drug Insert Controlled-release Elliptically shaped insert designed
delivery pilocarpine for continuous release of pilocarpine
following placement in the cul-de-sac
of the eye.
Intravaginal drug Insert Dinoprostone vaginal insert Hydrogel pouch containing prosta-
delivery glandin within a polyester retrieval
system.
Parenteral drug Intramuscular drug Depot injections Lyophylized microspheres containing
delivery products leuprolide acetate for depot suspension.
Water-immiscible injections Medroxyprogesterone acetate
(eg, oil) (Depo-Provera).
Subcutaneous drug Controlled-release insulin Basulin is a controlled-release, recom-
products binant human insulin delivered by
nanoparticulate technology.
Targeted delivery IV injection Daunorubicin citrate Liposomal preparation to maximize
systems liposome injection the selectivity of daunorubicin for
solid tumors in situ.
Implants Brain tumor Polifeprosan 20 with car- Implant designed to deliver carmus-
mustine implant tine directly into the surgical cavity
(Gliadel wafer) when a brain tumor is resected.
Intravitreal implant Fluocinolone acetonide Sterile implant designed to release
intravitreal implant fluocinolone acetonide locally to the
posterior segment of the eye.
570 Chapter 19
Examples of Modified-Release Oral For the repeat-action tablets, such as prolonged,
Dosage Forms sustained, delayed, and timed-release dosage forms,
The pharmaceutical industry uses various terms to may generally be considered as having the property
describe modified-release drug products. New and of prolonged-action. This dosage form purports to
novel drug delivery systems are being developed by describe just when and how much of a drug is
the pharmaceutical industry to alter the drug release released, and simplified curves of blood levels or
profile, which in turn results in a unique plasma drug clinical response claim to depict how the preparation
concentration-versus-time profile and pharmacody- will act in vivo. Since these products usually contain
namic effect. In many cases, the industry will patent the equivalent of 2–3 times the normal dose of the
their novel drug delivery systems. Due to the prolif- drug, it is of considerable importance to the physi-
eration of these modified-release dosage forms, the cian to know that the drug will actually be released
following terms are general descriptions and should in the designed manner.
not be considered definitive. A prolonged-action drug product is a formula-
An tion whose drug activity can continue for a longer
enteric-coated tablet is one kind of delayed-
release type within the modified-release dosage fam- time than conventional drugs. It is also one kind of
ily designed to release drug in the small intestine. modified-release drug product. The prolonged-
Different from the film coating on tablets or capsules release drug product prevents very rapid absorption
to prevent bitter taste from medicine or protect tab- of the drug, which could result in extremely high
lets from microbial growth as well as color altera- peak plasma drug concentration. Most prolonged-
tion, usually the enteric-coating materials are release products extend the duration of action but do
polymer-based barrier applied on oral medicine. not release drug at a constant rate. A prolonged-
This coating may delay release of the medicine until action tablet is similar to a first-order-release product
after it leaves the stomach, either for the purpose of except that the peak is delayed differently. A prolonged-
drug protection under harsh pH circumstance or for action tablet typically results in peak and trough
alleviation of irritation on cell membrane from the drug levels in the body. The product releases drug
drug itself. For example, aspirin irritates the gastric without matching the rate of drug elimination,
mucosal cells of the stomach. Then the enteric coat- resulting in uneven plasma drug levels in the body.
ing on the aspirin tablet may prevent the tablet from A sustained-release drug product is designed to
disintegration promptly and releasing its contents at release a drug at a predetermined rate for the constant
the low pH in the stomach. The coating and the tablet drug concentration maintaining during a specific
later dissolve and release the drug in the relative period of time. Usually, the drug may be delivered in
mild pH of the duodenum, where the drug is rapidly an initial therapeutic dose, followed by a slower and
absorbed with less irritation to the mucosal cells. constant release. The purpose of a loading dose is to
Mesalamine (5-aminosalicylic acid) tablets (Asacol, provide immediate or fast drug release to quickly pro-
Proctor & Gamble) are also a delayed-release tablet vide therapeutic drug concentrations in the plasma.
coated with acrylic-based resin that delays the The rate of release of the maintenance dose is designed
release of mesalamine until it reaches the terminal so that the amount of drug loss from the body by elimi-
ileum and colon. Mesalamine tablets could also be nation is constantly replaced. With the sustained-
considered as a release product, a constant plasma drug concentration
targeted-release dosage form.
The advantage for certain drugs is that the dos- is maintained with minimal fluctuations.
age form contains a sufficient amount of medication Sustained-release and extended-release drug
to last all day or all night. A products look similar since both of them have the
repeat-action tablet is
a type of modified-release drug product that is same release drugs in which those drugs dissolve and
designed to release one dose of drug initially, fol- release in the body over a period of time. The differ-
lowed by a second or more doses of drug at a later ence is that for the sustained-release drug product,
time. It provides the required dosage initially and the drug may release its medication properties over a
then maintains or repeats it at desired intervals. controlled mode within a certain period where the
Modified-Release Drug Products and Drug Devices 571
drug is released bit by bit in the body. The extended- First-order
release drug product is more toward an instant effect 7 release
medication where once administrated, the effects Zero-order
6
took place immediately and its extended effect would release
be often happened at an hourly basis. When the drug 5
concentration goes down, the extended-release drug
4
product may have the capability to maintain the
effectiveness by the formulation itself. Besides the 3 First-order
release with
tablets or capsules, other formulations including lipo- 2 incomplete
somes and drug-loaded polymeric nano-formulations dissolution after
1 12 hours
(eg, micelles, drug–polymer conjugates and hydro-
gels, etc) can also be counted as the sustained-release 0
0 2 4 6 8 10 12
drug product. Figure 19-1 shows the dissolution rate
Time (hours)
of three sustained-release products without loading FIGURE 192 Simulated plasma drug concentrations
dose. The plasma concentrations resulting from the resulting from three different sustained-release products in
sustained-release products are shown in Fig. 19-2. Fig. 19-1.
Various terms for extended-release drug prod-
ucts often imply that drug release is at a constant or
zero-order drug release rate. However, many of these multiple doses in Figs. 19-3 and 19-4, respectively.
drug products release the drug at a first-order rate. Drug absorption from conventional (immediate-
Some modified-release drug products are formulated release) dosage forms generally follows first-order
with materials that are more soluble at a specific pH, drug absorption.
and the product may release the drug depending on
the pH of a particular region of the gastrointestinal Frequently Asked Questions
(GI) tract. Ideally, an extended-release drug product »»What is the difference between extended release,
should release the drug at a constant rate, indepen- delayed release, sustained release, modified release,
dent of the pH, the ionic content, and other contents and controlled release?
within the entire segment of the gastrointestinal tract. »»Why does the drug bioavailability from some
An extended-release dosage form with zero- or conventional, immediate-release, drug products
first-order drug absorption is compared to drug resemble an extended-release drug product?
absorption from a conventional dosage form given in
100
First-order release 24 A
80 18
60 12
First-order B
release with 6
40 incomplete
dissolution 0
after 12 hours 0 4 8 12 16 20 24
20
Zero-order release Time (hours)
FIGURE 193 Plasma level of a drug from a conventional
0 tablet containing 50 mg of drug given at 0, 4, and 8 hours
0 2 4 6 8 10 12 (A) compared to a single 150-mg drug dose given in an extended-
Time (hours) release dosage form (B). The drug absorption rate constant
FIGURE 191 Drug dissolution rates of three different from each drug product is first order. The drug is 100% bio-
extended-release products in vitro. available and the elimination half-life is constant.
Dissolved (percent)
Plasma concentration
(mg/mL) Concentration (mg/mL)
572 Chapter 19
systemic drug absorption is limited by the rate of
24 drug release from the drug delivery system.
A
Unfortunately, most ER drug products that release a
18 drug by zero-order kinetics in vitro do not demon-
12 B strate zero-order drug absorption, in vivo. The lack
of zero-order drug absorption from these ER drug
6 products after oral administration may be due to a
0 number of unpredictable events happening in the
0 4 8 12 16 20 24
gastrointestinal tract during drug absorption.
Time (hours)
The ER oral drug products remain in the gastro-
FIGURE 194 Bioavailability of a drug from an immedi-
intestinal (GI) tract longer than conventional, imme-
ate-release tablet containing 50 mg of drug given at 0, 4, and
8 hours compared to a single 150-mg drug dose given in an diate-release, drug products. Thus, drug release from
extended-release dosage form. The drug absorption rate con- an ER drug product is more subject to be affected by
stant from the immediate-release drug product is first order, the anatomy and physiology of the GI tract, GI tran-
whereas the drug absorption rate constant from the extended- sit, pH, and its contents such as food compared to an
release drug product is zero order. The drug is 100% bioavail-
immediate-release oral drug product. The physio-
able and the elimination half-life is constant.
logic characteristics of the GI tract, including varia-
tions in pH, blood flow, GI motility, presence of
BIOPHARMACEUTIC FACTORS food, enzymes and bacteria, etc, affect the local
action of the extended-release drug product within
Some drugs are well-established medicine in the the GI tract and may affect the drug release rate from
treatment of specific diseases because of its effective- the product. In some cases, there may be a specific
ness and well tolerance; however, the relatively short absorption site or location within the GI tract in
plasma half-life requires frequent dosing associated which the extended-release drug product should
with a poor compliance. The poor pharmacokinetic release the drug. This specific drug absorption site or
(PK) of this drug in IR formulation refrains its location within the GI tract is referred to as an
broader application. Modified-release drug products absorption window. The absorption window is the
should produce a pharmacokinetic profile that pro- optimum site for drug absorption. If drug is not
vides the desired therapeutic efficacy and minimizes released and available for absorption within the
adverse events. In the case of delayed-release drug absorption window, the extended-release tablet
products, the enteric coating minimizes gastric irrita- moves further distally in the GI tract and incomplete
tion of the drug in the stomach. The major objective drug absorption may occur and may give rise to
of extended-release drug products is to achieve a unsatisfactory drug absorption in vivo despite excel-
prolonged therapeutic effect while minimizing lent in vitro release characteristics.
unwanted side effects due to fluctuating plasma drug
concentrations.
An ideal extended-release (ER) drug product Stomach
should demonstrate complete bioavailability, mini- The stomach is a muscular, hollow, dilated part of
mal fluctuations in drug concentration at steady the digestive system located on the left side of the
state, reproducibility of release characteristics inde- upper abdomen. The stomach receives food or liq-
pendent of food, and minimal diurnal variation. uids from the esophagus. In this “mixing and secreting”
Hence, ER drug product should release the drug at a organ, stomach secretes protein-digesting enzymes
constant or zero-order rate. As the drug is released called proteases and strong acids to aid in food
from the drug product, the drug is rapidly absorbed, digestion, through smooth muscular contortions
and the drug absorption rate should follow zero- before sending partially digested food (chyme) peri-
order kinetics similar to an intravenous drug infu- odically to the small intestines. However, the move-
sion. The drug product is designed so that the rate of ment of food or drug product in the stomach and
Plasma concentration
(mg/mL)
Modified-Release Drug Products and Drug Devices 573
small intestine is very different depending on the speeding up from ER formulation, which may cause
physiologic state. In the presence of food, the stom- high risk for patients at extreme cases by tablets
ach is in the digestive phase; in the absence of food, coating erosion (Jonkman, 1987). The solubilization
the stomach is in the interdigestive phase (Chapter 14). effect by bile micelles in the presence of food may
During the digestive phase, food particles or solids have a positive effect on drug absorption (Kawai
larger than 2 mm are retained in the stomach, et al, 2011). Negative food effects may take effect at
whereas smaller particles are emptied through the an opposite direction by increasing the viscosity in
pyloric sphincter at a first-order rate depending on the upper GI tract, delay the absorption rate, and
the content and size of the meals. During the interdi- prolong the passage time of ER drug product in GI
gestive phase, the stomach rests for a period of up to tract (Marasanapalle et al, 2009). A longer time of
30–40 minutes, coordinated with an equal resting retention in the stomach may expose the drug to
period in the small intestine. Peristaltic contractions stronger agitation in the acid environment. The
then occur, which end with strong housekeeper con- stomach has been described as having “jet mixing”
tractions that move everything in the stomach action, which sends mixture at up to -50 mm Hg
through to the small intestine. Similarly, large parti- pressure toward the pyloric sphincter, causing it to
cles in the small intestine are moved along only in open and periodically release chyme to the small
the housekeeper contraction period. intestine.
A drug may remain for several hours in the
stomach if it is administered during the digestive
phase. Fatty material, nutrients, and osmolality may Small Intestine and Transit Time
further extend the time of the drug staying in the The small intestine is about 10–14 ft in length. The
stomach. When the drug is administered during the duodenum is sterile, while the terminal part of the
interdigestive phase, the drug may be swept along small intestine that connects the cecum contains
rapidly into the small intestine. The drug release some bacteria. The proximal part of the small intes-
rates from some extended-release drug products tine has a pH of about 6, because of neutralization of
are affected by mechanism of drug release (Sujja- acid by bicarbonates secreted into the lumen by the
areevath et al, 1998), viscosity (Rahman et al, 2011), duodenal mucosa and the pancreas. The small intes-
pH and ironic strength (Asare-Addo et al, 2011), tine provides an enormous surface area for drug
and food (Abrahamsson et al, 2004). Dissolution of absorption because of the presence of microvilli. The
drugs in the stomach may also be affected by the small-intestine transit time of a solid preparation has
presence or absence of food. When food and nutri- been concluded to be about 3 hours or less in 95% of
ents are present, the stomach pH may change from the population (Hofmann et al, 1983). As Table 19-2
1 to 2 by stomach acid (usually HCl) secretion summarizes, the small intestinal transit time is more
about 3–5 because of the food and nutrients reproducible around 3–4 hours. The transit time
neutralization. from mouth to cecum ranges from 3 to 7 hours.
In one example, drug release from various the- Colonic transit time has the highest variation, which
ophylline ER formulations could be influenced is typically from 10 to 20 hours (Shareef et al, 2003;
(either increased or decreased) by concomitant intake Ritschel, 1991; Yu et al, 1996). Various investigators
of food compared to fasting conditions (Jonkman, have used the lactulose hydrogen test, which mea-
1989). Food intake can influence the rate of drug sures the appearance of hydrogen in a patient’s
release from the dosage form, the rate of drug breath, to estimate transit time. Lactulose is metabo-
absorption, the amount of drug absorbed, or all of lized rapidly by bacteria in the large intestine, yield-
these parameters simultaneously. The rate of drug ing hydrogen that is exhaled. Hydrogen is normally
release of various ER formulations can be affected absent in a person’s breath. These results and the use
by the composition of the coadministered meal. This of gamma-scintigraphy studies confirm a relatively
effect may result in both “positive” and “negative.” short GI transit time from mouth to cecum of
Positive food effects usually come with drug release 4–6 hours (Shareef et al, 2003). This technique has
574 Chapter 19
TABLE 192 pH Values against Transit Time at Different Segments of GI Tract
Fasting condition Food condition
Anatomical location pH Transition time (h) pH Transition time (h)
Stomach 1-3 0.5-0.7 4.3-5.4 1
Duodenum ~6 <0.5 5.4 <0.5
Jejunum 6-7 1.7 5.4-5.6 1.7
Heum 6.6-7.4 1.3 6.6-7.4 1.3
Cecum 6.4 4.5 6.4 4.5
Colon 6.8 13.5 6.8 13.5
been applied in the exploring of extended oro-cecal the colon, and drug transit is slow. Not much is
transit time in the intestine (Eisenmann et al, 2008). known about drug absorption in this area, although
This transit time interval was concluded to be too unabsorbed drug that reaches this region may be
short for extended-release dosage forms that last up to metabolized by bacteria. Incompletely absorbed
12 hours, unless the drug is to be absorbed in the colon. antibiotics may affect the normal flora of the bacte-
The colon has little fluid and the abundance of bacteria ria. The rectum has a pH of about 6.8–7.0 and con-
may make drug absorption erratic and incomplete. tains more fluid compared to the colon. Drugs are
In a Phase I study, 12 healthy males were given absorbed rapidly when administered as rectal prepa-
a controlled-release, new gastro-resistant, extended- rations. However, the transit rate through the rectum
release tablets with multimatrix structure (ie, MMX®- is affected by the rate of defecation. Presumably,
tablets containing 9 mg budesonide). The noninvasive drugs formulated for 24-hour duration must remain
technique of gamma-scintigraphy was employed to in this region to be absorbed.
monitor the gastrointestinal transit of orally ingested Several extended-release and delayed-release
dosage forms for the purpose of identification of the drug products, such as mesalamine delayed-release
exact time and region of disintegration and to follow tablets (Asacol), are formulated to take advantage of
the release of the active ingredient from the extended- the physiologic conditions of the GI tract (Shareef
release formulation. The effect of food was tested by et al, 2003). Enteric-coated beads have been found to
comparing plasma pharmacokinetics after intake of release drug over 8 hours when taken with food,
a high-fat and high-calorie breakfast with fasting because of the gradual emptying of the beads into
controls. The results showed that 153Sm-labeled the small intestine. Specially formulated “floating
MMX-budesonide extended-release tablets reached tablets” that remain in the top of the stomach have
the colonic region after a mean of 9.8 hours. Initial been used to extend the residence time of the product
tablet disintegration was observed in the ileum in in the stomach. None of these methods, however, is
42% of subjects, whereas in 33% the main site of consistent enough to perform reliably for potent
disintegration was either the ascending or the trans- medications. More experimental research is needed
verse colon. The budesonide plasma concentrations in this area. In 2012, Dr. Zhu et al (2012) designed a
were first detected after 6.8 ± 3.2 h (Brunner et al, large intestine–targeted oral delivery with pH-depen-
2006). dent nanoparticles containing vaccine nanoparticles
to control genitorectal viral infection. This new type
Large Intestine of extended-release drug system can induce colorec-
The large intestine is about 4–5 ft long. It consists of tal immunity in mice comparably to colorectal vac-
the cecum, the ascending and descending colons, cination and protected against rectal and vaginal
and eventually ends at the rectum. Little fluid is in viral challenge. Their conclusion showed that using
Modified-Release Drug Products and Drug Devices 575
this oral vaccine delivery system to target the large correlation (IVIVC) (see also Chapter 15). These
intestine, but not the small intestine, may represent a tests may not be pharmacopeial standard; however,
feasible new strategy for immune protection of rectal they should be sensitive, reliable, and discriminatory
and vaginal mucosa (Qiu et al, 2014). with regard to the in vitro drug release characteristics.
This technique is applied not only to immediate-
DOSAGE FORM SELECTION release drug products but also to extended-release
drug products with promising future (Cheng et al,
The properties of the drug and the size of the required 2014; Honório et al, 2013; Meulenaar et al, 2014).
dosage are important in formulating an extended-
release product. These properties will also influence
the selection of appropriate dissolution media, appa- ADVANTAGES AND
ratus, and test parameters to obtain in vitro drug DISADVANTAGES OF
release data that will reflect in vivo drug absorption. EXTENDED-RELEASE PRODUCTS
For example, a drug with low aqueous solubility
generally should not be formulated into a nondisinte- To maintain a long therapeutic effect, frequent admin-
grating tablet, because the risk of incomplete drug istration of conventional formulations of many drugs
dissolution is high. Instead, a drug with low solubility with short half-life is necessary. Otherwise, concentra-
at neutral pH should be formulated as an erodible tion under therapeutic window occurs frequently in the
tablet, so that most of the drug is released before it course treatment, which may induce drug resistance.
reaches the colon. The lack of fluid in the colon may Extended-release dosage forms may solve these issues
make complete drug dissolution difficult. Erodible by having a number of advantages in safety and effi-
tablets are more reliable for these drugs because the cacy over immediate-release drug products in that the
entire tablet eventually dissolves. frequency of dosing can be reduced, drug efficacy can
A drug that is highly water soluble in the acid pH be prolonged, and the incidence and/or intensity of
in the stomach but very insoluble at intestinal pH may adverse effects can be decreased.
be very difficult to formulate into an ER drug product.
An ER drug product with too much coating protection Advantages
may result in low drug bioavailability, while too little
coating protection may result in rapid drug release or 1. Sustained therapeutic blood levels of the drug
dose-dumping in the stomach. A moderate extension Extended-release drug products offer several
of duration with enteric-coated beads may be possi- important advantages over conventional dosage
ble. However, the risk of erratic performance is higher forms of the same drug by optimizing biophar-
than with a conventional dosage form. The osmotic maceutic, pharmacokinetic, and pharmacody-
type of controlled drug release system may be more namic properties of drugs. Extended release
suitable for this type of drug. allows for sustained therapeutic blood levels of
With most single-unit dosage forms, there is a the drug; sustained blood levels provide for a
risk of erratic performance due to variable stomach prolonged and consistent clinical response in
emptying and GI transit time. The size and shape of the patient. Moreover, if the drug input rate is
the single-unit dosage form will also influence GI constant, the blood levels should not fluctuate
transit time. Selection of a pellet or bead dosage form between a maximum and a minimum compared
may minimize the risk of erratic stomach emptying, to a multiple-dose regimen with an immediate-
because pellets are usually scattered soon after inges- release drug product (Chapter 8). Highly
tion. Disintegrating tablets have the same advantages fluctuating blood concentrations of drug may
because they break up into small particles soon after produce unwanted side effects in the patient if
ingestion. The ultimate goal of the dissolution test is the drug level is too high, or may fail to exert
used to predict the in vivo performance of products the proper therapeutic effect if the drug level is
from in vitro test by a proper in vitro–in vivo too low. In such a way, extended-release drug
576 Chapter 19
products may maintain a constant plasma drug tablets. For patients under nursing care, the cost
concentration within therapeutic window for of nursing time required to administer medica-
a prolonged period; extended-release dosage tion is decreased if only one drug dose is given
forms maximize the therapeutic effect of drugs to the patient each day.
while minimizing possible resistance. For some drugs with long elimination half-
2. Improved patient compliance lives, such as chlorpheniramine, the inherent
Another undoubted advantage of extended- duration of pharmacologic activity is long.
release formulation is improved patient Minimal fluctuations in blood concentrations of
compliance. It may provide the convenience these drugs are observed after multiple doses are
of supplying additional doses without the need administered. Therefore, there is no rationale for
of re-administration. It may reduce dosing extended-release formulations of these drugs.
frequency to an extent that once-daily dose is However, such drug products are marketed with
sufficient for therapeutic management through the justification that extended-release products
uniform plasma concentration providing minimize toxicity, decrease adverse reactions,
maximum utility of drug with reduction in local and provide patients with more convenience
and systemic side effects and cure or control and, thus, better compliance. In contrast, drugs
condition in shortest possible time by small- with very short half-lives need to be given at
est quantity of drug to assure greater patient frequent dosing intervals to maintain therapeutic
compliance. For example, if the patient needs to efficacy. For drugs with very short elimination
take the medication only once daily, he or she half-lives, an extended-release drug product
will not have to remember to take additional maintains the efficacy over a longer duration.
doses at specified times during the day. Further-
more, because the dosage interval is longer, the Disadvantages
patient’s sleep may not be interrupted to take
Beyond the advantages, there are also some disad-
another drug dose. With longer therapeutic
vantages of using extended-release medication, such
drug concentrations, the patient awakes without
as the following:
having subtherapeutic drug levels.
3. Reduction in adverse side effects and improve- 1. Dose-dumping
ment in tolerability Dose-dumping is defined either as the release
Drug plasma levels are maintained within a of more than the intended fraction of drug or
narrow window with no sharp peaks and with as the release of drug at a greater rate than the
the AUC of plasma concentration-versus-time customary amount of drug per dosage interval,
curve equivalent to the AUC from multiple such that potentially adverse plasma levels
dosing with immediate-release dosage form. may be reached. Dose-dumping is a phenom-
Because of the well-controlled drug concentra- enon whereby relatively large quantity of drug
tion in therapeutic and safe window, the possible in a controlled-release formulation is rapidly
side effects can be significantly decreased due released, introducing potentially toxic quantity
to the absence of drug plasma levels higher of the drug into systemic circulation (Dighe and
than toxic level. Meanwhile, the tolerability Adams, 1988). Dose-dumping can lead to a
of drug can be improved due to no drug level severe condition for patients, especially for a
lower than the minimum effective level. drug with narrow therapeutic index. Usually,
4. Reduction in healthcare cost the dose-dumping comes from the fault of
The patient may also derive an economic formulation design.
benefit in using an extended-release drug 2. Less flexibility in accurate dose adjustment
product. A single dose of an extended-release If the patient suffers from an adverse drug
product may cost less than an equivalent drug reaction or accidentally becomes intoxicated,
dose given several times a day in rapid-release the removal of drug from the system is more
Modified-Release Drug Products and Drug Devices 577
difficult with an extended-release drug product. In practice, Dm (mg) is released over a period of time
In conventional dosage forms, dose adjustments and is equal to the product of td (the duration of drug
are much simpler, for example, tablets can be release) and the zero-order rate k 0
r (mg/h). Therefore,
divided into two fractions. Equation 19.1 can be expressed as
3. Less possibility for high dosage
Orally administered extended-release drug D 0
tot = DI + kr td (19.2)
products may yield erratic or variable drug
absorption as a result of various drug interactions Ideally, the maintenance dose (Dm) is released after
with the contents of the GI tract and changes in DI has produced a blood level equal to the therapeu-
GI motility. The formulation of extended-release tic drug level (Cp). However, due to the limits of
drug products may not be practical for drugs that formulations, Dm actually starts to release at t = 0.
are usually given in large single doses (eg, 500 mg) Therefore, DI may be reduced from the calculated
in conventional dosage forms. Because the amount to avoid “topping.”
extended-release drug product may contain two
or more times the dose given at more frequent D 0 0
tot = DI − kr tp + kr td (19.3)
intervals, the size of the extended-release drug
product may have to be quite large, too large for Equation 19.3 describes the total dose of drug
the patient to swallow easily. needed, with tp representing the time needed to reach
Besides the above-mentioned disadvantages, peak drug concentration after the initial dose.
other issues including increased potential for For a drug that follows a one-compartment open
first-pass clearance and poor IVIVC correla- model, the rate of elimination (R) needed to maintain
tion are also the challenges. For example, with the drug at a therapeutic level (Cp) is
delayed release or enteric drug products, two
possible problems may occur if the enteric R = kVDCp (19.4)
coating is poorly formulated. First, the enteric
coating may become degraded in the stomach, where k 0
r must be equal to R in order to provide a
allowing for early release of the drug, possibly stable blood level of the drug. Equation 19.4 provides
causing irritation to the gastric mucosal lining. an estimation of the release rate (k 0
r ) required in the
Second, the enteric coating may fail to dissolve formulation. Equation 19.4 may also be written as
at the proper site, and therefore, the tablet may R = CpClT (19.5)
be lost from the body prior to drug release,
resulting in incomplete absorption (Nagaraju where ClT is the clearance of the drug. In designing
et al, 2010; Wilson et al, 2013). an extended-release product, DI would be the load-
ing dose that would raise the drug concentration in
KINETICS OF EXTENDED-RELEASE the body to Cp, and the total dose needed to main-
tain therapeutic concentration in the body would be
DOSAGE FORMS simply
The amount of drug required in an extended-release
D ( 9 6
tot = DI +C 1 .
pCl )
Tτdosage form to provide a sustained drug level in the
body is determined by the pharmacokinetics of the
For many sustained-release drug products, there is
drug, the desired therapeutic level of the drug, and
no built-in loading dose (ie, DI = 0). The dose needed
the intended duration of action. In general, the total
to maintain a therapeutic concentration for t hours is
dose required (Dtot) is the sum of the maintenance
dose (Dm) and the initial dose (DI) released immedi-
D0 = CpτClT (19.7)
ately to provide a therapeutic blood level.
Dtot = DI + Dm (19.1) where t is the dosing interval.
578 Chapter 19
TABLE 193 Release Rates for Extended-Release Drug Products as a Function of Elimination
Half-Lifea
Total (mg) to Achieve Duration
t1/2 (h) k (h-1) R (mg/h) 6 h 8 h 12 h 24 h
1 0.693 69.3 415.8 554.4 831.6 1663
2 0.347 34.7 208.2 277.6 416.4 832.8
4 0.173 17.3 103.8 138.4 207.6 415.2
6 0.116 11.6 69.6 92.8 139.2 278.4
8 0.0866 8.66 52.0 69.3 103.9 207.8
10 0.0693 6.93 41.6 55.4 83.2 166.3
12 0.0577 5.77 34.6 46.2 69.2 138.5
aAssume Cdesired is 5 mg/mL and the VD is 20,000 mL; R = kVDCp: no immediate-release dose.
Table 19-3 shows the influence of t1/2 on the
EXAMPLE »» »
amount of drug needed for an extended-release drug
product. Table 19-3 was constructed by assuming
What dose is needed to maintain a therapeutic
that the drug has a desired serum concentration of
concentration of 10 mg/mL for 12 hours in a
5 mg/mL and an apparent volume of distribution of
sustained-release product? (a) Assume that t1/2 for
20,000 mL. The release rate needed to achieve the
the drug is 3.46 hours and VD is 10 L. (b) Assume
desired concentration, R, decreases as the elimination
that t1/2 of the drug is 1.73 hours and VD is 5 L.
half-life increases. Because elimination is slower for
0.693
a. k = = 0.2/h a drug with a long half-life, the input rate should
3.46 be slower. The total amount of drug needed in the
Cl = kV = 0.2×10 = 2L/h
T D extended-release drug product is dependent on both
the release rate R and the desired duration of activity
From Equation 19.7,
for the drug. For a drug with an elimination half-life of
D0 = (10 mg/mL)(1000 mL/L)(12 h)(2 L/h)
4 hours and a release rate of 17.3 mg/h, the extended-
= 240,000 mg or 240 mg
release product must contain 207.6 mg to provide a
0.693
b. k duration of activity of 12 hours. The bulk weight of the
= = 0.4 h
1.73 extended-release product will be greater than this
Cl = 0.4×5= 2 L/h amount, due to the presence of excipients needed in
T
the formulation. The values in Table 19-3 show that, in
From Equation 19.7, order to achieve a long duration of activity (≥12 hours)
D0 = 10 × 2 × 1000 × 12 = 240,000 mg or 240 mg for a drug with a very short half-life (1–2 hours), the
In this example, the amount of drug needed in extended-release drug product becomes quite large
a sustained-release product to maintain thera- and impractical for most patients to swallow.
peutic drug concentration is dependent on both
VD and the elimination half-life. In part b of the
example, although the elimination half-life is PHARMACOKINETIC SIMULATION
shorter, the volume of distribution is also smaller. OF EXTENDED-RELEASE PRODUCTS
If the volume of distribution is constant, then the
The plasma drug concentration profiles of many
amount of drug needed to maintain Cp is depen-
extended-release products fit an oral one-compartment
dent simply on the elimination half-life.
model assuming first-order absorption and elimination.
Modified-Release Drug Products and Drug Devices 579
Various other models have been used to simu-
40
late plasma drug levels of extended-release products
(Welling, 1983). The plasma drug levels from a zero-
order, extended-release drug product may be simu-
30 lated with Equation 19.8.
Rapid release R
C = (1 −kt
− ( 9 8
p e ) 1 . )
kVD
20
where R = rate of drug release (mg/min), Cp = plasma
Sustained release drug concentration, k = overall elimination constant,
and VD = volume of distribution. In the absence of a
10
loading dose, the drug level in the body rises slowly
to a plateau with minimum fluctuations (Fig. 19-6).
This simulation assumes that (1) rapid drug release
0 occurs without delay, (2) perfect zero-order release
0 2 4 6 8 10 12
Time (hours) and absorption of the drug takes place, and (3) the drug
FIGURE 195 Plasma drug concentration of a sustained- is given exactly every 12 hours. In practice, the above
release and a regular-release product. Note the difference of assumptions are not precise, and fluctuations in drug
peak time and peak concentration of the two products. level do occur.
When a sustained-release drug product with a
loading dose (rapid release) and a zero-order main-
Compared to an immediate-release product, the tenance dose is given, the resulting plasma drug
extended-release product typically shows a smaller concentrations are described by
absorption rate constant, because of the slower absorp-
tion of the extended-release product. The time for D
C ika D
(e−kt e−kat ) s (1 e−kt
p = − + − ) (19.9)
peak concentration (tmax) is usually longer (Fig. 19-5), VD(ka − k) kVD
and the peak drug concentration (Cmax) is reduced. If
the drug is properly formulated, the area under the where Di = immediate-release (loading dose) dose
plasma drug concentration curve should be the same. and Ds = maintenance dose (zero-order). This
Parameters such as Cmax, tmax, and area under the expression is the sum of the oral absorption equation
curve (AUC) conveniently show how successfully the
extended-release product performs in vivo. For exam-
ple, a product with a tmax of 3 hours would not be very 30
satisfactory if the product is intended to last 12 hours.
Similarly, an excessively high Cmax is a sign of dose-
dumping due to inadequate formulation. The pharma- 20
cokinetic analysis of single- and multiple-dose plasma
data has been used by regulatory agencies to evaluate
many sustained-release products. The analysis is prac- 10
tical because many products can be fitted to this
model even though the drug is not released in a first- 0
order manner. The limitation of this type of analysis is 0 12 24 36
that the absorption rate constant may not relate to the Time (hours)
rate of drug dissolution in vivo. If the drug strictly fol- FIGURE 196 Simulated plasma drug level of an
extended-release product administered every 12 hours. The
lows zero-order release and absorption, the model
plasma level shows a smooth rise to steady-state level with no
may not fit the data. fluctuations.
Concentration (mg/mL)
Concentration (mg/mL)
580 Chapter 19
(first part) and the intravenous infusion equation CLINICAL EXAMPLES
(second part).
Methylphenidate HCl Extended-Release
Tablets (Concerta®)
Extended-Release Drug Product with Methylphenidate HCl is a CNS (central nervous sys-
Immediate-Release Component tem) stimulant indicated for the treatment of atten-
Extended-release drug products may be formulated tion deficit hyperactivity disorder (ADHD) and is
with or without an immediate-release loading dose. often used in children 6 years of age and older.
Extended-release drug products that are given to Methylphenidate is readily absorbed after oral
patients in daily multiple doses to maintain steady- administration and has an elimination t1/2 of about
state therapeutic drug concentrations do not need a 3.5 hours. Methylphenidate HCl extended-release
built-in loading dose when given subsequent doses. tablets (Concerta) have an osmotically active con-
Pharmacokinetic models have been proposed for trolled-release core with an immediate-release drug
extended-release drug products that have a rapid first- overcoat. Concerta uses osmotic pressure to deliver
order drug release component and a slow zero-order methylphenidate HCl at a controlled rate. The
release maintenance dose component. This model system, which resembles a conventional tablet in
assumes a long elimination t1/2 in which drug accumu- appearance, comprises an osmotically active trilayer
lation occurs until steady state is attained. The model core surrounded by a semipermeable membrane with
predicts spiking peaks due to the loading dose compo- an immediate-release drug overcoat. The trilayer
nent when the extended-release drug product is given core is composed of two drug layers containing
continuously in multiple doses. In this model, a rapid- the drug and excipients, and a push layer containing
release loading dose along with the extended-release osmotically active components. Each extended-
drug dose given in a daily multiple-dose regimen release tablet for once-a-day oral administration con-
introduces more drug into the body than is necessary. tains 18, 27, 36, or 54 mg of methylphenidate HCl
This is observed by a “topping” effect. As shown in USP and is designed to have 12-hour duration of
the example, amoxicillin extended-release tablets effect. After oral administration of Concerta, the
(Moxatag®) is designed to consist of three compo- plasma methylphenidate concentration increases
nents, one immediate-release and two delayed-release rapidly reaching an initial maximum at about 1 hour,
parts, each containing amoxicillin. The three compo- followed by gradual ascending concentrations over the
nents are combined in a specific ratio to prolong the next 5–9 hours after which a gradual decrease begins.
release of amoxicillin from Moxatag compared to Mean tmax occurs between 6 and 10 hours. When the
immediate-release amoxicillin. patient takes this product in the morning, the patient
When a loading dose is necessary, a rapid- or receives an initial loading dose followed by a mainte-
immediate-release drug product may be given sepa- nance dose that is eliminated by the evening when the
rately as a loading dose to initially bring the patient’s patient wants to go to sleep. Due to the short elimina-
plasma drug level to the desired therapeutic level. In tion t1/2, the drug does not accumulate.
certain clinical situations, an extended-release drug
product with an immediate-release component along
with a controlled-release core can provide a specific Oxymorphone Extended-Release Tablets
pharmacokinetic profile that provides rapid onset (Opana® ER)
and prolonged plasma drug concentrations that Oxymorphone extended-release tablets (Opana ER)
relates to the time course for the desired pharmaco- are approved for the management of chronic pain.
dynamic activity. For these extended-release drug The pharmacokinetic profile of oxymorphone ER is
products with initial immediate-release components, predictable, linear, and dose-proportional. Opana ER
the active drug must have a relatively short elimina- may maintain steady plasma levels over 12-hour
tion t1/2 so that the drug does not accumulate between period with t1/2 of about 9–11 hours. It has a low
dosing. fluctuation index of less than 1 after achieving
Modified-Release Drug Products and Drug Devices 581
steady state, as do its two metabolites. Oxymorphone Divalproex Sodium Extended-Release
is metabolized primarily via hepatic glucuronidation Tablets (Depakote® ER)
to one active metabolite (6-OH-oxymorphone) and Divalproex sodium is used to treat seizure disorders
to one inactive metabolite (oxymorphone-3-glucuro- and mental/mood conditions (such as manic phase
nide). It is neither metabolized by cytochrome P-450 of bipolar disorder), and to prevent migraine head-
(CYP) enzymes nor inhibited or induced by CYP aches. It works by restoring the balance of certain
substrates. And since oxymorphone ER has minimal natural substances (neurotransmitters) in the brain.
potential for pharmacokinetic interactions, its use with The mechanisms by which valproate exerts its
sedatives, tranquilizers, hypnotics, phenothiazines, therapeutic effects have not been established. It has
and other central nervous system (CNS) depressants been suggested that its activity in epilepsy is related
can produce additive effects. Hence, as with other to increased brain concentrations of gamma-amino-
opioids, vigilance is required in preventing pharma- butyric acid (GABA). The absolute bioavailability
codynamic interactions during therapy with oxymor- of divalproex sodium extended-release tablets
phone ER (Craig, 2010). administered as a single dose after a meal was
approximately 90% relative to intravenous infu-
Zolpidem Tartrate Extended-Release Tablets sion. The median time to maximum plasma valpro-
(Ambien® CR) ate concentrations (Cmax) after divalproex sodium
Zolpidem tartrate extended-release tablets are indi- extended-release tablet administration ranged from
cated for the treatment of insomnia characterized by 4 to 17 hours. Mean terminal t1/2 for valproate
difficulties with sleep onset and/or sleep maintenance. monotherapy ranged from 9 to 16 hours depending
Zolpidem has a mean elimination t1/2 of 2.5 hours. on the dosage applied.
Zolpidem tartrate extended-release tablets exhibit
biphasic absorption characteristics, which results in
TYPES OF EXTENDED-RELEASE
rapid initial absorption from the gastrointestinal tract
similar to zolpidem tartrate immediate release and PRODUCTS
then provides extended plasma concentrations beyond The pharmaceutical industry has been developing
3 hours after administration.1 Patients who use this newer modified-release drug products at a very rapid
product have a more rapid onset of sleep due to the pace. Many of these modified-release drug products
initial dose and are able to maintain sleep due to the have patented drug delivery systems. This chapter
maintenance dose. Due to the short elimination t1/2, provides an overview of some of the more widely
the drug does not accumulate. In adult and elderly used methods for the manufacture of modified drug
patients treated with zolpidem tartrate extended- products.
release tablets, there was no evidence of accumulation The extended-release drug product is designed
after repeated once-daily dosing for up to 2 weeks. A to contain a drug dose that will release drug at a
food-effect study compared the pharmacokinetics of desired rate over a specified period of time. As dis-
zolpidem tartrate extended-release tablets 12.5 mg cussed previously, the extended-release drug product
when administered while fasting or within 30 minutes may also contain an immediate-release component.
after a meal. Results demonstrated that with food, The general approaches to manufacturing an extended-
mean AUC and Cmax were decreased by 23% and release drug product include the use of a matrix
30%, respectively, while median Tmax was increased structure in which the drug is suspended or dis-
from 2 to 4 hours. The half-life was not changed. solved, the use of a rate-controlling membrane
These results suggest that, for faster sleep onset, through which the drug diffuses, or a combination of
zolpidem tartrate extended-release tablets should not both. None of the extended-release drug products
be administered with or immediately after a meal. works by a single drug-release mechanism. Most
extended-release products release drug by a combi-
1Approved label for Ambien CR, April 2010. nation of processes involving drug dissolution,
582 Chapter 19
permeation, erosion, and diffusion. The single most gastrointestinal tract. Once the drug is dissolved, the
important factor is water permeation into the drug rate of drug diffusion may be further controlled to a
product, without which none of the product release desirable rate. Table 19-4 describes some common
mechanisms would operate. Controlling the rate of extended-release product examples and the mecha-
water influx into the product generally dictates nisms for controlling drug release. Table 19-5 lists
the rate at which the drug dissolves in the the composition for some drugs.
TABLE 194 Examples of Oral Modified-Release Drug Products
Type Trade Name Rationale
Extended-Release Erosion tablet Constant-T Theophylline
Drug Products Tenuate Dospan Diethylpropion HCI dispersed in hydrophilic matrix
Tedral SA Combination product with a slow-erosion compo-
nent (theophylline, ephedrine HCI) and an initial-
release component theophylline, ephedrine HCI,
phenobarbital
Waxy matrix tablet Kaon CI Slow release of potassium chloride to reduce GI
irritation
Coated pellets in Ornade spansule Combination phenylpropanolamine HCI and
capsule chlorpheniramine with initial- and extended-release
component
Pellets in tablet Theo-Dur Theophylline
Leaching Ferro-Gradumet Ferrous sulfate in a porous plastic matrix that is excreted
(Abbott) in the stool; slow release of iron decreases GI irritation
Desoxyn gradumet Methamphetamine methylacrylate methylmethacry-
tablet (Abbott) late copolymer, povidone, magnesium stearate; the
plastic matrix is porous
Coated ion Tussionex Cation ion-exchange resin complex of hydrocodone
exchange and phenyltoloxamine
Flotation–diffusion Valrelease Diazapam
Osmotic delivery Acutrim Phenylpropanolamine HCI (Oros delivery system)
Procardia-XL GITS—Gastrointestinal therapeutic system with
NaCI-driven (osmotic pressure) delivery system for
nifedipine
Microencapsulation Bayer timed-release Aspirin
Nitrospan Microencapsulated nitroglycerin
Micro-K Extencaps Potassium chloride microencapsulated particles
Delayed-release diclofenac sodium Enteric coating dissolves at pH >5 for release of drug
drug products enteric-coated tablets in duodenum
mesalamine) delayed- Delayed-release tablets are coated with acrylic-based
release tablets resin, Eudragit S (methacrylic acid copolymer B, NF),
which dissolves at pH 7 or greater, releasing mesa-
lamine in the terminal ileum and beyond for topical
anti-inflammatory action in the colon
Orally disintegrating
tables
TABLE 195 Composition and Examples of Some Modified-Release Products
K-Tab (Abbott) 750 mg or 10 mEq of potassium chloride in a film-coated matrix tablet. The matrix may be
excreted intact, but the active ingredient is released slowly without upsetting the GI tract.
Inert ingredients: Cellulosic polymers, castor oil, colloidal silicon dioxide, polyvinyl acetate,
paraffin. The product is listed as a waxy/polymer matrix tablet for release over 8–10 h.
Toprol-XL tablets (Astra) Contains metoprolol succinate for sustained release in pellets, providing stable beta-blockade
over 24 h with one daily dose. Exercise tachycardia was less pronounced compared to
immediate-release preparation. Each pellet separately releases the intended amount of medication.
Inert ingredients: Paraffin, PEG, povidone, acetyltributyl citrate, starch, silicon dioxide, and magnesium
stearate.
Quinglute Dura tablets Contains 320 mg quinidine gluconate in a prolonged-action matrix tablet lasting 8–12 h and
(Berlex) provides PVC protection.
Inert ingredients: Starch, confectioner’s sugar and magnesium stearate.
Brontil Slow-Release Phendimetrazine tartrate 105 mg sustained pellet in capsule.
capsules (Carnrick) Slow Slow-release iron preparation (OTC medication) with 160 mg ferrous sulfate for iron deficiency.
Fe tablets (Ciba)
Inert ingredients: HPMC, PEG shellac, and cetostearyl alcohol.
Tegretol-XR tablets (Ciba Carbamazepine extended-release tablet.
Geneva) Inert ingredients: Zein, cetostearyl alcohol, PEG, starch, talc, gum tragacanth, and mineral oil.
Sinemed CR tablets Contains a combination of carbidopa and levodopa for sustained-release delivery. This is a special
(Dupont pharma) erosion polymeric tablet for Parkinson’s disease treatment.
Pentasa capsules Contains mesalamine for ulcerative colitis in a sustained-release mesalamine coated with
(Hoechst Marion/Roussel) ethylcellulose. For local effect mostly, about 20% absorbed versus 80% otherwise.
Isoptin SR (Knoll) Verapamil HCI sustained-release tablet.
Inert ingredients: PEG, starch, PVP, alginate, talc, HPMC, methylcellulose, and microcrystalline cellulose.
Pancrease capsules Enteric-coated microspheres of pancrelipase. Protects the amylase, lipase, and protease from the
(McNeil) action of acid in the stomach.
Inert ingredients: CAP, diethyl phthalate, sodium starch glycolate, starch, sugar, gelatin, and talc.
Cotazym-S (Organon) Enteric-coated microspheres of pancrelipase.
Eryc (erythromycin Erythromycin enteric-coated tablet that protects the drug from instability and irritation.
delayed-release capsules)
(Warner-Chilcott)
Dilantin Kapseals Extended-release phenytoin capsule which contains beads of sodium phenytoin, gelatin, sodium
(Parke-Davis) lauryl sulfate, glyceryl monooleate, PEG 200, silicon dioxide, and talc.
Micro-K Extencaps Ethylcellulose forms semipermeable film surrounding granules by microencapsulation for release
(Robbins) over 8–10 h without local irritation.
Inert ingredients: Gelatin and sodium lauryl sulfate.
Quinidex Extentabs 300-mg dose, 100-mg release immediately in the stomach and is absorbed in the small intestine.
(Robbins) The rest is absorbed later over 10–12 h in a slow-dissolving core as it moves down the GI tract.
Inert ingredients: White wax, carnauba wax, acacia, acetylated monoglyceride, guar gum, edible
ink, calcium sulfate, corn derivative, and shellac.
Compazine Spansules Initial dose of prochlorperazine release first, then release slowly over several hours.
(GSK) Inert ingredients: Glycerylmonostearate, wax, gelatin, sodium lauryl sulfate.
Slo-bid Gyrocaps A controlled-release 12–24-h theophylline product.
(Rhone-Poulenc Rorer)
Theo-24 capsules A 24-h sustained-release theophylline product.
(UCB Pharma) Inert ingredients: Ethylcellulose, edible ink, talc, starch, sucrose, gelatin, silicon dioxide, and dyes.
Sorbitrate SA (Zeneca) The tablet contains isosorbide dinitrate 10 mg in the outer coat and 30 mg in the inner coat.
Inert ingredients: Carbomer 934P, ethylcellulose, lactose magnesium stearate, and Yellow No. 10.
583
584 Chapter 19
Drug Release from Matrix describe the drug release from an ointment layer
A matrix is an inert solid vehicle in which a drug is containing suspended drug at an initial concentration
uniformly suspended. A variety of excipients based (or amount of drug loading per unit volume), which
on wax, lipid, as well as natural and synthetic poly- is substantially greater than the solubility of the drug
mers have been used as carrier material in the prepa- per unit volume in the vehicle matrix. The Higuchi
ration of such matrix type of drug delivery systems. equation describes the release rate of a matrix
The drug release from such matrix systems is mainly tablet:
controlled by the diffusion process, concomitant
swelling, and/or erosion processes. A matrix may be P
Q =
DS λ (A− 0.5SP)1/2 t
formed by compressing or fusing the drug and the (19.10)
matrix material together. When an erodible or
swellable polymer matrix is involved, the drug
where Q = amount of drug release per cm2 of surface
release kinetics is further complicated by the pres-
at time t, S = solubility of drug in g/cm3 in the dis-
ence of a second moving boundary, namely, the
solution medium, A = content of drug in insoluble
swelling or eroding front, which moves either oppo-
matrix, P = porosity of matrix, D = diffusion coeffi-
site to or in the same direction as the diffusion front.
cient of drug, and l = tortuosity factor.
Generally, the drug is present in a small percentage,
Figure 19-7B represents a matrix enclosed by an
so that the matrix protects the drug from rapid dis-
insoluble membrane, so the drug release rate is regu-
solution and the drug slowly diffuses out over time.
lated by the permeability of the membrane as well as
Most matrix materials are water insoluble, although
the matrix. Figure 19-7C represents a matrix tablet
some matrix materials may swell slowly in water.
enclosed with a combined film. The film becomes
Drug release using a matrix dosage form may be
porous after dissolution of the soluble part of the
achieved using tablets or small beads, depending on
film. An example of this is the combined film
the formulation composition and therapeutic objec-
formed by ethylcellulose and methylcellulose. Close
tive (Lee, 2011). Figure 19-7 shows three common
to zero-order release has been obtained with this
approaches by which matrix mechanisms are
type of release mechanism.
employed. In Fig. 19-7A, the drug is coated with a
soluble coating, so drug release relies solely on the
regulation of drug release by the matrix material. If Classification of Matrix Tablets
the matrix is porous, water penetration will be rapid Based on the retarded materials used, matrix tablets
and the drug will diffuse out rapidly. A less porous can be divided into five types: (1) hydrophobic matrix
matrix may give a longer duration of release. (plastic matrix); (2) lipid matrix; (3) hydrophilic
Unfortunately, drug release from a simple matrix matrix; (4) biodegradable matrix; and (5) mineral
tablet is not zero order. Five decades ago, Professor matrix. Matrix system can also be classified according
Takeru Higuchi was the first one in the pharmaceuti- to their porosity situation, including macroporous,
cal field to tackle this moving boundary mathemati- microporous, and nonporous system. By the usage
cal problem for drug release from matrix systems. frequency, matrix tablets can also be categorized as
The Higuchi equation was originally derived to follows.
Insoluble membrane
Soluble membrane Insoluble with “windows”
(coating) membrane created by
dissolving of the
Matrix Matrix soluble part in water
A B C Matrix
FIGURE 197 Examples of three different types of modified matrix-release mechanisms.
Modified-Release Drug Products and Drug Devices 585
Gum-Type Matrix Tablets Polymeric matrix tablets for oral use can be
Some excipients have a remarkable ability to swell regarded as release-controlling excipients, which can
in the presence of water and form a substance with be divided into water soluble (or hydrophilic) and
a gel-like consistency. When this happens, the gel insoluble carriers (or hydrophobic) (Grund et al,
provides a natural barrier to drug diffusion from 2014). Considering the application in formulation,
the tablet. Natural gum polysaccharides consisting they should be quite safe. However, for certain
of multiple sugar units linked together to create patients with reduced GI motility caused by disease,
large molecules. Natural gums are biodegradable polymeric matrix tablets should be avoided, because
and nontoxic, which hydrate and swell on contact accumulation or obstruction of the GI tract by matrix
with aqueous media, and these have been used for tablets has been reported (Franek et al, 2014). As an
the preparation of dosage form. They are used in oral sustained-release product, the matrix tablet has
pharmaceuticals for their diverse properties and not been popular. In contrast, the use of the matrix
applications. They can receive modification for the tablet in implantation has been more popular.
purpose of hydration rate control, pH-dependent The use of biodegradable polymeric material for
solubility adjustment, thickness alteration and vis- extended release has been the focus of more recent
cosity change, etc (Pachuau and Mazumder, 2012; research. Chitosan–carrageenan matrix tablets were
Rana et al, 2011). characterized and used for the controlled release of
Because the gel-like material is quite viscous highly soluble drug of trimetazidine hydrochloride
and may not disperse for hours, this approach pro- (Li et al, 2013). One such example is poly(lactic
vides a means for maintaining the drug for hours acid-co-glycolic acid) copolymer, which degrades to
until all the drug has been completely dissolved and lactic/glatic acid and eliminates the problem of
diffused into the intestinal fluid. Gelatin is a com- retrieval after implantation (Clark et al, 2014). And
mon gelling material. However, gelatin dissolves the associated mathematical modeling is used for the
rapidly after the gel is formed. Drug excipients such advanced analysis on the release/delivery process of
as methylcellulose, gum tragacanth, Veegum, and polymeric-based matrix tablets, including porous,
alginic acid form a viscous mass and provide a use- microporous, and nonporous matrix. With generat-
ful matrix for controlling drug release and dissolu- ing more and more complex models or a parametric
tion. Drug formulations with these excipients provide fitting process, these modeling efforts can help prac-
extended drug release for hours. titioners to achieve a better formulation design and
understanding (Peppas and Narasimhan, 2014).
Other polymers for drug formulations include
Polymeric Matrix Tablets polyacrylate, methacrylate, polyester, ethylene–vinyl
Various polymeric materials have been used to pro- acetate copolymer (EVA), polyglycolide, polylactide,
long the rate of drug release. The most important and silicone. Of these, the hydrophilic polymers,
characteristic of this type of preparation is that the such as polylactic acid and polyglycolic acid, erode
prolonged release may last for days or weeks rather in water and release the drug gradually over time
than for a shorter duration (as with other techniques). (Clark et al, 2014). Polymer properties may affect the
An early example of an oral polymeric matrix tablet integrity and drug release from insoluble matrices.
was Gradumet (Abbott Laboratories), which was Typical examples of insoluble carriers are Kollidon®
marketed as an iron preparation. The nonbiodegrad- SR (co-processed polyvinyl acetate and polyvinyl-
able plastic matrix provides a rigid geometric surface pyrrolidone, ratio 8:2), Eudragit® RS (ammonium
for drug diffusion, so that a relatively constant rate of methacrylate copolymer), and ethylcellulose. A
drug release is obtained. In the case of the iron prepa- hydrophobic and also a non-degradable polymer such
ration, the matrix reduces the exposure of the irritat- as EVA release the drug over a longer duration time
ing drug to the GI mucosal tissues. The matrix is of weeks or months. The rate of release may be con-
usually expelled unchanged in the feces after all the trolled by blending two polymers and increasing the
drug has leached out. proportion of the more hydrophilic polymer, thus
586 Chapter 19
increasing the rate of drug release. The addition of a have been used to manufacture beaded formulations
low-molecular-weight polylactide to a polylactide including pan coating, spray drying, fluid-bed dry-
polymer formulation increased the release rate of the ing, and extrusion-spheronization.
drug and enabled the preparation of an extended- An early approach to the manufacture of ER
release system (Kleiner et al, 2014; Krivoguz et al, drug products was the use of encapsulated drugs in
2013). The type of plasticizer and the degree of cross- a beaded or pellet formulation. In general, the beads
linking provide additional means for modifying the are prepared by coating the powdered drug onto
release rate of the drug. Many drugs are incorporated preformed cores known as nonpareil seeds. The
into the polymer as the polymer is formed chemically nonpareil seeds are made from slurry of starch,
from its monomer. Light, heat, and other agents may sucrose, and lactose. The drug-coated beads are then
affect the polymer chain length, degree of cross- coated by a variety of materials that act as a barrier
linking, and other properties. This may provide a way to drug release. The beads may have a blend of dif-
to modify the release rate of the polymer matrices ferent thicknesses to provide the desired drug
prepared. Drugs incorporated into polymers may release. The beads may be placed in a capsule (eg,
have release rates that last over days, weeks, or even amphetamine ER capsules, Adderall XR) or with
months. These vehicles have been often recom- the addition of other excipients compressed into
mended for protein and peptide drug administration. tablets (eg, metoprolol succinate extended-release
For example, EVA is biocompatible and was shown tablets, Toprol XL).
to prolong insulin release in rats. Pan coating is a modified method adopted from
Hydrophobic polymers with water-labile link- candy manufacturing. Cores or nonpareil seeds of a
ages are prepared so that partial breakdown of the given mesh size are slowly added to known amount
polymers allows for desired drug release without of fine drug powder and coating solution and rounded
deforming the matrix during erosion. And hydro- for hours to become coated drug beads. The drug-
philic polymer such as hypromellose (hydroxypro- coated beads are then coated with a polymeric layer,
pyl methylcellulose, HPMC) may be integrated with which regulates drug release rate by changing either
hydrophobic block, for example, polyacrylate poly- the thickness of the film or the composition of the
mers, Eudragit RL100, and Eudragit RS100 with or polymeric material. Coatings may be aqueous or non-
without incorporating ethylcellulose on a matrix- aqueous. Aqueous coatings are generally preferred.
controlled metformin hydrochloride drug delivery Nonaqueous coatings may leave residual solvents in
system (Jain et al, 2014; Viridén et al, 2009). For oral the product, and the removal of solvents during
drug delivery, the problem of incomplete drug manufacture presents danger to workers and the envi-
release from the matrix is a major hurdle that must ronment. Cores are coated by either sprayed pan coat-
be overcome with the polymeric matrix dosage form. ing or air-suspension coating. Once the drug beads
Another problem is that drug release rates may be are prepared, they may be further coated with a pro-
affected by the amount of drug loaded. For implanta- tective coating to allow a sustained or prolonged
tion and other uses, the environment is more stable release of the drug. Spray dry coating or fluid-bed
compared to oral routes, so a stable drug release coating is a more recent approach and has several
from the polymer matrix may be attained for days or advantages over pan coating. Drug may be dissolved
weeks. in a solution that is sprayed or dispersed in small
droplets in a chamber. A stream of hot air evaporates
the solvent and the drug becomes a dry powder. The
Slow-Release Pellets, Beads, or Granules powdered material, which is aerated, may be coated
Pellets or beads are small spherical particles that can with a variety of excipients to achieve the desired
be formulated to provide a variety of modified drug drug release. Several experimental process variables
release properties. The size of these beads can be for fluid-bed coating include inlet air temperature,
very small (microencapsulation) for injections or spray rate (g/min), atomizing air pressure, solid
larger for oral drug delivery. Several approaches content, and curing time. Pelletization may also be
Modified-Release Drug Products and Drug Devices 587
obtained by extrusion-spheronization in which the available, such as Beloc® ZOK, Antra® MUPS, and
powdered drug and excipients are mixed in a mixer/ Prevacid® SoluTabTM. Compaction of multiparticu-
granulator. The moist mixture is then fed through an lates into tablets could result in either a disintegrat-
extruder at a specified rate and becomes spheronized ing tablet providing a multiparticulate system during
on exit through small-diameter dies. A wide range of gastrointestinal transit or intact tablets due to the
extrusion screen sizes and configurations are avail- fusion of the multiparticulates in a larger compact.
able for optimization of pellet diameter. Usually, a disintegrant is included in the tablet, caus-
The use of various amounts of coating solution ing the beads to be released rapidly after administra-
can provide beads with various coating protection. tion. Formulation of a drug into pellet form may
A careful blending of beads is used to achieve a reduce gastric irritation, because the drug is released
desired drug release profile. The finished drug product slowly over a period of time, therefore avoiding high
(eg, beads in capsule or beads in tablet) may contain drug concentration in the stomach (Abdul et al, 2010).
a blend of beads coated with materials of different Figure 19-8 shows the two types of multiple-unit
solubility rates to provide a means of controlling pellets in tablets, coated by polymer (reservoir-type)
drug release and dissolution. (a) compaction of matrix and/or uncoated drug pel-
The orally administered extended-release drug lets (b). The drug release from both of the pellets
products may display in single or multiple-unit dos- shows significant extended characterization, regard-
age forms. In single-unit formulations, they contain less the polymer coating or matrix dispersion. For the
the active ingredient within the single tablet or cap- reservoir-type coated-pellet dosage forms, the poly-
sule, whereas multiple-unit dosage forms comprise of meric coating must be able to withstand the compac-
a number of discrete particles that are combined into tion force. It may deform but should not rupture since
one dosage unit. Both of them may exist as pellets, any crack on the coating layer may cause unexpected
granules, sugar seeds (nonpareil), minitablets, ion- drug release. The type and amount of coating agent,
exchange resin particles, powders, and crystals, with the size of subunits, selection of external additives,
drugs being entrapped in or layered around cores. In
this way, multiple-unit dosage forms offer several
Nonpareil seed
advantages over single-unit systems such as nondisin-
Drug layer
tegrating tablets or capsules, although the drug release Modied release/
profiles are similar. Once multiple-unit systems are taste masking coating
taken orally, the subunits of multiple-unit preparations
distribute readily over a large surface area in the gas-
trointestinal tract. And because of the small particles
in sizes (<2 mm), multiple-unit preparations can enable
them to be well distributed along the gastrointestinal
(a) MUPS containing polymer-coated pellets
tract, which could improve the bioavailability
(Kambayashi et al, 2014; Rosiaux et al, 2014). Some
products take advantage of bead blending to provide Drug in polymeric matrix
two doses of drug in one formulation. For example, a
blend of rapid-release beads with some pH-sensitive
enteric-coated material may provide a second dose of
drug release when the drug reaches the intestine.
The pellet dosage form can be prepared as a
capsule or tablet. When pellets are prepared as tab-
lets, the beads must be compressed lightly so that (b) MUPS containing matrix pellets
they do not break. This process is called as compac- FIGURE 198 Schematic representation of types of
tion of pellets, which is also a challenging area. Only multiple unit pellets system (MUPS) in tablets—(a) comprising
a few multiple-unit-containing tablet products are of coated pellets, and (b) uncoated/matrix pellets.
588 Chapter 19
and the rate and magnitude of pressure applied must are less affected by stomach emptying. Because
be considered carefully to maintain the desired drug numerous pellets are within a capsule, some pellets
release properties. will gradually reach the small intestine each time
Dextroamphetamine sulfate formulated as timed- the stomach empties, whereas a single extended-
release pellets in capsules (Dexedrine Spansule) is an release tablet may be delayed in the stomach for a
early example of a beaded dosage form. Another long time as a result of erratic stomach emptying.
older product is a pellet-type extended-release Stomach emptying time is particularly important in
product of theophylline (Gyrocap). Table 19-6 shows the formulation and in vivo behavior of enteric-
the frequency of adverse reactions after theophyl- coated products. Enteric-coated tablets may be
line is administered as a solution or as pellets. delayed for hours by the presence of food in the
If theophylline is administered as a solution, a high stomach, whereas enteric-coated pellets are rela-
drug concentration is reached in the body due to rapid tively unaffected by the presence of food.
drug absorption. Some side effects may be attributed
to the high concentration of theophylline. Pellet dos- Prolonged-Action Tablets
age forms allow drug to be absorbed gradually, there- An alternate approach to prolong the action of a
fore reducing the incidence of side effects by drug is to reduce the aqueous solubility of the drug,
preventing a high C so that the drug dissolves slowly over a period of
max.
Potassium chloride is irritating to the GI tract. several hours. The solubility of a drug is dependent
Studies reported reduced gastrointestinal side effects on the salt form used. An examination of the solu-
of the drug potassium chloride in pellet or micropar- bility of the various salt forms of the drug is per-
ticulate form. Formulation of potassium chloride in formed in early drug development. In general, the
pellet form reduces the chance of exposing high nonionized base or acid form of the drug is usually
concentrations of potassium chloride to the mucosal much less soluble than the corresponding salt. For
cells in the GI tract. example, sodium phenobarbital is more water solu-
Many extended-release cold products also ble than phenobarbital, the acid form of the drug.
employ the bead formulation approach. A major Diphenhydramine hydrochloride is more soluble
advantage of pellet dosage forms is that the pellets than the base form, diphenhydramine.
In cases where it is inconvenient to prepare a
less soluble form of the drug, the drug may be granu-
TABLE 196 Incidence of Adverse Effects of lated with an excipient to slow dissolution of the
Sustained-Release Theophylline Pellet Versus drug. Often, fatty or waxy lipophilic materials are
Theophylline Solutiona employed in formulations. Stearic acid, castor
Volunteers Showing Side Effects wax, high-molecular-weight polyethylene glycol
(Carbowax), glycerylmonosterate, white wax, and
Using Using Sustained- spermaceti oil are useful ingredients in providing an
Side Effects Solution Release Pellets oily barrier to slow water penetration and the disso-
Nausea 10 0 lution of the tablet. Many of the lubricants used in
tableting may also be used as lipophilic agents to
Headache 4 0
slow dissolution. For example, magnesium stearate
Diarrhea 3 0 and hydrogenated vegetable oil (Sterotex) are actu-
Gastritis 2 0 ally used in high percentages to cause sustained drug
release in a preparation. The major disadvantage of
Vertigo 5 0
this type of preparation is the difficulty in maintain-
Nervousness 3 1 ing a reproducible drug release from patient to
aAfter 5-day dosing at 600 mg theophylline/24 h, adverse reaction patient, because oily materials may be subjected to
points on fifth day: solution, 135; pellets, 18. digestion, temperature, and mechanical stress, which
From Breimer and Dauhof (1980), with permission. may affect the release rate of the drug.
Modified-Release Drug Products and Drug Devices 589
Another application of prolong-action tablets is is that resins may provide a potential means of inter-
also called as pulsatile drug delivery system. This action with nutrients and other drugs.
chrono-pharmaceutical formulation is usually used Ion exchange may be used in extended-release
in the treatment of circadian rhythm dysfunction liquid preparations. An added advantage is that the
diseases. This effort may improve the therapeutic technique provides some protection for very bitter or
efficacy of oral drug administration for some spe- irritating drugs. Ion exchange has been combined
cific chrono-treatment. In one of the studies, drug with a coating to obtain a more effective sustained-
was compressed into regular tablets with ingredients release product. Examples include dextromethorphan
of starch, lactose, magnesium stearate, etc. Then the polistirex (Delsyn®), an oral suspension formulated
tablet was put at a lower position into capsule with as an ion-exchange complex to mask the bitter taste
another erodible plug composed by hydroxypropyl and to prolong the duration of drug action, and
methylcellulose (HPMC): lactose, whose erodible TussionexPennkinetic®, an oral suspension contain-
process was controlled by osmotic extent from outer ing chlorpheniramine polistirex and hydrocodone
water. After determined time point, the drug-contained polistirex.
tablet was ejected from this pulsincap capsule by the A general mechanism for the formulation of
mechanism of osmotic control (Ranjan et al, 2013; cationic drugs is
Wu et al, 2006). The time-controlled devices can
also be prepared by tablet surface coating with dif- H+ − − + +
+ resin − SO3drug resin − SO3H + drug
ferent compositions in order to defer the onset of its Insoluble drug complex Soluble drug
release (Zhang et al, 2003). According to the coat-
ing agent(s) employed, various release mechanisms For anionic drugs, the corresponding mechanism is
can be involved, such as in the case of erodible,
reputable, or diffusive reservoir systems (Maroni Cl− + − + − −
+ resin − N (CH3)3 drug resin − N (CH3)3 Cl + drug
et al, 2010).
Insoluble drug complex Soluble drug
Ion-Exchange Products The insoluble drug complex containing the resin
and drug dissociates in the GI tract in the presence
Ion-exchange technique has been popularly applied
of the appropriate counterions. The released drug
in water purification and chemical extraction. Ion-
dissolves in the fluids of the GI tract and is rapidly
exchange preparations usually involve an insoluble
absorbed.
resin capable of reacting with either an anionic or a
cationic drug. An anionic resin is negatively charged
so that a positively charged cationic drug may attach Core Tablets
the resin to form an insoluble nonabsorbable resin– A core tablet is a tablet within a tablet. The inner
drug complex. Upon exposure in the GI tract, cations core is usually used for the slow-drug-release com-
in the gut, such as potassium and sodium, may dis- ponent, and the outside shell contains a rapid-release
place the drug from the resin, releasing the drug, dose of drug. Formulation of a core tablet requires
which is absorbed freely. Researchers already two granulations. The core granulation is usually
applied the combination technique of iontophoresis compressed lightly to form a loose core and then
and cation-exchange fibers as drug matrices for the transferred to a second die cavity, where a second
controlled transdermal delivery of antiparkinsonian granulation containing additional ingredients is
drug apomorphine (Malinovskaja et al, 2013). The compressed further to form the final tablet.
main disadvantage of ion-exchange preparations is The core material may be surrounded by hydro-
that the amount of cation–anion in the GI tract is not phobic excipients so that the drug leaches out over a
easily controllable and varies among individuals, prolonged period of time. This type of preparation is
making it difficult to provide a consistent mecha- sometimes called a slow-erosion core tablet, because
nism or rate of drug release. A further disadvantage the core generally contains either no disintegrant or
590 Chapter 19
insufficient disintegrant to fragment the tablet. The aqueous solution while stirring. The coating material,
composition of the core may range from wax to gum ethylcellulose, is dissolved in cyclohexane, and the
or polymeric material. Numerous slow-erosion tab- two liquids are added together with stirring and heat-
lets have been patented and are sold commercially ing. As the cyclohexane is evaporated by heat, the
under various trade names. ethylcellulose coats the microparticles of the acet-
The success of core tablets depends very much aminophen. The microencapsulated particles have a
on the nature of the drug and the excipients used. As slower dissolution rate because the ethylcellulose is
a general rule, this preparation is very much hard- not water soluble and provides a barrier for diffusion
ness dependent in its release rate. Critical control of of drug. The amount of coating material deposited on
hardness and processing variables are important in the acetaminophen determines the rate of drug dis-
producing a tablet with a consistent release rate. solution. The coating also serves as a means of
OSDrC®OptiDose™ is a new commercial core tablet reducing the bitter taste of the drug. In practice,
whose manufacture was conducted in a solvent-free, microencapsulation is not consistent enough to pro-
dry compression single process operation. Its single- or duce a reproducible batch of product, and it may be
multi-cored tablets with a range of dose forms necessary to blend the microencapsulated material in
including fixed-dose combination tablets offer dif- order to obtain a desired release rate.
ferentiated controlled-release functionality. This
product is produced by Catalent partnering with Osmotic Drug Delivery Systems
Sanwa Kagaku Kenkyusho Co., Ltd.
Osmotic drug delivery systems have been developed
Core tablets are occasionally used to avoid
for both oral extended-release products known as
incompatibility in preparations containing two physi-
gastrointestinal therapeutic systems (GITS) and for
cally incompatible ingredients. For example, buff-
parenteral drug delivery as an implantable drug
ered aspirin has been formulated into a core and
delivery (eg, osmotic minipump). Drug delivery is
shell to avoid a yellowing discoloration of the two
controlled by the use of an osmotically controlled
ingredients upon aging (Desai et al, 2013).
device in which a constant amount of water flows
Microencapsulation into the system causing the dissolving and releasing
of a constant amount of drug per unit time. Drug is
Microencapsulation is a process of encapsulating
released via a single laser-drilled hole in the tablet.
microscopic drug particles with a special coating mate-
Figure 19-9A describes an osmotic drug delivery
rial, therefore making the drug particles more desirable
system in the form of a tablet that contains an outside
in terms of physical and chemical characteristics.
semipermeable membrane and an inner core filled
A common drug that has been encapsulated is
with a mixture of drug and osmotic agent (salt solution).
aspirin. Aspirin has been microencapsulated with
ethylcellulose, making the drug superior in its flow
Hydromorphone HCl Laser-drilled hole
characteristics; when compressed into a tablet, the (drug layer) (point of drug release)
drug releases more gradually compared to a simple
compressed tablet (Dash et al, 2010). Usually, biode-
gradable polymers such as dextran, collagen, chitosan, Hard outer
shell
poly(lactide), ethylcellulose, and casein are natural (colored overcoat)
materials applied in microencapsulation. After form- Rate-
ing the encapsulation materials as flowing powder, it controlling Osmotic
membrane pump
is suitable for formulation as compressed tablets, (push layer)
hard gelatin capsules, suspensions, and other dosage
forms (Baracat et al, 2012; Singh et al, 2010).
FIGURE 199A Cross section of the extended-release
Many techniques are used in microencapsulat-
hydromorphone tablet. (Adapted with permission from Gupta S,
ing a drug. One process used in microencapsulating Sathyan G: Providing constant analgesia with OROS® hydro-
acetaminophen involves suspending the drug in an morphone. J Pain Symptom Manage 33(2 suppl):S19–S24, 2007.)
Modified-Release Drug Products and Drug Devices 591
(A) (B)
FIGURE 199B SEM micrograph of the membrane of controlled porosity osmotic pump (CPOP) tablet containing diltiazem
hydrochloride (A) before and (B) after dissolution studies.
When the tablet is placed in water, osmotic pressure Methylphenidate HCl (Concerta) extended-
is generated by the osmotic agent within the core. release tablet uses osmotic pressure to deliver meth-
Water moves into the device, forcing the dissolved ylphenidate HCl at a controlled rate. The system,
drug to exit the tablet through an orifice. The rate of which resembles a conventional tablet in appear-
drug delivery is relatively constant and unaffected ance, comprises an osmotically active trilayer core
by the pH of the environment. Figure 19-9B provides surrounded by a semipermeable membrane with an
the surface electronic micrograph (SEM) images of immediate-release drug overcoat. The trilayer core is
the membrane of controlled porosity osmotic pump composed of two drug layers containing the drug
(CPOP) tablet containing diltiazem hydrochloride and excipients, and a push layer containing osmoti-
(A) before and (B) after dissolution studies, which cally active components. A laser-drilled orifice on
can clearly find the drug-release mechanism under the drug-layer end of the tablet allows for exit of the
microscopic domain (Adibkia et al, 2014). drug. This product is similar to the gastrointestinal
Newer osmotic drug delivery systems are therapeutic systems discussed earlier. The biologi-
considered “push-pull” systems. Nifedine (Procardia cally inert components of the tablet remain intact
XL) extended-release tablets have the appearance of during gastrointestinal transit and are eliminated in
a conventional tablet. Procardia XL ER tablets have the stool as an insoluble tablet shell.
a semipermeable membrane surrounding an osmoti- The frequency of side effects experienced by
cally active drug core. The core itself is divided into patients using gastrointestinal therapeutic systems
two layers: an “active” layer containing the drug and was considerably less than that with conventional
a “push” layer containing pharmacologically inert tablets. When the therapeutic system was compared
(but osmotically active) components. As water from to the regular 250-mg tablet given twice daily, ocular
the gastrointestinal tract enters the tablet, pressure pressure was effectively controlled by the osmotic
increases in the osmotic layer and “pushes” against system. The blood level of acetazolanine using gas-
the drug layer, releasing drug through a laser-drilled trointestinal therapeutic systems, however, was
tablet orifice in the active layer. Drug delivery is considerably below that from the tablet. In fact,
essentially constant (zero order) as long as the the therapeutic index of the drug was measurably
osmotic gradient remains constant, and then gradu- increased by using the therapeutic system. The use
ally falls to zero. Upon swallowing, the biologically of extended-release drug products, which release
inert components of the tablet remain intact during drug consistently, may provide promise for adminis-
gastrointestinal transit and are eliminated in the tering many drugs that previously had frequent
feces as an insoluble shell. adverse side effects because of the drug’s narrow
592 Chapter 19
TABLE 197 OROS Osmotic Therapeutic Systemsa
Trade Name Manufacturer Generic Name Description
Acutrim Ciba Phenylpropanolamine Once-daily, over-the-counter appetite
suppressant
Covera-HS Searle Verapamil Controlled-Onset Extended-Release (COER-24)
system for hypertension and angina pectoris
DynaCirc CR Sandoz Pharmaceuticals Isradipine Treatment of hypertension
Efidac 24 Ciba Self-Medication Over-the-counter, 24-hour extended-release
tablets providing relief of allergy and cold
symptoms, containing either chlorphenira-
mine maleate, pseudoephedrine hydrochlo-
ride, or a combination of pseudoephedrine
hydrochloride/brompheniramine maleate
Glucotrol XL Pfizer Glipizide Extended-release tablets indicated as an
adjunct to diet for the control of hyperglyce-
mia in patients with non-insulin-dependent
diabetes
Minipress XL Pfizer Prazosin Extended-release tablets for treatment of
hypertension
Procardia XL Pfizer Nifedipine Extended-release tablets for treatment of
angina and hypertension
Adalat CR Bayer AG Nifedipine An Alza-based OROS system of nifedipine
introduced internationally
Volmax Glaxo-Wellcome Albuterol Extended-release tablets for the relief of
bronchospasm in patients with reversible
obstructive airway disease
aAlza’s OROS Osmotic Therapeutic Systems use osmosis to deliver drug continuously at controlled rates for up to 24 h.
therapeutic index. The osmotic drug delivery system hydrostatic pressure inside the system builds up,
has become a popular drug vehicle for many prod- thereby forcing the liquid formulation to break
ucts that require an extended period of drug delivery through the hydrated gelatin capsule shell at the deliv-
for 12–24 hours (Table 19-7). ery orifice and be pumped out of the system. At the
A newer osmotic delivery system is the end of the operation, liquid drug fill is squeezed out,
l-OrosSoftcap (Alza), which claims to enhance bio- and the gelatin capsule shell becomes flattened. The
availability of poorly soluble drug by formulating osmotic layer, located between the inner layer and the
the drug in a soft gelatin core and then providing rate-controlling membrane, is the driving force for
extended drug delivery through an orifice drilled into pumping the liquid formulation out of the system.
an osmotic-driven shell (Fig. 19-10). The soft gelatin This layer can gel when it hydrates. In addition, the
capsule is surrounded by the barrier layer, the expand- high osmotic pressure can be sustained to achieve a
ing osmotic layer, and the release-rate-controlling constant release. This layer should comprise, there-
membrane. A delivery orifice is formed through the fore, a high-molecular-weight hydrophilic polymer
three outer layers but not through the gelatin shell. and an osmotic agent. It is a challenge to develop a
When the system is administered, water permeates coating solution for a high-molecular-weight hydro-
through the rate-controlling membrane and activates philic polymer. A mixed solvent of water and ethanol
the osmotic engine. As the engine expands, was used for this coating composition.
Modified-Release Drug Products and Drug Devices 593
Delivery orice
Rate-controlling
membrane
Soft gelatin
Osmotic layer Liquid drug
formulation
Inner layer
Before Ingestion During Release
FIGURE 1910 Configuration of L-OrosSoftcap. (From Dong et al, 2002, with permission.)
Gastroretentive System from the stomach without any difference as to
The extended-release drug product should release whether the drug product was floating on top or sit-
the drug completely within the region in the GI tract ting at the bottom of the stomach (Adibkia et al,
in which the drug is optimally absorbed. Due to GI 2011; Eberle et al, 2014). Another gastroretentive
transit, the extended-release drug product continu- system is mucoadhesive or bioadhesive drug deliv-
ously moves distally down the GI tract. In some ery systems. These systems permit a given drug
cases, the extended-release drug product containing delivery system to be incorporated with the bio/
residual drug may exit from the body. Pharmaceutical mucoadhesive agents, enabling the device to adhere
formulation developers have used various approaches to the stomach (or other gastrointestinal) walls, thus
to retain the dosage form in the desired area of the resisting gastric emptying (Bhattarai et al, 2010).
gastrointestinal tract. One such approach is a gastro- Sometimes, bio/mucoadhesive substance is a natural
retentive system that can remain in the gastric region or synthetic polymer capable of adhering to biologi-
for several hours and prolong the gastric residence cal membrane (bioadhesive polymer) or the mucus
time of drugs (Arora et al, 2005). Usually, the gastro- lining of the GIT (mucoadhesive polymer).
retentive systems can be classified into several types The most important consideration in this type of
based on the mechanism applied such as (i) high- formulation appears to be the gelling strength of the
density systems; (ii) floating systems; (iii) expandable gum material and the concentration of gummy mate-
systems; (iv) superporous hydrogels; (v) mucoadhe- rial. Modification of the release rates of the product
sive or bioadhesive systems; (vi) magnetic systems; may further be achieved with various amounts of talc
and (vii) dual working systems (Adibkia et al, 2011). or other lipophilic lubricant. However, the gastrore-
One of the most commonly used gastroretentive tentive system is not feasible for drugs having solu-
systems is floating drug delivery systems (FDDS). bility or stability problems in gastric fluid or having
For example, diazepam (Valium) was formulated irritation on gastric mucosa. Drugs such as nifedip-
using methyl cellulose to provide sustained release ine, which is well absorbed along the entire GIT and
(Valrelease). The manufacturer of Valrelease claimed which undergoes significant first-pass metabolism,
that the hydrocolloid (gel) floated in the stomach to may not be desirable candidates for FDDS since the
give sustained-release diazepam. In other studies, slow gastric emptying may lead to reduced systemic
however, materials of various densities were emptied bioavailability.
594 Chapter 19
Transdermal Drug Delivery Systems TABLE 198 Examples of Transdermal
Skin represents the largest and most easily accessible Delivery Systems
organ of the body. A transdermal drug delivery sys- Type Trade Name Rationale
tem (patch) is a dosage form intended for delivering
Membrane- Transderm- Drug in reservoir,
drug across the skin for systemic drug absorption (see
controlled system Nitro drug release
Chapters 7 and 13). Transdermal drug absorption also (Novartis) through a rate-
avoids presystemic metabolism or “first-pass” effects. controlling poly-
The transdermal drug delivery systems deliver the meric membrane
drug through the skin in a controlled rate over an Adhesive Deponit Drug dispersed
extended period of time (Chapter 15, Table 15-12). diffusion- system in an adhesive
Examples of transdermal drug delivery systems are controlled system (Pharma- polymer and in a
listed in Tables 19-8 and 19-9. Transdermal delivery Schwartz) reservoir
drug products vary in patch design (Fig. 19-11). Matrix-dispersion Nitro-Dur Drug dispersed
Generally, the transdermal patch consists of (i) a system (Key) into a rate-
backing or support layer that protects the patch, (ii) a controlling
hydrophilic or
drug layer that might be in the form of a solid gel
hydrophobic
reservoir or in a matrix, (iii) a pressure-sensitive matrix molded
adhesive layer, and (iv) a release liner or protective into a transdermal
strip that is removed before placing the patch on the system
skin. In some cases, the adhesive layer may also con-
Microreservoir Nitro-Disc Combination
tain the active drug (Gonzalez and Cleary, 2010). system (Searle) reservoir and
The skin is a natural barrier to prevent the influx matrix-dispersion
of foreign chemicals (including water) into the body system
TABLE 199 Transdermal Delivery Systems
Trade Name Manufacturer Generic Name Description
Catapres-TTS Boehringer Ingelheim Clonidine Once-weekly product for the treatment of
hypertension
Duragesic Janssen Pharmaceutical Fentanyl Management of chronic pain in patients who require
continuous opioid analgesia for pain that cannot be
managed by lesser means
Estraderm Ciba-Geigy Estradiol Twice-weekly product for treating certain postmeno-
pausal symptoms and preventing osteoporosis
Nicoderm CQ Hoechst Marion Nicotine An aid to smoking cessation for the relief of nicotine-
withdrawal symptoms
Testoderm Alza Testosterone Replacement therapy in males for conditions associ-
ated with a deficiency or absence of endogenous
testosterone
Transderm-Nitro Novartis Nitroglycerin Once-daily product for the prevention of angina
pectoris due to coronary artery disease; contains
nitroglycerin in a proprietary, transdermal therapeutic
system
Transderm Scop Scopolamine Prevention of nausea and vomiting associated with
motion sickness
Modified-Release Drug Products and Drug Devices 595
Matrix Reservoir Multilaminate Drug-in-adhesive Backing
Drug
Membrane
Liner/skin
FIGURE 1911 The four basic configurations for transdermal drug delivery systems.
and the loss of water from the body (Guy, 1996). To metals, polymers, or polysaccharides. Solid-coated
be a suitable candidate for transdermal drug delivery, microneedles can be used to pierce the superficial
the drug must possess the right combination of skin layer followed by delivery of the drug.
physicochemical and pharmacodynamic properties. Microneedles can be used to deliver macromolecules
The drug must be highly potent so that only a small such as insulin, growth hormones, immunobiologi-
systemic drug dose is needed and the size of the cals, proteins, and peptides (Bariya et al, 2012).
patch (dose is also related to surface area) need not Transdermal drug delivery system has been exten-
be exceptionally large, not greater than 50 cm2 (Guy, sively studied for 40 years. By now, only about forty
1996). Physicochemical properties of the drug drug products were commercialized from twenty drug
include a small molecular weight (<500 Da), and substances source, due to the drug diffusion problem
high lipid solubility. The elimination half-life should since all drug delivery approaches need to overcome
not be too short, to avoid having to apply the patch the barrier function of skin. Drug diffusion may be
more frequently than once a day. controlled by a semipermeable membrane next to the
To enhance transdermal permeation, there are reservoir layer. In other cases, drug diffusion is con-
two main category techniques already recognized as trolled by passage through the epidermis layer of the
effective: (i) physical methods, including iontopho- skin. The transdermal delivery system generally con-
resis, electroporation, sonophoresis, and micronee- tains large drug concentrations to produce the ideal
dles; (ii) chemical methods, including prodrug, salt drug delivery with a zero-order rate. The patch may
formation, ion pairs, and chemical enhancers. Among contain residual drug when the patch is removed from
these approaches, microneedles and chemical enhanc- the application site.
ers look like more promising. For microneedles Nitroglycerin is commonly administered by
technique, it can disrupt skin barrier and inject drug transdermal delivery (eg, Nitro-Dur, Transderm-
directly. For chemical enhancer, it may decrease the Nitro®). Transdermal delivery systems of nitroglyc-
barrier function of stratum corneum (SC) for mole- erin may provide hours of protection against angina,
cules (Subedi et al, 2010). whereas the duration of nitroglycerin given in a
Microneedles were first reported to deliver cal- sublingual tablet (Nitrostat®) or sublingual spray
cein by permeation improvement in 1998 (Henry et al, (Nitrolingual) may be only a few minutes. The nitro-
1998). It can painlessly disrupt skin barrier and cre- glycerin patch is placed over the chest area and pro-
ate pores inside the skin to increase drug penetration. vides up to 12 hours of angina protection. In a study
In the recent years, microneedles have been exten- comparing these three dosage forms in patients, no
sively investigated for the delivery of compounds substantial difference was observed among the three
like diclofenac, desmopressin, and even vectors for preparations. In all cases, the skin was found to be
gene therapy (Badran et al, 2009). Despite the pos- the rate-limiting step in nitroglycerin absorption.
sible problems such as low dosage, accurate dose There were fewer variations among products than of
administration and patient compliance can be solved the same product among different patients.
by introducing development of dissolvable/degrad- After the application of a transdermal patch, there
able and hollow microneedles to deliver drugs at a is generally a lag time before the onset of the drug
higher dose and to engineer drug release. Besides action, because of the drug’s slow diffusion into the
the steel, microneedles may be fabricated from dermal layers of the skin. When the patch is removed,
micro-electromechanical systems employing silicon, diffusion of the drug from the dermal layer to the
596 Chapter 19
systemic circulation may continue for some time until In general, drugs given at a dose of over 100 mg
the drug is depleted from the site of application. The would require too large a patch to be used practi-
solubility of drug in the skin rather than the concentra- cally. However, new advances in pharmaceutic sol-
tion of drug in the patch layer is the most important vents may provide a mechanism for an increased
factor controlling the rate of drug absorption through amount of drug to be absorbed transdermally. Ideally,
the skin. Humidity, temperature, and other factors the increase in permeation enhancement should not
have been shown to affect the rate of drug absorption cause skin irritation or any other kind of damage to
through the skin. With most drugs, transdermal deliv- the skin. To achieve this goal, the localization of the
ery provides a more stable blood level of the drug than enhancer’s effect only to the stratum corneum is
oral dosing. However, with nitroglycerin, the sus- necessary, though it is very difficult. Azone, one of
tained blood level of the drug provided by transdermal the chemical permeation enhancers, is a solvent that
delivery is not desirable, due to induced tolerance to increases the absorption of many drugs through the
the drug not seen with sublingual tablets. skin. Azone is usually composed by organic solvents
Transdermal therapeutic systems (TTS) consist of such as dimethyl formamide, dimethylacetamide, etc
a thin, flexible composite of membranes, resembling a (Chen et al, 2014). These solvents can only be
small adhesive bandage, which is applied to the skin and regarded as relatively nontoxic.
delivers drug through intact skin into the bloodstream. Among physical transdermal permeation enhanc-
Some examples of products delivered using this system ers, for ionic drugs, absorption may be enhanced
are shown in Table 19-8. Transderm-Nitro consists of transdermally by iontophoresis, a method in which
several layers: (1) an aluminized plastic backing that an electric field is maintained across the epidermal
protects nitroglycerin from loss through vaporization; layer with special miniature electrodes. Some
(2) a drug reservoir containing nitroglycerin adsorbed drugs, such as lidocaine, verapamil, insulin, and
onto lactose, colloidal silicon dioxide, and silicone peptides, have been absorbed through the skin by
medical fluid; (3) a diffusion-controlling membrane iontophoresis. A process in which transdermal
consisting of ethylene–vinyl acetate copolymer; (4) a drug delivery is aided by high-frequency sound is
layer of silicone adhesive; and (5) a protective strip. called sonophoresis. Sonophoresis has been used
Other transdermal delivery manufacturers have with hydrocortisone cream applied to the skin to
made transdermal systems in which the adhesive enhance penetration for treating “tennis elbow”
functions both as a pressure-sensitive adhesive and as and other mild inflammatory muscular problems.
a controlling matrix. Dermaflex (Elan) is a uniquely Characteristic drug delivery enhancements in drug
passive transdermal patch system that employs a transport induced by therapeutic ultrasound have
hydrogel matrix into which the drug is incorporated. been approximately tenfold compared to passive
Dermaflex regulates both the availability and absorp- drug delivery. Many such novel systems are being
tion of the drug in a manner that allows for controlled developed by drug delivery companies (Azagury
and efficient systemic delivery of many drugs. et al, 2014).
An important limitation of transdermal prepara- Panoderm XL patch technology (Elan) is a new
tion is the amount of drug that is needed in the trans- system that delivers a drug through a concealed
dermal patch to be absorbed systemically to provide miniature probe, which penetrates the stratum cor-
the optimum therapeutic response. The amount of neum. Panoderm XL is fully disposable and may be
drug absorbed transdermally is related to the amount programmed to deliver drugs as a preset bolus, in
of drug in the patch, the size of the patch, and the continuous or pulsed regimen. The complexity of the
method of manufacture. A dose–response relation- device is hidden from the patient and is simple to
ship is obtained by applying a proportionally larger use. Panoderm (Elan) is an electrotransdermal drug
transdermal patch that differs only in surface area. delivery system that overcomes the skin diffusion
For example, a 5-cm2 transdermal patch will gener- barriers through the use of low-level electric current
ally provide twice as much drug absorbed systemi- to transport the drug through the skin. Several trans-
cally as a 2.5-cm2 transdermal patch. dermal products, such as fentanyl, hydromorphone,
Modified-Release Drug Products and Drug Devices 597
calcitonin, and LHRH (luteinizing hormone–releasing to reflect a change in intended use, dosage form,
hormone), are in clinical trials. More improvements strength, route of administration, or significant
in transdermal delivery of larger molecules and the change in dose
use of absorption enhancers will be available in 4. Any investigational drug, device, or biological
future transdermal delivery systems. product packaged separately that, according
Several additional studies that are unique to the to its proposed labeling, is for use only with
development of a transdermal drug delivery system another individually specified investigational
include (1) wear and adhesiveness of the patch, (2) skin drug, device, or biological product where it is
irritation, (3) skin sensitization, and (4) residual drug required to achieve the intended use, indication,
in the patch after removal. The FDA is asking drug or effect
companies to consider minimizing the amount of
Examples of combination products where the
residual drug left in transdermal patches. Marketed
components are physically, chemically, or otherwise
products that use transdermal and transmucosal drug
combined:
delivery systems can contain between 10% and 95%
of the initial active drug even after use, according to • Monoclonal antibody combined with a therapeutic
the FDA’s draft guidance published in the Federal drug
Register, August 3, 2010. Adverse events have been • Device coated or impregnated with a drug or
reported after patients have failed to remove a patch, biologic
resulting in increased or prolonged effects of the • Drug-eluting stent; pacing lead with steroid-coated
drug (eg, fentanyl patch). tip; catheter with antimicrobial coating; condom
with spermicide
Combination Products • Skin substitutes with cellular components; ortho-
Combination products are defined in 21 CFR 3.2(e).2
pedic implant with growth factors
• Prefilled syringes, insulin injector pens, metered
The term combination product includes the following:
dose inhalers, transdermal patches
1. A product comprised of two or more regulated • Drug or biological product packaged with a delivery
components, that is, drug/device, biologic/device, device
drug/biologic, or drug/device/biologic, that are • Surgical tray with surgical instruments, drapes,
physically, chemically, or otherwise combined and lidocaine or alcohol swabs
or mixed and produced as a single entity • Photosensitizing drug and activating laser/light
2. Two or more separate products packaged source
together in a single package or as a unit and • Iontophoretic drug delivery patch and controller
comprised of drug and device products, device
In summary, combination products consist of the
and biological products, or biological and drug
drug in combination with a device that is physically,
products
chemically, or otherwise combined or mixed and
3. A drug, device, or biological product packaged
produced as a single entity. The device and/or bio-
separately that, according to its investigational
logic is intended for use with the approved drug and
plan or proposed labeling, is intended for use
influences the route of administration and pharmaco-
only with an approved individually specified
kinetics of the drug.
drug, device, or biological product where it is
required to achieve the intended use, indica-
tion, or effect and where, upon approval of the Modified-Release Parenteral Dosage Forms
proposed product, the labeling of the approved Modified-release parenteral dosage forms are paren-
product would need to be changed, for example, teral dosage forms that maintain plasma drug con-
centrations through rate-controlled drug release from
2http://www.fda.gov/CombinationProducts/AboutCombination the formulation over a prolonged period of time
Products/ucm118332.htm. (Martinez et al, 2008; Patil and Burgess, 2010).
598 Chapter 19
Some examples of modified-release parenteral time. Both biodegradable and nonbiodegradable
dosage forms include microspheres, liposomes, drug polymers can be impregnated with drugs in a con-
implants, inserts, drug-eluting stents, and nanoparti- trolled drug delivery system. For example, levonorg-
cles. These formulations are designed by entrapment estrel implants (Norplant system, Wyeth-Ayerst) are
or microencapsulation of the drug into inert poly- a set of six flexible closed capsules made of silastic
meric or lipophilic matrices that slowly release the (dimethylsiloxane–methylvinylsiloxane copolymer),
drug, in vivo, for the duration of several days or up each containing 36 mg of the progestin levonorg-
to several years. Modified-release parenteral dosage estrel. The capsules are sealed with silastic adhesive
forms may be biodegradable or nonbiodegradable. and sterilized. The Norplant system is available in an
Nonbiodegradable implants need to be surgically insertion kit to facilitate subdermal insertion of all
removed at the end of therapy. six capsules in the mid-portion of the upper arm. The
dose of levonorgestrel is about 85 mg/day, followed
by a decline to about 50 mg/day by 9 months and to
Implants and Inserts about 35 mg/day by 18 months, declining further to
Despite the fact that oral route ought to be considered about 30 mg/day. The levonorgestrel implants are
as highly desirable by the patients, it still represents a effective for up to 5 years for contraception and then
huge challenge, such as low bioavailability for pep- must be replaced. An intrauterine progesterone con-
tides or proteins after oral administration. Alternative traceptive system (Progestasert, Alza) is a T-shaped
routes of administration (pulmonary, nasal, buccal, unit that contains a reservoir of 38 mg of progester-
transdermal, ocular, and rectal) have also shown one. Contraceptive effectiveness for Progestasert is
drawbacks such as enzymatic degradation or low/ enhanced by continuous release of progesterone into
variable absorption. As a result, there is a renewed the uterine cavity at an average rate of 65 mg/day for
interest in parenteral administration because of the 1 year.
more and more innovation on new inactive ingredi- A dental insert available for the treatment of
ent development, especially as many improvements peridontitis is the doxycycline hyclate delivery sys-
have been done in pain reduction. Among these tem (Atrigel®). This is a subgingival controlled-
approaches, biodegradable polymer-based implant release product consisting of two-syringe mixing
and insert display excellent drug delivery characters systems that, when combined, form a bioabsorbable,
and very good compatibility (Ding et al, 2006; Zhang flowable polymeric formulation. After administra-
et al, 2013). tion under the gum, the liquid solidifies and then
In situ forming implants based on phase separa- allows for controlled release of doxycycline for a
tion by solvent exchange are conventional preformed period of 7 days.
implants and microparticles for parenteral applica-
tions. After administration, the polymeric solutions
may precipitate at the site of injection and thus form- Nanotechnology-Derived Drugs
ing a drug-eluting depot. Then drug release may Nanotechnology is the manufacture of materials in the
initiate in three phases: (i) burst during precipitation nanometer size range, usually less than 100–200 nm.
of the depot, (ii) diffusion of drug through the poly- Nanotechnology has been applied to drug develop-
meric matrix, and (iii) finally drug release by implants ment, food, electronics, biomaterials, and other appli-
degradation at an extended style. They are easier to cations. Nanoscale materials have chemical, physical,
manufacture and their administration does not require or biological properties that are totally different with
surgery, therefore improving patient compliance. The comparison to those of their larger counterparts. Such
drawbacks of this drug delivery system are lack of differences may include altered surface area, mag-
reproducibility in depot shape, burst during solidifi- netic properties, altered electrical or optical activity,
cation, and potential toxicity (Parent et al, 2013). increased structural integrity, or altered chemical or
Polymeric drug implants can deliver and sustain biological activity (Nanotechnology, FDA 2007).
drug levels in the body for an extended period of Because of these properties, nanoscale materials have
Modified-Release Drug Products and Drug Devices 599
great potential for use in a variety of therapeutic Daunorubicin has been used for the treatment of
agents. Because of some of their special properties, ovarian cancer, AIDS-related Kaposi’s sarcoma,
nanoscale materials may pose different safety and and multiple myeloma. Two different liposomal for-
efficacy issues compared to their larger or smaller (ie, mulations of daunorubicin are currently marketed.
molecular) counterparts. DaunoXome® contains an aqueous solution of the
According to the materials composition, the citrate salt of daunorubicin encapsulated within lipid
nanoparticles can be categorized into two main aspects: vesicles (liposomes) composed of a lipid bilayer of
organic and inorganic. Organic-based nanoparticles distearoylphosphatidylcholine and cholesterol,
may be composed from biodegradable materials, such whereas Doxil® is doxorubicin HCl encapsulated in
as polylactide (PLA), polyglycolide (PGA), poly(lactide- liposomes that are formulated with surface-bound
co-glycolide) (PLGA), polyethylene glycol (PEG), methoxypolyethylene glycol (MPEG). The use of
etc, and some biocompatible materials, for example, MPEG is a process often referred to as pegylation, to
poly(propylene oxide) (PPO), polyvinylpyrrolidone protect liposomes from detection by the mononu-
(PVP), etc. Inorganic-based nanoparticles may come clear phagocyte system (MPS) and to increase blood
from gold, iron oxide, etc. All of them displayed bright circulation time. Each of these products has different
future in the area of controlled drug delivery (Ding pharmacokinetics, and they are not interchangeable.
et al, 2007, 2011, 2013). Another application of liposome is to change
In addition to the large surface area of nanopar- the pharmacokinetic profile and optimize the immu-
ticles, surface modification of the nanoparticles such nogenicity of loaded protein drugs. In one study,
as binding different chemical groups to the surface PEGylated phosphatidylinositol (PI) containing
with surfactants or biocompatible polymers (eg, liposome was designed to load recombinant FVIII
polyethylene glycol, PEG) changes the pharmacoki- by reducing immunogenicity and prolonging the
netics, toxicity, and surface reactivity of the nanopar- circulating half-life. Reduced activity in vitro and
ticles, in vivo. Therefore, nanoparticles can have a improved retention of activity in the presence of
wide variety of properties that are markedly different antibodies suggested strong shielding of FVIII by
from the same materials in larger particle forms the particle; thus, in vivo studies were conducted in
(Couvreur and Vauthier, 2006) (see also Chapter 18). hemophilia A mice showing that the apparent ter-
minal half-life was improved versus both free FVIII
and FVIII–PI, but exposure determined by area
Liposomes under the curve was reduced. The formation of
A liposome is a microvesicle composed of a bilayer inhibitory antibodies after subcutaneous immuniza-
of lipid amphipathic molecules enclosing an aqueous tion with FVIII–PI/PEG was lower than free FVIII
compartment (FDA Guidance for Industry, 2002). but resulted in a significant increase in inhibitors
Liposomes may be nanoparticle size or larger. Its following intravenous administration (Peng et al,
outer size can be controlled by the process of filter 2012).
pore, from 50 to 200 nm. Liposome drug products are Liposomes were first described in 1965 and
formed when a liposome is used to encapsulate a drug soon proposed as drug delivery systems, with numer-
substance within the lipid bilayer or in the interior ous important chemical structure improvements such
aqueous space of the liposome depending on the as remote drug loading, size homogeneity, long-
physicochemical characteristics of the drug. Liposomes circulating (PEGylated) modification, triggered release,
can be composed of naturally derived phospholipids combination drugs loading, etc. Liposomes have
with mixed lipid chains (like egg phosphatidylethanol- been led tonumerous clinical trials in such diverse
amine) or other surfactants. Liposome drug products areas as the delivery of anticancer, antifungal, and
exhibit a different pharmacokinetic and/or tissue distri- antibiotic drugs, the delivery of gene medicines, and
bution profile from the same drug substance (or active the delivery of anesthetics and anti-inflammatory
moiety) in a nonliposomal formulation given by the drugs. Some of liposome products are on the market,
same route of administration. and many more are in the pipeline. These lipidic
600 Chapter 19
TABLE 1910 Marketed and in Clinic Trial Liposomal and Lipid-Based Drug Products
Trade Name Manufacturer Generic Name Description
Marketed
Doxil/Caelyx Johnson & Johnson Doxorubicin Kaposi’s sarcoma, Ovarian cancer, Breast cancer,
Multiple myeloma + Velcade
Myocet Cephalon Doxorubicin Breast cancer + cyclophosphamide
DaunoXome Galen Daunorubicin Kaposi’s sarcoma
Amphotec Intermune Amphotericin B Invasive aspergillosis
DepoDur Pacira Morphine sulfate Pain following surgery
DepoCyt Pacira Cytosine + Arabinoside Lymphomatous, meningitis, Neoplastic
Diprivan AstraZeneca Propofol Anesthesia
Estrasorb King Estrogen Menopausal therapy
Marqibo Talon Vincristine Acute lymphoblastic leukemia
Clinic trials
SPI-077 Alza Cisplatin Solid tumors (Phase II)
CPX-351 Celator Cytarabine: daunorubicin Acute myeloid leukemia (Phase II)
MM-398 Merrimack CPT-11 Gastric and pancreatic cancer (Phase II)
Lipoplatin Regulon Cisplatin Non-small cell lung cancer (Phase III)
ThermoDox Celsion Thermosensitive Primary hepatocellular, carcinoma, Refractory
doxorubicin chest wall breast cancer, Colorectal liver
metastases (Phase III)
Stimuvax Oncothyreon/Merck Anti-MUC1 cancer vaccine Non-small cell lung cancer (Phase III)
Exparel Pacira Bupivacaine Nerve block (Phase II)
nanoparticles are the first nanomedicine delivery Polymer-Based Nano Drug Delivery System
system to make the transition from concept to clini- The term “polymer therapeutics” was coined to
cal application, and they are now an established describe the therapeutics associated with polymer,
technology platform with considerable clinical including polymeric drugs, polymer conjugates of
acceptance (Allen and Cullis, 2013). Table 19-10 proteins, drugs, and aptamers, together with those
lists the liposomal or lipid-based drug products in block copolymer micelles and multicomponent non-
the market or still in the clinical trials. From this viral vectors. These nonviral vectors may display as
table, not only the chemical drugs but also the anti- micelles, implants, inserts, and nanoparticles.
bodies, vaccine, nucleic acids, and gene medicine Poly(lactic-co-glycolic) acid (PLGA), poly(lactic
can be loaded into liposome, for treatment of infec- acid) (PLA), and polyglycolic acid (PGA) are per-
tions and for cancer treatment, for lung disease, and haps the most commonly studied polymers due to
for skin conditions. With surface bioconjugating of their versatility in tuning biodegradation time and
targeting molecules on the long-circulating liposome, high biocompatibility arising from their natural by-
the common “passive” liposomal drug delivery sys- products, lactic acid, and glycolic acid. Now polylac-
tem may evolve to “active” system in the coming tide has been commonly used in the surgery, while
future. polyglycolide or its drug conjugates are being
Modified-Release Drug Products and Drug Devices 601
increasingly used as a drug carrier. Their molecular 7 until before the next injection (Dreicer et al, 2011;
weight can be tailored to the expected extent upon the Periti et al, 2002).
clinic requirement. Because of the unique property of In the area of polymer therapeutics, polymeric
biodegradability and integration of quality-by-design drugs, polymeric sequestrants, and PEG conjugates
approach (QbD) concept during the development, (both protein conjugates and the PEG-aptamer con-
this polymer therapeutics can be applied to preclini- jugate) have progressed to market or under clinic
cal structure optimization of and to manufacturing trials. Table 19-11 shows the marketed and clinical
process control. trial polymeric therapeutics. Particular success sto-
Lupron Depot® is the first US Food and Drug ries include Copaxone as a treatment for multiple
Administration (FDA)-approved microparticle-based sclerosis (a complex random copolymer of three
depot drug delivery system. Lupron Depot consists amino acids), the PEGylated interferons (Pegasys;
of leuprolide encapsulated in PLGA microspheres. Peg-Intron), and the PEGylated rhG-CSF (Neulasta)
In order to improve the compliance of leuprolide as a more convenient once-a-cycle adjunct to cancer
injection, Takeda-Abbott Products developed this chemotherapy (Duncan and Vicent, 2013).
new class of controlled-release polymeric drug
delivery system for the treatment of advanced pros-
tate cancer. Lupron Depot has been approved for
Frequently Asked Questions
management of endometriosis and also for the treat-
»»How do patient-specific variables influence perfor-
ment of central precocious puberty. Lupron Depot
mance of modified-release dosage forms?
has been commercially successful, reaching annual
sales of nearly $1 billion (Anselmo and Mitragotri, »»What is the difference between the different types of
2014). Lupron Depot can be intramuscularly modified-release dosage forms?
injected, having dosage schedule as 7.5 mg 1×/
month, 22.5 mg 1× for every 3 months or 30 mg 1×
for every 4 months. The peptide drug is released
from these depot formulations at a functionally con-
stant daily rate for 1, 3, or 4 months, depending on CONSIDERATIONS IN THE
the polymer type (polylactic/glycolic acid [PLGA] EVALUATION OF MODIFIED-
for a 1-month depot and polylactic acid [PLA] for RELEASE PRODUCTS
depot of >2 months), with doses ranging between
3.75 and 30 mg. Mean peak plasma leuprorelin con- The development of a modified-release formulation
centrations (Cmax) of 13.1, 20.8 to 21.8, 47.4, 54.5, has to be based on a well-defined clinical need and
and 53 mg/L occur within 1–3 hours of depot subcu- on an integration of physiological, pharmacodynamic
taneous administration of 3.75, 7.5, 11.25, 15, and (PD), and pharmacokinetic (PK) considerations. The
30 mg, respectively, compared with 32–35 mg/L at two important requirements in the development of
36–60 minutes after a subcutaneous injection of extended-release products are (1) demonstration of
1 mg of a non-depot formulation. Sustained drug safety and efficacy and (2) demonstration of con-
release from the PLGA microspheres maintains trolled drug release.
plasma concentrations between 0.4 and 1.4 mg/L Safety and efficacy data are available for many
over 28 days after single 3.75, 7.5, or 15 mg depot drugs given in a conventional or immediate-release
injections. Mean areas under the concentration–time dosage form. Bioavailability data of the drug from
curve (AUCs) are similar for subcutaneous or intra- the extended-release drug product should demon-
venous injection of short-acting leuprorelin. A strate sustained plasma drug concentrations and
3-month depot PLA formulation of leuprorelin ace- bioavailability equivalent to giving the conven-
tate 11.25 mg ensures a Cmax of around 20 mg/L at tional dosage in the same total daily dose in two or
3 hours after subcutaneous injection and continuous more multiple doses. The bioavailability data
drug concentrations of 0.43–0.19 mg/L from day requirements are specified in the Code of Federal
602 Chapter 19
TABLE 1911 Marketed and Clinical Trials Polymeric Therapeutics
Trade Name Sub Class Composition Market/Clinic Trial
Copaxone Glu, Ala, Tyr copolymer Market
Vivagel Polymeric drugs Lysine-based dendrimer Phase III
Hyaluronic acid Hyalgal, Synvisc Market
Zinostatin Polymer–protein Styrene maleic anhydride-neocarzinostatin, Market (Japan)
Stimaler conjugates (SMANCS)
Cimzia PEG-anti-TNF Fab Market
Peg-intron PEGylated proteins PEG-Interferon alpha 2b Market
Neulasta PEG-hrGCSF Market
Macugen PEGylated-aptamer PEG-aptamer (apatanib) Market
CT-2103; Xyotax Polymer–drug conjugate Poly-glutamic acid (PGA)-paclitaxel Phase II/III
NKTR-118 PEG-naloxone Phase III
IT-101 Self-assembled polymer Polymer conjugated-cyclodextrin Phase II
conjugate nanoparticles nanoparticle-camptothecin
NK-6004 Block copolymer micelles Cisplatin block copolymer micelle Phase II
Regulations, 21 CFR 320.25(f). The important procedure that provides a meaningful in vitro–
points are as follows. in vivo correlation.
7. In vivo pharmacokinetic data consist of single
1. The product should demonstrate sustained
and multiple dosing comparing the extended-
release, as claimed, without dose-dumping
release product to a reference standard (usually
(abrupt release of a large amount of the drug in
an approved non-sustained-release or a solution
an uncontrolled manner).
product).
2. The drug should show steady-state levels com-
parable to those reached using a conventional The pharmacokinetic data usually consist of plasma
dosage form given in multiple doses, and which drug data and/or drug excreted into the urine.
was demonstrated to be effective. Pharmacokinetic analyses are performed to deter-
3. The drug product should show consistent phar- mine such parameters as t1/2, VD, tmax, AUC, and k.
macokinetic performance between individual
dosage units.
4. The product should allow for the maximum Pharmacodynamic and Safety
amount of drug to be absorbed while maintain- Considerations
ing minimum patient-to-patient variation. Pharmacokinetic and safety issues must be consid-
5. The demonstration of steady-state drug levels ered in the development and evaluation of a modified-
after the recommended doses are given should release dosage form. The most critical issue is to
be within the effective plasma drug levels for consider whether the modified-release dosage form
the drug. truly offers an advantage over the same drug in an
6. An in vitro method and data that demonstrate immediate-release (conventional) form. This advan-
the reproducible extended-release nature of tage may be related to better efficacy, reduced toxic-
the product should be developed. The in vitro ity, or better patient compliance. However, because
method usually consists of a suitable dissolution the cost of manufacture of a modified-release dosage
Modified-Release Drug Products and Drug Devices 603
form is generally higher than the cost for a conven-
tional dosage form, economy or cost savings for 100.0
patients also may be an important consideration. 67.0
Ideally, the extended-release dosage form should 33.5
provide a more prolonged pharmacodynamic effect
0
compared to the same drug given in the immediate- 8.40
release form. However, an extended-release dosage 5.93
8.00
form of a drug may have a different pharmacody- pH 3.47 5.33
00 0 2.67
1.
namic activity profile compared to the same drug Time (hours)
given in an acute, intermittent, rapid-release dosage FIGURE 1912 Topographical dissolution characteriza-
form. For example, transdermal patches of nitroglyc- tion of theophylline controlled release. Topographical dissolu-
erin, which produce prolonged delivery of the drug, tion characterization (as a function of time and pH) of Theo-24,
a theophylline controlled-release preparation, which has been
may produce functional tolerance to vasodilation
shown to have a greater rate and extent of bioavailability when
that is not observed when nitroglycerin is given dosed after a high-fat meal than when dosed under fasted
sublingually for acute angina attacks. Certain bacte- conditions. (From Skelly and Barr, 1987, with permission.)
ricidal antibiotics such as penicillin may be more
effective when given in intermittent (pulsed) doses
extended-release drug product (will discuss further
compared to continuous dosing. The continuous
at the next section in this chapter). The support-
blood level of a hormone such as a corticosteroid
ing documents have been involved in the FDA
might suppress adrenocorticotropic hormone (ACTH)
submission of New Drug Application (NDA),
release from the pituitary gland, resulting in atrophy
Abbreviated New Drug Application (ANDA), or
of the adrenal gland. Furthermore, drugs that act
Antibiotic Drug Application (AADA). Topographical
indirectly or cause irreversible toxicity may be less
plots of the dissolution data may be used to graph
efficacious when given in an extended-release rather
the percent of drug dissolved versus two variables
than in conventional dosage form.
(time, pH) that may affect dissolution simultane-
Because the modified-release dosage form may
ously. For example, Skelly and Barr have shown that
be in contact with the body for a prolonged period,
extended-release preparations of theophylline, such
the recurrence of sensitivity reactions or local tissue
as Theo-24, have a more rapid dissolution rate at a
reactions due to the drug or constituents of the dos-
higher pH of 8.4 (Fig. 19-12), whereas Theo-Dur is
age form are possible. For oral modified-release
less affected by pH (Fig. 19-13) (Skelly and Barr 1987).
dosage forms, prolonged residence time in the GI
tract may lead to a variety of interactions with GI
tract contents, and the efficiency of absorption may
be compromised as the drug moves distally from the
duodenum to the large intestine. 100.0
Moreover, dosage form failure due to either 66.6
dose-dumping or the lack of drug release may 33.2
have important clinical implications. Another pos-
0
sible unforeseen problem with modified-release 7.50 12
dosage forms is an alteration in the metabolic fate 5.33 8
pH 3.17 4
of the drug, such as nonlinear biotransformation or 1.00 0 Time (hours)
site-specific disposition. FIGURE 1913 Topographical dissolution characterization
Design and selection of extended-release prod- of theophylline extended release. Topographical dissolution
ucts are often aided by dissolution tests carried out at characterization (as a function of time and pH) of Theo-Dur, a
theophylline controlled-release preparation, the bioavailability
different pH units for various time periods to simu-
of which was essentially the same whether administered with
late the condition of the GI tract. This in vitro– food or under fasted conditions. (From Skelly and Barr, 1987,
in vivo correlation is also called as IVIVC for oral with permission.)
Percent Percent
604 Chapter 19
These dissolution tests in vitro may help predict TABLE 1912 Suggested Dissolution/Drug
the in vivo bioavailability performance of the dos- Release Studies for Modified-Release Dosage
age form. Forms
Dissolution studies
1. Reproducibility of the method.
Frequently Asked Question 2. Proper choice of medium.
»»Does the extended-release drug product have the 3. Maintenance of sink conditions.
same safety and efficacy compared to a conven- 4. Control of solution hydrodynamics.
tional dosage form of the same drug? 5. Dissolution rate as a function of pH, ranging from pH
1 to pH 8 and including several intermediate values.
6. Selection of the most discriminating variables
(medium, pH, rotation speed, etc) as the basis for the
dissolution test and specification.
EVALUATION OF MODIFIED-
Dissolution procedures
RELEASE PRODUCTS
1. Lack of dose dumping, as indicated by a narrow limit
Dissolution Studies on the 1-h dissolution specification.
2. Controlled-release characteristics obtained by
Dissolution requirements for each of the three employing additional sampling windows over time.
types of modified-release dosage form are pub- Narrow limits with an appropriate Q value system will
lished in the USP-NF. Some of the key elements for control the degree of first-order release.
the 3. Complete drug release of the drug from the dosage
in vitro dissolution/drug release studies are
form. A minimum of 75%–80% of the drug should be
listed in Table 19-12. Dissolution studies may be released from the dosage form at the last sampling
used together with bioavailability studies to predict interval.
in vitro–in vivo correlation of the drug release rate 4. The pH dependence/independence of the dosage
of the dosage forms. form as indicated by percent dissolution in water,
appropriate buffer, simulated gastric juice, or simu-
lated intestinal fluid.
In Vitro–In Vivo Correlations (IVIVC)
A general discussion of correlating in vitro drug Data from Skelly and Barr, 1987.
product performance (eg, dissolution rate) to an in vivo
biologic response (eg, blood-level-versus-time pro-
file) is discussed in Chapter 15. Ideally, the in vitro bioavailability parameters, the in vitro dissolution
drug release of the extended-release drug product test can serve as a surrogate marker for in vivo
should relate to the bioavailability of the drug in behavior and thereby confirm consistent therapeutic
vivo, so that changes in drug dissolution rates will performance of batches from routine production. The
correlate directly to changes in drug bioavailability. variability of the data should be reported and dis-
From the consideration of European Medicines cussed when establishing a correlation. In general,
Agency (EMA) and the Food and Drug Administration the higher the variability in the data used to generate
(FDA) on the quality control of oral modified-release the IVIVC, the less confidence can be placed on the
drug products, in vitro profile for drug products has predictive power of the correlation (Guidance for
relationship with pharmacokinetics (PK), pharmaco- Industry, 1997; Guideline on Quality of Oral Modified
dynamics (PD), and clinical efficacy/safety. In vitro Release Products, 2012).
dissolution testing is important as a necessary quality For modified-release dosage forms, IVIVC is
assurance not only for batch-to-batch consistency but highly desirable in that it provides a critical linkage
also to indicate consistency within a batch (ie, that between product quality and clinical performance.
individual dosage units will have the desired in vivo With an established IVIVC, an in vitro test, such as
performance). By establishing a meaningful correla- dissolution test, can serve as a critical tool for prod-
tion between in vitro release characteristics and in vivo uct and process understanding; aid product/process
Modified-Release Drug Products and Drug Devices 605
development, manufacturing, and control; provide developed as modified-release formulation. Additional
significantly increased assurance for consistent documentation specific to the modified-release dosage
product performance; and predict in vivo perfor- form includes studies evaluating factors affecting
mance throughout the life cycle of a modified-release the biopharmaceutic performance of the modified-
product (Qiu et al, 2014). release formulation. Moreover, the extended-release
A well-established IVIVC (Level A) is a point- dosage form should be available in several dosage
to-point correlation and may apply deconvolution strengths to allow flexibility for the clinician to
technique, in which in vivo absorption or in vivo dis- adjust the dose for the individual patient.
solution can be predicted from in vitro data and not Single-dose ranging studies and multiple-dose
Cmax and AUC. IVIVC may reduce the number of in steady-state crossover studies using the highest strength
vivo studies during product development, be helpful of the dosage form may be performed. In addition, a
in setting specifications, and be used to facilitate cer- food intervention bioavailability study is also per-
tain regulatory decisions (eg, scale-up and postap- formed since food interactions may be related to the
proval variations). Other correlation such as Level B, drug substance itself and/or the formulation, the latter
the mean in vitro dissolution time is compared either being most important in the case of modified-release
to the mean residence time or to the mean in vivo dis- products. The reference dosage form may be a solution
solution time. It is not a point-to-point correlation. of the drug or the full NDA-approved conventional,
Level C IVIVC establishes a single-point relationship immediate-release, dosage form given in an equal daily
between a dissolution parameter, for example, t50%. Its dose as the extended-release dosage form. If the dosage
correlation does not reflect the complete shape of the strengths differ from each other only in the amount of
plasma concentration time curve. Multiple Level C the drug–excipient blend, but the concentration of the
correlation relates one or several pharmacokinetic drug–excipient blend is the same in each dosage form,
parameters of interest to the amount of drug dissolved then the FDA may approve the NDA or ANDA on the
at several time points of the dissolution profile. In basis of single- and multiple-dose studies of the highest
general, AUC and Cmax of a complex modified-release dosage strength, whereas the other lower-strength dos-
product are dependent not only on the input rate and age forms may be approved on the basis of compara-
extent but also on drug properties and product design tive in vitro dissolution studies (Chapter 15). The latest
characteristics. Therefore, an attempt to develop such FDA Guidance for Industry should be consulted for
an IVIVC should be considered by the applicant. regulatory requirements (www.fda.gov/cder/guidance/
index.htm). Skelly et al (1990, 1993) have described
several types of such pharmacokinetic studies.
Pharmacokinetic Studies
In many cases, the active drug is first formulated in
an immediate-release drug product. After market Clinical Considerations of Modified-Release
experience with the immediate-release drug prod- Drug Products
uct, a manufacturer may design a modified or an Clinical efficacy and safety may be altered when
extended-release drug product based on the pharma- drug therapy is changed from a conventional, imme-
cokinetic profile of the immediate-release drug diate-release (IR) drug product given several times a
product as discussed earlier in this chapter. Various day to a modified, extended-release drug product
types of pharmacokinetic studies may be required given once or twice a day. Usually, the original mar-
by the Food and Drug Administration (FDA) for keted drug is a conventional, IR drug product. After
marketing approval of the modified-release drug experience with the IR drug product, a pharmaceuti-
product, depending on knowledge of the drug, its cal manufacturer (sponsor) may develop an extended-
clinical pharmacokinetics and pharmacodynamics, release product containing the same drug. In this
and its biopharmaceutic properties (Skelley et al, case, the sponsor needs to demonstrate that the
1990). Usually, a complete pharmacokinetic data pharmacokinetic profile of the extended-release drug
package is required for a new chemical entity product has sustained plasma drug concentrations
606 Chapter 19
compared to the conventional drug product. In addi- of the drug given in the same daily dose and com-
tion, the sponsor may perform a clinical safety and pared to other extended-release products containing
efficacy study comparing both drug products. the same active drug. Since the pharmacokinetic
Bupropion hydrochloride (Wellbutrin), an anti- profiles may differ, the practitioner needs to consult
depressant drug, is available as an immediate-release the FDA publication, Approved Drug Products with
(IR) drug product given three times a day, a sustained- Therapeutic Equivalence Evaluations (Orange Book),4
release3 (SR) drug product given twice a day, and an to determine which of these drug products may be
extended-release (XL) drug product given once a substituted.
day. Jefferson et al reviewed the pharmacokinetics of
these three products. These investigators reported
that although the pharmacokinetic profiles are differ- EXAMPLE »» »
ent for each drug product, the clinical efficacy for
each drug product is similar if bupropion hydrochlo- Methylphenidate Drug Products
ride is given in equal daily doses. According to the
Methylphenidate hydrochloride is a central
approved label information for Wellbutrin XL,
nervous system (CNS) stimulant indicated for
patients who are currently being treated with
the treatment of attention deficit hyperactiv-
Wellbutrin tablets at 300 mg/day (eg, 100 mg 3 times
ity disorder (ADHD). Numerous conventional
a day) may be switched to Wellbutrin XL 300 mg
and modified-release drug products containing
once daily. Patients who are currently being treated
methylphenidate hydrochloride are available
with Wellbutrin SR sustained-release tablets at 300
(Table 19-13). Although each of these methyl-
mg/day (eg, 150 mg twice daily) may be switched to
phenidate hydrochloride drug products has the
Wellbutrin XL 300 mg once daily. Thus, for bupro-
same indication, the prescriber needs to under-
prion HCl, the fluctuations in plasma drug concen-
stand which product would be most appropriate
tration-versus-time profiles do not affect clinical
for the patient.
efficacy as long as the patient is given the same daily
dose of drug (Jefferson et al, 2005).
Generic Substitution of Modified-Release EVALUATION OF IN VIVO
Drug Products
BIOAVAILABILITY DATA
Generic extended-release drug products may have
different drug-release mechanisms compared to The data from a properly designed in vivo bioavail-
the brand-drug product. The different drug-release ability study are evaluated using both pharmacoki-
mechanisms may lead to slightly different pharma- netic and statistical analysis methods. The evaluation
cokinetic profiles. Generic extended-release drug may include a pharmacokinetic profile, steady-state
products are approved by the FDA and are bio- plasma drug concentrations, rate of drug absorption,
equivalent based on AUC and C occupancy time, and statistical evaluation of the
max criteria and
therapeutic equivalence to the brand name equiva- computed pharmacokinetic parameters.
lent (Chapter 16). For some drugs, several different
modified-release products containing exactly the Pharmacokinetic Profile
same active ingredient are commercially available. The plasma drug concentration–time curve should
These modified-release drug products have different adequately define the bioavailability of the drug
pharmacokinetic profiles and may have different from the dosage form. The bioavailability data
clinical efficacy compared to the conventional form should include a profile of the fraction of drug
absorbed (Wagner–Nelson) and should rule out
3A sustained-release drug product may also be called an extended-
release drug product. 4www.fda.gov/Drugs/InformationOnDrugs/ucm129662.htm.
Modified-Release Drug Products and Drug Devices 607
TABLE 1913 Various Methylphenidate the fluctuation after the same drug given in an
Hydrochloride Drug Products immediate-release dosage form.
Drug
Product Formulation Comments Rate of Drug Absorption
Ritalin Immediate Conventional drug For the extended-release drug product to claim zero-
release product order absorption, an appropriately calculated input
Ritalin SR Extended ER drug product function such as used in the Wagner–Nelson
release with no initial dose approach should substantiate this claim. The differ-
Ritalin LA Extended Produces a bi-modal ence between first-order and zero-order absorption
release with an plasma concentration- of a drug is shown in Fig. 19-14. The rate of drug
initial IR dose time profile when absorption from the conventional or immediate-
given orally; not release dosage form is generally first order, as shown
interchangeable
by Fig. 19-14A. Drug absorption after an extended-
with Concerta
release dosage form may be zero order (Fig. 19-14B),
Concerta Extended Not interchangeable first order (see Fig. 19-14A), or an indeterminate
release with an for Ritalin LA
order (Fig. 19-14C). For many extended-release dos-
initial IR dose
age forms, the rate of drug absorption is first order,
Daytrana Film, extended Provides extended with an absorption rate constant ka smaller than the
release; release via transder-
elimination rate constant k. The pharmacokinetic
transdermal mal drug absorption
model when ka > k is termed flip-flop pharmacoki-
Methylin Solution; oral Immediate release netics and is discussed in Chapter 7.
drug product
Methylin Tablet, Immediate release
chewable; oral drug product Occupancy Time
Drugs for which the therapeutic window is known,
the plasma drug concentrations should be maintained
dose-dumping or lack of a significant food effect. above the minimum effective drug concentration
The bioavailability data should also demonstrate the (MEC) and below the minimum toxic drug concen-
extended-release characteristics of the dosage form tration (MTC). The time required to obtain plasma
compared to the reference or immediate-release
drug product.
100
Steady-State Plasma Drug Concentration A B C
The fluctuation between the C∞ (peak) and C∞
max min
(trough) concentrations should be calculated:
50
C∞ −C∞
Fluctation = max min
(1 .11
C∞ 9 )
av
0
where C∞
av is equal to [AUC]/t. Time (hours)
An ideal extended-release dosage form should FIGURE 1914 The fraction of drug absorbed using the
have minimum fluctuation between Cmax and Cmin. A Wagner–Nelson method may be used to distinguish between
the first-order drug absorption rate of a conventional (immedi-
true zero-order release will have no fluctuation. In
ate-release) dosage form (A) and an extended-release dosage
practice, the fluctuation in plasma drug levels after form (C). Curve B represents an extended-release dosage form
the extended-release dosage form should be less than with zero-order absorption rate.
Fraction of drug absorbed
608 Chapter 19
provide the public with the FDA’s latest submission
requirements for NDAs and ANDAs.
20 MTC
Statistical Evaluation
Variables subject to statistical analysis generally
10 MEC include plasma drug concentrations at each collec-
tion time, AUC (from zero to last sampling time),
AUC (from zero to time infinity), Cmax, tmax, and
elimination half-life t1/2. Statistical testing may
0 include an analysis of variance (ANOVA), computa-
0 2 4 6 8 10 12 tion of 90% and 95% confidence intervals on the
Time (hours)
difference in formulation means, and the power of
FIGURE 1915 Occupancy time.
ANOVA to detect a 20% difference from the refer-
ence mean.
drug levels within the therapeutic window is known
as occupancy time (Fig. 19-15). Frequently Asked Questions
»»Are extended-release drug products always more
Bioequivalence Studies efficacious than immediate-release drug products
containing the same drug?
Bioequivalence studies for extended-release drug
products are discussed in detail in Chapter 15. »»Why do some extended-release formulations of a
Bioequivalence studies may include (1) a fasting drug have a different efficacy profile compared to a
study, (2) a food-intervention study, and (3) a multi- conventional dosage form, given in multiple doses?
ple-dose study. The FDA’s Center for Drug Evaluation »»What are the advantages and disadvantages of a
and Research (CDER) maintains a website (www zero-order rate design for drug absorption?
.fda.gov/cder) that lists regulatory guidances to
CHAPTER SUMMARY
The goal of modified-release (MR) formulations is to anatomy and physiology of the gastrointestinal tract,
reduce the peak-to-trough fluctuations of drug con- gastrointestinal transit, pH, and its contents compared
centrations and, consequently, enable the less fre- to conventional oral drug products. Modified-release
quent administration of the drug. This is generally drug products may also have a different pharmacody-
accomplished by lowering the rate of drug release namic and safety profile compared to immediate-
with better patient compliance and thereby that of release drug products containing the same drug. With
drug absorption. In this drug product, the timing and help from the more and more biodegradable materials
the rate of drug release can be adjusted according to developed, various approaches have been used to
clinic requirement along with efficacy and safety manufacture modified- and extended-release drug
consideration, which cannot be achieved by conven- products including matrix tablets, coated beads,
tional dosage forms. Within the modified-release osmotic release, ion-exchange, liposome, polymeric
formulations, extended-release (ER) drug products therapeutics, etc. The administration method may not
are one of the most important compositions not only only limit in the area of oral route but also includes
minimizing the possible side effects derived from transdermal, injection, nasal, etc. Although the route
fluctuating plasma drug concentrations but also of administration and pharmacokinetic parameters
offering a prolonged therapeutic effect. Oral modi- may be different, the bioequivalence should be equal
fied-release drug products are easily affected by the or improved between immediate-release formulations
Plasma drug concentration (mg/mL)
Modified-Release Drug Products and Drug Devices 609
with modified-release drug products. More and more efficacy compared to other extended-release products
pharmacometrics have been applied to the in vivo containing the same active drug. The practitioner
and clinic prediction, including single-dose studies, needs to consult the FDA publication Approved Drug
steady-state studies, partial AUC calculation, in Products with Therapeutic Equivalence Evaluations
vitro–in vivo correlation (IVIVC) assay, etc. Overall, (Orange Book) to determine which of these drug
modified-release products may have different clinical products may be substituted.
LEARNING QUESTIONS
1. The design for most extended-release or 100
A
sustained-release oral drug products allows for B
the slow release of the drug from the dosage
form and subsequent slow absorption of the C
drug from the gastrointestinal tract.
a. Why does the slow release of a drug from 50
an extended-release drug product produce a
longer-acting pharmacodynamic response com-
pared to the same drug prepared in a conven-
tional, oral, immediate-release drug product?
0
b. Why do manufacturers of sustained-release 0 4 8 12
drug products attempt to design this dosage Time (hours)
form to have a zero-order rate of systemic FIGURE 1916 Dissolution profile of three different drug
drug absorption? products. Drug dissolved (percent).
2. The dissolution profiles of three drug products
are illustrated in Fig. 19-16. 3. A drug is normally given at 10 mg 4 times
a. Which of the drug products in Fig. 19-16 a day. Suggest an approach for designing a
releases drug at a zero-order rate of about 12-hour, zero-order release product.
8.3% every hour? a. Calculate the desired zero-order release rate.
b. Which of the drug products does not release b. Calculate the concentration of the drug in an
drug at a zero-order rate? osmotic pump type of oral dosage form that
c. Which of the drug products has an almost delivers 0.5 mL/h of fluid.
zero rate of drug release during certain hours 4. An industrial pharmacist would like to design a
of the dissolution process? sustained-release drug product to be given every
d. Suggest a common cause of slowing drug 12 hours. The active drug ingredient has an appar-
dissolution rate of many rapid-release drug ent volume of distribution of 10 L, an elimination
products toward the end of dissolution. half-life of 3.5 hours, and a desired therapeutic
e. Suggest a common cause of slowing drug plasma drug concentration of 20 mg/mL. Calcu-
dissolution of a sustained-release product late the zero-order release rate of the sustained-
toward the end of a dissolution test. release drug product and the total amount of drug
needed, assuming no loading dose is required.
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Targeted Drug
20 Delivery Systems and
Biotechnological Products
Susanna Wu-Pong
Chapter Objectives Many diseases occur as a result of variability in the genes involved
in producing essential enzymes or proteins in the body. The genes
»» Compare and contrast biologic
are coded in deoxyribonucleic acid (DNA), helical double-
and small-molecule drugs in
stranded molecules folded into chromosomes in the nucleus of
terms of their mechanism of
cells. The Human Genome Project was created more than a decade
action, design, and development
ago to sequence the human genome. This national effort is con-
hurdles.
tinuing to yield information on the role of genetics in congenital
»» Discuss why biologic drugs may defects, cancer, disorders involving the immune system, and other
require delivery and/or targeting diseases that have a genetic link.
systems. The ever-evolving genetic basis of disease will continue to
»» Describe the main methods provide novel opportunities for the development of new drugs to
used to deliver and target treat these disorders, particularly in the field of biotechnology.
biologic drugs and give The discovery of recombinant DNA (rDNA) technology and its
examples. application to new drug development has revolutionized the bio-
pharmaceutical industry. Previously, the pharmaceutical industry
»» Explain the difference between relied on the use of relatively simple small drug molecules to treat
active and passive targeting. disease. Modern molecular techniques have changed the face of
»» State whether generic biologics new drug development to include larger, more sophisticated and
exist, and if not, describe why. complex drug molecules. These large biopharmaceuticals have
enormous potential to treat disease in ways previously unavailable
»» Explain in general terms the
to small drug molecules. As a result, biotechnology, or the use of
pharmacokinetic differences
biological materials to create a specific product, in this case phar-
between small-molecule and
maceuticals, has become an important sector of the pharmaceutical
biologic drugs and why these
industry and accounts for the fastest growing class of new drugs
differences exist.
in the market. Nucleic acid, protein and peptide drugs, and diag-
nostics are the main drug products emerging from the biopharma-
ceutical industry.
BIOTECHNOLOGY
Protein Drugs
The human genome produces thousands of gene products that
prevent disease and maintain health. Many may have therapeutic
applications if supplemented to normal or supraphysiologic levels
in the body. Most of the biologic molecules listed in Table 20-1 are
normally present in the body in small concentrations but are used
615
616 Chapter 20
TABLE 201 A Sample of Approved Recombinant Drugs
Year Introduced, Company
Drug Indication Pharmacokinetics (Trade Name)
Aldesleukin; Renal cell carcinoma Half-life = 85 min; 1992 Chiron (Proleukin)
interleukin-2 Cl = 268 mL/min
Alteplase Acute myocardial infarction Half-life < 5 min; 1987 Genentech (Activase)
Acute pulmonary embolism Cl = 380–570 mL/min; 1990 Genentech (Activase)
Vd ≈ plasma volume
Antihemophilic factor Hemophilia B 1992 Armour (Mononine)
Antihemophilic factor Hemophilia A Half-life = 13 h 1992 Genetics Institute, Baxter
Healthcare, Bayer (ReFacto,
Recombinate, Kogenate,
Helixate FS)
Agalsidase-beta; Fabry’s disease Half-life = 45–102 min; 2003 Genzyme (Fabrazyme)
a-galactosidase A nonlinear kinetics
Anakinara; IL-1 Rheumatoid arthritis Half-life = 4–6 h 2001 Amgen (Kineret)
receptor antagonist
b-Glucocerebrosidase Type I Gaucher’s disease 1991 Genzyme (Ceredase)
b-Glucocerebrocidase Type I Gaucher’s disease 1994 Genzyme (Cerezyme)
CMV immune globulin CMV prevention in kidney 1990 Medimmune (CytoGam)
transplant
DNase Cystic fibrosis 1993 Genentech (Pulmozyme)
Drotrecogin-a; Severe sepsis Cl = 40 L/h 2001 Lilly (Xigris)
activated protein C
Erythropoietin Anemia associated with Half-life = 4–13 h 1989 Amgen; Johnson & Johnson;
chronic renal failure Kirin (Epogen); 1990 Ortho
Anemia associated with Biotech (Procrit) 1990 Amgen;
AIDS/AZT Ortho Biotech (Procrit) 1993
Anemia associated with cancer Amgen; Ortho Biotech (Procrit)
and chemotherapy
Factor VIII Hemophilia A 1993 Genentech; Miles (Kogenate)
Filgrastim; G-CSF Chemotherapy-induced Half-life = 3.5 h; 1991 Amgen (Neupogen)
neutropenia Vd = 150 mL/kg; 1994 Amgen (Neupogen)
Bone marrow transplant Cl = 0.5–0.7 mL/kg/min
Human insulin Diabetes 1982 Eli Lilly, Genentech (Humulin)
Interferon-a-2a Hairy cell leukemia; Half-life = 5.1 h; 1986 Hoffmann-La Roche
Vd = 0.4 L/kg; (Roferon-A)
Cl = 2.9 mL/min/kg
AIDS-related Kaposi’s sarcoma 1988 Hoffmann-La Roche
(Roferon-A)
Targeted Drug Delivery Systems and Biotechnological Products 617
TABLE 201 A Sample of Approved Recombinant Drug s (Continued)
Year Introduced, Company
Drug Indication Pharmacokinetics (Trade Name)
Interferon-a-2b Hairy cell leukemia; Half-life = 2–3 h 1986 Schering-Plough;
Biogen (Intron A)
AIDS-related Kaposi’s sarcoma 1991 Schering-Plough;
Biogen (Intron A)
Interferon-a-n3 Genital warts 1989 Interferon Sciences
(Alferon N injection)
Interferon-b-1b Relapsing/remitting multiple Half-life = 8 min–4.3 h; 1993 Chiron; Berlex (Betaseron)
sclerosis Cl = 9.4–28.9 mL/kg/min;
Vd = 0.25–2.9 L/kg
Interferon-b -1a Multiple sclerosis Half-life = 8.6–10 h 1996 Biogen (Avonex); 2002
Serano (Rebif )
Interferon-g -1b Management of chronic 1990 Genentech (Actimmune)
granulomatous disease
Human growth Short stature caused by 1994 Genentech (Nutropin)
hormone human growth hormone
deficiency
Hepatitis B vaccine, Hepatitis B prevention 1986 Merck; Chiron
MSD (Recombivax HB) Smith Kline
1989 Beecham; Biogen (Engerix-B)
Laronidase; Mucopolysaccharidosis I Half-life = 1.5–3.6 h; 2003 Biomarin (Aldurazyme)
a-L-iduronidase Cl = 1.7–2.7 mL/min/kg;
Vd = 0.24–0.6 L/kg
Pegadamase ADA-deficient SCID 1990 Enzon; Eastman Kodak
(PEG-adenosin) (Adagen)
PEG-L-asparaginase Refractory childhood acute 1994 Enzon (Oncaspar)
lymphoblastic leukemia
Reteplase; Acute myocardial infarction Half-life = 0.2–0.3 h; 1996 Boehringer Mannheim
plasminogen activator Cl = 7.5–9.7 mL/min/kg (Retavase)
Sargramostim Autologous bone marrow 1991 Hoechst-Roussel;
(GM-CSF) transplantation Immunex (Prokine)
Neutrophil recovery following 1991 Immunex; Hoechst-Roussel
bone marrow transplantation (Leukine)
Somatropin, hGH deficiency in children 1987 Eli Lilly (Humatrope)
somatrem 1985 Genentech (Protropin)
Tenecteplase Acute myocardial infarction Half-life = 90–130 min; 2002 Genentech (TNKase)
Cl = 99–119 mL/min;
Vd ≈ plasma vol.
From Yu and Fong, 1997, and www.fda.gov.cber/appr2003.
618 Chapter 20
for certain therapeutic indications. For example, administration. The manufacturing process and prod-
some diseases such as insulin-dependent diabetes uct are intricately linked. Small changes in the manu-
result from insufficient production of a natural facturing process may affect the sequence of the
product, in this case insulin. For these patients, the resulting protein, but more likely will affect the
treatment is to supplement the patient’s own insu- structure, yield, or activity of the protein. Therefore,
lin production with recombinant human insulin pharmaceutical controls and testing must be carefully
(eg, Humulin). Similarly, human recombinant designed, controlled, and monitored, and must also
growth hormone (Protropin, Nutropin) and gluco- be able to distinguish minor chemical or structural
cerebrocidase (Ceredase, Cerezyme) are used to changes that could affect the safety or efficacy in the
treat growth hormone deficiency and Gaucher’s product during each of these stages.
disease, respectively. Drug delivery of biologics can be a problem for
In contrast, interferons are proteins produced by therapeutic use because the protein drug must reach
the immune system in response to viral infection and the site of action physically and structurally intact.
other biologic inducers. When infection or cancer Biologic drugs are notoriously unstable in plasma
surpasses the capacity of the body’s immune system, and the gastrointestinal tract, so modifications to
recombinant interferons (Roferon-A, Intron A, improve drug delivery or stability are often required.
Alferon N, Actimmune, Infergen, Rebif) or other Currently, most biologic drugs are generally too
immune-enhancing molecules can be used to boost unstable for oral delivery and must usually be
immunity. Recombinant interferons and interleukins administered by parenteral routes, though a number
(Proleukin, Neumega) are therefore used to strengthen of protein and peptide drug candidates including
the immune system during infection, immunosup- calcitonin, lactoferrin, and glucocerebrocidase are in
pression, cancer, and multiple sclerosis. Erythropoietin clinical trials for oral delivery. However, other, non-
and derivatives (Epogen, Procrit, Aronesp) and parenteral routes of administration, such as intrana-
growth factors (Prokine, Leukine, Neupogen, sal and inhalation, are being investigated for biologic
Becaplermin) are also used to stimulate red and white drug and vaccine delivery. The first recombinant for
cell production for anemia or immune suppression inhalation, insulin (Exubera) was approved in 2006,
following chemotherapy. These molecules were orig- only to be withdrawn from the market 2 years later
inally available only by purification from human or because of poor patient and physician acceptance.
animal sources. Biotechnology, bioengineering, and More recently in 2014, another inhaled short-acting
the use of cell banks have enabled the large-scale and insulin product named Afrezza has been approved by
reproducible production of these naturally occurring the FDA. Lung function must be measured before
biologically derived drugs (Table 20-1). the drug can be prescribed for the patient. Fortunately,
The size and complexity of protein and nucleic because many of these recombinant protein drugs
acid drugs require extensive design and engineering are designed to act extracellularly, transmembrane
of the manufacturing and control processes to pro- delivery may not be required once the drug reaches
duce the drug in large quantities with consistent qual- the plasma.
ity. The size of a protein or peptide drug can range
from a few hundred to several hundred thousand Monoclonal Antibodies
daltons. The three-dimensional structure of a protein Another class of protein drugs is monoclonal anti-
or peptide drug is important for its pharmacodynamic bodies (mAbs). Antibodies are produced by the
activity, so the corresponding specific primary amino body’s immune system for specific recognition and
acid, secondary (alpha helix or beta sheet), tertiary removal of foreign bodies. The power of mAbs lies
(special relationship of secondary structures), or even in their highly specific binding of only one antigenic
quaternary orientation of subunits must be consid- determinant. As a result, mAb drugs, targeting
ered. A biotechnology-derived drug (also referred to agents, and diagnostics are creating new ways to
as a biologic drug or biopharmaceutical) must be treat and diagnose previously untreatable diseases
designed such that the structure is stable, reproduc- and to detect extraordinarily low concentrations of
ible, and accurate during manufacture, storage, and protein or other molecules (Table 20-2).
Targeted Drug Delivery Systems and Biotechnological Products 619
TABLE 202 Applications of Monoclonal cell and allow the hybrid cells (hybridoma) to grow in
Antibodies a test tube. The nonfused cells will die, and the
myeloma cells will be selectively destroyed with an
Cancer treatment
antitumor drug such as aminopterin (Fig. 20-1),
mAbs against leukemia and lymphomas have been used whereas the hybridoma cells will continue to grow.
in treatment with variable results. Regression of tumor is
Each hybridoma cell is then separated into a separate
produced in about 25%, although mostly transient.
growth chamber or well in which they are allowed to
Imaging diagnosis multiply. Each cell and its clones in the respective
mAbs may be used together with radioactive markers to growth chamber will make antibodies to only one
locate and visualize the location and extent of the tumors. antigen (mAb). The cells producing the desired anti-
Target-specific delivery body are selected by testing each well for mAb bind-
ing to the desired antigen. The desired cells (clones)
mAbs may be conjugated to drugs or other delivery sys-
are then expanded for mAb production. Since the
tems such as liposomes to allow specific delivery to target
sites. For example, urokinase was conjugated to an antifi- resulting mAb is of murine origin, often genetic engi-
brin mAb to dissolve fibrin clots. The carrier system would neering is used to “humanize” the mAb, thus mini-
seek fibrin sites and activate the conversion of plasmogen mizing an immune response to the therapeutic mAb.
to plasmin to cause fibrin to degrade. Monoclonal antibodies may be used therapeuti-
Transplant rejection suppression cally to neutralize unwanted cells or molecules.
Several mAbs with proven indications are listed in
In kidney transplants, an mAb against CD3, a membrane
protein of cytotoxic T cells that causes a rejection reaction, Tables 20-1, 20-2, and 20-3. Monoclonal antibodies
was very useful in suppressing rejection and allowing the are used as antivenoms (CroFab), for overdose of
transplant to function. The drug was called OKT3. mAbs digoxin (DigiFab), or to neutralize endotoxin (inves-
are also used for kidney and bone marrow transplants. tigative) or viral antigen (Nabi-HB). Monoclonal
antibodies (mAbs) are named by a source identi-
Theoretically, an almost infinite amount and fier preceding “-mab,” for example, -umab (human),
number of antibodies can be produced by the body to -omab (mouse), -zumab (humanized), and -ximab
respond immunologically to foreign substances con- (chimeric). Other common indications for mAb drugs
taining antigenic sites. These antigenic sites are usu- include imaging (ProstaScint, Myocint, Verluma),
ally on protein molecules, but nonprotein material or cancer (Campath, Ontak, Zevalin, Rituxan, Herceptin),
haptens may be conjugated to a protein to form an rheumatoid arthritis (Humira, Remicade), and trans-
epitope, or the part of the molecule that binds an anti- plant immunosuppression (Simulect, Thymoglobulin).
body. Periodic injections of an antigen into an animal Monoclonal antibodies are also used for more novel
result in production of antibodies that bind epitope. indications. For example, Abciximab (c7E3 Fab,
The serum of the animal will also contain antibodies ReoPro) is a chimeric mAb Fab (humanized) fragment
to antigens to which the animal has been previously specific for platelet glycoprotein IIb-IIIa receptors.
exposed. Though these mixtures of antibodies in the This drug is extremely effective in reducing fatalities
serum (polyclonal antibodies) are now considered too (0.50%) in subjects with unstable angina after angio-
impure for therapeutic use, they can be used for diag- plasty treatment.
nostic immunoassays. Monoclonal antibodies can also target and deliver
In contrast to polyclonal antibodies, mAbs are toxins specifically to cancer cells and destroy them
preparations that contain many copies of a single anti- while sparing normal cells (see below), and they are
body that will therefore bind to and only detect one important detectors used in laboratory diagnostics.
antigenic site. The purity of these preparations makes
them very useful as diagnostics, targeting agents, and
new therapeutic agents. However, the techniques for Gene Therapy
the preparation of mAbs are quite complicated. In Gene therapy refers to a pharmaceutical product that
mAb production, normal antibody-producing cells, delivers a recombinant gene to somatic cells in vivo
such as a mouse spleen cell, are fused with a myeloma (Ledley, 1996). In turn, the gene within the patients’
620 Chapter 20
Antigen A
Spleen
A’
Antibody-
secreting Myeloma
spleen cells tumor
HAT-sensitive
mutant
cell line
Fusion
B’
Growth in
HAT medium
Cloning
B
Blood
Hybrid Hybrid Hybrid
Mixed
antibodies
Antiserum Monoclonal
antibodies
Antigen
Blood cells
Antigen Antigen Antigen
FIGURE 201 Monoclonal antibody production. (A) A mouse is immunized with an antigen bearing three antigenic
determinants (distinct sites that can be recognized by an antibody). Antibodies to each determinant are produced in the spleen.
One spleen cell produces a single type of antibody. A spleen cell has a finite lifetime and cannot be cultured indefinitely in vitro.
(B) In the mouse, the antibody-producing cells from the spleen secrete into the blood. The liquid portion of the blood (serum)
therefore contains a mixture of antibodies reacting with all three sites on the antigen (antiserum). (A) A mutant cell derived from a
mouse myeloma tumor of an antibody-producing cell that has stopped secreting antibody and is selected for sensitivity to the drug
aminopterin (present in HAT medium). This mutant tumor cell can grow indefinitely in vitro but is killed by HAT medium. (B) The
mutant myeloma cell is fused by chemical means with spleen cells from an immunized mouse. The resulting hybrid cells can grow
indefinitely in vitro due to properties of the myeloma cell parent and can grow in HAT medium because of an enzyme provided
by the spleen cell parent. The unfused myeloma cells die because of their sensitivity to HAT, and unfused spleen cells cannot grow
indefinitely in vitro. The hybrid cells are cloned so that individual cultures are grown from a single hybrid cell. These individual cells
produce a single type of antibody because they derive from a single spleen cell. The monoclonal antibody isolated from these
cultures is specific for only one antigenic determinant on the original antigen. (From Brodsky FM: Monoclonal antibodies as magic
bullets. Pharm Res 5(1):1–9, January 1988, with permission.)
Targeted Drug Delivery Systems and Biotechnological Products 621
TABLE 203 Approved Monoclonal Antibody Drugs and In Vivo Diagnostics
mAb Product
(Trade Name) Target Indication
Abciximab (ReoPro) Platelet surface Half-life < 10 min Unstable angina, coronary
glycoprotein angioplasty or atherectomy
(PCTA), antiplatelet prevention of
blood clots
Adalimumab (Humira) Tumor necrosis factor Vd = 4–6 L; Cl = 12 mL/h; Rheumatoid arthritis
half-life = 2 wk
Alefacept (Amevive) CD2 (LFA) on lymphocytes Half-life = 270 h; Psoriasis
Cl = 0.25 mL/kg/h;
Vd = 94 mL/kg
Alemtuzumab (Campath) CD52 on blood cells Half-life = 12 d B-cell chronic lymphocytic
leukemia
Antithymocyte globulin T-lymphocyte antigens Half-life = 2–3 d Acute rejection in renal transplant
(rabbit) thymoglobulin patients
Basiliximab (Simulect) Interleukin-2 Half-life = 7.2 d; Renal transplantation
Vd = 8.6 L; immunosuppression
Cl = 41 mL/h
Capromab pendetide Prostate glycoprotein Half-life = 67 h; Diagnosing imaging agent in
(ProstaScint) Cl = 42 mL/h; prostate cancer
Vd = 4 L
Daclizumab (Zenapax) Interleukin-2 receptor Half-life = 20 d; Renal transplants
Cl = 15 mL/h; immunosuppression
Vd = 6 L
Denileukin diftitox Interleukin-2 mAb conju- Half-life = 70–80 min; Cutaneous T-cell lymphoma
(Ontak) gate to diptheria toxin Cl = 1.5–2 mL/min/kg;
Vd = 0.06–0.08 L/kg
Digoxin immune Digoxin Half-life = 15–20 h; Digoxin toxicity or overdose
Fab—Ovine (DigiFab) Vd = 0.3–0.4 L/kg
Etanercept (Enbrel) Tumor necrosis factor Half-life = 115 h; Rheumatoid arthritis
receptor Cl = 89 mL/h
Hepatitis B immune Hepatitis B Half-life = 25 d; Acute exposure to hepatitis B
globulin—human Cl = 0.4 L/d;
(Nabi-HB) Vd = 15 L
Ibritumomab tiuxetan CD28 on B cells Half-life = 30 h Follicular or transformed B-cell
(Zevalin) non-Hodgkin’s lymphoma
Imciromab pentetate Myosin Half-life = 20 h Imaging agent for detecting
(Myoscint) myocardial injury
Infliximab (Remicade) Tumor necrosis factor Half-life = 9.5 d; Crohn’s disease
Vd = 3 L Rheumatoid arthritis
Nofetumomab (Verluma) Carcinoma-associated Half-life = 10.5 h Detection of small cell lung
antigen, 99mTc labeled cancer
(Continued )
622 Chapter 20
TABLE 203 Approved Monoclonal Antibody Drugs and In Vivo Diagnostic s (Continued)
mAb Product
(Trade Name) Target Indication
Muromonab-CD3 CD3 on T cells Reversal of acute kidney
(Orthoclone OKT3) transplant rejection
Palivizumab (Synagis) RSV antigens Half-life = 197 h; RSV disease
Cl = 0.33 mL/h/kg;
Vd = 90 mL/kg
Rituximab (Rituxan) CD20 on B cells Half-life = 60 h Follicular, B-cell non-Hodgkin’s
lymphoma
Trastuzumab (Herceptin) Human epidermal growth Half-life = 1.7–12 d; Metastatic breast cancer whose
factor receptor Vd = 44 mL/kg tumors overexpress the HER-2
protein
cell produces a protein that has therapeutic benefit to target cells, and the transgene is expressed, though
the patient. The therapeutic approach in gene therapy the virus is not capable of replicating. Both retrovi-
is often the restoration of defective biologic function ruses, RNA viruses that have the ability to perma-
within cells or enhancing existing functions such as nently insert their genes into the chromosomes of the
immunity, as is frequently seen in inherited disorders host cells, and DNA viruses (which remain outside
and cancer. host chromosomes) have been used successfully in
Gene therapy has been applied to the rare genetic viral gene delivery. Most of the gene therapy trials
disorder lipoprotein lipase (LPL) deficiency. Patients worldwide involve the use of such viral delivery
who suffer from LPL deficiency have abnormally systems.
high levels of triglycerides and very low-density lipo- In addition to viral delivery systems (vectors),
proteins (VLDL) causing pancreatitis and cardiovas- nonviral approaches have been used with some suc-
cular disease. The LPL gene has been incorporated cess for in vivo gene delivery. The transgene is engi-
into a recombinant adeno-associated virus by uniQure, neered into a plasmid vector, which contains
a Dutch biotechnology company, which has been gene-expression control regions. These naked DNA
approved in the European Union (EU) as the LPL molecules may enter cells and express product in
gene therapy product Glybera. The drug is expected some cell types, such as muscle cells to produce
to be launched in the United States in the near future. small amounts of antigen that stimulate immunity to
Despite the recent approval in the EU, gene the antigen. This naked DNA delivery technique has
therapy continues to face several challenges. These been approved for veterinary use for West Nile virus.
challenges include gene delivery, sufficient extent However, usually either polymeric nanoparticles or
and duration of stable gene expression, and safety. lipid delivery systems (see below) are required in
Because the gene coding the therapeutic protein most other cell types to produce measurable levels
(transgene) must also contain gene control regions of transgene expression. Such vesicles or particles
such as the promoter, the actual rDNA (recombinant result in intracellular delivery of DNA to cells.
DNA) to be delivered to target cells’ nucleus can eas- An alternative to direct in vivo delivery is a cell-
ily be 10–20 kilobases (kb) in size. based approach that involves the administration of
Two main approaches have been used for in vivo transgenes to cells that have been removed from a
delivery of rDNA. The first is a virus-based approach patient. For example, cells (usually bone marrow
that involves replacing viral replicative genes with cells) are removed from the patient; genes encoding
the transgene, and then packaging the rDNA into the a therapeutic product are then introduced into these
viral particle. The recombinant virus can then infect cells ex vivo using a viral or nonviral delivery
Targeted Drug Delivery Systems and Biotechnological Products 623
system, and then the cells are returned into the the body. Vitravene (ISIS Pharmaceuticals), an oli-
patient. The advantage of ex vivo approaches is that gonucleotide targeted to cytomegalovirus, was the
systemic toxicity of viral or nonviral delivery sys- first antisense oligonucleotide drug approved by the
tems is avoided. US Food and Drug Administration (FDA). The cost
Effective gene therapy depends on several con- of a second oligonucleotide drug, Macugen, has
ditions. The vector must be able to enter the target made the treatment prohibitive given the availability
cells efficiently and deliver the corrective gene to the of cheaper, equally effective drugs. Both drugs act
nucleus without damaging the target cell. The cor- locally (in the eye) but several other antisense drugs
rective gene should be stably expressed in the cells, administered intravenously have also been approved
to allow continuous production of the functional such as Alicaforsen and Mipomirsen.
protein. Neither the vector nor the functional protein For this approach to be useful, the etiology and
produced from it should cause an immune reaction genetics of the disease must be known. For example,
in the patient. It is also difficult to control the amount in the case of viral infection, known sequences belong-
of functional protein produced after gene therapy, ing to vital genes can be targeted and inhibited by
and excess production of the protein could cause antisense drugs. Many antisense sequences are usually
side effects, although insufficient production is more tested to find the best candidate, since intra- and inter-
typically observed. Additional problems in gene molecular interactions can affect oligonucleotide
therapy include the physical and chemical properties activity and delivery. Though oligonucleotides are rel-
of DNA and RNA molecules, such as size, shape, atively well internalized compared to rDNA mole-
charge, surface characteristics, and the chemical cules, cellular uptake is often low enough to require
stability of these molecules and delivery systems. delivery systems, such as liposomes. Antisense and
In vivo problems may include bioavailability, distri- gene therapy approaches have also been combined
bution, and cellular and nuclear uptake of these using viral vectors to deliver an antisense sequence.
macromolecules into cells. Moreover, naked DNA In this case, the transgene is transcribed into an
and RNA molecules are rapidly degraded in the body mRNA molecule that is antisense and, therefore,
(Ledley, 1996). binds to the target mRNA. The resulting RNA–RNA
interaction is high affinity and results in inhibition of
translation of that mRNA molecule.
Antisense Drugs
Antisense drugs are drugs that seek to block DNA
transcription or RNA translation in order to moder- RNAi
ate many disease processes. Antisense drugs con- Like antisense oligonucleotides, RNAis, or RNA
sist of nucleotides linked together in short DNA interferences, are effective and potent sequence-
or RNA sequences known as oligonucleotides. specific inhibitors of gene expression. RNAi mole-
Oligonucleotides are designed knowing the sequence cules can be either single stranded (miRNAs, or
of target DNA/RNA (eg, messenger RNA) to block micro-RNAs) or double-stranded (siRNAs or small,
transcription or translation of that targeted protein. interfering RNAs) (for review, see Li and Rana,
An oligonucleotide that binds complementary 2014). The single-stranded RNA molecules are
(“sense”) mRNA sequences and blocks translation is based on the naturally occurring, cellular regulatory
referred to as antisense. To further stabilize the drug, micro-RNA molecules involved in gene regulation.
many chemical modifications have been made to the Like antisense technology, RNAi sequence-specific
oligonucleotide structure. The most common modi- gene inhibition is mediated by complementary binding
fication used involves substitution of nonbridging to the target mRNA, but translation inhibition occurs
oxygen in the phosphate backbone with sulfur, through target strand degradation via a molecular com-
resulting in a phosphorothioate-derived antisense plex called RISC (RNA-induced silencing complex).
oligonucleotide. Some of these drugs have been siRNAs require high homology in target base-pairing
designed to target viral disease and cancer cells in but miRNA can occur even with mismatches.
624 Chapter 20
RNAis are important therapeutically from two such as inhalers such as Afrezza, which delivers rapid
perspectives. First, miRNAs may be involved in the acting insulin to the lung.
pathogenesis of certain diseases and, therefore, may Formulating protein drugs for systemic use by
make useful therapeutic targets. Antisense molecules oral, or even any extravascular, route of administra-
targeted to miRNAs are in preclinical and early clini- tion is extremely difficult due to drug degradation
cal testing to determine whether miRNAs are viable and absorption from the site of administration. There
therapeutic targets. Second, RNAis themselves may are several requirements for effective oral drug
be a useful alternative to antisense oligonucleotides as delivery of protein and peptide drugs: (1) protection
sequence-specific inhibitory therapeutic molecules. of the drug from degradation while in the harsh envi-
siRNAs provide an advantage compared to antisense ronment of the digestive tract, (2) consistent absorp-
molecules because of the involvement of RISC, which tion of the drug in a manner that meets bioavailability
allows degradation of multiple target molecules upon requirements, (3) consistent release of the drug so
activation of a single siRNA molecule. that it enters the bloodstream in a reproducible man-
Chemical modification and delivery technolo- ner, (4) nontoxicity, and (5) delivery of the drug
gies that have been used for antisense oligonucle- through the GI tract or other organ and maintenance
otides are also applied to miRNA and siRNA drugs of pharmacologic effect similar to IV injection.
because of their comparable stability and transport Designing, evaluating, and improving protein
issues. miRNA and siRNA drugs are currently in and peptide drug stability is considerably more com-
clinical testing for diseases involving cancer, viral plex than for small conventional drug molecules.
infection, and cardiovascular disease. A change in quaternary structure, such as aggrega-
tion or deaggregation of the protein, may result in
loss of activity. Changes in primary structure of
Frequently Asked Questions
proteins frequently occur and include deamidation of
»»What is the most frequent route of administration of
the amino acid chains, oxidation of chains with sulf-
biologic compounds?
hydryl groups, and cleavage by proteolytic enzymes
»»What is the effect of glycosylation on the activity of a present throughout the body and that may be present
biologic compound? Give an example. due to incomplete purification. Because of protein
»»What kinds of biologic drugs are available and how drugs’ complex structures, impurities are much
are they used? Are they similar or different from harder to detect and quantify. In addition, proteins
small-molecule drugs? may be recognized as foreign substances in the body
and become actively phagocytized by the reticuloen-
dothelial system (RES), resulting in the inability of
DRUG CARRIERS AND TARGETING these proteins to reach the intended target. Proteins
may also have a high allergenic or immunogenic
Formulation and Delivery of Protein Drugs potential, particularly when nonhuman genes or pro-
Advances in biotechnology have resulted in the com- duction cells are used.
mercial production of naturally produced active drug Because of the many stability and delivery prob-
substances for drug therapy (Table 20-1). These sub- lems associated with protein and nucleic acid drugs,
stances hold great potential for more specific drug new delivery systems are being tested to improve their
action with fewer side effects. However, many natu- in vivo properties. Carriers can be used to protect the
rally produced substances are complex molecules, drug from degradation, improve transport or delivery
such as large-molecular-weight proteins and pep- to cells, decrease clearance, or a combination of the
tides. Conventional delivery of protein and peptide above. In this chapter, carriers used for both small
drugs is generally limited to injectables and implant- traditional drug and biopharmaceutical drug delivery
able dosage forms. Insulin pumps for implantation are reviewed. Carriers may be covalently bound to the
have been developed for precise control of sugar levels drug, where drug release is usually required for phar-
for diabetes, as well as other novel delivery methods macologic activity. Noncovalent drug carriers such as
Targeted Drug Delivery Systems and Biotechnological Products 625
Polymeric backbone Positively charged polymers such as polyethylene-
diamine (PEI), polylysine, cyclodextrin, dendrimers,
and chitosan (Fig. 20-3) are used in noncovalent
Device to control Spacer Homing complexes for macromolecular drugs, such as gene
physical arm device or oligonucleotide therapy. For example, polymer–
chemical properties DNA complexes improve DNA delivery to cells in
part by providing some protection from nuclease
Drug
degradation in vivo. An added advantage of com-
FIGURE 202 Site-specific polymeric carrier. plexed cationic polymers is that targeting agents such
as receptor ligands can be covalently attached to the
polymer rather than the drug to provide cell-specific
liposomes typically require uncoating of the drug for
targeting. Cationic polymer use in vivo is limited
biologic activity to occur.
because of polymer toxicity, stability, efficacy, and
dissociation of the complex.
Polymeric Delivery Systems Polymers may also be covalently conjugated to
Polymers can be designed to include a wide range of drugs to improve their solubility or pharmacokinetic
physical and chemical properties and are popularly properties. Polymers with molecular weights greater
used in drug formulations because of their versatility. than 30–50 kDa bypass glomerular filtration, thereby
Polymers initially were used to prolong drug release extending the duration of drug circulation in the body.
in controlled-release dosage forms. The development Polyethylene glycol (PEG) is used to improve the
of site-specific polymer or macromolecular carrier clearance of some drugs, such as adenosine deami-
systems is a more recent extension of earlier research. nase (PEG-ADA), filgrastim (Neulasta), pegaptanib
The basic components of site-specific polymer car- (Macugen), interferon (PEG-Intron and PEGASYS),
riers are (1) the polymeric backbone (Fig. 20-2), asparaginase (Oncospar), and several others. Dextrans
(2) functional chains to enhance the physical charac- are large polysaccharide molecules (MW 2000 to
teristics of the carrier system, (3) the drug covalently 1 million Da) with good water solubility, stability, and
or electrostatically attached to the polymer chain, low toxicity. Drugs with a free amino or hydroxyl
and possibly (4) a site-specific component (homing group may be linked chemically to hydroxyl groups in
device) for recognizing the target. Improved physical dextrans by activation of the dextran with periodate,
characteristics may include improved aqueous solu- azide, or other agents.
bility. In the case of polymeric prodrugs, a spacer The molecular weight of the polymer carrier is
group may be present, bridging the drug and the car- an important consideration in designing these dosage
rier. The spacer chain may influence the rate at which forms. Generally, large-molecular-weight polymers
the drug will hydrolyze from the prodrug system. At have longer residence time and diffuse more slowly.
present, most site-specific polymeric drug carriers However, large polymers are also more prone to
are limited to parenteral administration and primarily capture by the reticuloendothelial system. To gain
utilize soluble polymers. specificity, a monoclonal antibody, a recognized
A B C
Solubilizer, Pharmacon, Homing
polyglutamic acid (PGA) p-phenylenediamine (PDM) device
NH CH CO NH CH CO NH CH CO
CH2 CH2 CH2
COO– CO CO NH Immunoglobulin
Cl
NH N
Cl
FIGURE 203 An example of a drug-polymer conjugate. A = solubilizer, IG = immunoglobulin; polyglutamic acid (PGA);
B = Pharmacon, p-phenylenediamine (PDM); C = homing device. (Reproduced with permission from Shaikh R, Raj Singh TR, Garland MJ,
Woolfson AD, Donnelly RF. Mucoadhesive drug delivery systems. J Pharm Bioall Sci 3(1):89–100, February 5, 2011.)
626 Chapter 20
sugar moiety, or a small cell-specific ligand may be drug delivery for controlled release or oral delivery.
incorporated as a targeting agent into the delivery Many anticancer drugs such as methotrexate, cyto-
system. For example, exposed galactose residues are sine arabinoside, and 6-fluorodeoxyuridine have
recognized by hepatocytes, whereas mannose or each been conjugated with albumin. Paclitaxel has
l-fructose is recognized by surface receptors in been formulated into an albumin-bound nanoparticle
macrophages. (Abraxane) to allow increased drug accumulation
In addition to use as regular carriers, polymers into breast cancer tissue without the use of Cremophor,
may also be formulated into microparticles and a toxic solvent frequently associated with adverse
nanoparticles. In such delivery systems, the thera- reactions such as hypersensitivity and demyelination,
peutic agent is encapsulated within a biodegradable and possibly decreased drug penetration. In a novel
polymeric and/or lipid colloidal particle that is in the approach, Levemir insulin and Victoza glucagon are
micrometer or nanometer size range, respectively. chemically modified specifically to create high-
Micro- and nanosphere formulations are useful for affinity binding to endogenous albumin, resulting in
solubilizing poorly soluble drugs, improving oral the prolongation of the respective half-lives from
bioavailability, protecting against degradation, or minutes to hours. 99mTc aggregated to albumin is also
providing sustained drug delivery. The small size of commonly used as an imaging agent.
nanospheres generally allows good tissue penetra-
tion while providing protection or sustained release.
The size of the microsphere and nanosphere has Liposomes
a profound impact on an encapsulated drug’s in vivo Liposomes have an aqueous, drug- or imaging
properties and disposition. At over 12 mm, particles agent-containing interior surrounded by an exterior
are lodged in the capillary bed at the site of the injec- lipid bilayer, and typically range in size from 0.5 to
tion. From 2 to 12 mm, particles are retained at the 100 mm. Liposomes have been used successfully to
lung, spleen, or liver. Particles less than 0.5 mm reduce side effects of antitumor drugs and antibiot-
(500 nm) deposit into the spleen and bone marrow. ics. For example, doxorubicin liposomes (Doxil)
In gene therapy, particles smaller than 100 nm dem- have reduced cardiotoxicity and emetic side effects.
onstrate higher gene expression in vitro compared to Amphotericin B may have reduced nephrotoxicity
larger particles (Panyam and Labhasetwar, 2003). side effects when formulated with liposomes. An
More recently, nanoparticles are believed to accumu- innovative liposome-related product (Abelcet) con-
late in cancer tissue because of hyperpermeability of sists of amphotericin B complexed with two phos-
the permeating vascular endothelia due to fenestra- pholipids, l-a-dimyristoylphosphatidylcholine and
tions in the micrometer range, also known as the l-a-dimyristoylphosphatidylglycerol (Liposome
enhanced permeation and retention (EPR) effect. Company, www.lipo.com). The lipid drug complex
Delivery systems may be used to differentially target releases the drug at the site of infection and reduces
certain cancer cell types or stage of disease based on renal toxicity of amphotericin B without altering its
such permeabilities (see Ferrari, 2010). Though antifungal activity. A more representative liposome
some peptides and nucleic acids have been success- product is AmBisome (NeXstar), which consists of
fully formulated into nanospheres, protein denatur- very fine liposomes of amphotericin B. The product
ation and degradation can be significant during significantly reduces the side effects of amphoteri-
encapsulation. cin B. Daunorubicin citrate liposome (DaunoXome,
NeXstar) is an aqueous solution of the citrate salt of
the antineoplastic daunorubicin encapsulated within
Albumin lipid vesicles. The distearoylphosphotidylcholine
Albumin is a large protein (MW 69,000 Da) that is and cholesterol (2:1 molar ratio) liposome formula-
distributed in the plasma and extracellular water. tion in DaunoXome attempts to maximize the selec-
Albumin has been experimentally conjugated or tivity of daunorubicin into solid brain tumors. Once
complexed with many drugs to improve site-specific in the tumor, daunorubicin is released and exerts its
Targeted Drug Delivery Systems and Biotechnological Products 627
– – Liposomes may be used to improve intracellular
– – –
– – delivery, in which case the liposome must also be
– – Polar head designed to fuse with the plasma or endosome mem-
– – group
brane. Lipids or fusogenic peptides that facilitate
– –
membrane fusion, such as phosphatidylethanolamine
–
– – –
–
– – or arginine-containing or amphipathic cell-penetrating
– – – –
– – –
– peptides, respectively, have been used to improve
– –
– – – – liposome intracellular delivery. Peptides such as tat
– – or octa-arginine have also been used for intracellular
– – targeting and increased uptake of genes. Cationic
– – lipids, such as N-[1-(2,3-dioleyloxy)propyl]-N,N,N-
– – Hydrophobic
– – trimethylammonium chloride (DOTMA), or oleoyl-
– – – chain
phoshphatidylethanolamine (DOPE), are also
FIGURE 204 Diagrammatic representation of a liposome commonly used for in vitro delivery of DNA. When
showing polar head group and hydrophobic chain. cationic lipids are mixed with DNA, a particle forms
from DNA–lipid charge interactions. The cationic
antineoplastic activity. Liposome formulations have lipid is believed to destabilize biological membranes
also been prepared with cytarabine (Depocyte) and resulting in improved intracellular DNA delivery.
other drugs. The in vivo use of cationic lipids is limited by sys-
There are three general ways of preparing con- temic toxicity due to the positive charge of the lipid.
ventional liposomes: (1) phase separation, (2) spray or Combinations of modifications to liposomes may
shear method through orifice, and (3) coacervation. also be employed to increase residence time in the
The choice of method depends on the drug, the yield body including PEG to make the liposome invisible
requirements, and the nature of the lipids. Formation (ie, “stealth” liposomes) to macrophages combined
of the liposome bilayer depends on the hydrophobic with a targeting antibody and/or cationic lipids.
and hydrophilic orientation of the lipids (Fig. 20-4). However, PEG coatings may prevent recognition of
Liposomes have different electrical surface targeting agents when placed simultaneously on
charges depending on the type of material used. nanoparticle delivery systems (see Ferrari, 2010).
Common anionic lipid materials are phosphatidylcho-
line and cholesterol. The phosphatidyl group is
amphiphilic, with the choline being the polar group. Frequently Asked Questions
This structure allows each molecule to attach to others »»What is meant by targeted drug delivery? How does
through hydrophobic and hydrophilic interactions. gene therapy differ from targeted drug delivery?
Thermodynamically, liposomes are in equilibrium »»Why are macromolecular carrier systems used for
between different membrane conformations or struc- targeted drug delivery?
tures (lipid polymorphism). Thus, some seemingly
stable liposome systems exhibit leakage and generally
do not have long shelf lives. TARGETED DRUG DELIVERY
Liposomes can be engineered to be site specific.
Generally, site specificity is conferred by the type of Most conventional dosage forms deliver drug into
lipid or by inclusion of a targeting agent, such as a the body that eventually reaches the site of action by
monoclonal antibody or a tumor-specific antigen, distribution and passive diffusion. In addition, the
into the liposome bilayer (see Targeted Drug Delivery, drug also distributes to nontarget site tissues. Because
below) or just above a protective polymer layer, such of nonselective distribution, a much larger dose is
as PEG. Magneto-, light- and thermosensitive lipo- given to the patient to achieve therapeutic concen-
somes have also been developed to enable site- trations in the desired tissue. However, drug action
specific drug release. at nontarget sites may result in toxicity or other
628 Chapter 20
adverse reactions. Delivery systems that target the more fully earlier in this chapter. To date three anti-
drug only to the desired site of drug action allow for body-drug conjugates have been FDA approved
more selective, safe, and effective therapeutic activity. including brentuximab vedotin (Adcetris) to treat
For biopharmaceuticals, selective and targeted drug Hodgkin’s lymphoma and anaplastic large cell lym-
therapy could result in a significant reduction in tox- phoma and trastuzumab emtansine (Kadcyla) to treat
icity, dose, and cost. breast cancer. Gemtuzumab ozogamicin (Mylotarg)
Targeted drug delivery or site-specific drug to treat acute myelogenous leukemia was also previ-
delivery refers to drug carrier systems that place the ously approved, though later withdrawn from the
drug at or near the receptor site. Friend and Pangburn market in 2010 due to marginal clinical benefit.
(1987) have classified site-specific drug delivery into
three broad categories or drug targeting: (1) first- General Considerations in Targeted
order targeting, which refers to drug delivery sys-
Drug Delivery
tems that deliver the drug to the capillary bed of the
active site; (2) second-order targeting, which refers Considerations in the development of site-specific or
to the specific delivery of drug to a special cell type targeted drug delivery systems include (1) the ana-
such as the tumor cells and not to the normal cells; tomic and physiologic characteristics of the target
and (3) third-order targeting, which refers to drug site, including capillary permeability to macromole-
delivery specifically to the internal (intracellular) cules and cellular uptake of the drug (Molema et al,
site of cells. An example of third-order drug target- 1997); (2) the physicochemical characteristics of the
ing is the receptor-mediated entry of a drug complex therapeutically active drug; (3) the physical and
into the cell by endocytosis followed by lysosomal chemical characteristics of the carrier; (4) the selec-
release of the lysosomally active drug. Numerous tivity of the drug–carrier complex; (5) any impurities
techniques have been developed for site-specific introduced during the conjugation reaction linking
delivery. Ideally, site-specific carriers guide the drug the drug and the carrier that may be immunogenic,
to the intended target site (tissues or organ) in which be toxic, or produce other adverse reactions.
the receptor is located without exposing the drug to
other tissues, thereby avoiding adverse toxicity. Target Site
Much of the research in targeted drug delivery has The accessibility of the drug–carrier complex to the
been in cancer chemotherapy. target site may present bioavailability and pharmaco-
Site-specific drug delivery has also been charac- kinetic problems, which also include anatomic and/or
terized as passive or active targeting (Takakura and physiologic considerations. For example, targeting a
Hashida, 1996). Passive targeting refers to the drug into a brain tumor requires a different route of
exploitation of the natural (passive) disposition pro- drug administration (intrathecal injection) than target-
files of a drug carrier, which are passively deter- ing a drug into the liver or spleen. Moreover, the per-
mined by its physicochemical properties relative to meability of the blood vessels or biologic membranes
the anatomic and physiologic characteristics of the to macromolecules or drug–carrier complex may be a
body. Active targeting refers to alterations of the barrier preventing delivery and intracellular uptake of
natural disposition of a drug carrier, directing it to these drugs (Molema et al, 1997).
specific cells, tissues, or organs. Active targeting
employing receptor-mediated endocytosis is a satu-
rable, nonlinear process that depends on the drug– Site-Specific Carrier
carrier concentration, whereas passive targeting is To target a drug to an active site, one must consider
most often a linear process over a large range of whether there is a unique property of the active site
doses. that makes the target site differ from other organs or
One approach to active targeting is the use of tissue systems in the body. The next consideration is
ligands or monoclonal antibodies, which can target to take advantage of this unique difference so that
specific cells. Monoclonal antibodies were discussed the drug goes specifically to the site of action and not
Targeted Drug Delivery Systems and Biotechnological Products 629
to other tissues in which adverse toxicity may occur. not the “magic bullet” for drug targeting that many
In many cases the drug is complexed with a carrier people had hoped. One difficulty encountered is that
that targets the drug to the site of action. For exam- the large molecule reduces the total amount of active
ple, one of the first approved drugs developed using drug that can be easily dosed (ie, the ratio of drug to
pharmacogenomic principles is Herceptin (trastu- carrier). In contrast, conventional carriers or target-
zumab), a monoclonal antibody designed to bind to ing agents that are not specific are often many orders
the human epidermal growth factor receptor. This of magnitude smaller in size, and a larger effective
receptor is overexpressed on HER-2 positive breast drug dose may be given more efficiently. Antibody
cancer cells. Therefore, the drug will preferentially fragments comprised of either the double- or single-
bind HER-2 positive breast cancer cells, though chain variable regions are also being tested as smaller
other noncancerous cells may also express the recep- drug targeting agents (see Srivastava et al, 2014, and
tor. Trastuzumab has also been approved as a drug van der Meel et al, 2013, for review).
conjugate as discussed above, where the antibody is In addition to employing monoclonal antibodies
linked to anticancer/antimicrotubule agents that may, in liposomes and other delivery systems as described
for example, be released in the lysosome after inter- above, mAbs may be conjugated directly to drugs as
nalization. Similarly, trastuzumab has also been used mentioned above. The resulting conjugate can theo-
as targeting agents for anticancer drug-encapsulated retically deliver the drug directly to a cell that
nanoparticles in clinical studies. The successful expresses a unique surface marker. For example, a
application of these delivery systems requires the tumor cell may overexpress the interleukin-2 recep-
drug–carrier complex to have both affinity for the tar- tor. In this case, a cytotoxic molecule such as recom-
get site and favorable pharmacokinetics for delivery to binant diptheria toxin is coupled to an mAb specific
the organ, cells, and subcellular target sites. An addi- for the interleukin-2 receptor (Ontak). The conjugate
tional problem, particularly in the use of protein car- delivers the toxin preferentially to these tumor cells.
riers, is the occurrence of adverse immunological An overall tumor response rate for Ontak is 38%,
reactions—an occurrence that is partially overcome by with side effects including acute hypersensitivity
designing less immunoreactive proteins. Humanized reaction (69%) and vascular leak syndrome (27%)
mAbs are an example of a therapeutic protein engi- (Foss, 2001). Zolimomab aritox (Orthozyme-CD5,
neered to be less immunoreactive. Xoma/Ortho Biotech) is an investigational immuno-
conjugate of monoclonal anti-CD5 murine IgG and
Drugs the ricin A-chain toxin. This conjugate is used in the
treatment of steroid-resistant graft-versus-host dis-
Most of the drugs used for targeted drug delivery are
ease after allogeneic bone marrow transplants for
highly reactive drugs that have potent pharmacody-
hematopoietic neoplasms, such as acute myeloge-
namic activities with a narrow therapeutic range.
nous leukemia. Myoscint is an 111In-labeled mAb
These drugs are often used in cancer chemotherapy.
targeted to myosin that is used to image myocardial
Many of these drugs may be derived from biologic
injury in patients with suspected myocardial infarc-
sources, made by a semisynthetic process using a
tion. An immune response to mAb drugs may
biologic source as a precursor, or produced by
develop, since mAbs are produced in mouse cells.
recombinant DNA techniques. The drugs may also
“Humanized” mAbs are genetically engineered to
be large macromolecules, such as proteins, and are
produce molecules that are less immunogenic.
prone to instability and inactivation problems during
processing, chemical manipulation, and storage.
Oral Immunization
Targeting Agents Antigens or fragmented antigenic protein may be
Properly applied, drug targeting can improve the delivered orally and stimulate gut-associated lym-
therapeutic index of many toxic drugs. However, phoid tissue (GALT) in the gastrointestinal tract.
monoclonal antibodies (see discussion above) are This represents a promising approach for protecting
630 Chapter 20
many secretory surfaces against a variety of infec- prolonged circulation in the body (Table 20-1). In
tious pathogens, but products have not yet reached addition, since biologics are typically eliminated
clinical trials. Immunization against salmonella and from the body by non-cytochrome-mediated mecha-
Escherichia coli in chickens was investigated for nisms, drug–drug interactions with small-molecule
agricultural purposes. Particulate antigen delivery drugs is less likely to occur.
systems, including several types of microspheres, The size and generally hydrophilic nature of the
have been shown to be effective orally inducing vari- nucleic acid and protein molecules also often pre-
ous types of immune response. Encapsulation of clude the use of diffusional and paracellular trans-
antigens with mucosal adjuvants can protect both the port pathways available to small drug molecules.
antigen and the adjuvant against gastric degradation The capillary wall in most organs and tissues limits
and increase the likelihood that they will reach the passage of macromolecules such as albumin. A typi-
site of absorption. cal vector is 20–150 nm, and monoclonal antibodies
are composed of four polypeptide chains (over 1200
amino acids in total). Such compounds would be
PHARMACOKINETICS OF expected to have limited diffusional access to most
BIOPHARMACEUTICALS tissues, except the liver, spleen, bone marrow, and
tumor tissues, which have higher vascular permea-
The unusual nature of biopharmaceuticals compared bility. As a result, the volume of drug distribution is
to traditional drugs presents development challenges often smaller for the larger protein and nucleic acid
for scientists in the biotechnology industry. Because drugs because of vascular confinement or binding to
of the size and complexity of biopharmaceuticals, specific tissues. Indeed, the volume of distribution
stability and delivery are major developmental issues for some of these drugs approximates plasma vol-
with these new drugs. The prerequisite of the main- ume: the apparent volume of distribution at steady
tenance of higher-order structure adds a new dimen- state of the mAb Nebacumab is 0.11 ± 0.03 L/kg
sion to formulation, drug delivery, and stability (Romano et al, 1993), and of Simulect is approxi-
testing of biologic drugs. Pharmacokinetic studies mately 7.5 L.
are often complicated by bioanalytic challenges, Because of the stability and distribution limita-
since preservation of primary structure or an isotope tions of large biologic drugs, delivery systems such
label alone does not necessarily coincide with bio- as conjugates, nanoparticles, liposomes, and viral
logic activity, and effective concentrations are often vectors as described above have been used to
much lower compared to conventional drugs. improve activity and delivery. The pharmacokinetics
Once in the body, protein and nucleic acid drugs of recombinant viral gene delivery systems have
are subject to rapid degradation by endogenous pro- been difficult to measure because of the relatively
teases and nucleases that are present in the serum, low doses given and often inefficient transgene
tissues, and cells. Unmodified phosphodiester DNA expression. As a result, gene expression and trans-
and RNA are extremely labile in the body, with half- gene persistence in tissues are used to determine
lives of the order of a few minutes. Houk et al (2001) pharmacokinetic profiles (NIH Report, 2002).
report that naked DNA clearance in rats is rapid and Nonviral and naked DNA delivery systems are rela-
depends on the conformation of the plasmid: super- tively well characterized in comparison to viral
coiled, open circular, versus linear. Many of the early delivery systems. Hengge et al (2001), using poly-
recombinant protein drugs also have half-lives of the merase chain reaction (PCR), demonstrate that intra-
order of a few minutes, such as alteplase (Activase) muscular or cutaneous injection of a DNA vaccine
and interleukin-2 (Proleukin) (Table 20-1). However, resulted in gene expression primarily in surrounding
if immediate stability or immunigenicity concerns tissues unless extremely high doses were adminis-
can be remedied by chemical modification or bioen- tered. Zhou et al (2009) used real-time PCR (RT-PCR)
gineering, the biopharmaceutical may be large to demonstrate two-compartment pharmacokinetic
enough to escape glomerular filtration and enjoy a profiles of naked DNA and simple and reversibly
Targeted Drug Delivery Systems and Biotechnological Products 631
stabilized DNA (rSDN) polymer nanoparticles, with already approved for marketing. If satisfactory mass
mean retention time increasing from 4.5 minutes balance information is already available for the
with naked DNA to almost 23 minutes with the approved drug product, a limited mass balance study
reversibly rSDN. can be undertaken for the new drug product. Comparison
Liposome delivery systems are fairly well char- of the absorption, distribution, metabolism, and excre-
acterized in terms of their pharmacokinetic proper- tion (ADME) of the liposome and nonliposome drug
ties. Liposome encapsulation may reduce the VD product forms should be made, using a crossover or a
(Minchin et al, 2001), and may (Houk et al, 2001) or parallel noncrossover study design that employs an
may not (Minchin et al, 2001) improve upon DNA appropriate number of subjects.
half-life by several hours. However, lipid delivery
systems are also rapidly cleared by the mononuclear
phagocyte system (spleen and liver) unless injected BIOEQUIVALENCE OF
intratumorally (Nomura et al, 1997). In addition, BIOTECHNOLOGY-DERIVED
liposomes may enhance an immune response to DRUG PRODUCTS
the drug and complement activation, also resulting in
rapid clearance. The dosage form or formulation of a drug product
Alternatively, liposomes can be designed to may change during the course of drug development.
evade phagocyte detection and improve circulation In addition, since the product quality (number and
time by coating with polyethylene glycol (PEG), type of contaminants for example) and even product
which minimizes opsonin-dependent clearance. microheterogeneities (degree of glycosylation, post-
In vivo, the PEG provides a “bulky” head group that translational modifications, genetic variants, etc) are
serves as a barrier to prevent interaction with the a function of the manufacturing process, the protein
plasma opsonins. The hydrated groups sterically or nucleic acid drug itself will continue to evolve
inhibit hydrophobic and electrostatic interaction of a prior to approval of the biologics licence agreement
variety of blood components at the liposome surface, (BLA). Likewise, the initial drug formulation used
thereby evading recognition by the reticuloendothe- in early clinical studies (eg, Phase I/II) may not be
lial system. An example of this concept is the stealth the same formulation as the drug formulation used in
liposome, which led to reduction in the volume of later clinical trials (Phase III) or the marketed formu-
distribution, half-life extension (Gabizon et al, 2003), lation. Therefore, even genetically “identical”
and eventual marketing (Doxil) in the United States. recombinant drugs will differ because of differences
Optimal formulation of a PEGylated liposome can in variables such as cell, cell clone, manufacturing,
improve liposome stability from 1% to 31% of dose purification and storage, formulation, expression
remaining in the body at 24 hours postinjection system, or raw chemicals. Such variations may result
(Allen et al, 2002). in profound differences in bioavailability, immuno-
The pharmacokinetics of a liposomal formula- genicity, adverse reactions, and efficacy. Because of
tion can be different from those of a nonliposomal such differences, biological “generics” are instead
product given by the same route of administration. referred to as “biosimilars.” A pathway for FDA
For new liposome products, the FDA (draft guid- approval of biosimilars has been defined as part of
ance, see http://www.fda.gov/downloads/Drugs the 2009 Biologics Price Competition and Innovation
/GuidanceComplianceRegulatoryInformation Act (BPCI Act). Under this Act, companies may
/Guidances/ucm070570.pdf) recommends a compar- submit a 351(k) application for their biosimilar can-
ative mass balance study be performed to assess the didate. The FDA then considers the “totality of the
differences in systemic exposure and pharmacoki- evidence” in terms of the interchangability between
netics between liposome and nonliposome drug prod- the candidate and reference drug. The candidate
ucts when (1) the two products have the same active should be “highly similar” and have “no clinically
moiety, (2) the two products are given by the same meaningful difference” between the two. Product
route of administration, and (3) one of the products is immunogenicity should be evaluated via at least one
632 Chapter 20
clinical study, and variability between lots of the
innovator product should be determined as a guide to Frequently Asked Questions
the candidate’s product variability. The FDA now
»»What are the major differences in drug distribution
also provides recommendations regarding develop- and elimination between conventional molecules
ment of biosimilars and quality considerations of and biotechnological compounds?
analytical factors that should be considered when
submitting a 351(k) application. Also see Chapter 15 »»What are the many ways antibodies are used
therapeutically?
for more details on bioequivalence.
LEARNING QUESTIONS
1. Explain why most drugs produced by biotech- 3. Doxorubicin (Adriamycin) is available as
nology cannot be given orally. What routes of a conventional solution and as a liposomal
drug administration would you recommend for preparation. What effect would the liposomal
these drugs? Why? preparation have on the distribution of doxoru-
2. What is meant by site-specific drug delivery? bicin compared to an injection of the conven-
Describe several approaches that have been tional doxorubicin injection?
used to target a drug to a specific organ.
ANSWERS
Frequently Asked Questions the molecular weight of the drug. Although both
What is the most frequent route of administration of drugs are b-interferons, glycosylation affects the
biologic compounds? pharmacokinetics, the stability, and the efficacy of
these drugs.
• The most frequent route of administration for
biologic compounds is parenteral (eg, IM or IV). What kind of biologic drugs are available and how
For example, b-interferon for multiple sclerosis are they used? Are they similar or different from
is given IM to allow gradual drug release into the small-molecule drugs?
systemic circulation. • The distribution of a biotechnology compound
depends on its physicochemical characteristics.
What is the effect of glycosylation on the activity of
Many peptides, proteins, and nucleotides have
a biologic compound? Give an example.
polar chains so that a major portion of the drug
• Glycosylation is the addition of a carbohydrate is distributed in the extracellular fluid with a
group to the molecule. For example, Betaseron volume of 7–15 L. Drugs that easily penetrate
(interferon-b-1a) is not glycosylated, whereas into the cell have higher volumes of distribution,
Avonex (interferon-b-1b) is glycosylated. Gly- about 15–45 L, due to the larger volume of intra-
cosylation will increase the water solubility and cellular fluid.
Targeted Drug Delivery Systems and Biotechnological Products 633
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Ferrari, M. Frontiers in cancer nanomedicine: Directing mass cokinetics and in vivo gene expression of naked plasmid DNA
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Gros L, Ringsdorf H, Schupp H: Polymeric antitumor agents on a Takakura Y, Hashida M: Macromolecular carrier systems for tar-
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Relationship Between
21 Pharmacokinetics
and Pharmacodynamics
Mathangi Gopalakrishnan, Vipul Kumar, and
Manish Issar
Chapter Objectives PHARMACOKINETICS AND
»» Quantitatively describe the PHARMACODYNAMICS
relationship between drug,
receptor, and the pharmacologic The role of pharmacokinetics (PK) to derived dosing regimens to
response. achieve therapeutic drug concentrations for optimal safety and effi-
cacy will be discussed in the next two chapters. A more objective
»» Explain why the intensity approach for designing a drug’s dosing regimen would need to link
of the pharmacologic the exposure of the drug within the body to the desirable (efficacy)
response increases with drug and undesirable (safety/toxicity) effects of the drug. At the site of
concentrations and/or dose up action, the drug interacts with a receptor that may be located within
to a maximum response. a cell or on special cell membranes. This drug–receptor interaction
»» Explain the difference between initiates a cascade of events resulting in a pharmacodynamic
an agonist, a partial agonist, and response or effect. Thus, pharmacodynamics (PD) refers to the
an antagonist. relationship between drug concentration at the site of action (recep-
tor) and the observed pharmacologic response. This chapter
»» Describe the difference between
describes how the exposure of a drug over time (dose, concentra-
a reversible and a nonreversible
tions, dosing regimens) can be related to the desirable and undesir-
pharmacologic response.
able effects of the drug. Just as the PK of a drug has been described
»» Define the term biomarker and via mathematical models such as a one- or two-compartmental
explain how biomarkers may be model, the relationship between drug concentration and effect can
used in the clinical development also be described using mathematical models. These PK-PD models
of drugs. can further be applied for simulations and prediction of drug action.
This chapter is organized as follows: First, formal definitions of
»» Show how the Emax and
terms and those used interchangeably in the PK-PD literature are
sigmoidal Emax model describe
provided. Second, an introduction to how the PK-PD principles are
the relationship of the
integrated into drug development is provided. In addition, the chapter
pharmacodynamic response to
briefly describes the drug receptor theory and the use of biomarkers.
drug concentration.
This is followed by the theoretical basis of PK-PD relationship.
»» Define the term Lastly, the chapter describes the different types of possible PK-PD
pharmacokinetic– relationships showing how the time course of drug action relates to
pharmacodynamic model drug concentration in the body. Examples and case studies are pro-
and provide equations that vided in the chapter to integrate therapeutic concepts and drug
quantitatively simulates the time development perspectives.
course of drug action.
635
636 Chapter 21
»» Explain the effect compartment Definitions for Exposure, Response, and Effect
in the pharmacodynamic model Various terminologies have been used to describe PK and PD.
and name the underlying To avoid confusion, current correct terminology and definitions
assumptions. of these terms are provided and such definitions will be followed
»» Describe the effect of changing throughout this chapter.
drug dose and/or drug The relationship between PK and PD is also referred to as
elimination half-life on the exposure-response relationship or concentration-response relation-
duration of drug response. ship or concentration–effect relationship. Exposure-response
information is used to determine the safety and efficacy of drugs
»» Describe how observed drug
in the process of drug approval, more importantly to understand
tolerance or unusual hysteresis-
the benefit–risk of drugs during the drug approval process and to
type drug response may be
derive dosing information.
explained using PD models
based on simple drug receptor
theory. Exposure
The term exposure can be defined as any dose or drug input to the
»» Define the term drug exposure
body or various measures of acute or integrated drug concentra-
and explain how it is used to
tions in plasma or other biological fluid (eg, Cmax, Cmin, Css, AUC).
improve drug therapy and
Exposure is related to a measure of drug amount at a particular site
safety.
in the body from which it elicits a response. Commonly used expo-
sure measures are dose of a drug and plasma concentrations (Cp).
Any input to characterize the pharmacokinetic aspect of the drug
is a measure of exposure.
Response
A response (R) refers to a direct measure of the pharmacologic
observation. For example, measure of diastolic blood pressure
(DBP) at some time point is considered as a response.
R(t) = Response at time, t : Diastolic blood pressure
Effect
Effect, E refers to a change in the biological response from one
time to another. In other words, an effect is a derived or calculated
value from an observed response. For example, change from base-
line in diastolic blood pressure is the effect.
E = Effect : Change from baseline in DBP at 8 weeks
To further illustrate, let us consider the DBP measured at the
beginning of a clinical trial in a subject as 92 mm Hg, denoted as
R(t = 0), and DBP measured at the end of 8 weeks of the trial,
R(t = 8) is 82 mm Hg. Here, R(t = 0) and R(t = 8) are the responses.
The effect, E, which is of interest, is change from baseline in DBP
at 8 weeks calculated as –10 mm Hg and is denoted below:
E = R(t = 8) − R(t = 0) = 82 mm Hg − 92 mm Hg = −10 mm Hg
Relationship Between Pharmacokinetics and Pharmacodynamics 637
Effects include a broad range of endpoints or bio- Kimko and Pinheiro, 2014). In general, the current
markers ranging from clinically remote biomarkers drug development process is a series of developmen-
(eg, receptor occupancy) to a presumed mechanistic tal and evaluative steps carried out from the stage of
effect (eg, % angiotensin converting enzyme [ACE] an Investigational New Drug Application (IND)
inhibition) to a potential surrogate (eg, change from leading to the submission of New Drug Application
baseline in blood pressure or change in lipids etc). (NDA). The regulatory bodies like the Food and
Often, the scientific community uses response and Drug administration (FDA) and the European
effect interchangeably. Medicines Agency (EMA) review the NDA and pro-
vide approval/disapproval for the new drugs to be
used in the market. The applicable process as it per-
PK-PD Information Flow in Drug tains to the US FDA is illustrated as an example in
Development Fig. 21-1.
The role of PK and PD in the drug development There are predominantly four phases in the
process is considered to be impactful and scientists drug development process as shown in Fig. 21-1.
have reiterated its importance in drug development The details of the four phases in drug development
and decision making (Derendorf et al, 2000; Sheiner and how the PK-PD information at each of the
and Steimer, 2000; Gobburu and Marroum, 2001; phases can be useful are described briefly here and
1–3 years 2–10 years 1–2 years
Discovery, Clinical Research and
Preclinical Testing, Development
Research and 20–80 healthy volunteers
Development
Phase I
First in human, PK, tolerability
50–100 patients
Initial synthesis Phase II NDA Postmarketing
of compounds Review Surveillance
Evidence of effectiveness, safety
Animal testing 1000–3000 patients
Phase III
Short-term safety
Verify effectiveness, long-term
safety and adverse reactions
Long-term safety
IND submitted to FDA NDA submitted to FDA
30-day safety review 10–12 months review
FIGURE 211 New drug development process. (Adapted from Peck et al, 1994.)
638 Chapter 21
Preclinical
Clinical Studies
Studies
1. Assay
development
PK Guided Dose Escalation
2. In vitro PD
First in Human Dose (FIH)
3. PK-PD
Maximum Recommended Starting Dose (MRSD)
(toxicity) in
rodents
Conc vs Time Dose/Exposure-response
trials PK screen in
large efcacy trials
Primate PK-PD Toxicity vs Conc SUBMIT
Metabolism NDA
PK/PD in special
Concentration-controlled populations
Animal Testing trials
Phase I
Phase II
Phase III
FIGURE 212 PK, PD, and toxicity information during the drug development process. (Adapted from Peck et al, 1994.)
shown in Fig. 21-2. The initial phase is the preclini- dose, and PK characteristics of the drug and metab-
cal testing phase. During this phase, the new olite (if any) are obtained. The initial studies may
molecular entities are tested for biological activity help establish the appropriate dosing program for
in experimental animals from mice to primate mod- Phase II studies by means of the observed dose/
els. The toxicity and safety data available at this exposure-safety relationship.
stage are used to proceed for safety evaluation in Phase II studies are conducted in a small group
humans at the IND stage. The preclinical PK-safety of patients to assess if the drug exhibits anticipated
information is helpful in deriving first-in-human therapeutic benefit or not in the intended population.
(FIH) doses or maximum recommended starting The principal goal of Phase II studies is to provide
dose (MRSD) by means of allometric scaling. evidence for the efficacy or proof of effect of the
Moreover, preclinical studies on pharmacodynamic investigational drug. Additionally, the PK-PD infor-
activity from different exposures/dose may indicate mation gained in Phase-II studies are used to build
the likely steepness of the dose–response curves dose-exposure-response relationship to obtain a
in humans. rational dosing strategy for Phase III studies. The
After discovery and preclinical testing, the new exposure-response relationships can be used to
molecular entity (NME) enters the clinical testing design strategies for dose optimization and individu-
phase. Typically, the clinical testing phase consists alized dosing in Phase III trials. In order to avoid
of early phase (Phase I and II) and late phase clinical failure in the Phase III trials mainly due to wrong
trials (Phase III). During Phase I studies, the PK and dose/dosing regimen selection, it is imperative to
tolerability of the NME are studied in healthy volun- accrue/leverage valuable information that is gained
teers by means of dose escalation. Information on in Phase II studies and apply it to design Phase III
initial parameters of toxicity, maximum tolerated trials to increase likelihood of success.
PK-PD (toxicity)
Relationship Between Pharmacokinetics and Pharmacodynamics 639
Phase III studies used for drug approval are con- Typically, the drug–receptor interaction results in a
sidered pivotal trials and typically two adequate and cascade of downstream events eliciting a PD
well-controlled clinical trials are submitted for drug response. The interaction of drug with a receptor fol-
approval. Phase III studies are conducted in a larger lows the law of mass action (Clark, 1927), which can
patient population and are designed to document the be described as per the receptor occupancy theory,
clinical efficacy and safety of the investigational drug which is described in greater detail under the section
and further refine the dose-exposure-response relation- Emax Drug-Concentration Effect Model.
ship. The information gained in preclinical and clinical Typically, a single drug molecule interacts with
studies become part of the drug label that ultimately a receptor with a single binding site to produce a
reaches the prescriber and hence the patient. pharmacologic response, as illustrated below.
The preceding section discussed the implications
of PK-PD relationship in the drug development pro- [Drug] + [Receptor] ⇔
cess. To understand how a drug elicits a response, it [Drug − receptor complex] → Response
is necessary to understand the process at a cellular
and a molecular level. The following section describes where the brackets [ ] denote molar concentrations.
the interaction of a drug molecule with a receptor, This scheme illustrates the occupation theory
resulting in a pharmacodynamic response. for the interaction of a drug molecule with a receptor
molecule. More recent schemes consider a drug that
Drug–Receptor Interaction binds to macromolecules as a ligand. Thus, the
reversible interaction of a ligand (drug) with a recep-
Receptors are cellular proteins that interact with
tor may be written as follows (Neubig et al, 2003):
endogenous ligands (such as neurotransmitters and
hormones) to elicit a physiological response thereby
K
regulating cellular functions (Blumenthal and 1 K2
L + R↽⇀ LR↽⇀LR*
Garrison, 2011). Understanding the role of receptor–
endogenous ligands interaction in physiology and where L is generally referred to as ligand concentra-
pathophysiology enables targeting of specific recep- tion (since many drugs are small molecules) and LR
tors for therapeutic benefit. There are different types is analogous to the (drug–receptor complex). LR* is
of receptors that are located either outside or inside the activated form that results in the effect.
of cell membranes. Various types of receptors, their The last step is written to accommodate different
localization, and some representative examples are modes of how LR leads to a drug effect. For example,
listed in Table 21-1. the interaction of a subsequent ligand with the recep-
The drug–receptor interactions involve weak tor may involve a conformation change of the receptor
chemical forces or bonds (eg, hydrogen bonding, or simply lead to an additional effect. In this chapter,
ionic electrostatic bonds, Van der Waals forces). effect and response are used interchangeably.
TABLE 211 Selected Examples of Drug Receptors
Type Description Examples
Ion channels Located on cell surface or transmembrane; Acetylcholine (nicotinic)
governs ion flux
G-protein coupled Located on cell surface or transmembrane; GTP Acetylcholine (muscarinic) a – and b-adrenergic
receptor involved in receptor action receptor proteins Eicosanoids
Transcription factors Within cell in cytoplasm, activate or suppress DNA Steroid hormones Thyroid hormone
transcription
Partially adapted from Moroney (2011) and Katzung et al (2011).
640 Chapter 21
Full agonist
Partial agonist
Inactive compound
Inverse agonist
Log [Drug]
FIGURE 213 Representation of different drug–receptor interactions. (Adapted from Goodman Gilman, Chapter 3, 12th edition.)
This model makes the following assumptions: agonist, inverse agonist, or antagonist. Agonist is an
agent that interacts with a receptor producing effects
1. The drug molecule combines with the receptor
similar to that of an endogenous ligand (eg, stimula-
molecule as a bimolecular association, and the
tion of the m opioid receptor by morphine [Yaksh and
resulting drug–receptor complex disassociates
Wallace, 2011]). Antagonist on the other hand is an
as a unimolecular entity.
agent that blocks the effect of an agonist by binding to
2. The binding of drug with the receptor is fully
the receptor, thereby inhibiting the effect of an endog-
reversible.
enous ligand or agonist (eg, atenolol, a blood pressure-
3. The basic model assumes a single type of
lowering agent is a b1-receptor antagonist) (Westfall
receptor binding site, with one binding site
and Westfall, 2011). A partial agonist is an agent that
per receptor molecule. It is also assumed that
produces a response similar to an agonist but can-
a receptor with multiple sites may be modeled
not reach a maximal response as that of an agonist
after this (Cox, 1990).
(eg, buspirone, an anxiolytic agent is a partial agonist
4. The occupancy of the drug molecule at one
of 5-HT
receptor site does not change the affinity of 1a receptor) (O’Donnell and Shelton, 2011). An
inverse agonist selectively binds to the inactive form of
more drug molecules to complex at additional
the receptor and shifts the conformational equilibrium
receptor sites.
toward the inactive state (eg, famotidine, a gastric
5. Each receptor has equal affinity for the drug
acid production inhibitor is an inverse agonist of H
molecule. 2
receptor) (Skidgel et al, 2011). The manner in which
The model is not suitable for drugs with alloste- different drugs/ligands interact with the receptors can
ric binding to receptors, in which the binding of one be represented graphically as shown in Fig. 21-3.
drug molecule to the receptor affects the binding of
subsequent drug molecules, as in the case of oxygen
molecules binding to iron in hemoglobin. As more RELATIONSHIP OF DOSE TO
receptors are occupied by drug molecules, a greater PHARMACOLOGIC EFFECT
pharmacodynamic response is obtained until a maxi-
mum response is reached. The onset, intensity, and duration of the pharmaco-
Based on the interaction of the drug with the logic effect depend on the dose and the pharmacoki-
receptor, a drug can be classified as an agonist, partial netics of the drug. As the dose increases, the drug
Response
Relationship Between Pharmacokinetics and Pharmacodynamics 641
Slope = m
Max
response
A small increase
in response occurs
by a given dose
change
A large increase in
response occurs by
a given dose change
in this region
Log drug concentration
Drug dose FIGURE 216 Graph of log drug concentration versus
FIGURE 214 pharmacologic effect. Only the linear portion of the curve is
A plot of pharmacologic response versus
shown.
dose on a linear scale.
concentration at the receptor site increases, and the response is also proportional to the log plasma drug
pharmacologic response (effect) increases up to a concentration within a therapeutic range, as shown
maximum effect. A plot of the pharmacologic effect in Fig. 21-6.
to dose on a linear scale generally results in a hyper- Mathematically, the relationship in Fig. 21-6
bolic curve with maximum effect at the plateau may be expressed by the following equation, where
(Fig. 21-4). The same data may be compressed and m is the slope, e is an extrapolated intercept, and E is
plotted on a log-linear scale and result in a sigmoid the drug effect at drug concentration C:
curve (Fig. 21-5).
For many drugs, the graph of the log dose– E = m log C + e (21.1)
response curve shows a linear relationship at a dose
range between 20% and 80% of the maximum Solving for log C yields
response, which typically includes the therapeutic
dose range for many drugs. For a drug that follows E − e
logC = (21.2)
one-compartment pharmacokinetics, the volume of m
distribution is constant; therefore, the pharmacologic
However, after an intravenous dose, the concentra-
tion of a drug in the body in a one-compartment
open model is described as follows:
kt
logC = logC )
0 − (21.3
2.3
By substituting Equation 21.2 into Equation 21.3,
we get Equation 21.4, where E0 = effect at concen-
tration C0:
E − e E0 − e kt
= −
m m 2.3
Log dose (21.4)
FIGURE 215 A typical log dose-versus-pharmacologic kmt
E = E0 −
response curve. 2.3
Pharmacologic response
Pharmacologic effect
Pharmacologic effect
642 Chapter 21
The theoretical pharmacologic response at any time A
after an intravenous dose of a drug may be calculated
using Equation 21.4. Equation 21.4 predicts that the 0
pharmacologic effect will decline linearly with time
20
for a drug that follows a one-compartment model,
with a linear log dose–pharmacologic response. From 40
this equation, the pharmacologic effect declines with
60
a slope of km/2.3. The decrease in pharmacologic
effect is affected by both the elimination constant k 80
and the slope m. For a drug with a large m, the phar-
100
macologic response declines rapidly and multiple 0 2 4 6 8
doses must be given at short intervals to maintain the Time (hours)
pharmacologic effect.
B
The relationship between pharmacokinetics and
pharmacologic response can be demonstrated by 10
observing the percent depression of muscular activ-
ity after an IV dose of ± tubocurarine. The decline
5
of pharmacologic effect is linear as a function of
time (Fig. 21-7). For each dose and resulting phar-
macologic response, the slope of each curve is the
2
same. Because the values for each slope, which
include km (Equation 21.4), are the same, the sensi-
tivity of the receptors for ± tubocurarine is assumed 1
0 2 4 6 8
to be the same at each site of action. Note that a plot Time (hours)
FIGURE 218 Mean plasma concentrations of LSD
and performance test scores as a function of time after IV
administration of 2 mg LSD per kilogram to five normal human
100 subjects. (Data from Aghajanian and Bing, 1964.)
80 of the log concentration of drug versus time yields a
straight line.
60 A second example of the pharmacologic effect
declining linearly with time was observed with
40 lysergic acid diethylamide (LSD) (Fig. 21-8). After
an IV dose of the drug, log concentrations of drug
20 decreased linearly with time except for a brief dis-
tribution period. Furthermore, the pharmacologic
0 effect, as measured by the performance score of
0 5 10 15 20 each subject, also declined linearly with time.
Time (minutes) Because the slope is governed in part by the elimi-
FIGURE 217 Depression of normal muscle activity nation rate constant, the pharmacologic effect
as a function of time after IV administration of 0.1–0.2 mg declines much more rapidly when the elimination
± tubocurarine per kilogram to unanesthetized volunteers, rate constant is increased as a result of increased
presenting mean values of six experiments on five subjects.
Circles represent head lift; squares, hand grip; and triangles, metabolism or renal excretion. Conversely, a longer
inspiratory flow. (Adapted from Johansen et al, 1964, with pharmacologic response is experienced in patients
permission.) when the drug has a longer half-life.
Depression of normal activity (percent)
Plasma concentration (ng/mL) Performance (percent of control)
Relationship Between Pharmacokinetics and Pharmacodynamics 643
RELATIONSHIP BETWEEN DOSE Solution
AND DURATION OF ACTIVITY (t a. The t
eff), eff for a 100-mg dose is calculated as
follows. Because V
SINGLE IV BOLUS INJECTION d = 10,000 mL,
The relationship between the duration of the phar- 100 mg
C = = 10 µg/mL
0 10,000 mL
macologic effect and the dose can be inferred from
Equation 21.3. After an intravenous dose, assuming For a one-compartment-model IV dose,
a one-compartment model, the time needed for any C = C –kt
0e . Then,
drug to decline to a concentration C is given by the 0.1 10 −(1.0)t
= e eff
following equation, assuming the drug takes effect
immediately: teff = 4.61 h
2.3(logC − logC)
t 0 b. The t′
= (21.5) eff for a 1000-mg dose is calculated as
k follows (prime refers to a new dose). Because
V
Using C d = 10,000 mL,
eff to represent the minimum effective drug
concentration, the duration of drug action can be 1000 mg
C
obtained as follows: 0′ = = 100 µg/mL
10,000 mL
and
2.3[log(D V
0 / D ) − logC ]
t eff (2 .6)
eff = 1
k C ′ = C ′e−kte′ff
eff 0
Some practical applications are suggested by this 0.1= 100e−(1.0)te′ff
equation. For example, a doubling of the dose will
not result in a doubling of the effective duration of
t
pharmacologic action. On the other hand, a doubling e′ff = 6.91 h
of t1/2 or a corresponding decrease in k will result in The percent increase in teff is, therefore, found as
a proportional increase in duration of action. A clini-
t ′ − t
cal situation is often encountered in the treatment of eff eff
t = ×100
eff
t
infections in which C eff
eff is the bactericidal concentra-
tion of the drug, and, in order to double the duration Percent increase in teff
of the antibiotic, a considerably greater increase than 6.91− 4.61
simply doubling the dose is necessary. = ×100
4.61
= 50%
This example shows that a tenfold increase in the
PRACTICE PROBLEM dose increases the duration of action of a drug (teff)
The minimum effective concentration (MEC or C by only 50%.
eff)
in plasma for a certain antibiotic is 0.1 mg/mL. The
drug follows a one-compartment open model and EFFECT OF BOTH DOSE AND
has an apparent volume of distribution, Vd, of 10 L
and a first-order elimination rate constant of 1.0 h–1. ELIMINATION HALF-LIFE ON THE
DURATION OF ACTIVITY
a. What is the teff for a single 100-mg IV dose of
this antibiotic? A single equation can be derived to describe the
b. What is the new teff or t′eff for this drug if the relationship of dose (D0) and the elimination half-
dose were increased tenfold, to 1000 mg? life (t1/2) on the effective time for therapeutic activity
644 Chapter 21
(teff). This expression is derived below: the drug. In certain disease states, pathophysiologic
changes in hepatic or renal function will decrease
ln Ceff = ln C0 – kteff the elimination of a drug, as observed by a pro-
Because C0 = D0/VD,
longed t1/2. This prolonged t1/2 will lead to retention
D of the drug in the body, thereby increasing the dura-
lnC 0
eff = ln
− kt
V eff tion of activity of the drug (t
d eff) as well as increasing
the possibility of drug toxicity.
D To improve antibiotic therapy with the penicillin
kteff = ln 0
− ln Ceff (21.7)
V
and cephalosporin antibiotics, clinicians have inten-
d
tionally prolonged the elimination of these drugs by
giving a second drug, probenecid, which competi-
1 D
= 0 /V
t d tively inhibits renal excretion of the antibiotic. This
eff ln
k C eff approach to prolonging the duration of activity of anti-
biotics that are rapidly excreted through the kidney has
Substituting 0.693/t1/2 for k,
been used successfully for a number of years. Similarly,
D Augmentin is a combination of amoxicillin and clavu-
teff = 1.44t 0
1/2 lnV (21.8)
dCeff lanic acid; the latter is an inhibitor of b-lactamase.
This b-lactamase is a bacterial enzyme that degrades
From Equation 21.8, an increase in t1/2 will increase penicillin-like drugs. The data in Table 21-2 illustrate
the teff in direct proportion. However, an increase in how a change in the elimination t1/2 will affect the teff
the dose, D0, does not increase the teff in direct pro- for a drug. For all doses, a 100% increase in the t1/2
portion. The effect of an increase in VD or Ceff can be will result in a 100% increase in the teff. For example,
seen by using generated data. Only the positive solu- for a drug whose t1/2 is 0.75 hour and that is given at a
tions for Equation 21.8 are valid, although mathemat- dose of 2 mg/kg, the teff is 3.24 hours. If the t1/2 is
ically a negative teff can be obtained by increasing Ceff increased to 1.5 hours, the teff is increased to 6.48 hours,
or VD. The effect of changing dose on teff is shown in an increase of 100%. However, the effect of doubling
Fig. 21.9 using data generated with Equation 21.8. A the dose from 2 to 4 mg/kg (no change in elimination
nonlinear increase in teff is observed as dose increases. processes) will only increase the teff to 3.98 hours, an
increase of 22.8%. The effect of prolonging the elimi-
nation half-life has an extremely important effect on the
EFFECT OF ELIMINATION HALF-LIFE treatment of infections, particularly in patients with
ON DURATION OF ACTIVITY high metabolism, or clearance, of the antibiotic.
Therefore, antibiotics must be dosed with full consider-
Because elimination of drugs is due to the processes
ation of the effect of alteration of the t1/2 on the t
of excretion and metabolism, an alteration of any of eff.
Consequently, a simple proportional increase in dose
these elimination processes will affect the t1/2 of
will leave the patient’s blood concentration below the
effective antibiotic level most of the time during drug
6 therapy. The effect of a prolonged teff is shown in
lines a and c in Fig. 21-10, and the disproportionate
4 increase in teff as the dose is increased tenfold is shown
in lines a and b.
2
SUBSTANCE ABUSE POTENTIAL
0
0 4 8 12 16 The rate of drug absorption has been associated with
Dose (mg/kg) the potential for substance abuse. Drugs taken by the
FIGURE 219 Plot of teff versus dose. oral route have the lowest abuse potential. For example,
teff (hours)
Relationship Between Pharmacokinetics and Pharmacodynamics 645
TABLE 212 Relationship between Elimination
Half-Life and Duration of Activity 100
Dose t1/2 = 0.75 h t1/2 = 1.5 h
(mg/kg) teff (h) teff (h)
10 b
2.0 3.24 6.48
3.0 3.67 7.35
4.0 3.98 7.97 1
5.0 4.22 8.45
6.0 4.42 8.84 a c
0.1 Ceff
7.0 4.59 9.18
8.0 4.73 9.47
9.0 4.86 9.72 0
0 2 4 6
10 4.97 9.95 Time (hours)
11 5.08 10.2 FIGURE 2110 Plasma level–time curves describing the
12 5.17 10.3 relationship of both dose and elimination half-life on duration
of drug action. Ceff = effective concentration. Curve a = single
13 5.26 10.5 100-mg IV injection of drug; k = 1.0 h–1. Curve b = single 1000-mg
IV injection; k = 1.0 h–1. Curve c = single 100-mg IV injection;
14 5.34 10.7
k = 0.5 h–1. VD is 10 L.
15 5.41 10.8
16 5.48 11.0
DRUG TOLERANCE AND PHYSICAL
17 5.55 11.1
DEPENDENCY
18 5.61 11.2
The study of drug tolerance and physical dependency
19 5.67 11.3
is of particular interest in understanding the actions of
20 5.72 11.4 abused drug substances, such as opiates and cocaine.
Drug tolerance is a quantitative change in the sensi-
tivity of the drug at the receptor site and is demon-
coca leaves containing cocaine alkaloid have been strated by a decrease in pharmacodynamic effect after
chewed by South American Indians for centuries repeated exposure to the same drug. The degree of
(Johanson and Fischman, 1989). Cocaine abuse has tolerance may vary greatly (Cox, 1990). Drug toler-
become a problem as a result of the availability of ance has been well described for organic nitrates,
cocaine alkaloid (“crack” cocaine) and because of the opioids, and other drugs. For example, the nitrates
use of other routes of drug administration (intravenous, relax vascular smooth muscle and have been used for
intranasal, or smoking) that allow a very rapid rate of both acute angina (eg, nitroglycerin sublingual spray or
drug absorption and onset of action (Cone, 1995). transmucosal tablet) or angina prophylaxis (eg, nitro-
Studies on diazepam (de Wit et al, 1993) and nicotine glycerin transdermal, oral controlled-release isosor-
(Henningfield and Keenan, 1993) have shown that the bide dinitrate). Well-controlled clinical studies have
rate of drug delivery correlates with the abuse liability shown that tolerance to the vascular and antianginal
of such drugs. Thus, the rate of drug absorption influ- effects of nitrates may develop. For nitrate therapy, the
ences the abuse potential of these drugs, and the route use of a low nitrate or nitrate-free periods has been
of drug administration that provides faster absorption advocated as part of the therapeutic approach. The
and more rapid onset leads to greater abuse. magnitude of drug tolerance is a function of both the
Log plasma concentration (mg/mL)
646 Chapter 21
dosage and the frequency of drug administration. HYPERSENSITIVITY AND ADVERSE
Cross-tolerance can occur for similar drugs that act on
RESPONSE
the same receptors. Tolerance does not develop uni-
formly to all the pharmacologic or toxic actions of Many drug responses, such as hypersensitivity and
the drug. For example, patients who show tolerance allergic responses, are not fully explained by pharma-
to the depressant activity of high doses of opiates codynamics and pharmacokinetics. Allergic responses
will still exhibit “pinpoint” pupils and constipation. generally are not dose related, although some penicillin-
The mechanism of drug tolerance may be due to sensitive patients may respond to threshold skin
(1) disposition or pharmacokinetic tolerance or concentrations, but otherwise no dose–response
(2) pharmacodynamic tolerance. Pharmacokinetic relationship has been established. Skin eruption is a
tolerance is often due to enzyme induction (discussed common symptom of drug allergy. Allergic reactions
in earlier chapters), in which the hepatic drug clear- can occur at extremely low drug concentrations.
ance increases with repeated drug exposure. Some urticaria episodes in patients have been traced
Pharmacodynamic tolerance is due to a cellular or to penicillin contamination in food or to penicillin
receptor alteration in which the drug response is less contamination during dispensing or manufacturing of
than what is predicted in the patient given subsequent other drugs. A patient’s allergic reactions are impor-
drug doses. Measurement of serum drug concentra- tant data that must be recorded in the patient’s profile
tions may differentiate between pharmacokinetic along with other adverse reactions. Penicillin allergic
tolerance and pharmacodynamic tolerance. reaction in the population is often detected by skin
Acute tolerance, or tachyphylaxis, which is the test with benzylpenicilloyl polylysine (PPL). The
rapid development of tolerance, may occur due to a incidence of penicillin allergic reaction occurs in
change in the sensitivity of the receptor or depletion about 1%–10% of patients. The majority of these
of a cofactor after only a single or a few doses of the reactions are minor cutaneous reactions such as urti-
drug. Drugs that work indirectly by releasing norepi- caria, angioedema, and pruritus. Serious allergic
nephrine may show tachyphylaxis. Drug tolerance reactions such as anaphylaxis are rare, with an inci-
should be differentiated from genetic factors that dence of 0.021%–0.106% for penicillins (Lin, 1992).
account for normal variability in the drug response. For cephalosporins, the incidence of anaphylactic
Physical dependency is demonstrated by the reaction is less than 0.02%. Anaphylactic reaction for
appearance of withdrawal symptoms after cessation of cefaclor was reported to be 0.001% in a postmarket-
the drug. Workers exposed to volatile organic nitrates in ing survey. There are emerging trends showing that
the workplace may initially develop headaches and diz- there may be a difference between the original and
ziness followed by tolerance with continuous exposure. the new generations of cephalosporins (Anne and
However, after leaving the workplace for a few days, Reisman, 1995). Cross-sensitivity to similar chemi-
the workers may demonstrate nitrate withdrawal symp- cal classes of drugs can occur.
toms. Factors that may affect drug dependency may Allergic reactions may be immediate or delayed
include the dose or amount of drug used (intensity of and have been related to IgE mechanisms. In b-lactam
drug effect), the duration of drug use (months, years, (penicillin) drug allergy, immediate reactions occur in
and peak use), and the total dose (amount of drug × about 30–60 minutes, but either a delayed reaction or
duration). The appearance of withdrawal symptoms an accelerated reaction may occur from 1 to 72 hours
may be abruptly precipitated in opiate-dependent sub- after administration. Anaphylactic reaction may occur
jects by the administration of naloxone (Suboxone®), in both groups. Although some early evidence of
an opioid antagonist that has no agonist properties. cross-hypersensitivity between penicillin and cephalo-
sporin was observed, the incidence in patients sensitive
to penicillin shows only a twofold increase in sensi-
Frequency Asked Question tivity to cephalosporin compared with that of the gen-
»»How does the rate of systemic drug absorption affect eral population. The report rationalized that it is safe
the abuse potential of drugs such as cocaine or heroin? to administer cephalosporin to penicillin-sensitive
patients and that the penicillin skin test is not useful in
Relationship Between Pharmacokinetics and Pharmacodynamics 647
identifying patients who are allergic to cephalospo- utilized as a biomarker for drug approval. Bone
rin, because of the low incidence of cross-reactivity mineral density is relatively simpler and easier to
(Anne and Reisman, 1995). In practice, the clinicians measure, and hence shorter trials are required.
should evaluate the risk of drug allergy against the Aminobisphosphonate, risedronate 5 mg once daily
choice of alternative medication. Some earlier reports (Actavis, 1998) was approved based on fracture as
showed that cross-sensitivity between penicillin and the endpoint. Subsequently 35 mg once weekly and
cephalosporin was due to the presence of trace peni- two 75-mg tablets monthly were approved based on
cillin present in cephalosporin products. changes in bone mineral density.
Along similar lines, if we assume that the pro-
gression of disease and treatment intervention is
Biological Markers (Biomarkers) similar among adults and children populations, then
As described previously, the interaction of the drug drug approvals in pediatric population can be based
with the receptor results in a cascade of events ulti- on PK studies (exposure) and/or biomarker data. For
mately leading to a PD response. The PD response example, sotalol (a beta-blocker) that was approved
measured could be a biomarker level that could be for ventricular tachycardia in adults using atrial
linked to a clinical endpoint. This section provides fibrillation and flutter as endpoints was approved in
an overview of biomarkers and surrogate endpoints the pediatric population based on a PK study and its
and its application in drug development. effect on QTc and heart rate (Gobburu, 2009).
Biomarkers are a set of parameters that can be Besides bridging preclinical and clinical phases
measured quantitatively to represent a healthy or a of development, biomarkers can also be used as
pathological process within the body. It could be as (i) a diagnostic tool to detect and diagnose disease
simple as a physical measurement like blood pressure conditions in patients (eg, elevated blood glucose
or a biochemical such as blood glucose to greater levels are indicative of onset of diabetes mellitus),
complex situations that involves genomic markers (ii) a tool for the staging of disease (eg, levels of
such as Taq1B polymorphism in the cholesteryl ester prostate-specific antigen concentration in blood
transfer protein (CETP) gene that code for choles- that is correlated to tumor growth and metastasis),
terol ester transfer protein (Kuivenhoven et al, 1998) (iii) an indicator of disease prognosis (anatomically
or the HER2 (a tyrosine kinase that is a member of measuring size of tumors), and (iv) a predictive and
the epidermal growth factor receptor [EGFR] family) monitoring tool to assess the extent of clinical
expression in metastatic breast cancer (Shak, 1999). response to a therapeutic intervention (eg, measuring
Lesko and Atkinson (2001) have proposed a working blood cholesterol as a means to assess cardiac disease
definition of a biological marker, referring to it as a or viral load used to assess the efficacy of an antiviral
physical sign or laboratory measurement that occurs therapy) (Biomarkers Definitions Working, 2001).
in association with a pathological process and that A surrogate endpoint is a biomarker that is
has putative diagnostic and/or prognostic utility. intended to substitute a clinically meaningful end-
Biomarkers when utilized in a logical and ratio- point. Thus, a surrogate endpoint is expected to pre-
nal way could help accelerate clinical drug develop- dict the presence or absence of clinical benefit or
ment by fostering informed decision making and can harm based on epidemiologic, therapeutic, patho-
bridge preclinical mechanistic studies and empirical physiologic, or other forms of scientific evidence
clinical trials. Some examples where use of biomark- (Lesko and Atkinson, 2001). In a way, a surrogate
ers leads to accelerated drug development are endpoint is a subset of biomarkers; however, it
described below. The number of fractures is consid- should be realized that not all biomarkers could
ered as a primary response variable for approving achieve the status of a surrogate endpoint. Whereas,
drugs to treat osteoporosis, and such trials are typi- a clinical endpoint relates a clinically meaningful
cally lengthy and hence very costly. To approve a measure of how a patient feels, functions, or survives
different dosing regimen for drugs already approved (Strimbu and Tavel, 2010). Blood pressure is proba-
based on the number of fractures as the primary end- bly one of the well-studied surrogates that correlates
point, changes in the bone mineral density can be well to the cardiovascular health of the individual.
648 Chapter 21
Elevated blood pressure (also called hypertension) is infarction who frequently experienced premature
known to be a direct cause of stroke, heart failure, ventricular contractions where sudden death was
renal failure, and accelerated coronary artery dis- considered as a primary outcome. These drugs were
ease, and lowering blood pressure can lead to reduc- successful in suppressing arrhythmias but, on the
tion in the rates of morbidity and mortality outcomes contrary, were responsible to increase the risk of
(Temple, 1999). Another example where a surrogate death from other causes (Echt et al, 1991). In this
endpoint that has created immense interest is the case the surrogate endpoint “arrhythmia” was unable
CD4+ count in the treatment of AIDS and HIV infec- to capture the effect of the treatment on the true out-
tions (Weiss and Mazade, 1990). The surrogate end- come “death” of the treatment.
points not only reduce the overall cost of the trial but In the drug development process, the rationale
also allow shorter follow-up periods than would be to introduce a biomarker or surrogate endpoint
possible during clinical endpoint studies. should begin as early as possible, typically as a
Among the successes of surrogate endpoints in receptor or enzyme-based high-throughput screen-
predicting clinical outcomes, certain failures of per- ing rationale during the preclinical phases. As newer
ceived surrogate endpoints not predicting meaningful technologies develop through genomics and pro-
clinical outcomes have created controversies doubt- teomics, these existing biomarkers would evolve
ing whether surrogate markers should be a principal further as correct clinical targets get identified. The
driver for making decisions for drug approvals ability of a surrogate endpoint to predict clinical
(Colburn, 2000). To this context, one of many exam- outcome is equally good as the intermediate bridge
ples where surrogate endpoints that have been proven that is developed to link the surrogate to the clinical
to mislead clinical outcomes posing greater threat to endpoint. As long as the mechanism of drug action
health and safety of thousands of patients happened to efficacy and toxicity is thoroughly studied, the
to be in the Cardiac Arrhythmia Suppression Trial surrogate endpoints would be predictive of clinical
(CAST). In this trial, three antiarrhythmic drugs outcomes. Examples of biomarkers described in
flecainide, ecainide, and moricizine were compared Table 21-3 that substitute for specific clinical end-
to a placebo treatment in patients with myocardial points may differ from one another in their predictive
TABLE 213 Examples of Biomarkers/Surrogate Endpoints and Their Respective Clinical Endpoints
Therapeutic Class Biomarker/Surrogate Clinical Endpoint
Physiological markers
Antihypertensive drugs Reduced blood pressure Reduced stroke
Drugs for glaucoma Reduced intraocular pressure Preservation of vision
Drugs for osteoporosis Increased bone density Reduced fracture rate
Antiarrhythmic drugs Reduced arrhythmias Increased survival
Laboratory markers
Antibiotics Negative culture Clinical cure
Antiretroviral drugs Increased CD4 counts and reduced viral RNA Increased survival
Antidiabetic drugs Reduced blood glucose Reduced morbidity
Lipid-lowering drugs Reduced cholesterol Reduced coronary artery disease
Drugs for prostate cancer Reduced prostate specific antigen Tumor response
Adapted from Atkinson (2001).
Relationship Between Pharmacokinetics and Pharmacodynamics 649
ability; nonetheless, their clinical utility cannot be Components of PK-PD Models
underestimated. The use of mathematical modeling to link the PK of
the drug to the time course of drug effects (PD) has
evolved greatly since the pioneering work of Gerhard
Frequently Asked Questions
Levy in the mid-1960s (Levy, 1964, 1966). Today,
»»What is a drug receptor?
PK-PD modeling is a scientific discipline in its own,
»»Explain why a drug that binds to a receptor may be which characterizes the PK of a drug, relates PK to the
an agonist, a partial agonist, or an antagonist. PD, and is then applied for predictions of the response
»»If we need to develop a drug where only 25% of under new conditions (eg, new dose or dosing regi-
maximal activation is needed to achieve therapeutic men). For any PK-PD model, the conceptual frame-
benefit, what type of agent among the four classes work of the relationship is depicted in Fig. 21-11
will you pick and why? (Jusko et al, 1995; Mager et al, 2003). The scheme
describes that there may be at least four intermediary
»»What are the other utilities of biomarkers besides
being used as a bridging tool to link preclinical and components between drug in plasma (Cp) and the mea-
clinical drug development? sured response (R).
The first component of the PK-PD framework is
the administration of the drug and the time course of
Types of Pharmacodynamic Response drug in the relevant biological fluid (plasma, Cp).
PD responses can be continuous, discrete (categorical), The drug gets eliminated from the body depending
and time-to-event outcomes. Continuous PD responses on its disposition kinetics. The concentration–time
can take any value in a range such as blood glucose profile of the drug in plasma is typically represented
levels, blood pressure readings, or enzyme levels. by a PK model or function given as
Categorical or discrete responses are either binary,
Cp = f (θPK , X , t) (21.9)
for example, death or no death, or ordinal, for example,
graded pain scores or counts over a time period, such The PK model or function can be thought as a one-
as the number of seizures in a month. Time-to-event compartment model after an intravenous bolus
outcomes constitute continuous measures of time but administration described as
with censoring, for example, time to relapse or time
until transplant. In this chapter, we will deal with Dose CL
t
p = ⋅ − ⋅
C e V (21.10)
continuous PD responses only. V
kin
C Response
p k C
eo e Biosignal
R
Transduction
CL
Biosensor kout
process
Disposition Biophase Biosignal
kinetics Response
distribution ux
Pharmacokinetics Pharmacodynamics
FIGURE 2111 Basic components of PD models of drug action. (Adapted from Jusko et al, 1995).
650 Chapter 21
Here, qPK denotes the fundamental PK parameters drug concentration between plasma and the bio-
namely, clearance (Cl), and volume of distribution (VD). phase, and kin and kout, which are formation and
X refers to the subject variables such as dose, dosing degradation rate constants of the biosignal, and the
regimen, and t is the time. The drug concentration in role of these three rate constants may influence the
plasma then distributes to the site of action or the type of the PK-PD relationship. When the biophase
effect site referred to as biophase concentrations, Ce. distribution represents a rate-limiting step (ie, ke0 is
The plasma concentrations, Cp, are assumed to be slow compared to kin or kout) for drugs in producing
proportional to the biophase concentrations, Ce, and their response, a distributional delay or a link com-
the distribution of the drug to the effect site is gov- partment model is used to explain the PK-PD rela-
erned by a distributional rate constant namely, ke0. tionship. The drug elicits a direct response, but there
The effect site or the biophase concentrations then is a delay in the response due to distributional delay
serve as the driving function responsible for pharma- in the drug to reach the biophase. On the other hand,
codynamic response, R, by influencing the produc- if the distribution of the drug to effect site is very fast,
tion or degradation of the biosignal. The formation then the process involving the formation or degrada-
rate constant for the biosignal is denoted as kin and tion of the biosignal may take over. Such instances
the degradation rate constant is denoted as k occur when the drug acts via an indirect mechanism
out.
Analogous to PK Equation 21.9 above, the time and the biosensor process (depicted in Fig. 21-11)
course of response is described by a mathematical may stimulate or inhibit the production or degrada-
function as tion of the biosignal. In such a case, an indirect
response model is used to describe the PK-PD rela-
R = f (θPD , Cp or Ce , Z) (21.11) tionship. The biosensor process involves interaction
between the drug and the pharmacological target and
The mathematical function can be thought of as an can be explained by the receptor theory.
equation linking the pharmacodynamic response to In summary, the conceptual PK-PD framework
the drug concentrations. Here, q can be considered broadly applicable to various
PD represents the
fundamental pharmacodynamic parameters, namely drugs with different mechanism of action and the
maximum effect, Emax and potency of the drug, final PK-PD model chosen to describe should
EC50, which are described in detail in later sections; encompass principles of pharmacology of the drug
Cp and Ce are the concentrations of the drug in and the system. The various PD models described
plasma or at the biophase, and Z represents a vector here in this section are dealt with in detail with
of drug-independent system parameters. As seen examples in the following sections.
from Fig. 21-11, the effect site concentrations affect
formation or degradation of the biosignal via a bio-
sensor process, and further undergo a transduction Pharmacodynamic Models
process to elicit the response. Thus, biosignal can be PD models involve complex mechanisms that may
considered as a biomarker and is related to clinical not be easily simplified. Researchers have employed
endpoint or the response. Depending on the nature empirical, semi-mechanistic, or mechanistic models
of the experiment, either only data on the biosignal to explain the complex mechanisms of drug action.
is measured or both biosignals and the clinical out- The predictive ability of empiric models might be
come information may be available. In a typical limited under new scenarios such as new dose or
situation, it might not be possible to capture all dosing regimen. The understanding of drug response
components of PK-PD framework; rather the mani- is greatly enhanced when PK modeling techniques
festation of the response will depend on which of are combined with clinical pharmacology, resulting
the processes dominate the overall response. For in the development of mechanism-based PK-PD
example, there are three rate constants involved, models. In this section, we will explore in details
namely ke0, which controls the distribution of the different types of PD models with examples.
Relationship Between Pharmacokinetics and Pharmacodynamics 651
Noncompartmental PK-PD Models PK-PD index referred to as T > MIC. It may be
Under this approach, PK parameters like peak worth realizing that better predictions of clinical
plasma drug concentrations (Cmax), area under the efficacy using PK-PD indices can be sought if pro-
curve (AUC), and half-life (t1/2) are often correlated tein binding is adequately factored into these consid-
to PD parameters like half maximal inhibitory con- erations as the therapeutic effect of a drug is often
centration (IC50). Such PK-PD relationship has been produced by the free fraction of the drug rather than
applied successfully among antimicrobials where the the total drug concentrations in plasma. Thus the
minimum inhibitory concentration (MIC) is often the most relevant concentrations are the free drug con-
PD parameter. The PK parameters Cmax, AUC, and centrations at the site of action, and it has been
t1/2 are considered because they are often influenced shown that antibiotics that distribute to the intersti-
by the choice of drug or by the manner the anti- tial fluid may in fact have much lower tissue concen-
biotics are administered (route and dosing regimen). trations compared to plasma (Lorentzen et al, 1996).
Large doses of antibiotics when administered via Figure 21-12 shows the three MIC-based PK-PD
intravenous route can produce high C indices for a hypothetical antimicrobial drug.
max, whereas a
large AUC can be achieved by administering a large Now let’s understand what these indices really are
dose that has a relatively longer plasma half-life or by and how they relate to the two distinct patterns associ-
multiple dosing. A longer half-life drug will persist in ated with killing of antimicrobials (Craig, 2002), viz:
the plasma for an extended time compared to a drug (a) concentration-dependent and (b) time-dependent
with shorter half-life. Thus, the manner by which killing patterns.
these PK parameters relate to the MIC of the infect- Concentration-dependent killing pattern is asso-
ing pathogen becomes a key factor to the observed ciated with a higher rate and extent of killing with
effect. Hence, the MIC is then designated to play an increasing concentrations of the drug above the MIC
important role as a PD parameter. Usually, the PK of the pathogen. Hence, drugs that follow this pat-
parameters Cmax and AUC are divided by the MIC tern can maximize killing by maximizing their sys-
yielding PK-PD indices, namely Cmax/MIC, AUC/ temic drug exposure that is often represented by
MIC (or AUIC), whereas the time over which drug peak plasma drug concentration (Cmax) and the extent
concentrations remain above its MIC is another of exposure (AUC). The Cmax/MIC ratio relates to the
30
Cmax/MIC
25
20
AUC24/MIC
15
10
MIC
5
0
0 5 10 15 20 25
Time (hours)
t > MIC
FIGURE 2112 MIC-based PK-PD indices for the evaluation of a hypothetical anti-infective agent. MIC: minimum inhibitory
concentrations; PD: pharmacodynamics; PK: pharmacokinetics. (Adapted from Schuck and Derendorf, 2005.)
Concentration (mg/L)
652 Chapter 21
10 10 10
8 8 8
6 6 6
4 4 4
2 2 2
0 0 0
10 100 1000 1 10 100 1000 0 25 50 75 100
24-Hour AUC/MIC Peak/MIC Time above MIC
FIGURE 2113 Relationship between three PD parameters (24-hour AUC/MIC ratio, Cmax/MIC ratio, and percentage of time
that serum levels exceed above MIC) and the number of S. pneumoniae ATCC 10813 in the thighs of neutropenic mice after 24 hours
of therapy with temafloxacin. Each point represents one data for one mouse. The dotted line reflects the number of bacteria at the
time of therapy initiation.
efficacy of drugs that exhibit a concentration- survival rates. However, the PK-PD index that would
dependent killing pattern. Figure 21-13 shows a plot most likely correlate to the killing would be the %T
of colony-forming units (CFUs) against three PK-PD > MIC; which is the percentage of time within the
indices: AUC/MIC ratio, Cmax/MIC ratio, and time dosing interval during which the systemic drug con-
above MIC in a mouse infection model where an centrations remain above the MIC of the drug for the
infection in the thigh due to Streptococcus pneu- pathogen. In contrast to aminoglycosides and fluoro-
moniae was treated with temafloxacin (Craig, 2002). quinolones, all b-lactam antibiotics and macrolides
It was interesting to note that there was no correla- (Vogelman et al, 1988; Craig, 1995) follow a time-
tion between CFU/thigh and the percentage of time dependent bactericidal activity. To illustrate this kill-
the drug levels exceeded the MIC in the serum. ing pattern, Craig (1995) studied the activity of
However, an excellent relationship was evident cefotaxime against the standard strain of Klebseilla
between CFU/thigh and the AUC/MIC ratio followed pneumoniae in the lungs of a neutropenic mice
by Cmax/MIC. The AUC/MIC and Cmax/MIC ratios model. In this study, pairs of mice were treated with
have been the PK-PD indices that often well corre- multiple dose regimens that varied by the dose and
late with the therapeutic efficacy of aminoglycoside the dosing interval (ie, a 500-mg single oral dose,
and fluoroquinolone antimicrobials. Most often and 250 mg bid, 125 mg qid, and so on). Lungs were
so in the above example, the AUC/MIC ratio shows assessed for remaining CFUs after 24 hours of ther-
a better correlation to efficacy compared to the Cmax/ apy and the PK-PD indices Cmax/MIC, AUC/MIC,
MIC ratio. However, the latter index may be more and %T > MIC were determined for each dosing
relevant and thus important where there is a signifi- regimen. Figure 21-14A and 21-14B showed poor
cant risk of emergence of a resistant microbial relationship between the CFU per lung and the Cmax/
subpopulation. MIC, AUC/MIC ratios. A highly significant correla-
Time-dependent killing produces higher sys- tion between the CFU remaining per lung and the
temic concentrations beyond a threshold value or duration of time that serum levels were above the
MIC and does not cause a proportional increase in MIC (%T > MIC) was evident. Thus depending upon
the killing rate of the microbes. In fact the killing the type of antimicrobial, there would be one PK-PD
proceeds at a zero-order rate when systemic drug index that would be highly correlated to its anti-
concentrations are above the MIC for its pathogen, microbial efficacy. It may be worth considering
and under such conditions, a minimal correlation that percent time above MIC could be enhanced by
is expected between Cmax/MIC and the pathogen dose fractionation such that the total daily dose
Log CFU/thigh at 24 hours
10
Relationship Between Pharmacokinetics and Pharmacodynamics 653
A B C
10
2
9 R = 94%
8
7
6
5
0.1 1 10 100 1000 10000 10 30 100 300 1000 3000 0 20 40 60 80 100
Peak/MIC ratio 24-Hour AUC/MIC ratio Time above MIC (percent)
CFU = Colony-forming unit
FIGURE 2114 (A–C). Relationship between three PD parameters (Cmax/MIC ratio, 24-hour AUC/MIC ratio, and percentage of
time that serum levels exceed above MIC) and the number of K. pneumoniae ATCC 43816 in the lungs of neutropenic mice after 24
hours of therapy with cefotaxime. Each point represents one mouse. Animals were infected by a 45-minute aerosol given 14 hours
prior to therapy. The dotted line reflects the number of bacteria at the time of therapy initiation (7.5 log10 colony forming units
[CFU]/lung). The R2 value in (C) represents the percentage of variation in bacterial numbers that could be attributed to differences in
time above MIC. (Adapted from Craig, 1995.)
remains constant. Table 21-4 illustrates some of the be derived using the receptor occupancy theory.
specific PK-PD indices that correlate with efficacy The theory and derivation are described in detail
in the animal infection models for different class of as follows.
antimicrobials. In general, as the drug is administered, one or
more drug molecules may interact with a receptor to
Emax Drug-Concentration Effect Model form a complex that in turn elicits a pharmacody-
namic response.
Receptor occupancy theory forms the basis of phar-
macodynamic response evaluation and is routinely R +C ↔ RC (21.12)
employed to describe concentration–effect/exposure-
response relationship in drug discovery and develop- The rate of change of the drug–receptor (RC) com-
ment. The origins of the fundamental PD models can plex is given by the following equation:
d[RC]
= kon ⋅ (RT − RC) ⋅C − koff ⋅RC (21.13)
dt
TABLE 214 PK-PD Indices Determining the
Efficacy for Different Antimicrobials where RT is the maximum receptor density, C is the
PK-PD Index Antimicrobial concentration of the drug at the site of action, kon is
the second-order association rate constant, and koff is
% Time above Penicillins, cephalosporins, aztreonam,
the first-order dissociation rate constant. The term
MIC carbapenems, tribactams, macrolides,
clindamycin, oxazolidinones, flucytosine (RT − RC) represents the free receptors, R, available
as the total number of receptors, or the maximum
Peak/MIC Aminoglycosides, fluoroquinolones,
receptor density can be written as RT = R + RC. Under
ratio daptomycin, vancomycin, amphotericin B
d[RC]
AUC/MIC Aminoglycosides, fluoroquinolones, equilibrium conditions, that is, when = 0, the
dt
ratio daptomycin, vancomycin, ketolides, above equation becomes:
quinupristin/dalfopristin, tetracyclines,
fluconazole kon ⋅ (RT − RC) ⋅C = koff ⋅RC (21.14)
Log10 CFU per lung at 24 hours
654 Chapter 21
Upon further rearrangement we get Here, KD has the units of concentration and represents
k the concentration at which 50% of Emax is achieved.
on ⋅RT ⋅C = RC ⋅ (kon ⋅C + koff ) (21.15)
On substituting KD = EC50 yields the classical Emax
k ⋅R ⋅C
RC on T concentration–effect relationship as below:
= (21.16)
k + k ⋅C
off on
Emax ⋅C
R ⋅C E = (21.22)
RC T
= (21.17) EC50 +C
k
off +C
k E
on max refers to the maximum possible effect that can
be produced by a drug and EC50 is the sensitivity
RT ⋅C
RC = (21.18) parameter or the potency parameter representing the
KD +C
drug concentration producing 50% of Emax. As the
where KD is the equilibrium dissociation constant fundamental PK parameters of a drug are clearance
k (Cl) and volume of distribution (VD), Emax and EC
( off ). Under the assumption that the magnitude of 50
kon are the fundamental PD parameters for a drug, and
effect, E, is proportional to the [RC] complex, the hence they define the pharmacodynamic properties
fraction of maximum possible effect, Emax, is equal of the drug. From Equation 21.22, it can be inferred
E that the typical effect–concentration relationship is
to the fractional occupancy, fb =
E , of the recep-
max curvilinear as shown in Fig. 21-15 with parameters
tor, which can be described as as Emax = 100 and EC50 = 50 µg/mL .
E [RC] The Hill equation or the sigmoidal Emax model
fb = =
Ema R (21.19) contains an additional parameter, typically repre-
x T
sented as g and called as the Hill coefficient. The sig-
Hence, moidal Emax model is shown in Equation 21.23 below:
RT ⋅C
E ⋅C γ
KD +C E = max
γ (21.23)
E = Emax ⋅ (21.20)
R EC50 +C γ
T
E ⋅C
E m
= ax (21.21) The Hill coefficient, g (or the slope term), describes
kD +C the steepness of the effect–concentration relationship.
100
Emax = 100
75
50
25
EC50 = 50 mg/mL
0
0 100 200 300 400 500
Plasma concentration (mg/mL)
FIGURE 2115 The Emax concentration–effect relationship. Fifty percent of the maximum effect is achieved at the EC50
concentration.
Effect
Relationship Between Pharmacokinetics and Pharmacodynamics 655
Gamma 0.5 1 2 3 4 5
200
150
100
50
0
0 100 200 300 400 500
Plasma concentration (mg/mL)
FIGURE 2116 Effect of varying Hill coefficients on the Emax concentration–effect relationship.
Some researchers also describe g as the number of Emax model under the conditions that drug concentra-
drug molecules binding to a receptor. When more tion (C) << EC50, reducing Equation 21.22 to the
drug molecules bind (typically g > 5), the effect– following:
concentration relationship is very steep. Figure 21-16
shows the sigmoidal Emax model for different Hill E = S ⋅C (21.24)
coefficient values. As seen from Fig. 21-16, values of
where mathematically S is defined as the slope of
g less than or equal to unity have broader slopes, and
linear concentration–effect relationship line (Holford
as g increases, the steepness of the relationship
and Sheiner, 1981). Pharmacodynamically, S is the
increases with values of g > 4 signifying an all-or-
effect produced by 1 unit of drug concentration. This
none response. The utility of the Hill coefficient in
relationship can be observed visually in Fig. 21-15,
model building is usually considered as an empirical
when the concentration is <<EC50, the concentration–
device to provide improved model fit for the data.
effect (C-E) follows approximately linear relation-
However, the value of Hill coefficient potentially is
ship. This model assumes that effect will continue to
from its real application in terms of treatment adher-
increase as the drug concentration is increased,
ence. For example, if a drug has a steep concentration–
although as we know there is always a maximal phar-
effect relationship, then missing a dose can have
macological effect (Emax) beyond which increasing
greater impact on the response for a subject as com-
drug concentrations does not yield further increase in
pared to a drug for which the Hill coefficient is
the effect. Also, the concentration–effect relationship
around unity. Examples of drugs where an Emax is seldom linear over a broad range of drug concentra-
model was used to describe the PK-PD relationships
tions. Thus, this simple model has limited application
will be discussed in detail in a later section on direct
in PD modeling. Nonetheless, a specific PD effect
effect models.
where linear C-E model is utilized extensively is in
evaluation of drug effects on cardiac repolarization
Linear Concentration-Effect Model (as measured by QT interval from an electrocardio-
Linear concentration-effect model is based on the gram [ECG]) in humans (Garnett et al, 2008; Russell
assumption that the effect (E) is proportional to the et al, 2008; Florian et al, 2011). Linear C-E model
drug concentration, typically the plasma drug con- has been applied to describe the concentration–QTc
centration (C). This model can be derived from the relationship for moxifloxacin (Florian et al, 2011)
Effect
656 Chapter 21
200
150
100
50
Slope: 3.1 ms per mg/mL
0
0 1 2 3 4 5 6
Moxioxacin (mg/mL)
FIGURE 2117 ∆∆QTcF versus concentration predictions with 90% confidence interval (CI). Data points depict quantile means
±90% CI. Decile ranges are displayed along the x axis.
as shown in Fig. 21-17 and also applied for modeling Additive and Proportional Drug
concentration–QTc relationship for new drugs under Effect Models
development. Furthermore, the concentration–QTc The fundamental Emax model (Equation 21.22) or the
relationship and analysis has played a key role in the linear effect model (Equation 21.24) signifies that
US FDA regulatory review of new drugs for pro- when the drug concentration is not present, then there
arrhythmic risk evaluation (Garnett et al, 2008). is no effect. But often, there exists a baseline response,
which implies that even when the drug is not present,
Log-Linear Concentration-Effect Model there exists a baseline response. The effect of baseline
The log-linear model is based on the assumption that can be additive or proportional to the drug effect lead-
effect is proportional to the log of drug concentration ing to additive or proportional drug response model.
and can be described as:
Additive Drug Effect Model
E = S ⋅ log C + E0 (21.25) When a drug exhibits additive drug effect, it implies
that the drug response is independent of the baseline
as represented by the equation below:
where S is the same as that described for the linear
concentration-effect model previously and E0 is the R(t) = R(0) + E (21.26)
baseline effect. This model is also a special case of
Emax model as the log C versus effect follows a nearly where R(t) is the drug response at time t, R(0) is the
linear relationship between 20% and 80% of E response at baseline or time = 0, and E represents the
max
(Meibohm and Derendorf, 1997). The limitation of drug effect, which could be linear as in Equation 21.27,
this model is that it can predict neither the effect or Emax type of relationship as shown in Equation 21.28:
when drug concentrations are zero nor the maximal
effect (Emax). This model has been used to describe Additive linear drug effect model:
concentration–effect relationship for (i) synthesis rate
of prothrombin complex activity in relation to warfarin R(t) = R(0) + S ⋅C (21.27)
plasma concentrations (Nagashima et al, 1969) and Additive Emax drug effect model:
(ii) propranolol concentration and reduction of
exercise-induced tachycardia (Coltart and Hamer, E ⋅C
R(t) R(0) max
= + (21.28)
1970) (Fig. 21-18). EC50 +C
∆∆QTcF (ms)
Relationship Between Pharmacokinetics and Pharmacodynamics 657
100
80
60
40
20
0
2 5 10 20 50 100 200
Log, plasma propranolol (ng/mL)
FIGURE 2118 Log plasma concentration/response relationship for orally administered (°) and intravenously administered (•)
propranolol.
Here, C is the plasma concentration at any time t. effect for the linear and the Emax drug effect model,
The interpretation of Emax is the maximal drug effect where the slope is positive, is shown in Fig. 21-19.
that can be obtained and has the same units as the The slopes for the different baseline responses remain
response. Based on the equations above, it can be the same. Depending on whether it is a stimulatory
inferred that there is a constant baseline response (positive slope: S > 0 or Emax > 0 ) or an inhibitory
added to the drug effect, or in other words, the drug effect (negative slope: S < 0 or Emax < 0), the graphs
effect is independent of the baseline response. The have an increasing or a decreasing trend with increas-
baseline response in mathematical terms can be con- ing concentrations.
sidered similar to an intercept term. The additive drug
Baseline response 60 80 100 Baseline response 60 80 100
300
150
200
100
100
Additive linear effect Additive Emax effect
0 100 200 300 400 500 0 100 200 300 400 500
Plasma concentration (mg/mL) Plasma concentration (mg/mL)
FIGURE 2119 Additive drug effect (linear and Emax) upon varying baseline values. For the linear effect model, S = 0.5 units
was used. For the Emax model, the drug effect parameters are Emax = 100 units and EC50 = 50 mg/mL.
Response
% Block of exercise tachycardia
Response
658 Chapter 21
The argatroban concentration producing 50% of
Exercise: Using Excel, create the graph for a linear maximal aPTT response (EC50) was estimated as
effect model with a slope of –0.3 at three different 959 ng/mL and the maximal aPTT response from
baseline values. Similarly for Emax model with baseline ( Emax) was estimated as 84.4 seconds, and
negative Emax value, inhibitory. the baseline aPTT response is estimated at 32 seconds
as evident from Fig. 21-20. The article also consid-
ered different subject-specific factors, such as hepatic
Application: One of the examples where an additive status, that might explain the variability seen in the
Emax effect model was used is to explain the PK-PD data, which is beyond the scope of this chapter. The
relationship of activated plasma thromboplastin time PK-PD relationship developed was used for simula-
(aPTT) to argatroban concentrations (Madabushi et al, tions based on which pediatric dosing recommen-
2011). Argatroban is a synthetic thrombin inhibitor dations were derived and are currently available in
and is approved in the United States to be used for argatroban label (http://www.accessdata.fda.gov
prophylaxis or as anticoagulant therapy for adult /drugsatfda_docs/label/2014/020883s016lbl.pdf,
subjects with heparin-induced thrombocytopenia accessed, June 17, 2014, section 8.4).
(HIT). Initially, there was no dosing recommendations
for argatroban in pediatric subjects with HIT and often Proportional Drug Effect Model
extrapolated from adult dose. Madabushi et al used As the name suggests, the response at any time depends
PK (argatroban concentrations) and PD (aPTT) data proportionally on the baseline response. If the baseline
from healthy adults and pediatric patients to derive response is higher, depending on whether we have
dosing recommendations of argatroban in pediatric stimulatory or inhibitory drug effect, a greater stimula-
subjects with HIT. They used a direct additive Emax tion or inhibition can be expected. The general form of
model to describe the argatroban concentration–aPTT a proportional drug effect model is given as
relationship as shown below:
R(t) = R(0) ⋅ (1+ E) (21.30)
aPTT (t, seconds) = aPTT (t = 0, seconds) where R(t) is the drug response at time t, R(0) is the
response at baseline or time = 0, and E represents the
E ⋅C 9)
max (seconds)
(21.2
+ drug effect, which could be linear or Emax type of
EC50 +C relationship as shown below:
200 Healthy adults
Pediatric patients
Population mean
150
100
50
0
0.1 1 10 100 1000 10,000
Plasma argatroban (ng/mL)
FIGURE 2120 Predicted argatroban plasma concentration–aPTT relationship. Filled circles: healthy adults; open circles:
pediatric patients (Madabushi et al, 2011).
aPTT (seconds)
Relationship Between Pharmacokinetics and Pharmacodynamics 659
Proportional linear drug effect model (stimulatory) As seen from Fig. 21-21, the response is depen-
dent on the baseline value with a steeper decrease
R(t) = R(0) ⋅ (1+ S ⋅C) (21.31) for the largest baseline as compared to small base-
line. For both linear (proportional increase) and the
Proportional E inhibitory Imax effect, for a baseline of 150 units,
max drug effect model (stimulatory)
the decrease in response is much higher as com-
pared to the baseline value of 60 units, but the
= ⋅
Sm ⋅C
R(t) R(0)
1+ ax
+C
(21.32) fractional decrease from the baseline value is the
SC50
same. For example, let us consider the right graph in
Fig. 21-21, with the baseline value as 150 and 60.
Proportional Emax drug effect model (Inhibitory) When baseline is 150 units, the response decreased
to 95 units upon increase in drug concentrations,
= ⋅
Im ⋅C
R(t) R(0)
1 ax
− +C
(21.33) whereas when baseline is 60 units, the maximum
IC50 inhibitory response in the presence of drug reaches
38 units. Thus, the absolute difference in the response
where C is the plasma concentration of the drug at is 55 units for higher baseline and 22 units for lower
time t. However, the interpretation of Smax or Imax is baseline, whereas the fractional decrease in response
different from that of an additive effect model. They 150 − 95
(I
represent fractional stimulation or inhibition from max) is = 0.37 for the higher baseline and
150
the baseline response or, in other words, represents 60 − 38
= 0.37 for the lower baseline. Hence, the
proportional change (increase or decrease) of the 60
response from baseline and hence a unitless quantity. R0 − R
general expression for min
Imax = , where R
R 0 The drug concentrations at which 50% of Smax or Imax 0
is obtained refer to SC50 and IC50, respectively, and is the response at time t = 0 or at baseline and Rmin is
these have the units of concentration. The propor- the maximum inhibitory response.
tional drug effect for three different baseline values The same argument can be applied when there
of a response is depicted in Fig. 21-21. is a stimulatory effect on the baseline. Typically such
Baseline response 60 100 150 Baseline response 60 100 150
150
Proportional Emax effect
750 Proportional linear effect
120
500
90
250 60
0 100 200 300 400 500 0 100 200 300 400 500
Plasma concentration (mg/mL) Plasma concentration (mg/mL)
FIGURE 2121 Proportional drug effect (linear and Emax) model upon varying baseline values. For the linear effect, a propor-
tional increase of 0.01 (s = 0.01) was used and for the Imax effect model, the value of Imax = 0.40 (40% decrease from baseline).
Response
Response
660 Chapter 21
discussed previously is an example of a direct effect
Dose
where the argatroban plasma concentrations were
S · Cp directly related to aPTT response via an Emax model.
Cp Response/effect
Emax·
γ
Cp
γ Effect Compartment or Link Model
EC + γ
50 Cp
Cl Some drugs may produce a delayed pharmacologic
response that may not directly parallel the time
FIGURE 2122 Schematic diagram for a direct effect course of the plasma drug concentration. The maxi-
model. mum pharmacologic response produced by the drug
may be observed after the plasma drug concentration
has peaked. In such cases, the drug distribution to the
a proportional drug effect model is employed for
site of action or biophase may represent a rate-limiting
drugs wherever baseline response plays an important
step for drugs to elicit the biological response. The
role (eg, blood pressure–lowering drugs).
delay could be caused due to convection transport
The model description so far dealt with the dif-
and diffusion processes that deliver the drug to the
ferent types of the drug concentration–effect rela-
site of action. To describe the delay in effect, Sheiner
tionships (eg, linear, Emax, additive drug effect,
et al (1979) proposed a hypothetical effect com-
proportional drug effect). As described in the section
partment as a mathematical link between the time
(Components of PK-PD models), the site at which
course of plasma concentrations and the pharmaco-
the concentration–effect relationship drives the PD
dynamic effect. The effect compartment models
process leads to further PD models that are used for
account for this delay by representing it as an addi-
describing the different mechanisms by which the
tional compartment between the plasma concentra-
drug acts. For this section, the notation “Cp” is used
tion and the effect defined by a first-order equilibrium
to refer to plasma concentrations of the drug.
rate constant, ke0 as shown in Fig. 21-23. The hypo-
thetical effect site concentration is represented as Ce.
Direct Effect Model The equilibrium rate constant, ke0, accounts for the
When the distribution of the drug to the site of action is delay in the drug concentrations reaching the effect
very rapid and when the drug elicits the response by a site or the biophase, and therefore, the time course
direct mechanism (no biosensor process involved), then of concentration at the effect site mimics the time
a model directly linking the concentration to the drug course of the pharmacodynamic effect. The effect
response can be used. Such a model is referred to as a compartment model is also called as a distributional
direct effect model. The direct effect model could be delay model or a link model, since the effect site
linearly related to concentrations or via an Emax model concentrations now are linked to the pharmacody-
as shown in Fig. 21-22. The time course of plasma namic effect.
concentrations and the time course of effect will be One of the important assumptions in this model
in parallel to each other. The argatroban example is that the amount of drug entering the hypothetical
Dose
Cp k C
eo e Response/effect
Emax · Ce
EC50 + Ce
Cl
FIGURE 2123 Schematic diagram for effect compartment model.
Relationship Between Pharmacokinetics and Pharmacodynamics 661
effect compartment is considered negligible and PD is accounted by the equilibration rate constant
hence need not be reflected in the PK of the drug. ke0. When there is a temporal difference between the
The rate of change of drug concentration at the effect PK and the PD, and when time-matched response
site is then given as and plasma concentrations are plotted, the plot
dC depicts a hysteresis loop, which is anticlockwise in
e = ke0 ⋅ (Cp −Ce ) (21.34) nature as seen in Fig. 21-25. Another feature of the
dt
effect compartment models is, though the peak
The effect site concentration, Ce, profile is governed effects will be delayed relative to plasma concentra-
by the plasma concentration, Cp, and the equilibra- tions, the times at which peak Ce occurs and hence
tion rate constant, ke0. A large value of ke0 would the peak effect occurs are dose independent. Another
imply that the effect site concentrations closely fol- type of time-dependent pharmacologic response
low the plasma concentration profile and the effect may occur due to development of tolerance, induced
compartment is rapidly equilibrating, whereas a metabolite deactivation, reduced response, or trans-
smaller ke0 value would signify that the effect com- location of receptors at the site of action. This type
partment equilibrates slowly with Ce profile and of time-dependent pharmacological response is
hence the effect is delayed as compared to Cp. The characterized by a clockwise profile when the phar-
effect is then linked to the effect site concentrations macological response is plotted versus the plasma
typically via an Emax model as drug concentration over time (Fig. 21-26). Drugs
E like fentanyl (lipid soluble, opioid anesthetic) and
ma ⋅C
E = x e (21.35) alfentanyl (a closely related drug) display a clock-
EC50 +Ce
wise hysteresis loop apparently due to lipid parti-
Figure 21-24 depicts the Cp , Ce, and response profile tioning effect of these drugs. Similarly, euphoria
for a hypothetical drug with two different ke0 values. produced by cocaine also displayed a clockwise
As seen from the figure, the Ce profile mimics the profile when responses were plotted versus plasma
time course of PD and the delay between the PK and cocaine concentration (Fig. 21-27).
Variable C E Ce Variable C E Ce
Ke0 = 0.05/h 5 Ke0 = 0.5/h
5
4
4
3 3
2 2
1 1
0 0
0 5 10 15 20 0 5 10 15 20
Time (hours) Time (hours)
FIGURE 2124 Simulated concentration–response time profiles obtained using effect compartment model to describe the
influence of ke0: distributional delay rate constant. C: plasma concentration; Ce: concentrations at the hypothetical effect site; E: drug
effect. Drug concentrations from a one-compartment model is used to derive the effect using the effect compartment model, with
Emax= 20 units, EC50 = 4 mg/mL.
Plasma concentration, mg/mL or Response (units)
Plasma concentration, mg/mL or Response (units)
662 Chapter 21
25
2.5
2
1.5
1
0.5
0
0 1 2 3 4 5 6
Plasma concentration (mg/mL)
FIGURE 2125 Anticlockwise hysteresis loop to describe the temporal difference between PK and PD.
Application: One of the early examples where an healthy adults. The Digit Symbol Substitution Test
effect compartment model was used to describe the (DSST) was used as the pharmacodynamic response
PK-PD relationship is to compare the PD effects of as it was thought to be a sensitive measure for drug-
midazolam and diazepam using a surrogate measure induced changes in psychomotor performances than
for psychomotor performance (Mould et al, 1995). electroencephalogram (EEG). Plasma concentrations
In the study, the PK and PD of midazolam and of diazepam, midazolam, and DSST were measured
diazepam were compared after two intravenous at different times up to 180 minutes. The authors
infusions of 0.03 and 0.07 mg/kg of midazolam and described the PK-DSST relationship using an effect
0.1 and 0.2 mg/kg of diazepam on four occasions in compartment model with additive baseline effect,
A B
25
20
20
15
15
10
10
5
5 LEGEND:
Predicted
Measured
0 0
0 10 20 30 0 500 1000 1500
Fentanyl concentration (mg/L) Alfentanyl concentration (mg/L)
FIGURE 2126 Response of the EEG spectral edge to changing fentanyl (A) and alfentanyl (B) serum concentrations. Plots are
data from single patients after rapid drug infusion. Time is indicated by arrows. The clockwise hysteresis indicates a significant time
lag between blood and effect site.
Spectral edge (Hz)
Response (units)
Spectral edge (Hz)
Relationship Between Pharmacokinetics and Pharmacodynamics 663
4 induce their effects not by direct interaction with the
receptors, but rather the interaction with receptors
3
might affect the production or degradation of an
Clockwise
2 endogenous compound and the subsequent response
is mediated by those substances. The earliest refer-
1 ence to a PK-PD model using an indirect mechanism
of action for a drug was described for the anticoagu-
0
20 70 120 170 220 lant effect of warfarin by Nagashima et al (1969). A
Cocaine (ng/mL) systematic modeling approach for characterizing
FIGURE 2127 Clockwise hysteresis loop typical of toler- diverse types of indirect response models into four
ance is seen after intranasal administration of cocaine when basic models was described by Sharma et al (Sharma
related to degree of euphoria experienced in volunteers. and Jusko, 1996). The context where the use of an
indirect response model may arise was briefly
explained in the section on conceptual PK-PD frame-
as there was a slight delay in the pharmacodynamic
work. The characteristics of four basic indirect
effect as compared to the plasma concentrations
response models that are most commonly used are
of the drugs. The estimated distributional delay
described in detail.
half-life (t1/2 − ke0) of midazolam was 3.2 minutes
The four basic indirect response models arise
and of diazepam was 1.2 minutes. The use of effect
when the factors controlling the input or production
compartment model was able to collapse the temporal
(k
difference between the PK and DSST as seen from the in) of the response variable is either stimulated or
inhibited, or the loss or degradation (kout) of an endog-
hysteresis plots in a representative subject (Figs. 21-28
enous compound or the response variable is either
and 21-29). Based on this analysis, the authors were
stimulated or inhibited. The rate of change of a
able to confirm the fact that midazolam has a delayed
response variable in the absence of the drug is given as
onset of peak effect and the potency of midazolam
was 6 times higher than that of diazepam. Moreover, dR
= kin − k R 1 3 )
the use of DSST as a surrogate measure instead of dt out ⋅ (2 . 6
EEG was supported by this analysis.
where kin represents the zero-order production rate
constant of the response and kout represents the first-
Indirect Response Models order degradation rate constant of the response vari-
When the pharmacological response is seen immedi- able. It is assumed that kin and kout fully account for
ately in parallel to the plasma drug concentrations, the production and degradation of the response.
pharmacodynamic models such as linear model, Emax In the presence of the drug, inhibition of kin or kout by
model, or sigmoid Emax models are used to model the drug concentration gives rise to the model I and
PK-PD relationship. When there is a delay in the model II and stimulation of kin or kout in the presence
pharmacological response as compared to the drug of drug leads to model III and model IV. Model I is
concentrations, an effect compartment or the link the inhibition of kin and model II is the inhibition of
model is used. The use of an effect compartment kout as shown in Fig. 21-30.
model is justified when the delay in the pharmacody-
namic response can be attributed to the distribution of Inhibition of Production of Response,
the drug to the effect site characterized by a hypo- kin (Model I) and Inhibition of Degradation
thetical effect compartment. The equilibrium between of Response, kout (Model II)
the plasma and the effect site is characterized by the The rate of change of response in model I is
equilibration rate constant as described under the described as
section Effect Compartment or Link Model.
Many drugs, however, exhibit pharmacological dR
= kin ⋅ (1− E) − k
response via an indirect mechanism. The drugs might ou ⋅R (21.37)
dt t
Euphoria (degrees)
664 Chapter 21
Midazolam
40
30
20
10
0
–10
0 100 200 300 400 0 200 400 600 800
A B
Diazepam
40
30
20
10
0
–10
0 300 600 900 1200 1500 0 500 1000 1500 2000 2500
Plasma concentration (ng/mL)
C D
FIGURE 2128 Plasma concentration versus effect (DSST score) in subject 6 after 0.03 mg/kg midazolam (a), 0.07 mg/kg
midazolam (b), 0.1 mg/kg diazepam (c), and 0.2 mg/kg diazepam (d).
and the rate of change of response in model II is to the maximal fractional inhibition of production or
explained by degradation of the response by the drug and always
takes a value between 0 and 1 (0 < I
dR max ≤1), and IC50
= k is the plasma concentration producing 50% of the
in − kout ⋅ (1− E) ⋅R (21.38)
dt
maximal inhibition achieved at the effect site. Since
where the inhibitory action of the drug is given by stationarity is assumed for all models, in the absence
I dR
max ⋅Cp
E = . Here, C of drug at steady state, = 0; hence
IC p represents the plasma con-
50 +C dt
p
centration of the drug as a function of time, Imax refers kin = kout ⋅R0 (21.39)
DSST score (number correct)
Relationship Between Pharmacokinetics and Pharmacodynamics 665
Midazolam
100
80
60
40
20
0
0 20 40 60 0 25 50 75 100 125 150
A B
Diazepam
100
80
60
40
20
0
0 100 200 300 400 500 0 300 600 900 1200
Predicted concentration (ng/mL) at effect compartment
C D
FIGURE 2129 Percent maximal effect versus predicted concentration at the effect site after determination of ke0 and collapse of
hysteresis loop in subject 6 after 0.03 mg/kg midazolam (a), 0.07 mg/kg midazolam (b), 0.1 mg/kg diazepam (c), and 0.2 mg/kg diazepam (d).
kin Response kout
R
Model I Model II
dR Imax · Cp dR Imax · Cp
= kin · 1 – – kout · R = k – k
IC in out · 1 – · R
d t 50 + Cp d t IC50 + Cp
0 < Imax ≤ 1
FIGURE 2130 Schematic diagram for basic indirect response models I and II. In model I, the drug inhibits the production of
response. In model II, the drug inhibits the degradation of the response.
Percent maximal effect
666 Chapter 21
Dose (mg) 10 100 1000 Dose (mg) 10 100 1000
50
45 70 Inhibition of kout–Model II
40 Inhibition of kin–Model I
60
35
30 50
0 20 40 60 0 20 40 60
Time (hours) Time (hours)
FIGURE 2131 Simulated response profiles for model I and model II. Three intravenous doses were used and plasma concentra-
tions follow a one-compartment model. The PD parameters used are kin = 5 mg/h; kout = 0.1/h; Imax = 5; and IC50 = 10 mg/L or mg/mL.
Thus the response variable, R, begins at predeter- model, wherein, when the drug concentrations are
mined baseline value R0, changes with drug concen- much higher, there is complete blockade of degrada-
trations, and returns to the baseline value. This tion of the response variable and there is a buildup of
assumption further reduces the number of functional response to its maximum, and as concentrations
parameters in the models described above. When the decrease, the system returns to its baseline response.
plasma drug concentrations are very high, that is, at The response profiles for model I and model II at three
steady state (Cp >> IC50 ), the value of IC50 is insig- different doses of the drug are shown in Fig. 21-31.
nificant, and when I = 1, then the value of E = 1
max
(Cp cancels out), and hence complete inhibition of Stimulation of Production of Response kin
production of the response variable occurs in model I. (Model III) and Stimulation of Degradation of
Later, when drug concentrations reduce to low Response kout (Model IV)
values (Cp << IC50 ), the value of E = 0, and hence the Model III and model IV represent the stimulation of
production of the response variable will return to kin factors that control the production (kin) and dissipa-
and the PD system returns to its baseline value, R0. The tion (kout) of the drug response, respectively, as
same concept is applicable to inhibition of the kout shown in Fig. 21-32.
kin Response kout
R
Model III Model IV
dR Smax · Cp dR Smax · Cp
= kin · 1 + – kout · R = k – kout · 1 + – · R
d SC in
t 50 + Cp d t SC50 + Cp
Smax > 0
FIGURE 2132 Schematic diagram for basic indirect response models III and IV. In model III, the drug stimulates the produc-
tion of response. In model IV, the drug stimulates the degradation of the response.
Response
Response
Relationship Between Pharmacokinetics and Pharmacodynamics 667
The rate of change of drug response in model III maximal stimulation of the loss of factors control-
is given as ling the drug response. The response profiles for
model III and model IV at three different doses of
dR
= kin ⋅ (1+ E) − kou R
dt t ⋅ (21.40) the drug are shown in Fig. 21-33.
In general, the characteristics of the four basic indi-
whereas in the case of model IV, the differential rect response models can be summarized as follows:
equation corresponds to
1. There is a delay in the maximal PD response
dR (Rmax) as compared to the peak plasma concen-
= kin − kout ⋅ (1+ E) ⋅R (21.41)
dt trations of the drug (Cmax), which is attributed
S to the indirect mechanism by which the drug
max ⋅Cp
Here, the drug effect E is described as E = , acts.
SC50 + Cp
2. The response time profiles show a slow decline
providing a stimulatory effect for the factors control-
or rise in the response variable to a maximum
ling the response. S refers to the maximal frac-
max value (Rmax) dictated by the steady-state con-
tional stimulation of production or degradation of
centrations of the drug followed by a gradual
the response by the drug and always takes a value
k
greater than 0 (S return to baseline conditions
max > 0), and SC50 is the plasma ( in or R0 ) as
k
concentration producing 50% of the maximal stimu- out
drug concentrations decline below IC50 or SC50 lation achieved at the effect site. As described in the
inhibitory models, in the absence of drug, the drug values.
response is at its baseline value as expressed in 3. Typically, the initial rate of decline or rise in
Equation 21.40. As drug concentrations become the response profiles is governed by kout, inde-
much higher (Cp >> SC50 ), there is maximal buildup pendent of dose. The gradual return to baseline
of response (model III) based on the value of S ,
max after Rmax is reached is governed by both kin
and as drug concentrations decrease, the response and the elimination rate constant of the drug
returns to its baseline value. In the case of model IV, CL
(k
the steady-state concentrations of the drug produce el = ) .
V
Dose (mg) 10 100 1000 Dose (mg) 10 100 1000
150 Stimulation of kin–Model III 60 Stimulation of kout–Model IV
55
125
50
100
45
75
40
50 35
0 20 40 60 0 20 40 60
Time (hours) Time (hours)
FIGURE 2133 Simulated response profiles for model III and model IV. Three intravenous doses were used and plasma concen-
trations follow a one-compartment model. The PD parameters used are kin = 5 mg/h; kout = 0.1/h; Smax=5; SC50 = 10 mg/L or mg/mL.
Response
Response
668 Chapter 21
4. The time to peak pharmacodynamic response was measured in terms of histamine-induced flare area
(t ) occurs at later times for larger doses (cm2) and wheal area (cm2) at different time points
Rmax
owing to the increased duration of the plasma till 24 hours after administration of the mizolastine. A
drug concentrations above IC50 or SC50 values. PK-PD model was developed to predict the mizolastine
pharmacodynamics and further use the model for
Complete reviews of the basic properties of these
prediction purposes. The authors used an indirect
models and the application of these models for dif-
response model to describe the flare area response
ferent drugs are described in literature (Jusko and
over time considering inhibition of the production of
Ko, 1994; Sharma and Jusko, 1998). Two applica-
histamine (model I) in the presence of mizolastine
tions of the indirect response models in the context
concentrations as given below.
of drug development are described here.
dFlarearea I C
= k ⋅Application: Indirect response models have been 1 max ⋅
in − k Flare
dt IC +
− out ⋅ area
50 C
used in the context of making decisions on dosing
recommendations or selection of drug candidates early (21.42)
in the drug development process. A physiologic indirect
response model was developed to characterize the time where C refers to the plasma mizolastine concentra-
course of the flare area (cm2) after oral administration tions, Flarearea refers to the area of the histamine-
of single ascending doses of mizolastine, a new induced flare on the skin, Imax is the maximum fractional
H1-receptor antagonist in healthy volunteers (Nieforth inhibition (kin) of production of histamine response
et al, 1996). The in vivo test in which histamine- indicated by area of flare, IC50 is the plasma concentra-
induced skin wheal and flare reactions are inhibited tion of mizolastine producing 50% of the Imax, and kout
by H1-receptor antagonist is considered a predictive is the first-order rate constant for the flare disappear-
test for demonstrating the clinical antiallergic activity ance. The PK-PD model provided adequate fit of the
of investigative H1-receptor antagonists. In this data as seen in Fig. 21-34. As seen from Fig. 21-34,
study, mizolastine was orally administered to healthy there is a dose-dependent inhibition in the flare area
volunteers at 4 different doses (5, 10, 15, and 20 mg) with inhibition sustained at higher doses, which are
including placebo. The pharmacodynamic response indicative of indirect mechanism of action of the drug.
1000
5 mg
900
10 mg
800 15 mg
20 mg
700
600
500
400
300
200
100
0
0 4 8 12 16 24
Time (hours)
FIGURE 2134 Plasma time–concentration profiles of mizolastine at 4 different doses and observed and predicted flare area–
time course profiles after oral administration of 5, 10, 15, and 20 mg of mizolastine. An indirect response model with inhibition of
production of response (model I) was used to predict the flare area responses.
Plasma concentrations (ng/mL)
Relationship Between Pharmacokinetics and Pharmacodynamics 669
22 22
5 mg 10 mg
20 20
18 18
16 16
14 14
12 12
10 10
8 8
6 6
4 4
2 2
0 0
0 4 8 12 18 20 24 0 4 8 12 18 20 24
Time (hours) Time (hours)
22 22
15 mg 20 mg
20 20
18 18
16 16
14 14
12 12
10 10
8 8
6 6
4 4
2 2
0 0
0 4 8 12 18 20 24 0 4 8 12 18 20 24
Time (hours) Time (hours)
FIGURE 2134 (Continued )
The authors reported 92% maximal inhibition (Imax) of the abatacept–IL-6 suppression relationship and to pre-
flare area by the drug with 50% of the maximal inhibi- dict IL-6 suppressions at different doses not studied in
tion (IC50) obtained at 21 ng/mL of mizolastine. clinical studies by clinical trial simulations. An indirect
Another application of an indirect response model response model where there is stimulation of IL-6 deg-
is in deciding the dosing regimen for abatacept, a radation (model IV) was used to describe the abatacept-
recombinant soluble fusion protein, used in the treat- IL-6 relationship as shown below:
ment of rheumatoid arthritis (RA) (Roy et al, 2007).
The pharmacodynamic response to abatacept was mea- dC − S ⋅C
IL 6 max p
= k
dt in − kout ⋅ 1+ C ( 1 4 )
SC +
⋅ IL−6 2 . 3
sured in terms of a biomarker, interleukin-6 (IL-6), as
50 Cp
abatacept causes reduction of IL-6 levels, and increased
IL-6 levels are indicated in RA disease pathology. The where C represents serum IL-6 concentrations.
IL−6
authors utilized data from Phase II and Phase III studies The developed PK-PD model adequately described
of abatacept (at doses, 2 and 10 mg/kg) to characterize the IL-6 data, and further simulations using the
Flare area (cm2) Flare area (cm2)
Flare area (cm2) Flare area (cm2)
670 Chapter 21
25
IL-6 following 2 mg/kg dose
IL-6 following 20 mg/kg dose
20 IL-6 following 10 mg/kg dose
IL-6 following 50 mg/kg dose
15
10
5
0
0 30 60 90 120 150 180 210 240 270 300
Time (days)
FIGURE 2135 Simulated average serum interleukin-6 (IL-6) concentrations versus time by abatacept dose. Simulated median
IL-6 concentrations over time for 2 mg/kg abatacept (solid line), 10 mg/kg abatacept (long dashed line), 20 mg/kg abatacept (inter-
mediate dashed line), and 50 mg/kg abatacept (short dashed line).
model at doses unstudied in the clinical studies Systems Pharmacodynamic Models
revealed that the studied 10 mg/kg doses produced The field of PK-PD modeling has made tremendous
increased suppression than 2 mg/kg dose (Fig. 21-35). progress over the last two decades in progressing
But higher than 10 mg/kg did not offer any additional from empirical PK-PD models to mechanism-based
therapeutic benefit, and hence the PK-PD analysis PK-PD models. Although mechanistic PK-PD mod-
and simulations supported the recommended abata- eling incorporates drug–receptor interaction and/or
cept doses studied in the clinical trials. physiology into consideration, these models still
focus on the specific subsystem of physiology that is
impacted by the drug. Systems pharmacodynamic
Frequently Asked Questions
models aim to incorporate all known and understood
»»Explain why the log-linear model cannot be used to biological processes that control body events into the
determine effect when concentration is zero. Describe
model (Jusko, 2013). These models capture multi-
which simple model could be used in such situation.
tude of processes via mathematical equations incor-
»»Explain why doubling the dose of a drug does not porating homeostasis as well as feedback mechanisms
double the pharmacodynamic effect of the drug. that are hallmark of complex biological systems.
»»What is meant by a hysteresis loop? Why do some Thus, systems pharmacology models represent prob-
drugs follow a clockwise hysteresis loop and other ably the most complex models in the area of PK-PD
drugs follow a counterclockwise hysteresis loop? modeling. The greatest advantage of systems models
is that they can be used to assess impact of perturb-
»»What is meant by an effect compartment? How does
ing one process on the overall biological system
the effect compartment differ from pharmacokinetic
compartments, such as the central compartment under consideration. The challenge that still remains
and the tissue compartment? with systems models includes multitude of mathe-
matical equations, functions, and parameter values
»»Why are in vitro or ex vivo biomarkers not useful for each step of biological process. In the interim,
for monitoring the clinical progress of drug treat-
models that are more mature than mechanism-based
ment? What are the main considerations for using
PK-PD model but somewhat less than the complete
biomarkers to monitor drug treatment or disease
progression? systems pharmacology models are being employed
as depicted by Fig. 21-36.
Simulated IL–6 (pg/mL)
Relationship Between Pharmacokinetics and Pharmacodynamics 671
Levels of modeling complexity
Enhanced Systems
Mechanistic
physiologic pharmacologic
PK/PD models
models models
Rigorous analysis of Unravel mechanisms of Assemble known
preclinical and clinical drug action physiology and
data pharmacology
Capture rate limiting steps
Robust tting ? Simulation
FIGURE 2136 Range and types of modeling complexity at three modeling levels of quantitative and systems pharma-
cology (QSP) (Jusko, 2013).
This hybrid approach was utilized by Earp et al’s was rejected after review by the FDA in April 1999
PK-PD model for dexamethasone effects in rat model on the basis that at a given dose, (a) the desired
of collagen-induced arthritis as shown in Fig. 21-37. maximal effect (change in pulmonary capillary
wedge pressure [PCWP]) was not achieved instan-
taneously and (b) the PCWP could not be achieved
PK-PD Models and Their Role in Drug without the undesired effect of hypotension. The
Approval and Labeling FDA recommended the sponsor to optimize nesirit-
The impact of PK-PD modeling in regulatory deci- ide dosing regimen that would result in instanta-
sion making has been increasing over the last many neous effect on PCWP (benet) and minimize the
years. The US FDA has been utilizing PK-PD model- hypotension (risk). As part of the regulatory review,
ing and simulation for drug approval as well as labeling- nesiritide exposure–response data were modeled to
related decisions (Bhattaram et al, 2005, 2007). To develop a PK-PD model. The PK-PD model was
illustrate the role of PK-PD in regulatory decision then applied to evaluate different dosing regimens
making and approval, two examples from approved via simulations. The analysis suggested that a load-
drugs are described below. ing dose followed by a maintenance infusion should
result in faster onset of desired action. Additionally,
Case 1: Nesiritide the simulations suggested that the lower infusion
Case 1 demonstrates how PK-PD modeling and rates might result in smaller effect on undesired side
simulation can be applied to learn from an existing effect of hypotension. The analysis indicated that a
set of clinical trials result and design the future clini- loading bolus dose of 2 mg/kg with a maintenance
cal trials with greater probability of success, which dose of 0.01 mg/min/kg infusion could provide opti-
in this example resulted in the approval of drug by mal risk–benet prole. The sponsor investigated
the FDA (Bhattaram et al, 2005). Nesiritide this PK-PD simulations-based modeling dosing regi-
(Natrecor®), a recombinant human brain natriuretic men in an actual clinical trial for management of
peptide, was being developed for the treatment of acute CHF and submitted the results for supporting
acute decompensated congestive heart failure (CHF). a modied dosing regimen (Publication Committee
The New Drug Application (NDA) for nesiritide for the, 2002). The modeled and actual results are
672 Chapter 21
TCYT
T1IL-Iβ T19IL-Iβ IL-1β mRNA
GR mRNA kt2 kt2 kin_IL-1β
kin_GRm kout_GRm kt2
ksyn_GR k
T27 Rem out_IL-Iβ
IL-Iβ
k6 on_D DRDEX k
DEX T kt2
+ GR DRCST DRN
k6on_C kT
T1 T24
1L-6 1L-6 IL-6 mRNA
kt3 kt3 kin_IL-6
kdgr_ kre_C + kre_D
R kt3
kout_IL-6
kin_CST
Corticosterone T1TNF- T29
α TNF-α TNF-α mRNA
ko k k
ut_CST t1 kt1 in_TNF-α
kt1 kout_TNF-α
Disease endpoints
OBI kOB
kOB
OB
kOB kOC
Paw edema
Bone density OC kin_Paw kout_Paw
kgrowth_bone kgrowth_bone/Rmax k
k growth
OC
FIGURE 2137 Model schematic for corticosteroid and cytokine inter-regulation during arthritis progression. Lines with
arrows indicate conversion to or turnover of the indicated responses. Lines ending in closed circles indicate an effect is being
exerted by the connected factors.
shown in Fig. 21-38. The drug was subsequently 100 0
approved by the FDA for treatment of acute CHF in
May 2001. 25
–1
Case 2: Micafungin 20
–2
This example focuses on how the US FDA as a regu-
latory authority recommended approval for a particu- 15
Systolic BP
lar dosage for micafungin, a semisynthetic lipopeptide –3
formulated as an intravenous infusion for the treatment 10
of esophageal candidiasis (Bhattaram et al, 2007).
The review involved dose optimization by quantify- –4
5 PCWP
ing the exposure-response relationship by performing
a benet-to-risk assessment over a dynamic range of
0 –5
doses. Micafungin is an antifungal agent that belongs 0 1 2 3
to the echinocandin class of compounds. The pro- Time (hours)
posed dosage for treatment of esophageal candidia- FIGURE 2138 Typical time course of nesiritide plasma
sis was 150 mg given every 24 hours for a period of concentrations (—), and the effects on the PCWP (• indicates
2–3 weeks (FUJISAWA, 2005). During the review a observed; – – – – indicates model predicted), and systolic blood
pressure (systolic BP; ∆ indicates observed; . . . . . indicates model
thorough assessment of the dose to the clinical effec-
predicted) after a 2 mg/kg bolus followed by a fixed-dose infu-
tiveness was performed from two available Phase II sion of 0.01 mg/kg/min. Data for the initial 3 hours are being
trials and a registration study where the endoscopic shown here.
Nesiritide concentrations (mg/L)
Placebo corrected hemodynamics (mm Hg)
Relationship Between Pharmacokinetics and Pharmacodynamics 673
100 20
80 16
60 12
40 8
20 4
0 0
0 50 100 150
Dose (mg)
FIGURE 2139 Benefit–risk plot for micafungin. The solid line represents the proportion of patients with endoscopic response
increased with dose. The dotted like represents incidence of elevations in alkaline phosphatase levels (>3 × ULN) with dose.
response rate (proportion of patients that were cleared micafungin were able to achieve a maximal response
of the infection at the end of the therapy) was the as the primary endpoint (Fig. 21-39). Interestingly
primary endpoint. A clinical response endpoint was patients who were treated with higher dose (150 mg)
considered as a secondary parameter for effectiveness. had a 15% lower relapse compared to the lower dose
Biochemical markers like alkaline phosphatase, serum that was associated with a much lower clinical cure
glutamic oxaloacetic transaminase (SGOT), serum rate. Of all biochemical markers the alkaline phospha-
glutamic pyruvic transaminases (SGPT), and total tase was correlated to the entire dynamic range of
bilirubin were assessed for a relationship between dose studied (12.5–150 mg). These elevations in the
enzymatic elevations to the dose of antifungal agent. liver enzymes were transient, which returned to nor-
It was observed that both 100- and 150-mg doses of mal levels upon discontinuation of the treatment.
CHAPTER SUMMARY
Both agonist and antagonist drug effects can be drug disposition processes, as well as plasma and
quantitatively simulated by PK-PD models. The tissue drug binding. In addition, pharmacogenomics
most common models are Emax models mechanisti- of the drug and disease processes must be considered
cally based on drug receptor theory. Although most in the model. Appropriately developed PK-PD mod-
drug responses are complex, pharmacologic response els may be applied to predict onset, intensity, and
versus log dose type of plots have been shown to duration of action of a drug. Toxicokinetics may also
follow sigmoid type of curve (S-curve) with maxi- be applied to explain the side effects or drug–drug
mum response peaking when all receptors become interactions.
saturated. In vitro screening preparations are useful The progress of a disease or its response to a
to study EC50, potency, and mechanism of a drug. therapeutic agent is often accompanied by biologic
However, pharmacologic response in a patient is changes (markers or biomarkers) that are observable
generally far more complicated. Physiologically and/or measurable. Biomarkers (BMs) may be
based PD models must consider how the drug is selected and validated to monitor the course of drug
delivered to the active site and the effect of various response in the body. BMs should be mechanistically
Proportion of patients
with favorable endoscopic response (%)
Number of patients,
alkaline phosphatase 3 × ULN
674 Chapter 21
based and fulfill a number of clinically relevant crite- useful tool in expediting drug development, and
ria in order to be useful as potential clinical end- many reviews and discussions are available about this
points. BM together with PK-PD could be a very application.
LEARNING QUESTIONS
1. On the basis of the graph in Fig. 21-40, answer 3. What is the difference between a partial and an
“true” or “false” to statements (a) through (e) inverse agonist? Name a drug its therapeutic
and state the reason for each answer. class that behaves like a (i) partial agonist and
a. The plasma drug concentration is more (ii) inverse agonist?
related to the pharmacodynamic effect of the 4. What is the difference between biomarkers and
drug compared to the dose of the drug. surrogate endpoints? Elaborate your answer by
b. The pharmacologic response is directly giving an example.
proportional to the log plasma drug 5. Explain why subsequent equal doses of a drug
concentration. do not produce the same pharmacodynamic
c. The volume of distribution is not changed by effect as the first dose of a drug.
uremia. a. Provide an explanation based on pharmaco-
d. The drug is exclusively eliminated by kinetic considerations.
hepatic biotransformation. b. Provide an explanation based on pharmaco-
e. The receptor sensitivity is unchanged in the dynamic considerations.
uremic patient. 6. How are the parameters AUC and teff used in
2. How would you define a response and an pharmacodynamic models?
effect? Identify whether the following is a 7. What class of drug tends to have a lag
pharmacodynamic response or a pharmacody- time between the plasma and the effect
namic effect: compartment?
a. Change from baseline in HbA1c at the end 8. Name an example of a pharmacodynamic
of 26 weeks response that does not follow a drug dose–
b. Blood histamine levels response profile?
c. Number of sleep awakenings at week 4 9. What is AUIC with regard to an antibiotic?
d. Percent reduction in seizures at the end of 10. What is the difference between IC50 and EC50?
8 weeks Are the values reproducible from one lab to
e. Measure of body weight at the end of another? In functional studies, the antagonist
52 weeks IC50 is most useful if the concentration of the
agonist is below maximal. Higher concentra-
tions of the agonist will increase the IC50 of
the competitive antagonist well above its equi-
librium dissociation constant. Even with low
agonist concentrations, the IC50 from func-
tional studies, like an agonist EC50 or maximal
B
response, is dependent on the conditions of
the experiment (tissue, receptor expression,
type of measurement, etc). True or false?
A
11. Ki refers to the equilibrium dissociation
Time constant of a ligand determined in inhibition
FIGURE 2140 Graph of pharmacologic response E as a studies. The Ki for a given ligand is typi-
function of time for the same drug in patients with normal cally determined in a competitive radioligand
(A) and uremic (B) kidney function, respectively. binding study by measuring the inhibition of
Pharmacologic effect (E)
Relationship Between Pharmacokinetics and Pharmacodynamics 675
the binding of a reference radioligand by the 14. What are the three types of pharmacodynamic
inhibiting ligand under equilibrium condi- responses? Give an example for each type of
tions. Why? PD responses that will help to differentiate
12. What is the dissociation constant K in the fol- between them.
lowing interaction between a drug ligand L and 15. Explain the principal difference between
a drug receptor R: concentration-dependent and time-dependent
killing patterns associated with the use of
k
L + R+1↽⇀ LR antibiotics. What PK-PD index would be most
k
−1
appropriate to predict the therapeutic efficacy
|L|
P of antibiotics associated with respect to these
LR =
|L| +K two killing patterns?
16. For an investigative antibiotic under early
where K is expressed as k–1/k+1 and PLR is the discovery, a series of efficacy studies in mice
proportion of receptor occupied by L. thigh infection model were conducted. Fol-
How many binding sites are assumed in the lowing are the results for three PK-PD indi-
above model? ces of AUC/MIC ratio, Cmax/MIC ratio, and
13. Which one of the following would you select (%) time above MIC. Analyze these results
as a biomarker for a type 2 diabetic patient? and determine what PK-PD index is best
State the reasons that support your selection. correlated to the log CFU reduction. Explain
a. Blood sugar level why you picked the particular PK-PD index.
b. Blood insulin level 17. The below graph shows a concentration–effect
c. HbA1C relationship for three hypothetical drugs.
Log (CFU) Log (CFU) (%) Time Log (CFU)
AUC/MIC Ratio Reduction Cmax/MIC Ratio Reduction above MIC Reduction
31 8.9 1.4 7.8 18 7.7
32 8.4 2.6 8.8 25 5.7
40 7.5 2.7 9.1 27 8.8
61 6.7 4.7 8.6 35 3.9
64 5.9 4.9 7.9 35 4.2
88 5.8 5.7 6.8 36 5.3
93 5.3 9.4 6.7 37 6.0
108 5.6 9.7 6.4 39 2.7
122 5.0 10.8 5.0 41 8.6
125 4.2 11.1 3.5 45 2.2
168 3.7 12.6 4.3 50 4.3
172 3.9 20.3 6.0 55 6.8
210 4.2 21.4 7.6 58 8.9
676 Chapter 21
226 3.4 34.3 3.0 71 2.2
250 4.2 37.2 3.3 75 4.1
328 3.6 44.3 5.7 75 3.8
488 3.5 47.8 5.4 81 2.0
488 2.3 50.7 3.0 85 6.5
500 3.1 91.8 4.0 99 8.8
841 2.5 97.6 1.9 99 2.5
862 3.2 99.1 3.9 99 3.8
952 2.6 183.5 2.7 100 3.0
975 2.0 190.5 2.5 100 3.1
975 2.8 383.6 2.2 100 3.2
1025 2.2 398 1.9 100 3.5
(Hint: Plot each PK-PD index against log CFU reduction.)
Assuming all drugs produce a maximum effect from baseline. (Hint: Use the same approach as
of 5 units, determine EC50 for each drug X, Y, for Imax, but in opposite direction.)
and Z. What does EC50 signify? 19. Based on the graphs below, identify what kind
of a PK-PD relationship can be assumed for
5 this hypothetical drug.
150 61
4
3
100 57
2
1 50 53
0
0 100 200 300 400 500
Plasma concentration (mg/mL) 0 49
0 5 10 15 20 25
Time (hour)
18. Assume a drug exhibits a proportional drug
effect which is stimulatory in nature. Derive the 20. Hysteresis: what is the rationale for observing
expression for Smax the fractional stimulation hysteresis in drug therapeutics?
Effect
Concentration (mg/L)
Effect (units)
Relationship Between Pharmacokinetics and Pharmacodynamics 677
ANSWERS
Learning Questions enzymes (autoinduction), thereby decreasing
1. a. True. Drug concentration is more precise the elimination half-life, resulting in lower
because an identical dose may result in steady-state drug concentrations.
different plasma drug concentration in dif- b. Pharmacodynamic considerations: The
ferent subjects due to individual differences patient develops tolerance to the drug,
in pharmacokinetics. resulting in the need for a higher dose to
b. True. The kinetic relationship between drug produce the same effect.
response and drug concentration is such that 7. CNS drugs.
the response is proportional to log concen- 8. An allergic response to a drug may be
tration of the drug. unpredictable and does not generally follow
c. True. The data show that after IV bolus a dose–response relationship.
dose, the response begins at the same point, 9. AUC/MIC or AUIC is a pharmacokinetic
indicating that the initial plasma drug con- parameter incorporating MIC together in
centration is the same. In uremic patients, order to provide better prediction of antibi-
the volume of distribution may be affected otic response (cure percent). An example is
by changes in protein binding and electro- ciprofloxacin. AUIC is a good predictor of
lyte levels, which may range from little or percent cure in infection treated at various dose
no effect to strongly affecting the VD. regimens.
d. False. The drug is likely to be excreted 14. Continuous, categorical, and time-to-event
through the kidney, since the slope (elimina- responses are the three types of responses.
tion) is reduced in uremic patients. Blood pressure measurement is an example
e. True. Assuming that the volume of distribu- of continuous response. Mild, moderate, and
tion is unchanged, the starting pharmaco- severe status of an adverse event like diarrhea
logic response should be the same if the is an example for a discrete response. Time
receptor sensitivity is unchanged. In a few until relapse is an example of a time-to-event
cases, receptor sensitivity to the drug can be outcome. Here time to relapse is a continu-
altered in uremic patients. For example, the ous response, but not all patients would have
effect of digoxin will be more intense if the relapse. Therefore, patients who do not have
serum potassium level is depleted. relapse are censored, hence the distinction
2. a. Effect from continuous response.
b. Response 17. EC50 signifies the concentration of the drug
c. Response at which 50% of Emax (maximum effect is
d. Effect achieved or also referred to as the potency of the
e. Response drug). Smaller the EC50 value, more potent is the
3. A partial agonist is an agent that produces drug. For X (solid line), Emax is approximately
a response similar to an agonist but cannot 5 units, and EC50 approximately 25 mg/mL. This
reach a maximal response as that of an agonist. can be obtained by eyeballing the concentra-
However, an inverse agonist selectively binds to tion corresponding to an effect of 2.5 units.
the inactive form of the receptor and shifts the For Y (short dotted line), EC50 is approxi-
conformational equilibrium toward the inactive mately 100 mg/mL. For Z (long dotted line),
state. An example of a partial agonist is buspi- EC50 is approximately 250 mg/mL.
rone and famotidine being an inverse agonist. 19. The maximal drug concentrations are achieved
5. a. Pharmacokinetic considerations: Subsequent at about 2.5 hours and the corresponding PD
doses induce the hepatic drug-metabolizing response occurs at the same time indicat-
678 Chapter 21
ing that the drug–effect relationship can be a distributional delay of the drug reaching the
explained by a direct effect model. effect site, or it could be based on the mecha-
20. Hysteresis occurs when there is time lag nism of action of the drug. Typically hysteresis
between the concentration and the correspond- plots are observed when the maximum effect
ing effect. It could be manifested when there is occurs later than the maximum concentrations.
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Application
22 of Pharmacokinetics
to Clinical Situations
Vincent H. Tam
Chapter Objectives The success of drug therapy is highly dependent on the choice of
the drug, the drug product, and the design of the dosage regimen.
»» Define Medication Therapy
The choice of the drug is generally made by the physician after
Management (MTM) and explain
careful patient diagnosis and physical assessment. The choice of
how MTM can improve the
the drug product (eg, immediate release vs modified release) and
success of drug therapy.
dosage regimen is based on the patient’s individual characteristics
»» Explain what “critical-dose drugs” and known pharmacokinetics of the drug as discussed in earlier
are and name an example. chapters. Ideally, the dosage regimen is designed to achieve a
»» Define therapeutic drug desired drug concentration at a receptor site to produce an optimal
monitoring and explain which therapeutic response with minimum adverse effects. Individual
drugs should be monitored variation in pharmacokinetics and pharmacodynamics makes the
through a therapeutic drug design of dosage regimens difficult. Therefore, the application of
monitoring service. pharmacokinetics to dosage regimen design must be coordinated
with proper clinical evaluation of the patient. For certain critical-
»» Calculate a drug dosage dose drugs, monitoring both the patient and drug regimen is
regimen in an individual patient important for proper efficacy.
for optimal drug therapy for
a drug that has complete
pharmacokinetic information MEDICATION THERAPY MANAGEMENT
and for a drug that has
incomplete pharmacokinetic Medication Therapy Management (MTM) was officially recog-
information. nized by the US Congress in the Medicare Prescription Drug,
Improvement, and Modernization Act of 2003.1 The objective of
»» Explain the relationship of this act is to improve the quality, effectiveness, and efficiency of
changing the dose and/or the healthcare delivery including prescription drugs. An MTM pro-
dosing interval on the C ∞max, C ∞min, gram is developed in cooperation with pharmacists and physicians
and C ∞av. to optimize therapeutic outcomes through improved medication
»» Define drug–drug interactions use. MTM provides consultative, educational, and monitoring ser-
and the mechanisms of drug– vices to patients to obtain better therapeutic outcomes from medi-
drug interactions, and provide cations by the enhanced understanding of medication therapy,
examples. improved compliance, control of costs, and prevention of adverse
events and drug interactions. MTM programs have been developed
»» Provide instructions to a
for specific practice areas such as elderly care, diabetes, and
patient who has missed a dose
asthma (Barnett et al, 2009).
and discuss the therapeutic
implications.
1www.cms.gov/PrescriptionDrugCovContra/082_MTM.asp.
681
682 Chapter 22
»» Explain how the INDIVIDUALIZATION OF DRUG DOSAGE
pharmacokinetics of a drug may REGIMENS
be altered in special populations,
such as the elderly, infants, Not all drugs require rigid individualization of the dosage regi-
obese patients, and patients men. Many drugs have a large margin of safety (ie, exhibit a
with renal or hepatic disease. wide therapeutic window), and strict individualization of the
dose is unnecessary. For a number of drugs generally recog-
»» Explain how Bayesian theory can
nized as safe and effective (GRAS), the US Food and Drug
help determine the probability
Administration (FDA) has approved an over-the-counter (OTC)
of a diagnostic test to give
classification for drugs that the public may buy without pre-
accurate results.
scription. In addition, many prescription drugs, such as ibupro-
»» Define population fen, loratidine, omeprazole, naproxen, nicotine patches, and
pharmacokinetics and others, that were originally prescription drugs have been
explain how population approved by the FDA for OTC status. These OTC drugs and
pharmacokinetics enables the certain prescription drugs, when taken as directed, are generally
estimate of pharmacokinetic safe and effective for the labeled indications without medical
parameters from relatively supervision. For drugs that are relatively safe and have a broad
sparse data obtained from study safety-dose range, such as the penicillins, cephalosporins, and
subjects. tetracyclines, the antibiotic dosage is not dose titrated precisely
but is based rather on the clinical judgment of the physician to
maintain an effective plasma antibiotic concentration above a
minimum inhibitory concentration. Individualization of the
dosage regimen is very important for drugs with a narrow thera-
peutic window (also known as critical-dose drugs and narrow
therapeutic index [NTI] drugs), such as digoxin, aminoglyco-
sides, antiarrhythmics, anticoagulants, anticonvulsants, and
some antiasthmatics, such as theophylline. Critical-dose drugs
are defined as those drugs where comparatively small differ-
ences in dose or concentration lead to dose- and concentration-
dependent, serious therapeutic failures and/or serious adverse
drug reactions. These adverse reactions may be persistent,
irreversible, slowly reversible, or life threatening, or could
result in inpatient hospitalization or prolongation of existing
hospitalization, persistent or significant disability or incapacity,
or death. Adverse reactions that require significant medical
intervention to prevent one of these outcomes are also consid-
ered to be serious (Guidance for Industry, 2006).
The objective of the dosage regimen design is to produce a
safe plasma drug concentration that does not exceed the mini-
mum toxic concentration or fall below a critical minimum drug
concentration below which the drug is not effective. For this
reason, the dose of these drugs is carefully individualized to
avoid plasma drug concentration fluctuations due to intersub-
ject variation in drug absorption, distribution, or elimination
processes. For drugs such as phenytoin, a critical-dose drug that
follows nonlinear pharmacokinetics at therapeutic plasma drug
concentrations, a small change in the dose may cause a huge
Application of Pharmacokinetics to Clinical Situations 683
increase in the therapeutic response and possible TABLE 221 Therapeutic Range for Commonly
adverse effects. Monitored Drugs
Amikacin 20–30 μg/mL
THERAPEUTIC DRUG MONITORING Carbamazepine 4–12 μg/mL
Many drugs, such as nonsteroidal anti-inflammatory Digoxin 1–2 ng/mL
drugs (NSAIDs) such as ibuprofen, and calcium
Gentamicin 5–10 μg/mL
channel-blocking agents, such as nifedipine, have a
wide therapeutic range and do not need therapeutic Lidocaine 1–5 μg/mL
drug monitoring. In addition, OTC drugs such as Lithium 0.6–1.2 mEq/L
various cough and cold remedies, analgesics, and
Phenytoin 10–20 μg/mL
other products are also generally safe when used as
directed. Therapeutic monitoring of plasma drug Procainamide 4–10 μg/mL
concentrations is valuable only if a relationship Quinidine 1–4 μg/mL
exists between the plasma drug concentration and
Theophylline 10–20 μg/mL
the desired clinical effect or between the plasma
drug concentration and an adverse effect. For those Tobramycin 5–10 μg/mL
drugs in which plasma drug concentration and clini- Valproic acid 50–100 μg/mL
cal effect are not directly related, other pharmacody-
Vancomycin 20–40 μg/mL
namic or “surrogate” parameters may be monitored.
For example, clotting time may be measured directly From Schumacher (1995), with permission.
in patients on warfarin anticoagulant therapy.
Glucose concentrations are often monitored in dia- whereas other patients may show drug efficacy at
betic patients using insulin products. Asthmatic serum drug concentrations below 10 μg/mL.
patients may use the bronchodilator, albuterol taken In administering potent drugs to patients, the
by inhalation via a metered-dose inhaler. For these physician must maintain the plasma drug level within
patients, FEV1 (forced expiratory volume) may be
used as a measure of drug efficacy. In cancer chemo- 50 LEGEND:
therapy, dose adjustment for individual patients may Therapeutic range
depend more on the severity of side effects and the 40 p < 0.001
patient’s ability to tolerate the drug. For some drugs
that have large inter- and intrasubject variability, 30
clinical judgment and experience with the drug are
needed to dose the patient properly. 20
The therapeutic range for a drug is an approxi-
mation of the average plasma drug concentrations 10
that are safe and efficacious in most patients. When
using published therapeutic drug concentration 0
ranges, such as those in Table 22-1, the clinician No toxicity Mild Potentially serious Severe
14.6 ± 4 27.6 ± 4.2 40.5 ± 8.6 46.5 ± 5.6
must realize that the therapeutic range is essentially N = 32 N = 6 N = 6 N = 6
a probability concept and should never be considered FIGURE 221 Correlation between the frequency and
as absolute values (Evans et al, 1992; Schumacher, severity of adverse effects and plasma concentration of the-
1995). For example, the accepted therapeutic range ophylline (mean ± SD) in 50 adult patients. Mild symptoms of
for theophylline is 10–20 μg/mL. Some patients may toxicity included nausea, vomiting, headache, and insomnia.
A potentially serious effect was sinus tachycardia, and severe
exhibit signs of theophylline intoxication such as
toxicity was defined as the occurrence of life-threatening
central nervous system excitation and insomnia at cardiac arrhythmias and seizures. (Adapted from Hendeles and
serum drug concentrations below 20 μg/mL (Fig. 22-1), Weinberger, 1980, with permission.)
Serum concentration (mg/mL)
684 Chapter 22
a narrow range of therapeutic concentrations (see TABLE 222 Factors Producing Variability in
Table 22-1). Various pharmacokinetic methods (or Drug Response
nomograms) may be used to calculate the initial dose
Patent Factors Drug Factors
or dosage regimen. Usually, the initial dosage regi-
men is calculated based on body weight or body Age Bioavailability and
biopharmaceutics
surface after a careful consideration of the known
pharmacokinetics of the drug, the pathophysiologic Weight Pharmacokinetics (including
condition of the patient, and the patient’s drug history absorption, distribution, and
elimination)
including nonprescription drugs and nutraceuticals.
Because of interpatient variability in drug Pathophysiology Drug interactions
absorption, distribution, and elimination as well as Nutritional status Receptor sensitivity
changing pathophysiologic conditions in the patient,
Genetic variability Rapid or slow metabolism
therapeutic drug monitoring (TDM) or clinical phar-
Gender
macokinetic (laboratory) services (CPKS) have been
established in many hospitals to evaluate the response
of the patient to the recommended dosage regimen.
and pharmacodynamics are part of the overall con-
The improvement in the clinical effectiveness of the
siderations in the selection of a drug for inclusion in
drug by TDM may decrease the cost of medical care
the drug formulary. An Institutional Pharmacy and
by preventing untoward adverse drug effects. The
Therapeutic Committee (IPTC) periodically reviews
functions of a TDM service are listed below.
clinical efficacy data on new drug products for inclu-
• Select drug. sion in the formulary and on older products for
• Design dosage regimen. removal from the formulary. Drugs with similar
• Evaluate patient response. therapeutic indications may differ in dose and phar-
• Determine need for measuring serum drug concen- macokinetics. The pharmacist may choose one drug
trations. over another based on therapeutic, adverse effect,
• Assay for drug concentration in biological fluids. pharmacokinetic (dosing convenience), and cost con-
• Perform pharmacokinetic evaluation of drug con- siderations. Other factors include patient-specific
centrations. information such as medical history, pathophysiologic
• Readjust dosage regimen, if necessary. states, concurrent drug therapy, known allergies, drug
• Monitor serum drug concentrations. sensitivities, and drug interactions; all are important
• Recommend special requirements. considerations in drug selection (Table 22-2). As dis-
cussed in Chapter 13, the use of pharmacogenetic data
Drug Selection may become another tool in assisting in drug selection
for the patient.
The choice of drug and drug therapy is usually made
by the physician. However, many practitioners con-
sult with the clinical pharmacist in drug product Dosage Regimen Design
selection and dosage regimen design. Increasingly, The main objective of designing an appropriate dosage
clinical pharmacists in hospitals and nursing care regimen for the patient is to provide a drug dose and
facilities are closely involved in prescribing, moni- dosing interval that achieve a target drug concentration
toring, and substitution of medications as part of a at the receptor site. Once the proper drug is selected for
total MTM program. The choice of drug and the the patient, a number of factors must be considered
drug product is made not only on the basis of thera-
peutic consideration but also based on cost and
2A drug formulary contains a list of prescription drug products
therapeutic equivalency.
that will be reimbursed fully or partially by the prescription
Hospitals and various prescription reimburse- plan provider. Drug products not listed in the formulary may be
ment plans have a drug formulary.2 Pharmacokinetics reimbursed if specially requested by the physician.
Application of Pharmacokinetics to Clinical Situations 685
when designing a therapeutic dosage regimen. Usually, develop competency and experience in clinical phar-
the manufacturer’s dosing recommendations in the macology and therapeutics in addition to the neces-
package insert will provide guidance on the initial sary pharmacokinetic skills. Several mathematical
starting dose and dosing interval in the typical patient approaches to dosage regimen design are given in
population. These recommendations are based upon later sections of this chapter and in Chapter 24.
clinical trials performed during and after drug develop- Dosage regimen guidelines obtained from the
ment. The package insert containing the FDA-approved literature and from approved product labeling are
label suggests an average dose and dosage regimen for often based upon average patient response. However,
the “average” patient who was enrolled in these stud- substantial individual variation to drug response can
ies. Genetic variation, drug interactions, or physiologic occur. The design of the dosage regimen must be
conditions such as disease or pregnancy may change based upon clinical assessment of the patient. Labeling
the pharmacokinetics and/or pharmacodynamics of a for recently approved drugs provides information for
drug, therefore requiring dosing regimen individualiza- dosing in patients with renal and/or hepatic disease.
tion. First, the known pharmacokinetics of the drug, Frequently, drug dose adjustment of another coad-
including its absorption, distribution, and elimination ministered drug may be necessary due to drug–drug
profile, are considered in the patient who is to be interactions. For example, an elderly patient who is on
treated. Some patients may have unusual first-pass haloperidol (Haldol®) may require a reduction of his
metabolism (eg, fast or slow metabolizers) that will usual morphine dose. With many new drugs, pharma-
affect bioavailability after oral administration and the cogenetic information is also available and should be
elimination half-life after systemic dug absorption. considered for dosing individual patients. For exam-
Second, the physiology of the patient, age, weight, ple, the extents of drug resistance are important con-
gender, and nutritional status will affect the disposition siderations during dosage regimen design in cancer
of the drug and should be considered. Third, any patho- and anti-infective chemotherapy.
physiologic conditions, such as renal dysfunction,
hepatic disease, or congestive heart failure, may change
the normal pharmacokinetic profile of the drug, and the Pharmacokinetics of the Drug
dose must be carefully adjusted. Fourth, the effect of Various popular drug references list pharmacokinetic
long-term exposure to the medication in the patient parameters such as clearance, bioavailability, and
must be considered including the possibility of drug elimination half-life. The values for these pharmaco-
abuse by the patient. In addition, personal lifestyle fac- kinetic parameters are often obtained from small clini-
tors, such as cigarette smoking, alcohol abuse, and cal studies. Therefore, it is difficult to determine
obesity, are other issues that are known to alter the whether these reported pharmacokinetic parameters
pharmacokinetics of drugs. Lastly, lack of patient com- are reflected in the general population or in a specific
pliance (ie, patient noncompliance) in taking the medi- patient group. Differences in study design, patient
cation can also be a problem in achieving effective population, and data analysis may lead to conflicting
therapeutic outcomes. values for the same pharmacokinetic parameters. For
An optimal dosing design can greatly improve example, values for the apparent volume of distribu-
the safety and efficacy of the drug, including reduced tion and clearance can be estimated by different meth-
side effects and a decrease in frequency of TDM and ods, as discussed in previous chapters.
its associated costs. For some drugs, TDM will be Ideally, the effective target drug concentration
necessary because of the unpredictable nature of and the therapeutic window for the drug should be
their pharmacodynamics and pharmacokinetics. obtained. When using the target drug concentration in
Changes in drug or drug dose may be required after the development of a dosage regimen, the clinical
careful patient assessment by the pharmacist, includ- pharmacist should know whether the reported target
ing changes in the drug’s pharmacokinetics, drug drug concentration represents an average steady-state
tolerance, cross-sensitivity, or history of unusual drug concentration, a peak drug concentration, or a
reactions to related drugs. The pharmacist must trough concentration.
686 Chapter 22
Drug Dosage Form (Drug Product) for adequacy, accuracy, and patient compliance with
The dosage form of the drug will affect drug bio- the drug therapy. In many situations, sound clinical
availability and the rate of absorption and thus the judgment may preclude the need for measuring
subsequent pharmacodynamics of the drug in the serum drug concentrations.
patient (see also Chapter 15). The choice of drug dos-
age form may be based on the desired route of drug
Measurement of Drug Concentrations
administration, the desired onset and duration of the
clinical response, cost, and patient compliance. For Before biological samples are taken from the patient,
example, an extended-release drug product instead of the need to determine serum drug concentrations
an immediate-release drug product may provide a should be assessed by the practitioner. In some
longer duration of action and better patient compli- cases, adverse events may not be related to the serum
ance. An orally disintegrating tablet (ODT) may be drug concentration but preclude the patient from
easier for the patient who has difficulty in swallow- using the prescribed drug. For example, allergy or
ing a conventional tablet. Patients with profuse vom- mild nausea may not be dose related. Plasma, serum
iting may prefer the use of a transdermal delivery saliva, urine, and occasionally tissue drug concentra-
system rather than an oral drug product. Available tions may be measured for (1) clinical drug monitor-
dosage forms and strengths are usually listed under ing to improve drug therapy, (2) drug abuse screening,
the How Supplied section in the package insert. and (3) toxicology evaluation such as poisoning and
drug overdose. Examples of common drugs that may
Patient Compliance be measured are listed in Table 22-3. In addition,
many prescription medications (eg, opiates, benzodi-
Factors that may affect patient compliance include
azepines, NSAIDs, anabolic steroids) and nonpre-
the cost of the medication, complicated instructions,
scription drugs (eg, dextromethorphan, NSAIDs) can
multiple daily doses, difficulty in swallowing, type
also be abused. Analyses have been used for mea-
of dosage form, and adverse drug reactions. The
surement of the presence of abused drugs in blood,
patient who is in an institution may have different
urine, saliva, hair, and breath (alcohol).
issues compared to an ambulatory patient. Patient
A major assumption made is that serum drug
compliance in institutions is maintained by the
concentrations relate to the therapeutic and/or toxic
healthcare personnel who provides/administers the
effects of the drug. For many drugs, clinical studies
medication on schedule. Ambulatory patients must
have demonstrated a therapeutically effective range
remember to take the medication as prescribed to
of serum concentrations. Knowledge of the serum
obtain the optimum clinical effect of the drug. It is
drug concentration may clarify why a patient is not
very important that the prescriber or clinical pharma-
responding to the drug therapy or why the drug is
cist consider the patient’s lifestyle and personal
having an adverse effect. In some cases, the practi-
needs when developing a drug dosage regimen. The
tioner may want to verify the accuracy of the dosage
FDA-approved labeling in the package insert con-
regimen.
tains Patient Counseling Information to improve
The timing of the blood sample and the number of
patient compliance. There are also sections on
blood samples to be taken from the patient must be
Information for Patients and Medication Guide.
considered. In many cases, a single blood sample gives
insufficient information. Occasionally, more than one
Evaluation of Patient’s Response blood samples are needed to clarify the adequacy of the
After the drug and drug products are chosen and the dosage regimen. When ordering serum drug concentra-
patient receives the initial dosage regimen, the prac- tions to be measured, a single serum drug concentration
titioner should evaluate the patient’s clinical response. may not yield useful information unless other factors
If the patient is not responding to drug therapy as are considered. For example, the dosage regimen of the
expected, then the drug and dosage regimen should drug should be known, including the dose and the dos-
be reviewed. The dosage regimen should be reviewed age interval, the route of drug administration, the time
Application of Pharmacokinetics to Clinical Situations 687
TABLE 223 Drugs Commonly Measured in Serum, Plasma, or Other Tissues
Therapeutic Drug Monitoring Drug Abuse Screen Drug Overdose or Poisoning
Anticonvulsants Alcohol Alcohol
Carbamazepine, phenytoin, Cotinine Ethyl alcohol, methanol
valproic acid, primidone
Antibiotics Anabolic steroids Opiates
Aminglycosides (gentamicin), Opiates Heroin, morphine, codeine deriva-
vancomycin tives, methadone, buprenorphine
Heroin, morphine, codeine derivatives, metha- Stimulants
done, buprenorphine
Cardiovascular agents Stimulants Cocaine, amphetamine, metham-
Digoxin, lidocaine, procainamide, Cocaine, amphetamine, methamphetamine phetamine, pseudoephedrine
quinidine
Immunosupressants Cannabinoids Hallucinogens and related drugs
Cyclosporine, tacrolimus, sirolimus Marijuana, hashish These drugs are subject to overdose
and/or poisoning
Antipsychotics Other drugs
Clozapine Barbiturates, benzodiazepines,
tricyclics
Other drugs Hallucinogens and related drugs Inhalants
Lithium, theophylline Phencyclidine, PCP, ketamine, MDMA (ecstasy, Nitrous oxide, paint thinners,
3,4-methylenedioxy-N-methylamphetamine) solvents
Hormonal drugs Other drugs Heavy metals
TSH, thyroxin, estrogens Barbiturates, benzodiazepines, various Lead, mercury, arsenic, chromium
hypnotics and sedatives
Various nonprescription medications
such as acetaminophen
Nicotine from tobacco is often included in some drug abuse literature, but is not usually part of a drug abuse screen.
of sampling (peak, trough, or steady state), and the type been achieved, the plasma drug concentration during
of drug product (eg, immediate-release or extended- the postdistributive phase is better correlated with the
release drug product). tissue concentration and, presumably, the drug con-
In practice, trough serum concentrations are easier centration at the site of action. In some cases, the
to obtain than peak or C∞ samples under a multiple- clinical pharmacist may want an early-time sample
av
dose regimen. In addition, there are limitations in that approximates the peak drug level, whereas a
terms of the number of blood samples that may be blood sample taken at three or four elimination half-
taken, total volume of blood needed for the assay, and lives during multiple dosing will approximate the
time to perform the drug analysis. Schumacher (1985) steady-state drug concentration. The practitioner who
has suggested that blood sampling times for TDM orders the measurement of serum concentrations
should be taken during the postdistributive phase for should also consider the cost of the assays, the risks
loading and maintenance doses, but at steady state for and discomfort for the patient, and the utility of the
maintenance doses. After distribution equilibrium has information gained.
688 Chapter 22
Assay for Drug Sensitivity
Drug analyses are usually performed either by a Sensitivity is the minimum detectable level or con-
clinical chemistry laboratory or by a clinical phar- centration of drug in serum that may be approxi-
macokinetics laboratory. A variety of analytic tech- mated as the lowest drug concentration that is two to
niques are available for drug measurement, such as three times the background noise. A minimum quan-
high-pressure liquid chromatography coupled with tifiable level (MQL) or minimum detectable limit
mass spectrometry (LCMS), immunoassay, and (MDL) is a statistical method for the determination
other methods. The methods used by the analytic of the precision of the lower level.
laboratory may depend on such factors as the physi-
cochemical characteristics of the drug, target drug Linearity and Dynamic Range
concentration, amount (volume) and nature of the Dynamic range refers to the relationship between the
biologic specimen (serum, urine, saliva), available drug concentration and the instrument response (or
instrumentation, cost for each assay, and analytical signal) used to measure the drug. Many assays show a
skills of the laboratory personnel. The laboratory linear drug concentration–instrument response rela-
should have a standard operating procedure (SOP) tionship. Immunoassays generally have a nonlinear
for each drug analysis method and follow good labo- dynamic range. High serum drug concentrations, above
ratory practices (GLP). Moreover, analytic methods the dynamic range of the instrument response, must be
used for the assay of drugs in serum or plasma diluted before assay. The dynamic range is determined
should be validated with respect to specificity, lin- by using serum samples that have known (standard)
earity, sensitivity, precision, accuracy, stability, and drug concentrations (including a blank serum sample
ruggedness. The times to perform the assays and or zero drug concentration). Extrapolation of the assay
receive the results are important factors that should results above or below the measured standard drug
be considered if the clinician needs this information concentrations may be inaccurate if the relationship
to make a quick therapeutic decision. between instrument response and extrapolated drug
concentration is unknown.
Specificity
Precision
Chromatographic evidence is generally required to
demonstrate that the analytic method is specific for Precision is a measurement of the variability or
detection of the drug and other analytes, such as an reproducibility of the data. Precision measurements
active metabolite. The method should demonstrate are obtained by replication of various drug concen-
that there is no interference between the drug and its trations and by replication of standard concentration
metabolites and endogenous or exogenous sub- curves prepared separately on different days. A suit-
stances such as other drugs that the patient may have able statistical measurement of the dispersion of the
taken. In addition, the internal standard should be data, such as standard deviation or coefficient of
resolved completely and also demonstrate no inter- variation, is then performed.
ference with other compounds. Immunoassays
depend on an antibody and antigen (usually the drug Accuracy
to be measured) reaction. The antibody should be Accuracy refers to the difference between the average
specific for the drug analyte, but may instead also assay values and the true or known drug concentrations.
cross-react with drugs that have similar structures, Control (known) drug serum concentrations should be
including related compounds (endogenous or exog- prepared by an independent technician using such tech-
enous chemicals) and metabolites of the drug. niques to minimize any error in their preparation. These
Colorimetric and spectrophotometric assays are usu- samples, including a “zero” drug concentration, are
ally less specific. Interference from other materials assayed by the technician assigned to the study along
may inflate the results. with a suitable standard drug concentration curve.
Application of Pharmacokinetics to Clinical Situations 689
Stability serum, or average drug levels. Moreover, the meth-
Standard drug concentrations should be maintained odology for the drug assay used in the analytical
under the same storage conditions as the unknown laboratory may be different in terms of accuracy,
serum samples and assayed periodically. The stabil- specificity, and precision.
ity study should continue for at least the same length The assay results from the analytical laboratory
of time as the patient samples are to be stored. may show that the patient’s serum drug levels are
Freeze–thaw stability studies are performed to deter- higher, lower, or similar to the expected serum lev-
mine the effect of thawing and refreezing on the els. The pharmacokineticist should evaluate these
stability of the drug in the sample. On occasion, a results while considering the patient and the patient’s
previously frozen biologic sample must be thawed pathophysiologic condition. Table 22-4 lists a num-
and reassayed if the first assay result is uncertain. ber of factors the pharmacokineticist should consider
Plasma samples obtained from subjects on a drug when interpreting serum drug concentration. Often,
study are usually assayed along with a minimum of additional data, such as a high serum creatinine and
three standard processed serum samples containing high blood urea nitrogen (BUN), may help verify
known standard drug concentrations and a minimum that an observed high serum drug concentration in a
of three control plasma samples whose concentrations patient is due to lower renal drug clearance because
are unknown to the analyst. These control plasma of compromised kidney function. In another case, a
samples are randomly distributed in each day’s run. complaint by the patient of overstimulation and
Control samples are replicated in duplicate to evaluate insomnia might corroborate the laboratory’s finding
both within-day and between-day precision. The con- of higher-than-anticipated serum concentrations of
centration of drug in each plasma sample is based on theophylline. Therefore, the clinician or pharmaco-
each day’s processed standard curve. kineticist should evaluate the data using sound clini-
cal judgment and observation. The therapeutic
Ruggedness decision should not be based solely on serum drug
concentrations.
Ruggedness is the degree of reproducibility of the test
results obtained by the analysis of the same samples
by different analytical laboratories or by different Dosage Adjustment
instruments. The determination of ruggedness mea- From the serum drug concentration data and patient
sures the reproducibility of the results under normal observations, the clinician or pharmacokineticist
operational conditions from laboratory to laboratory, may recommend an adjustment in the dosage regi-
instrument to instrument, and analyst to analyst. men. Ideally, the new dosage regimen should be
Because each method for drug assay may have calculated using the pharmacokinetic parameters
differences in sensitivity, precision, and specificity, derived from the patient’s serum drug concentra-
the clinical pharmacokineticist should be aware of tions. Although there may not be enough data for a
which drug assay method the laboratory used. complete pharmacokinetic profile, the pharmacoki-
neticist should still be able to derive a new dosage
Pharmacokinetic Evaluation regimen based on the available data and the pharma-
cokinetic parameters in the literature that are based
After the serum or plasma drug concentrations are
on average population data.
measured, the clinical pharmacokineticist must eval-
uate the data. Many laboratories report total drug
(free plus bound drug) concentrations in the serum. Monitoring Serum Drug Concentrations
The pharmacokineticist should be aware of the usual In many cases, the patient’s pathophysiology may be
therapeutic range of serum drug concentrations from unstable, either improving or deteriorating further. For
the literature. However, the literature may not indi- example, proper therapy for congestive heart failure
cate whether the reported values were trough, peak will improve cardiac output and renal perfusion,
690 Chapter 22
TABLE 224 Pharmacokinetic Evaluation of response can be monitored in lieu of actual serum drug
Serum Drug Concentrations concentration. For example, prothrombin time might
Serum Concentrations Lower Than Anticipated be useful for monitoring anticoagulant therapy and
blood pressure monitoring for antihypertensive agents.
Patient compliance
Error in dosage regimen Special Recommendations
Wrong drug product (controlled release instead of imme- At times, the patient may not be responding to drug
diate release) therapy because of other factors. For example, the
Poor bioavailability patient may not be following instructions for taking
the medication (patient noncompliance). The patient
Rapid elimination (efficient metabolizer)
may be taking the drug after a meal instead of before
Reduced plasma–protein binding or may not be adhering to a special diet (eg, low-salt
Enlarged apparent volume of distribution diet). Therefore, the patient may need special instruc-
tions that are simple and easy to follow. It may be
Steady state not reached
necessary to discontinue the drug and prescribe
Timing of blood sample another drug from the same therapeutic class.
Improving renal/hepatic function
Drug interaction due to stimulation of elimination enzyme Frequently Asked Questions
autoinduction
»»Can therapeutic drug monitoring be performed
Changing hepatic blood flow without taking blood samples?
Serum Concentrations Higher Than Anticipated »»What are the major considerations in therapeutic
Patient compliance drug monitoring?
Error in dosage regimen
Wrong drug product (immediate release instead of con-
trolled release) CLINICAL EXAMPLE
Rapid bioavailability Dosage and Administration of Lanoxin®
Smaller-than-anticipated apparent volume of distribution (Digoxin) Tablets, USP
Slow elimination (poor metabolizer) In the new package insert, dosing information is avail-
able under Dosage and Administration. In addition,
Increased plasma–protein binding
the section under Clinical Pharmacology provides
Deteriorating renal/hepatic function valuable information for therapeutic considerations
Drug interaction due to inhibition of elimination such as:
Serum Concentration Correct but Patient Does Not • Mechanism of action
Respond to Therapy • Pharmacodynamics
Altered receptor sensitivity (eg, tolerance) • Pharmacokinetics
Drug interaction at receptor site Lanoxin (digoxin) is one of the cardiac (or digitalis)
glycosides indicated for the treatment of congestive
Changing hepatic blood flow
heart failure and atrial fibrillation. According to the
approved label3 for Lanoxin, the recommended
thereby increasing renal drug clearance. Therefore,
continuous monitoring of serum drug concentrations
is necessary to ensure proper drug therapy for the 3Lanoxin (digoxin) tablets, USP, NDA 20405/S-004, GlaxoSmith-
patient. For some drugs, an acute pharmacologic Kline, August 2009.
Application of Pharmacokinetics to Clinical Situations 691
dosages of digoxin may require considerable modifi- measurement should not be used alone as the basis
cation because of individual sensitivity of the patient for increasing or decreasing the dose of the drug.
to the drug, the presence of associated conditions, or To allow adequate time for equilibration of
the use of concurrent medications. In selecting a digoxin between serum and tissue, sampling of
dose of digoxin, the following factors must be serum concentrations should be done just before the
considered: next scheduled dose of the drug (trough level). If
this is not possible, sampling should be done at least
1. The body weight of the patient. Doses should
6–8 hours after the last dose, regardless of the route
be calculated based upon lean (ie, ideal) body
of administration or the formulation used. On a
weight.
once-daily dosing schedule, the concentration of
2. The patient’s renal function, preferably
digoxin will be 10%–25% lower when sampled at
evaluated on the basis of estimated creatinine
24 versus 8 hours, depending upon the patient’s
clearance.
renal function. On a twice-daily dosing schedule,
3. The patient’s age: Infants and children require
there will be only minor differences in serum
different doses of digoxin than adults. Also,
digoxin concentrations whether sampling is done at
advanced age may be indicative of diminished
8 or 12 hours after a dose.
renal function even in patients with normal
If a discrepancy exists between the reported
serum creatinine concentration (ie, below
serum concentration and the observed clinical
1.5 mg/dL).
response, the clinician should consider the following
4. Concomitant disease states, concurrent
possibilities:
medications, or other factors likely to alter the
pharmacokinetic or pharmacodynamic profile 1. Analytical problems in the assay procedure.
of digoxin. 2. Inappropriate serum sampling time.
3. Administration of a digitalis glycoside other
Serum Digoxin Concentrations than digoxin.
4. Conditions causing an alteration in the sensitiv-
In general, the dose of digoxin used should be deter-
ity of the patient to digoxin.
mined based on clinical grounds. However, measure-
5. Serum digoxin concentration may decrease
ment of serum digoxin concentrations can be helpful
acutely during periods of exercise without any
to the clinician in determining the adequacy of
associated change in clinical efficacy due to
digoxin therapy and in assigning certain probabili-
increased binding of digoxin to skeletal muscle.
ties to the likelihood of digoxin intoxication. About
two-thirds of adults considered adequately digi- An important statement in the approved label for
talized (without evidence of toxicity) have serum Lanoxin is the following, which is in bold for emphasis:
digoxin concentrations ranging from 0.8 to “It cannot be overemphasized that both the adult
2.0 ng/mL; lower serum trough concentrations of and pediatric dosage guidelines provided are based
0.5–1 ng/mL may be appropriate in some adult upon average patient response and substantial
patients. About two-thirds of adult patients with individual variation can be expected. Accordingly,
clinical toxicity have serum digoxin concentrations ultimate dosage selection must be based upon
greater than 2.0 ng/mL. Since one-third of patients clinical assessment of the patient.”
with clinical toxicity have concentrations less than
2.0 ng/mL, values below 2.0 ng/mL do not rule out
the possibility that a certain sign or symptom is Adverse Events and Therapeutic Monitoring
related to digoxin therapy. Rarely, there are patients An adverse drug reaction, also called a side effect or
who are unable to tolerate digoxin at serum concen- adverse event (AE), is any undesirable experience
trations below 0.8 ng/mL. Consequently, the serum associated with the use of a medicine in a patient.
concentration of digoxin should always be inter- AEs can range from mild to severe. Serious AEs are
preted in the overall clinical context, and an isolated those that can cause disability, are life threatening,
692 Chapter 22
result in hospitalization or death, or cause birth CLINICAL EXAMPLE
defects.4 Some AEs are expected and are docu-
mented in the literature and in the approved labeling Serum Vancomycin Concentrations
for the drug. Other AEs may be unexpected. The Vancomycin is a glycopeptide antibiotic commonly
severity of these AEs and whether the AE is related to used in the treatment of serious Gram-positive infec-
the patient’s drug therapy should be considered. The tions. Nephrotoxicity is often cited as an adverse
FDA maintains safety information and an AE report- effect, especially when high dose therapy is used for
ing program (MedWatch) that provides important and a prolonged duration. The feasibility of using vanco-
timely medical product information to healthcare pro- mycin as a continuous infusion has been examined
fessionals, including information on prescription and recently in a variety of settings (eg, in intensive care
over-the-counter drugs, biologics, medical devices, units and as outpatient parenteral therapy).
and special nutritional products.
It is sometimes difficult to determine whether the 1
AE in the patient is related to the drug, due to progres-
sion of the disease or other pathology, or due to some 0.8
unknown source. There are several approaches to deter-
mining whether the observed AE is due to the drug:
0.6
1. Check that the correct drug product and dose
was ordered and given to the patient.
0.4
2. Verify that the onset of the AE was after the
drug was taken and not before.
3. Determine the time interval between the begin- 0.2
ning of drug treatment and the onset of the event.
4. Discontinue the drug and monitor the patient’s 0
status, looking for improvement. 0 20 40 60 80
5. Rechallenge or restart the drug, if appropriate, Steady state vancomycin concentration (mg/L)
and monitor for recurrence of the AE. (From Ingram PR: JAC 2008; Spapen: Ann Intensive
Care, 2011; Norton K: JAC, 2014.)
For some drugs, there may be an AE due to the
initial exposure to the drug. However, the patient
Regardless of the clinical setting, the likelihood
may become desensitized to the AE after longer drug
of nephrotoxicity was found to be significantly
treatment or drug dose titration. The clinician should
higher if the steady-state vancomycin concentrations
be familiar with the drug and relevant literature con-
were >25–32 μg/mL. Unless there is a compelling
cerning AEs. Generally, the manufacturer of the drug
clinical reason to do otherwise, it would be prudent
can also be a resource to consult.
to adjust dosing and maintain serum vancomycin
concentrations to below 25 μg/mL.
Frequently Asked Questions
»»Why are drugs that demonstrate high intrasubject
variability generally safer than critical-dose drugs? DESIGN OF DOSAGE REGIMENS
»»What type of drugs should be monitored? Several methods may be used to design a dosage
regimen. Generally, the initial dosage of the drug is
»»How does one determine whether an adverse event
estimated using average population pharmacokinetic
is drug related?
parameters obtained from the literature and modified
according to the patient’s known diagnosis, patho-
4FDA Consumer Health Information, Aprill 11, 2008 (http:// physiology, demographics, allergy, and any other
www.fda.gov/downloads/ForConsumers/ConsumerUpdates known factor that might affect the patient’s response
/ucm107976.pdf). to the dosage regimen.
Probability of nephrotoxicity
Application of Pharmacokinetics to Clinical Situations 693
After initiation of drug therapy, the patient is Dosage Regimens Based on Population
then monitored for the therapeutic response by clini- Averages
cal and physical assessment. After evaluation of the
The method most often used to calculate a dosage
patient, adjustment of the dosage regimen may be
regimen is based on average pharmacokinetic param-
needed. If necessary, measurement of plasma drug
eters obtained from clinical studies published in the
concentrations may be used to obtain the patient’s
drug literature. This method may be based on a fixed
individual pharmacokinetic parameters from which
or an adaptive model (Greenblatt, 1979; Mawer,
the data are used to modify the dosage regimen.
1976).
Further TDM in the patient may be needed.
The fixed model assumes that population aver-
Various clinical pharmacokinetic software pro-
age pharmacokinetic parameters may be used
grams are available for dosage regimen calculations.
directly to calculate a dosage regimen for the patient,
The dosing strategies are based generally on pharma-
without any alteration. Usually, pharmacokinetic
cokinetic calculations that were previously performed
parameters such as absorption rate constant ka, bio-
manually. Computer automation and pharmacoki-
netic software packages improve the accuracy of the availability factor F, apparent volume of distribution
calculation, make the calculations “easier,” and have VD, and elimination rate constant k are assumed to
an added advantage of maintaining proper documen- remain constant. Most often the drug is assumed to
tation (see Appendix A). However, the use of these follow the pharmacokinetics of a one-compartment
software programs should not replace good clinical model. When a multiple-dose regimen is designed,
judgment. multiple-dosage equations based on the principle of
superposition (see Chapter 9) are used to evaluate
• The package insert (PI) is a useful source for dose the dose. The practitioner may use the usual dosage
regimen. The section Use in Specific Populations suggested by the literature and then make a small
provides information that may apply to individual adjustment of the dosage based on the patient’s
patients. weight and/or age.
• Pregnancy The adaptive model for dosage regimen calcula-
• Labor and delivery tion uses patient variables such as weight, age, sex,
• Nursing mothers body surface area, and known patient pathophysiol-
• Pediatric use ogy, such as renal disease, as well as the known popu-
• Geriatric use lation average pharmacokinetic parameters of the
• Hepatic impairment drug. In this case, calculation of the dosage regimen
• Renal impairment takes into consideration any changing pathophysiol-
• Gender effect ogy of the patient and attempts to adapt or modify the
dosage regimen according to the needs of the patient.
In some cases, pharmacogenetic data may be helpful
Individualized Dosage Regimens in determining dosing. For example, clopidogrel
The most accurate approach to dosage regimen (Plavix) has a black box warning cautioning use in
design is to calculate the dose based on the pharma- patients who have slow CYP2D6 metabolism and who
cokinetics of the drug in the individual patient. This will, therefore, have slower activation of the prodrug to
approach is not feasible for calculation of the initial the active metabolite. However, an appropriate dose
dose. However, once the patient has been medicated, regimen has not been established for these patients.
the readjustment of the dose may be calculated using The adaptive model generally assumes that pharmaco-
pharmacokinetic parameters derived from measure- kinetic parameters such as drug clearance do not
ment of the serum drug levels from the patient after change from one dose to the next. However, some
the initial dose. Most dosing programs record the adaptive models allow for continuously adaptive
patient’s age and weight and calculate the individual change with time in order to simulate more closely the
dose based on creatinine clearance and lean body changing process of drug disposition in the patient,
weight. especially during a disease state (Whiting et al, 1991).
694 Chapter 22
Dosage Regimens Based on Partial Pharmaceutical manufacturers provide dos-
Pharmacokinetic Parameters age recommendations in the approved label for
For many drugs, the entire pharmacokinetic pro- many marketed drugs in the form of a table or as
file of the drug is unknown or unavailable. a nomogram. These are general guidelines to aid
Therefore, the pharmacokineticist needs to make the clinician in establishing an initial dosage
some assumptions in order to calculate the dosage regimen for patients. The tables may include
regimen in the absence of pharmacokinetic data in loading and maintenance doses that are modified
animals or humans. For example, a common for the demographics of the patient (eg, age,
assumption is to let the bioavailability factor F weight) and for certain disease states (eg, renal
equal 1 or 100%. Thus, if the drug is less than insufficiency).
fully absorbed systemically, the patient will be For drugs with a narrow therapeutic range,
undermedicated rather than overmedicated. Some such as theophylline, a guide for monitoring serum
of these assumptions will depend on the safety, drug concentrations is given. Another example is
efficacy, and therapeutic range of the drug. The the aminoglycoside antibiotic, tobramycin sulfate
use of population pharmacokinetics (discussed USP (Nebcin, Eli Lilly), which is eliminated pri-
later in this chapter) employs average patient marily by renal clearance. Thus, the dosage of
population characteristics and only a few serum tobramycin sulfate should be reduced in direct pro-
drug concentrations from the patient. Population portion to a reduction in creatinine clearance (see
pharmacokinetic approaches to TDM have Chapter 24). The manufacturer provides a nomo-
increased with the increased availability of com- gram for estimating the percent of the normal dose
puterized databases and the development of statis- of tobramycin sulfate assuming the serum creati-
tical tools for the analysis of observational data nine level (mg/100 mL) has been obtained.
(Schumacher, 1985).
Empirical Dosage Regimens
Nomograms and Tabulations in Dosage In many cases, the physician selects a dosage regi-
Regimen Designs men for the patient without using any pharmacoki-
For ease of calculation of dosage regimens, many netic variables. In such a situation, the physician
clinicians rely on nomograms to calculate the makes the decision based on empirical clinical data,
proper dosage regimen for their patients. The use personal experience, and clinical observations. The
of a nomogram may give a quick dosage regimen physician characterizes the patient as representative
adjustment for patients with characteristics requir- of a similar well-studied clinical population that has
ing adjustments, such as age, body weight, and used the drug successfully.
physiologic state. In general, the nomogram of a
drug is based on population pharmacokinetic data
collected and analyzed using a specific pharmaco- CONVERSION FROM INTRAVENOUS
kinetic model. In order to keep the dosage regi-
INFUSION TO ORAL DOSING
men calculation simple, complicated equations
are often solved and the results displayed dia- After the patient’s dosing is controlled by intrave-
grammatically on special scaled axes or as a table nous infusion, it is often desirable to continue to
to produce a simple dose recommendation based medicate the patient with the same drug using the
on patient information. Some nomograms make oral route of administration. When intravenous infu-
use of certain physiologic parameters, such as sion is stopped, the serum drug concentration
serum creatinine concentration, to help modify decreases according to first-order elimination kinet-
the dosage regimen according to renal function ics (see Chapter 6). For most oral drug products, the
(see Chapter 24). time to reach steady state depends on the first-order
Application of Pharmacokinetics to Clinical Situations 695
elimination rate constant for the drug. Therefore, if
EXAMPLE »» »
the patient starts the dosage regimen with the oral
drug product at the same time as the intravenous
An adult male asthmatic patient (age 55 years,
infusion is stopped, then the exponential decline of
78 kg) has been maintained on an intravenous
serum levels from the intravenous infusion should be
infusion of aminophylline at a rate of 34 mg/h. The
matched by the exponential increase in serum drug
steady-state theophylline drug concentration was
levels from the oral drug product.
12 μg/mL and total body clearance was calculated
The conversion from intravenous infusion to a
as 3.0 L/h. Calculate an appropriate oral dosage
controlled-release oral medication given once or
regimen of theophylline for this patient.
twice daily has become more common with the
availability of more extended-release drug prod- Solution
ucts, such as theophylline (Stein et al, 1982) and Aminophylline is a soluble salt of theophylline
quinidine. Computer simulation for the conversion and contains 85% theophylline (S = 0.85). Theo-
of intravenous theophylline (aminophylline) ther- phylline is 100% bioavailable (F = 1) after an oral
apy to oral controlled-release theophylline demon- dose. Because total body clearance, ClT = kVD,
strated that oral therapy should be started at the Equation 22.2 may be expressed as
same time as intravenous infusion is stopped
D C∞Cl
0 av T
(Iafrate et al, 1982). With this method, minimal = (22.3)
τ SF
fluctuations are observed between the peak and
trough serum theophylline levels. Moreover, giving The dose rate, D0/τ (34 mg/h), was calculated on the
the first oral dose when IV infusion is stopped may basis of aminophylline dosing. The patient, however,
make it easier for the nursing staff or patient to will be given theophylline orally. To convert to oral
comply with the dosage regimen. theophylline, S and F should be considered.
Either of these methods may be used to calcu-
SFD
late an appropriate oral dosage regimen for a patient Theophylline dose rate 0
=
τ
whose condition has been stabilized by an intrave-
(0.85)(1)(34)
nous drug infusion. Both methods assume that the = = 28.9mg/h
1
patient’s plasma drug concentration is at steady
state. The theophylline dose rate of 28.9 mg/h must be
converted to a reasonable schedule for the patient
with a consideration of the various commercially
Method 1
available theophylline drug products. There-
Method 1 assumes that the steady-state plasma drug fore, the total daily dose is 28.9 mg/h × 24 h or
concentration, Css, after IV infusion is identical to 693.6 mg/d. Possible theophylline dosage sched-
the desired C∞ after multiple oral doses of the drug.
av ules might be 700 mg/d, 350 mg every 12 hours, or
Therefore, the following equation may be used: 175 mg every 6 hours. Each of these dosage regi-
mens would achieve the same C∞
av but different C∞
max
SFD and C∞
min, which should be calculated. The dose of
C∞ 0
=
av (22.1)
kV τ 350 mg every 12 hours could be given in sustained-
D
release form to avoid any excessive high drug con-
D C∞ centration in the body.
0 avkV D
= (22.2)
τ SF
Method 2
where S is the salt form of the drug and D0/t is the Method 2 assumes that the rate of intravenous infu-
dosing rate. sion (mg/h) is the same desired rate of oral dosage.
696 Chapter 22
EXAMPLE »» » PRACTICE PROBLEMS
1. Pharmacokinetic data for clindamycin were
Using the example in method 1, the following cal- reported by DeHaan et al (1972) as follows:
culations may be used.
k = 0.247 h−1
Solution
The aminophylline is given by IV infusion at a t1/2 = 2.81 h
rate of 34 mg/h. The total daily dose of amino- V 2
D = 43.9 L/1.73 m
phylline is 34 mg/h × 24 h = 816 mg. The equiva-
lent daily dose in terms of theophylline is 816 × What is the steady-state concentration of the
0.85 = 693.6 mg. Thus, the patient should receive drug after 150 mg of the drug is given orally
approximately 700 mg of theophylline per day every 6 hours for a week? (Assume the drug is
or 350 mg controlled-release theophylline every 100% absorbed.)
12 hours.
Solution
1.44D t F
C∞ = 0 1/2
av VDτ
DETERMINATION OF DOSE 1.44 ×150,000 × 2.81×1
= µg/mL
The calculation of the starting dose of a drug and 43,900 × 6
dosing interval is based on the objective of deliver- = 2.3µg/mL
ing a desirable (target) therapeutic level of the drug
in the body. For many drugs, the desirable thera- 2. According to Regamey et al (1973), the elimi-
peutic drug levels and pharmacokinetic parameters nation half-life of tobramycin was reported to
are available in the literature. However, the litera- be 2.15 hours and the volume of distribution
ture in some cases may not yield complete drug was reported to be 33.5% of body weight.
information, or some of the information available
a. What is the dose for an 80-kg individual if
may be equivocal. Therefore, the pharmacokineti-
a steady-state level of 2.5 μg/mL is desired?
cist must make certain necessary assumptions in
Assume that the drug is given by intravenous
accordance with the best pharmacokinetic informa-
bolus injection every 8 hours.
tion available.
For a drug that is given in multiple doses for an
extended period of time, the dosage regimen is usu- Solution
ally calculated to maintain the average steady-state Assuming the drug is 100% bioavailable as a result
blood level within the therapeutic range. The dose of IV injection,
can be calculated with Equation 22.4, which
1.44D t F
expresses the C∞ in terms of dose (D0), dosing inter- C∞ 0 1/2
av av =
VDτ
val (t), volume of distribution (VD), and the elimina-
tion half-life of the drug. F is the fraction of drug 1.44 × 2.15×1× D
2.5 = 0
absorbed and is equal to 1 for drugs administered 80 × 0.335×1000 × 8
intravenously. 2.5×80 × 0.335×1000 × 8
D0 = µg
1.44 × 2.15
D0 = 173 mg
1.44D
C 0t∞ 1/2F
av = (22.4)
VDτ The dose should be 173 mg every 8 hours.
Application of Pharmacokinetics to Clinical Situations 697
b. The manufacturer has suggested that in EFFECT OF CHANGING DOSE AND
normal cases, tobramycin should be given
DOSING INTERVAL ON C Ç
at a rate of 1 mg/kg every 8 hours. With this max, C Çmin ,
dosage regimen, what would be the average AND C Çav
steady-state level?
During intravenous infusion, Css may be used to
monitor the steady-state serum concentrations. In
Solution contrast, when considering TDM of serum concen-
trations after the initiation of a multiple-dosage regi-
1.44 ×1×1000 × 2.15
C∞ men, the trough serum drug concentrations or C∞
av = min
0.335×1000 ×8 may be used to validate the dosage regimen. The
C∞ blood sample withdrawn just prior to the administra-
av = 1.16µg/mL
tion of the next dose represents C∞ . To obtain C∞
min max,
the blood sample must be withdrawn exactly at the
Because the bactericidal concentration of an anti-
time for peak absorption, or closely spaced blood
biotic varies with the organism involved in the
samples must be taken and the plasma drug concen-
infection, the prescribed dose may change. The
trations graphed. In practice, an approximate time
average plasma drug concentration is used to indi-
for maximum drug absorption is estimated and a
cate whether optimum drug levels have been
blood sample is withdrawn. Because of differences
reached. With certain antibiotics, the steady-state
in rates of drug absorption, C∞
peak and trough levels are sometimes used as thera- max measured in this
manner is only an approximation of the true C∞
peutic indicators. (See Chapter 21 for discussion of max.
The C∞ is used most often in dosage calcula-
time above minimum effective concentration av
tion. The advantage of using C∞ as an indicator for
[MIC].) For example, the effective concentration of av
deciding therapeutic blood level is that C∞ is deter-
tobramycin was reported to be around 4–5 μg/mL av
for peak levels and around 2 μg/mL for trough lev- mined on a set of points and generally fluctuates less
els when given intramuscularly every 12 hours than either C∞
max or C∞ . Moreover, when the dosing
min
(see Table 22-1). Although peak and trough levels interval is changed, the dose may be increased pro-
are frequently reported in clinical journals, these portionally, to keep C∞ constant. This approach
av
drug levels are only transitory in the body. Peak works well for some drugs. For example, if the drug
and trough drug levels are less useful pharmacoki- diazepam is given either 10 mg TID (three times a
∞
netically, because peak and trough levels fluctuate day) or 15 mg BID (twice daily), the same Cav is
more and are usually reported less accurately than obtained, as shown by Equation 22.1. In fact, if the
average plasma drug concentrations. When the daily dose is the same, the C∞ should be the same (as
av
average plasma drug concentration is used as a long as clearance is linear). However, when monitor-
therapeutic indicator, an optimum dosing interval ing serum drug concentrations, C∞ cannot be mea-
av
must be chosen. The dosing interval is usually set sured directly but may be obtained from AUC/t
at approximately one to two elimination half-lives during multiple-dosage regimens. As discussed in
of the drug, unless the drug has a very narrow Chapter 9 the C∞ is not the arithmetic average of
av
therapeutic index. In this case the drug must be C∞ and C∞ ecause serum concentrations decline
min max b
given in small doses more frequently or by IV exponentially.
infusion. Of note, once the average plasma drug The dosing interval must be selected while con-
concentration is known, the overall daily drug sidering the elimination half-life of the drug; other-
exposure can be easily transformed and repre- wise, the patient may suffer the toxic effect of a high
sented by the area under concentration–time curve C∞
max or subtherapeutic effects of a low C∞ even if
min
(AUC). the C∞ is kept constant. For example, using the same
av
698 Chapter 22
example of diazepam, the same C∞ is achieved at as the penicillins, which have relatively low toxic-
av
10 mg TID or 60 mg every other day. Obviously, the ity, may be given at intervals much longer than their
C∞
ma of the latter dose regimen would produce a C∞
x max elimination half-lives without any toxicity prob-
several times larger than that achieved with 10-mg- lems. Drugs having a narrow therapeutic range,
TID dose regimen. In general, if a drug has a rela- such as digoxin and phenytoin, must be given rela-
tively wide therapeutic index and a relatively long tively frequently to minimize excessive “peak-and-
elimination half-life, then flexibility exists in chang- trough” fluctuations in blood levels. For example,
ing the dose or dosing interval, t, using C∞ as an the common maintenance schedule for digoxin is
av
indicator. When the drug has a narrow therapeutic 0.25 mg/d and the elimination half-life of digoxin
index, C∞
ma and C∞
x max must be monitored to ensure is 1.7 days. In contrast, penicillin G is given at
safety and efficacy. 250 mg every 6 hours, while the elimination half-
As the dose or dosage intervals change propor- life of penicillin G is 0.75 hour. Penicillin is given
tionately, the C∞ may be the same but the steady- at a dosage interval equal to 8 times its elimination
av
state peak, C∞
ma , and trough, C∞
x , drug levels will half-life, whereas digoxin is given at a dosing inter-
min
change. C∞
max is influenced by the dose and the dos- val only 0.59 times its elimination half-life. The
age interval. An increase in the dose given at a longer toxic plasma concentration of penicillin G is over
dosage interval will cause an increase in C∞
max and a 100 times greater than its effective concentration,
decrease in C∞ . In this case C∞
mi max may be very close whereas digoxin has an effective concentration of
n
or above the minimum toxic drug concentration 1–2 ng/mL and a toxicity level of 3 ng/mL. The
(MTC). However, the C∞ may be lower than the toxic concentration of digoxin is only 1.5 times
min
minimum effective drug concentration (MEC). In effective concentration. Therefore, a drug with a
this latter case the low C∞ may be subtherapeutic large therapeutic index (ie, a large margin of safety)
min
and dangerous for the patient, depending on the can be given in large doses and at relatively long
nature of the drug. dosing intervals.
DETERMINATION OF FREQUENCY DETERMINATION OF BOTH DOSE
OF DRUG ADMINISTRATION AND DOSAGE INTERVAL
The drug dose is often related to the frequency of Both the dose and the dosing interval should be con-
drug administration. The more frequently a drug is sidered in the dosage regimen calculations. For intra-
administered, the smaller the dose is needed to venous multiple-dosage regimens, the ratio of
obtain the same C∞ . Thus, a dose of 250 mg every C∞ ∞
av max /Cmin may be expressed by
3 hours can be changed to 500 mg every 6 hours
without affecting the average steady-state plasma C∞ C0
p /(1− e−kτ )
max
concentration of the drug. However, as the dosing = (22.5)
C∞
min C0e−kτ
p (1− e−kτ )
intervals get longer, the dose required to maintain
the average plasma drug concentration gets cor-
which can be simplified to
respondingly larger. When an excessively long
dosing interval is chosen, the larger dose may C∞
max 1
result in peak plasma levels that are above toxic =
C∞ − (
τ
min e k 22.6)
drug concentration and trough plasma concentra-
tions that are below the minimum effective con- From Equation 22.6, a maximum dosage interval, t,
centration, even though C∞ will remain the same may be calculated that will maintain the serum con-
av
(see Chapter 9). centration between desired C∞ and C∞
mi max . After the
n
In general, the dosing interval for most drugs is dosage interval is calculated, then a dose may be
determined by the elimination half-life. Drugs such calculated.
Application of Pharmacokinetics to Clinical Situations 699
PRACTICE PROBLEM As a further check on the dosage regimen, calculate
C∞ .
av
The elimination half-life of an antibiotic is 3 hours
with an apparent volume of distribution equivalent to
∞ D0 2000
20% of body weight. The usual therapeutic range for Cav = =
VDkτ (200)(0.231)(4.76)
this antibiotic is between 5 and 15 μg/mL. Adverse
C∞
toxicity for this drug is often observed at serum con- av = 9.09µg/mL
centrations greater than 20 μg/mL. Calculate a dos-
age regimen (multiple IV doses) that will just By calculation, the dose of this antibiotic should be
maintain the serum drug concentration between 5 2 mg/kg every 4.76 hours to maintain the serum drug
and 15 μg/mL. concentration between 5 and 15 μg/mL.
In practice, rather than a dosage interval of 4.76
Solution hours, the dosage regimen and the dosage interval
should be made as convenient as possible for the
From Equation 22.6, determine the maximum pos-
patient, and the size of the dose should take into
sible dosage interval t.
account the commercially available drug formula-
tion. Therefore, the dosage regimen should be recal-
15 1
= culated to have a convenient value (below the
5 e−(0.693/3)τ
maximum possible dosage interval) and the dose
e−0.231τ
= 0.333
adjusted accordingly.
Take the natural logarithm (ln) on both sides of the
equation.
DETERMINATION OF ROUTE OF
−0.231τ = −1.10 ADMINISTRATION
τ = 4.76 h
Selection of the proper route of administration is an
important consideration in drug therapy. The rate of
Then determine the dose required to produce from
drug absorption and the duration of action are influ-
C∞
max Equation 22.7 after substitution of C0
p = D0 /VD:
enced by the route of drug administration. However,
the use of certain routes of administration is pre-
D0 /V C∞ D cluded by physiologic and safety considerations. For
max =
1− e k (22.7)
− τ
example, intra-arterial and intrathecal drug injec-
tions are less safe than other routes of drug adminis-
Solve for dose D0, letting VD = 200 mL/kg (20% tration and are used only when absolutely necessary.
body weight). Drugs that are unstable in the gastrointestinal tract
such as proteins or drugs that undergo extensive
D0 /20015 = first-pass effect are not suitable for oral administra-
1 e−(0.231)(4.76)
−
tion. For example, insulin is a protein that is
D0 = 2 mg/kg degraded in the gastrointestinal tract by proteolytic
enzymes. Drugs such as xylocaine and nitroglycerin
To check this dose for therapeutic effectiveness, cal- are not suitable for oral administration because of
culate C∞ and C∞ . high first-pass effect. These drugs, therefore, must
min av
be given by an alternative route of administration.
Intravenous administration is the fastest and
(D /V ) −kτ ( 0.231)(4.76)
0 D e (2000/200)e −
C∞
min = =
1− e−kτ 1 e−(0.231)(4.76) most reliable way of delivering a drug into the circu-
−
latory system. Drugs administered by intravenous
C∞
min = 4.99µg/mL bolus are delivered to the plasma immediately and
700 Chapter 22
the entire dose is immediately subject to elimination. after oral administration than after intramuscular
Consequently, more frequent drug administration is injection. Some drugs, such as haloperidol decano-
required. Drugs administered extravascularly must ate, are very oil-soluble products that release very
be absorbed into the bloodstream, and the total slowly after intramuscular injection.
absorbed dose is eliminated more slowly. The fre-
quency of administration can be lessened by using
routes of administration that give a sustained rate of DOSING INFANTS AND CHILDREN
drug absorption. Intramuscular injection generally Infants and children have different dosing require-
provides more rapid systemic absorption than oral ments than adults (Bartelink et al, 2006; FDA
administration of drugs that are not very soluble. Guidance for Industry, 2000; Leeder et al, 2010).
Certain drugs are not suitable for administration Information for pediatric dosings was generally
intramuscularly because of erratic drug release, pain, lacking in the past. In December 1994, the FDA
or local irritation. Even though the drug is injected required drug manufacturers to determine whether
into the muscle mass, the drug must reach the circula- existing data were sufficient to support information
tory system or other body fluid to become bioavail- on pediatric use for drug labeling purposes and
able. The anatomic site of drug deposition following implemented a plan to encourage the voluntary col-
intramuscular injection will affect the rate of drug lection of pediatric data. The FDA Modernization
absorption. A drug injected into the deltoid muscle is (FDAMA) authorized an additional 6 months of pat-
more rapidly absorbed than a drug injected similarly ent protection for manufacturers that conducted
into the gluteus maximus, because there is better pediatric clinical trials. As a consequence of various
blood flow in the former. In general, the method of legislative initiatives later, the results of pediatric
drug administration that provides the most consistent studies conducted on 322 drugs and biological prod-
and greatest bioavailability should be used to ensure ucts are available to help dosing in children.5 The
maximum therapeutic effect. The various routes of studies reveal important new information regarding
drug administration can be classified as either extra- dosing and pharmacokinetic differences between
vascular or intravascular and are listed in Table 22-5. children and adults (Leeder et al, 2010). Dosing of
Precipitation of an insoluble drug at the injec- drugs in this population requires a thorough consid-
tion site may result in slower absorption and a eration of the differences in the pharmacokinetics
delayed response. For example, a dose of 50 mg of and pharmacology of a specific drug in the preterm
chlordiazepoxide (Librium) is more quickly absorbed newborn infant, newborn infant (birth to 28 days),
infant (28 days–23 months), young child (2–5 years),
older child (6–11 years), adolescent (12–18 years),
TABLE 225 Common Routes of Drug and adult. Unfortunately, the pharmacokinetics and
Administration pharmacodynamics of most drugs are still not well
known in children under 12 years of age.6 The varia-
Parenteral Extravascular
tion in body composition and the maturity of liver,
Intravascular Enteral kidney, and other organ functions are potential
Intravenous injection (IV bolus) Buccal sources of differences in pharmacokinetics with
respect to age. For convenience, “infants” are here
Intravenous infusion (IV drip) Sublingual
Intra-arterial injection Oral
5http://www.fda.gov/downloads/ScienceResearch/SpecialTopics/
Intramuscular injection Rectal
PediatricTherapeuticsResearch/UCM163159.pdf; accessed July 2,
Intradermal injection Inhalation 2009.
6The FDA issued a Guidance for Industry, Qualifying for Pediatric
Subcutaneous injection Transdermal Exclusivity under Section 505(A) of the Federal Food, Drug, and
Cosmetic Act (June 1998), to encourage drug manufacturers to
Intrathecal injection
develop dosage guidelines for children.
Application of Pharmacokinetics to Clinical Situations 701
arbitrarily defined as children of 0–2 years of age. TABLE 226 Comparison of Newborn and
However, within this group, special consideration is Adult Renal Clearancesa
necessary for infants less than 4 weeks (1 month)
Average Average
old, because their ability to handle drugs often dif- Infant Adult
fers from that of more mature infants.
In addition to different dosing requirements for Body weight (kg) 3.5 70
the pediatric population, there is a need to select Body water
pediatric dosage forms that permit more accurate
(%) 77 58
dosing and patient compliance. For example, liquid
pediatric drug products may have a calibrated drop- (L) 2.7 41
per or a premeasured teaspoon (5 mL) for more Inulin clearance
accurate dosing and also have a cherry flavor for
(mL/min) Approx 3 130
pediatric patient compliance. Pediatric drug formula-
tions may also contain different drug concentrations k (min–1) 3/2700 = 0.0011 130/41,000 =
0.0032
compared to the adult drug formulation and must be
considered in order to prevent dosage errors. Because t1/2 (min) 630 220
of the small muscle mass in an infant, alternative PAH clearance
drug delivery such as an intramuscular antibiotic
(mL/min) Approx 12 650
drug injection into the gluteus medius may be consid-
ered for a pediatric patient, as opposed to the deltoid k (min–1) 12/2800 = 650/41,000 =
muscle for an adult patient. However, body composi- 0.0043 0.016
tion is different in infants compared to adults. t1/2 (min) 160 43
In general, complete hepatic function is not
aComputations are for a drug distributed in the whole body water, but
attained until the third week of life. Oxidative pro- any other VD would give the same relative values.
cesses are fairly well developed in infants, but there is
a deficiency of conjugative enzymes, in particular,
glucuronidation. For example, kernicterus is a form of
TABLE 227 Elimination Half-Lives of Drugs
jaundice in the newborn characterized by very high
in Infants and Adults
levels of unconjugated bilirubin in the blood. Since
the tissues protecting the brain (the blood–brain bar- Half-Life in Half-Life in
rier) are not well formed in newborns, unconjugated Drug Neonatesa (h) Adults (h)
bilirubin may enter the brain and cause brain damage. Penicillin G 3.2 0.5
In addition to reduced liver function in infants, altered
Ampicillin 4 1–1.5
drug distribution may occur due to reduction in drug
binding to plasma albumin and to different body com- Methicillin 3.3/1.3 0.5
position, especially water and fat content. Carbenicillin 5–6 1–1.5
Newborns show only 30%–50% of the renal
Kanamycin 5–5.7 3–5
function of adults on the basis of activity per unit of
body weight (Table 22-6). Drugs that are heavily Gentamicin 5 2–3
dependent on renal excretion will have a sharply a0–7 days old.
decreased elimination half-life. For example, the
penicillins are excreted for the most part through the
kidneys. The elimination half-lives of such drugs are based on body surface area or body weight. Dosage
much increased in infants, as shown in Table 22-7. based on the child’s age and body weight, and nor-
When dosage guidelines are not available for a malized to drug dosages in adults, was used in the
drug, empirical dose adjustment methods are often past. However, pharmacokinetic parameters may
used. These empirical dose adjustment methods are vary as a function of age. Dosage based on body
702 Chapter 22
surface area has the advantage of avoiding some bias introduced below for discussion in clinical situations.
due to obesity or unusual body weight, because the Defining “elderly” is difficult. The geriatric popula-
height and the weight of the patient are both consid- tion is often arbitrarily defined as patients who are
ered. The body surface area method gives only a older than 65 years, and many of these people live
rough estimation of the proper dose, because the active and healthy lives. In addition, there is an
pharmacokinetic differences between patients of the increasing number of people who are living beyond
same body surface area are not considered. Dosage 85 years old, who are often considered the “older
regimens for the newborn, infant, and child must elderly” population. The aging process is more often
consider the changing physiologic development of associated with physiologic changes during aging
the patient and the pharmacokinetics of the specific rather than purely chronological age. Chronologically,
drug for that age group. In the package insert of new the elderly have been classified as the young old
drugs, under the section on Use in Specific (ages 65–75 years), the old (ages 75–85 years), and
Populations, pediatric use information should be the old old (ages >85 years) (Abernethy, 2001).
consulted for drug-specific information. Performance capacity and the loss of homeo-
static reserve decrease with advanced age but occur
to a different degree in each organ and in each
PRACTICE PROBLEM patient. Physiologic and cognitive functions tend to
The elimination half-life of penicillin G is 0.5 hour change with the aging process and can affect compli-
in adults and 3.2 hours in neonates (0–7 days old). ance, therapeutic safety, and efficacy of a prescribed
Assuming that the normal adult dose of penicillin G drug. The elderly also tend to be on multiple drug
is 4 mg/kg every 4 hours, calculate the dose of peni- therapy due to concomitant illness(es). Decreased
cillin G for an 11-lb infant. cognitive function in some geriatric patients, compli-
cated drug dosage schedules, and/or the high cost of
drug therapy may result in poor drug compliance,
Solution
resulting in lack of drug efficacy, possible drug inter-
actions, and/or drug intoxication.
τ1 (t1/2)= 1 Several objectively measured vital physiologic
τ 2 (t1/2)2 functions related to age show that renal plasma flow,
t glomerular filtration, cardiac output, and breathing
1/2 = 0.5 h
capacity can drop from 10% to 30% in elderly sub-
4 × 3.2 jects compared to those at age 30 years. The physi-
τ 2 = = 25.6 h
0.5 ologic changes due to aging may necessitate special
considerations in administering drugs in the elderly.
Therefore, this infant may be given the following For some drugs, an age-dependent increase in
dose: adverse drug reactions or toxicity may be observed.
This apparent increased drug sensitivity in the
11 lb
Dose = 4 mg/kg = = 20 mg every 24 h elderly may be due to pharmacodynamic and/or
2.2 lb/kg pharmacokinetic changes (Mayersohn, 1994;
Schmucker, 1985).
Alternatively, 10 mg every 12 hours would achieve The pharmacodynamic hypothesis assumes that
the same C∞ .
av age causes alterations in the quantity and quality of
target drug receptors, leading to altered drug response.
DOSING THE ELDERLY Quantitatively, the number of drug receptors may
decline with age, whereas qualitatively, a change in the
Elderly subjects are considered as specific popula- affinity for the drug may occur. Alternatively, the phar-
tions and a formal discussion is given in Chapter 23. macokinetic hypothesis assumes that age-dependent
However, some relevant basic information is increases in adverse drug reactions are due to
Application of Pharmacokinetics to Clinical Situations 703
physiologic changes in drug absorption, distribution, dose for a 75-year-old patient, assuming that
and elimination, including renal excretion and hepatic the volume of distribution per body weight is
clearance. not changed by the patient’s age?
In the elderly, age-dependent alterations in drug
absorption may include a decline in the splanchnic Solution
blood flow, altered gastrointestinal motility, increase
The longer elimination half-life of the aminoglyco-
in gastric pH, and alteration in the gastrointestinal
side in elderly patients is due to a decrease in renal
absorptive surface. The incidence of achlorhydria in
function. A good inverse correlation has been
the elderly may have an effect on the dissolution of
obtained of elimination half-life to the aminoglyco-
certain drugs such as weak bases and certain dosage
side and creatinine clearance. To maintain the same
forms that require an acid environment for disinte-
average concentration of the aminoglycoside in the
gration and release (Mayersohn, 1994). From a dis-
elderly as in young adults, the dose may be reduced.
tribution consideration, drug–protein binding in the
plasma may decrease as a result of decrease in the
1.44DN (t1/2)N 1.44D
albumin concentration, and the apparent volume of 0(tC∞ 1/2)0
av = =
τNVN τ 0Vdistribution may change due to a decrease in muscle 0
mass and an increase in body fat. Renal drug excre- DN (t1/2)N D0(t1/2)0
tion generally declines with age as a result of =
τN τ 0
decrease in the glomerular filtration rate (GFR) and/
or active tubular secretion. Moreover, the activity of Keeping the dose constant,
the enzymes responsible for drug biotransformation
may decrease with age, leading to a decline in DN = D0
hepatic drug clearance.
Elderly patients may have several different where DN is the new dose and D0 is the old dose.
pathophysiologic conditions that require multiple τ 0 (t1/2)= 0
drug therapy that increases the likelihood for a drug τN (t1/2)interaction. Moreover, increased adverse drug reac- N
tions and toxicity may result from poor patient com- 282
τ 0 = 12× = 31.6 h
pliance. Both penicillin and kanamycin show 107
prolonged t1/2 in the aged patient, as a consequence
of an age-related gradual reduction in the kidney size Therefore, the same dose of the aminoglycoside may
and function. The Gault–Cockroft rule for calculat- be administered every 32 hours without affecting the
ing creatinine clearance clearly quantitates a reduc- average steady-state level of the aminoglycoside.
tion in clearance with increased age (see Chapter 24). 2. The clearance of lithium was determined to
Age-related changes in plasma albumin and α1-acid be 41.5 mL/min in a group of patients with an
glycoprotein may also be a factor in the binding of average age of 25 years. In a group of elderly
drugs in the body. patients with an average age of 63 years, the
clearance of lithium was 7.7 mL/min. What
percentage of the normal dose of lithium should
PRACTICE PROBLEMS be given to a 65-year-old patient?
1. An aminoglycoside has a normal elimination
Solution
half-life of 107 minutes in young adults. In
patients 70–90 years old, the elimination half- The dose should be proportional to clearance;
life of the aminoglycoside is 282 minutes. The therefore,
normal dose of the aminoglycoside is 15 mg/kg 7.7×100
Dose reductions (%) = = 18.5%
per day divided into two doses. What is the 41.5
704 Chapter 22
The dose of lithium may be reduced to about 20% of b. What would be the steady-state level of felodip-
the regular dose in the 65-year-old patient without ine in the elderly if dose and dosing interval are
affecting the steady-state blood level. unchanged?
c. Can felodipine be given safely to elderly
patients?
CLINICAL EXAMPLE
Hypertension is common in elderly patients. The Solution
pharmacokinetics of felodipine (Plendil), a calcium
channel antagonist for hypertension, was studied in a. The higher AUC in the elderly compared to
young and elderly subjects. After a dose of 5 mg oral young adults is due to the decreased drug clear-
felodipine, the AUC and Cmax in the elderly patients ance in the older subjects.
(67–79 years of age, mean weight 71 kg) were three b. The elderly have more side effects with
times that of the young subjects (20–34 years of age, felodipine compared to young adults. Factors that
mean weight 75 kg), as shown in Fig. 22-2. Side may have increased side effects in the elderly
effects of felodipine in the elderly patients, such as could be (1) reduced hepatic blood flow, (2)
flushing, were reported in 9 of 11 subjects, and pal- potassium depletion in the body, (3) increased
pitation was reported in 3 of 11 subjects, whereas bioavailability, or (4) reduced clearance.
only 1 of 12 of the young subjects reported side FD
c. C∞ 0
av = (22.8)
effects. Systemic clearance in the elderly was 248 ± Cl
τ
108 L/h compared to 619 ± 214 L/h in the young
subjects. The bioavailability of felodipine was If D0, F, and t are the same, the steady-state drug
reported to be about 15.5% in the elderly and 15.3% concentration, C∞ , will be inversely proportional to
av
in the young subjects. (Concomitant medications clearance:
included a diuretic and a beta-blocker.) C∞
av elderly Clyoung
=
a. What is the main cause for the difference in the C∞ Cl
av young elderly
observed AUC between the elderly and young
subjects? C∞
av elderly 619
= = 2.5
C∞ 248
av young
(Note: Cl is in the denominator in Equation 22.8 and
is inversely related to concentration.) The steady con-
centration of felodipine will be 250% or 2.5 times that
15 in the young subjects.
Changes in Renal Function with Age
10
Many studies have shown a general decline in GFR
with age. Lindeman (1992) reported that the GFR as
5 measured by creatinine clearance (see Chapter 24)
decreases at a mean rate of 1% per year after 40 years
0 of age. However, there is considerable variation in
0 4 8 12 16 20 24 28 this rate of decline in normal healthy aging adults. In
Time (hours) a previous study by Lindeman et al (1985), approxi-
FIGURE 222 Plasma concentrations (mean ± SD) of mately two-thirds of the subjects (162 of 254) had
felodipine after an oral dose during steady-state treatment
declining creatinine clearances, whereas about one-
with 5 mg twice daily in healthy subjects (n = 12) [■] and elderly
hypertensive patients (n = 1] [●]. (From Landahl et al, 1988, with third of the subjects (92 of 254) had no decrease in
permission.) creatinine clearance. Since muscle mass and urinary
Concentration (nmol/mL)
Application of Pharmacokinetics to Clinical Situations 705
creatinine excretion decrease at nearly the same rate A patient is considered obese if actual body
in the elderly, mean serum concentrations may stay weight exceeds ideal or desirable body weight by
relatively constant. Creatinine clearance measured by 20%, according to Metropolitan Life Insurance
serum creatinine concentrations only (see Chapter 24) Company data (latest published tables). Ideal or
may yield inaccurate GFR function if urinary creati- desirable body weights are based on average body
nine excretion is not measured. weights and heights for males and for females con-
sidering age. Athletes who have a greater body
EXAMPLES »» » weight due to greater muscle mass are not consid-
ered obese. Obesity often is defined by body mass
1. An elderly 85-year-old adult patient with con- index (BMI), a value that normalizes body weight
gestive heart failure has a serum creatinine of based on height. BMI is expressed as body weight
1.0 mg/dL. The 24-hour urinary creatinine excre- (kg) divided by the square of the person’s height
tion was 0.7 g. Based on the serum creatinine (meters) or kg/m2. BMI is calculated according to
only, this patient has normal renal function, the following two equations:
whereas based on both serum creatinine concen-
tration and total 24-hour urinary creatinine excre- weight (lb)
BM =
I
tion, the patient has a GFR of less than 50 mL/min.
×
2
703
height (in)
In practice, serum creatinine clearance is often
estimated from serum creatinine concentration = weight (kg)
BMI
alone for dose adjustment. In elderly subjects, the
10,000
height (cm)2
×
clinician should carefully assess the patient, since
substantial deviation from the true clearance may An extensive study on obesity has been pub-
occur in some elderly subjects. lished by the National Institutes of Health, National
2. Diflunisal pharmacokinetics was studied in Heart, Lung and Blood Institute (2003), giving five
healthy young and old subjects. After a single weight classifications based on BMI:
dose of diflunisal, the terminal plasma half-life,
mean residence time, and apparent volume of Classification BMI (kg/m2)
distribution were higher in elderly subjects than
in young adults (Erikson et al, 1989). This study Underweight <18.5
shows that renal function in elderly subjects Normal body weight 18.5–24.9
is generally reduced somewhat compared to
Overweight 25–29.9
younger patients because of a diminished rate
of glomerular filtration. Obese 30–39.9
Extreme obesity >40
DOSING THE OBESE PATIENTS BMI correlates strongly with total body fat in
nonelderly adults; it is commonly used as a surrogate
Obesity is a major problem in the United States and is for total body fat. Excess body fat increases the risk
discussed formally under specific population in of death and major comorbidities such as type 2
Chapter 23. Only simple points regarding dosing in diabetes, hypertension, dyslipidemia, cardiovascular
clinical situations are introduced below. Obesity has disease, osteoarthritis of the knee, sleep apnea, and
been associated with increased mortality resulting from some cancers. An obese patient (BMI > 30) has a
increases in the incidence of hypertension, atheroscle- greater accumulation of fat tissue than is necessary
rosis, coronary artery disease, diabetes, and other con- for normal body functions. Adipose (fat) tissue has a
ditions compared to nonobese patients (Blouin and smaller proportion of water compared to muscle tis-
Warren, 1999; National Institutes of Health, National sue. Thus, the obese patient has a smaller proportion
Heart, Lung and Blood Institute 2003). of total body water to total body weight compared to
706 Chapter 22
the patient of ideal body weight, which could affect The following equations have been used for estimat-
the apparent volume of distribution of the drug. For ing LBW, particularly for adjustment of dosage in
example, Abernethy and Greenblatt (1982) showed a renally impaired patients:
significant difference in the apparent volume of dis-
tribution of antipyrine in obese patients (0.46 L/kg) LBW(males) = 50 kg+ 2.3 kg
compared to ideal-body-weight patients (0.62 L/kg) for each inch over 5 ft (22.9)
based on actual total body weight. Ideal body weight
(IBW) refers to the appropriate or normal weight for LBW(females) = 45.5 kg+ 2.3 kg
a male or female based on age, height, weight, and or each inch over 5 ft (22.10)
frame size; ideal body weights are generally obtained
from the latest table of desirable weights for men where LBW is lean body weight.
and women compiled by the Metropolitan Life
Insurance Company. EXAMPLE »» »
BMI is not a very accurate measure of adiposity
in certain individual patients, particularly in people Calculate the lean body weight for an adult male
with elevated lean body mass, such as athletes, and patient who is 5 ft 9 in (175.3 cm) tall and weighs
in children. Other approaches have been used to 264 lb (120 kg).
predict the relationship of obesity to cardiovascular Solution
risk, such as waist circumference, waist-to-hip ratio, Using Equation 22.9,
and the waist-to-hip-to-height index (Green and LBW = 50 + (2.3 × 9) = 70.7 kg
Duffull, 2004).
In addition to differences in total body water per
kilogram body weight in the obese patient, the
greater proportion of body fat in these patients could PHARMACOKINETICS OF DRUG
lead to distributional changes in the drug’s pharmaco- INTERACTIONS
kinetics due to partitioning of the drug between lipid
and aqueous environments (Blouin and Warren, A drug interaction generally refers to a modification
1999). Drugs such as digoxin and gentamicin are of the expected drug response in the patient as a
very polar and tend to distribute into water rather than result of exposure of the patient to another drug or
into fat tissue. Although lipophilic drugs are associ- substance. Some unintentional drug interactions pro-
ated with larger volumes of distribution in obese duce adverse reactions in the patient, whereas some
patients compared to hydrophilic drugs, there are drug interactions may be intentional, to provide an
exceptions and the effect of obesity on specific drugs improved therapeutic response or to decrease adverse
must be considered for accurate dosing strategy. drug effects. Drug interactions may include drug–drug
Other pharmacokinetic parameters may be interactions, food–drug interactions, or chemical–
altered in the obese patient as a result of physiologic drug interactions, such as the interaction of a drug
alterations, such as fatty infiltration of the liver with alcohol or tobacco. A listing of food interactions
affecting biotransformation and cardiovascular is given in Chapter 14. A drug–laboratory test interac-
changes that may affect renal blood flow and renal tion pertains to an alteration in a diagnostic clinical
excretion (Abernethy and Greenblatt, 1982). laboratory test result because of the drug.
Dosing by actual body weight may result in Drug interactions may cause an alteration in the
overdosing of drugs such as aminoglycosides (eg, pharmacokinetics of the drug due to an interaction
gentamicin), which are very polar and are distributed in drug absorption, distribution, or elimination
in extracellular fluids. Dosing of these drugs is based (Tables 22-8 and 22-9). Drug interactions can also
on ideal body weight. Lean body weight (LBW) has be pharmacodynamic interactions at the receptor site
been estimated by several empirical equations based in which the competing drug potentiates or antago-
on the patient’s height and actual (total) body weight. nizes the action of the first drug. Pharmaceutical drug
Application of Pharmacokinetics to Clinical Situations 707
TABLE 228 Sources of Drug Interactions
Type of Drug
Interaction Source Example
Pharmacokinetic Absorption Drug interactions can affect the rate and the extent of systemic
drug absorption (bioavailability) from the absorption site, result-
ing in increased or decreased drug bioavailability.
Distribution Drug distribution may be altered by displacement of the drug
from plasma protein or other binding sites due to competition
for the same binding site.
Hepatic elimination Drugs that share the same drug-metabolizing enzymes have a
potential for a drug interaction.
Renal clearance Drugs that compete for active renal secretion may decrease
renal clearance of the first drug. Probenecid blocks the active
renal secretion of penicillin drugs.
Pharmacodynamic Drug receptor site Pharmacodynamic drug interactions at the receptor site in
which the competing drug potentiates or antagonizes the
action of the first drug.
Pharmaceutical Pharmaceutical interactions are An IV solution of aminophylline has an alkaline pH and should
compounding caused by a chemical or physical not be mixed with such drugs as epinephrine which decompose
incompatibility when two or more in an alkaline pH.
drugs are mixed together
interaction occurs when physical and/or chemical St. John’s wort reduces the plasma drug concentra-
incompatibilities arise during extemporaneous phar- tions of indinavir, a protease inhibitor used to treat
maceutical compounding. Pharmaceutical drug HIV infection and AIDS.
interactions, such as drug–excipient interactions, Screening for drug interactions is generally per-
are considered during the development and manu- formed whenever multiple drug products are dispensed
facture of new and generic drug products. to the patient. However, the pharmacist should ask the
The risk of a drug interaction increases with mul- patient when dispensing any medication whether the
tiple drug therapy, multiple prescribers, poor patient patient is taking over-the-counter (OTC) drugs, herbal
compliance, and patient risk factors, such as predis- supplements, or contraceptive drugs. Some patients do
posing illness (diabetes, hypertension, etc) or advanc- not realize that these products may interact with their
ing age. Multiple drug therapy has become routine in drug therapy. There are many computer programs that
most acute and chronic care settings. Elderly patients will “flag” a potential drug interaction. However, the
and patients with various predisposing illnesses tend pharmacist needs to determine the clinical significance
to be a population using multiple drug therapy. A of the interaction and whether there is an alternate drug
recent student survey found an average of 8–12 drugs or alternate dosage regimen design that will prevent the
per patient used in a group of hospital patients. drug interaction. The clinical significance of a potential
An important source of drug interactions is the drug interaction should be documented in the litera-
combination of herbal remedies (sometimes referred ture. The likelihood of a drug interaction may be clas-
to as neutraceuticals or dietary supplements) with sified as an established drug interaction, probable drug
drug therapy. Although many herbal products are safe interaction, possible drug interaction, or unlikely drug
when taken alone, many drug–herbal interactions have interaction. The dose and the duration of therapy, the
been reported (Izzo and Ernst, 2009). For example, onset (rapid, delayed), the severity (major, minor) of
St. John’s wort is an inducer of cytochrome P-450, the potential interaction, and extrapolation to related
which is involved in the metabolism of many drugs. drugs should also be considered.
708 Chapter 22
TABLE 229 Pharmacokinetic Drug Interactions
Drug Interaction Examples (Precipitant Drugs) Effect (Object Drugs)
Bioavailability
Complexation/chelation Calcium, magnesium, or Tetracycline complexes with divalent cations, causing a
aluminum and iron salts decreased bioavailability
Adsorption binding/ionic Cholestyramine resin Decreased bioavailability of thyroxine, and digoxin; binds
interaction (anionexchange resin binding) anionic drugs and reduces absorption. Some antacid may
cause HCl salt to precipitate out in stomach.
Adsorption Antacids (adsorption) Charcoal, Decreased bioavailability of antibiotics
antidiarrheals Decreased bioavailability of many drugs
Increased GI motility Laxatives, cathartics Increases GI motility, decreases bioavailability for drugs
which are absorbed slowly; may also affect the bioavail-
ability of drugs from controlled-release products
Decreased GI motility Anticholinergic agents Propantheline decreases the gastric emptying of acet-
aminophen (APAP), delaying APAP absorption from the
small intestine
Alteration of gastric pH H-2 blockers, antacids Both H-2 blockers and antacids increase gastric pH; the
dissolution of ketoconazole is reduced, causing decreased
drug absorption
Alteration of intestinal flora Antibiotics (eg, tetracyclines, Digoxin has better bioavailability after erythromycin;
penicillin) erythromycin administration reduces bacterial inactivation
of digoxin
Inhibition of drug metabo- Monoamine oxidase inhibitors Hypertensive crisis may occur in patients treated with
lism in intestinal cells (MAO-I) (eg, tranylcypromine, MAO-I and foods containing tyramine
phenelzine)
Distribution
Protein binding Warfarin–phenylbutazone Displacement of warfarin from binding
Phenytoin–valproic acid Displacement of phenytoin from binding
Hepatic Elimination
Enzyme induction Smoking (polycyclic aromatic Smoking increases theophylline clearance
hydrocarbons) Barbiturates Phenobarbital increases the metabolism of warfarin
Enzyme inhibition Cimetidine Decreased theophylline, diazepam metabolism
Mixed-function oxidase
Fluvoxamine Diazepam t1/2 longer
Quinidine Decreased nifedipine metabolism
Fluconazole Increased levels of phenytoin, warfarin
Other enzymes Monoamine oxidase inhibitors, Serious hypertensive crisis may occur following ingestion
MAO-I (eg, pargyline, tranylcy- of foods with a high content of tyramine or other pressor
promine) substances (eg, cheddar cheese, red wines)
Inhibition of biliary Verapamil Decreased biliary secretion of digoxin causing increased
secretion digoxin levels
(Continued)
Application of Pharmacokinetics to Clinical Situations 709
TABLE 229 Pharmacokinetic Drug Interactions (Continued)
Drug Interaction Examples (Precipitant Drugs) Effect (Object Drugs)
Renal Clearance
Glomerular filtration rate Methylxanthines (eg, caffeine, Increased renal blood flow and GFR will decrease time
(GFR) and renal blood flow theobromine) for reabsorption of various drugs, leading to more rapid
urinary drug excretion
Active tubular secretion Probenecid Probenecid blocks the active tubular secretion of penicillin
and some cephalosporin antibiotics
Tubular reabsorption and Antacids, sodium bicarbonate Alkalinization of the urine increases the reabsorption of
urine pH amphetamine and decreases its clearance
Alkalinization of urine pH increases the ionization of salicy-
lates, decreases reabsorption, and increases its clearance
Diet
Charcoal hamburgers Theophylline Increased elimination half-life of theophylline decreases
Terfenadine, cyclosporin due to increased metabolism
Blood levels of terfenadine and cyclosporine increase due
to decreased metabolism
Grapefruit juice Lovastatin, simvastatin, nife- Grapefruit juice is a moderate CYP3A inhibitor and
dipine increases plasma drug concentrations
Alcohol (ethanol) Acetaminophen Possible hepatotoxicity
Alcohol (ethanol) May increase or decrease absorption of many drugs
Environmental
Smoking Theophylline Cigarette smoke contains aromatic hydrocarbons that
induce cytochrome isozymes involved in metabolism of
theophylline, thereby shortening the elimination t1/2
Pharmacodynamic
Alcohol (ethanol) Antihistamines, opioids Increased drowsiness
Virus Drug Interactions
Reye’s syndrome Aspirin Aspirin in children exposed to certain viral infections such
as influenza B virus leads to Reye’s syndrome
Preferably, drugs that interact should be avoided aminotransferase (ALT), aspartate aminotransferase
or doses of each drug should be given sufficiently far (AST), or other markers of hepatic metabolism (see
apart so that the interaction is minimized. In situa- Chapter 24), should be undertaken. In general, if the
tions involving two drugs of choice that may interact, therapeutic response is predictable from serum drug
dose adjustment based on pharmacokinetic and thera- concentration, dosing at regular intervals may be
peutic considerations of one or both of the drugs may based on a steady-state concentration equation such
be necessary. Dose adjustment may be based on as Equation 22.1. When the elimination half-life is
clearance or elimination half-life of the drug. lengthened by drug interaction, the dosing interval
Assessment of the patient’s renal function, such as may be extended or the dose reduced according to
serum creatinine concentration, and liver function Equation 22.4. Some examples of pharmacokinetic
indicators, such as alkaline phosphatase, alanine drug interactions are listed in Table 22-9. A more
710 Chapter 22
complete discussion of pharmacologic and therapeu- Some examples of pharmacokinetic drug interac-
tic drug interactions of drugs is available in standard tions are discussed in more detail below and in Chapters
textbooks on clinical pharmacology. 12 and 13. Many side effects occur as a result of
Many drugs affect the cytochrome P-450 (CYP) impaired or induced (enhanced) drug metabolism.
family of hemoprotein enzymes that catalyze drug Changes in pharmacokinetics due to impaired drug
biotransformation (see also Chapters 12 and 13). metabolism should be evaluated quantitatively. For
Dr. David A. Flockhart, Indiana University School of example, acetaminophen is an OTC drug that has been
Medicine, has compiled an excellent website that used safely for decades, but incidences of severe
lists various drugs that may be substrates or inhibi- hepatic toxicity leading to coma have occurred in some
tors of cytochrome P-450 isozymes (http://medicine. subjects with impaired liver function because of chronic
iupui.edu/flockhart). Some examples of substrates of alcohol use. Drugs that have reactive intermediates,
CYPs are: active metabolites, and/or metabolites with a longer
half-life than the parent drug need to be considered
carefully if there is a potential for a drug interaction. A
CYP1A2 Amitriptyline, fluvoxamine
polar metabolite may also distribute to a smaller fluid
CYP2B6 Cyclophosphamide volume, leading to high concentration in some tissues.
CYP2C9 Ibuprofen, fluoxetine, tolbutamide, Drug interactions involving metabolism may be tempo-
amitriptyline ral, observed as a delayed effect. Temporal drug interac-
CYP2C19 Omeprazole, S-methenytoin, amitriptyline tions are more difficult to detect in a clinical situation.
CYP2D6 Propanolol, amitriptyline, fluoxetine,
paroxetine
CYP2E1 Halothane INHIBITION OF DRUG METABOLISM
CYP3A4 Erythromycin, clarithromycin, midazolam, Numerous clinical instances of severe adverse reac-
diazepam tions as a result of drug interaction involving a
CYP3A5 Clarithromycin, simvastatin, indinavir change in the rate of drug metabolism have been
reported. Knowledge of pharmacokinetics allows the
CYP3A6 Erythromycin, clarithromycin, diltiazam
clinical pharmacist to evaluate the clinical signifi-
cance of the drug interaction. Pharmacokinetic mod-
Many calcium channel blockers, macrolides, and els help determine the need for dose reduction or
protease inhibitors are substrates of CYP3A4, discontinuing a drug. In assessing the situation, the
CYP3A5, or CYP3A6. An enzyme substrate may pathophysiology of the patient and the effect of
competitively interfere with other substrates’ metabo- chronic therapy on drug disposition in the patient
lism if coadministered. Drug inducers of CYPs may must be considered. A severe drug reaction in a
also result in drug interactions by accelerating the rate patient with liver impairment has resulted in near-
of drug metabolism. When an unusually high plasma fatal reaction in subjects taking otherwise safe doses
level is observed as a result of coadministration of a of acetaminophen. In some patients with traumatic
second drug, pharmacists should check whether the injury or severe cardiovascular disease, blood flow
two drugs share a common CYP metabolic pathway. may be impaired, resulting in delayed drug absorp-
New substrates are still being discovered. For exam- tion and distribution. Many incidents of serious tox-
ple, many proton pump inhibitors are substrates of icity or accidents are caused by premature
CYP2C19, and many calcium channel blockers are administration of a “booster dose” when the expected
CYP3A4 substrates. It is important to assess the clini- response is not immediately observed. Potent drugs
cal significance with the prescriber before alarming such as morphine, midazolam, lidocaine, sodium
the patient. It is also important to suggest an alterna- thiopental, and fentanyl can result in serious adverse
tive drug therapy to the prescriber if a clinically sig- reactions if the kinetics of multiple dosing are not
nificant drug interaction is likely to be occurring. carefully assessed.
Application of Pharmacokinetics to Clinical Situations 711
EXAMPLES »» »
1. Fluvoxamine doubles the half-life of diazepam: 3. Theophylline clearance is decreased by cimetidine:
The effect of fluvoxamine on the pharmacoki- Controlled studies have shown that cimetidine
netics of diazepam was investigated in healthy can decrease theophylline plasma clearance by
volunteers (Perucca et al, 1994). Concurrent flu- 20%–40% (apparently by inhibiting demethyl-
voxamine intake increased mean peak plasma ation) (Loi et al, 1997). Prolongation of half-life
diazepam concentrations from 108 to 143 ng/mL, by as much as 70% was found in some patients.
and oral diazepam clearance was reduced from Elevated theophylline plasma concentrations
0.40 to 0.14 mL/min/kg. The half-life of diazepam with toxicity may lead to nausea, vomiting, car-
increased from 51 to 118 hours. The area under diovascular instability, and even seizure. What
the plasma concentration–time curve for the could happen to an asthmatic patient whose
diazepam metabolite N-desmethyldiazepam was meals are high in protein and low in carbohy-
also significantly increased during fluvoxamine drate, and who takes Tagamet 400 mg BID?
treatment. These data suggest that fluvoxamine (Hint: Check the effect of food on theophylline,
inhibits the biotransformation of diazepam and below.)
its active N-demethylated metabolite. 4. Interferon-β reduces metabolism of theophyl-
In this example, the dosing interval, τ, may line: Theophylline pharmacokinetics was also
be increased twofold to account for the dou- examined before and after interferon treatment
bling of elimination half-life to keep average (Okuno et al, 1993). Interferon-β treatment reduced
steady-state concentration unchanged based the activities of both O-dealkylases by 47%. The
on Equation 22.4. The rationale for this recom- total body clearance of theophylline was also
mendation may be demonstrated by sketching decreased (from 0.76 to 0.56 mL/kg/min) and its
a diagram showing how the steady-state plasma elimination half-life was increased (from 8.4 to
drug level of diazepam differs after taking 10 mg 11.7 hours; p < 0.05). This study provided the first
orally twice a day with or without taking fluvox- direct evidence that interferon-β can depress the
amine for a week. activity of drug-metabolizing enzymes in the
human liver. What percent of steady-state theoph-
1.44D0t1 2F ylline plasma concentration would be changed by
∞ /
Cav =
VDτ the interaction? (Use Equation 22.8.)
5. Torsades de pointes interaction: A life-threatening
2. Quinidine inhibits the metabolism of nifedip- ventricular arrhythmia associated with prolon-
ine and other calcium channel-blocking agents: gation of the QT interval, known as torsades de
Quinidine coadministration significantly inhib- pointes, caused the removal of the antihistamine
ited the aromatization of nifedipine to its major terfenadine (Seldane) from the market because
first-pass pyridine metabolite and prolonged of drug interactions with cisapride, astemizole,
the elimination half-life by about 40% (Schellens and ketoconazole. Clinical symptoms of torsades
et al, 1991). The interaction between quinidine de pointes include dizziness, syncope, irregular
and nifedipine supports the involvement of a heartbeat, and sudden death. The active me-
common cytochrome P-450 (P450 3A4) in the tabolite of terfenadine is not cardiac toxic and
metabolism of the two drugs. Other calcium is now marked as fexofenadine (Allegra), a non-
channel antagonists may also be affected by a sedative antihistamine.
similar interaction. What could be a potential 6. Cimetidine and diazepam interaction: The admin-
problem if two drugs metabolized by the same istration of 800 mg of cimetidine daily for 1 week
isozyme are coadministered? increased the steady-state plasma diazepam and
712 Chapter 22
with coordination, and/or fever. A complete list is
nordiazepam concentrations due to a cimetidine- posted on the FDA website, http://www.fda.gov/
induced impairment in microsomal oxidation of Drugs/DrugSafety/ucm265305.htm (accessed August
diazepam and nordiazepam. The concurrent 26, 2011).
administration of cimetidine caused a decrease
in total metabolic clearance of diazepam and its
metabolite, nordiazepam (Lima et al, 1991). How INDUCTION OF DRUG METABOLISM
would the following pharmacokinetic param-
Cytochrome P-450 isozymes are often involved in
eters of diazepam be affected by the coadminis-
the metabolic oxidation of many drugs (see
tration of cimetidine?
Chapter 12). Many drugs can stimulate the produc-
a. Area under the curve in the dose interval tion of hepatic enzymes. Therapeutic doses of phe-
(AUC0–24 h) nobarbital and other barbiturates accelerate the
b. Maximum plasma concentration (Cmax) metabolism of coumarin anticoagulants such as
c. Time to peak concentration (tp) warfarin and substantially reduce the hypoprothrom-
d. Elimination rate constant (k) binemic effect. Fatal hemorrhagic episodes can
e. Total body clearance (ClT) result when phenobarbital is withdrawn and warfarin
f. Inhibition of monoamine oxidase (MAO) dosage maintained at its previous level. Other drugs
known to induce drug metabolism include carbam-
azepine, rifampin, valproic acid, and phenytoin.
Enzymatic stimulation can shorten the elimination
INHIBITION OF MONOAMINE half-life of the affected drug. For example, pheno-
OXIDASE (MAO) barbital can result in lower levels of dexamethasone
in asthmatic patients taking both drugs. St. John’s
Nonhepatic enzymes can be involved in drug inter- wort, a herbal supplement, also induces cytochrome
actions. For example, drug interactions have been P-450 isozymes and is known to reduce plasma drug
reported for patients taking the antibacterial drug concentrations of digoxin, indinavir, and other drugs.
linezolid (Zyvox) who are concurrently taking cer-
tain psychiatric medications that work through the
serotonin system of the brain (serotonergic psychiat- INHIBITION OF DRUG ABSORPTION
ric medications). Linezolid is a reversible mono-
amine oxidase inhibitor (MAOI). Serotonergic Various drugs and dietary supplements can decrease
psychiatric medications may include antidepressant the absorption of drugs from the gastrointestinal
drugs such as citalopram, paroxetine, fluoxetine, tract. Antacids containing magnesium and aluminum
sertraline, and other drugs that affect the serotoner- hydroxide often interfere with absorption of many
gic pathway in the brain. MAOIs, such as phenelzine drugs. Coadministration of magnesium and alumi-
and isocarboxazid, are also contraindicated. Although num hydroxide caused a decrease of plasma levels of
the exact mechanism of this drug interaction is perfloxacin. The drug interaction is caused by the
unknown, linezolid inhibits the action of monoamine formation of chelate complexes and is possibly also
oxidase A—an enzyme responsible for breaking due to adsorption of the quinolone to aluminum
down serotonin in the brain. It is believed that when hydroxide gel. Perfloxacin should be given at least 2
linezolid is given to patients taking serotonergic psy- hours before the antacid to ensure sufficient thera-
chiatric medications, high levels of serotonin can peutic efficacy of the quinolone.
build up in the brain, causing toxicity. This is referred Sucralfate is an aluminum glycopyranoside
to as serotonin syndrome. Its signs and symptoms complex that is not absorbed but retards the oral
include mental changes (confusion, hyperactivity, absorption of ciprofloxacin. Sucralfate is used in the
memory problems), muscle twitching, excessive local treatment of ulcers. Cholestyramine is an
sweating, shivering or shaking, diarrhea, trouble anion-exchange resin that binds bile acid and many
Application of Pharmacokinetics to Clinical Situations 713
drugs in the gastrointestinal tract. Cholestyramine PRACTICAL FOCUS
can bind digitoxin in the GI tract and shorten the
elimination half-life of digitoxin by approximately Some drugs can change urinary pH and, thereby,
30%–40%. Absorption of thyroxine may be reduced affect the rate of excretion of weak electrolyte drugs
by 50% when it is administered closely with in the urine. Which of the following treatments
cholestyramine. would be most likely to decrease the elimination t1/2
of aspirin? Explain the rationale for your answer.
1. Calcium carbonate PO
INHIBITION OF BILIARY EXCRETION
2. Sodium carbonate PO
The interaction between digoxin and verapamil 3. IV sodium bicarbonate
(Hedman et al, 1991) was studied in six patients
(mean age 61 ± 5 years) with chronic atrial fibrilla-
tion. The effects of adding verapamil (240 mg/d) on EFFECT OF FOOD ON DRUG
steady-state plasma concentrations of digoxin were DISPOSITION
studied. Verapamil induced a 44% increase in steady-
state plasma concentrations of digoxin. The biliary Diet–Theophylline Interaction
clearance of digoxin was determined by a duodenal Theophylline disposition is influenced by diet.
perfusion technique. The biliary clearance of digoxin A protein-rich diet will increase theophylline clear-
decreased by 43%, from 187 ± 89 to 101 ± 55 mL/ ance. Average theophylline half-lives in subjects on
min, whereas the renal clearance was not signifi- a low-carbohydrate, high-protein diet increased from
cantly different (153 ± 31 vs 173 ± 51 mL/min). 5.2 to 7.6 hours when subjects were changed to a high-
carbohydrate, low-protein diet. A diet of charcoal-
broiled beef, which contains polycyclic aromatic
ALTERED RENAL REABSORPTION hydrocarbons from the charcoal, resulted in a
DUE TO CHANGING URINARY pH decrease in theophylline half-life of up to 42% when
compared to a control non-charcoal-broiled-beef
The normal adult urinary pH ranges from 4.8 to 7.5 diet. Irregular intake of vitamin K may modify the
but can increase due to chronic antacid use. This anticoagulant effect of warfarin. Many foods, espe-
change in urinary pH affects the ionization and reab- cially green, leafy vegetables such as broccoli and
sorption of weak electrolyte drugs (see Chapter 12). spinach, contain high concentrations of vitamin K.
An increased ionization of salicylate due to an In one study, warfarin therapy was interfered with
increase in urine pH reduces salicylate reabsorption inpatients receiving vitamin K, broccoli, or spinach
in the renal tubule, resulting in increased renal excre- daily for 1 week (Pedersen et al, 1991).
tion. Magnesium aluminum hydroxide gel (Maalox),
120 mL/d for 6 days, decreased serum salicylate
levels from 19.8 to 15.8 mg/dL in 6 subjects who had Grapefruit–Drug Interactions
achieved a control serum salicylate level of The ingredients in a common food product, grape-
0.10 mg/dL with the equivalent of 3.76 g/d aspirin fruit juice, taken in usual dietary quantities, can sig-
(Hansten et al, 1980). Single doses of magnesium nificantly inhibit the metabolism by gut-wall
aluminum hydroxide gel did not alter urine pH sig- cytochrome P-450 3A4 (CYP3A4) (Spence, 1997).
nificantly. Five milliliters of Titralac (calcium car- For example, grapefruit juice increases average felo-
bonate with glycine) 4 times a day or magnesium dipine levels about threefold, increases cyclosporine
hydroxide for 7 days also increased urinary pH. In levels, and increases the levels of terfenadine, a com-
general, drugs with pKa values within the urinary pH mon antihistamine. In the case of terfenadine, Spence
range are affected the most. Basic drugs tend to have (1997) reported the death of a 29-year-old man who
longer half-lives when urinary pH is increased, espe- had been taking terfenadine and drinking grapefruit
cially near its pKa. juice 2–3 times per week. Death was attributed to
714 Chapter 22
terfenadine toxicity. Grapefruit juice can also affect The resolution of the issues causing variability in
P-gp-mediated efflux of some drugs. patients allows for the development of an optimum
dosing strategy for a population, subgroup, or indi-
vidual patient. The importance of developing opti-
ADVERSE VIRAL DRUG mum dosing strategies has led to an increase in the
INTERACTIONS use of PopPK approaches in new drug development.
Recent findings have suggested that some interactions
of viruses and drugs may predispose individuals to Introduction to Bayesian Theory
specific disease outcomes (Haverkos et al, 1991). For Bayesian theory was originally developed to improve
example, Reye’s syndrome has been observed in chil- forecast accuracy by combining subjective prediction
dren who had been taking aspirin and were concur- with improvement from newly collected data. In the
rently exposed to certain viruses, including influenza diagnosis of disease, the physician may make a pre-
B virus and varicella zoster virus. The mechanism by liminary diagnosis based on symptoms and physical
which salicylates and certain viruses interact is not examination. Later, the results of laboratory tests are
clear. However, the publication of this interaction has received. The clinician then makes a new diagnostic
led to the prevention of morbidity and mortality due to forecast based on both sets of information. Bayesian
this complex interaction (Haverkos et al, 1991). theory provides a method to weigh the prior informa-
tion (eg, physical diagnosis) and new information
(eg, results from laboratory tests) to estimate a new
POPULATION PHARMACOKINETICS probability for predicting the disease.
In developing a drug dosage regimen, we assess
Population pharmacokinetics (PopPK) is the study
the patient’s medical history and then use average or
of variability in plasma drug concentrations between
population pharmacokinetic parameters appropriate
and within patient populations receiving therapeutic
for the patient’s condition to calculate the initial
doses of a drug. Traditional pharmacokinetic studies
dose. After the initial dose, plasma or serum drug
are usually performed on healthy volunteers or
concentrations are obtained from the patient that
highly selected patients, and the average behavior of
provide new information to assess the adequacy of
a group (ie, the mean plasma concentration–time
the dosage. The dosing approach of combining old
profile) is the main focus of interest. PopPK exam-
information with new involves a “feedback” process
ines the relationship of the demographic, genetic,
and is, to some degree, inherent in many dosing
pathophysiological, environmental, and other drug-
methods involving some parameter readjustment
related factors that contribute to the variability
when new serum drug concentrations become
observed in safety and efficacy of the drug. The
known. The advantage of the Bayesian approach is
PopPK approach encompasses some of the follow-
the improvement in estimating the patient’s pharma-
ing features (FDA Guidance for Industry, 1999):
cokinetic parameters based on Bayesian probability
• The collection of relevant pharmacokinetic infor- versus an ordinary least-squares-based program. An
mation in patients who are representative of the example comparing the Bayesian method with an
target population to be treated with the drug alternative method for parameter estimation from
• The identification and measurement of variability some simulated theophylline data will be shown in
during drug development and evaluation the next section. The method is particularly useful
• The explanation of variability by identifying fac- when only a few blood samples are available.
tors of demographic, pathophysiological, environ- Because of inter- and intrasubject variability, the
mental, or concomitant drug-related origin that may pharmacokinetic parameters of an individual patient
influence the pharmacokinetic behavior of a drug must be estimated from limited data in the presence
• The quantitative estimation of the magnitude of the of unknown random error (assays, etc), known
unexplained variability in the patient population covariates and variables such as clearance, weight,
Application of Pharmacokinetics to Clinical Situations 715
and disease factor, etc, and possible structural
(kinetic model) error. From the knowledge of mean Thus, the laboratory test that estimates the likeli-
population pharmacokinetic parameters and their hood ratio and the preliminary diagnostic evalu-
variability, Bayesian methods often employ a special ation are both used in determining the posterior
weighted least-squares (WLS) approach and allow probability. The results of this calculation show that
improved estimation of patient pharmacokinetic with a positive diagnosis by the physician and a
parameters when there is a lot of variation in data. positive value for the laboratory test, the probabil-
The methodology is discussed in more detail under ity that the patient actually has the disease is 84.2%.
the Bayes estimator in the next section and also
under pharmacokinetic analysis. Bayesian probability theory when applied to dos-
ing of a drug involves a given pharmacokinetic param-
eter (P) and plasma or serum drug concentration (C), as
EXAMPLE »» »
shown in Equation 22.11. The probability of a patient
with a given pharmacokinetic parameter P, taking into
After diagnosing a patient, the physician gave the
account the measured concentration, is Prob(P/C):
patient a probability of 0.4 of having a disease. The
physician then ordered a clinical laboratory test. A Prob(P) ⋅Prob(C /P)
Prob(P /C) = (22.11)
positive laboratory test value had a probability of Prob(C)
0.8 of positively identifying the disease in patients
where Prob(P) = the probability of the patient’s
with the disease (true positive) and a probability of
parameter within the assumed population distribution,
0.1 of positive identification of the disease in sub-
Prob(C/P) = the probability of measured concentra-
jects without the disease (false positive). From the
tion within the population, and Prob (C) = the uncon-
prior information (physician’s diagnosis) and cur-
ditional probability of the observed concentration.
rent patient-specific data (laboratory test), what is
the posterior probability of the patient having the
disease using the Bayesian method? EXAMPLE »» »
Solution Theophylline has a therapeutic window of 10–20
Prior probability of having the disease (positive) = 0.4 μg/mL. Serum theophylline concentrations above
Prior probability of not having the disease 20 μg/mL produce mild side effects, such as nau-
(negative) = 1 − 0.4 = 0.6 sea and insomnia; more serious side effects, such
Ratio of disease positive to disease negative = as sinus tachycardia, may occur at drug concentra-
0.4/0.6 = 2/3, or the physician’s evaluation shows a tions above 40 μg/mL; at serum concentrations
2/3 chance for the presence of the disease above 45 μg/mL, cardiac arrhythmia and seizure
The probability of the patient actually having the may occur (see Fig. 22-1). However, the probability
disease can be better evaluated by including of some side effect occurring is by no means certain.
the laboratory findings. For this same patient, the Side effects are not determined solely by plasma
probability of a positive laboratory test of 0.8 for concentration, as other known or unknown vari-
the detection of disease in positive patients (with ables (called covariates) may affect the side effect
disease) and the probability of 0.1 in negative outcome. Some patients have initial side effects
patients (without disease) are equal to a ratio of of nausea and restlessness (even at very low drug
0.8/0.1 or 8/1. This ratio is known as the likelihood concentrations) that later disappear when therapy
ratio. Combining with the prior probability of 2/3, is continued. The clinician should therefore assess
the posterior probability ratio is the probability of side effects in the patient, order
a blood sample for serum theophylline determina-
Posterior probability ratio = (2/3) (8/1) = 16/3
tion, and then estimate a combined (or posterior)
Posterior probability = 16/(16 + 3) = 84.2%
probability for side effects in the patient.
716 Chapter 22
1.0 networks using the Bayesian concept. Bayesian
0.9 results were comparable to those of an experienced
0.8 electrocardiographer (Heden et al, 1996). In pharma-
a cokinetics, Bayesian theory is applied to “feed-
0.7 b forward neural networks” for gentamicin concentration
0.6 c
predictions (Smith and Brier, 1996). A brief literature
0.5 d search of Bayesian applications revealed over 400
0.4 e therapeutic applications between 1992 and 1996.
0.3 Bayesian parameter estimations were most frequently
0.2 used for drugs with narrow therapeutic ranges, such
0.1 as the aminoglycosides, cyclosporin, digoxin, anti-
convulsants (especially phenytoin), lithium, and the-
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 ophylline. The technique has now been extended to
Prior probability cytotoxic drugs, factor VIII, and warfarin. Bayesian
FIGURE 223 Conditional probability curves relating prior methods have also been used to limit the number of
probability of toxicity to posterior probability of toxicity of STC, samples required in more conventional pharmacoki-
theophylline serum concentrations: (a) 27–28.9; (b) 23–24.9; netic studies with new drugs (Thomson and Whiting,
(c) 19–20.9; (d) 15–16.9; and (e) 11–12.9 (all STC in μg/mL). (From
Schumacher GE et al: Applying decision analysis in therapeutic 1992). The main disadvantage of Bayesian methods is
drug monitoring: using decision trees to interpret serum the subjective selection of prior probability. Therefore,
theophylline. Clin Pharm 5(4):325–333, 1986, with permission.) it is not considered to be unbiased by many statisti-
cians for drug approval purposes.
The decision process is illustrated graphically in
Fig. 22-3. The probability of initial (prior) estimation Adaptive Method or Dosing with Feedback
of side effects is plotted on the x axis, and the final In dosing drugs with narrow therapeutic ratios, an
(posterior) probability of side effects is plotted on the initial dose is calculated based on mean population
y axis for various serum theophylline concentrations. pharmacokinetic parameters. After dosing, plasma
For example, a patient was placed on theophylline drug concentrations are obtained from the patient. As
and the physician estimated the chance of side more blood samples are drawn from the patient, the
effects to be 40%, but therapeutic drug monitoring calculated individualized patient pharmacokinetic
showed a theophylline level of 27 μg/mL. A vertical parameters become increasingly more reliable. This
line of prior probability at 0.4 intersects curve a at type of approach has been referred to as adaptive or
about 0.78 or 78%. Hence, the Bayesian probability Bayesian adaptive method with feedback when a spe-
of having side effects is 78% taking both the labora- cial extended least-squares algorithm is used. Many
tory and physician assessments into consideration. ordinary least-squares (OLS) computer software
The curves (a–e in Fig. 22-3) for various theophyl- packages are available to clinical practice for param-
line concentrations are called conditional probability eter and dosage calculation (see Appendix A). Some
curves. Bayesian theory does not replace clinical software packages record medical history and provide
judgment, but it provides a quantitative tool for adjustments for weight, age, and in some cases, dis-
incorporating subjective judgment (human) with ease factors. A common approach is to estimate the
objective (laboratory assay) in making risk decisions. clearance and volume of distribution from intermittent
When complex decisions involving several variables infusion (see Chapter 6). Abbottbase Pharmacokinetic
are involved, this objective tool can be very useful. Systems (1986 and 1992) is an example of patient-
Bayesian probability is used to improve forecast- oriented software that records patient information and
ing in medicine. One example is its use in the diagno- dosing history based on 24-hour clock time. An
sis of healed myocardial infarction (HMI) from a adaptive-type algorithm is used to estimate pharmaco-
12-lead electrocardiogram (ECG) by artificial neural kinetic parameters. The average population clearance
Posterior probability
Application of Pharmacokinetics to Clinical Situations 717
and volume of distribution of drugs are used for initial The weighted least-squares function in Equation 22.14
estimates, and the program computes patient-specific was suggested by Sheiner and Beal (1982). The
Cl and VD as serum drug concentrations are entered. equation represents the least-squares estimation of
The program accounts for renal dysfunction based on the concentration by minimizing deviation squares
creatinine clearance, which is estimated from serum (first summation term of Equation 22.14), and devia-
creatinine concentration using the Cockroft–Gault tion of population parameter squares (second sum-
equation (see Chapter 24). The software package mation term). Equation 22.14 is called the Bayes
allows specific parameter estimation for digoxin, the- estimator. This approach is frequently referred to as
ophylline, and aminoglycosides, although other drugs extended least-squares (ELS).
can also be analyzed manually.
Many least-squares (LS) and weighted least- Intrasubject Ci = f (P,Xi ) + ε i
squares (WLS) algorithms are available for estimat- (22.14)
ing patient pharmacokinetic parameters. Their Intersubject P Pk = k + ηk
common objective involves estimating the parameters
2
with minimum bias and good prediction, often as 2
n (C −Cˆ S P Pˆi i) ( k − k)
evaluated by mean predictive error. The advantage of OBJBAYES = ∑ +
σ 2 ∑ 2
i=1 i ω
the Bayesian method is the ability to input known k=1 k
information into the program, so that the search for
the real pharmacokinetic parameter is more efficient For n number of drug plasma concentration data, i is
and, perhaps, more precise. For example, a drug is an index to refer to each data item, Ci is the ith con-
administered by intravenous infusion at a rate, R, to a centration, Ĉi is the ith model-estimated concentra-
patient. The drug is infused over t hours (t may be tion, and s2 is the variance of random error, ei (assay
0.5–2 hours for a typical infusion). The patient’s errors, random intrasubject variation, etc). There is a
clearance, ClT, may be estimated from plasma drug series of population parameters in the model for the
concentration taken at a known time according to a kth population parameter, P ⋅ ˆk Pk is the estimated
one-compartment model equation. Sheiner and Beal population parameter and hk is the kth parameter
(1982) simulated a set of theophylline data and esti- random error with variance of 2
ω k.
mated parameters from the data using one- and two- To compare the performance of the Bayesian
serum concentrations, assuming different variabilities. method to other methods in drug dosing, Sheiner and
These investigators tested the method with a Bayesian Beal (1982) generated some theophylline plasma
approach and with an OLS method, OBJOLS. drug concentrations based on known clearance. They
added various error levels to the data and divided the
Ci = f (P,ti )ε i (22.12) patients into groups with one and two plasma drug
samples. The two pharmacokinetic parameters used
2
n Ci Ci were based on population pharmacokinetics for the-
OBJOLS ∑ ( − )
= 2 . 3
σ 2 ( 2 1 )
i ophylline derived from the literature: (1) for P
i=1 1, a VD
of 0.5 L/kg and coefficient of variation of 32%; and
(2) for P2, clearance of 0.052 L/kg/h and coefficient
The Bayes Estimator of variation of 44%.
When the pharmacokinetic parameter, P, is esti- The data were then analyzed using the Bayesian
mated from a set of plasma drug concentration data method and a second (alternative) approach in deter-
(C mining the pharmacokinetic parameter (ClT). In the
i) having several potential sources of error with
different variance, the OLS method for parameter presence of various levels of error, the Bayesian
estimation is no longer adequate (it yields trivial approach was robust and resulted in better estima-
estimates). The intersubject variation, intrasubject tion of clearance in both the one- and two-sample
variance, and random error must be minimized groups (Fig. 22-4 and Table 22-10). The success of
properly to allow efficient parameter estimation. the Bayesian approach is due to the ability of the
718 Chapter 22
A B
(0.33)
0.16 (0.22) 0.16
0.14 0.14
0.12 0.12
0.10 0.10
0.08 0.08
0.06 0.06
0.04 0.04
0.02 0.02
0 0
0 0.04 0.08 0.12 0 0.04 0.08 0.12
True clearance (L/kg) True clearance (L/kg)
FIGURE 224 Plots of predicted clearance versus true (simulated) clearance for predictions by the Bayesian (<inline>) and
alternative (<inline>) methods. The diagonal line on each graph is the line of identity. A shows results for one-sample group;
B shows results for two-sample group. (From Sheiner and Beal, 1982, with permission.)
algorithm to minimize the total mean square terms of facilitated by response criteria defined through a first-
errors. A more precise clearance estimation will lead order (FO) Taylor series expansion. Among other
to more accurate dose estimation in the patient. computer software packages available, the NPEM2
The implementation of the Bayesian (ELS) (USC*PACK) is a nonparametric maximum expecta-
approach uses the NONMEM computer software, tion maximization method that makes no parametric
TABLE 2210 Performance of Clearance Estimation Methods
Mean Clearance Error (éSEM) as Percent of Mean Clearance
Error Absolute Error
ω ω a
Cla
V
D
Method σ σ Example 1 Example 2 Example 1 Example 2
Alternative — — –5.77 (5.8) –2.82 (3.3) 37.1 (4.5) 26.4 (2.1)
Bayesian 1 1 –1.02 (3.0) –1.08 (3.1) 22.2 (2.0)b 21.7 (2.2)b
3/2 1 –4.94 (3.4) –3.77 (3.0) 25.6 (2.3)b 23.1 (2.1)b
2/3 1 5.02 (3.2) 2.52 (3.4) 23.7 (2.2)b 23.5 (2.4)
1 3/2 0.44 (3.0) –0.26 (3.1) 22.5 (2.1)b 21.4 (2.2)b
1 2/3 –0.76 (3.0) –1.56 (3.1) 22.5 (1.9)b 21.7 (2.2)
aRatio of standard deviation of clearance (or VD) to σ used in the Bayesian method. All ratios are divided by the correct ratio so that a value of unity
signifies that the correct ratio itself was used.
bMean absolute error of Bayesian method less than that of alternative (p < 0.05).
From Sheiner and Beal (1982), with permission.
Estimated clearance (L/kg)
Estimated clearance (L/kg)
Application of Pharmacokinetics to Clinical Situations 719
assumptions about the mean and standard deviation method compared favorably with other methods
of the distribution. The program can also discover (Tables 22-11 and 22-12). The steady-state method
unrecognized subpopulations. NONMEM also fea- was also useful, but none of the methods was suffi-
tures FOEM, a first-order expectation maximization ciently accurate, probably due to other variables, such
method. Generally, finding a set of best parameter as saturation kinetics or the use of an inappropriate
estimates to describe the data involves minimizing compartment model.
the error terms; alternatively, another paradigm that Model fitting in pharmacokinetics often involves
maximizes the probability of the parameter estimates the search for a set of parameters that fits the data, a
in the distribution serves the same purpose equally situation analogous to finding a point within a large
well or better. Thus, the first-order expectation maxi- geometric space. The OLS approach of iteratively
mization (FOEM) paradigm is also available in minimizing the error terms may not be adequate
NONMEM and in other programs, such as P-PHARM when data are sparse, but are fine when sufficient
(Mentre and Gomeni, 1995). data and good initial estimates are available. The
Bayesian approach uses prior information, and, in
essence, guides the search pointer to a proximity in
Comparison of Bayes, Least-Squares, Steady- the geometric space where the estimates are more
State, and Chiou Methods likely to be found (reducing variability but increas-
For theophylline dosing, the Bayes method and others, ing subjectivity). Many algorithms use some form of
including the conventional steady-state method, were gradient- or derivative-based method; other algo-
compared by Hurley and McNeil (1988). The Bayes rithms use a variable sequential simplex method.
TABLE 2211 Pharmacokinetic Parameter Estimates (Mean ± SD)
Method Cla (L/h/kg IBW) kb(h–1) VD (L/kg IBW)
Least-squares
Day 1 0.0383 ± 0.0129 0.105 ± 0.014 0.519 ± 0.291
Final 0.0391 ± 0.0117 0.095 ± 0.064 0.511 ± 0.239
Chiou
1 0.0399 ± 0.0306
2 0.0437 ± 0.0193
3 0.0438 ± 0.0212
Steady-state clearance
0.0408 ± 0.0174
Bayesian
1 0.0421 ± 0.0143 0.081 ± 0.030 0.534 ± 0.0745
2 0.0424 ± 0.0158 0.082 ± 0.035 0.532 ± 0.0802
3 0.0408 ± 0.0182 0.078 ± 0.037 0.531 ± 0.0820
4 0.0403 ± 0.0147 0.077 ± 0.027 0.530 ± 0.0787
Final 0.0372 ± 0.0113 0.070 ± 0.026 0.536 ± 0.0741
Cl = total body clearance, k = elimination rate constant, VD = volume of distribution, IBW = ideal body weight.
aCalculated from least-squares estimates.
bCalculated by Bayesian estimates.
From Hurley and McNeil (1988), with permission.
720 Chapter 22
TABLE 2212 Predictive Accuracy at the End of fit of the model), and the parameters are effi-
of Infusion 1a ciently estimated from the model with most least-
squares programs. Traditional pharmacokinetic
Mean Mean Percent
Prediction Absolute Prediction parameter estimation is very accurate, provided that
Method Error (mg/L) Error (%) enough samples can be taken for the individual
patient. The disadvantage is that only a few rela-
Least-squares
tively homogeneous healthy subjects are included in
Day 1 –0.06 (–1.1, 0.95) 17.6 (13.4, 21.7) pharmacokinetic studies, from which dosing in dif-
Chiou ferent patients must be projected.
In the clinical setting, patients are usually less
1 0.96 (–1.7, 3.60) 36.8 (27.3, 46.3)
homogeneous; patients vary in sex, age, and body
2 –1.7 (–3.3, –0.08) 20.8 (14.1, 27.5) weight; they may have concomitant disease and
3 –1.5 (–3.7, 0.80) 27.7 (17.8, 37.5) may be receiving multiple drug treatments. Even
the diet, lifestyle, ethnicity, and geographic loca-
Bayesian
tion can differ from a selected group of “normal”
1 –0.61 (–1.7, 0.50) 18.8 (14.1, 23.6) subjects. Further, it is often not possible to take
2 –0.65 (–2.0, 0.69) 22.7 (16.3, 29.2) multiple samples from the same subject, and, there-
fore, no data are available to reflect intrasubject
3 0.16 (–1.1, 1.40) 21.7 (16.1, 27.2)
difference, so that iterative procedures for finding
4 –0.15 (–1.2, 0.96) 19.8 (15.6, 24.1) the maximum likelihood estimate can be complex
and unpredictable due to incomplete or missing
aFigures in parentheses are 95% confidence intervals.
data. However, the vital information needed about
From Hurley and McNeil (1988), with permission.
the pharmacokinetics of drugs in patients at differ-
ent stages of their disease with various therapies
can only be obtained from the same population, or
A discussion of the pharmacokinetic estimation
from a collection of pooled blood samples. The
methods was given by D’Argenio and Schumitzky
advantages of population pharmacokinetic analysis
(1979). Some common pharmacokinetic algorithms
using pooled data were reviewed by Sheiner and
for parameter estimation are (1) Newton–Raphson
Ludden (1992) and included a summary of popula-
with first and second derivatives, (2) Gauss–Newton
tion pharmacokinetics for dozens of drugs.
method, (3) Levenberg–Marquardt method, and
Pharmacokinetic analysis of pooled data of plasma
(4) Nelder–Mead simplex method. The Gauss–Newton
drug concentration from a large group of subjects
method was used in the early versions of NONLIN.
may reveal much information about the disposition
As discussed in relation to the mixed-effect models
of a drug in a population. Unlike data from an indi-
in later sections, assuming a relationship such as ClR
vidual subject collected over time, inter- and intra-
proportional to Clcr (technically called linearization)
subject variations must be considered. Both
reduces the minimum number of data necessary for
pharmacokinetic and nonpharmacokinetic factors,
parameter estimation.
such as age, weight, sex, and creatinine concentra-
tion, should be examined in the model to determine
Analysis of Population Pharmacokinetic Data the relevance to the estimation of pharmacokinetic
Traditional pharmacokinetic studies involve taking parameters.
multiple blood samples periodically over time in a The nonlinear mixed-effect model (or NONMEM)
few individual patients, and characterizing basic is so called because the model uses both fixed and
pharmacokinetic parameters such as k, VD, and Cl; random factors to describe the data. Fixed factors such
because the studies are generally well designed, as patient weight, age, gender, and creatinine clear-
there are fewer parameters than data points (ie, that ance are assumed to have no error, whereas random
provide sufficient degree of freedom to reflect lack factors include inter- and intraindividual differences.
Application of Pharmacokinetics to Clinical Situations 721
NONMEM is a statistical program written in Fortran A second approach, the first-order (FO) method,
(see Appendix A) that allows Bayesian pharmacoki- is also used but is perhaps less well understood. The
netic parameters to be estimated using an efficient estimation procedure is based on minimization of an
algorithm called the first-order (FO) method. The extended least-squares criterion, which was defined
parameters may now be estimated also with a first- through an FO Taylor series expansion of the
order conditional estimate (FOCE) algorithm. In response vector about the fixed effects and which
addition, to pharmacokinetic parameters, many exam- utilized a Newton–Raphson-like algorithm (Beal and
ples of population plasma data have been analyzed to Sheiner, 1980). This method attempts to fit the data
determine population factors. Multiplicative coeffi- and partition the unpredictable differences between
cients or parameters for patient factors may also be theoretical and observed values into random error
estimated. terms. When this model includes concomitant
NONMEM fits plasma drug concentration data effects, it is called a mixed-effect statistical model
for all subjects in the groups simultaneously and (Beal and Sheiner, 1985).
estimates the population parameter and its variance. The advantage of the FO model is that it is appli-
The parameter may be clearance and/or VD. The cable even when the amount of time–concentration
model may also test for other fixed effects on the data obtained from each individual is small,
drug due to factors such as age, weight, and creati- provided that the total number of individuals is suf-
nine clearance. ficiently large. For example, in the example cited
The model describes the observed plasma drug by Beal and Sheiner (1985), 116 plasma concentra-
concentration (Ci) in terms of a model with: tions were collected from 39 patients with various
weight, age, gender, serum creatinine, and conges-
1. Pk = fixed effect parameters, which include
tive heart failure conditions. The two-stage method
pharmacokinetic parameters or patient factor
was not suitable, but the FO method was useful for
parameters. For example, P1 is Cl, P2 is the
analyzing this set of data. With a large number of
multiplicative coefficient including creatinine
factors and only limited data, and with hidden fac-
factor, and P3 is the multiplicative coefficient
tors possibly affecting the pharmacokinetics of the
for weight.
drug, the analysis may sometimes be misleading.
2. Random effect parameters, including (a) the
Beal and Sheiner (1985) suggested that the main
variance of the structural (kinetic) parameter,
concomitant factor should be measured whenever
Pk, or intersubject variability within the popu-
possible. Several examples of population pharma-
lation, 2
ω k; and (b) the residual intrasubject
cokinetic data analysis using clinical data are listed
variance or variance due to measurement errors,
below. Typically, a computer method is used in the
fluctuations in individual parameter values, and
data analysis based on a statistical model using
all other errors not accounted for by the other
either the weighted least-squares (WLS) or the
parameters.
extended least-squares (ELS) method in estimating
There are generally two reliable and practical the parameters. In the last few years, NONMEM
approaches to population pharmacokinetic data analy- has been regularly updated and improved. Many
sis. One approach is the standard two-stage (STS) drugs have been analyzed with population pharma-
method, which estimates parameters from the plasma cokinetics to yield the information not obtainable
drug concentration data for an individual subject dur- using the traditional two-stage method (Sheiner and
ing the first stage. The estimates from all subjects are Ludden, 1992). An added feature is the develop-
then combined to obtain an estimate of the parameters ment of a population model involving both pharma-
for the population. The method is useful because cokinetics and pharmacodynamics, the so-called
unknown factors that affect the response in one population PK/PD models.
patient will not carry over and bias parameter esti- One example involving analysis of population
mates of the others. The method works well when plasma concentration data involved the drug pro-
sufficient drug concentration–time data are available. cainamide. The drug clearance of an individual in a
722 Chapter 22
group may be assumed to be affected by several fac- (1994) using Monte Carlo (random or stochastic)
tors (Whiting et al, 1986). These factors include simulations. The precision and bias of the esti-
body weight, creatinine clearance, and a clearance mated parameters were considered. The Akaike
factor P1 described in the following equation: Information Criterion and the Schwarz Criterion
lead to selection of the most appropriate model
Cl more often than does the F test, which tends to
drug j = P1 + P2(Ccreatinine j )
choose the simpler model even when the more
+ P complex model is informative. The F test is also
3(weight j )+ ηClj (22.15)
more sensitive to deficient sampling designs.
Clearance was quite robust among the different
where hClj is the intersubject error of clearance and methods and generally well estimated. Other phar-
its variance is w2
Clj. macokinetic parameters are more sensitive to
In another mixed-effect model involving the model choice, particularly the apparent elimina-
analysis of lidocaine and mexiletine, Vozeh et al tion rate constant. Prediction of concentrations is
(1984) tested age, sex, time on drug therapy, and generally more precise when a suitable model is
congestive heart failure (CHF) for effects on drug chosen.
clearance. The effects of CHF and weight on VD
were also examined. The test statistic, DELS (differ-
ence extended least-squares), was significant for Decision Analysis Involving Diagnostic Tests
CHF and moderately significant for weight on lido- Diagnostic tests may be performed to determine the
caine clearance. presence or absence of a disease. A scheme for the
Population pharmacokinetics may be analyzed predictability of a disease by a diagnostic test is
from various clinical sites. The information content shown in Table 22-13. A true positive, represented
is better when sampling is strategically designed. by a, indicates that the laboratory test correctly
Proper sampling can yield valuable information predicted the disease, whereas a false positive, rep-
about the distribution of pharmacokinetic parameters resented by b, shows that the laboratory test incor-
in a population. Pooled clinical drug concentrations rectly predicted that the patient had the disease
taken from hospital patients are generally not well when, in fact, the patient did not have the disease.
controlled and are much harder to analyze. A mixed- In contrast, a true negative, represented by d, cor-
effect model can yield valuable information about rectly gave a negative test in patients without the
various demographic and pathophysiologic factors disease, whereas a false negative, represented by c,
that may influence drug disposition in the patient incorrectly gave a negative test when, in fact, the
population. patient did have the disease.
Model Selection Criteria
CLINICAL EXAMPLE
Data analysis in pharmacokinetics frequently
selects either a monoexponential or a polyexpo- A new diagnostic test for HIV+/AIDS was developed
nential that will better describe the concentration– and tested in 5772 intravenous drug users. The
time relationship. The selection criteria for the results of this study are tabulated in Table 22-14.
better model are determined by the goodness-of- From the results in Table 22-14, a total of 2863 sub-
fit, taking into account the number of parameters jects had a positive diagnostic test for HIV+/AIDS
involved. Three common model selection criteria and 2909 subjects had a negative diagnostic test for
are (1) the Akaike Information Criterion (AIC), HIV+/AIDS. Further tests on these subjects showed
(2) the Schwarz Criterion (SC), and (3) the F test that 2967 subjects actually had HIV+/AIDS, although
(α = 0.05). The performance characteristics of 211 of these subjects had negative diagnostic test
these criteria were examined by Ludden et al results. Moreover, 107 subjects who had a positive
Application of Pharmacokinetics to Clinical Situations 723
TABLE 2213 Errors in Decision Predictability
Diagnostic Test Result
Decision Disease Present Disease Absent Totals
Accept disease Test positive Test positive
Present (True positive) a (False positive) b a + b
Reject disease Test negative Test negative
Present (False negative) c (True negative) d c + d
Totals a + c b + d a + b + c + d
TABLE 2214 Results of HIV+/AIDS Test
Diagnostic Test Result
Decision Disease Present Disease Absent Totals
Accept HIV+/AIDS present 2756 107 2863
Reject HIV+/AIDS present 211 2698 2909
Totals 2967 2805 5772
diagnostic test result did not, in fact, have HIV+/ a + d
AIDS after further tests were made. Total predictability =
a + b + c + d
1. The positive predictability of the test is the 2756+ 2698
likelihood that the test will correctly predict =
5772
the disease if the test is positive and is esti-
= 0.945 (94.5%)
mated as
a 2756 4. The sensitivity of the test is the likelihood that
Positive predictability = =
a + b 2863 a test result will be positive in a patient with the
disease and is estimated as
= 0.963 (96.3%)
a 2756
2. The negative predictability of the test is the Sensitivity = = = 0.929 (92.9%)
a + c 2967
likelihood that the patient will not have the
disease if the test is negative and is estimated 5. The specificity of the test is the likelihood that
as a test result will be negative in a patient without
the disease and is estimated as
d 2698
Negative predictability = =
c + d 2909 d 2698
Specificity = = = 0.962 (96.2%)
b + d 2805
= 0.927 (92.7%)
Analysis of the results in Table 22-14 shows that
3. The total predictability of the test is the likeli- a positive result from the new test for HIV+/AIDS will
hood that the patient will be predicted correctly only predict the disease correctly 94.5% of the time.
and is estimated as Therefore, the clinician must use other measures to
724 Chapter 22
predict whether the patient has the disease. These of a region bounded by its network of blood vessel is
other measures may include physical diagnosis of the based on the movement of drug between the blood
patient, other laboratory tests, normal incidence of the vessels and the interstitial and intracellular spaces of
disease in the patient population (in this case, intrave- the region. The conventional pharmacokinetic
nous drug users), and the experience of the clinician. approach for calculating systemic clearance and vol-
Each test has different predictive values. ume of distribution tends to average various drug
distributions together, such that the local perturba-
tions are neglected. Regional pharmacokinetics (see
REGIONAL PHARMACOKINETICS Mather, 2001, Chapter 10) supplement systemic
pharmacokinetics when inadequate information is
Pharmacokinetics is the study of the time course of provided by conventional pharmacokinetics.
drug concentrations in the body. Pharmacokinetics is Various homeostatic physiologic functions may
based generally on the time course of drug concen- be responsible for the nonequilibrium of drug con-
trations in systemic blood sampled from either a vein centrations between local tissue regions and the
or an artery. This general approach is useful as long blood. For example, most cells have an electrochemi-
as the drug concentrations in the tissues of the body cal difference across the cell membrane consisting of
are well reflected by drug concentrations in the a membrane potential of negative 70 mV inside the
blood. Clinically, the blood drug concentration may membrane relative to the outside. Moreover, regional
not be proportional to the drug concentration in tis- differences in pH normally exist within a cell. For
sues. For example, after IV bolus administration, the example, the pH within the lysosome is between 4
distributive phase is attributed to temporally differ- and 5, which could allow a basic drug to accumulate
ent changes in mixing and redistribution of drug in within the lysosome with a concentration gradient of
organs such as the lung, heart, and kidney (Upton, 400-fold to 160,000-fold over the blood. Other expla-
1990). The time course for the pharmacodynamics of nations for regional drug concentration differences
the drug may have no relationship to the time course have been reviewed by Upton (1990), who also con-
for the drug concentrations in the blood. The phar- siders that dynamic processes may be more impor-
macodynamics of the drug may be related to local tant than equilibrium processes in affecting dynamic
tissue drug levels and the status of homeostatic response. Thus, regional pharmacokinetics is another
physiologic functions. After an IV bolus dose, Upton approach in applying pharmacokinetics to pharmaco-
(1990) reported that lignocaine (lidocaine) rapidly dynamics and clinical effect.
accumulates in the spleen and kidney but is slowly
sequestered into fat. More than 30 minutes were
needed before the target-site (heart and brain) drug
levels established equilibrium with drug concentra-
Frequently Asked Questions
tions in the blood. These regional equilibrium fac-
»»What is meant by population pharmacokinetics?
tors are often masked in conventional pharmacokinetic
What advantages does population pharmacokinetics
models that assume rapid drug equilibrium. have over classical pharmacokinetics?
Regional pharmacokinetics is the study of phar-
macokinetics within a given tissue region. The tissue »»Why is it possible to estimate individual pharmaco-
region is defined as an anatomic area of the body kinetic parameters with just a few data points using
the Bayesian method?
between specified afferent and efferent blood vessels.
For example, the myocardium includes the region »»Why is pharmacokinetics important in studying drug
perfused by the coronary arterial (afferent) and the interactions?
coronary sinus (efferent) blood vessels. The selection
Application of Pharmacokinetics to Clinical Situations 725
CHAPTER SUMMARY
Successful drug therapy involves the selection of the dosing requirements than adults. Dosing of drugs in
drug, the drug product, and the development of a this population requires a thorough consideration of
dosage regiment that meets the needs of the patient. the differences in the pharmacokinetics and phar-
Often, drug dosage regimens are based on average macology of a specific drug in the preterm newborn
population pharmacokinetics. Ideally, the dosage infant, newborn infant, infant, young child, older
regimen can be developed for the individual patient child, adolescent, and the adult. Unfortunately, the
by taking into consideration the patient’s demo- pharmacokinetics and pharmacodynamics of most
graphics, genetics, pathophysiology, environmental drugs are not well known in children under 12 years
issues, possible drug–drug interactions, known vari- of age. Obesity often is defined by body mass index
ability in drug response, and other drug-related (BMI). For some drugs, dosing is based on ideal
issues. The development of Medication Therapy body weight. A drug interaction generally refers to
Management (MTM) and therapeutic drug monitor- a modification of the expected drug response in the
ing services can improve patient compliance and the patient as a result of exposure of the patient to
success of drug therapy. Drug dosage regimens may another drug or substance. Drug–drug interactions
be calculated in an individual patient based on com- may cause an alteration in the pharmacokinetics of
plete or incomplete pharmacokinetic information. the drug due to an interaction in drug absorption,
Changes in the dose and/or in the dosing interval can distribution, or elimination. Bayesian theory can
affect the C∞ ∞ ∞
max ,Cmin, and C . help determine the probability of a diagnostic test
av
Pharmacokinetics of a drug may be altered in to give accurate results. Population pharmacokinet-
special populations, such as the elderly, infants, ics (PopPK) is the study of variability in plasma
obese patients, and patients with renal or hepatic drug concentrations between and within patient
disease. Elderly patients may have several different populations receiving therapeutic doses of a drug
pathophysiologic conditions that require multiple and enables the estimate of pharmacokinetic param-
drug therapy that increases the likelihood for a drug eters from relatively sparse data obtained from study
interaction. Infants and children have different subjects.
LEARNING QUESTIONS
1. Why is it harder to titrate patients with a 4. The normal elimination half-life of cefaman-
drug whose elimination half-life is 36 hours dole is 1.49 hours and the apparent volume
compared to a drug whose elimination is of distribution (VD) is 39.2% of body weight.
6 hours? The elimination half-life for a patient with
2. Penicillin G has a volume of distribution of a creatinine clearance of 15 mL/min was
42 L/1.73 m2 and an elimination rate constant reported by Czerwinski and Pederson (1979) to
of 1.034 h–1. Calculate the maximum peak be 6.03 hours, and cefamandole’s VD is 23.75%
concentration that would be produced if the of body weight. What doses of cefamandole
drug was given intravenously at a rate of should be given to the normal and the uremic
250 mg every 6 hours for a week. patient (respectively) if the drug is admin-
3. Dicloxacillin has an elimination half-life of istered intravenously every 6 hours and the
42 minutes and a volume of distribution of desired objective is to maintain an average
20 L. Dicloxacillin is 97% protein bound. steady concentration of 2 μg/mL?
What would be the steady-state free concentra- 5. The maintenance dose of digoxin was reported to
tion of dicloxacillin if the drug was given intra- be 0.5 mg/d for a 60-kg patient with normal renal
venously at a rate of 250 mg every 6 hours? function. The half-life of digoxin is 0.95 days and
726 Chapter 22
the volume of distribution is 306 L. The bioavail- half-life for this drug is 30 hours and its appar-
ability of the digoxin tablet is 0.56. ent volume of distribution is 4 L/kg. The drug
a. Calculate the steady-state concentration of is 80% bioavailable when given orally, and the
digoxin. suggested therapeutic serum concentrations for
b. Determine whether the patient is adequately this drug range from 0.001 to 0.002 μg/mL.
dosed (effective serum digoxin concentra- a. This cardiotonic drug is commercially sup-
tion is 1–2 ng/mL). plied as 0.075-mg, 0.15-mg, and 0.30-mg
c. What is the steady-state concentration if the white, scored, compressed tablets. Using
patient is dosed with the elixir instead of these readily available tablets, what dose
the tablet? (Assume the elixir to be 100% would you recommend for this patient?
bioavailable.) b. Are there any advantages for this patient to
6. An antibiotic has an elimination half-life of give smaller doses more frequently com-
2 hours and an apparent volume of distribution pared to a higher dosage less frequently?
of 200 mL/kg. The minimum effective serum Any disadvantages?
concentration is 2 μg/mL and the minimum c. Would you suggest a loading dose for this
toxic serum concentration is 16 μg/mL. A drug? Why? What loading dose would you
physician ordered a dosage regimen of this recommend?
antibiotic to be given at 250 mg every 8 hours d. Is there a rationale for preparing a con-
by repetitive intravenous bolus injections. trolled-release product of this drug?
a. Comment on the appropriateness of this dos- 11. The dose of sulfisoxazole (Gantrisin, Roche)
age regimen for an adult male patient recommended for an adult female patient (age
(23 years, 80 kg) whose creatinine clearance 26 years, 63 kg) with a urinary tract infec-
is 122 mL/min. tion was 1.5 g every 4 hours. The drug is 85%
b. Would you suggest an alternative dosage bound to serum proteins. The elimination half-
regimen for this patient? Give your reasons life of this drug is 6 hours and the apparent
and suggest an alternative dosage regimen. volume of distribution is 1.3 L/kg. Sulfisoxa-
7. Gentamycin (Garamycin, Schering) is a highly zole is 100% bioavailable.
water-soluble drug. The dosage of this drug in a. Calculate the steady-state plasma concentra-
obese patients should be based on an estimate of tion of sulfisoxazole in this patient.
the lean body mass or ideal body weight. Why? b. Calculate an appropriate loading dose of
8. Why is the calculation for the loading dose sulfisoxazole for this patient.
(DL) for a drug based on the apparent volume c. Gantrisin (sulfisoxazole) is supplied in
of distribution, whereas the calculation of the tablets containing 0.5 g of drug. How many
maintenance dose is based on the elimination tablets would you recommend for the load-
rate constant? ing dose?
9. A potent drug with a narrow therapeutic index d. If no loading dose was given, how long would
is ordered for a patient. After making rounds, it take to achieve 95%–99% of steady state?
the attending physician observes that the 12. The desired plasma level for an antiarrhythmic
patient is not responding to drug therapy and agent is 5 μg/mL. The drug has an apparent
orders a single plasma-level measurement. volume of distribution of 173 mL/kg and an
Comment briefly on the value of measuring the elimination half-life of 2 hours. The kinetics of
drug concentration in a single blood sample the drug follow the kinetics of a one-compart-
and on the usefulness of the information that ment open model.
may be gained. a. An adult male patient (75 kg, 56 years of
10. Calculate an oral dosage regimen for a cardio- age) is to be given an IV injection of this
tonic drug for an adult male (63 years old, 68 kg) drug. What loading dose (DL) and infusion
with normal renal function. The elimination rate (R) would you suggest?
Application of Pharmacokinetics to Clinical Situations 727
b. The patient did not respond very well to drug
Drug A Drug B Drug C
therapy. Plasma levels of drug were mea-
sured and found to be 2 μg/mL. How would Rate of infusion 10 20 15
you readjust the infusion rate to increase the (mg/h)
plasma drug level to the desired 5 μg/mL? k (h–1) 0.5 0.1 0.05
c. How long would it take to achieve 95%
Cl (L/h) 5 20 5
of steady-state plasma drug levels in this
patient assuming no loading dose was given
and the apparent VD was unaltered? 16. The effect of repetitive administration of
13. An antibiotic is to be given to an adult male phenytoin (PHT) on the single-dose pharmaco-
patient (75 kg, 58 years of age) by intravenous kinetics of primidone (PRM) was investigated
infusion. The elimination half-life for this drug by Sato et al (1992) in three healthy male
is 8 hours and the apparent volume of distribu- subjects. The peak concentration of unchanged
tion is 1.5 L/kg. The drug is supplied in 30-mL PRM was achieved at 12 and 8 hours after the
ampules at a concentration of 15 mg/mL. The administration of PRM in the absence and the
desired steady-state serum concentration for presence of PHT, respectively. The elimination
this antibiotic is 20 mg/mL. half-life of PRM was decreased from 19.4 ±
a. What infusion rate (R) would you suggest 2.2 (mean ± SE) to 10.2 ± 5.1 hours (p < 0.05),
for this patient? and the total body clearance was increased
b. What loading dose would you suggest for from 24.6 ± 3.1 to 45.1 ± 5.1 mL/h/kg (p <
this patient? 0.01) in the presence of PHT. No significant
c. If the manufacturer suggests a starting infu- change was observed for the apparent volume
sion rate of 0.2 mL/h/kg of body weight, of distribution between the two treatments.
what is the expected steady-state serum Based on pharmacokinetics of the two drugs,
concentration in this patient? what are the possible reasons for phenytoin
d. You would like to verify that this patient to reduce primidone elimination half-life and
received the proper infusion rate. At what increase its renal clearance?
time after the start of the IV infusion would 17. Itraconazole (Sporanox, Janssen) is a lipophilic
you take a blood sample to monitor the drug with extensive lipid distribution. The
serum antibiotic concentration? Why? drug levels in fatty tissue and organs contain
e. Assume that the serum antibiotic concentra- 2–20 times the drug levels in the plasma. Little
tion was measured and found to be higher or no drug was found in the saliva and in the
than anticipated. What reasons, based on cerebrospinal fluid, and the half-life is 64 ±
sound pharmacokinetic principles, would 32 hours. The drug is 99.8% bound. How do
account for this situation? (a) plasma drug–protein binding, (b) tissue
14. Nomograms are frequently used in lieu of drug distribution, and (c) lipid tissue partition-
pharmacokinetic calculations to determine an ing contribute to the long elimination half-life
appropriate drug dosage regimen for a patient. for itraconazole?
Discuss the advantages and disadvantages for 18. JL (29-year-old man, 180 kg) received oral
using nomograms to calculate a drug dosage ofloxacin 400 mg twice a day for presumed
regimen. bronchitis due to Streptococcus pneumoniae.
15. Based on the following pharmacokinetic data His other medications were the following:
for drugs A, B, and C: (a) Which drug takes the 400 mg cimetidine, orally, 3 times a day;
longest time to reach steady state? (b) Which 400 mg metronidazole, as directed. JL was still
drug would achieve the highest steady-state having a fever of 100.1°C a day after taking
drug concentration? (c) Which drug has the the quinolone antibiotic. Comment on any
largest apparent volume of distribution? appropriate action.
728 Chapter 22
ANSWERS
Frequently Asked Questions demographic sector are more reflective of the dis-
ease states and pharmacogenetics of the patients
Can therapeutic drug monitoring be performed with- treated. Population pharmacokinetics allow data
out taking blood samples? from previous patients to be used in addition to
• Therapeutic drug monitoring (TDM) may be per- the limited blood sample from the individual
formed by sampling other biologic fluids, such patient. The type of information obtained is less
as saliva or, when available, tissue or ear flu- constrained and is sometimes dependent on the
ids. However, the sample must be correlated to model and algorithm used for analysis. However,
blood or special tissue level. Urinary drug con- many successful examples have been reported in
centrations generally are not reliable. Saliva is the literature.
considered an ultrafiltrate of plasma and does Why is it possible to estimate individual pharmaco-
not contain significant albumin. Saliva drug con- kinetic parameters with just a few data points using
centrations represent free plasma drug levels and the Bayesian method?
have been used with limited success to monitor
some drugs. • With the Bayesian approach, the estimates of
Pharmacodynamic endpoints such as prothrombin patient parameters are constrained more narrow-
clotting time for warfarin, blood glucose concen- ly, to allow easier parameter estimation based on
trations for antidiabetic drugs, blood pressure for information provided from the population. The
antihypertensive drugs, and other clinical observa- information is then combined with one or more
tions are useful indications that the drug is dosed serum concentrations from the patient to obtain a
correctly. set of final patient parameters (generally Cl and
VD). When no serum sample is taken, the Bayesian
What are the major considerations in therapeutic approach is reduced to a priori model using only
drug monitoring? population parameters.
• The major considerations in TDM include the Why is pharmacokinetics important in studying drug
pathophysiology of the patient, the blood sample interactions?
collection, and the data analysis. Clinical assess-
ment of patient history, drug interaction, and • Pharmacokinetics provides a means of study-
demographic factors are all part of a successful ing whether an unusual drug action is related to
program for therapeutic drug monitoring. pharmacokinetic factors, such as drug disposition,
distribution, or binding, or is related to pharma-
What is meant by population pharmacokinetics? codynamic interaction, such as a difference in
What advantages does population pharmacokinetics receptor sensitivity, drug tolerance, or some other
have over classical pharmacokinetics? reason. Many drug interactions involving enzyme
• Most pharmacokinetic models require well- inhibition, stimulation, and protein binding were
controlled studies in which many blood samples discovered as a result of pharmacokinetic, pharma-
are taken from each subject and the pharmacoki- cogenetic, and pharmacodynamic investigations.
netic parameters estimated. In patient care situ-
ations, only a limited number of blood samples Learning Questions
is collected, which does not allow for the com-
plete determination of the drug’s pharmacoki- 1. Steady-state drug concentrations are achieved
netic profile in the individual patient. However, in approximately 5 half-lives. For a drug
the data from blood samples taken from a large with a half-life of 36 hours, steady-state drug
Application of Pharmacokinetics to Clinical Situations 729
concentrations are achieved in approximately 5. a.
180 hours (or 7.5 days). Thus, dose adjustment Dose = 0.5×106 ng
in patients is difficult for drugs with very long (1.44)(DFt )
C∞ = 1/2
half-lives. In contrast, steady-state drug concen- av VDτ
trations are achieved in approximately 20–30
(1.44)(0.5×106 )(0.56)(0.95)
hours (or 1 day) for drugs whose half-lives are =
(306,000)(1)
4–6 hours.
= 1.25 ng/mL
D b. The patient is adequately dosed.
2. C∞ 0 1
max =
V (1− e−kτ ) c. F = 1; using the above equation, the C ∞ is
D av
2.2 ng/mL; although still effective, the C ∞
av
250,000 1
C∞ will be closer to the toxic serum concentra-
max =
42,000 (1− e−(6)(1.034) )
tion of 3 ng/mL.
250,000 1 6. The ClCr for this patient shows normal kidney
C∞
max = ( ) = 5.96 µg/mL
42,000 0.998 function.
t 2 h k 0.693/2 0.3465 h 1
1/2 = = = −
At steady state, the peak concentration of peni- VD = 0.2 L/kg×80 kg = 16 L
cillin G will be 5.96 μg/mL.
a. D
D 250,000 0 /V∞ D 250/16
Cmax = = = 16.68 mg/L
3. C∞
av = = = 2.10 µg/mL 1− e−kτ 1− e−(0.3465)(8)
kVDτ (0.99)(20,000)(6)
C∞ = C∞ e−kτ = −(0.3465)(8)
min max 16.68e = 1.04 mg/L
Free drug concentration at steady state = 2.10
The dosage regimen of 250 mg every 8
(1 − 0.97) = 0.063 μg/mL.
hours gives a C∞ above 16 mg/L and a C∞
max min
below 2 mg/L. Therefore, this dosage regi-
4. C∞ 1.44D0Ft= 1/2
av VDτ men is not correct.
b. Several trials might be necessary to obtain a
For the Normal Patient: more optimal dosing regimen. One approach
is to change the dosage interval, t, to 6 hours
VD = (0.392)(1)(1000) = 392 mL/kg and to calculate the dose, D0:
∞ (1.44)(D0)(1)(1.49) D ∞
C 0 = CmaxVD(1− e−kτ )
av = = 2 µg/mL
(392)(6) = (16)(16)(1− e−(0.3465)(6)) = 224 mg
(392)(6)(2) C∞ = C∞ e−kτ = 16e−(0.3465)(6)
min max = 2 mg/L
D0 = = 2192 µg/kg = 2.2 mg/kg
(1.44)(1.49)
A dose of 224 mg given every 6 hours should
achieve the desired drug concentrations.
For the Uremic Patient:
10. Assume desired C∞
av = 0.0015 µg/mL and
τ = 24 h.
VD = (23.75)(1)(1000) = 237.5 mL/kg
FD 1.44t
C∞ 0 1/2
(1.44)(D )(1)(6.03) av =
V
C∞ 0 Dτ
av = = 2 µg/mL
(237.5)(6) C∞
avVDτ
D0 =
(2)(237.5)(6) F1.44t1/2
D0 = = 328.2 µg/mL
(1.44)(6.03) (0.0015)(4)(68)(24)
D0 = = 0.283 mg
= (0.80)(1.44)(30)
0.3 mg/kg
Give 0.283 mg every 24 hours.
730 Chapter 22
a. For a dosage regimen of one 0.30-mg tablet d. The time to achieve 95%–99% of steady
daily state is, approximately, 5t1/2 without a load-
ing dose. Therefore,
(0.80)(0.3)(1.44)(30)
C∞
av = = 0.0016 µg/mL
5× 6 = 30 h
(4)(68)(24)
which is within the therapeutic window. R
12. a. C
b. A dosage regimen of 0.15 mg every 12 hours ss = R = CsskVkV D
D
would provide smaller fluctuations between
C∞ and C∞ ompared to a dosage regimen 0.693
max min c R = (5) (0.173)(75) 22.479 mg/h
of 0.30 mg every 24 hours. 2
=
c. Since the elimination half-life is long DL = CssVD = (5)(0.173)(75) = 64.875 mg
(30 hours), a loading dose is advisable.
R
1 old Rnew
=
DL =
Dm C
1− e−kτ ss, old Css, new
b.
1 22.479 Rnew
D = Rnew = 56.2 mg/h
L =
0.30 − 2 5
e−(0.693/30)(24) = 0.70 mg
1
c. 4.32t1/2 = 4.32 (2) = 8.64 h
For cardiotonic drugs related to the digitalis
glycosides, it is recommended that the 13. t1/2 = 8 h k = 0.693/8 = 0.0866 h−1
loading dose be administered in several
portions with approximately half the total VD = (1.5 L/kg) (75 kg) = 112.5 L
as the first dose. Additional fractions may
be given at 6- to 8-hour intervals, with Css = 20 µg/mL
careful assessment of the clinical response
before each additional dose. a. R = CssVD = (20)(0.0866)(112.5)
d. There is no rationale for a controlled-
= 194.85 mg/h
release drug product because of the long
elimination half-life of 30 hours inherent in
the drug. b. DL = CssVD = (20) (112.5) = 2250 mg
Alternatively, DL = R/k = 194.85/0.0866 =
2250 mg
∞ FD 1.44t
11. a. C = 0 1/2
av VDτ c. 0.2 mL of a 15-mg/mL solution contains 3 mg.
∞ (1500)(1.44)(6)
C R = 3 mg/h/kg× 75 kg = 225 mg/h
av = = 39.6 µg/mL
(1.3)(63)(4)
R 225
Css = = = 23.1mg/L
1 kVD (0.0866)(112.5)
b. D = D
L M ( − τ
1− e k )
The proposed starting infusion rate given by
c. A DL of 4.05 g is needed, which is equiva- the manufacturer should provide adequate
lent to 8 tablets containing 0.5 g each. drug concentrations.
Application of Pharmacokinetics to Clinical Situations 731
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Application of Pharmaco-
23 kinetics to Specific
Populations: Geriatric,
Obese, and Pediatric Patients
S.W. Johnny Lau*, Lily K. Cheung, and
Diana Shu-Lian Chow
SPECIFIC AND SPECIAL POPULATIONS
The biggest issue in PK/PD and drug therapy is variability in
response. Variability factors that affect pharmacokinetics and phar-
macodynamics influence clinical trials and dose regimen designs.
Early in drug development, the term “pharmacokinetics in disease
states” was used to describe disease factors that affect PK. This
term is concise but proved inadequate in the regulatory and clinical
environment. The term “population” pharmacokinetics was then
used to emphasize that the PD response can be quite different
dependent on the demographic of the subjects. In the clinical trial
and labeling environment, the term “specific populations” may be
used to convey important specific medical conditions such as can-
cer or other pathophysiologic conditions that greatly influence the
patient’s outcome. The terms “specific” and “special” have been
used in different occasions referring to different subject popula-
tions or patient conditions.
A population approach refers to the many factors that influ-
ence PK/PD as both intrinsic and extrinsic. Some of these factors
were also discussed in Chapter 22. For example, PK differences in
systemic exposure as a result of changes in age, gender, racial,
weight, height, disease, genetic polymorphism, and organ impair-
ment are well known clinically. These influences may be summa-
rized as intrinsic factors.
Extrinsic factors summarize information associated with the
patient environment. Extrinsic factors are quite numerous and
diverse. Details are discussed in International Conference on
Harmonisation (ICH–E5, http://ich.org/) for clinical trials and
evaluations. Some examples that are referenced in this guidance
include the medical environment, use of other drugs (interaction),
tobacco, alcohol, and food habits.
*Disclaimer: The geriatric section of this chapter reects the views and opinions
of this author and does not represent the views and opinions of the Food and Drug
Administration. This author declares no conict of interest.
735
736 Chapter 23
The term “specific populations” in this chapter is aged 65 and over will be 88.5 million, more than
conveniently chosen to refer to populations that have double the population estimate of 40.2 million in 2010
important differences in pharmacokinetics due to age (U.S. Census Bureau, 2010). Figure 23.1-1 shows the
(pediatric, young adult, and elderly patients) or weight age distribution of the US population in the next 4
(obesity). Additional alterations in pharmacokinetics decades (U.S. Census Bureau, 2010).
may occur due to renal impairment, hepatic impair- This aging phenomenon is consistent with that of
ment (Chapter 24), pregnancy, various pathophysio- other countries like Canada, Denmark, France,
logic conditions, and drug–drug interactions discussed Germany, Italy, Japan, and the United Kingdom
elsewhere. (Christensen et al, 2009). Figure 23.1-2 shows the age
This chapter focuses on three specific popula- distribution of the German population in the next 4
tions, which are divided into the following modules: decades (Christensen et al, 2009).
Aging is a complex and multifactorial process
Module I Application of Pharmacokinetics to
that is an outcome of the accumulation of various
the Geriatric Patients
functional deficits of multiorgan systems occurring
Module II Application of Pharmacokinetics to
over time at varying rates. No reliable biological
the Obese Patients
marker for aging currently exists despite numerous
Modula III Application of Pharmacokinetics to
research efforts. We rely on the chronological age to
the Pediatric Patients
stratify the aging population. Due to the expected
increase in the aging population, it may be advisable
to divide the older population into 3 subgroups:
MODULE I: APPLICATION OF young-old, age 65–75 years; old, age 75–85 years;
PHARMACOKINETICS TO THE and old-old, age ≥85 years, to better understand the
processes and changes of aging as well as its impact
GERIATRIC PATIENTS on drug therapy (Klotz, 2008).
Objectives Drug therapy is an important medical interven-
tion for the care of older patients. Persons aged 65
• List the demographic changes in the coming decades. and older are the most medicated group of patients
• Describe the effects of age on pharmacokinetics in and receive the highest proportion of medications
older adults. (Schwartz and Abernethy, 2009). Older patients usu-
• Describe the effects of age on pharmacodynamics ally have more disease burden and thus take multiple
in older adults. drug therapies that result in polypharmacy.
• Describe the confounders of pharmacokinetics and Polypharmacy is commonly defined as the use of
pharmacodynamics in older adults. multiple medications or the use of a medication that
• Describe the emerging approaches to avoid adverse is not indicated (Bushardt et al, 2008). Polypharmacy
drug events in older adults. can cause multiple drug interactions and results in
• Describe the measures to help older adults adhere adverse drug events (Hilmer and Gnjidic, 2009).
to taking their medications. Underrepresentation of the older population in
• Describe the emerging methods to study pharma- clinical trials is very common across multiple thera-
cology in older adults. peutic areas such as cancer, dementia, epilepsy,
incontinence, transplantation, and cardiovascular
disease. This underrepresentation phenomenon is
Demographic Changes in the also common to the pharmacokinetic and pharmaco-
Coming Decades dynamic trials (Chien and Ho, 2011; Mangoni et al,
The age group of 65 and over will be the fastest 2013). Understanding the effect of aging on pharma-
growing segment of the population in the United States cokinetics and pharmacodynamics is important since
for the next 4 decades due primarily to the migration of it can help maximize the therapeutic effects and
the Baby Boom generation into this age group. In 2050, minimize the adverse effects of medications for bet-
the projected number of people in the United States ter care of older patients.
Application of Pharmaco kinetics to Specific Populations: Geriatric, Obese, and Pediatric Patients 737
Male Age Female
100+
2010
95 2030
2050
90
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
5
0
3 2 1 0 0 1 2 3
Millions Millions
FIGURE 23.11 Age and sex structure of the population for the United States: 2010, 2030, and 2050. (U.S Census Bureau)
Effects of Age on Pharmacokinetics absorption upon oral administration does not appear
in Older Adults to alter in advancing age especially for drugs that
show passive diffusion-mediated absorption
Drug Absorption
(Schwartz, 2007; Klotz, 2009).
Gastrointestinal. The most common route of drug
administration is oral. Aging results in many Transdermal. The transdermal route of drug
physiological changes in the gastrointestinal tract delivery has good potential for application in older
such as increased gastric pH, delayed gastric patients since it is simple to use by the patients or
emptying, decreased splanchnic blood flow, their caregivers and may reduce adverse effects
decreased absorption surface, and decreased especially for the management of pain and
gastrointestinal motility. Despite these changes, drug neurological conditions that require sustained
738 Chapter 23
1956 2006 2050
95
80
65
50
35
15
0
750 500 250 0 0 250 500 750 750 500 250 0 0 250 500 750 750 500 250 0 0 250 500 750
Population (in 1000) Population (in 1000) Population (in 1000)
FIGURE 23.12 Population pyramids for Germany in 1956, 2006, and 2050. Horizontal bars are proportional to number of
men (grey) and women (green). Data for 2050 are based on the German Federal Statistical Office’s 1-W1 scenario, which assumes a
roughly constant total fertility rate of 1.4, yearly net migration of 100,000 and life expectancy in 2050 reaching 83.5 years for men
and 88.0 years for women. (Christensen et al, 2009)
effective plasma drug concentrations. Age-related passage across the capillary endothelium. Polypeptides
changes in hydration and lipids result in increased of less than about 5000 g/mole primarily pass through
barrier function of the stratum corneum for relatively the capillary pathway, whereas those of greater than
hydrophilic compounds. Highly lipophilic chemicals about 20,000 g/mole primarily enter blood via the
may be able to dissolve readily into the stratum lymphatic pathway (Rowland and Tozer, 2011). The
corneum even when the available lipid medium is skin blood supply and lymphatic drainage change
reduced. No significant differences in absorption of with age (Ryan, 2004). Thus, subcutaneous absorption
drugs from transdermal delivery systems appear to of drugs may be affected with aging and has clinical
exist between young and old individuals (Kaestli consequences. The subcutaneous route is of particular
et al, 2008). Transdermal absorption of fentanyl was interest since it is the most common route of
suggested to be reduced in the older patients resulting administration for therapeutic peptides and proteins,
in dose adjustments, whereas transdermal absorption which become increasingly important in the
of buprenorphine is little affected because of age therapeutic arena.
(Vadivelu and Hines, 2008). Nevertheless, more
research is necessary to better understand how age- Pulmonary. Lung anatomy and physiology change
related changes in skin may affect transdermal drug with age. Older individuals show a decrease of the
absorption. alveolar surface, a variation of lung elasticity, a
decrease of the alveolar capillary volume combined
Subcutaneous. Subcutaneous drug absorption is with a decline of the ventilation/perfusion ratio, a
through the vascular capillaries and lymphatic decrease of the pulmonary diffusion capacity for
channels. Molecular size primarily determines the carbon monoxide, and an increase of the pulmonary
Age (years)
Application of Pharmaco kinetics to Specific Populations: Geriatric, Obese, and Pediatric Patients 739
residual volume. Thus, age is an important parameter 1999). Human and rabbit eyes are very similar; their
that affects the pharmacokinetics of inhaled drugs anatomical and physiological differences are well
(Siekmeier and Scheuch, 2008). documented (Francoeur et al, 1983). Choroidal
In a study of young (18–45 years of age) and thickness becomes thinner with older age, whereas
older (over 65 years) patients with type 2 diabetes, Bruch’s membrane thickens with older age in
absorption was comparable among the 2 groups fol- humans. Thickness changes of choroid and Bruch’s
lowing a single inhalation of insulin but the older membrane may affect drug permeability from
patients had less glucose reduction suggesting the subconjunctiva or episcleral space into the retina and
need for higher doses in the older patients. There the vitreous (Kuno and Fujii, 2011). More research
were no statistically significant differences for the is necessary for better ocular drug delivery in older
mean insulin AUC and Cmax values between the young patients who suffer from age-related macular
and older patients (Henry et al, 2003). To the contrary, degeneration, cataract, glaucoma, and diabetic
the concentrations of isoflurane and sevoflurane retinopathy (Harvey, 2003).
(inhalation anesthetic drugs) necessary to maintain
adequate depth of anesthesia are less in older age Drug Distribution
(Matsuura et al, 2009). Factors such as plasma protein concentration, body
There has been very little research for the phar- composition, blood flow, tissue-protein concentra-
macokinetic and pharmacodynamic characteristics tion, and tissue fluid pH are important for drug dis-
of new inhaled drugs in older patients and the tribution. Of these factors, the changes in plasma
effects of lung aging and copathologies are not protein concentration and in body composition are
known, particularly in the very old. Moreover, dec- the two major factors of aging on drug distribution
rements in cognition, praxis, and executive function (Mayersohn, 1994).
that are highly prevalent in frail older individuals Albumin and α1-acid glycoprotein are the major
have a profoundly detrimental effect on inhaler drug binding proteins in plasma (see Chapter 11). In
technique. Thus, it is likely that a large proportion general, the blood albumin concentration is about
of older patients may be unable to use drugs tar- 10% lower in older people but α1-acid glycoprotein
geted for alveolar absorption because accurate and is higher in older people (McLean and Le Couteur,
reliable inhalation performance may not be achiev- 2004). These changes in plasma proteins are gener-
able. However, cognitively intact older individuals ally not due to aging itself but to the pathophysiolog-
with good neurological, pulmonary, and musculo- ical changes or disease states that may occur more
skeletal performance may be able to use inhaled frequently in older patients. Also these changes in
treatments in the same manner as younger individu- plasma proteins may not affect the clinical exposure
als (Allen, 2008). of a patient to a drug. Thus, no adjustments in dosing
regimens may be necessary in general except in rare
Intramuscular. The intramuscular drug absorption is case of a drug with a high extraction ratio and nar-
very similar to the subcutaneous drug absorption row therapeutic index that is parenterally adminis-
(Rowland and Tozer, 2011). Intramuscular absorption tered such as intravenous dosing of lidocaine or,
of the two benzodiazepines, diazepam and midazolam, rarer, a drug with a narrow therapeutic index that is
does not appear to alter with older age (Divoll et al, administered orally and has a very rapid pharmaco-
1988; Holazo et al, 1988). However, the effect of kinetic–pharmacodynamic equilibration time (Benet
advancing age on the absorption of drugs upon and Hoener, 2002).
intramuscular administration in older patients has not In contrast to plasma protein binding, we know
been adequately evaluated. little about the binding processes of drugs with tissues
and their responses to aging. This phenomenon may
Ocular. Cornea shows decreases in permeability to a be due to the experimental difficulty to measure tissue
variety of compounds with different physicochemical binding in vitro without disrupting the integrity of the
properties between young and old rabbits (Ke et al, tissue and its protein content (Mayersohn, 1994).
740 Chapter 23
With advancing age, the decrease in lean body isozymes are CYP3A, CYP2D6, CYP2C9,
mass includes a decrease in total body water. The total CYP2C19, CYP1A2, CYP2B6, and CYP2E1.
body water for an 80-year-old is 10%–20% lower than In vitro data showed that the content and activi-
a 20-year-old (Vestal, 1997; Beaufrère and Morio, ties of various CYP isozymes from liver microsomal
2000). Thus, the distribution volume of hydrophilic preparations did not decline with advancing age in
drugs such as digoxin, theophylline, and aminoglyco- the range of 10–85 years (Parkinson et al, 2004).
sides will decrease with aging (Shi and Klotz, 2011). Figure 23.1-3 shows the effects of age on CYP
With advancing age, in contrast, body fat is activities in vitro from nearly 150 samples of human
18%–36% higher in men and 33%–45% higher in liver microsomes (Parkinson et al, 2004). The sam-
women (Vestal, 1997; Beaufrère and Morio, 2000). ples represent 3 age groups, namely, <20 years,
This increase in body fat may provide partial expla- 20–60 years, and 60+ years. The liver microsomal
nation for the increase in volume of distribution for CYP activity is highly variable but not significantly
lipophilic drugs such as benzodiazepines (Greenblatt different in the CYP activities between the age group
et al, 1991). Thus, plasma drug concentrations will of 20–60 years and the age group of 60+ years
decrease with equivalent doses in the absence of (Parkinson et al, 2004).
changes in drug elimination. Hepatic drug clearance via CYP metabolism
Assuming that the therapeutic goal is to achieve that is studied for many drugs in older individuals
the same plasma drug concentration in the older is either unchanged or modestly decreased with
patient, the changes in volume of distribution of a reductions in clearance reported to be in the range
drug will only be relevant for drugs that are admin- of 10%–40%. These data usually originate from the
istered as single doses or for determining the loading young-old and old individuals, who were generally
doses of drugs in which the use of a loading dose is in good health. The clearance of two CYP3A sub-
appropriate. For safety concerns, the loading doses strates, amlodipine and erythromycin, was evalu-
of drugs or drugs for one-time use should generally ated in the old and old-old frail as well as nursing
be lower in older patients than younger patients. home patients and was not changed compared to
Thus, weight-based loading regimens should be rou- younger individuals in these patient groups (Kang
tinely used (Schwartz, 2007). et al, 2006; Schwartz, 2006). However, a study of
old-old patients and nursing home residents showed
Hepatic and Extrahepatic Drug Metabolism that the oral clearance of atorvastatin, a CYP3A
substrate, decreased in men (Schwartz and Verotta,
Human liver, gastrointestinal tract, kidneys, lung,
2009). A more recent study identified age as a sig-
and skin contain quantitatively important amounts of
nificant factor in predicting the concentrations of
enzymes for drug metabolism. However, almost all
atorvastatin for patients up to 86 years of age and
organs have some metabolic activity. In vivo drug
recommended dose reduction (DeGorter et al,
metabolism usually consists of two processes,
2013). These observations are consistent with early
namely, the degradative and synthetic processes
pharmacokinetic studies that old age was associ-
(also known as the Phase I and Phase II metabolism,
ated with increased exposure of atorvastatin
respectively). Phase I metabolism is catalyzed by
(Gibson et al, 1996).
membrane-bound enzymes in the endoplasmic retic-
Phase II drug metabolism does not seem to
ulum and Phase II metabolism occurs primarily in
change with age based on the following studied reac-
the cytosol, with the exception of the UDP-
tions and prototype substrates (Benedetti et al, 2007):
glucuronosyltransferases that are also bound to the
endoplasmic reticulum membranes. Phase I metabo- • Glucuronidation—lorazepam, oxazepam, and
lism is primarily catalyzed by enzymes of the cyto- acetaminophen
chrome P450 monoxygenase system (CYP450), and • Sulfation—acetaminophen
the key members in this family of drug-metabolizing • Acetylation—isoniazid and procainamide
Application of Pharmaco kinetics to Specific Populations: Geriatric, Obese, and Pediatric Patients 741
< 20 years (n = 19–23)
2.5 < 20-60 years (n = 74–86)
60+ years (n = 29–33)
2
1.5
1
0.5
0
CYP1A2 CYP2A6 CYP2B6 CYP2C8 CYP2C9 CYPC19 CYP2D6 CYP2E1 CYP3A4 CYP4A11
FIGURE 23.13 The effects of age on CYP activities in vitro with nearly 150 samples of human liver microsomes. The CYPC19
on the horizontal axis means CYP2C19.
No general approach has been developed to esti- renal tubular secretory processes, all decline with
mate age-related changes in hepatic and extrahepatic increasing age (Davies and Shock, 1950). Renal
drug metabolism, perhaps partly because hepatic and tubular reabsorption also decreases, at least measured
extrahepatic drug metabolism processes are affected as glucose reabsorption, and appears to parallel the
by complex and heterogeneous factors that involve decline in GFR (Miller et al, 1952).
genetic and environmental influences (Klotz, 2009). Measured GFR is the best overall indicator of
The liver undergoes many changes with aging renal function but it is cumbersome to collect urine
that includes reduction in blood flow and size of the for extended period of time (24 hours) and is more
liver. The reduction in blood flow suggests a reduc- prone to error of measurement. Diurnal variation in
tion in clearance of high extraction ratio or nonre- GFR and day-to-day variation in creatinine excretion
strictively cleared drugs. It is more difficult to may also contribute to the errors for GFR estimation
interpret the effect of changes in liver size on drug with timed urine collection. Thus, the following two
clearance (McLean and Le Couteur, 2004). formulas are commonly used to estimate GFR based
In general, the reduction of drug metabolism on serum creatinine:
with advancing age appears modest. The Cockcroft–Gault (CG) equation for creati-
nine clearance as GFR estimate (Cockcroft and Gault,
Drug Excretion 1976):
Renal drug clearance is the most consistent and pre- (140 − age in years)× (weight in kg)
dictable age-related change in pharmacokinetics. Clcr (mL/min) =
72× (serumcreatinine inmg/dL)
Renal function including renal blood flow, glomerular
filtration rate (GFR; measured as mean inulin clear- (23.1.1)
ance decreased from 122.8 to 65.3 mL/min/1.73 m2 For women, the Clcr estimate should be reduced by
between 20 and 90 years of age in 70 men), and active 15%.
CYP Activity
(Relative to the < 20 years group)
742 Chapter 23
The Modification of Diet in Renal Disease concentration alone may lead to serious errors in
(MDRD) equation for GFR estimate (Levey et al, assessing the severity of renal disease in the older
2006): population. A retrospective medical record review
study showed that serum creatinine concentration is
an inadequate screening test for renal failure in older
GFR (mL/min/1.73 m2)
patients as well as it leads to underinvestigation and
= 175 × (standardized serum creatinine)–1.154
underrecognition of renal failure in the older popula-
× (age)–0.203 × (0.742 if female)
tion (Swedko et al, 2003).
× (1.212 if African American) (23.1.1)
Drugs that are eliminated primarily via glo-
merular filtration, including aminoglycoside antibi-
The CG equation-estimated creatinine clear- otics, lithium, and digoxin, have an elimination
ance predicts a linear decrease with age that is clearance that decreases with age in parallel with
steeper than the nonlinear decline predicted via the the decline in measured or calculated creatinine
MDRD equation. Either one of these equations clearance (Ljungberg and Nilsson-Ehle, 1987;
gives a reasonable estimate that is sufficiently accu- Cusack et al, 1979; Sproule et al, 2000). The renal
rate to determine drug dose for drugs that have clearance of drugs undergoing active renal tubular
predominant renal clearance. Extensive discussions secretion also decreases with aging. For example,
for the merits of CG equation and MDRD equation the decrease in renal tubular secretion of cimetidine
to estimate renal function exist but with no clear parallels the decrease in creatinine clearance in
resolution (Spruill et al, 2009; Stevens and Levey, older patients (Drayer et al, 1982). Conversely, the
2009; Nyman et al, 2011). The major disadvantage ratios of renal drug clearance/creatinine clearance
of the MDRD equation is the limited information of both procainamide and N-acetylprocainamide
available on dosage adjustments as many of the decrease in the older patients, suggesting that with
age-adjusted recommendations are based on the CG aging the renal tubular secretion of these drugs
equation. Both CG and MDRD equations were not declines more rapidly than creatinine clearance
derived from significant numbers of people over (Reidenberg et al, 1980).
the age of 70 years, which may be the greatest The Baltimore Longitudinal Study of Aging fol-
limitation of these equations (Schwartz and lowed 254 healthy volunteers for up to 25 years and
Abernethy, 2009). prospectively found that creatinine clearance via
Serum creatinine concentration is a common 24-hour urine collection decreased 0.75 mL/min/year
endogenous glomerular filtration marker in clinical (Lindeman et al, 1985). However, one-third of these
practice. Creatinine is predominantly produced from participants had no decrease in creatinine clearance in
creatine and phosphocreatine in skeletal muscle with about 20 years. Later studies showed that aging itself
small contribution from ingestion of meat (Sandilands may have a minor effect on kidney function but the
et al, 2013). Lean muscle mass declines at a rate of confounding factors such as hypertension and chronic
about 1% a year after 30 years of age with multiple heart diseases account for the decline of kidney func-
causes (Morley et al, 2010). Creatinine is freely fil- tion (Fliser et al, 1997a, 1997b). The recent Italian
tered at the glomerulus and is not reabsorbed, but up Longitudinal Study on Aging also showed that the
to 15% is actively secreted by the tubules (Traynor et al, age-related reduction of kidney function was associ-
2006). For renally impaired patients, the age-associ- ated with coexisting cardiovascular diseases and other
ated decrease in creatinine production may signifi- risk factors (Baggio et al, 2005).
cantly blunt an increase of serum creatinine
concentration despite a marked decrease in the GFR
and creatinine clearance. This is a particular issue Age-Related Changes in Transporters
with small women or in malnourished individuals Transporters such as P-glycoprotein, organic anion
whose creatinine production is well below normal transporting peptide, organic cation transporter, and
(Perrone et al, 1992). Thus, serum creatinine organic anion transporter involve in drug absorption,
Application of Pharmaco kinetics to Specific Populations: Geriatric, Obese, and Pediatric Patients 743
distribution, metabolism, and excretion (see Chapters survived to reach old age and these participants
11 and 12). However, very few published data exist may be unique regarding the variable of interest
for the effect of aging on the expression and function
These limitations may prevent the generalizabil-
of drug transporters. P-glycoprotein is one of the
ity of the results for the pharmacodynamic studies to
better characterized drug transporters. The relatively
the entire older population. Anyhow, longitudinal
few published articles so far provided conflicting
pharmacodynamic studies that measure individual
results on the impact of advancing age on
rates of aging for the specified variable are rare.
P-glycoprotein activity and expression (Mangoni,
The following are examples to illustrate the
2007). For example, an ex vivo uptake study of
effect of aging on the pharmacodynamics of specific
MDR1-encoded P-glycoprotein in leukocytes from
therapeutic areas. For more comprehensive listings,
healthy older and frail older participants as well as
the readers can refer to other published articles
healthy young participants showed that aging and
(Bowie and Slattum, 2007; Trifirò and Spina, 2011;
frailty had minor impact on this validated cellular
Corsonello et al, 2010).
P-glycoprotein model (Brenner and Klotz, 2004).
However, a positron emission tomography study
showed that older participants have significantly Drugs That Act on the Central Nervous Systems
reduced P-glycoprotein function in the internal cap- Benzodiazepines. Changes in pharmacodynamics
sule and corona radiata white matter and in orbito- rather than pharmacokinetics with increasing age can
frontal regions, which may partly explain the be more relevant to explain the altered response to
vulnerability of aging brain to white matter degen- benzodiazepines. Many studies documented a greater
eration (Bartels et al, 2009). sensitivity to the clinical action of benzodiazepines in
older people, which is not attributable to the differences
Effects of Age on Pharmacodynamics in plasma concentrations, half-life, or apparent volume
in Older Adults of distribution of drugs. The exact mechanisms
Age-related pharmacokinetic changes are generally responsible for the increased sensitivity to
well characterized as discussed above. However, benzodiazepines with aging are unknown. No
limited information exists for age-related changes in significant age-related differences in GABA receptor
pharmacodynamics. This may be partly due to the binding properties or GABA receptor number are
relatively simpler bioanalytical methods that involve observable, both in animal models (Bickford and
determining drug concentrations in serial samples of Breiderick, 2000) and in humans (Sundman et al,
biomaterial versus the challenge to develop and vali- 1997). Diazepam, flurazepam, flunitrazepam, nitraze,
date appropriate measures of drug responses. midazolam, and triazolam show age-related increase
Majority of information for the age-related differ- in sensitivity to cognitive and sedative effects of
ences in human pharmacodynamics originate from benzodiazepines in the absence of significant
cross-sectional studies. Cross-sectional studies assume pharmacokinetic changes (Swift et al, 1985; Castleden
that the mean differences observed between age groups et al, 1977; Greenblatt et al, 1981, 2004; Kanto et al,
reflect the change that occurs in study participants with 1981; Albrecht et al, 1999).
the passage of time without directly observing the same
participants in longitudinal studies. This assumption Drugs That Act on the Cardiovascular System
may be invalid because of the following (Bowie and
Beta-adrenergic Receptors. Pharmacodynamic
Slattum, 2007; Trifirò and Spina, 2011):
sensitivity to beta-adrenergic drugs declines with
• Difficulties to differentiate chronological age ver- age. A reduced response to both agonist and
sus biological age or physiological effects versus antagonist of cardiac β1 and bronchial β2 receptors
pathological effects is observable (Vestal et al, 1979; Scott et al, 1995).
• Selective mortality effects since the oldest study These age-related changes in response to beta-
cohort includes only those participants who adrenergic drugs are not attributable to reduced beta
744 Chapter 23
receptor density or affinity, but it may be the result may be influenced not only by the aging process
of impaired signal transduction of beta receptor in itself but also by the psychopathology of psychiatric
older people (Doyle et al, 1982; Landmann et al, disorders, including schizophrenia, depression, or
1981). Beta-adrenoreceptors are coupled with Gs dementia (Meltzer, 1999). Thus, the effects of psy-
proteins, which in turn are linked to adenylate cyclase. chotropic drugs in the older patients may differ
Age-associated decreases in Gs activity are observed between patients with and without these mental
in vitro from human heart beta receptors (White et al, diseases.
1994). A downregulation of beta-adrenergic receptors The arrhythmogenic potential of antipsychotic
may also explain the higher systemic drug and antidepressant drugs, which may lead to QTc
concentration necessary with increasing age to reach interval prolongation as well as polymorphic ven-
the desired effect (Scarpace et al, 1991). The reduced tricular tachycardia, torsade de pointes, and sudden
beta receptor sensitivity does not imply the absence of cardiac death, is significantly higher in older patients
safety issues for both beta agonists and beta antagonists with preexisting cardiovascular disease or who are
in older patients. The risk–benefit ratio for the treated with concomitant QTc prolonging drugs
treatment of beta receptor antagonists needs careful (Vieweg et al, 2009).
evaluation because higher doses may be more effective In general, the interindividual pharmacokinetic
but with safety concerns (Dobre et al, 2007). variability is prominent, which is usually due not
only to the influence of age-related physiological
Drugs That Act on Blood Clotting changes but also to the impact of comorbidities and
Warfarin. Evidence exists of a greater inhibition of drug interactions (Shi and Klotz, 2011). Mallet et al
synthesis of vitamin K-dependent clotting factors at recommend a multiprofessional team approach to
similar plasma warfarin concentrations in older manage drug interactions and optimize drug therapy
patients than young patients. However, the exact in older patients (Mallet et al, 2007).
mechanism of this age-related change in sensitivity
is unknown. Age is one of the strongest predictors of Effect of Age on Dosing the Older Adults
the anticoagulant effects of warfarin (Miao et al, Based on the limited knowledge for the impact of
2007; Schwartz, 2007). aging on pharmacokinetic and pharmacodynamic
properties, it is difficult to make definite dosage rec-
Confounders of Pharmacokinetics and ommendations for older patients. The complex inter-
Pharmacodynamics in Older Adults actions among comorbidity, polypharmacy, changes
in pharmacodynamic sensitivity, and relatively mod-
Factors such as pharmacogenetic polymorphisms,
est pharmacokinetic changes in the older patients
nutrition, concomitant medications, smoking, and
warrant the dosing recommendation to follow the
drinking habits can influence the disposition and
conventional wisdom of “start low and go slow”
action of drugs in older patients. Another confound-
(Schwartz and Abernethy, 2009; Shi and Klotz,
ing factor for drug disposition and action in older
2011).
patients can be frailty (Shi and Klotz, 2011; Sitar,
2012). Wynne reported that frailty may impair con-
jugation pathways (sulfation and glucuronidation) Emerging Approaches to Avoid Adverse
for metoclopramide (Wynne et al, 1993). However, Drug Eventsin Older Adults
the definition of frailty is still being developed. The Beers list (also known as Beers criteria) has
Nevertheless, frailty is associated with higher been widely used as a reference for pharmacists and
inflammatory markers such as C-reactive protein, physicians in the United States to improve the use of
interleukin-6, or tumor necrosis factor-alpha (Fried medication in older patients. A gerontologist, Mark
et al, 2009; Clegg et al, 2013). H. Beers, advocated the use of explicit criteria
The function of different neurotransmitters in developed through consensus panels for identifying
dopaminergic, serotonergic, and cholinergic systems inappropriate use of medications in older patients.
Application of Pharmaco kinetics to Specific Populations: Geriatric, Obese, and Pediatric Patients 745
The Beers list was originally developed for frail The anticholinergic risk scale method ranks
older individuals living in nursing homes. medications for anticholinergic potential on a
Subsequently, it was updated and expanded to 3-point scale (0, no or low risk; 3, high anticholin-
include new medical conditions and generalized to ergic potential). The anticholinergic risk scale score
the older population regardless of their frailty status for a patient is the sum of points for the patient’s
or place of residence. The current Beers list is the number of medications (Rudolph et al, 2008). The
fourth rendition after revision of the 1991, 1997, list of rated medication was selected in 2005, so
and 2003 editions (The American Geriatrics Society newer medications will not apply. No allowance is
2012 Beers Criteria Update Expert Panel, 2012). included for drug dosage or potentially important
The Europeans also compiled a list that guides the factors such as renal and hepatic function (Bostock
prevention of inappropriate use of medications in et al, 2010).
older patients (Laroche et al, 2007). Some of Beers The drug burden index method characterizes
list’s limitations were obsolete drugs, drug–drug medications with respect to risk in two risk groups:
interactions, and prescribing omission errors. There (1) drugs with anticholinergic effects and (2) drugs
were also attempts to improve the limitations of with sedative effects. Medications with both anticho-
Beers list such as the STOPP/START criteria linergic and sedative effects were classified as anti-
(O’Mahony et al, 2010). STOPP and START stand cholinergic (Hilmer et al, 2007, 2009). The following
for “Screening Tool of Older Persons’ Prescriptions” factors were used in the equation for total drug bur-
and “Screening Tool to Alert doctors to Right den (TDB):
Treatment.”
An estimated one-third to more than one half of
TDB = BAC + Bs (23.1.3)
the most commonly prescribed medications for older
patients have anticholinergic (conventional with pub-
lished literature but antimuscarinic for pharmacologi-
where BAC and BS each represent the linear additive
cal accuracy) effects (Tune et al, 1992; Chew et al,
sum of D/(d + D) for every anticholinergic (AC) or
2008). These anticholinergic effects have been linked
sedative (S) drug to which the person is exposed, D
with cognitive impairment in older patients (Cancelli
is the daily dose taken by the person, and d is the
et al, 2008). Drugs with sedative adverse effects are
minimum efficacious daily dose (minimum daily
also of concern for older patients since these sedative
dose approved by the Food and Drug Administration).
effects can cause falls and bone fractures (Leipzig
Both prescription and over-the-counter drugs are
et al, 1999; Ensrud et al, 2002), which may further
included in the analysis. The major limitation of the
cause older patients to lose independence.
drug burden index method is the lack of consider-
Scientists and clinicians have developed at least
ation for patient’s factors such as renal and hepatic
the following methods to quantitate the overall anti-
function, which may have major impact on the anti-
cholinergic effects of medications for older patients:
cholinergic adverse effects and clinical outcomes
• Serum anticholinergic activity (Bostock et al, 2010).
• Anticholinergic risk scale A recent article advocates the application of
• Drug burden index pharmacokinetic and pharmacodynamic mecha-
nisms of anticholinergic drugs for safer use of these
Serum anticholinergic activity, as measured via
drugs in older patients (de Leon, 2011).
a radioreceptor assay, quantifies a patient’s overall
anticholinergic burden caused by all drugs and their
metabolites (Mulsant et al, 2003; Chew et al, 2008). Measures to help Older Adults Adhere to
Serum anticholinergic activity measurement is expen- Taking Their Medications
sive and is not readily available to practitioners, and The errors of drug administration are high in many
interpretation of the results in clinical practice is dif- older patients, and these errors can cause both effi-
ficult (Bostock et al, 2010). cacy and safety concerns. Older patients may likely
746 Chapter 23
have the following unique set of needs for taking the United States is guided by the “Guideline for the
their medications: Study of Drugs Likely to Be Used in the Elderly”
published in November 1989. Approaches to clinical
• The ability to remember and organize the medica-
trial design have been further informed in Europe and
tions especially for multiple medications with dif-
the United States by the European Medicines Agency
ferent dosing regimens
documents “Studies in Support of Special Populations:
• The reduced visual abilities to accurately measure
Geriatrics” and “ICH Topic E7, Studies in Support of
the medications or to read the instruction on the
Special Populations: Geriatrics. Questions and
label of medications
Answers.” An underlying theme of these documents,
• Instability of their hands to hold medications
as stated in the November 1989 Food and Drug
• Dexterity of their ngers to accurately measure the
Administration guideline, is that “drugs should be
dose especially for liquid formulations or to open
studied in all age groups, including the older popula-
the medications’ container
tion, for which they will have significant utility.”
Scientists discussed measures such as organizer for In 1997, the Food and Drug Administration
medications, devices with improved visualization of established the Geriatric Use subsection, as a part of
graduation for measurement, eye-drop applicator, and the PRECAUTIONS section, in the labeling for
deblistering machine for oral dosage forms in blister human prescription drugs to include more compre-
packs to help older patients adhere to taking their hensive information about the use of a drug or bio-
medications (Breitkreutz and Boos, 2007). Alternative logical product in persons aged 65 years and older
formulations, delivery methods, and administration (Food and Drug Administration, 1997).
options for psychotropic medications may be neces- Population pharmacokinetic and pharmacody-
sary for older patients with behavioral and psychologi- namic approach with sparse sampling through covari-
cal symptoms of dementia (Muramatsu et al, 2010). ate analysis in clinical efficacy and safety trials is an
For the future, scientists, engineers, clinicians, option to evaluate the effects of age on pharmacokinet-
and businesspersons need to work together to develop ics and pharmacodynamics. Some scientists refer this
age-appropriate products that can better deliver the approach as the “top-down approach” (Tsamandouras
medications to meet older patients’ needs. et al, 2015). The population pharmacokinetic and phar-
macodynamic approach is particularly suitable for the
older patients since extensive blood sampling for the
Emerging Methods to Study Pharmacology older patients may be too invasive and the studied
in Older Adults patients more resemble the intended patient population
The current regulatory environment has the follow- than a dedicated pharmacokinetic or pharmacodynamic
ing two publications for the study of drugs in the study that requires extensive blood sampling in rather
older population: healthy older participants. A recent example is the
application of population pharmacokinetics to study
• “Guideline for the Study of Drugs Likely to Be
participants living in the community and in nursing
Used in the Elderly” published in November 1989
homes and found that advancing age (relevant only to
by the United States Food and Drug Administra-
men) and concomitant medications with cytochrome
tion (Food and Drug Administration, 1989)
3A4 inhibitors lowered the apparent clearance of orally
• “Guideline for Industry: Studies in Support of Special
administered atorvastatin (Schwartz and Verotta, 2009).
Populations: Geriatrics” and “ICH Topic E7, Studies
The Food and Drug Administration has a guidance on
in Support of Special Populations: Geriatrics. Ques-
the design, execution, and analysis of population phar-
tions and Answers” published on August 1994 and
macokinetics (Food and Drug Administration, 1999).
July 2011, respectively, by the European Medicines
Physiologically based pharmacokinetic modeling
Agency (European Medicines Agency, 1994, 2011)
is another tool that has potential to study drug disposi-
Currently, the inclusion of older individuals in clini- tion and action in the older population (Rowland
cal trials of drugs under evaluation for registration in et al, 2011). Some scientists refer this approach as the
Application of Pharmaco kinetics to Specific Populations: Geriatric, Obese, and Pediatric Patients 747
“bottom-up” approach, which is more mechanistic in Clinical Examples of Concomitant Medication
nature (Food and Drug Administration, 1997). Recent in Older Patients
examples of the application of the physiologically The following two examples are modified from a
based pharmacokinetic modeling approach include reference (Mallet et al, 2007). Example 1 illustrates
understanding the effect of renal impairment on the an older patient’s multiple drug interaction poten-
pharmacokinetics of diltiazem, paroxetine, and repa- tials. Example 2 illustrates another older patient’s
glinide as well as pharmacometrics in pregnancy prescribing cascade and drug interactions.
(Rowland Yeo et al, 2011; Ke et al, 2014).
Scientists have compiled physiological parame-
ters for healthy and health-impaired people 65 years
of age and older for the physiologically based phar- EXAMPLE 1 • • •
macokinetic models (Thompson et al, 2009). Others An 82-year-old man was hospitalized for general
used the physiologically based pharmacokinetic deterioration. His medical history included renal
modeling approach to predict metabolic drug clear- transplant 18 years ago, type 2 diabetes mel-
ance with advancing age (Polasek et al, 2013). litus, atrial fibrillation, congestive heart failure,
Scientists are applying the physiologically based and early Alzheimer’s dementia. He was taking
pharmacokinetic modeling approach to estimate cyclosporine, prednisone, warfarin, digoxin, furo-
drug dosing in children (Barrett et al, 2012). Thus, semide, levothyroxine, losartan, glyburide, done-
applying the physiologically based pharmacokinetic pezil, lactulose, calcium carbonate, vitamin D, and
modeling approach to understand drug disposition ginkgo biloba. A week before admission, clarithro-
and action for the older patients seems appropriate mycin was started to treat bronchitis.
(Della Casa Alberighi, 2013; Johnston et al, 2013). Discussion of this 82-year-old patient’s
Scientists have been working on the systems medications:
biology of aging, which is intrinsically complex,
• Potential drug–drug interactions:
being driven by multiple causal mechanisms
– Clarithromycin + warfarin: Clarithromycin is
(Kirkwood, 2011). In general, the systems biology
a CYP3A4 inhibitor. Warfarin is a CYP3A4 sub-
approach combines the following:
strate. This combination has risk of increased
• Data-driven modeling, often using the large vol- warfarin exposure and anticoagulant effect.
umes of data generated by functional genomics – Clarithromycin + cyclosporine: Clarithromy-
technologies cin is a CYP3A4 inhibitor. Cyclosporine is a
• Hypothesis-driven experimental studies to investigate CYP3A4 substrate. This combination has
causal pathways and identify their parameter values risk of increased cyclosporine exposure and
in an unusually quantitative manner, which enables nephrotoxicity.
us to better understand the contributions of individual – Calcium carbonate + levothyroxine:
mechanisms and their interactions as well as allows decreased absorption of levothyroxine.
for the design of experiments to explicitly test the – Ginkgo biloba + warfarin: increased risk of
complex predictions arising from such models hemorrhage.
– Donepezil, cyclosporine, and losartan: All
The learning from these systems biology studies will
are CYP3A4 substrates with potential risk of
help us understand healthier aging. Healthier aging
interaction.
is aimed at the compression of morbidity in older
– Losartan and glyburide: All are CYP2C9 sub-
age (Myint and Welch, 2012). The compression of
strates with potential risk of interaction.
morbidity hypothesis states that the age of onset of
• Potential drug–disease interactions:
chronic illness may be postponed more than the age
– Prednisone in patient with congestive
at death, squeezing most of the morbidity in life into
heart failure to cause fluid and electrolyte
a shorter period with less lifetime disability (Fries,
disturbances.
1980; Fries et al, 2011).
748 Chapter 23
– Prednisone in diabetic patient to increase recurrent falls. The initial assessment attributed
requirements for insulin or oral hypoglyce- his falls to worsening instability secondary to
mic agents. suboptimally treated Parkinson’s disease. Thus,
Indiana University, School of Medicine, Depart- his carbidopa and levodopa dose was increased.
ment of Medicine, Division of Clinical Pharma- Risperidone was prescribed for nighttime agi-
cology, P450 Drug Interaction Table. http:// tated behavior (haloperidol was discontinued).
medicine.iupui.edu/clinpharm/ddis/main-table He was still taking paroxetine.
/ Indianapolis, IN 46202 Discussion of this 75-year-old patient’s
Therapeutic plan for this 82-year-old patient: medications: Paroxetine and haloperidol can
Management of drug interactions in older both cause extrapyramidal adverse effects lead-
patients needs a team effort and communication ing to this patient’s tremors. Moreover, these two
is pivotal to achieve this goal. Several clinicians drugs are CYP2D6 substrates with potential risk
may take care of this patient, such as nephrolo- of mutual interaction to increase exposure of
gist, endocrinologist, cardiologist, neurologist, paroxetine and haloperidol, which leads to the
geriatrician, and family practice physician to extrapyramidal adverse effects. A prescribing
prescribe medications. The pharmacist is likely cascade started with the prescription of carbi-
to have access to this patient’s most complete dopa and levodopa. Carbidopa and levodopa’s
medication records and may help the following: possible central nervous system adverse effects
• Communicate with clarithromycin’s prescriber may cause the prescription of risperidone, which
for the potential interaction between clar- itself can cause extrapyramidal adverse effects.
ithromycin and cyclosporine as well as warfa- Also, risperidone and paroxetine are CYP2D6
rin. May need to recommend azithromycin or substrates with potential risk of interaction.
other antibiotic as alternative to minimize the Indiana University, School of Medicine,
potential CYP3A4 inhibition for cyclosporine Department of Medicine, Division of Clinical
and warfarin. Pharmacology, P450 Drug Interaction Table.
• Communicate with the patient or caregiver to http://medicine.iupui.edu/clinpharm/ddis
take calcium carbonate and levothyroxine at /main-table/ Indianapolis, IN 46202
least 4 hours apart to prevent the potential of Therapeutic plan for this 75-year-old patient:
calcium carbonate interfering with the absorp- The pharmacist is likely to have access to this
tion of levothyroxine. patient’s most complete medication records and
• Communicate with the nurse or caregiver to may help the following:
watch for signs of worsening congestive heart • Communicate with the neurologist that the
failure such as shortness of breath and fluid patient is taking paroxetine and haloperidol for
retention as well as signs of fall from hypoten- the treatment of psychotic depression, which
sion or hypoglycemia for further evaluation. may cause the extrapyramidal adverse effects
and tremors. This may alert the neurologist to
recognize the prescribing cascade and stop it.
EXAMPLE 2 • • • • Communicate with the primary-care physician
A 75-year-old man was taking paroxetine and that dose reduction for paroxetine and halo-
haloperidol for the treatment of psychotic peridol may be necessary for this patient.
depression. His primary-care physician sent him • Communicate with the nurse or caregiver for
for a neurological consult of his new-onset trem- mouth, dental, and bowel hygiene to watch for
ors. The neurologist started him with carbidopa potential anticholinergic adverse effects. Parox-
and levodopa for probable Parkinson’s disease. etine has strong anticholinergic effect per the
He was eventually hospitalized after several 2012’s Beers list.
Application of Pharmaco kinetics to Specific Populations: Geriatric, Obese, and Pediatric Patients 749
SUMMARY
The number of people 65 years of age and older in Age-related changes in pharmacodynamics
the United States will more than double to 88.5 mil- are more difficult to study than age-related changes
lion in the year 2050 from that in year 2010. A simi- in pharmacokinetics due to difficulties in estab-
lar trend occurs in other developed countries in the lishing validated drug responses for pharmacody-
world as well. Careful consideration of drug therapy namics. In general, older patients have increased
is essential to take care of older patients, who usually sensitivity to drugs that act in the central nervous
have comorbidities and concurrently take multiple system and blood clotting system. However, older
medications. Knowledge of age’s effect on pharma- patients have decreased sensitivity to drugs that
cokinetics and pharmacodynamics will help maxi- act on the adrenergic receptors in autonomic ner-
mize the therapeutic effects and minimize the vous system.
adverse effects of drugs. In general, dosing recommendation in older
Oral absorption of drugs does not appear to alter patients should follow the conventional wisdom of
with advancing age despite physiological changes in “start low and go slow.”
the gastrointestinal tract. Plasma albumin concentra- Tools such as the Beers list may help appropri-
tion decreases about 10% with advancing age, whereas ate prescribing in the older population. Several
plasma α1-acid glycoprotein concentration increases approaches emerged such as the serum anticholin-
due to comorbidities. These changes usually do not ergic activity, anticholinergic risk scale, and drug
result in dose adjustments except for rare cases. Phase burden index to quantitate the anticholinergic bur-
I or degradative process of drug metabolism decreases den of certain drugs may assist prescribing medi-
to some extent and may require dose adjustments, cations for older patients to reduce adverse drug
whereas Phase II or synthetic process of drug metabo- events. Older individuals also have unique needs
lism do not change with advancing age. In general, the for adherence to take their medications. Emerging
overall decrease in drug metabolism due to advancing methods also exist to study pharmacology in older
age seems modest. Renal drug clearance is the most patients such as the population pharmacokinetics/
consistent and predictable age-related change in phar- pharmacodynamics, physiologically based phar-
macokinetics. The decrease in renal function may not macokinetics/pharmacodynamics, and systems
be due to aging itself but due to comorbidity such as biology.
hypertension and chronic heart diseases.
LEARNING QUESTIONS
1. Which of the following is the most appropriate that can affect pharmacokinetics in older
choice related to aging? patients?
a. Increased extracellular fluid volume a. Changes in gastrointestinal function that
b. Increased hepatic blood flow lead to reduced drug absorption
c. Increased amount of sleep required b. Increase in total body water
d. Increased subcutaneous fat as a percentage c. Decrease in body fat
of total body mass d. Decrease in serum albumin concentrations
e. Increased size of alveolar ducts in the lung with advancing age
2. Which of the following is the most appropri- e. Decrease in creatinine clearance with
ate choice to describe age-associated changes advancing age
750 Chapter 23
3. Which of the following statement regarding c. Older patients regularly take about 4–5
renal function and pharmacokinetics in older medications.
patients is most accurate? d. Adverse drug reactions in older patients
a. Decreased muscle mass is the reason for appear unrelated to the number of medica-
normal or low serum creatinine concentra- tions taken.
tion in older patients even in the presence of e. Taking over-the-counter medications and
decreased renal function. nutritional supplements other than those
b. Renal tubular secretion is not changed with prescribed can contribute to polypharmacy.
aging. 5. Which of the following statements concern-
c. Serum creatinine concentration of 1.5 mg/dL ing the safety of medications used by older
reflects normal renal function in older men. patients is wrong?
d. Glomerular function always declines with a. Chlorpropamide can cause hypoglycemia.
aging. b. Benzodiazepines have large volume of dis-
e. Gentamicin can be used safely in older tribution and are thus relatively safe for use
patients with serum creatinine concentra- in older people.
tions of 1.7 mg/dL. c. Amantadine’s excretion depends on renal
4. Which of the following regarding medication use function and may cause confusion and falls if
by older patients in the United States is wrong? the dose is not adjusted for renal impairment.
a. Older patients count about 13% of the d. Diphenhydramine may exacerbate urinary
United States population but consume retention of older men.
25%–30% of all medications. e. Meperidine is not an effective oral analgesic
b. Institutionalized older residents usually take in dosages commonly used and may cause
3–8 medications a day. neurotoxicity.
ANSWERS
Learning Questions such as diabetes and chronic heart diseases.
1. The correct answer is e. The size of alveo- Gentamicin’s elimination is via renal excretion
lar ducts increases with aging, which causes and serum creatinine concentration of 1.7 mg/dL
a decrease in the lung surface area. a and b reflects renal impairment.
are wrong statements. Older persons need 4. The correct answer is d. d is a wrong state-
less sleep but need short naps during the day. ment. a, b, c, and e are correct statements.
Increase of subcutaneous fat, as a percentage of 5. The correct answer is b. Benzodiazepines tend
total body mass, is not a change associated with to distribute to fat tissues and thus have a large
aging. Fat as a percentage of total body mass volume of distribution. With increasing age, we
increases in older persons. However, fat redis- tend to gain body fat and thus need longer time to
tributes from subcutaneous to truncal areas. eliminate benzodiazepines than younger adults.
Thus, this leads to a net loss of subcutaneous Benzodiazepines show age-related increase in sen-
fat and increases the risk of pressure ulcers. sitivity to cognitive and sedative functions. Aman-
2. The correct answer is e. d and e are correct but tadine is primarily excreted unchanged in the urine
d is most likely not significantly enough that via glomerular filtration and tubular secretion.
requires dose adjustment. a, b, and c are wrong All sulfonylurea drugs including chlorpropamide
statements. are capable of causing severe hypoglycemia.
3. The correct answer is a. b and c are wrong Diphenhydramine has high anticholinergic adverse
statements. Per longitudinal studies, renal func- effects, which can exacerbate the urinary retention
tion as reflected via glomerular function may issue of older men with prostate hypertrophy. e is a
not change with aging except with comorbidity correct statement per the 2012’s Beers list.
Application of Pharmaco kinetics to Specific Populations: Geriatric, Obese, and Pediatric Patients 751
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Rowland M, Peck C, Tucker G: Physiologically-based pharma- Swift CG, Ewen JM, Clarke P, et al: Responsiveness to oral diaz-
cokinetics in drug development and regulatory science. Annu epam in the elderly: Relationship to total and free concentra-
Rev Pharmacol Toxicol 51:45, 2011. tions. Br J Clin Pharmacol 20:111, 1985.
Rowland M, Tozer TN: Protein drugs. In Rowland M, Tozer TN The American Geriatrics Society 2012 Beers Criteria Update
(eds). Clinical Pharmacokinetics and Pharmacodynamics: Expert Panel: American Geriatrics Society Updated Beers
Concepts and Applications. Philadelphia, PA, Lippincott Criteria for Potentially Inappropriate Medication Use in Older
Williams & Wilkins Publisher, 2011, p 633. Adults. J Am Geriatr Soc 60:616, 2012.
754 Chapter 23
Thompson CM, Johns DO, Sonawane B, et al: Database for physi- Reports, P25-1138, http://www.census.gov/prod/2010pubs
ologically based pharmacokinetic (PBPK) modeling: Physi- /p25-1138.pdf. Washington, DC, 20233, 2010.
ological data for healthy and health-impaired elderly. J Toxicol Vadivelu N, Hines RL: Management of chronic pain in the elderly:
Environ Health B Crit Rev 12:1, 2009. Focus on transdermal buprenorphine. Clin Interv Aging 3:421,
Traynor J, Mactier R, Geddes CC, et al: How to measure renal 2008.
function in clinical practice. BMJ 333:733, 2006. Vestal RE: Aging and pharmacology. Cancer 80:1302, 1997.
Trifirò G, Spina E: Age-related changes in pharmacodynamics: Vestal RE, Wood AJ, Shand DG: Reduced beta-adrenoceptor sen-
Focus on drugs acting on central nervous and cardiovascular sitivity in the elderly. Clin Pharmacol Ther 26:181, 1979.
systems. Curr Drug Metab 12:611, 2011. Vieweg WV, Wood MA, Fernandez A, et al: Proarrhythmic risk
Tsamandouras N, Rostami-Hodjegan A, Aarons L: Combining the with antipsychotic and antidepressant drugs: Implications in
“bottom-up” and “top-down” approaches in pharmacokinetic the elderly. Drugs Aging 26:997, 2009.
modelling: Fitting PBPK models to observed clinical data. Br White M, Roden R, Minobe W, et al: Age-related changes in beta-
J Clin Pharmacol 79:48, 2015. adrenergic neuroeffector systems in the human heart. Circula-
Tune L, Carr S, Hoag E, et al: Anticholinergic effects of drugs tion 90:1225, 1994.
commonly prescribed for the elderly: potential means for Wynne HA, Yelland C, Cope LH, et al: The association of age and
assessing risk of delirium. Am J Psychiatry 149:1393, 1992. frailty with the pharmacokinetics and pharmacodynamics of
U.S. Census Bureau: The next four decades: The older popula- metoclopramide. Age Ageing 22:354, 1993.
tion in the United States: 2010 to 2050. Current Population
FURTHER READING
Cusack BJ: Pharmacokinetics in older persons. Am J Geriatr Kim J, Mak M: Geriatric drug use. In Alldredge BK, Corelli
Pharmacother 2:274, 2004. RL, Ernst ME, et al (eds). Koda-Kimble and Young’s Applied
Gronich N, Abernethy DR: Pharmacology across the aging con- Therapeutics: The Clinical Use of Drugs. Philadelphia PA,
tinuum. In Waldman SA, Terzic A (eds). Pharmacology and Lippincott Williams & Wilkins, 2013, p 2359.
Therapeutics: Principles to Practice. Philadelphia, PA, Lau SWJ, Abernethy DR: Drug therapy in the elderly. In Atkinson
Saunders, 2009, p 257. AJ, Huang S-M, Lertora JJ, et al (eds). Principles of Clinical
Hilmer SN, McLachlan AJ, Le Couteur DG: Clinical pharmacol- Pharmacology. Waltham, MA, Academic Press, 2012, p 437.
ogy in the geriatric patient. Fundam Clin Pharmacol 21:217, Salles N: Basic mechanisms of the aging gastrointestinal tract.
2007. Dig Dis 25:112, 2007.
Katzung BG: Special aspects of geriatric pharmacology. In Vestal RE, Gurwitz JH: Geriatric pharmacology. In Carruthers
Katzung BG, Masters SB, Trevor AJ (eds). Basic and Clini- SG, Hoffman BB, Melmon KL, et al (eds). Clinical Phar-
cal Pharmacology. New York, NY, McGraw-Hill Companies, macology: Basic Principles in Therapeutics. New York, NY,
Inc., 2012, p 1051. McGraw-Hill Companies, Inc., 2000, p 1151.
MODULE II: APPLICATION OF • Describe the differences in renal elimination
between obese and non-obese patients.
PHARMACOKINETICS TO THE • Apply pharmacokinetic principles in drug dosing
OBESE PATIENTS for obesity.
• Estimate creatinine clearance for obese patients.
Objectives
• Describe the prevalence and the impact of obesity
on individuals and to the society. Introduction
• Classify obesity based on body mass index. Obesity, defined as body mass index (BMI) of 30 or
• Explain the differences of volume distribution in higher, has been recognized as a “disease” in 2013 by
obese versus non-obese patients. the American Medical Association, requiring a range
• Identify the differences in metabolism between of medical interventions to advance treatment and
obese and non-obese patients. prevention (AMA, 2013). The prevalence of obesity
Application of Pharmaco kinetics to Specific Populations: Geriatric, Obese, and Pediatric Patients 755
has increased substantially worldwide in recent years TABLE 23.21 Classification of Obesity Based
(Kopelman, 2000; Berghofer et al, 2008). The medical on BMI
care costs related to obesity are staggering, and much
Classification BMI (kg/m2)
of the cost is associated with obesity-related chronic
conditions, including diabetes, hypertension, high cho- Underweight <18.5
lesterol, stroke, heart disease, certain cancers, and Normal body weight 18.5–24.9
arthritis (Malnick et al, 2006). In addition, obesity was
Overweight 25–29.9
associated with significantly increased mortality from
cardiovascular diseases and obesity-related cancers Obese 30–39.9
(Flegal et al, 2007). Individuals with obesity also have Morbidly obese ≥40
significantly lower health-related quality-of-life scores
than those individuals with normal weights (Jia et al,
2005), with or without the corresponding chronic (Winter, 2010). Some clinicians use 30% as their
diseases. criteria for clinically obese. IBW is a weight with the
Individuals with severe obesity, defined as lowest mortality (Metropolitan Life Insurance
BMI ≥ 40, are a rapidly growing sector among the Company, 1959) derived from the data at
obese population in the United States. While the Metropolitan Life Insurance Company. Morbidly
population of obesity in the US adults increased by obese may also refer to a patient’s TBW at least 95%
4.97% from 2003–2004 to 2007–2008 (Ogden et al, over the IBW. Table 23.2-2 details the weight
2006), the population of severe obesity has increased descriptors and related formulas to estimate the
by 18.75% during the same period of time. weight descriptors.
Classification of obesity is most commonly In general, obese individuals have more fat tis-
using BMI, a value that normalizes body weight sue and less lean tissue per kilogram of TBW, as
based on height (Table 23.2-1) (World Health compared to their non-obese counterparts (Cheymol,
Organization, 1998). It is calculated as body weight 2000). Since the actual fat content in body tissues is
in kilograms divided by the height in meters squared. difficult to measure in a clinical setting, the excess
Clinically, a patient may be considered obese weight, or so-called fat weight, in an obese individ-
when the total body weight (TBW) is equal to or ual is commonly calculated as the difference between
greater than 20% of ideal body weight (IBW) TBW and IBW.
TABLE 23.22 Weight Descriptors and Related Equations
Weight Descriptor Equation No. Ref.
BMI [Weight (kg)/height (cm)2] × 10,000 (cm2/m2) 23.2.1 World Health Organization
(1998)
Ideal body weight (IBW), kg Male: 50 + 2.3 × [Height (inches) – 60] 23.2.2 Devine (1974)
Female: 45.5 + 2.3 × [Height (inches) – 60]
Total body weight (TBW), kg Measured body weight 23.2.3
Adjusted body weight IBW + 0.4 × (TBW – IBW) 23.2.4 Bauer et al (1983)
(Adj. BW), kg
Lean body weight Male: (9270 × TBW)/(6680 + 216 × BMI) 23.2.5 Janmahasatian et al (2005)
(LBW2005), kg Female: (9270 × TBW)/(8780 + 244 × BMI) 23.2.6
756 Chapter 23
The excess fat tissue and its accompanying increased or decreased (α1-acid glycoprotein) with
physiological changes in the obese individuals may obesity, resulted in an altered concentration of the
have a significant impact on drug disposition. unbound drug. At present, the impact of obesity on
plasma protein binding of medications is still largely
Pharmacokinetic Changes in Obesity inconclusive.
Absorption
Metabolism
Information currently available on the absorption
and bioavailability of medications in the obese popu- Drug metabolism primarily occurs in the liver
lation is scarce and inconclusive. Limited studies through Phase I reactions and Phase II conjugation.
included a study comparing the absorption and bio- A majority of the obese patients have fatty infiltra-
availability of metformin between patients under- tion in the liver (Moretto et al, 2003), resulted in
went gastric bypass surgery and their BMI-matched nonalcoholic fatty liver disease (NAFLD), with or
(nonsurgery) cohorts showed a 50% increase of without inflammation of the liver. Therefore, the
bioavailability in the surgery group after the surgery Phase I and II enzyme activities in obesity may be
(Padwal et al, 2011). Another study comparing oral affected by the fatty infiltration of the liver and its
atorvastatin exposure before and after gastric bypass associated changes.
surgery in the same patient showed variable results 1. Phase I Metabolism
(Skottheim et al, 2009). a. Cytochrome P450 (CYP) 3A4
It has been reported that CYP 3A4 meta-
Distribution bolic activity was reduced in the obese
Drug distribution, measured as volume of distribu- patients, either significantly, as for carba-
tion (VD), is influenced by the size of the tissue, tis- mazepine and triazolam (Abernethy et al,
sue perfusion, plasma protein binding, tissue 1984; Caraco et al, 1995), or not signifi-
membrane permeability, etc (Rowland and Tozer, cantly, as for midazolam and cyclosporine
2011). The obese individuals have an increased total (Greenblatt et al, 1984; Yee, 1988), when
tissue mass and adipose tissue mass (Cheymol, compared to the non-obese patients. The
1993, 2000). Thus, the volume of distribution for weight-normalized clearances were invari-
many drugs may be increased in the obese popula- ably lower in the obese patients.
tion. However, studies have shown that physico- b. CYP2E1
chemical characteristics of the drug, namely, Various studies showed consistent and
lipophilicity, plays a major role in the drug distribu- significant increases in the clearance of CYP
tion (Cheymol, 1988; Medico and Walsh, 2010) in 2E1 substrates in the obese patients, includ-
the obese population. Generally, in the obese ing chlorzoxazone, enflurane, sevoflurane,
patients, lipophilic medications showed a larger and halothane (Miller et al, 1980; Bentley
increased volume of distribution, and hydrophilic et al, 1982; Higuchi et al, 1993; Lucas et al,
medications showed a less increased volume of dis- 1999; Emery et al, 2003). These data lead
tribution, as compared to the non-obese patients. us to believe there is an increase of activity
Still, there are exceptions to this rule (Flechner et al, of CYP2E1 in obesity. When normalized for
1989; Wojcicki et al, 2003). For example, cyclospo- body weight, clearance values of these drugs
rine is highly lipophilic, its volume of distribution in are approximately equal among obese and
non-obese patients was 295 L, but in obese patients, non-obese individuals, which suggests that
its volume of distribution was only 229 L. In addi- CYP2E1activity increases with body weight.
tion, the concentrations of plasma binding pro- CYP2E1 mediates the metabolism of fatty
teins—albumin, α1-acid glycoprotein, and acids, ketones, and ethanol. Chronic expo-
lipoproteins—may be unchanged (albumin), sure to the sesubstrates in large amounts
Application of Pharmaco kinetics to Specific Populations: Geriatric, Obese, and Pediatric Patients 757
induces CYP2E1, leading to free-radical for- and mercaptopurine (Balis, 1986) in the
mation, lipid peroxidation, and liver injury obese versus non-obese children showed
(Lieber, 2004; Buechler and Weiss, 2011). significantly increased enzyme activity in
Fatty infiltration of the liver is likely to the obese group.
rise with increasing body weight, which may B. Phase II Metabolism
be the underlying cause of the increase in a. Uridine diphosphate glucuronosyltransferase
CYP2E1 enzyme activity (Brill et al, 2012). (UGT)
c. CYP2D6 UGT enzymes catalyze the conjugation
Studies on dexfenfluramine and nebivolol of endogenous substances and exogenous
showed a trend toward increased CYP2D6 compounds, and are involved in approxi-
activity in the obese patients (Cheymol et al, mately 50% of the Phase II metabolism for
1995, 1997). However, its activity may vary drugs. Since the liver is the main organ for
based on its genetic polymorphisms (May, UGT enzyme activities, liver disease or an
1994; Van den Anker, 2010). increased size of the liver, as occurred in
d. CYP1A2 the obese patients, may correlate with UGT
Studies on caffeine and theophylline activities. Studies showed a significantly
showed a trend of higher clearance in the increased clearance in the obese group for
obese group, indicating a slight increase medications metabolized via this pathway,
in CYP1A2 activity in the obese patients including acetaminophen in adults (Brill
(Jusko et al, 1979; Abernethy et al, 1985; et al, 2012), oxazepam, and lorazepam
Kamimori et al, 1987; Zahorska-Markiewicz (Abernethy et al, 1982b, 1983). With the
et al, 1996). exception of oxazepam, the weight-normal-
e. CYP2C9 ized clearance values were either the same
Studies on glimepiride and ibuprofen or slightly lower in the obese group.
showed a small but significantly increased b. Other Phase II metabolic enzymes
CYP2C9 activity in the obese patients Besides UGT, other Phase II metabolic
(Abernethy and Greenblatt, 1985a; Shukla processes include N-acetyl-, methyl,
et al, 2004), and studies on glipizide and glutathione, and sulfate conjugation of
phenytoin showed an insignificant increase substrates. The study on procainamide,
in the obese group (Abernethy and Green- which is metabolized via N-acetylation,
blatt, 1985b; Jaber et al, 1996). While showed an increased, but not statistically
normalized for body weight, a lower enzyme significant, plasma clearance in the obese
activity of CYP2C9 was associated with the group (Christoff et al, 1983). The weight-
obese group. normalized clearance for procainamide was
f. CYP2C19 lower in the obese group. As for studies with
The only one study for CYP2C19 activities busulfan, which is metabolized via gluta-
showed that the clearance of diazepam was thione S-transferase, showed a significantly
significantly higher in the obese group, and increased Cl/F in the obese group, while the
no difference was shown for desmethyldi- weight-normalized clearance was signifi-
azepam (Abernethy et al, 1981a, 1982a). cantly lower in the obese group (Gibbs et al,
While adjusted for body weight, a lower 1999).
enzyme activity was shown in the obese c. Blood flow in the liver
group for both drugs. Obesity is associated with absolute increases
g. Xanthine oxidase in cardiac output and blood volume, as
Studies in comparing xanthine oxidase compared to non-obese subjects (Alexander
activities using caffeine (Chiney et al, 2011) et al, 1962; Alexander, 1964). Yet the effect
758 Chapter 23
of obesity on liver blood flow is not fully (Abernethy et al, 1981b; Sparreboom et al,
determined, partly because nonalcoholic 2007) showed a trend toward higher tubular
fatty liver disease increases fat deposition in secretion in the obese group, but the difference
the liver, resulting in sinusoidal narrowing was not statistically significant.
and altered morphology of the liver (Farrell C. Tubular reabsorption
et al, 2008). It appears that tubular reabsorption of lithium
Drugs with high-extraction ratio, such as was significantly lower in the obese group
propofol, sufentanil, and paclitaxel, could as compared with the non-obese group in the
potentially serve as markers of liver blood one study available (Reiss et al, 1994). In
flow, because they are rapidly metabolized this study, the renal clearance of lithium was
and sensitive to changes in the blood flow significantly increased in the obese patients,
of the liver, and less sensitive to changes in while their glomerular filtration rates were
enzyme activities. Studies of these drugs not different between obese and non-obese
showed higher clearances in the obese sub- groups.
jects (Schwartz et al, 1991; Sparreboom
et al, 2007; Cortinez et al, 2010; Van Dosing Considerations in the Obese Patients
Kralingen et al, 2011). However, studies
Studies for various drugs have been conducted to
on propranolol, a drug with high-extraction
evaluate appropriate dosing regimens for obese
ratio but less clearance rate, showed vari-
patients. It is not possible to list all the studies and
able results (Cheymol et al, 1997; Wojcicki
dosing recommendations in this text. However,
et al, 2003).
based on the findings from the pharmacokinetic
studies, principles of drug dosing for the obese
Renal Elimination patients may be adopted to calculate loading dose
Many drugs are eliminated through kidney via glo- and maintenance dose.
merular filtration, tubular secretion, and tubular
A. Loading dose
reabsorption. The size of the kidney, renal plasma
The loading dose is primarily based on V
flow, and urine flow rate may influence the function D.
In general, the weight used to calculate the
of the kidney.
loading dose depends on how the drug is
A. Glomerular filtration distributed in the lean and fat tissues in the
Studies comparing clearance of drugs that are body. If the drug is primarily distributed into
primarily eliminated by glomerular filtration the lean mass, IBW will be used to calculate
showed a significantly higher clearance in the the loading dose. In contrast, if the drug is
obese group for vancomycin (Bauer et al, largely distributed into the fat tissues, TBW
1998), daptomycin (Dvorchik and Damp- will be used. If the distribution is somewhere
housse, 2005), and enoxaparin (Barras et al, in between, an adjusted weight may be used
2009). Studies for carboplatin (Sparreboom (Allen, 2008).
et al, 2007) and dalteparin (Yee and Duffull, B. Maintenance dose
2000) showed higher clearances in the obese The maintenance dose primarily depends on
group, but not statistically significant as com- drug clearance (Cl). The most commonly used
pared to the non-obese group. equations to estimate glomerular filtration rate
B. Tubular secretion (GFR) are Cockcroft–Gault (CG) equation
A significantly higher tubular secretion in the (Cockcroft and Gault, 1976) and Modification
obese group was reported for procainamide, of Diet in Renal Disease (MDRD) equation
ciprofloxacin, and cisplatin (Christoff et al, (Levey et al, 1999). The MDRD equation was
1983; Allard et al, 1993; Sparreboom et al, developed with six variables—age, gender, Scr,
2007). Studies for topotecan and digoxin blood urea nitrogen, albumin, and race—to
Application of Pharmaco kinetics to Specific Populations: Geriatric, Obese, and Pediatric Patients 759
estimate GFR in patients with chronic kidney Her height in centimeter (cm) = 65 (inches) ×
disease. 2.54 (cm/inch), which is 165.1 cm
The CG equation estimates creatinine clear- Her BMI = 58.4 kg/m2
ance (Clcr) as a surrogate of GFR. She is morbidly obese, according to the classi-
fication of obesity based on BMI (Table 23.2-1).
[(140 – age) × (Weight in kg)]/[72 × serum
It is recommended to use adjusted body weight
creatinine] × 0.85 if female (23.1.1)
to estimate Clcr from the CG equation for patients
who are overweight, obese, or morbidly obese.
Clearance of the endogenous creatinine in serum
• In order to calculate Adj. BW, IBW needs to be
(Scr) is dependent on GFR and renal tubular
calculated first, using Equation 23.2.3:
secretion. The production of the endogenous
IBW = 45.5 + 2.3 × [Height (inches) – 60] kg
creatinine is affected by diet and muscle mass.
Her IBW = 57 kg
To estimate Clcr by the CG equation, it is recom-
mended to use TBW in underweight patients, • Calculate Adj. BW using Equation 23.2.4:
IBW in patients with normal weight, and Adj. BW = IBW + 0.4 × (TBW – IBW) kg
adjusted body weight for overweight, obese, and Her Adj. BW = 97.8 kg
morbidly obese patients (Winter et al, 2012). A • Calculate Clcr (mL/min) by CG equation (Equa-
recent study (Pai, 2010) reported that using lean tion 23.1.1) using Adj. BW:
body weight (LBW) in the CG equation pro- Clcr (mL/min) = [(140-age) × (Weight in kg)]/
vides a practical estimation of GFR for drug [72 × serum creatinine] × 0.85
dosing in obesity. Her estimated Clcr = 87 mL/min
Applying the pharmacokinetic principles and
using modified weight strategies may help with bet-
ter drug dosing for the obese. However, due to limi-
EXAMPLE 2 • • •
tations on published pharmacokinetic studies in
obesity, and interindividual variations within the A 45-year-old male was admitted to the hospi-
obese population, individualized therapeutic drug tal with chief complaints of shortness of breath,
monitoring, especially for drugs with narrow thera- wheezing, chills, and fever. Past medical history
peutic index, is warranted. included hypertension, arthritis, and asthma.
The patient’s weight and height were 300 lb and
Clinical Examples on Estimating Creatinine 5′-4″, respectively, and his serum creatinine is
Clearance in Obesity 1.2 mg/dL.
Discussion:
• Calculate BMI as in Example 1; the answer is
51.6 kg/m2.
EXAMPLE 1 • • •
• Calculate IBW using Equation 23.2.2:
A 50-year-old female, BT, was admitted to the hos- IBW = 50 + 2.3 × [Height (inches) – 60] kg
pital with sepsis. Her height is 5 feet and 5 inches, His IBW = 59.2 kg
and weight was 350 lb. Her serum creatinine is 1.2 • Calculate Adj. BW as in Example 1:
mg/dL. The team has decided to start BT on an His Adj. BW = 90 kg
antibiotic regimen.
• Calculate Clcr (mL/min) using Adj. BW for weight:
Discussion:
Clcr (mL/min) = [(140 – age) × (Weight in kg)]/
• First, calculate BMI for BT using Equation 23.2.1: (72 × serum creatinine)
Her TBW in kilogram = 350 (lb)/2.2 (lb/kg), His estimated Clcr = 99 mL/min
which is 159.1 kg
760 Chapter 23
SUMMARY
Our understanding of obesity and its implications obese and non-obese groups was limited in these
continues to improve, as more research has been studies. As a note, the weight-normalized clearance
devoted to this arena. However, the complexity of values may provide quantitative difference informa-
physiological changes in obesity combined with tion for clearance (Brill et al, 2012).
obesity-related comorbidities frequently incurred in Renal clearance is increased in the obese patients
the obese population may render pharmacokinetic due to increased glomerular filtration and tubular secre-
studies challenging. More studies are needed on tion. The impact of obesity on tubular reabsorption is
drug absorption in the obese population, as well as currently inconclusive due to limited data. Weight-
specific studies on drug distribution, metabolism, normalized clearances for all drugs studied for renal
and elimination in obesity. elimination showed similar or lower values in the obese
For Phase I metabolism, CYP3A4 activity was group, as compared to the non-obese group.
consistently lower in the obese group, while the In terms of drug dosing, even with the same
enzyme activities of CYP2E1 and xanthine oxidase BMI, individual obese patient may present with
were consistently higher in the obese group. Other unique body composition and fat distribution. Thus,
Phase I metabolism enzymes showed trends toward drug dosing for the obese patients remains to be
higher activities in the obese group, but the results elusive. Presently, in an effort to ensure optimal
were not conclusive. For Phase II metabolism, UGT- therapeutic outcome for drug therapies in obesity,
mediated drug clearances were significantly higher we need to keep abreast with published pharmacoki-
in the obese group. Liver blood flow may be netic data, apply the information to patients pru-
increased in obesity, but the number of the drugs dently, and provide individualized therapeutic
studied is small, and the weight difference between monitoring as indicated.
LEARNING QUESTIONS
A 45-year-old female was admitted to the hospital 3. Which of the following CYP450 isoenzymes
with chief complaints of shortness of breath, wheez- showed a reduced activity in the obese patients?
ing, chills, and fever. Past medical history included a. CYP3A4
hypertension, arthritis, and asthma. The patient’s b. CYP2E1
weight and height were 300 lb and 5′-4″, respectively. c. CYP2C9
1. Which of the following answers is correct for d. CYP2D6
this patient’s body mass index (BMI)? e. Xanthine oxidase
a. 35.0 4. Which of the following statements most
b. 39.3 accurately reflects the physiological changes
c. 60.9 commonly occurred with obesity?
d. 54.2 a. Glomerular filtration is usually increased in
e. 51.6 the obese patients.
2. If this patient has a serum creatinine of 1.0 mg/dL, b. Tubular reabsorption is usually increased in
calculate her estimated creatinine clearance in the obese patients.
mL/min using adjusted body weight (Adj. BW) c. Tubular secretion is usually decreased in the
in the Cockcroft–Gault equation. obese patients.
a. 115.3 d. The activity of uridine diphosphate glucuro-
b. 98.0 nosyltransferase is usually decreased in the
c. 61.3 obese patients.
d. 152.9 e. The size of the kidney is usually smaller in
e. 120.0 the obese patients.
Application of Pharmaco kinetics to Specific Populations: Geriatric, Obese, and Pediatric Patients 761
5. Which of the following statements most c. The TBW should always be used to cal-
accurately reflects an appropriate drug dosing culate the maintenance dose for the obese
strategy for the obese patients? patients.
a. The TBW should always be used to calcu- d. The IBW should always be used to calculate
late the loading dose for the obese patients. the maintenance dose for the obese patients.
b. The IBW should always be used to calculate e. Applying the pharmacokinetic principles
the loading dose for the obese patients. and using modified weight strategies, com-
bining with therapeutic drug monitoring.
ANSWERS
Learning Questions 3. a.
1. a. 4. a.
2. b. 5. e.
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14:860, 1964. Cheymol G, Weissenburger J, Poirier JM, et al: The pharmacoki-
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June 18, 2013. beta-adrenoceptor blockers in obese and normal volunteers.
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762 Chapter 23
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and obese subjects. Eur J Clin Pharmacol 51:493, 1997b. new predicting equation. Modification of Diet in Lieber, C.S.
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propofol pharmacokinetics: Derivation of a pharmacokinetic May DG: Genetic differences in drug disposition. J Clin Pharma-
model. Br J Anaesth 105:448, 2010. col 34:881, 1994.
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Geneva, WHO, June 3-5, 1998.
MODULE III: APPLICATION OF (Rowland and Tozer, 2011; Murphy, 2012). The age
of 21 years is consistently used in several well-
PHARMACOKINETICS TO THE
known sources (Avery, 1994; Kliegman et al, 2011;
PEDIATRIC PATIENTS Rudolph et al, 2011).
Objectives
Inadequate Guidance in Dosing
• List the demographic definition of pediatric Recommendation for Pediatric Patients
population. Pediatric patients have different dosing requirements
• Understand inadequacy of current guidance in from those for adults (ICH E11 Guideline, 2000;
dosing recommendation for pediatric patients. Bartelink et al, 2006; Leeder et al, 2010; Benavides
• Describe the age-dependent differences in physi- et al, 2011). Information for pediatric dosing was
ological functions and pharmacokinetic (ADME) generally lacking in the past. For most (75%) of
consequences of drugs. drugs, pediatric patients are still dosed as “off-label”
• Describe the effects of age on pharmacodynamics usage without specific pediatric dosing recommen-
of drugs. dations (Benavides et al, 2011).
• Discuss the studies to help rational dosing in pedi- When dosage guidelines are not available for a
atric patients. drug, empirical dose adjustment methods are often
• Describe the emerging approaches to study phar- used. Dosage normalized based on the child’s age or
macology in pediatric population. body weight from adult drug dosages was used through
the Young’s rule [Adult Dose × (Age ÷ (Age + 12)) =
Child’s Dose] and Clark’s rule [Adult Dose × (Weight ÷
Pediatric Population 150) = Child’s Dose], respectively. Dosage based on
Pediatric subjects are not miniature adults, nor body surface area has an advantage of avoiding bias
belong to a homogeneous population as their ana-
tomical development and physiological functions TABLE 23.31 Age Ranges of Pediatric
vary depending on their age brackets. Therefore, the Subpopulations
pharmacokinetic characteristics of medications dif- Premature (preterm) Born at gestational age
fer among pediatric subpopulations. The pediatric neonates <38 weeks
subpopulations consist of preterm or term neonates, Neonates (term newborn) 0–4 weeks postnatal age
infants, children, and adolescents, with the age
Infants 1 month to 2 years of age
ranges defined in Food and Drug Administration
(1 month to <12 months
(FDA) Guidance for Industry (Table 23.3-1) (FDA, old)
2014). The upper age limits used to define the pedi-
Children 2–12 years of age
atric subpopulations vary among experts (FDA,
(1–12 years old)
1997; Rowland and Tozer, 2011; Murphy, 2012) as
given in parentheses of Table 23.3-1, including for Adolescents 12–21 years of age
(13–16, 18, or 19 years old)
adolescents up to the age of 16, 18, 19, or 21 years
764 Chapter 23
due to obesity or unusual body weight, because both with increasing emptying and transit time, but biliary
the height and the weight of the patient are considered. function is near the adult pattern. In children, the
However, these dosages are rough estimates and often emptying and transit time is still increasing up to
inadequate to reflect the developmental and physiologi- 4 years of age to mature, but pH and biliary function
cal differences that lead to pharmacokinetic conse- are similar to those of adults (Kearns et al, 2003). As
quences among the pediatric subpopulations, as well as a consequence, the higher pH in neonates and infants
between pediatric and adult populations. Therefore, result in higher bioavailability (F) of acid-labile
pediatric subjects should not be considered as small drugs, such as penicillin G, ampicillin, and nafcillin,
adults in the aspect of pharmacokinetics. Pediatric drug but lower F of phenobarbital (weak acid) that may
use information should be consulted in the product require a higher dose as compared to those for chil-
label’s Use in Specific Populations subsection. dren and adults (O’Connor et al, 1965; Sliverio and
In December 1994, the FDA required drug Poole, 1973; Morselli, 1977). The fast GI transit
manufacturers to determine whether existing data reduces the rate and extent of absorption in neonates,
were sufficient to support information on pediatric infants, and young children. The neonates are diffi-
use for drug labeling purposes and implemented a cult to absorb fat-soluble vitamins compared to
plan to encourage the voluntary collection of pediat- infants and children due to the immature biliary
ric data. The FDA Modernization Act (FDAMA) function (Heubi et al, 1982).
505(A) authorized a pediatric exclusivity with an
additional 6 months of patent protection for manu- Drug Distribution
facturers who conducted pediatric clinical trials Factors such as plasma protein concentration, body
(FDA, 1997). As a consequence, the pediatric studies composition, blood flow, tissue-protein concentration,
resulted in 202 product label changes in 2007–2012 and tissue fluid pH are important for drug distribution.
with the inclusion of new indications and enhanced Of these factors, the changes in (a) plasma protein
pediatric safety information for pediatric population concentration, (b) total body fat, as well as (c) total
(Leeder et al, 2010). These studies reveal significant body water and extracellular water are the three major
new information regarding dosing and pharmacoki- factors exerting significant effects on drug distribution
netic differences between children and adults in pediatric population (Murphy, 2012).
(Maples et al, 2006). The total body water is high, constituting 75%–
The rational, effective, and safe dosing of drugs 90% of total body weight in neonates and infants up
in the pediatric population requires a thorough under- to the first 6 months of life, compared to about 60%
standing of the differences in developmental pharma- in children and adults (O’Connor et al, 1965). As a
cology, pharmacokinetics, and pharmacodynamics of result, the apparent volume of distribution (V) of
a specific drug, among individual subpopulations, as hydrophilic drugs is age dependent, as illustrated in
well as between pediatric and adult subjects. Table 23.3-2 with the well-documented case of gen-
tamicin (Shevchuk and Taylor, 1990; Semchok et al,
1995). The extracellular fluid (ECF) is high in neo-
Age-Dependent Differences in Physiological
nates, 45%, as compared to 25%–26% in adults, but
Functions and Impacts on Pharmacokinetics
approaching adult value in one year of life. The total
of Drugs
body fat is less, 12% in neonates and infants, but
Absorption peaks at 30% in one year, then decreasing gradually
The physiological variables for oral absorption, such to adult value of 18%. Therefore, when we dose on
as gastric pH, gastric emptying time, intestinal tran- a weight (kg) basis, lower plasma concentrations for
sit time, and biliary function, are distinct among hydrophilic drugs are expected in neonates and
neonates, infants, and children. In neonates, the gas- young infants, due to their higher percentage of total
tric pH is >4, and gastric emptying and intestinal body water and ECF for drug distribution out of
transit are faster and irregular with immature biliary blood circulation. The age-dependent V of lipophilic
function (Murphy, 2012). In infants, the pH is 2–4 drugs is less apparent (Table 23.3-2).
Application of Pharmaco kinetics to Specific Populations: Geriatric, Obese, and Pediatric Patients 765
TABLE 23.32 Age-Dependent Apparent 1980; Payne et al, 1989; Burtin et al, 1994; Hines
Volumes of Distribution of Gentamicin and and McCarver, 2002).
Diazepam Significant impacts of the age-dependent devel-
opment of Phase I enzymes on the pharmacokinetics
V (L/kg)
Age Gentamicin Diazepam have been documented. The hepatic metabolism of
carbamazepine (substrate of CYP3A4) is increased
<34 weeks postnatal 0.67 in infants and children as compared to neonates and
34–48 weeks 0.52 1.3–2.6 adults (Korinthenberg et al, 1994). Phenytoin (sub-
postnatal strate of CYP2C9) exhibits varying half-lives of
1–4.9 years 0.38 75 hours in preterm infants, 20 hours in first week of
term infants, and 8 hours after the second week of
5–9.9 years 0.33
life (Besunder et al, 1988). With diazepam (substrate
10–16 years 0.31 of CYP2C19), the age-dependent changes in oxida-
Adults 0.30 1.6–3.2 tive metabolism result in the shortest half-life in
children, 7–37 hours, as compared to those of
25–100 hours in neonates and infants, and 20–50
hours in adults (Morselli et al, 1973).
The protein concentrations are low in the neo- Clinical observations are consistent that hepatic
nates and infants up to one year old. The changes in metabolism is age dependent in pediatric patients.
circulating plasma proteins, albumin and α-acid Hepatic metabolism in children of 3–10 years of age
glycoprotein, affect the distribution of highly bound is greater than that of adults. The greater hepatic
drugs. In neonates and young infants, phenytoin has clearance in this subpopulation remains significant
a higher unbound fraction of the drug in circulation even after the correction for the age-dependent liver
to exert activity (MacKichan, 1992). The competi- weight (Murry et al, 1995). Therefore, the doses
tive binding of bilirubin on albumin is also a relevant required for this subpopulation of children are often
issue in neonates, in that a higher unbound fraction higher on the body weight basis, as compared to
of a drug will be resulted from the displacement by adolescents and adults.
bilirubin in binding of the drug to albumin (Allegaert
et al, 2008). Phase II Enzymes-Related Metabolism. The
ontogeny of conjugation reactions is less well
Hepatic and Extrahepatic Drug Metabolism established than that involving Phase I drug-
The developmental differences in drug-metaboliz- metabolizing enzymes. Among the Phase II drug-
ing enzymes and transporters are still inadequately metabolizing enzymes, glucuronosyltransferase
characterized (Allegaert et al, 2008; Murphy, (UGT) has reduced activity in neonates and young
2012). children but approaches adult level by adolescents.
For example, kernicterus is a form of jaundice in the
Phase I Enzymes-Related Metabolism. In newborn characterized by very high levels of
neonates, Phase I enzymes of CYPs 3A4, 2D6, 2C9, unconjugated bilirubin in the blood. Since the tissues
and 2C19 are all reduced, with 30%–40%, 20%, protecting the brain (the blood–brain barrier) are not
30%, and 30% of adult activities, respectively well formed in newborns, unconjugated bilirubin
(Litterst et al, 1975; Neims et al, 1976). In infants, may enter the brain and cause brain damage. Another
CYP2D6 remains reduced, but reaches adult pattern example is that the glucuronide/sulfate ratios of
by the age of 1 year (Mortimer et al, 1990). Other acetaminophen increases as UGT system matures,
CYP enzymes, CYP3A4, -2C9, and -2C19, reach with 0.34 in newborn and 0.8 in children of 3–10
adult levels by 6 months of life, peak in young years old, as compared to 1.61 and 1.8–2.3 in
children at ages of 3–10 years, and decline to adult adolescents and adults (Miller et al, 1976).
levels at puberty (Morselli et al, 1973; Chiba et al, Sulfotransferase (SULT) has reduced activity in
766 Chapter 23
neonates, but higher activity in infants and children adults cannot be extrapolated to the pediatric popula-
(Murphy, 2012). Methyltransferase in children has tion, because the varied metabolic changes among the
increased activities, 50% higher than that in adults pediatric subpopulations may result in subtherapeutic
(Maples et al, 2006). concentrations of one agent in young children, such as
nevirapine (metabolized by CYP3A4 and CYP2B6),
Excretion but overdosing of another agent, such as lamivudine
The rates of glomerular filtration, tubular secretion, of high fe = 0.7 (eliminated by GFR and active tubular
and tubular reabsorption are slower at birth, but rap- secretion), in neonates (Ellis et al, 2007). The recom-
idly rise to adult levels in 8–12 months of age (van mended lamivudine dose for infants and children is
den Anker, 1995). Therefore, drugs of high fe (frac- 4 mg/kg twice daily, whereas the dose for neonates
tion excreted in urine unchanged) require longer dos- <28 days of age is halved due to the premature devel-
ing intervals to accommodate the slower drug renal opment of kidney functions (Panel on Antiretroviral
clearance. The prolonged dosing interval allows a Therapy and Medical Management of HIV-Infected
longer period of time to excrete drug molecules into Children, 2010).
urine and minimize drug accumulation in circulation.
As a result, similar systemic drug concentrations can Age-Dependent Differences on
be maintained as to those with more mature renal Pharmacodynamics of Drugs
function. For example, the dosing interval of amino- In contrast to the current understanding of age-
glycoside is suitable as 24 hours for term newborns, dependent pharmacokinetics, much less information
but is required to be 36–48 hours for preterm new- is available for the developmental impacts on drug
born (Schwartz et al, 1987; Brion et al, 1991). actions at the receptor level (pharmacodynamics)
In summary, the understanding of differences in (Holford, 2010). Several age-dependent differences
developmental changes and their impacts on phar- in treatment responses are recognized (Murphy,
macokinetics (ADME) of medications is essential to 2012), not related to the PK differences but in inter-
interpret pharmacokinetic observations correctly and action between the drug and its corresponding recep-
to recommend rational modification in dosing regi- tor (warfarin and cyclosporine), or in the relation
men for an effective and safe therapy in the pediatric between the plasma drug concentration and the
population. pharmacological effect (sedation effect of mid-
In recent years, antiretroviral therapy has been azolam). The pediatric study decision tree (Fig. 23.3-1)
used in HIV-infected pediatric patients. An estimated from the FDA asks significant questions on potential
260,000 children were newly infected with HIV in age-dependent pharmacodynamics in each step, con-
2012 (UNAIDS, 2013). The disposition of antiretrovi- cerning disease progress, medical intervention, con-
ral therapy is significantly affected by the differential centration response, and PK/PD to achieve target
pharmacokinetic characteristics among the pediatric concentration between pediatric and adult popula-
subpopulations. The impacts can be drug specific. tions (FDA Guidance to Industry, 2003).
The oral absorption of antiretrovirals is affected
by the presence of food in GI tract of infants. For
Emerging Approaches to Study
example, the F of nelfinavir (a weak acid drug) in
newborns and infants <2 years of age is lower than Pharmacology in Pediatric Population
those in older children, due to the food effect, higher (Knibbe et al, 2011; Himebauch and
gastric pH or both (Hirt et al, 2006). Decreased albu- Zuppa, 2014)
min contents in newborns and neonates cause The awareness has grown in the past 20 years on the
increases in the unbound fraction of highly protein- age-dependent pharmacokinetics of medications,
bound anti-HIV drugs, such as enfuvirtide (>90% resulting from physiological and pharmacological
bound), that result in increased efficacy and toxicity differences across the entire pediatric age range, and
(Bellibas et al, 2004). The current cocktail regimen between pediatric and adult populations. With the
with fixed-dose combinations of antiretrovirals for legislative incentive from the FDA (Best
Application of Pharmaco kinetics to Specific Populations: Geriatric, Obese, and Pediatric Patients 767
Reasonable to assume (pediatrics vs adults)
Similar disease progression?
Similar response to intervention?
No Yes to both
Conduct PK studies Reasonable to assume (pediatrics vs adults)
Conduct safety/efcacy trials Similar concentration-response (C-R)?
No
No Yes
Is there a PD measurement Conduct PK studies to
that can be used to predict efcacy? achieve levels similar to adults
Conduct safety trials
Yes
Conduct PK/PD studies to get C-R for PD measurement
Conduct PK studies to achieve target concentrations based on C-R
Conduct safety trials
FIGURE 23.31 Pediatric study decision tree from FDA.
Pharmaceuticals for Children Act [BPCA] of 2002 exponent values of 0.75 for Cl and of 1 for V.
(FDA, 2002) and Pediatric Research Equity Act However, the allometric exponent for scaling Cl has
[PREA] of 2003 (FDA, 2003), and EU [Pediatric been recognized to vary with ages in subpopulations
Regulation 2007]), an increasing number of studies of pediatric population (Wang et al, 2013). For
on pediatric PK and PD were conducted from both example, the exponents for propofol to scale down
academic and industrial settings. from adults to neonates, infants, children, and ado-
In general, the clinical pediatric PK data are lescents are 1.11, 0.60, 0.70, and 0.74, respectively
scarce and often do not cover the entire pediatric age (Wang et al, 2013). Therefore, the current allometric
range. In addition, the study enrollment is small and scaling approach may be of value for scaling from
the number of observations per pediatric subject is adults to adolescents and perhaps children, while it
limited due to constraints in the volume and fre- is inadequate for scaling from adults to neonates, or
quency of blood sampling. Advances have been between pediatric subpopulations (Wang et al, 2013).
made in descriptive pediatric population PK models On the other hand, the pediatric PBPK modeling
for specific drugs and particular age range to over- and simulation have been increasingly employed in
come these constraints (Knibbe et al, 2011). pediatric drug development, as well as in FDA regula-
Two approaches are emerging to more effi- tory review and decision making (Leong et al, 2012).
ciently study pharmacokinetics of drugs in pediatric The PBPK model is capable of integrating the factors
population for trial design, execution, and data that address developmental and maturational changes
analysis. The approaches are allometric scaling affecting ADME processes of PK in pediatric sub-
(Knibbe et al, 2011; Wang et al, 2013) and physio- populations (Barrett et al, 2012). The PBPK model is
logical-based pharmacokinetic (PBPK) modeling most commonly implemented in pediatric drug devel-
(Leong et al, 2012; Himebauch and Zuppa, 2014). opment, for first-time-in-pediatrics (FTIP) dose selec-
In performing allometric scaling, the pharmaco- tion, which is a critical milestone and decision point
kinetic parameters of clearance (Cl) and volume in pediatric drug development (Edginton, 2011), sim-
distribution (V) of pediatric subjects are often pre- ulation-based clinical trial design (Mouksassi et al,
dicted by scaling down from adult values with fixed 2009), systemic exposure–response correlation, and
768 Chapter 23
safety assessments of target organ toxicity and in non- population total clearance (Cltot) in children is 3.96
systemic biodistribution targets. L/h (Vassal et al, 2008), whereas that of adults is
about 2.5 L/h (Nguyen et al, 2006). The Cltot varies
Clinical Example of Rational Dosing in among the subjects in the strata, with the greatest
Pediatric Patients value for subjects of 9- to 16-kg body weight, and
reducing to approach the adult value at body weight
Busulfan is a bifunctional alkylating agent (MW
>34 kg. With the specifically derived Cltot, the ratio-
246.31 Da) and used for the preparative regimen
nal doses are derived for individual subsets of pedi-
before blood, bone marrow, or stem cell transplanta-
atric patients, based on the following relationship:
tion. Before the FDA approval of IV Busulfex® in
1999 for parenteral administration, patients had to
Total dose (mg/kg) = Cl
eceive 35 tablets q6h around the clock for 4 days tot × (Target AUC)
r
(total 16 doses). Moreover, the drug triggered vomit-
The dose levels adjusted are 1, 1.2, 1.1, and 0.95 mg/kg,
ing and resulted in erratic systemic exposure, AUC,
for patients with body weights of <9, 9–16, 16–23, and
in patients. However, the grafting success depends
23–34 kg, respecitvely, higher than the dose of
on reaching target AUC of 900–1500 mMol•min, and
0.8 mg/kg for adults. The resulting busulfan AUCs are
adverse effect is observed when AUC is >1500
all well within the theraputic range of 900–1500
mMol•min. Therefore, dosing busulfan precisely and
mMol•min (Fig. 23.3-2B).
effectively is challenged in adults, and even more so
in pediatric patients due to the constraints in thera-
peutic drug monitoring in the pediatric population. Other Considerations
With the IV Busulfex, the age-dependent clear- In addition to different dosing requirements for the
ance is characterized based on 5 body weight strata pediatric population, there is a need to select age-
from <9 kg to >34 kg (Fig. 23.3-2A; Vassal et al, appropriate dosage forms that permit more accurate
2008) for 55 pediatric patients 0.3–17.2 years old dosing and better patient compliance. For example,
with 20 subjects younger than 4 years old. The liquid pediatric drug products may have a calibrated
A
6
5
4
3
2
1
g n 3]
9
k
kg
]
kg
]
kg
] kg ldr
e [3
< 16 23 34 34
< Chi lts
[9
– 6– 3–
[1 [2 Adu
Weight strata (kg)
FIGURE 23.32 Busulfan clearance (A) and AUC with adjusted doses (B) among body weight strata.
Bu clearance (mL·min–1·kg–1)
Application of Pharmaco kinetics to Specific Populations: Geriatric, Obese, and Pediatric Patients 769
B
2300
2100
1900
1700
1500
1300
1100
900
700
<
9
kg
[9
–1
6
kg
]
[1
6–
23
kg
]
[2
3–
34
kg
]
<
34
kg
Chil
dr
en [3
3]
Adu
lts
Weight strata (kg)
FIGURE 23.32 (Continued)
dropper or a premeasured teaspoon (5 mL) for more must be considered in order to prevent dosage errors.
accurate dosing and also have a cherry flavor for Moreover, the oral absorption of medications in neo-
pediatric patient compliance. Pediatric drug formu- nates and infants may be well affected by the pres-
lations may also contain different drug concentra- ence of milk or infant formula in GI tract.
tions compared to the adult drug formulation and
SUMMARY
Pediatric subjects consist of four subpopulation composition of total body water and total body fat
groups, namely, neonates, infants, children, and ado- and plasma protein concentrations for highly bound
lescents. The pharmacokinetics of medications in drugs. The drug clearance (Cl) is affected by Phase
pediatric patients is distinct from those of adult sub- I- and II-mediated metabolisms and renal excretion.
jects, as well as among the pediatric subpopulations. The Phase I metabolisms in neonates and infants are
Therefore, a thorough understanding of their devel- lower than those in adults. However, these metabo-
opmental and physiological differences and the lisms in children of ages of 3–10 years are often
resulting impacts on pharmacokinetics (ADME) of higher than those in adults that require higher dose
medications is essential to interpret pharmacokinetic on body weight basis, than those for adolescents and
observations correctly and to recommend rational adults. The Phase II metabolizing enzyme capacities
modification in dosing regimen for an effective and approach adult levels in childhood. The renal func-
safe therapy in the pediatric population. tion is immature in neonates but matures within the
The absorptions in neonates and infants differ first year of life. The age-dependent variations in
from those of children and adolescents, due to the these clearance processes are unique among pediat-
high gastric pH, short gastric emptying time and ric subpopulations. As a result, pediatric dose adjust-
intestinal transit time, and immature biliary function. ment is challenging as it is drug specific and age
The drug distribution (V) is affected by the dependent.
Bu AUC (µMol·min)
770 Chapter 23
The current understanding in age-related phar- and industrial settings. Emerging approaches of
macodynamic variations between pediatric and adult population PK, PBPK, and allometric scaling have
populations, as well as those among pediatric sub- been gaining acceptance in FTIP dose selection,
populations, is still limited, and requires more stud- rational clinical trial design, trial execution, and data
ies to fill the knowledge gap. analysis. It is anticipated that more useful PK/PD
With the legislative incentive from the FDA and information will be generated in the next few
EU, an increasing number of studies on pediatric PK decades to facilitate future rational and safe drug
and PD have been performed from both academic therapy in pediatrics.
LEARNING QUESTIONS
1. Which of the following groups belongs to the pediatric population?
a. Children
b. Infants
c. Adolescents
d. Neonates
e. All of the above
2. Pediatric population has unique ADME characteristics from those of adults. In addition, the ADME are
distinct among the subpopulations of pediatric subjects. Fill in the blanks in the following table, using ↓
(lower than adult capacity), ↑ (higher than adult capacity), and ↔ (similar or near [~ ↔] adult capacity).
Physiological or PK
Characteristic Neonate Infant Child Adolescent
Absorption
Gastric pH _____ ↑ ↑ ↔
GI transit time _____ ↓ _____ ↔
Biliary function ↓ _____ ↔ ↔
Distribution
Total water/ECF _____ _____ ↓~ ↔ ↔
Total body fat ↓ ↓ _____ _____
Plasma protein ↓ _____ ↔ ↔
Metabolism
CYP enzymes ↓↓ _____ _____ ↔
Phase II enzymes ↓ ↓ _____ ↔
Excretion
Glomerular filtration ↓ _____ ↔ ↔
Tubular secretion _____ ~ ↔ ↔ ↔
Tubular reabsorption
Application of Pharmaco kinetics to Specific Populations: Geriatric, Obese, and Pediatric Patients 771
3. Temozolomide (Temodar®) is an antineoplastic for the treatment of seizures. The Cls of VA
alkylating agent, indicated for refractory (first are 13 mL/kg/h for children and 8 mL/kg/h
relapse) anaplastic astrocytoma. The recom- for adults. The V and F of VA are 0.14 L/kg
mended treatment protocol is oral doses of and 1, respectively. The therapeutic plasma VA
200 mg/m2/day for 5 days and repeated every concentrations are 50–100 mg/L. The toxicity
28 days. The F of temozolomide is 0.98 with is observed as >200 mg/L.
an empty stomach and 0.6 when the drug is WS has normal hepatic and renal functions.
taken with fatty food. The Cl and t1/2 of the (a) Predict the steady state trough concentra-
drug are 100 mL/min/m2 and 1.8 hours, respec- tion (Css,min) for WS, and (b) comment on
tively. The available capsule strengths are 5, the adequacy of his current regimen, using a
20, 100, and 250 mg. 1-compartment intravenous bolus model.
CB is a 15-month-old patient of 7-kg body 5. The elimination half-life of penicillin G is
weight (0.3 m2). (a) What is the Cl of temozolo- 0.5 hour in adults and 3.2 hours in neonates
mide in CB? (b) Recommend a regimen for CB, (0–7 days old). Assuming that the normal adult
which F is to be used? (c) Predict the Css,ave. dose of penicillin G is 4 mg/kg every 4 hours,
4. WS, an 8-year-old, 25-kg male, is receiving calculate the dose of penicillin G for an 11-lb
a 250-mg capsule of valproic acid (VA) q12h infant.
ANSWERS
Learning Questions
1. E
2.
Physiological or PK
Characteristic Neonate Infant Child Adolescent
Absorption
Gastric pH ↑↑ ↑ ↑ ↔
GI transit time ↓↓ ↓ ↔ ↔
Biliary function ↓ ~ ↔ ↔ ↔
Distribution
Total water/ECF ↑ ↑ ↓~ ↔ ↔
Total body fat ↓ ↓ ↑ by 1–10 yo ↔
Plasma protein ↓ ↓~ ↔ ↔ ↔
Metabolism
CYP enzymes ↓↓ ↓ ~ ↔ by 1 yo ↑ ↔
Phase II enzymes ↓ ↓ ↔ ↔
Excretion
Glomerular filtration ↓ ↔ ↔ ↔
Tubular secretion ↓ ~ ↔ ↔ ↔
Tubular reabsorption
772 Chapter 23
3. (a) Cl = (100 mL/min/m2)(0.3 m2) k = Cl/V = (0.325 L/h)/3.5 L
= 30 mL/min = 0.093 h–1
= [30 (60)/1000] L/h = 1.8 L/h Css,min = [(D/V) e–k • t]/(1 – e–k • t)
= [(250 mg)/(3.5 L)][e–(0.093)(12)
The Cl in the infant is significantly lower ]/
[1 – e–(0.093)(12)
than that of 10.3 L/h in adults with 1.73 m2 ]
of body surface area. = (71.43 mg/L)(0.328)/(0.672)
= 34.8 mg/L ~ 35 mg/L
(b) D/τ = (200 mg/m2/day)(0.3 m2)
= 60 mg/day = 60 mg/24 hours (b) The Css,min is below the therapeutic range
= 20 mg/8 hours of 50–100 mg/L. The current regimen is
The dose will be given with 3 × 20-mg required to be modified.
capsules or in divided doses per day. Discussion: If Cl of 8 mg/kg/h for adults
is misused,
(c) Css,ave = [F D]/[Cl • t]
Cl = (8 mL/kg/h)(25 kg)
Which F is to be used? = 200 mL/h = 0.20 L/h
F = 0.6 (not 0.98) is used to predict the k = Cl/V = (0.20 L/h)/3.5 L
Css,ave, because infants are fed regularly; = 0.057 h–1
therefore, the medication is NOT given Css,min = [(D/V) e–k • t]/(1 – e–k • t)
to the infant with empty stomach, and = [(250 mg)/(3.5 L)][e–(0.057)(12)]/
infant formula in general is rich in the fat [1 – e–(0.057)(12)]
content. = (71.43 mg/L)(0.505)/(0.495)
= 72.8 mg/L ~ 73 mg/L
Css,ave = [F D]/[Cl • t]
(overestimated for ~ 2 times)
= [(0.6)(60 mg)]/[(1.8 L/h)(24 h)]
= 0.83 mg/L The comment on the regimen will then
be mistakenly made as adequate, because
The Css,ave will be overestimated by 1.6 the overestimated trough concentration of
times as 1.36 mg/L, if an incorrect F (0.98) 73 mg/L is within the therapeutic range
is selected. of 50–100 mg/L!
4. (a) The one-compartment IV bolus model
can be used to estimate the concentration,
because VA is rapidly (with very high ka)
t1 (t1/2)1
=
and completely absorbed. t2 (t1/2)2
For the one-compartment IV bolus model, t1/2 = 0.5 h (23.1.3)
Css,max = C0/(1 – e–k • t) 4 × 3.2
Css,min = Css,max e
–k • t t2 = = 25.6 h
0.5
= C0 e
–kt/(1 – e–k • t)
= [(D/V)e–kt]/(1 – e–k • t) Therefore, this infant may be given the fol-
D = 250 mg t = 12 h lowing dose:
V = (0.14 L/kg)(25 kg) = 3.5 L
k = Cl/V Dose = 4 mg/kg [11 lb/(2.2 lb/kg)]
What is the Cl for AH? = 20 mg every 24 h
Cl = (13 mL/kg/h)(25 kg) Alternatively, 10 mg every 12 hours would
= 325 mL/h = 0.325 L/h achieve the same Css,ave.
Application of Pharmaco kinetics to Specific Populations: Geriatric, Obese, and Pediatric Patients 773
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Dose Adjustment in Renal
24 and Hepatic Disease
Yuen Yi Hon
Chapter Objectives RENAL IMPAIRMENT
»» List the common causes of Chronic kidney disease (CKD) is a worldwide public health prob-
chronic kidney disease (CKD) lem affecting more than 50 million people, and more than 1 million
and describe how CKD affects of them are receiving kidney replacement therapy (Levey et al,
drug elimination. 2009). The kidney is an important organ in regulating body fluids,
»» Compare the advantages electrolyte balance, removal of metabolic waste, and drug excre-
and disadvantages of the tion from the body. Impairment or degeneration of kidney function
use of drugs or endogenous affects the pharmacokinetics of drugs. Some of the more common
substances as markers for the causes of kidney failure include disease, injury, and drug intoxica-
measurement of renal function. tion. Table 24-1 lists some of the conditions that may lead to
chronic or acute renal failure. Acute diseases or trauma to the
»» Describe the relationships
kidney can cause uremia, in which glomerular filtration is impaired
between creatinine clearance,
or reduced, leading to accumulation of excessive fluid and blood
serum creatinine concentration,
nitrogenous products in the body. Uremia generally reduces glo-
and glomerular filtration rate.
merular filtration and/or active secretion, which leads to a decrease
»» Explain and contrast the in renal drug excretion resulting in a longer elimination half-life of
methods of Cockcroft–Gault the administered drug.
and Modification of Diet in In addition to changing renal elimination directly, uremia can
Renal Disease (MDRD) for affect drug pharmacokinetics in unexpected ways. For example,
the calculation of creatinine declining renal function leads to disturbances in electrolyte and
clearance. fluid balance, resulting in physiologic and metabolic changes that
»» List the causes for fluctuating may alter the pharmacokinetics and pharmacodynamics of a drug.
serum creatinine concentration Pharmacokinetic processes such as drug distribution (including
in the body. both the volume of distribution and protein binding) and elimina-
tion (including both biotransformation and renal excretion) may
»» Calculate the dose for a drug in a also be altered by renal impairment. Both therapeutic and toxic
patient with renal disease. responses may be altered as a result of changes in drug sensitivity
»» Describe quantitatively using at the receptor site. Overall, uremic patients have special dosing
equations how renal or hepatic considerations to account for such pharmacokinetic and pharma-
disease can alter the disposition codynamic alterations.
of a drug.
»» Describe hemoperfusion and PHARMACOKINETIC CONSIDERATIONS
the limitations for its use.
Uremic patients may exhibit pharmacokinetic changes in bio-
availability, volume of distribution, and clearance. The oral
bioavailability of a drug in severe uremia may be decreased
775
776 Chapter 24
»» Distinguish between as a result of disease-related changes in gastrointestinal motility
hemodialysis and peritoneal and pH that are caused by nausea, vomiting, and diarrhea.
dialysis and calculate dose Mesenteric blood flow may also be altered. However, the oral
adjustments of a drug in bioavailability of a drug such as propranolol (which has a high
patients undergoing dialysis. first-pass effect) may be increased in patients with renal impair-
ment as a result of the decrease in first-pass hepatic metabolism
»» Describe the principle of the
(Bianchetti et al, 1978).
fraction of drug excreted
The apparent volume of distribution depends largely on
unchanged (fe) method and how
drug–protein binding in plasma or tissues and total body water.
it is applied to adjust doses in
Renal impairment may alter the distribution of the drug as a result
renal disease.
of changes in fluid balance, drug–protein binding, or other factors
»» Explain the principle involved in that may cause changes in the apparent volume of distribution (see
the Giusti–Hayton method. Chapter 11). The plasma protein binding of weak acidic drugs in
»» Describe the effects of hepatic uremic patients is decreased, whereas the protein binding of weak
disease on the pharmacokinetics basic drugs is less affected. A decrease in drug–protein binding
of a drug. results in a larger fraction of free drug and an increase in the vol-
ume of distribution. However, the net elimination half-life is gen-
»» List the reasons why dose erally increased as a result of the dominant effect of reduced
adjustment in patients with glomerular filtration. Protein binding of the drug may be further
hepatic impairment is more compromised due to the accumulation of metabolites of the drug
difficult than dose adjustment in and various biochemical metabolites, such as free fatty acids and
patients with renal disease. urea, which may compete for the protein-binding sites for the
»» Explain how liver function tests active drug.
relate to drug absorption and Total body clearance of drugs in uremic patients is also
disposition. reduced by either a decrease in the glomerular filtration rate (GFR)
and possibly active tubular secretion or a reduced hepatic clear-
»» List the pharmacokinetic
ance resulting from a decrease in intrinsic hepatic clearance.
properties of a drug for which
In clinical practice, estimation of the appropriate drug dos-
dose adjustment would not be
age regimen in patients with impaired renal function is based
required in patients with renal or
on an estimate of the remaining renal function of the patient
hepatic impairment.
and a prediction of the total body clearance. A complete phar-
macokinetic analysis of the drug in the uremic patient may not
be possible. Moreover, the patient’s uremic condition may not
be stable and may be changing too rapidly for pharmacokinetic
analysis. Each of the approaches for the calculation of a dosage
regimen has certain assumptions and limitations that must be
carefully assessed by the clinician before any approach is
taken. Dosing guidelines for individual drugs in patients with
renal impairment may be found in various reference books,
such as the Physicians’ Desk Reference, and in the medical
literature (Bennett 1988, 1990; St. Peter et al, 1992). Most
newly approved drugs now contain dosing instructions for
CKD patients.
Dose Adjustment in Renal and Hepatic Disease 777
TABLE 241 Common Causes of Kidney Failure
Pyelonephritis Inflammation and deterioration of the pyelonephrons due to infection, antigens, or other idiopathic
causes.
Hypertension Chronic overloading of the kidney with fluid and electrolytes may lead to kidney insufficiency.
Diabetes mellitus The disturbance of sugar metabolism and acid-base balance may lead to or predispose a patient to
degenerative renal disease.
Nephrotoxic drugs/ Certain drugs taken chronically may cause irreversible kidney damage—eg, the aminoglycosides, phen-
metals acetin, and heavy metals, such as mercury and lead.
Hypovolemia Any condition that causes a reduction in renal blood flow will eventually lead to renal ischemia and
damage.
Neophroallergens Certain compounds may produce an immune type of sensitivity reaction with nephritic syndrome—eg,
quartan malaria nephrotoxic serum.
GENERAL APPROACHES FOR DOSE For IV infusions, the same Css is maintained. (Css is
the same as C∞
ADJUSTMENT IN RENAL DISEASE av after the plasma drug concentration
reaches steady state.)
Several approaches are available for estimating the The design of dosage regimens for uremic
appropriate dosage regimen for a patient with renal patients is based on the pharmacokinetic changes that
impairment. Each of these approaches has similar have occurred as a result of the uremic condition.
assumptions, as listed in Table 24-2. Most of these Generally, drugs in patients with uremia or kidney
methods assume that the required therapeutic plasma impairment have prolonged elimination half-lives
drug concentration in uremic patients is similar to that and a change in the apparent volume of distribution.
required in patients with normal renal function. In less severe uremic conditions, there may be neither
Uremic patients are maintained on the same C∞
av after edema nor a significant change in the apparent vol-
multiple oral doses or multiple IV bolus injections. ume of distribution. Consequently, the methods for
TABLE 242 Common Assumptions in Dosing Renal-Impaired Patients
Assumption Comment
Creatinine clearance accurately measures Creatinine clearance estimates may be biased. Renal impairment should also be
the degree of renal impairment verified by physical diagnosis and other clinical tests.
Drug follows dose-independent Pharmacokinetics should not be dose dependent (nonlinear).
pharmacokinetics
Nonrenal drug elimination remains Renal disease may also affect the liver and cause a change in nonrenal drug
constant elimination (drug metabolism).
Drug absorption remains constant Unchanged drug absorption from gastrointestinal tract.
Drug clearance, Clu, declines linearly with Normal drug clearance may include active secretion and passive filtration and
creatinine clearance, ClCr may not decline linearly.
Unaltered drug–protein binding Drug-protein binding may be altered due to accumulation of urea, nitrogenous
wastes, and drug metabolites.
Target drug concentration remains Changes in electrolyte composition such as potassium may affect response
constant to the effect of digoxin. Accumulation of active metabolites may cause more
intense pharmacodynamic response compared to parent drug alone.
778 Chapter 24
dose adjustment in uremic patients are based on an infusion, R, must be changed to a new value, Ru, for
accurate estimation of the drug clearance in these the uremic patient, as described by the equation
patients.
Several specific clinical approaches for the cal- R Ru
Css = N =
ClT Clu
culation of drug clearance based on monitoring kid- T (24.5)
ney function are presented later in this chapter. Two (normal) (uremic)
general pharmacokinetic approaches for dose adjust-
ment include methods based on drug clearance and
methods based on the elimination half-life. Dose Adjustment Based on Changes in the
Elimination Rate Constant
Dose Adjustment Based on Drug Clearance The overall elimination rate constant for many drugs
is reduced in the uremic patient. A dosage regimen
Methods based on drug clearance try to maintain the
may be designed for the uremic patient either by
desired C∞
av after multiple oral doses or multiple IV
reducing the normal dose of the drug and keeping
bolus injections as total body clearance, ClT, changes.
the frequency of dosing (dosage interval) constant or
The calculation for C∞
av is
by decreasing the frequency of dosing (prolonging
FD the dosage interval) and keeping the dose constant.
C∞ 0
= (24.1)
av Cl τ Doses of drugs with a narrow therapeutic range
T
should be reduced—particularly if the drug has
For patients with uremic condition or renal impair- accumulated in the patient prior to deterioration of
ment, total body clearance will change to a new kidney function.
value, CluT . Therefore, to maintain the same desired The usual approach to estimating a multiple-
C∞
av , the dose must be changed to a uremic dose, Du
0 , dosage regimen in the normal patient is to maintain
or the dosage interval must be changed to t u, as a desired C∞
av , as shown in Equation 24.1. Assuming
shown in the following equation: the VD is the same in both normal and uremic
patients and t is constant, then the uremic dose Du
0 is
DN Du
a fraction (ku/kN) of the normal dose:
C∞ 0 0
av = =
ClN N Clu u
T τ Tτ (24.2)
DNk u
(normal) (uremic) Du 0
0 = N (24.6)
k
where the superscripts N and u represent normal and When the elimination rate constant for a drug in
uremic conditions, respectively. the uremic patient cannot be determined directly,
Rearranging Equation 24.2 and solving for Du
0 indirect methods are available to calculate the pre-
dicted elimination rate constant based on the renal
DNCluτ u
Du = 0 T
0 (24.3) function of the patient. The assumptions on how
ClNτ N
T these dosage regimens are calculated include the
following:
If the dosage interval t is kept constant, then the
uremic dose Du
0 is equal to a fraction (Clu lNTC T ) of the 1. The renal elimination rate constant (kR)
normal dose, as shown in the equation decreases proportionately as renal function
decreases. (Note that kR is the same as ke as
DNClu used in previous chapters.)
Du 0 T
0 = (24.4)
ClN 2. The nonrenal routes of elimination (primar-
T
ily, the rate constant for metabolism) remain
For IV infusions the same desired Css is maintained unchanged.
both for patients with normal renal function and for 3. Changes in the renal clearance of the drug are
patients with renal impairment. Therefore, the rate of reflected by changes in the creatinine clearance.
Dose Adjustment in Renal and Hepatic Disease 779
The overall elimination rate constant is the sum total MEASUREMENT OF GLOMERULAR
of all the routes of elimination in the body, including
FILTRATION RATE
the renal rate and the nonrenal rate constants:
Several drugs and endogenous substances have been
k u u u
= k + k (24.7)
nr R used as markers to measure GFR. These markers are
carried to the kidney by the blood via the renal artery
where knr is the nonrenal elimination rate constant and are filtered at the glomerulus. Several criteria are
and kR is the renal excretion rate constant. necessary to use a drug as a marker to measure GFR:
Renal clearance is the product of the apparent
1. The drug must be freely filtered at the
volume of distribution and the rate constant for renal
glomerulus.
excretion:
2. The drug must neither be reabsorbed nor
actively secreted by the renal tubules.
CluR = k u u
RVD (24.8)
3. The drug should not be metabolized.
4. The drug should not bind significantly to
Rearrangement of Equation 24.8 gives
plasma proteins.
1 5. The drug should neither have an effect on the
k u u
R = ClR (24.9)
V u
D filtration rate nor alter renal function.
6. The drug should be nontoxic.
Assuming that the apparent volume of distribution
7. The drug may be infused in a sufficient dose
and nonrenal routes of elimination do not change in
to permit simple and accurate quantitation in
uremia, then k u N u N
nr = knr and VD = VD .
plasma and in urine.
Substitution of Equation 24.9 into Equation 24.7
yields Therefore, the rate at which these drug markers are
filtered from the blood into the urine per unit of time
k u kN u 1
= (2 . 0
nr +Cl 4 1 )
R reflects the GFR of the kidney. Changes in GFR
V N
D reflect changes in kidney function that may be
From Equation 24.10, a change in the renal clear- diminished in uremic conditions.
ance Clu Inulin, a fructose polysaccharide, fulfills most
R due to renal impairment will be reflected in
a change in the overall elimination rate constant ku. of the criteria listed above and is therefore used as a
Because changes in the renal drug clearance cannot standard reference for the measurement of GFR. In
be assessed directly in the uremic patient, CluR is usu- practice, however, the use of inulin involves a time-
ally related to a measurement of kidney function by consuming procedure in which inulin is given by
the GFR, which in turn is estimated by changes in intravenous infusion until a constant steady-state
the patient’s creatinine clearance. plasma level is obtained. Clearance of inulin may
then be measured by the rate of infusion divided by
the steady-state plasma inulin concentration.
Frequently Asked Questions Although this procedure gives an accurate value for
»»What are the main causes of uremia? GFR, inulin clearance is not used frequently in clini-
cal practice.
»»How does renal impairment affect the pharmaco-
The clearance of creatinine is used most exten-
kinetics of a drug that is primarily eliminated by
sively as a measurement of GFR. Creatinine is an
hepatic clearance?
endogenous substance formed from creatine phos-
»»What are the main factors that influence drug dosing phate during muscle metabolism. Creatinine produc-
in renal disease? tion varies with age, weight, and gender of the
»»Name and contrast the two methods for adjusting individual. In humans, creatinine is filtered mainly at
drug dose in renal disease. the glomerulus, with no tubular reabsorption.
However, a small amount of creatinine may be
780 Chapter 24
actively secreted by the renal tubules, and the values (24 hours) to obtain a reliable excretion rate. Creatinine
of GFR obtained by the creatinine clearance tend to clearance is expressed in mL/min and serum creati-
be higher than GFR measured by inulin clearance. nine concentration in mg/dL or mg%. Other Clcr
Creatinine clearance tends to decrease in the elderly methods based solely on serum creatinine are gener-
patient. As mentioned in Chapter 22, the physiologic ally compared to the creatinine clearance obtained
changes due to aging may necessitate special consid- from the 24-hour urinary creatinine excretion.
erations in administering drugs in the elderly. The following equation is used to calculate cre-
Measurement of blood urea nitrogen (BUN) is a atinine clearance in mL/min when the serum creati-
commonly used clinical diagnostic laboratory test nine concentration is known:
for renal disease. Urea is the end product of protein
catabolism and is excreted through the kidney. rate of urinary excretion of creatinine
Cl
Normal BUN levels range from 10 to 20 mg/dL. cr =
serum concentration of creatinine
Higher BUN levels generally indicate the presence
CuV
(24.11)
×100
of renal disease. However, other factors, such as Clcr =
Ccr ×1440
excessive protein intake, reduced renal blood flow,
hemorrhagic shock, or gastric bleeding, may affect
increased BUN levels. The renal clearance of urea is where Ccr = creatinine concentration (mg/dL) of the
by glomerular filtration and partial reabsorption in the serum taken at the 12th hour or at the midpoint of
renal tubules. Therefore, the renal clearance of urea is the urine-collection period, V = volume of urine
less than creatinine or inulin clearance and does not excreted (mL) in 24 hours, Cu = concentration of
give a quantitative measure of kidney function. creatinine in urine (mg/mL), and Clcr = creatinine
clearance in mL/min.
Creatinine is eliminated primarily by glomerular
SERUM CREATININE filtration. A small fraction of creatinine also is elimi-
CONCENTRATION AND nated by active secretion and some nonrenal elimina-
CREATININE CLEARANCE tion. Therefore, Clcr values obtained from creatinine
measurements overestimate the actual GFR.
Under normal circumstances, creatinine production Creatinine clearance has been normalized both
is roughly equal to creatinine excretion, so the serum to body surface area, using 1.73 m2 as the average,
creatinine level remains constant. In a patient with and to body weight for a 70-kg adult male. Creatinine
reduced glomerular filtration, serum creatinine will distributes into total body water, and when clearance
accumulate in accordance with the degree of loss of is normalized to a standard VD, similar drug half-
glomerular filtration in the kidney. The serum creati- lives in adults and children correspond to identical
nine concentration alone is frequently used to deter- clearances.
mine creatinine clearance, Clcr. Creatinine clearance Creatinine clearance values must be considered
from the serum creatinine concentration is a rapid carefully in special populations such as elderly,
and convenient way to monitor kidney function. obese, and emaciated patients. In elderly and emaci-
Creatinine clearance may be defined as the vol- ated patients, muscle mass may have declined, thus
ume of plasma cleared of creatinine per unit time. lowering the production of creatinine. However,
Creatinine clearance can be calculated directly by serum creatinine concentration values may appear to
dividing the rate of urinary excretion of creatinine by be in the normal range because of lower renal creati-
the patient’s serum creatinine concentration. The nine excretion. Thus, the calculation of creatinine
approach is similar to that used in the determination clearance from serum creatinine may give an inac-
of drug clearance. In practice, the serum creatinine curate estimation of the renal function. For obese
concentration is determined at the midpoint of the patients, generally defined as patients more than 20%
urinary collection period and the rate of urinary over ideal body weight (IBW), creatinine clearance
excretion of creatinine is measured for the entire day should be based on ideal body weight. Estimation of
Dose Adjustment in Renal and Hepatic Disease 781
creatinine clearance based on total body weight Therefore, creatinine clearance, Clcr, is most often
(TBW) would exaggerate the Clcr values in obese estimated from the patient’s Ccr. Several methods
patients. Women with normal kidney function have are available for the calculation of creatinine clear-
smaller creatinine clearance values than men, which ance from the serum creatinine concentration. The
are approximately 80%–85% of those in men with more accurate methods are based on the patient’s age,
normal kidney function. height, weight, and gender. These methods should be
Several empirical equations have been used to used only for patients with intact liver function and no
estimate lean body weight (LBW) based on the abnormal muscle disease, such as hypertrophy or dys-
patient’s height and actual (total) body weight (see trophy. Moreover, most of the methods assume a sta-
Chapter 22). The following equations have been ble creatinine clearance. The unit for Clcr is mL/min.
used to estimate LBW in renally impaired patients:
Adults
LBW (males) = 50 kg The method of Cockcroft and Gault (1976) shown in
+ 2.3 kg for each inch over 5 ft Equation 24.12 is used to estimate creatinine clear-
ance from serum creatinine concentration. This
LBW (females) = 45.5 kg method considers both the age and the weight of the
+ 2.3 kg for each inch over 5 ft patient. For males
[140 − age (year)]× body weight (kg)
Cl
For the purpose of dose adjustment in renal patients, cr =
72 ×Ccr
normal creatinine clearance is generally assumed to be
(24.12)
between 100 and 125 mL/min per 1.73 m2 for a subject
of ideal body weight: Clcr = 108.8 ± 13.5 mL/1.73 m2
For females, use 90% of the Clcr value obtained in
for an adult female and Clcr = 124.5 ± 9.7 mL/1.73 m2
males. In some hospitals, 85% is used for female
for an adult male (Scientific Tables; Diem and
subjects (Stevens et al, 2006).
Lentner, 1973). Creatinine clearance is affected by
The nomogram method of Siersback-Nielsen et al
diet and salt intake. As a convenient approximation,
(1971) estimates creatinine clearance on the basis of
the normal clearance has often been assumed by
age, weight, and serum creatinine concentration, as
many clinicians to be approximately 100 mL/min.
shown in Fig. 24-1. Cockcroft and Gault (1976)
compared their method with the nomogram method
Frequently Asked Questions in adult males of various ages. Creatinine clearances
»»Why is creatinine clearance difficult to predict? estimated by both methods were comparable. Both
»»Why is creatinine clearance used in renal disease? methods also demonstrated an age-related linear
decline in creatinine excretion, which may be due to
»»What patient-specific factors influence the accuracy the decrease in muscle mass with age.
of Clcr estimates?
»»How is Clcr determined? Children
There are a number of methods for calculation of
Calculation of Creatinine Clearance creatinine clearance in children, based on body length
from Serum Creatinine Concentration and serum creatinine concentration. Equation 24.13 is
a method developed by Schwartz et al (1976):
The problems of obtaining a complete 24-hour urine
collection from a patient, the time necessary for urine 0.55 body length (cm)
collection, and the analysis time preclude a direct Clcr = (24.13)
Ccr
estimation of creatinine clearance. Serum creatinine
concentration, Ccr, is related to creatinine clearance where Clcr is given in mL/min/1.73 m2. The value 0.55
and is measured routinely in the clinical laboratory. represents a factor used for children aged 1–12 years.
782 Chapter 24
Clearance Scr
(mL/min) (mg/dL)
0.4
Weight
150 (kg)
140 0.5
120 120
0.6 Clcr
100 100 Serum (mL/min/1.73 m )
creatinine 0.7
80 80 R (mg/100 mL)
5.0 0.8 160 Ht
Age 140
60 60 4.0 (cm)
0.9 120
(years) 100 200
3.0 1.0
50 50 80 180
70 160
2.0 60 140
1.2 50
40 40 25 120
45 25 1.4 40
1.4 100
65 45 1.2 30 90
30 30 65 1.0 80
85 0.8 1.6 75
85 20
1.8 15 60
105 0.6
105 2.0 50
20 0.4 10
8 40
2.5 6 30
5
3.0 4
3
3.5
10 2
4.0
FIGURE 241 Nomogram for evaluation of endog-
4.5
enous creatinine clearance. To use the nomogram, connect
5.0
the patient’s weight on the second line from the left with the
5.5
patient’s age on the fourth line with a ruler. Note the point of 6.0
intersection on R and keep the ruler there. Turn the right part
of the ruler to the appropriate serum creatinine value and the
left side will indicate the clearance in mL/min. (Reproduced FIGURE 242 Nomogram for rapid evaluation of
with permission from Kampmann J, et al: Rapid evaluation of endogenous creatinine clearance (Clcr) in pediatric patients
creatinine clearance. Lancet 1(7709):1133–1134, 1971.) (aged 6–12 years). To predict Clcr, connect the child’s Scr (serum
creatinine) and Ht (height) with a ruler and read the Clcr where
the ruler intersects the center line. (From Traub and Johnson,
Another method of calculating creatinine clear- 1980, with permission.)
ance in children uses the nomogram of Traub and
Johnson (1980) as shown in Fig. 24-2. This nomo-
line R with the creatinine concentration point of
gram is based on observations from 81 children aged
1 mg/dL, and extend the line to intersect the “clearance
6–12 years and requires the patient’s height and
line.” The extended line will intersect the clearance
serum creatinine concentration.
line at 130 mL/min, giving the creatinine clearance for
the patient.
PRACTICE PROBLEMS 2. What is the creatinine clearance for a 25-year-
old male patient with a Ccr of 1 mg/dL? The
1. What is the creatinine clearance for a 25-year-
patient is 5 ft, 4 in in height and weighs 103 kg.
old male patient with Ccr of 1 mg/dL and a
body weight of 80 kg?
Solution
Solution The patient is obese and the Clcr calculation should
be based on ideal body weight.
Using the nomogram (see Fig. 24-1), join the points
at 25 years (male) and 80 kg with a ruler—let the
LBW (males) = 50 kg + [2.3 × 4] = 59.2 kg
line intersect line R. Connect the intersection point at
Dose Adjustment in Renal and Hepatic Disease 783
TABLE 243 Classification of Renal Function Based on Estimated GFR (eGFR) or Estimated
Creatinine Clearance (Clcr)
Stage Descriptionb eGFRc (mL/min/1.73m2) Cl a d
cr (mL/min)
1 Normal GFR ≥90 ≥90
2 Mild decrease in GFR 60–89 60–89
3 Moderate decrease in GFR 30–59 30–59
4 Severe decrease in GFR 15–29 15–29
5 End-stage renal disease (ESRD) <15 Not on dialysis <15 Not on dialysis
Requiring dialysis Requiring dialysis
aIn some situations, collection of 24-hour urine samples for measurement of creatinine clearance, or measurement of clearance of an exogenous
filtration marker, may provide better estimates of GFR than the prediction equations. The situations include determination of GFR for patients in the
following scenarios: undergoing kidney replacement therapy; acute renal failure; extremes of age, body size, or muscle mass; conditions of severe
malnutrition or obesity; disease of skeletal muscle; or on a vegetarian diet.
bStages of renal impairment are based on K/DOQI Clinical Practice Guidelines for chronic kidney disease (CKD) from the National Kidney Foundation
in 2002; GFR: glomerular filtration rate.
ceGFR: estimate of GFR based on an MDRD equation.
dClcr: estimated creatinine clearance based on the Cockcroft-Gault equation.
Using the Cockcroft–Gault method (Equation 24.12), dose adjustment of many antibiotics is necessary
the Clcr can be calculated. only when the GFR, as measured by Clcr, is less than
50 mL/min. For aminoglycosides and vancomycin,
(140 − 25) × (59.2 kg)
Cl
cr = = 94.6 mL/min dose adjustment is individualized according to the wide
72(1) range of Clcr. Therefore, dose adjustment for all drugs
on the basis of these Clcr methods alone is not justified.
The serum creatinine methods for the estimation of
the creatinine clearance assume stabilized kidney
function and a steady-state serum creatinine concen- Estimated Glomerular Filtration Rate (eGFR)
tration. In acute renal failure and in other situations Using Modification of Diet in Renal Disease
in which kidney function is changing, the serum (MDRD) Formula or Using the Chronic Kidney
creatinine may not represent steady-state conditions. Disease–Epidemiology Collaboration
If C (CKD–EPI) Equations
cr is measured daily and the Ccr value is constant,
then the serum creatinine concentration is probably Various approaches for the estimation of GFR from
at steady state. If the Ccr values are changing daily, serum creatinine have been published (Levey et al,
then kidney function is changing. 1999, 2009; FDA Guidance for Industry, 2010). The
Although the Cockcroft–Gault method for esti- MDRD equation is a simple and effective method
mating Clcr has some biases, this method has gained and several versions of the MDRD equations have
general acceptance for the determination of renal been published. For example,1
impairment (Schneider et al, 2003; Hailmeskel et al,
1999; Spinler et al, 1998). A suggested representation eGFR (mL/min/1.73 m2) = 175 × (Ccr)
−1.154
of patients with various degrees of renal impairment × (age)−0.203 × (0.742 if female)
based on creatinine clearance is shown in Table 24-3. × (1.212 if African American)
The practice problems show that, depending on the
formula used, the calculated Clcr can vary considerably. where eGFR is estimated GFR using the MDRD
Consequently, unless a clinically significant change equation.
in the creatinine clearance occurs, dosage adjustment
may not be needed. According to St. Peter et al (1992), 1FDA Guidance, 2010.
784 Chapter 24
The MDRD equation does not require weight or disease state and patient conditions such as age,
height measurements and the results are normalized gender, and endogenous factors that affect creatinine
to 1.73 m2 body surface area, which is an accepted synthesis and elimination (Table 24-4). These estima-
average adult surface area. tion methods are referred to as creatinine-based
The Chronic Kidney Disease–Epidemiology methods in the clinical literature (Stevens et al, 2006;
Collaboration (CDK-EPI) reviewed various approaches Levey et al, 2009). Two creatinine-based methods
for GFR measurements based on serum creatinine that have been extensively studied and widely applied
concentration and other factors (Levey et al, 2009). are the Cockcroft–Gault and the MDRD study equa-
Based on the same four variables as the MDRD equa- tions. The Cockcroft–Gault has a longer history of
tion, the CDK-EPI equation uses a two-slope “spline” use but the original equation was based on fewer
to model the relationship between estimated GFR and subjects. The MDRD method is a more recent method
serum creatinine, and a different relationship for age, based on more subjects with application better
sex, and race. In the validation data set, the CKD-EPI defined for certain groups of patients. For example,
equation performed better than the MDRD equation, the relationship of serum creatinine concentration
with less bias (median difference between measured
and estimated GFR of 2.5 vs 5.5 mL/min/1.73 m2)
especially at higher GFR (p < .001 for all subsequent TABLE 244 Factors Affecting Creatinine
comparisons). The CKD-EPI equation is more accu- Generation
rate than the MDRD equation and could replace it for Effect on
routine clinical use (Levey et al, 2009). However, no Serum
comparison between the CKD-EPI and the Cockcroft– Factor Creatinine
Gault methods has been made, especially in the more
Aging Decreased
important issue of how to relate the calculated GFR to
individual drug clearance and, ultimately, an opti- Female Sex Decreased
mized drug dosing regimen in the patients. A limita- Race or ethnic group
tion of the CKD-EPI method is that the sample
Black Increased
contained a limited number of elderly people and
racial and ethnic minorities with measured GFR. Hispanic Decreased
Each equation for the calculation of renal func- Asian Decreased
tion from serum creatinine concentrations gives some-
Body habitus
what different results. The Cockcroft–Gault method
for estimating Clcr has been used most frequently and Muscular Increased
tends to be the preferred approach at this time. The Amputation Decreased
FDA Guidance for Industry (2010) on impaired renal
Obesity No Change
function includes a classification of renal function
based on creatinine clearance (see Table 24-3). Chronic illness
Although the two methods, estimated GFR (eGFR) Malnutrition, inflammation, decon- Decreased
using the MDRD equation and calculated creatinine ditioning (eg, cancer, severe cardiovas-
clearance using the Cockcroft–Gault method, do not cular disease, hospitalized patients)
give the same values, the classification in Table 24-3 Neuromuscular diseases Decreased
brackets the values for diminishing renal function.
Diet
Comparison of Methods for the Vegetarian diet Decreased
Measurement of GFR
Ingestion of cooked meat Increased
The estimate of GFR based on serum creatinine con-
(From Stevens LA, M.D., Coresh J, Greene T, Levey AS: Assessing Kidney
centration is widely used, even though serum creati- Function—Measured and Estimated Glomerular Filtration Rate, N Eng J
nine concentrations are known to fluctuate with Med 354(23):2473–2483, 2006, with permission.)
Dose Adjustment in Renal and Hepatic Disease 785
and GFR may be different between subjects with While the MDRD method will provide more
diabetic nephropathy and those without real renal accurate renal function of the patients, drug clear-
disease. Some reports indicated that the MDRD ance is not entirely governed by GFR. Reabsorption
method is less biased for obese and diabetic patients, and nonrenal elimination are also important for
whereas other studies do not find a difference between many drugs. Therefore, the MDRD method should
the two methods. be compared with previous methods and see how
The Cockcroft–Gault formula was developed accurately it adjusts drug doses for different drugs in
initially with the data from 249 men with Clcr ranging different uremic patients. For many new drugs, drug
from 30 to 130 mL/min. The equation is described dosing information for renal-impaired patients is
as below. now available and should be consulted in the pack-
age insert. In patients with chronic kidney disease,
Clcr = [(140 − age) × weight](72 × Ccr ) the following recommendations are good practices
× 0.85 (for female subjects) (24.12) that physicians and pharmacists should be aware of
(Munar and Singh, 2007):
The Cockcroft–Gault formula systematically over-
estimates GFR because of the tubular secretion of 1. Assess the use of OTC and herbal medicine to
creatinine. In addition, the equation is not adjusted ensure proper indication, and avoid medications
for body surface area, making it difficult to compare with toxic metabolites, or use the least nephro-
creatinine clearance value obtained from this method toxic agents.
and that from other methods. Typically, normal val- 2. Use alternative medications if potential drug
ues for creatinine clearance are normalized by a interactions exist.
body surface area of 1.73 m2, which requires a mea- 3. Use caution for drugs with active metabolites
surement of height of the patients. that can exaggerate pharmacologic effects in
The MDRD study equation was developed in patients with renal impairment.
1999 with the use of data from 1628 patients with 4. Adjust dosages of drugs cleared renally based
chronic kidney disease. Its estimated GFR is adjusted on the patient’s kidney function (calculated
for body-surface area. The estimating equation is as Clcr or eGFR); determine initial dosages
using published guidelines and adjust based on
GFR (mL/min/1.73 m2) = 186 × (C patient response or monitoring if appropriate.
cr)
−1.154
× (age)−0.203 × 0.742 (if the subject is female)
× 1.212 (if the subject is black)
This equation was revised in 2005 for use with a DOSE ADJUSTMENT
standardized serum creatinine assay that yields serum FOR UREMIC PATIENTS
creatinine values that are 5% lower.
Dose adjustment for drugs in uremic or renally
GFR (mL/min/1.73 m2) = 175 impaired patients should be made in accordance with
× (standardized Ccr)
−1.154 × (age)−0.203 changes in pharmacodynamics and pharmacokinet-
× 0.742 (if the subject is female) or ics of the drug in the individual patient. Whether
× 1.212 (if the subject is black) renal impairment will alter the pharmacokinetics of
the drug enough to justify dosage adjustment is an
In the MDRD study population, 91% of the GFR important consideration. For many drugs that are
estimates were within 30% of the measured values, eliminated primarily by metabolism or biliary secre-
and this approach was more accurate than the use of tion, uremia may not alter pharmacokinetics suffi-
the Cockcroft–Gault equation. The Cockcroft–Gault ciently to warrant dosage adjustment.
equation was reported to be less accurate than the Active metabolites of the drug may also be
MDRD study equation in older and obese people. formed and must be considered for additional phar-
Both methods are less accurate in healthy subjects. macologic effects when adjusting dose. For some
786 Chapter 24
drugs, the free drug concentrations may need to be concentrations, patient data (height, weight, age,
considered due to decreased or altered protein bind- gender), and the pharmacokinetics of the drug. As
ing in uremia. Combination products that contain discussed by Chennavasin and Brater (1981), each
two or more active drugs in a fixed-dose combina- nomogram has errors in its assumptions and drug
tion may be differentially affected by decreased database.
renal function and thus, the use of combination drug Most methods for dose adjustment in renal dis-
products in uremic patients should be discouraged. ease assume that nonrenal elimination of the drug is
The following methods may be used to estimate not affected by renal impairment and that the
initial and maintenance dose regimens. After initiat- remaining renal excretion rate constant in the uremic
ing the dosage, the clinician should continue to moni- patient is proportional to the product of a constant
tor the pharmacodynamics and pharmacokinetics of and the Clcr:
the drug. He or she should also evaluate the patient’s
renal function, which may be changing over time. k = k + αCl (24.14)
u nr cr
Basis for Dose Adjustment in Uremia where knr is the nonrenal elimination rate constant
and a is a constant.
The loading drug dose is based on the apparent vol-
Equation 24.14 is similar to Equation 24.10,
ume of distribution of the patient. It is generally
where a = 1/VD, and it can be used for the construc-
assumed that the apparent volume of distribution is
tion of a nomogram. Figure 24-3 shows a graphical
not altered significantly, and therefore, the loading
representation of Equation 24.14 for four different
dose of the drug is the same in uremic patients as in
drugs, each with a different renal excretion rate con-
subjects with normal renal function.
stant. The fractions of drug excreted unchanged in
The maintenance dose is based on clearance of
the urine (fe) for drugs A, B, C, and D are 5%, 50%,
the drug in the patient. In the uremic patient, the rate
75%, and 90%, respectively. A Clcr of ≥80 mL/min is
of renal drug excretion has decreased, leading to a
considered an adequate GFR in subjects with normal
decrease in total body clearance. Most methods for
renal function. The uremic elimination rate constant
dose adjustment assume nonrenal drug clearance to be
(ku) is the sum of the nonrenal elimination rate con-
unchanged. The fraction of normal renal function
stant and the renal elimination rate constant, which is
remaining in the uremic patient is estimated from Clcr. decreased due to renal impairment. If the patient has
After the remaining total body clearance in the
complete renal shutdown (ie, Clcr = 0 mL/min), then the
uremic patient is estimated, a dosage regimen may be
intercept on the y axis represents the percent of drug
developed by (1) decreasing the maintenance dose,
elimination due to nonrenal drug elimination routes.
(2) increasing the dosage interval, or (3) changing
both maintenance dose and dosage interval.
Although total body clearance is a more accurate 100 Drug A
index for drug dosing, the elimination half-life of the
drug is more commonly used for dose adjustment 80
because of its convenience. Clearance allows for the Drug B
prediction of steady-state drug concentrations, while 60
elimination half-life yields information on the time it Drug C
40
takes to reach steady-state concentration.
20
Nomograms Drug D
0
Nomograms are charts available for use in estimating 0 20 40 60 80 100
dosage regimens in uremic patients (Bjornsson, 1986; Creatinine clearance (mL/min)
Chennavasin and Craig Brater, 1981; Tozer, 1974). FIGURE 243 Relationship between creatinine clearance
The nomograms may be based on serum creatinine and the drug elimination rate constant.
Uremic elimination constant (%ku)
Dose Adjustment in Renal and Hepatic Disease 787
Drug D, which is excreted 90% unchanged in the 3. Determine ku for the patient.
urine, has the steepest slope (equivalent to a in 4. Make the dose adjustment in accordance with
Equation 24.14) and is most affected by small pharmacokinetic principles.
changes in Clcr. On the other hand, drug A, which is a. When Clcr = 0,
excreted only 5% unchanged in the urine (ie, 95%
eliminated by nonrenal routes), is least affected by a ku = knr + kR
decrease in creatinine clearance.
In complete renal shutdown (kR = 0), ku = knr = 0.06 h–1
The nomogram method of Welling and Craig
(1976) provides an estimate of the ratio of the ure- (see Table 24-5, group F).
mic elimination rate constant (ku) to the normal Alternatively, find ku/kN in Fig. 24-4 for group F
elimination rate constant (kN) on the basis of Clcr
at Clcr = 0 mL/min:
(Fig. 23-4). For this method, Welling and Craig ku
(1976) provided a list of drugs grouped according to = 0.425
kN
the amount of drug excreted unchanged in the urine
(Table 24-5). From the ku/kN ratio, the uremic dose Since kN = 0.15 h–1 for group F in Table 24-5, then
can be estimated according to Equation 24.15:
k = 0.425 (0.15) = 0.0638 h−1
k u
Uremic dose u
= × normal dose (24.15)
kN 0.0638
Uremic dose = 500 mg
When the dosage interval t is kept constant, the ure- 0.15
mic dose is always a smaller fraction of the normal = 212 mg every 6 hours
dose. Instead of reducing the dose for a uremic
patient, the usual dose is kept constant and the dos-
age interval t is prolonged according to the follow- b. At Clcr = 10 mL/min,
ing equation:
ku
k = 0.48
Dosage interval in uremia, N
τ u = × τ 4 1 )
k N (2 . 6 kN
u
k = −1
N 0.15 h
where tu is the dosage interval for the dose in uremic
patients and tN is the dosage interval for the dose in
k = = −1
u (0.48)(0.15) 0.072 h
patients with normal renal function.
0.072
Dose = 500 mg = 240 mg
0.15
PRACTICE PROBLEM
Lincomycin is given at 500 mg every 6 hours to a Alternatively,
75-kg healthy patient. What doses would be used
(a) in complete renal shutdown (Clcr = 0) and (b) when Dose = (0.48) (500) = 240 mg
Clcr = 10 mL/min?
Fraction of Drug Excreted Unchanged
Solution
(fe) Methods
To use the nomogram method, follow the steps
For many drugs, the fraction of drug excreted
below:
unchanged (fe) is available in the literature. Table 24-6
1. Use Table 24-5 to locate the group to which the lists various drugs with their fe values and elimination
drug belongs. half-lives. The fe method for estimating a dosage regi-
2. Find ku/kN at the point corresponding to Clcr of men in the uremic patient is a general method that
the patient (see Fig. 24-4). may be applied to any drug whose fe is known.
788 Chapter 24
TABLE 245 Elimination Rate Constants for Various Drugsa
Group Drug kN (h–1) knr (h–1) knr/kN%
A Minocycline 0.04 0.04 100.0
Rifampicin 0.25 0.25 100.0
Lidocaine 0.39 0.36 92.3
Digitoxin 0.114 0.10 87.7
B Doxycycline 0.037 0.031 83.8
Chlortetracycline 0.12 0.095 79.2
C Clindamycin 0.16 0.12 75.0
Chloramphenicol 0.26 0.19 73.1
Propranolol 0.22 0.16 72.8
Erythromycin 0.39 0.28 71.8
D Trimethoprim 0.054 0.031 57.4
Isoniazid (fast) 0.53 0.30 56.6
Isoniazid (slow) 0.23 0.13 56.5
E Dicloxacillin 1.20 0.60 50.0
Sulfadiazine 0.069 0.032 46.4
Sulfamethoxazole 0.084 0.037 44.0
F Nafcillin 1.26 0.54 42.8
Chlorpropamide 0.020 0.008 40.0
Lincomycin 0.15 0.06 40.0
G Colistimethate 0.154 0.054 35.1
Oxacillin 1.73 0.58 33.6
Digoxin 0.021 0.007 33.3
H Tetracycline 0.120 0.033 27.5
Cloxacillin 1.21 0.31 25.6
Oxytetracycline 0.075 0.014 18.7
I Amoxicillin 0.70 0.10 14.3
Methicillin 1.40 0.19 13.6
J Ticarcillin 0.58 0.066 11.4
Penicillin G 1.24 0.13 10.5
Ampicillin 0.53 0.05 9.4
Carbenicillin 0.55 0.05 9.1
(Continued)
Dose Adjustment in Renal and Hepatic Disease 789
TABLE 245 Elimination Rate Constants for Various Drugs a (Continued)
Group Drug kN (h–1) knr (h–1) knr/kN%
K Cefazolin 0.32 0.02 6.2
Cephaloridine 0.51 0.03 5.9
Cephalothin 1.20 0.06 5.0
Gentamicin 0.30 0.015 5.0
L Flucytosine 0.18 0.007 3.9
Kanamycin 0.28 0.01 3.6
Vancomycin 0.12 0.004 3.3
Tobramycin 0.32 0.010 3.1
Cephalexin 1.54 0.032 2.1
a
kN is for patients with normal renal function, knr is for patients with severe renal impairment, and knr/kN% = percent of normal elimination in severe
renal impairment.
From Welling and Craig (1976), with permission.
100 A 1.0
90
B
80
C
70
1.5
60
D
50 2.0
E
F
40 2.5
G 3.0
30
H 4.0
20 5.0
I
10 J 10.0
K 20.0
0 L
0 20 40 60 80 100
Creatinine clearance (mL/min)
FIGURE 244 This nomograph describes the changes in the percentage of normal elimination rate constant (left ordinate) and
the consequent geometric increase in elimination half-life (right ordinate) as a function of creatinine clearance. The drugs associated
with the individual slopes are given in Table 24-5. (From Welling and Craig, 1976, with permission.)
ku (%)
kN
t1/2 uremic
t1/2 normal
790 Chapter 24
TABLE 246 Fraction of Drug Excreted Unchanged (fe) and Elimination Half-Life Values
Drug fe t1/2 normal (h)a Drug fe t1/2 normal (h)a
Acebutolol 0.44 ± 0.11 2.7 ± 0.4 Cimetidine 0.77 ± 0.06 2.1 ± 1.1
Acetaminophen 0.03 ± 0.01 2.0 ± 0.4 Clindamycin 0.09–0.14 2.7 ± 0.4
Acetohexamide 0.4 1.3 Clofibrate 0.11–0.32 13 ± 3
Active metabolite 16–30 Clonidine 0.62 ± 0.11 8.5 ± 2.0
Allopurinol 0.1 2–8 Colistin 0.9 3
Alprenolol 0.005 3.1 ± 1.2 Cyclophosphamide 0.3 5
Amantadine 0.85 10 Cytarabine 0.1 2
Amikacin 0.98 2.3 ± 0.4 Dapsone 0.1 20
Amiloride 0.5 8 ± 2 Dicloxacillin 0.60 ± 0.07 0.7 ± 0.07
Amoxicillin 0.52 ± 0.15 1.0 ± 0.1 Digitoxin 0.33 ± 0.15 166 ± 65
Amphetamine 0.4–0.45 12 Digoxin 0.72 ± 0.09 42 ± 19
Amphotericin B 0.03 360 Disopyramide 0.55 ± 0.06 7.8 ± 1.6
Ampicillin 0.90 ± 0.08 1.3 ± 0.2 Doxycycline 0.40 ± 0.04 20 ± 4
Atenolol 0.85 6.3 ± 1.8 Erythromycin 0.15 1.1–3.5
Azlocillin 0.6 1.0 Ethambutol 0.79 ± 0.03 3.1 ± 0.4
Bacampicillin 0.88 0.9 Ethosuximide 0.19 33 ± 6
Baclofen 0.75 3–4 Flucytosine 0.63–0.84 5.3 ± 0.7
Bleomycin 0.55 1.5–8.9 Flunitrazepam 0.01 15 ± 5
Bretylium 0.8 ± 0.1 4–17 Furosemide 0.74 ± 0.07 0.85 ± 0.17
Bumetanide 0.33 3.5 Gentamicin 0.98 2–3
Carbenicillin 0.82 ± 0.09 1.1 ± 0.2 Griseofulvin 0 15
Cefalothin 0.52 0.6 ± 0.3 Hydralazine 0.12–0.14 2.2–2.6
Cefamandole 0.96 ± 0.03 0.77 Hydrochloro- 0.95 2.5 ± 0.2
thiazide
Cefazolin 0.80 ± 0.13 1.8 ± 0.4
Indomethacin 0.15 ± 0.08 2.6–11.2
Cefoperazone 0.2–0.3 2.0
Isoniazid
Cefotaxime 0.5–0.6 1–1.5
Rapid 0.07 ± 0.02 1.1 ± 0.2
Cefoxitin 0.88 ± 0.08 0.7 ± 0.13 acetylators
Cefuroxime 0.92 1.1 Slow acetylators 0.29 ± 0.05 3.0 ± 0.8
Cephalexin 0.96 0.9 ± 0.18 Isosorbide dinitrate 0.05 0.5
Chloramphenicol 0.05 2.7 ± 0.8 Kanamycin 0.9 2.1 ± 0.2
Chlorphentermine 0.2 120 Lidocaine 0.02 ± 0.01 1.8 ± 0.4
Chlorpropamide 0.2 36 Lincomycin 0.6 5
Chlorthalidone 0.65 ± 0.09 44 ± 10 Lithium 0.95 ± 0.15 22 ± 8
(Continued)
Dose Adjustment in Renal and Hepatic Disease 791
TABLE 246 Fraction of Drug Excreted Unchanged (fe) and Elimination Half-Life Values (Continued)
Drug fe t1/2 normal (h)a Drug fe t1/2 normal (h)a
Lorazepam 0.01 14 ± 5 Prazosin 0.01 2.9 ± 0.8
Meperidine 0.04–0.22 3.2 ± 0.8 Primidone 0.42 ± 0.15 8.0 ± 4.8
Methadone 0.2 22 Procainamide 0.67 ± 0.08 2.9 ± 0.6
Methicillin 0.88 ± 0.17 0.85 ± 0.23 Propranolol 0.005 3.9 ± 0.4
Methotrexate 0.94 8.4 Quinidine 0.18 ± 0.05 6.2 ± 1.8
Methyldopa 0.63 ± 0.10 1.8 ± 0.2 Rifampin 0.16 ± 0.04 2.1 ± 0.3
Metronidazole 0.25 8.2 Salicylic acid 0.2 3
Mexiletine 0.1 12 Sisomicin 0.98 2.8
Mezlocillin 0.75 0.8 Sotalol 0.6 6.5–13
Minocycline 0.1 ± 0.02 18 ± 4 Streptomycin 0.96 2.8
Minoxidil 0.1 4 Sulfinpyrazone 0.45 2.3
Moxalactam 0.82–0.96 2.5–3.0 Sulfisoxazole 0.53 ± 0.09 5.9 ± 0.9
Nadolol 0.73 ± 0.04 16 ± 2 Tetracycline 0.48 9.9 ± 1.5
Nafcillin 0.27 ± 0.05 0.9–1.0 Thiamphenicol 0.9 3
Nalidixic acid 0.2 1.0 Thiazinamium 0.41
Neostigmine 0.67 1.3 ± 0.8 Theophylline 0.08 9 ± 2.1
Netilmicin 0.98 2.2 Ticarcillin 0.86 1.2
Nitrazepam 0.01 29 ± 7 Timolol 0.2 3–5
Nitrofuraniton 0.5 0.3 Tobramycin 0.98 2.2 ± 0.1
Nomifensine 0.15–0.22 3.0 ± 1.0 Tocainide 0.20–0.70 1.6–3
(0.40 mean)
Oxacillin 0.75 0.5
Tolbutamide 0 5.9 ± 1.4
Oxprenolol 0.05 1.5
Triamterene 0.04 ± 0.01 2.8 ± 0.9
Pancuronium 0.5 3.0
Trimethoprim 0.53 ± 0.02 11 ± 1.4
Pentazocine 0.2 2.5
Tubocurarine 0.43 ± 0.08 2 ± 1.1
Phenobarbital 0.2 ± 0.05 86 ± 7
Valproic acid 0.02 ± 0.02 16 ± 3
Pindolol 0.41 3.4 ± 0.2
Vancomycin 0.97 5–6
Pivampicillin 0.9 0.9
Polymyxin B 0.88 4.5 Warfarin 0 37 ± 15
aHalf-life is a derived parameter that changes as a function of both clearance and volume of distribution. It is independent of body size, because it is
a function of these two parameters (Cl, VD), each of which is proportional to body size. It is important to consider that half-life is the time to eliminate
50% of the “drug” from the body (plasma), not the time in which 50% of the effect is lost.
Data from Chennavasin P, Brater DC: Nomograms for drug use in renal disease, Clin Pharmacokinet 6(3):193–214, May–June 1981; Dettli L: Drug dosage
in renal disease, Clin Pharmacokinet 1(2):126–34, 1976; Gilman AG et al: Pharmacological Basis of Therapeutics, MacMillan, New York, 1980.
792 Chapter 24
The Giusti–Hayton (1973) method assumes that ku/kN can be calculated from the fraction of drug
the effect of reduced kidney function on the renal excreted by the kidney, normal creatinine clearance,
portion of the elimination constant can be estimated and the creatinine clearance in the uremic patient.
from the ratio of the uremic creatinine clearance to
the normal creatinine clearance.
PRACTICE PROBLEM
k u Clu
r cr
= (24.17) The maintenance dose of gentamicin is 80 mg every
kN ClN
r cr 6 hours for a patient with normal renal function.
Calculate the maintenance dose for a uremic patient
where k u
r is the uremic renal excretion rate constant
with creatinine clearance of 20 mL/min. Assume a
and kN
r is the normal renal excretion rate constant.
normal creatinine clearance of 100 mL/min.
Clu
k u kN cr
= (24.18)
r r ClN Solution
cr
From the literature, gentamicin is reported to be
Because the overall uremic elimination rate constant, 100% excreted by the kidney (ie, fe = 1). Using
ku, is the sum of renal and nonrenal elimination, Equation 24.21,
k k u + k u
u = nr r ku 20
= 1−11− 0.2
100 =
k
Clu (24.19) N
u N cr ku = knr + kr ClNc r Because
Dividing Equation 24.19 by kN Du ku k
= or D = D u
×
DN k u N k
k k u kN N N
u nr Clu
= + r cr
(24.20)
kN k k ClNN N
cr where Du = uremic dose and DN = normal dose,
Let f = kN
e r /kN = fraction of drug excreted unchanged Du = 80 mg × 0.2 = 16 mg
in the urine and 1 u
− fe = knr /kN fraction of drug
excreted by nonrenal routes. Substitution into The maintenance dose is 16 mg every 6 hours.
Equation 24.20 yields the Giusti–Hayton equation, Alternatively, the dosing interval can be adjusted
where G is the Giusti–Hayton factor, which can be without changing the dose:
calculated from fe and the ratio of uremic to normal
τ
clearance: u kN k
= or N
τ u = τN ×
τN ku ku
k u
u Cl 1
= (1 cr
− fe ) + f
k e N τ u = 6 h × = 30 h
N Clcr 0.2
where tu and tN are dosing intervals for uremic and
or normal patients, respectively. The patient may be
given 80 mg every 30 hours.
k Clu
u Other approaches for using fraction of drug
1 1 cr
= − fe −
N = G (24.21)
kN Cl excreted unchanged have been developed by Tozer
cr
(1974) and Bjornsson (1986). These methods use fe for
The Giusti–Hayton equation is useful for most drugs dosing regimen design and the following equation:
for which the fraction of drug excreted by renal
routes has been reported in the literature. The ratio Q = 1− fe (1− kf ) (24.22)
Dose Adjustment in Renal and Hepatic Disease 793
where Q is the dosage adjustment factor, The usual dose of gentamicin sulfate = 1 mg/kg
k = u N
f Clcr /Clcr and fe is the fraction of unchanged every 8 hours. Therefore, for a 75-kg adult, the
drug excreted renally. Actually, Q is exactly the same as usual dose is 75 mg every 8 hours. The uremic
G in Equation 24.21, as developed by Giusti–Hayton dose may be estimated by:
approach in 1973. i. Reducing the maintenance dose and keeping
The value of Q in Equation 24.22 is multi- the dosing interval constant:
plied by the normal dose, DN, to give the uremic k
dose, Du:
Uremic dose u
= × normal dose
kN
D Uremic dose = 0.39 × 75 = 29.25 mg
u =Q × DN (24.23)
Give 29.25 mg (about 30 mg) every 8 hours.
Because the concentration of gentamicin
PRACTICE PROBLEMS sulfate solution is 40 mg/mL, 30 mg genta-
micin sulfate is equivalent to 0.75 mL.
ii. Increasing the dosing interval and keeping
1. An adult male patient (52 years old, 75 kg)
the maintenance dose constant:
whose serum creatinine is 2.4 mg/dL is to
be given gentamicin sulfate for a confirmed k
Dosage interval in uremia, N
τ = × τ
u k N
Gram-negative infection. The usual dose u
of gentamicin in adult patients with normal
tu = 2.564 × 8 = 20.5 h (2.564 is the
renal function is 1 mg/kg every 8 hours by
reciprocal of 0.39)
multiple IV bolus injections. Gentamicin
sulfate (Garamycin) is available in 2-mL vials Give 75 mg every 20.5 hours.
containing 40 mg of gentamicin sulfate per iii. Change both the maintenance dose and
milliliter. Calculate (a) the Clcr in this patient dosing interval. Using the dosing rate
by the Cockcroft–Gault method and (b) the D = 29.25 mg/8 h = 3.66 mg/h, a dose of
t
appropriate dosage regimen of gentamicin 23.9 mg every 6 hours or 43.8 mg every
sulfate for this patient in mg and mL. 12 hours will produce the same average
steady-state plasma drug concentration.
Solution Although each estimated dosage regimen
shown above produces the same average
a. The creatinine clearance is calculated by the steady-state plasma drug concentration, peak
Cockcroft–Gault method using Equation 24.12: drug concentration, and trough drug concen-
tration, the duration of time in which the
(140 drug concentration will be above or below
− 52)(75)
Clcr = = 38.19 mL/min
72(2.4) the minimum effective plasma drug concen-
tration will be different. The choice of an
appropriate dosage regimen requires consid-
b. The initial dose of gentamicin sulfate in this eration of these issues: the patient, the safety,
patient may be estimated using Equation 24.21. and efficacy of the drug.
Normal creatinine clearance is assumed to 2. Calculate the dose adjustment needed for
equal 100 mL/min. The fraction of dose uremic patients with (a) 75% of normal kidney
excreted unchanged in the urine, fe, = 0.98 for function (ie, Clu / N
cr Clcr = 75%); (b) 50% of
gentamicin sulfate (Table 24-6). normal kidney function; and (c) 25% of normal
kidney function. Make calculations for (i) a
ku 38.19 drug that is 50% excreted by the kidney, and
=
Q = 1− 0.981− 0.39
100 =
kN (ii) a drug that is 75% excreted by the kidney.
794 Chapter 24
TABLE 247 Dosage Adjustment in Uremic Patients
Percent of Normal Dose
Fraction of Drug Excreted 50% 25% 10% 0%
Unchanged (kr/kN) or fe Normal ClCr Normal ClCr Normal ClCr Normal ClCr
0.25 87 81 77 75
0.50 75 62 55 50
0.75 62 44 32 25
0.90 55 32 19 10
Solution Percent of uremic patient’s renal elimination
The values for percent of normal dose in uremic constant = 75% × 10% = 7.5% normal
patients with various renal functions are listed in Percent of uremic patient’s overall elimination
Table 24-7. The percent of dose adjustment in a constant = 7.5% + (100% – 75%)
given uremic state is obtained using the procedure = 7.5% + 25% = 32.5%
detailed below. The important facts to remember are
(1) although the elimination rate constant is usually Therefore, the uremic patient’s dose should be
composed of two components, only the renal com- 32.5% of that of normal patient. Table 24-7 provides
ponent is reduced in a uremic patient and (2) the some calculated dose adjustments for drugs elimi-
kidney function of the uremic patient may be nated to various degrees by renal excretion in differ-
expressed as a percent of uremic Clucr /normal ClNcr . ent stages of renal failure.
The reduction in the renal elimination rate constant
can be estimated from the percent of kidney function
remaining in the patient. The steps involved in mak- General Clearance Method
ing the calculations are as follows: The general clearance method is based on the meth-
ods discussed above. This method is popular in clini-
a. Determine fe or the fraction of drug excreted by
cal settings because of its simplicity. The method
the kidney.
assumes that creatinine clearance, Clcr, is a good
b. Determine kf by dividing Clu of the uremic
cr indicator of renal function and that the renal clear-
patient by ClNcr. ance of a drug, ClR, is proportional to Clcr. Therefore,
c. Calculate Q (Equation 24.22). the renal drug clearance, CluR , in the uremic patient is
d. Multiply Q by the normal dose to give the
fraction of normal dose required for a uremic Clu
patient. Clu cr
R = ×Cl (21.24)
ClN R
cr
3. What is the dose for a drug that is 75% excreted
unchanged through the kidney in a uremic patient Clu
with a creatinine clearance of 10 mL/min? Clu C cr
= lnr +ClR ClN (24.25)
cr
Solution where Clu is the total body clearance in the uremic
patient.
fe = 75%
If the ratio Clu N
cr /Clcr and ClR are known, the
10
Renal function of uremic patient = total body clearance in the uremic patient may be
100
estimated using Equation 24.25. Alternatively, if the
= 10% normal normal total body clearance, Cl, and fe are known,
Dose Adjustment in Renal and Hepatic Disease 795
Equation 24.26 may be obtained by substitution in absence of reliable information assuring the validity
Equation 24.25: of these assumptions, the equations should be dem-
onstrated as statistically reliable in practice. A statis-
Clu tical approach was used by Wagner (1975), who
Cl C (1 ) cr
u = l − fe + fe Cl (24.26)
ClNcr established a linear relationship between creatinine
concentration and the first-order elimination rate
Equation 24.26 calculates drug clearance in the ure- constant of the drug in patients. The Wagner method
mic patient using the fraction of drug excreted is described in greater detail in the third edition of
unchanged (fe), total body clearance of the drug (Cl) this book.
in the normal subject, and the ratio of creatinine This method takes advantage of the fact that the
clearance of the uremic to that of the normal patient. elimination rate constant for a patient can be obtained
Dividing Equation 24.26 on both sides by Cl from the creatinine clearance, as follows:
yields the ratio Clu/Cl, reflecting the fraction of the
uremic/normal drug dose. k% = a + b Clcr (23.28)
Cl C u
u l
(1 f cr
= − e ) + f (
Cl e 24.27) The values of a and b are determined statistically for
ClNcr each drug from pooled data on uremic patients. The
method is simple to use and should provide accu-
rate determination of elimination rate constants for
PRACTICE PROBLEM patients when a good linear relationship exists
A 34-year-old, 110-lb female patient is to be given between elimination rate constant and creatinine con-
tobramycin for sepsis. The usual dose of tobramycin centration. The theoretical derivation of this approach
is 150 mg twice a day by intravenous injection. The is as follows:
creatinine clearance in this patient has decreased to k% = total elimination rate constant
a stable level of 50 mL/min. The fraction of tobra- knr = nonrenal elimination rate constant
mycin excreted unchanged is 0.9. Calculate the kr = renal excretion rate constant
appropriate dose of tobramycin for this patient. Cl = total body clearance of drug
Solution Cl
R =
f Cl
cr (24.29)
e = 0.9 and apply Equation 24.27:
Cl = R Cl
cr
Cl u
u Cl
(1 r
= − fe ) + f c
Cl e ClNcr
Since k = knr + kr,
Clu 50
= 1− 0.9 + 0.9 = 0.55
Cl 100 R
k = k
nr + Cl
V cr
D
Therefore, the dose for the uremic patient = 150 mg ×
100R
0.55 = 82.5 mg (given twice a day). 100k = 100k + Cl
nr V cr (24.30)
D
The Wagner Method k% = a + b Clcr
The methods for renal dose adjustment discussed in
the previous sections assume that the volume of distri- Equation 24.30 can also be used with drugs that
bution and the fraction of drug excreted by nonrenal follow the two-compartment model. In such cases,
routes are unchanged. These assumptions are conve- the terminal half-life is used, and the terminal
nient and hold true for many drugs. However, in the slope of the elimination curve (b) is substituted for
796 Chapter 24
the elimination rate constant k. Since the equation references to potentiation of sedative and analgesic
assumes a constant nonrenal elimination constant (knr) drug effects in renal, liver, and other multisystem
and volume of distribution, any change in these two disease states.
parameters will result in an error in the estimated Another assumption in the use of these meth-
elimination rate constant. ods is that pharmacologic response is unchanged in
the uremic patient. This assumption may be unreal-
istic for drugs that act differently in the disease
Frequently Asked Questions state, and possible changes in pharmacodynamic
»»What are the advantages and disadvantages of effects in patients with renal and other diseases
using serum creatinine concentrations for the must be considered. For example, the pharmaco-
measurement of renal function? logic response with digoxin is dependent on the
potassium level in the body, and potassium level in
»»What is the most accurate approach for the
the uremic patient may be rather different from that
estimation of glomerular filtration rate?
of the normal individual. In a patient undergoing
»»Why does each method based on serum creatinine dialysis, loss of potassium may increase the poten-
concentrations for dosage adjustment in renal tial for toxic effect of the drug digoxin. In addition,
impairment give somewhat different values? neuromuscular-blocking drugs may be potentiated
»»What are the pharmacokinetic considerations in or antagonized by changes in potassium, phos-
designing a dosing regimen? Why is dosing once a phate, and hydrogen ion concentration brought
day for aminoglycosides recommended by many about by uremic states, and morphine potentiation
clinicians? has been reported in hypocalcemic states.
For many drugs, studies have shown that the
incidence of adverse effects is increased in uremic
Limitations of Dose Adjustment Methods patients. It is often impossible to distinguish whether
in Uremic Patients the increase in adverse effect is due to a pharmaco-
All of the methods mentioned previously have simi- kinetic change or a pharmacodynamic change in the
lar limitations (see Table 24-2). For example, the receptor sensitivity to the drug. Serum creatinine
drug must follow dose-independent kinetics and the concentration may not rise for some time until Clcr
volume of distribution of the drug must remain rela- has fallen significantly, thereby adding to the uncer-
tively constant in the uremic patient. It is usually tainty of any method that depends on serum Clcr for
assumed that the nonrenal routes of elimination, dose adjustment. In any event, these observations
such as hepatic clearance or knr, do not change. If point out the fact that dose adjustment must be
there is a change in an active metabolite formation or regarded as a preliminary estimation to be followed
elimination in uremia, then both parent and active with further adjustments in accordance with the
metabolites must be considered when adjusting a observed clinical response.
dosage regimen for patients with renal disease,
because potential side effects may result from an
increase in the half-life of the parent drug and/or an EXTRACORPOREAL REMOVAL
accumulation of the active metabolites. OF DRUGS
Bodenham et al (1988) have shown that although
lorazepam pharmacokinetics were not significantly Patients with end-stage renal disease (ESRD) and
altered in patients with chronic renal failure, the those who have become intoxicated with a drug as a
clearance of lorazepam glucuronide, a major metabo- result of drug overdose require supportive treatment
lite, was reduced significantly. Therefore, there are to remove the accumulated drug and its metabolites.
potential sedative side effects in the renally impaired Several methods are available for the extracorporeal
patient as a result of the longer metabolite half-life. removal of drugs, including hemoperfusion, hemofil-
Bodenham and coworkers (1988) also cited literature tration, and dialysis. The objective of these methods is
Dose Adjustment in Renal and Hepatic Disease 797
to rapidly remove the undesirable drugs and metabo- Continuous ambulatory peritoneal dialysis (CAPD)
lites from the body without disturbing the fluid and is the most common form of peritoneal dialysis.
electrolyte balance in the patient. Many diabetic patients become uremic as a result of
Patients with impaired renal function may be tak- lack of control of their disease. About 2 L of dialysis
ing other medication concurrently. For these patients, fluid is instilled into the peritoneal cavity of the
dosage adjustment may be needed to replace drug loss patient through a surgically placed resident catheter.
during extracorporeal drug and metabolite removal. The objective is to remove accumulated urea and
other metabolic waste in the body. The catheter is
sealed and the patient is able to continue in an ambu-
Dialysis latory mode. Every 4–6 hours, the fluid is emptied
Dialysis is an artificial process in which the accumu- from the peritoneal cavity and replaced with fresh
lation of drugs or waste metabolites is removed by dialysis fluid. The technique uses about 2 L of dialysis
diffusion from the body into the dialysis fluid. Two fluid; it does not require a dialysis machine and can
common dialysis treatments are peritoneal dialysis be performed at home.
and hemodialysis. The principle underlying both
processes is that as the uremic blood or fluid is Hemodialysis
equilibrated with the dialysis fluid across a dialysis Hemodialysis uses a dialysis machine and filters
membrane, waste metabolites from the patient’s blood through an artificial membrane. Hemodialysis
blood or fluid diffuse into the dialysis fluid and are requires access to the blood vessels to allow the blood
removed. The dialysate is balanced with electrolytes to flow to the dialysis machine and back to the body.
and with respect to osmotic pressure. The dialysate For temporary access, a shunt is created in the arm,
contains water, dextrose, electrolytes (potassium, with one tube inserted into an artery and another tube
sodium, chloride, bicarbonate, acetate, calcium, etc), inserted into a vein. The tubes are joined above the
and other elements similar to normal body fluids skin. For permanent access to the blood vessels, an
without the toxins. arteriovenous fistula or graft is created by a surgi-
cal procedure to allow access to the artery and
Peritoneal Dialysis vein. Patients who are on chronic hemodialysis
Peritoneal dialysis uses the peritoneal membrane in treatment need to be aware of the need for infection
the abdomen as the filter. The peritoneum consists of control of the surgical site of the fistula. At the start
visceral and parietal components. The peritoneum of the hemodialysis procedure, an arterial needle
membrane provides a large natural surface area for allows the blood to flow to the dialysis machine, and
diffusion of approximately 1–2 m2 in adults; it is per- blood is returned to the patient to the venous side.
meable to solutes of molecular weights ≤30,000 Da Heparin is used to prevent blood clotting during the
(Merck Manual, 1996–1997). However, only a small dialysis period.
portion of the total splanchnic blood flow (70 mL/min During hemodialysis, the blood flows through
out of 1200 mL/min at rest) comes into contact with the dialysis machine, where the waste material is
the peritoneum and gets dialyzed. Placement of a removed from the blood by diffusion through an
peritoneal catheter is surgically simpler than hemodi- artificial membrane before the blood is returned to
alysis and does not require vascular surgery and hepa- the body. Hemodialysis is a much more effective
rinization. The dialysis fluid is pumped into the method of drug removal and is preferred in situations
peritoneal cavity, where waste metabolites in the body when rapid removal of the drug from the body is
fluid are discharged rapidly. The dialysate is drained important, as in overdose or poisoning. In practice,
and fresh dialysate is reinstilled and then drained peri- hemodialysis is most often used for patients with
odically. Peritoneal dialysis is also more amenable to end-stage renal failure. Early dialysis is appropriate
self-treatment. However, slower drug clearance rates for patients with acute renal failure in whom resump-
are obtained with peritoneal dialysis compared to tion of renal function can be expected and in patients
hemodialysis, and thus longer dialysis time is required. who are to be renally transplanted. Other patients
798 Chapter 24
may be placed on dialysis according to clinical judg- of the dialysate is similar to plasma but may be
ment concerning the patient’s quality of life and risk/ altered according to the needs of the patient. Many
benefit ratio (Carpenter and Lazarus, 1994). dialysis machines use a hollow fiber or capillary dia-
Dialysis may be required from once every 2 days lyzer in which the semipermeable membrane is made
to 3 times a week, with each treatment period lasting into fine capillaries, of which thousands are packed
for 2–4 hours. The time required for dialysis depends into bundles with blood flowing through the capillaries
on the amount of residual renal function in the patient, and the dialysate circulating outside the capillaries.
any complicating illness (eg, diabetes mellitus), the The permeability characteristics of the membrane and
size and weight of the patient, including muscle mass, the membrane surface area are determinants of drug
and the efficiency of the dialysis process. Dosing of diffusion and ultrafiltration.
drugs in patients receiving hemodialysis is affected The efficacy of hemodialysis membranes for the
greatly by the frequency and type of dialysis machine removal of vancomycin by hemodialysis has been
used and by the physicochemical and pharmacoki- reviewed by De Hart (1996). Vancomycin is an anti-
netic properties of the drug. Factors that affect drug biotic effective against most Gram-positive organ-
removal in hemodialysis are listed in Table 24-8. isms such as Staphylococcus aureus, which may be
These factors are carefully considered before hemodi- responsible for vascular access infections in patients
alysis is used for drug removal. undergoing dialysis. In De Hart’s study, vancomycin
In hemodialysis, blood is pumped to the dia- hemodialysis in patients was compared using a
lyzer by a roller pump at a rate of 300–450 mL/min. cuprophan membrane or a cellulose acetate and
The drug and metabolites diffuse from the blood polyacrylonitrile membrane. The cellulose acetate
through the semipermeable membrane. In addition, and polyacrylonitrile membrane is considered a
hydrostatic pressure also forces the drug molecules “high-flux” filter. Serum vancomycin concentrations
into the dialysate by ultrafiltration. The composition decreased only 6.3% after dialysis when using the
TABLE 248 Factors Affecting Dialyzability of Drugs
Physicochemical and Pharmacokinetic Properties of the Drug
Water solubility Insoluble or fat-soluble drugs are not dialyzed—eg, glutethimide, which is very water
insoluble.
Protein binding Tightly bound drugs are not dialyzed because dialysis is a passive process of diffusion—
eg, propranolol is 94% bound.
Molecular weight Only molecules with molecular weights of less than 500 are easily dialyzed—eg,
vancomycin is poorly dialyzed and has a molecular weight of 1800.
Drugs with large volumes of distri- Drugs widely distributed are dialyzed more slowly because the rate-limiting factor
bution is the volume of blood entering the machine—eg, for digoxin, VD = 250–300 L.
Drugs concentrated in the tissues are usually difficult to remove by dialysis.
Characteristics of the Dialysis Machine
Blood flow rate Higher blood flows give higher clearance rates.
Dialysate Composition of the dialysate and flow rate.
Dialysis membrane Permeability characteristics and surface area.
Transmembrane pressure Ultrafiltration increases with increase in transmembrane pressure.
Duration and frequency of dialysis
Dose Adjustment in Renal and Hepatic Disease 799
cuprophan membrane, whereas the serum drug con- Alternatively, using Equation 24.31,
centration decreased 13.6%–19.4% after dialysis with (30 −12)
the cellulose acetate and polyacrylonitrile membrane. ClD = 350 mL/min × = 210 mL/min
30
In dialysis involving uremic patients receiving
drugs for therapy, the rate at which a given drug is These calculations show that the two terms are the
removed depends on the flow rate of blood to the same. In practice, dialysance has to be measured
dialysis machine and the performance of the dialysis experimentally by determining Ca, Cv, and Q. In dos-
machine. The term dialysance is used to describe the ing of drugs for patients on dialysis, the average
process of drug removal from the dialysis machine. plasma drug concentration of a patient is given by
Dialysance is a clearance term similar in meaning to FD
renal clearance, and it describes the amount of blood C∞ 0
av = (24.32)
(ClT +ClD ) τ
completely cleared of drugs (in mL/min). Dialysance
is defined by the equation where F represents fraction of dose absorbed, ClT is
total body drug clearance of the patient, C∞
av is average
Q(Ca −Cv )
steady-state plasma drug concentration, and t is the
ClD = (24.31)
C dosing interval.
a
In practice, if ClD is 30% or more of ClT, adjust-
where Ca = drug concentrations in arterial blood ment is usually made for the amount of drug lost
(blood entering kidney machine), Cv = drug concen- in dialysis.
tration in venous blood (blood leaving kidney The elimination half-life, t1/2, for the drug in the
machine), Q = rate of blood flow to the kidney patient off dialysis is related to the remaining total
machine, and ClD = dialysance. Dialysance is some- body clearance, ClT, and the volume of distribution,
times referred to as dialysis clearance. VD, as shown below.
0.693
t1/2 = V (24 33)
Cl D .
T
PRACTICE PROBLEM
Drugs that are easily dialyzed will have a high dialysis
Assume the flow rate of blood to the dialysis clearance, ClD, and the elimination half-life, t1/2, is
machine is 350 mL/min. By chemical analysis, the shorter in a patient on dialysis.
concentrations of drug entering and leaving the
machine are 30 and 12 mg/mL, respectively. What is 0.693V
t D
1/2 = (24.34)
the dialysis clearance? ClT +ClD
Cl +Cl
Solution k T D
ON = (24.35)
VD
The rate of drug removal is equal to the volume of
blood passed through the machine divided by the where kON is the first-order elimination half-life of
arterial difference in blood drug concentrations the drug in the patient on dialysis.
before and after dialysis. Thus, The fraction of drug lost due to elimination and
dialysis may be estimated from Equation 24.36.
Rate of drug removal = 350 mL/min
× (30 – 12) mg/mL = 6300 mg/min Fraction of drug lost 1 −(C )
= − e lT +ClD t /VD (24.36)
Since clearance is equal to the rate of drug removal Equation 24.36 is based on first-order drug elimination
divided by the arterial concentration of drug, and the substitution of t hours for the dialysis period.
Several hypothetical examples illustrating the
6300 µg/min use of Equation 24.36 have been developed by
ClD = = 210 mL/min
30 µg/mL Gambertoglio (1984). These are given in Table 24-9.
800 Chapter 24
TABLE 249 Predicted Effects of Hemodialysis on Drug Half-Life and Removal in the Overdose Setting
Drug VD (L) Cl (mL/min) ClD (mL/min) t1/2 off (h) t1/2 on (h) FLa
Digoxinb 560 150 20 43 38 0.07
Digoxinc 300 40 20 86 58 0.05
Ethchlorvynol 300 35 60 99 36 0.07
Phenobarbital 50 5 70 115 8 0.30
Phenytoin 100 5 10 231 77 0.04
Salicylic acid 40 20 100 23 4 0.51
aFL = fraction lost during a dialysis period of 4 hours.
bParameters for a patient with normal renal function.
cParameters for a patient with no renal function.
From Gambertoglio (1984), with permission.
Equation 24.36 shows that as VD increases, the is very low and the drug concentration declines
fraction of drug lost decreases. The fraction of drug slowly. In this example, the drug has an elimination
lost during a 4-hour dialysis period for phenobarbital t1/2 of 48 hours during the interdialysis period. When
and salicylic acid was 0.30 and 0.50, respectively, the patient is placed on dialysis, the drug clearance
whereas for digoxin and phenytoin, the fraction of (sum of the total body clearance and the dialysis
drug lost was only 0.07 and 0.04, respectively. Both clearance) removes the drug more rapidly.
phenobarbital and salicylic acid are easily dialyzed
because of their smaller volumes of distribution,
small molecular weights, and aqueous solubility. In CLINICAL EXAMPLES
contrast, digoxin has a large volume of distribution
and phenytoin is highly bound to plasma proteins, 1. The aminoglycoside antibiotics, such as genta-
making these drugs difficult to dialyze. Thus, dialy- micin and tobramycin, are eliminated primarily
sis is not very useful for treating digoxin intoxica- by the renal route. Dosing of these aminogly-
tion, but is useful for salicylate overdose. cosides is adjusted according to the residual
An example of the effect of hemodialysis on renal function in the patient as estimated by
drug elimination is shown in Fig. 24-5. During the creatinine clearance. During hemodialysis or
interdialysis period, the patient’s total body clearance peritoneal dialysis, the elimination half-lives
for these antibiotics are significantly decreased.
After dialysis, the aminoglycoside concentra-
tions are below the therapeutic range, and the
During hemodialysis
patient needs to be given another dose of the
aminoglycoside antibiotic.
2. An adult male (73 years old, 65 kg) with
diabetes mellitus is placed on hemodialysis.
His residual creatinine clearance is <5 mL/min.
Interhemodialysis The patient is given tobramycin, an aminogly-
coside antibiotic, at a dose of 1 mg/kg by IV
bolus injection. Tobramycin is 90% excreted
Time (hours) unchanged in the urine, is less than 10% bound
FIGURE 245 Effect of dialysis on drug elimination. to plasma proteins, and has an elimination
Log drug concentration
Dose Adjustment in Renal and Hepatic Disease 801
half-life of approximately 2.2 hours in patients 1.58 mg 0.547 mg
with normal renal function. In this patient, (21.45 L) − (21.45 L)
L L
tobramycin has an elimination t1/2 of 50 hours
during the interdialysis period and an elimina- = 22.16 mg
tion t1/2 of 8 hours during hemodialysis. The
apparent volume of distribution for tobramycin e. Tobramycin dose (replenishment dose) needed
is about 0.33 L/kg. For this patient, calculate to be given to the patient after hemodialysis:
(a) the initial plasma antibiotic concentra- The recommended ranges of peak and trough
tion after the first dose of tobramycin; (b) the concentrations of tobramycin (Mathews, 1995)
plasma drug concentration just before the are 5–10 mg/L (peak) and 0.5–<2 mg/L (trough).
start of hemodialysis (48 hours after the initial The usual replenishment dose of tobramycin
tobramycin dose); (c) the plasma drug concen- after hemodialysis is 1–1.5 mg/kg.
tration at the end of 4 hours of hemodialysis; If a replenishment dose of 65 mg (ie, 1 mg/kg)
(d) the amount of drug lost from the body after is given to the patient, then the plasma drug concen-
dialysis; and (e) the tobramycin dose (replenish- tration is estimated as
ment dose) needed to be given to the patient
after hemodialysis. Plasma drug concentration after 65 mg
Solution 65 mg
given by IV bolus injection = + 0.547 mg/L
21.45 L
a. Initial plasma antibiotic concentration after the
first dose of tobramycin: = 3.58 mg/L
1mg
Patient dose = × 65 kg = 65 mg after hemodialysis.
kg
The patient is given 65 mg of tobramycin by
0.33 L IV bolus injection after completion of hemodialysis
VD = × 65 kg = 21.45 L
kg to produce a tobramycin plasma concentration of
3.58 mg/L.
Plasma drug concentration,
D 65 mg
C0 0 Hemoperfusion
p = = = 3.03 mg/L
VD 21.45 L Hemoperfusion is the process of removing drug by
b. Plasma drug concentration just before the start of passing the blood from the patient through an adsor-
hemodialysis (48 hours after the initial tobramycin bent material and back to the patient. Hemoperfusion
dose): After 48 hours, the plasma drug concen- is a useful procedure for rapid drug removal in acci-
tration declines according to first-order kinetics: dental poisoning and drug overdose. Because the
drug molecules in the blood are in direct contact
Cp = 3.03 e–(0.693/50) (48) = 1.58 mg/L with the adsorbent material, any molecule that has
great affinity for the adsorbent material will be
c. Plasma drug concentration at the end of a removed. The two main adsorbents used in hemoper-
4-hour hemodialysis: fusion include (1) activated charcoal, which adsorbs
C both polar and nonpolar drug, and (2) Amberlite
p = 1.58 e–(0.693/8) (4) = 0.547 mg/L
resins. Amberlite resins, such as Amberlite XAD-2
d. Amount of drug lost from the body after dialysis: and Amberlite XAD-4, are available as insoluble
polymeric beads, with each bead containing an
Amt of drug lost after dialysis = agglomerate of cross-linked polystyrene micro-
Amt of drug in the body before dialysis – spheres. The Amberlite resins have a greater affinity
Amt of drug in the body after dialysis for nonpolar organic molecules than activated charcoal.
802 Chapter 24
The important factors for drug removal by hemoper- therapies are hemofiltration methods, replacement
fusion include affinity of the drug for the adsorbent, fluid must be administered to the patient to replace
surface area of the adsorbent, absorptive capacity of fluid lost to the hemofiltrate, though the volume
the adsorbent, rate of blood flow through the adsor- of fluid removed can be easily controlled compared
bent, and the equilibration rate of the drug from the to intermittent hemofiltration. Heparin infusions are
peripheral tissue into the blood. also provided for anticoagulation.
Continuous renal replacement therapy (CRRT)
includes continuous veno-venous hemofiltration
Hemofiltration
(CVVH) and continuous arteriovenous hemofiltration
An alternative to hemodialysis and hemoperfusion is (CAVH). In CAVH, blood passes through a hemofilter
hemofiltration. Hemofiltration is a process by which that is placed between a cannulated femoral artery
fluids, electrolytes, and small-molecular-weight sub- and vein. A dialysis filter may be added to CAVH to
stances are removed from the blood by means of improve small-molecule clearance. Circulating dialy-
low-pressure flow through hollow artificial fibers or sate on the outside of the filters allows more efficient
flat-plate membranes (Bickley, 1988). Because fluid toxin removal. However, this method is inefficient
is also filtered out of the plasma during hemofiltra- (10–15 mL filtered per minute) and complex and is
tion, replacement fluid is administered to the patient not widely used in comparison to CVVH.
for volume replacement. Hemofiltration is a slow, CVVH provides a hemofilter that is placed
continuous filtration process that removes non- between cannulated femoral, subclavian, or internal
protein-bound small molecules (<10,000 Da) from jugular veins. Rather than relying on arterial pres-
the blood by convective mass transport. The clear- sure to filter blood, a pump can be used to provide
ance of the drug depends on the sieving coefficient and filtration rates greater than 100 mL/min. Like CAVH,
ultrafiltration rate. Hemofiltration provides a creati- a dialysis filter may be added to CVVH to improve
nine clearance of approximately 10 mL/min (Bickley, clearance of small molecules.
1988) and may have limited use for drugs that are As with other extracorporeal removal systems,
widely distributed in the body, such as aminoglyco- hemofiltration methods can alter drug pharmacoki-
sides, cephalosporins, and acyclovir. A major prob- netics. A study by Hansen et al (2001) showed that
lem with this method is the formation of blood clots acute renal failure patients on CVVH demonstrated a
within the hollow filter fibers. 50% decrease in clearance of levofloxacin. However,
because of the large volume and moderate renal
Continuous Renal Replacement Therapy clearance of fluoroquinolones, levofloxacin does not
Because of the initial loss of fluid that results during require dosing adjustment.
hemofiltration, intermittent hemofiltration results in
concentration of red blood cells in the resulting Drug Removal during Continuous Renal
reduced plasma volume. Therefore, blood becomes Replacement Therapy
more viscous with a high hematocrit and high col-
During CAVH, solutes are removed by convection.
loid osmotic pressure at the distal end of the hemo-
The efficiency of the removal of drugs is related to
filter. Predilution may be used to circumvent this
the sieving coefficient S, which reflects the solute
problem, but this method is rarely used because of
removal ability during hemofiltration and is equal to
cost and inefficiency.
the ratio of solute concentration in the ultrafiltrate
Continuous replacement therapy allows ongo-
to the solute concentration in the retentate. When S = 1,
ing removal of fluid and toxins by relying on a
the solute passes freely through the membrane.
patient’s own blood pressure to pump blood through
When S = 0, the solute is retained in the plasma. S is
a filter. The continuous filtration is better tolerated
constant and independent of blood flow; therefore,
by patients than intermittent therapy and provides
optimal control of circulating volumes and ongoing
toxin removal. Because continuous replacement Cl = S × rateuf (24.37)
Dose Adjustment in Renal and Hepatic Disease 803
where rateuf is the ultrafiltration rate. The concentra- The major difficulty in estimating hepatic clear-
tion of drug in the ultrafiltrate is also equal to the ance in patients with hepatic disease is the complex-
unbound drug concentration in the plasma. So, the ity and stratification of the liver enzyme systems. In
amount of drug removed during CAVH is contrast, creatinine clearance has been used suc-
cessfully to measure kidney function and renal
Amount removed per time unit = Cp × a × rateuf clearance of drugs. Clinical laboratory tests measure
(24.38) only a limited number of liver functions. Some clini-
cal laboratory tests, such as the aspartate amino-
where a = the unbound fraction. transferase (AST) and alanine aminotransferases
(ALT), are common serum enzyme tests that detect
liver cell damage rather than liver function. Other
Frequently Asked Questions laboratory tests, such as serum bilirubin, are used to
»»Which pharmacokinetic properties of a drug would measure biliary obstruction or interference with bile
predict a greater or lesser rate of elimination in a flow. Presently, no single test accurately assesses
patient undergoing dialysis? the total liver function. Usually, a series of clinical
»»Drug clearance is often decreased 20%–50% in many laboratory tests are used in clinical practice to
patients with congestive heart failure (CHF). Explain detect the presence of liver disease, distinguish
how it may affect drug disposition. among different types of liver disorders, gauge the
extent of known liver damage, and follow the
response to treatment. A few tests have been used
EFFECT OF HEPATIC DISEASE to relate the severity of hepatic impairment to pre-
ON PHARMACOKINETICS dicted changes in the pharmacokinetic profile of a
drug (FDA Guidance for Industry, 2003). Examples
Hepatic disease can alter drug pharmacokinetics of these tests include the ability of the liver to
including absorption and disposition as well as phar- eliminate marker drugs such as antipyrine, indocya-
macodynamics including efficacy and safety. Hepatic nine green, monoethylglycine-xylidide, and galac-
disease may include common hepatic diseases, such tose. Furthermore, endogenous substrates, such as
as alcoholic liver disease (cirrhosis) and chronic albumin or bilirubin, or a functional measure, such
infections with hepatitis viruses B and C, and less as prothrombin time, has been used for the evalua-
common diseases, such as acute hepatitis D or E, tion of liver impairment.
primary biliary cirrhosis, primary sclerosing cholan-
gitis, and a1-antitrypsin deficiency (FDA Guidance
for Industry, 2003). In addition, drug-induced hepa- Dosage Considerations in Hepatic Disease
totoxicity is the leading cause of acute liver failure in Several physiologic and pharmacokinetic factors are
the United States (Chang and Schiano, 2007). relevant in considering dosage of a drug in patients
Drugs are often metabolized by one or more with hepatic disease (Table 24-10). Chronic disease
enzymes located in cellular membranes in different or tissue injury may change the accessibility of some
parts of the liver. Drugs and metabolites may also be enzymes as a result of redirection or detour of hepatic
excreted by biliary secretion. Hepatic disease may blood circulation. Liver disease affects the quantita-
lead to drug accumulation, failure to form an active tive and qualitative synthesis of albumin, globulins,
or inactive metabolite, increased bioavailability and other circulating plasma proteins that subse-
after oral administration, and other effects including quently affect plasma drug protein binding and dis-
possible alteration in drug–protein binding. Liver tribution (see Chapter 12). As mentioned, most liver
disease may also alter kidney function, which can function tests indicate only that the liver has been
lead to accumulation of a drug and its metabolites damaged; they do not assess the function of the
even when the liver is not primarily responsible for cytochrome P-450 enzymes or intrinsic clearance by
elimination. the liver.
804 Chapter 24
TABLE 2410 Considerations in Dosing Patients with Hepatic Impairment
Item Comments
Nature and severity of liver disease Not all liver diseases affect the pharmacokinetics of the drugs to the same extent.
Drug elimination Drugs eliminated by the liver >20% are less likely to be affected by liver disease. Drugs
that are eliminated mainly via renal route will be least affected by liver disease.
Route of drug administration Oral drug bioavailability may be increased by liver disease due to decreased first-pass
effects.
Protein binding Drug–protein binding may be altered due to alteration in hepatic synthesis of albumin.
Hepatic blood flow Drugs with flow-dependent hepatic clearance will be more affected by change in
hepatic blood flow.
Intrinsic clearance Metabolism of drugs with high intrinsic clearance may be impaired.
Biliary obstruction Biliary excretion of some drugs and metabolites, particularly glucuronide metabolites,
may be impaired.
Pharmacodynamic changes Tissue sensitivity to drug may be altered.
Therapeutic range Drugs with a wide therapeutic range will be less affected by moderate hepatic
impairment.
Because there is no readily available measure of distribution or drug disposition in many unpredictable
hepatic function that can be applied to calculate ways that can affect drug safety.
appropriate doses, enzyme-dependent drugs are usu-
ally given to patients with hepatic failure in half-
doses, or less. Response or plasma levels then must Fraction of Drug Metabolized
be monitored. Drugs with flow-dependent clearance Drug elimination in the body may be divided into
are avoided if possible in patients with liver failure. (1) fraction of drug excretion unchanged, fe, and
When necessary, doses of these drugs may need to (2) fraction of drug metabolized. The latter is usu-
be reduced to as low as one-tenth of the conventional ally estimated from 1 – fe; alternatively, the fraction
dose for an orally administered agent. Starting ther- of drug metabolized may be estimated from the ratio
apy with low doses and monitoring response or of Clh/Cl, where Clh is hepatic clearance and Cl is
plasma levels provides the best opportunity for safe total body clearance. Knowing the fraction of drug
and efficacious treatment. eliminated by the liver allows estimation of total
If some of the efflux proteins that normally pro- body clearance when hepatic clearance is reduced.
tect the body against drug accumulation are reduced or Drugs with low fe values (or, conversely, drugs
not functioning, this could potentially cause hepatic with a higher fraction of metabolized drug) are
drug injury as drug concentration begins to increase. more affected by a change in liver function due to
Compounds that form glucuronide, sulfate, glutathi- hepatic disease.
one (GSH), and other substrates that are involved in
phase II metabolism (see Chapter 12) may be depleted Clh = Cl(1− fe ) (24.39)
during hepatic impairment, potentially interrupting the
normal path of drug metabolism. Indeed, even albumin Equation 24.39 assumes that drug metabolism occurs
or alpha-1-acid glycoprotein (AAG) concentrations in the liver and the unchanged drug is excreted in the
can be altered in hepatic impairment and affect drug urine. Assuming that there is no enzyme saturation
Dose Adjustment in Renal and Hepatic Disease 805
and a drug exhibits linear kinetics, dosing adjust- [ClR]normal = renal clearance of drug in normal subject
ment may be based on residual hepatic function in Clnormal = total clearance of drug in normal subject
patients with hepatic disease as shown in the follow- Clhepatitis = total clearance of drug in patient with
ing example. hepatitis
fe = fraction of drug excreted unchanged
1 – fe = fraction of drug metabolized
PRACTICE PROBLEM
and Dhepatitis and Dnormal are the doses in a hepatitis
The hepatic clearance of a drug in a patient is reduced patient and in a normal liver function patient, respec-
by 50% due to chronic viral hepatitis. How is the total tively. Substituting in Equation 24.44 with RL = 0.5
body clearance of the drug affected? What should be and fe = 0.4,
the new dose of the drug for the patient? Assume that
renal drug clearance (fe = 0.4) and plasma drug pro- Dhepatitis
= 0.5(1− 0.4) + 0.4 = 0.3+ 0.4
tein binding are not altered. D
normal
= 0.7 (or 70%)
Solution
The residual liver function (RL) is estimated by The adjusted dose of the drug for the hepatic patient
is 70% of that for the normal subject as a result of the
[Clh ]hepatitis 50% decrease in hepatic function in the above case
RL =
[Clh ]normal (fe = 0.4).
An example of a correlation established between
[Clh ]hepatitis = RL [Clh ]normal actual residual liver function (measured by marker)
and hepatic clearance was reported for cefoperazone
Substituting Clnormal(1 – fe) for [Clh]normal (Hu et al, 1995) and other drugs in patients with cir-
rhosis. The method should be applied only to drugs
[Clh ]hepatitis = RL Clnormal (1– fe ) (24.40) that have linear pharmacokinetics or low protein
binding, or that are nonrestrictively bound.
Assuming no renal clearance deterioration due to Many variables can complicate dose correction
hepatitis when binding profoundly affects distribution, elimi-
nation, and penetration of the drug to the active site.
Clhepatitis = [Clh ]hepatitis + [ClR ]normal (24.41) For drugs with restrictive binding, the fraction of free
drug must be used to correct the change in free drug
Substituting Equation 24.41 with Equation 24.40 concentration and the change in free drug clearance.
and Clnormal fe for [ClR]normal In some cases, the increase in free drug is partly off-
set by a larger volume of distribution resulting from
Clhepatitis = RL Clnormal (1− fe ) +Clnormal fe (24.42) the decrease in protein binding. Since there are many
variables that complicate dose correction for patients
Clhepatitis = Clnormal[RL(1− fe ) + f ] (24.43)
e with hepatic disease, dose correction is limited to
D drugs whose hepatic metabolism is approximated by
hepatitis Clhepatitis RL(1− fe ) + f
e
= = (24.44) linear pharmacokinetics.
Dnormal Clnormal 1
where RL = residual liver function. Active Drug and the Metabolite
[Clh]normal = hepatic clearance of drug in normal For many drugs, both the drug and the metabolite
subject contribute to the overall therapeutic response of the
[Clh]hepatitis = hepatic clearance of drug in patient with drug to the patient. The concentration of both the drug
hepatitis and the metabolite in the body should be known.
806 Chapter 24
When the pharmacokinetic parameters of the metabo- changes in renal function such as GFR, the above
lite and the drug are similar, the overall activity of the physiologic model equation may not be adequate for
drug can become more or less potent as a result of a accurate prediction of changes in hepatic clearance.
change in liver function; that is, (1) when the drug is Calculations based on model equations must be cor-
more potent than the metabolite, the overall pharma- roborated by clinical assessment.
cologic activity will increase in the hepatic-impaired
patient because the parent drug concentration will Pathophysiologic Assessment
be higher; (2) when the drug is less potent than In practice, patient information about changes in
the metabolite, the overall pharmacologic activity hepatic blood flow may not be available, because
in the hepatic patient will decrease because less of special electromagnetic (Nuxmalo et al, 1978) or
the active metabolite is formed. ultrasound techniques are required to measure blood
Changes in pharmacologic activity due to flow and are not routinely available. The clinician/
hepatic disease may be much more complex when pharmacist may have to make an empirical estimate
both the pharmacokinetic parameters and the phar- of the blood flow change after examining the patient
macodynamics of the drug change as a result of the and reviewing the available liver function tests.
disease process. In such cases, the overall pharmaco- Various approaches have been used diagnosti-
dynamic response may be greatly modified, making cally to assess hepatic impairment. The Child–Pugh
it necessary to monitor the response change with the (or Child–Turcotte–Pugh) score assesses the overall
aid of a pharmacodynamic model (see Chapter 21). hepatic impairment as mild, moderate, or severe
(Figg et al, 1995; Lucey et al, 1997). The score
Hepatic Blood Flow and Intrinsic Clearance employs five clinical measures of liver disease,
Blood flow changes can occur in patients with chronic including total bilirubin, serum albumin, International
liver disease (often due to viral hepatitis or chronic Normalized Ratio (INR), ascites, and hepatic enceph-
alcohol use). In some patients with severe liver cir- alopathy (Tables 24-11 and 24-12). Different publica-
rhosis, fibrosis of liver tissue may occur, resulting in tions use different measures. Some older references
intra- or extrahepatic shunt. Hepatic arterial-venous substitute prothrombin time (PT) prolongation for
shunts may lead to reduced fraction of drug extracted INR. The original classification used nutrition, which
(see Chapter 12) and an increase in the bioavailability
of drug. In other patients, resistance to blood flow
may be increased as a result of tissue damage and TABLE 2411 Child-Pugh Classification of
fibrosis, causing a reduction in intrinsic hepatic Severity of Liver Disease
clearance.
Points Assigned
The following equation may be applied to esti-
mate hepatic clearance of a drug after assessing Parameter 1 2 3
changes in blood flow and intrinsic clearance (Clint): Ascites Absent Slight Moderate
QCl Bilirubin, mg/dL ≤ 2 2–3 >3
Cl int
= (24.45)
h Q +Cl
int Albumin, g/dL >3.5 2.8–3.5 <2.8
Alternatively, when both Q and the extraction ratio, Prothrombin time
ER, are known in the patient, Cl may also be Seconds over 1–3 4–6 >6
estimated: control
INR <1.8 1.8–2.3 >2.3
Cl =Q (ER) (24.46)
Encephalopathy None Grade Grade 3–4
1–2
Unlike changes in renal disease, in which serum
creatinine concentration may be used to monitor Data from Trey et al (1966).
Dose Adjustment in Renal and Hepatic Disease 807
TABLE 2412 Severity Classification Schemes TABLE 2413 Drugs with Significantly
for Liver Disease Decreased Metabolism in Chronic Liver Disease
Child–Turcotte Classification Antipyrine Caffeine
Grade A Grade B Grade C Cefoperazone Chlordiazepoxide
Bilirubin <2.0 2.0–3.0 >3.0 Chloramphenicol Diazepam
(mg/dL) Erythromycin Hexobarbital
Albumin >3.5 3.0–3.5 <3.0 Metronidazole Lidocaine
(g/dL)
Meperidine Metoprolol
Ascites None Easily Poorly
controlled controlled Pentazocine Propranolol
Neurological None Minimal Advanced Tocainide Theophylline
disorder
Verapamil Promazine
Nutrition Excellent Good Poor
Data from Howden et al (1989), Williams (1983), and Hu et al (1995).
Data from Brouwer et al (1992).
distribution may occur outside the liver. Extrahepatic
was later replaced by PT prolongation. The model metabolism and other hemodynamic changes may
for end-stage liver disease, or MELD, is a scoring also occur and can be accounted for more com-
system for assessing the severity of chronic liver pletely by monitoring total body clearance of the
disease based on mortality after liver surgery drug using basic pharmacokinetics. For example,
(Cholongitas et al, 2005; Kamath and Kim, 2007). lack of local change in hepatic drug clearance should
Unfortunately, neither one of these approaches for not be prematurely interpreted as “no change” in
assessing hepatic disease and hepatic impairment overall drug clearance. Reduced albumin and AAG,
provides direct predictability or correlation with the for example, may change the volume of distribution
pharmacokinetics of a drug. of the drug and therefore, alter total body clearance
While chronic hepatic disease is more likely to on a global basis.
change the metabolism of a drug (Howden et al, 1989), Chronic liver disease has been shown to decrease
acute hepatitis due to hepatotoxin or viral inflammation the metabolism of many drugs as shown in Table 24-13.
is often associated with marginal or less severe changes However, the amount of decrease in metabolism is
in metabolic drug clearance (Farrel et al, 1978). The difficult to assess.
clinician should make an assessment based on accept-
able risk criteria on a case-by-case basis. EXAMPLE »» »
In general, basic pharmacokinetics treats the
body globally and more readily applies to dosing After IV bolus administration of 1 g of cefopera-
estimation. However, drug clearance based on indi- zone to normal and chronic hepatitis patients, uri-
vidual eliminating organs is more informative and nary excretion of cefoperazone was significantly
provides more insight into the pharmacokinetic increased in cirrhosis patients, from 23.95% ± 5.06%
changes in the disease process. A practical method for normal patients to 51.09% ± 11.50% in cirrhosis
for dosing hepatic-impaired patients is still in the patients (Hu et al, 1995). Explain (a) why there is a
early stages of development. While the hepatic change in the percent of unchanged cefoperazone
blood flow model (see Chapter 12) is useful for excreted in the urine of patients with cirrhosis,
predicting changes in hepatic clearance resulting and (b) suggest a quantitative test to monitor the
from alterations in hepatic blood flow, Qa and Qv, hepatic elimination of cefoperazone (Hint: Consult
extrahepatic changes can also influence pharmaco- Hu et al, 1994).
kinetics in hepatic-impaired patients. Global changes in
808 Chapter 24
Liver Function Tests and Hepatic urinary bilirubin. Unconjugated hyperbilirubi-
Metabolic Markers nemia results from either increased bilirubin
Drug markers used to measure residual hepatic func- production or defects in hepatic uptake or con-
tion may correlate well with hepatic clearance of one jugation. Conjugated hyperbilirubinemia results
drug but correlate poorly with another substrate from defects in hepatic excretion.
metabolized by a different enzyme within the same 4. Prothrombin time (PT; normal, 11.2–13.2 s):
cytochrome P-450 subfamily. Some useful marker With the exception of Factor VIII, all coagula-
compounds are listed below. tion factors are synthesized by the liver. There-
fore, hepatic disease can alter coagulation.
1. Aminotransferase (normal ALT: male, Decreases in PT (the rate of conversion of
10–55 U/L; female, 7–30 U/L; normal AST: prothrombin to thrombin) are suggestive of acute
male, 10–40 U/L; female, 9–25 U/L): Amino- or chronic liver failure or biliary obstruction.
transferases are enzymes found in many tissues Vitamin K is also important in coagulation, so
that include serum aspartate aminotransferase vitamin K deficiency can also decrease PT.
(AST, formerly SGOT) and alanine amino-
transferase (ALT, formerly SGPT). ALT is liver
specific, but AST is found in liver and many EXAMPLE »» »
other tissues, including cardiac and skeletal
muscles. Leakage of aminotransferases into the Paclitaxel, an anticancer agent for solid tumors and
plasma is used as an indicator for many types leukemia, has extensive tissue distribution, high
of hepatic disease and hepatitis. The AST/ALT plasma protein binding (approximately 90%–95%),
ratio is used in differential diagnosis. In acute and variable systemic clearance. Average pacli-
liver injury, AST/ALT is ≤1, whereas in alco- taxel clearance ranges from 87 to 503 mL/min/m2
(5.2–30.2 L/h/m2
holic hepatitis the AST/ALT > 2. ), with minimal renal excretion
2. Alkaline phosphatase (normal: male, (10%) of the parent drug (Sonnichsen and Relling,
45–115 U/L; female, 30–100 U/L): Like 1994). Paclitaxel is extensively metabolized by the
aminotransferase, alkaline phosphatase (AP) is liver to three primary metabolites. Cytochrome
normally present in many tissues, and it is also P-450 enzymes of the CYP3A and CYP2C subfami-
present on the canalicular domain of the hepa- lies appear to be involved in hepatic metabolism of
tocyte plasma membrane. Plasma AP may be paclitaxel. What are the precautions in administer-
elevated in hepatic disease because of increased ing paclitaxel to patients with liver disease?
AP production and released into the serum.
In cholestasis, or bile flow obstruction, AP Solution
release is facilitated by bile acid solubilization Although paclitaxel has first-order pharmacokinet-
of the membranes. Marked AP elevations may ics at normal doses, its elimination may be satu-
indicate hepatic tumors or biliary obstruction rable in some patients with genetically reduced
in the liver, or disease in other tissues such as intrinsic clearance due to CYP3A or CYP2C. The
bone, placenta, or intestine. clinical importance of saturable elimination will
3. Bilirubin (normal total = 0–1.0 mg/dL: direct = be greatest when large dosages are infused over a
0–0.4 mg/dL): Bilirubin consists of both a shorter period of time. In these situations, achiev-
water-soluble, conjugated, “direct” fraction able plasma concentrations are likely to cause
and a lipid-soluble, unconjugated, “indirect” saturation of binding. Thus, small changes in dos-
fraction. The unconjugated form is bound to age or infusion duration may result in dispropor-
albumin and is, therefore, not filtered by the tionately large alterations in paclitaxel systemic
kidney. Since impaired biliary excretion results exposure, potentially influencing patient response
in increases in conjugated (filtered) bilirubin, and toxicity.
hepatobiliary disease can result in increases in
Dose Adjustment in Renal and Hepatic Disease 809
Hepatic Impairment and Dose Adjustment In contrast, Muirhead et al (2002) studied the
Hepatic impairment may not sufficiently alter the effects of age and renal and hepatic impairments on
pharmacokinetics of some drugs to require dosage the pharmacokinetics, tolerability, and safety of
adjustment. Drugs that have the following properties sildenafil (Viagra), a drug used to treat erectile dys-
are less likely to need dosage adjustment in patients function. Muirhead et al (2002) observed significant
with hepatic impairment (FDA Guidance for differences in Cmax and AUC between the young and
Industry, 2003): the elderly subjects for both the parent drug and the
metabolite. In addition, the hepatic impairment study
• The drug is excreted entirely via renal routes of demonstrated that pharmacokinetics of sildenafil
elimination with no involvement of the liver. was altered in subjects with chronic stable cirrhosis,
• The drug is metabolized in the liver to a small extent as shown by a 46% reduction in CL/F and a 47%
(<20%), and the therapeutic range of the drug is increase in Cmax compared with subjects with normal
wide, so that modest impairment of hepatic clear- hepatic function. Sildenafil pharmacokinetics was
ance will not lead to toxicity of the drug directly or affected by age and by renal and hepatic impair-
by increasing its interaction with other drugs. ments, suggesting that a lower starting dose of 25 mg
• The drug is gaseous or volatile, and the drug and should be considered for patients with severely com-
its active metabolites are primarily eliminated via promised renal or hepatic function.
the lungs.
For each drug case, the physician needs to assess the
degree of hepatic impairment and consider the known
Frequently Asked Questions
pharmacokinetics and pharmacodynamics of the drug.
For example, Mallikaarjun et al (2008) studied the »»How do changes in drug–protein binding affect dose
adjustment in patients with renal and/or hepatic
effects of hepatic or renal impairment on the pharma-
disease?
cokinetics of aripiprazole (Abilify), an atypical
antipsychotic used to treat schizophrenia. These »»Which pharmacokinetic properties of a drug are
investigators concluded that there were no meaningful more likely to be affected by renal disease or liver
differences in aripiprazole pharmacokinetics between hepatotoxicity?
groups of subjects with normal hepatic or renal func- »»Can you quantitatively predict the change in the
tion and those with either hepatic or renal impairment. pharmacokinetics of a drug that normally has high
Thus, the adjustment of the aripiprazole does not hepatic clearance in a patient with hepatic impair-
appear to be required in populations with hepatic or ment? Explain.
renal impairment.
CHAPTER SUMMARY
The kidney and liver are important organs involved filtration rate. Creatinine clearance values must be
in regulating body fluids, electrolyte balance, considered carefully in special populations such
removal of metabolic waste, and drug excretion from as elderly, obese, and emaciated patients. The
the body. Impairment of kidney or liver function Crockcroft–Gault method is frequently used to esti-
affects the pharmacokinetics of drugs as well as mate creatinine clearance from serum creatinine
safety and efficacy. Renal function may be assessed concentration. Dose adjustment in renal disease is
by several methods. Creatinine clearance calculated based on the fraction of drug that is really excreted
by using the serum concentration of endogenous and generally assumes that nonrenal drug elimina-
creatinine is used most often to measure glomerular tion remains constant. Different approaches for dose
810 Chapter 24
adjustment in renal disease give somewhat different stratification of the liver enzyme systems. Presently,
values. Patients with ESRD and other patients with- no single test accurately assesses the total liver
out kidney function require supportive treatment function. Various approaches such as the Child–
such as dialysis to remove the accumulated drug and Pugh (or Child–Turcotte–Pugh) score have been
its metabolites. The objective of these dialysis meth- used diagnostically to assess hepatic impairment.
ods is to rapidly remove the undesirable drugs and Hepatic impairment may not sufficiently alter the
metabolites from the body without disturbing the pharmacokinetics of some drugs to require dosage
fluid and electrolyte balance in the patient. Dosage adjustment. Physicians and/or pharmacists must
adjustment may be needed to replace drug loss dur- understand the pharmacokinetic and pharmaco-
ing extracorporeal drug and metabolite removal. The dynamic properties of each drug in patients with
major difficulty in estimating hepatic clearance in hepatic and/or renal impairment for proper dose
patients with hepatic disease is the complexity and adjustment.
LEARNING QUESTIONS
1. The normal dosing schedule for a patient on 5. A patient on intramuscular lincomycin 600 mg
tetracycline is 250 mg PO (by mouth) every every 12 hours was found to have a creatinine
6 hours. Suggest a dosage regimen for this clearance of 5 mL/min. Should the dose be
patient when laboratory analysis shows that his adjusted? If so, (a) adjust the dose by keeping the
renal function has deteriorated from a Clcr of dosing interval constant; (b) adjust the dosing
90 mL/min to a Clcr of 20 mL/min. interval and give the same dose; and (c) adjust
2. A patient receiving antibiotic treatment is on both dosing interval and dose. What are the dif-
dialysis. The flow rate of serum into the kidney ferences in the adjustment methods?
machine is 50 mL/min. Assays show that the 6. Calculate the creatinine clearance for a woman
concentration of drug entering the machine is (38 years old, 62 kg) whose serum creatinine is
5 mg/mL and the concentration of drug in the 1.8 mg/dL using the method of Cockcroft–Gault.
serum leaving the machine is 2.4 mg/mL. The 7. Would you adjust the dose of cephamandole,
drug clearance for this patient is 10 mL/min. an antibiotic that is 98% excreted unchanged
To what extent should the dose be increased if in the urine, for the patient in Question 6? If
the average concentration of the antibiotic is to so, why?
be maintained? 8. What assumptions are usually made when
3. Glomerular filtration rate may be measured by adjusting a dosage regimen according to the
either insulin clearance or creatinine clearance. creatinine clearance in a patient with renal
a. Why is creatinine or insulin clearance used failure?
to measure GFR? 9. The usual dose of gentamicin in patients with
b. Which clearance method, insulin or cre- normal renal function is 1 mg/kg every 8 hours
atinine, gives a more accurate estimate of by multiple IV bolus injections. Using the
GFR? Why? nomogram method (see Fig. 24-4), what dose
4. A uremic patient has a urine output of 1.8 L/24 h of gentamicin would you recommend for a
and an average creatinine concentration of 55-year-old male patient weighing 72 kg with a
2.2 mg/dL. What is the creatinine clearance? creatinine clearance of 20 mL/min?
How would you adjust the dose of a drug nor- 10. A single intravenous bolus injection (1 g) of an
mally given at 20 mg/kg every 6 hours in this antibiotic was given to a male anephric patient
patient (assume the urine creatinine concentra- (age 68 years, 75 kg). During the next 48
tion is 0.1 mg/mL and creatinine clearance is hours, the elimination half-life of the antibiotic
100 mL/min)? was 16 hours. The patient was then placed on
Dose Adjustment in Renal and Hepatic Disease 811
hemodialysis for 8 hours and the elimination a. What is the basis of these methods for the
half-life was reduced to 4 hours. calculation of drug dosage regimens in
a. How much drug was eliminated by the end uremic patients?
of the dialysis period? b. What is the validity of the assumptions upon
b. Assuming the apparent volume of distribu- which these calculations are made?
tion of this antibiotic is 0.5 L/kg, what was 12. After assessment of the uremic condition of
the plasma drug concentration just before the patient, the drug dosage regimen may be
and after dialysis? adjusted by one of two methods: (a) by keep-
11. There are several pharmacokinetic methods ing the dose constant and prolonging the dos-
for adjustment of a drug dosage regimen for age interval, t, or (b) by decreasing the dose
patients with uremic disease based on the and maintaining the dosage interval constant.
serum creatinine concentration in that patient. Discuss the advantages and disadvantages
From your knowledge of clinical pharmacoki- of adjusting the dosage regimen using either
netics, discuss the following questions: method.
ANSWERS
Frequently Asked Questions binding is reduced. Reduction in GFR is more def-
inite; it is invariably accompanied by a reduction
What are the main factors that influence drug dosing in drug clearance and by an increase in the elimi-
in renal disease? nation half-life of the drug.
• Renal disease can cause profound changes in the Name and contrast the two methods for adjusting
body that must be evaluated by assessing the patient’s drug dose in renal disease.
condition and medical history. Renal dysfunction
is often accompanied by reduced protein–drug • Two approaches to dose adjustment in renal dis-
binding and by reduced glomerular filtration rate ease are the clearance method and the elimination
in the kidney. Some changes in hepatic clearance rate constant method. The methods are based on
may also occur. While there is no accurate method estimating either the uremic ClR or the uremic kR
for predicting the resulting in vivo changes, a de- after the creatinine clearance is obtained in the
crease in albumin may increase fu, or the fraction uremic patient.
of free plasma drug concentration in the body.
What are the pharmacokinetic considerations in design-
The fu is estimated from fu = 1 – fb, where fb is
ing a dosing regimen? Why is dosing once a day for
the fraction of bound plasma drug. For the uremic
aminoglycosides recommended by many clinicians?
patient, the fraction of drug bound fb′ is affected by
a change in plasma protein: fb′/fb = p′/4.4, where • Aminoglycosides are given as a larger dose spaced
p is the normal plasma protein concentration farther apart (once daily). Keeping the same total
(4.4 g/dL assuming albumin is the protein involved) daily dose of the aminoglycoside improves the
and p′ is the uremic plasma protein concentration; response (efficacy) and possibly lessens side effects
fb′ is the fraction of drug bound in the uremic in many patients. Model simulation shows reduced
patient. Since fu′ or the fraction of unbound drug is exposure (AUC) to the effect compartment (toxicity),
increased in the uremic patient, the free drug con- while the activity is not altered. The higher drug dose
centration may be increased and, sometimes, lead produces a higher peak drug concentration. In the
to more frequent side effects. On the other hand, an case of gentamicin, the marketed drug is chemically
increase in plasma free drug in the uremic patient composed of three related, but distinctly different,
is offset somewhat by a corresponding increase in chemical components, which may distribute dif-
the volume of distribution as plasma protein–drug ferently in the body.
812 Chapter 24
How do changes in drug–protein binding affect dose Using Equation 24.31,
adjustment in patients with renal and/or hepatic
Q(C C )
disease? Cl a − v
D =
C
a
• Hepatic disease may reduce albumin and a1-acid
glycoprotein (AAG) concentrations resulting in 50(5− 2.4)
ClD = = 26 mL/min
decreased drug protein binding. Blood flow to the 5
liver may also be affected. Generally, for a drug with Total drug clearance = 10 + 26 = 36 mL/min.
linear binding, fu may be increased as discussed in Since the drug clearance is increased from 10
FAQ #1. Consult Chapter 10 also for a discussion of to 36 mL/min, the dose should be increased if
restrictive clearance of drugs. Examples of binding dialysis is going to continue. Since dose is
to AAG are the protease inhibitors for AIDS. directly proportional to clearance,
Drug clearance is often decreased 20%–50% in Du 36
many patients with congestive heart failure (CHF). = = 3.6
DN 10
Explain how it may affect drug disposition.
The new dose should be 3.6 times the dose
• Congestive heart failure (CHF) can reduce renal given before dialysis if the same level of
or hepatic blood flow and decrease hepatic and antibiotics is to be maintained.
renal drug clearance. In CHF, less blood flow is 4. The creatinine clearance of a patient is deter-
available in the splanchnic circulation to the small mined experimentally by using Equation 24.11,
intestine and may result in less systemic drug bio-
availability after oral drug administration. Severe CuV ×100
Clcr =
disturbances to blood flow will affect the pharma- Ccr ×1440
cokinetics of many drugs. Myocardiac infarction
(0.1)(1800)(100)
(MI) is a clinical example that often causes drug Clcr = = 5.68 mL/min
(2.2)(1440)
clearance to be greatly reduced, especially for
drugs with large hepatic extraction.
Assuming that the normal Clcr in this patient is
Learning Questions 100 mL/min, the uremic dose should be 5.7%
of the normal dose, since kidney function is
1. The normal dose of tetracycline is 250 mg PO drastically reduced:
every 6 hours. The dose of tetracycline for the
uremic patient is determined by the ku/kN ratio, (0.057) (20 mg/kg) = 1.14 mg/kg given
which is determined by the kidney function, as every 6 hours
in Fig. 24-4. From line H in the figure, at Clcr
of 20 mL, ku/kN = 40%. In order to maintain 5. From Fig. 24-4, line F, at a Clcr of 5 mL/min,
the average concentration of tetracycline at the
same level as in normal patients, the dose of ku
= 45%
k
tetracycline must be reduced. N
Du ku
= = 40% a. The dose given should be as follows:
DN kN
Du = (250) (0.40) = 100 mg (0.45) (600 mg) = 270 mg every 12 hours
2. The drug in this patient is eliminated by the b. Alternatively, the dose of 600 mg should be
kidneys and the dialysis machine. given every
Therefore,
100
12× = 26.7 h
Total drug clearance = ClT + ClD 45
Dose Adjustment in Renal and Hepatic Disease 813
c. Since it may be desirable to give the drug 9. Gentamycin is listed in group K (Table 24-5).
once every 24 hours, both dose and dosing From the nomogram in Fig. 24-4,
interval may be adjusted so that the patient
will still maintain an average therapeutic Clcr = 20 mL/min
blood level of the drug, which can then be k
u
given at a convenient time. Using the equa- = 25%
k
tion for C∞ n
av,
Uremic dose = 25% of normal dose = (0.25)
D
C∞ 0 (1 mg/kg) = 0.25 mg/kg
av =
kVDτ For a 72-kg patient:
D0 = 600 mg Uremic dose = (0.25)(75) = 18.8 mg
τ = 26.7 h
The patient should receive 18.8 mg every
600
C∞ 8 hours by multiple IV bolus injections.
av =
kVD × 26.7
10. a. During the first 48 hours postdose, t1/2 = 16 h.
For IV bolus injection, assuming first-order
To maintain C∞
av the same, calculate a new dose, elimination:
DN, with a new dosing interval, tN, of 24 hours.
D D = −k
B D0e
t
C∞ N
av =
kVD (24) DB = 1000e−(0.693/16) (48)
Thus,
D
600 D B = 125 mg remaining in body just before
N
= dialysis
26.7 (24) During dialysis, t1/2 = 4 h, and
Therefore, DB = 125e–(0.693/4)(8) = 31.3 mg after dialysis
24 Drug eliminated during dialysis = 125 mg −
DN = × 600 = 539 mg 31.3 mg = 93.7 mg
26.7
b. V
The drug can also be given at 540 mg daily. D = (0.5 L/kg) (75kg) = 37.5 L
Drug concentration just before dialysis:
6. For females, use 85% of the Clcr value obtained
in males.
Cp = 125 mg/37.5 L = 3.33 mg/L
0.85[140 − age(year)] body weight (kg)
Clcr =
72(Clcr ) Drug concentration just after dialysis:
0.85[140 − 38]62
Clcr = = 41.5 mL/min
(72)(1.8) Cp = 31.3 mg/37.5 L = 0.83 mg/L
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Empirical Models,
25 Mechanistic Models,
Statistical Moments, and
Noncompartmental Analysis
Corinne Seng Yue and Murray P. Ducharme
Chapter Objectives The study of pharmacokinetics describes the absorption, distribu-
tion, and elimination of a drug and its metabolites in quantitative
»» Describe the differences
terms (see Chapter 1). Ideally, a pharmacokinetic model uses the
between empirical and
observed time course for drug concentrations in the body and,
mechanistic models.
from these data, obtains various pharmacokinetic parameters to
»» Understand the differences predict drug dosing outcomes, pharmacodynamics, and toxicity.
between different types of In developing a model, certain underlying assumptions are
compartmental analyses. made by the pharmacokineticist as to the type of pharmacokinetic
»» Describe the physiologic model, the order of the rate processes, tissue blood flow, the
pharmacokinetic model with method for the estimation of the plasma or tissue volume, and
equations and underlying other factors. Even with a more general approach such as the non-
assumptions. compartmental method, first-order drug elimination is often
assumed in the calculation of AUC∞
0 . In selecting a model for data
»» List the differences in data analysis, the pharmacokineticist may choose more than one
analysis between the physiologic method of modeling, depending on many factors, including experi-
pharmacokinetic model, the mental conditions, study design, and completeness of data. The
classical compartmental model, goodness-of-fit to the model and the desired pharmacokinetic
and the noncompartmental parameters are other considerations. Each estimated pharmacoki-
approaches. netic parameter has an inherent variability because of the variabil-
»» Describe interspecies ity of the biological system and of the observed data.
scaling and its application In spite of challenges in the construction of these pharmaco-
in pharmacokinetics and kinetic models, such models have been extremely useful in
toxicokinetics. describing the time course of drug action, improving drug therapy
by enhancing drug efficacy, and minimizing adverse reactions
»» Describe the statistical moment
through more accurate dosing regimens. Pharmacokinetic models
theory and explain how it
are used routinely within the development process of new mole-
provides a unique way to
cules or drug delivery systems.
study time-related changes in
Models can be broadly categorized as empirical or mecha-
macroscopic events.
nistic. Empirical models are focused on describing the data with
»» Define mean residence time the specification of very few assumptions about the data being
(MRT) and how it can be analyzed. An example of an empirical model is one that is used
calculated. for allometric scaling, a type of prediction of PK parameters across
diverse species. On the other hand, mechanistic models specify
assumptions and attempt to incorporate known factors about the
systems surrounding the data into the model, while describing
817
818 Chapter 25
»» Define the mean transit time the available data (Bonate, 2011). Both physiological modeling
(MTT) and how it can be used to and compartmental modeling fall into the latter category.
calculate the mean dissolution Pharmacokinetic parameters can also be calculated without the
time (MDT), or in vivo mean specification of compartments in an almost model-independent
dissolution time, for a solid drug manner, using noncompartmental analysis derived from statistical
product given orally. moment theory. This chapter will touch upon the aforementioned
types of pharmacokinetic models, as well as noncompartmental
»» Using MRT, derive equations to
analysis.
estimate other pharmacokinetic
parameters such as mean
absorption time and total EMPIRICAL MODELS
volume of distribution.
Allometric Scaling
Various approaches have been used to compare and predict the
pharmacokinetics of a drug among different species. Interspecies
scaling is a method used in toxicokinetics and for the extrapolation
of therapeutic drug doses in humans from nonclinical animal drug
studies. Toxicokinetics is the application of pharmacokinetics to
toxicology for interpolation and extrapolation based on anatomic,
physiologic, and biochemical similarities (Mordenti and Chappell,
1989; Bonate and Howard, 2000; Mahmood, 2000, 2007; Hu and
Hayton, 2001; Evans et al, 2006).
The basic assumption in interspecies scaling is that physio-
logic variables, such as clearance, heart rate, organ weight, and
biochemical processes, are related to the weight or body surface
area of the animal species (including humans). It is commonly
assumed that all mammals use the same energy source (oxygen)
and energy transport systems across animal species (Hu and
Hayton, 2001). Interspecies scaling uses a physiologic variable, y,
that is graphed against the body weight of the species on log–log
axes to transform the data into a linear relationship (Fig. 25-1).
The general allometric equation obtained by this method is
y = bWa (25.1)
where y is the pharmacokinetic or physiologic property of interest,
b is an allometric coefficient, W is the weight or surface area of the
animal species, and a is the allometric exponent. Allometry is the
study of size.
Both a and b vary with the drug. Examples of various pharma-
cokinetic or physiologic properties that demonstrate allometric
relationships are listed in Table 25-1.
In the example shown in Fig. 25-1, the apparent methotrexate
volume of distribution is related to body weight B of five animal
species by the equation Vb = 0.859B0.918.
The allometric method gives an empirical relationship that
allows for approximate interspecies scaling based on the size of
Empirical Models, Mechanistic Models, Statistical Moments, and Noncompartmental Analysis 819
100 relationship between biperiden intrinsic clearance
r = 0.994 with body weight and MLP:
p < .01 Man
Clint × MLP = 1.36 107 0.892
× × B (25.2)
10
Monkey
Dog where MLP is the maximum life-span potential of the
species, B is the body weight of the species, and Clint
1 is the hepatic intrinsic clearance of the free drug.
Although further model improvements are needed
Rat
Vb = 0.859B0.918 before accurate prediction of pharmacokinetic param-
0.1 eters can be made from animal data, some interesting
Mouse results were obtained by Sawada et al (1985) on nine
acid and six basic drugs. When interspecies differ-
0.01
0.01 0.1 1 10 100 ences in protein–drug binding are properly consid-
Body weight, B (kg) ered, the volume of distribution of many drugs may
be predicted with 50% deviation from experimental
FIGURE 251 Interspecies correlation between
methotrexate volume of distribution Vb and body weight. values (Table 25-2).
Linear regression analysis was performed on logarithmically The application of MLP to pharmacokinetics
transformed data. (From Boxenbaum, 1982, with permission.) has been described by Boxenbaum (1982). Initially,
hepatic intrinsic clearance was considered to be
related to volume or body weight. Indeed, a plot of
the log drug clearance versus body weight for vari-
ous animal species resulted in an approximately lin-
the species. Not considered in the method are certain
ear correlation (ie, a straight line). However, after
specific interspecies differences such as gender,
correcting intrinsic clearance by MLP, an improved
nutrition, pathophysiology, route of drug administra-
log–linear relationship was achieved between free
tion, and polymorphisms. Some of these more spe-
drug Cl
cific cases, such as the pathophysiologic condition of int and body weight for many drugs. A pos-
sible explanation for this relationship is that the
the animal or human, may preclude pharmacokinetic
biochemical processes, including Clint, in each ani-
or allometric predictions.
mal species are related to the animal’s normal life
Interspecies scaling has been refined by consider-
expectancy (estimated by MLP) through the evolu-
ing the aging rate and life span of the species. In terms
tionary process. Animals with a shorter MLP have
of physiologic time, each species has a characteristic
higher basal metabolic rates and tend to have higher
life span, its maximum life-span potential (MLP),
intrinsic hepatic clearance and thus metabolize drugs
which is controlled genetically (Boxenbaum, 1982).
faster. Boxenbaum (1982, 1983) postulated a con-
Because many energy-consuming biochemical pro-
stant “life stuff” in each species, such that the faster
cesses, including drug metabolism, vary inversely
the life stuff is consumed, the more quickly the life
with the aging rate or life span of the animal, this
stuff is used up. In the fourth-dimension scale (after
allometric approach has been used for drugs that are
correcting for MLP), all species share the same
eliminated mainly by hepatic intrinsic clearance.
intrinsic clearance for the free drug.
Through the study of various species in han-
dling several drugs that are metabolized predomi- (MLP)(Cl
nantly by the liver, some empirical relationships int )
= constant (25.3)
B
regarding drug clearance of several drugs have been
related mathematically in a single equation. For Cl ×
int = aB
(25.4)
example, the hepatic intrinsic clearance of biperiden
in rat, rabbit, and dog was extrapolated to humans Extensive work with caffeine in five species (mouse,
(Nakashima et al, 1987). Equation 25.2 describes the rat, rabbit, monkey, and humans) by Bonati et al (1985)
Methotrexate Vb (L)
820 Chapter 25
TABLE 251 Examples of Allometric Relationship for Interspecies Parameters
Physiologic or Pharmacokinetic Property Allometric Exponenta Allometric Coefficientb
Basal O2 consumption (mL/h) 0.734 3.8
Endogenous N output (g/h) 0.72 0.000042
O2 consumption by liver slices (mL/h) 0.77 3.3
Clearance
Creatinine (mL/h) 0.69 8.72
Inulin (mL/h) 0.77 5.36
PAH (mL/h) 0.80 22.6
Antipyrine (mL/h) 0.89 8.16
Methotrexate (mL/h) 0.69 10.9
Phenytoin (mL/h) 0.92 47.1
Aztreonam (mL/h) 0.66 4.45
Ara-C and Ara-U (mL/h) 0.79 3.93
Volume of distribution (VD)
Methotrexate (L/kg) 0.92 0.859
Cyclophosphamide (L/kg) 0.99 0.883
Antipyrine (L/kg) 0.96 0.756
Aztreonam (L/kg) 0.91 0.234
Kidney weight (g) 0.85 0.0212
Liver weight (g) 0.87 0.082
Heart weight (g) 0.98 0.0066
Stomach and intestines weight (g) 0.94 0.112
Blood weight (g) 0.99 0.055
Tidal volume (mL) 1.01 0.0062
Elimination half-life
Methotrexate (min) 0.23 54.6
Cyclophosphamide (min) 0.24 36.6
Digoxin (min) 0.23 98.3
Hexobarbital (min) 0.35 80.0
Antipyrine (min) 0.07 74.5
Turnover times
Serum albumin (1/day) 0.30 5.68
Total body water (1/day) 0.16 6.01
RBC (1/day) 0.10 68.4
Cardiac circulation (min) 0.21 0.44
From Ritschel and Banerjee (1986).
TABLE 252 Relationship between Predicted and Observed Values of Various Pharmacokinetic Parameters in Humans
for 15 Drugs
V (L/kg) Clm (mL/min per kg) t1/2, Z (min)
Drug Observed Predicted Percenta Observed Predicted Percenta Observed Predicted Percenta
Phenytoin 0.640 0.573 10.5 0.574 0.483 15.9 792 822 3.79
Quinidine 3.20 3.69 22.2 2.91 3.25 11.7 470 785 67.0
Hexobarbital 1.27 0.735 42.1 3.57 4.25 19.0 261 120 54.0
Pentobarbital 0.999 1.57 57.2 0.524 0.964 84.0 1340 1126 16.0
Phenylbutazone 0.122b 0.0839c 31.2 0.0205 0.0162 21.0 4110 3590 12.7
Warfarin 0.108 0.109 0.926 0.0367 0.0165 55.0 2040 4560 124
Tolbutamide 0.112 0.116 3.57 0.180 0.0589 67.3 434 1360 214
Chlorpromazine 11.2b 9.05c 19.2 4.29 4.63 7.93 1810 1350 25.2
Propranolol 3.62 3.77 4.14 11.2 15.56 38.9 167 135 19.2
Pentazocine 5.56 7.19 29.3 18.3 11.6 36.6 203 408 101
Valproate 0.151 0.482 219 0.110 0.159 44.5 954 2110 121
Diazepam 0.950 1.44 51.6 0.350 2.13 509 1970 469 76.2
Antipyrine 0.869 0.878 1.04 0.662 0.664 3.02 654 917 40.2
Phenobarbital 0.649 0.817 25.9 0.0530 0.0825 55.7 6600 5870 11.0
Amobarbital 1.04 1.21 16.3 0.556 1.01 81.7 1360 827 39.2
aAbsolute percent of error.
bThe value of VSS.
cPredicted from the value of VSS in the rat.
From Sawada et al (1985).
821
822 Chapter 25
verified this approach. Caffeine is a drug that is metab- xenobiotic clearance (Cl). Published literature has
olized predominantly by the liver. For caffeine, focused on whether the basal metabolic rate scale is
a 2/3 or 3/4 power of the body mass (BW). When the
Q = 0.0554 × B0.894 uncertainty in the determination of a b value is rela-
tively large, a fixed-exponent approach might be
L = 0.0370 × B0.849 feasible according to Hu and Hayton. In this regard,
0.75 might be used for substances that are eliminated
where B is body weight, L is liver weight, and Q is mainly by metabolism or by metabolism and excre-
the liver blood flow. tion combined, whereas 0.67 might apply for drugs
Hepatic clearance for the unbound drug did not that are eliminated mainly by renal excretion. The
show a direct correlation among the five species. researchers pointed out that genetic (intersubject)
After intrinsic clearance was corrected for MLP difference may be a limitation for using a single
(calculation based on brain weight), an excellent universal constant.
relationship was obtained among the five species Brightman et al (2006) demonstrated the applica-
(Fig. 25-2). tion of a PK-PD model, based on human parameters
More recently, the subject of interspecies scal- to estimate plasma pharmacokinetics of xenobiotics in
ing was investigated using Cl values for 91 sub- humans. The model was parameterized through an
stances for several species by Hu and Hayton (2001). optimization process, using a training set of in vivo
These investigators used Y = a (BW)b in their analy- data taken from the literature. On average, the vertical
sis, similar to Equation 25.1 above but with different divergence of the predicted plasma concentrations
symbols: Y = biological variable dependent on the from the observed data was 0.47 log units, on a semi-
body weight of the species, a = allometric coefficient, log concentration–time plot. They also evaluated the
b = allometric exponent, and BW = body weight of method against other predictive methods that involve
the species. One issue discussed by Hu and Hayton scaling from in vivo animal data. In terms of predict-
is the uncertainty in the allometric exponent (b) of ing human clearance for the test set, the model was
found to match or exceed the performance of three
published interspecies scaling methods, which tend to
give overprediction. The article concludes that the
Clint = (0.38 x 105) x B1.196 (L/MLP) generic physiologically based pharmacokinetic model
100 Man
is a means of integrating readily determined in vitro
and/or in silico data, and useful for predicting human
10
Monkey xenobiotic kinetics in drug discovery.
Rabbit
1
Rat
0.1 MECHANISTIC MODELS
Compartmental Models
0.01 Mouse
The essence of compartmental analysis is to create a
0.001 mathematical and statistical model defined by inte-
0.01 0.1 1 10 100 grated, matrix, and/or partial differential equations
Body weight, B (kg) (equations that have derivatives with respect to more
FIGURE 252 Caffeine (free drug) Clint per maximum life- than one variable) that describe the PK or PD behav-
span potential (MLP) in mammalian species as a function of iour of a drug. The model is then “fitted” to the data
body weight. MLP values were calculated for monkeys, rabbits, using least squares, Bayesian, and/or maximum
rats, and mice employing the following numeric values: MLP =
10.389 × (brain weight)0.636 × (body weight)0.225. (Data from likelihood techniques so that mean parameter esti-
Boxenbaum, 1982; Armstrong E: Relative brain size and mates along with their variability are obtained in an
metabolism in mammals. Science 220(4603):1302–1304, 1983.) individual or population (most often nowadays)
Clint (L/MLP) x 10
–5
Empirical Models, Mechanistic Models, Statistical Moments, and Noncompartmental Analysis 823
SFGC Infusion
RES
CL1 CL3
Vss Vmax Bone marrow
Km CL4 &
Red blood cells
CL CL
2 3
TBI
Iron lost through
blood sampling
Drug-bound iron Iron not bound to drug
FIGURE 253 Final compartmental pharmacokinetic model for sodium ferric gluconate complex. Cl1: clearance of sodium fer-
ric gluconate complex iron (SFGC-I) to the reticuloendothelial system (RES) compartment; Cl2: clearance of SFGC-I directly to trans-
ferrin; Vss: the apparent steady-state volume of distribution of SFGC-I; Cl3: clearance of iron entering and exiting the marrow and red
blood cell compartment; Cl4: clearance of TBI to the RES; Km: iron concentration associated with half of the maximal rate of exchange
between the RES and TBI compartments; Vmax: maximal rate of exchange between the RES and TBI compartments;
along with a residual variability or error component. retaining individual information, in order to obtain
An illustration of a compartmental model developed estimates of population mean and variance as well as
to describe the PK of sodium ferric gluconate com- quantify sources of variability (Ette and Williams,
plex is presented in Fig. 25-3 (Seng Yue, 2013). 2004; Ludden, 1988). These types of compartmental
Although a compartmental model can never analyses will be described in this chapter.
explain the “true” mechanisms underlying PK and/or At the core of compartmental analyses is nonlin-
PD behaviour, important correlations between ear regression. In contrast with linear regression,
covariates and parameters may point the way to fur- where data are being fitted with a straight line defined
ther studies or provide deeper mechanistic under- by a slope and intercept, nonlinear regression depends
standing (Sheiner, 1984). Among other advantages on equations whose partial derivatives (with respect to
of the compartmental method are its use in special each of the parameters) involve other model parame-
populations (such as pediatric or hepatic impairment ters (Gabrielsson and Weiner, 2006). The equations
patients) and its potential partitioning of variability used to describe the model depicted in Fig. 25-3 are
into interindividual, intraindividual, interoccasion, presented in Table 25-3.
and residual sources (Ette and Williams, 2004). Another important difference between the two
Various types of compartmental analyses exist, types of regressions is that linear regressions have
ranging from individual analysis to population PK analytical solutions, such that the functions can be
modeling including the naïve pooled data approach, manipulated to obtain a specific equation for the solu-
the standard two-stage approach, and nonlinear mixed- tion, while only numerical solutions exist for nonlinear
effect modeling that includes among others the itera- regressions. For nonlinear equations, approximate
tive two-stage, the first-order conditional estimation solutions to the equations can only be obtained through
(FOCE) and the MLEM (maximum likelihood expec- iterative processes that are described in further detail
tation maximization) approaches (Sheiner, 1984; below. Various software programs are available to per-
Rodman et al, 2006; Steimer et al, 1984). In these last form such analyses, and many of them are described in
approaches, all data are modeled simultaneously while more details in Appendix A.
824 Chapter 25
TABLE 253 Differential Equations Describing Compartmental Pharmacokinetic Model for Sodium
Ferric Gluconate Complex
Compartment Equation
Serum dX(1) Cl +Cl
= R(1) 1 2
− ⋅X (1)
dt V
ss
Reticuloendothelial system dX(2) Cl
= 1 Cl Cl V
⋅ x
X (1) 3
+ ⋅X (4) 4
+ ⋅X (3) ma
− ⋅X (2)
dt V V RBC V TBI Km ⋅V RBC + X (2)
ss − − −
Transferrin bound iron dX(3) Cl
= 2 V C
⋅ (1) + max l4 Cl
X ⋅ (2) − ⋅ (3) 3
X X − ⋅X (3)
dt V Km ⋅V RBC + X (2) V TBI V TBI
ss − − −
Red blood cells (marrow) dX(4) Cl
= 3 Cl
⋅X (3) 3
− ⋅X (4) − K0 ⋅R (2)
dt V TBI V RBC
− −
Cl1: Clearance of SFGC-I to the reticuloendothelial system (RES) compartment; Cl2: Clearance of SFGC-I directly to transferrin; Vss: the apparent
steady-state volume of distribution of SFGC-I; V_TBI: volume of distribution associated with TBI; Cl3: clearance of iron entering and exiting the marrow
and red blood cell compartment; V_RBC: marrow and red blood cell compartment; Cl4: clearance of TBI to the RES; Km: Iron concentration associ-
ated with half of the maximal rate of exchange between the RES and TBI compartments; Vmax: Maximal rate of exchange between the RES and TBI
compartments.
Individual Analysis values. In other words, the goal is to minimize the
As its name implies, individual analysis involves differences between the predicted and observed values
the development of a model using data from one (represented by ei in Equation 25.5), and generally the
source (such as one human or one animal). Because least-squares and maximum likelihood approaches are
of the error that is always inherent in data, whether it used to quantify these differences (Bonate, 2011).
be related to the collection procedures themselves or Various least-squares metrics (often termed
to analytical assays, a model can never perfectly predict “residual sum of squares”) can be used to quantify
the observed data. The relationship between observed these differences, and they are outlined in Table 25-4
and predicted concentration values must therefore (Gabrielsson and Weiner, 2006; Bonate, 2011).
account for this error, as defined in Equation 25.5. In OLS is inherently biased because it tends to
this equation, X favor model estimates that provide better predictions
i represents a vector of known values
(such as dose and sampling times), Ci represents the for larger observations compared to smaller ones.
vector of observed concentrations, ei represents the The WLS and ML/ELS approaches are an improve-
measurement errors, fj represents the vector of model ment over the OLS method since they account for
parameters (in other words the pharmacokinetic the magnitude of observations (and their relative
parameters), and ƒi is the function that relates Ci to f variability) by incorporating a weighting factor into
j
and Xi. The subscript i represents the total number of their formulas. The ML/ELS approaches differ from
observations or values. the weighted least-squares approach, because they
deal with the probability of observing the actual data
C given the model and its parameter estimates. In these
i = fi (φj ,Xi ) + ε i (25.5)
methods, the function that is being minimized is the
The aim of PK compartmental analysis is to log likelihood (LL), or the probability of observing
develop a model that is associated with predicted con- the actual concentration values given a set of model
centration values (or whatever observation is being parameter estimates. The function for LL is pre-
studied) that are as close as possible to the observed sented in Equation 25.6. It should be noted that the
Empirical Models, Mechanistic Models, Statistical Moments, and Noncompartmental Analysis 825
TABLE 254 Comparison of Least-Squares Methods
Method Objective Function Formula Characteristics
n
Ordinary least squares (OLS) OOLS = ∑(C −Cˆ )2 No weighting
i i
i=1
n
Weighted least squares (WLS) OWLS = ∑Wi (Ci −Cˆ 2
i ) Model and parameters must be defined and stated
i=1 empirically
n
Extended least squares (ELS) O = ∑[Wi (C
ˆ
i −C 2 ˆ
ELS i ) + ln(var(Ci ))] Models can be defined, but parameters of the models
or Maximum Likelihood (ML) i=1 are fitted within the procedure, eg, Wi = 1/ var(Ĉi )
Ĉi = predicted ith concentration value, Ci = observed ith concentration value, Wi = weighting factor, n = number of observations, var = variance
only difference between ELS and ML is in the always use the same structural model (eg, a two-
assumptions that are specified about the distribution compartment model) to fit all individuals’ data for a
of the variance parameters. In the ML approach, the specific drug under study, while individual analyses
distribution is assumed to be normal, while the ELS could theoretically use different models to fit data
approach makes no such assumption (Beal and from different subjects (eg, a one-compartment
Sheiner, 1989). model for some subjects and a two-compartment
model for others).
∧
n n ∑ (Ci −C 2
i )
n In a population analysis, observed concentra-
LL(C |θ) = − ln(2π ) − ln −
2 2 n 2 tions must be ascribed to specific subjects, as
defined in Equation 25.7, which is analogous to
(25.6) Equation 25.5. In this equation, Xij represents a vec-
tor of known values (represented by i) for the jth
Because it is easier to minimize a positive number
subject, Cij represents the vector of observed concen-
rather than a negative one, the LL is often multiplied
trations for the jth subject, e
by –2 to obtain a positive number called the “–2 log ij represents the measure-
ment errors for the jth subject, fj represents the
likelihood” (–2LL).
vector of model parameters for the jth subject, and ƒij
is the function that relates Cij to fj and Xij.
Population Analysis
Population analysis can be viewed as an extension of Cij = fij (φj ,Xij ) + ε ij (25.7)
individual analyses, since it attempts to develop a
model that predicts concentration data associated Each individual has a distinct set of PK model
with different individuals or animals. The general parameters (fj) that will provide the best predicted
concept is similar to that embraced by individual values for that individual’s observed data. However,
analysis, except that the model must also take into as previously mentioned, there is also a typical pro-
consideration interindividual variability. The result- file of “population predictions” that is associated
ing model is therefore able to predict concentration with population PK model parameters (q) that can be
values for each individual within the population, but regarded as mean values. The relationship between
it also provides an “overall” (mean or population) set the mean PK parameters and individual PK param-
of predictions. In other words, the model describes eters is described by Equation 25.8, where g is a
the behavior of the whole population as well as the known function that relates fj to q using the indi-
behavior of each individual within this population. vidual’s characteristics such as height or weight,
Another distinction is that a population analysis will denoted by zj. The last term, hj, represents random
826 Chapter 25
(unexplained or uncontrollable) variability that also by NONMEM®, proceed by first fitting the data in a
causes fj to deviate from q. reverse manner so they obtain population mean esti-
mates followed in a second step with individual data
φj = g(θ ,z j ) + η j (25.8) estimates (therefore called “post hocs”). The fixed
effects (variables that can be controlled, such as dose
There are various types of population compartmental or pharmacokinetic parameters) and random effects
analyses, but the most basic type is the “naïve-average (uncontrollable factors like interoccasion variability)
data” method, where the average concentration values are fitted simultaneously with respect to population
at given time points are computed from the entire data- mean and variability estimates as well as the residual
set, and then a model is developed using these average variability.
values. A similar method is the “naïve pooled data”
approach, where data from different individuals are
treated as though they were obtained from a single Algorithms for Numerical Problem Solving
individual, and then analyzed using the individual Since many combinations of parameter estimates
approach. must be evaluated in order to find the parameters that
The two-stage approach to population compart- minimize one of the objective functions described
mental analyses offers some improvement over the previously, many algorithms have been developed to
previous ones. In essence, data from each subject are systematically do so. Some algorithms apply linear-
first fitted individually (in other words using the ization techniques to approximate the model using
individual approach but using the same structural linear equations.
model to fit each individual’s data), and in the second For individual population analyses, Cauchy’s
step, population parameter estimates are obtained. method employs a first-order Taylor series expan-
Different types of two-stage approaches exist, such sion, Newton or Newton–Raphson-based methods
as the standard two-stage (STS) approach, the global utilize a second-order Taylor series expansion while
two-stage (GTS) approach, and finally a mixed- the Gauss–Newton method iteratively uses multiple
effect modeling approach known as the iterative two- linear regressions via first-order Taylor series expan-
stage approach (IT2S or ITS). In the STS approach, sion. The Levenberg–Marquardt method is another
the population parameter estimates (for mean and algorithm that includes a modification of the Gauss–
variance) are determined by calculating the mean Newton method. Finally, in contrast with the algo-
and variance of the individual PK parameters, while rithms previously described, the Nelder–Mead
the GTS approach actually estimates expectations simplex approach does not involve linearization
for the mean and variance through an iterative pro- procedures. This technique involves the examination
cess. The ITS method is a nonlinear mixed-effect of the response surface (in order to find the lowest
modeling technique that uses a more refined iterative point) using a series of moving and contracting or
approach utilizing a mixture of ML and MAP (maxi- expanding polyhedra (three-dimensional objects
mum a posteriori probability) techniques. Within composed of flat polygonal faces joined by vertices).
each population iteration, prior values are used to This approach has been implemented in the
estimate individual PK parameters in the first step, ADAPT-II to ADAPT 5 software series.
while individual values are then used in the second Some of the algorithms used in the context of
step to recalculate a newer, more probable set of population compartmental analyses include the first-
population parameters. Steps one and two are subse- order (FO) method, first-order conditional estimation
quently repeated until there is little to no difference (FOCE) approach, the stochastic approximation of
between the new and old prior distributions (eg, until EM (SAEM), and the maximum likelihood expecta-
the algorithm “converges”). tion maximization (MLEM) method, to name a few.
In contrast with the iterative two-stage approach, In both the FO and FOCE algorithms as implemented
other types of nonlinear mixed-effect modeling tech- within NONMEM, the minimum objective function
niques, such as that of the FOCE method implemented is sought out by linearization of the model through a
Empirical Models, Mechanistic Models, Statistical Moments, and Noncompartmental Analysis 827
series of first-order Taylor series expansions of the In some cases, it may be of interest to better under-
error model. The difference between the FO and stand the sources of variability by attributing vari-
FOCE algorithms is that in the former, interindivid- ability to specific patient characteristics. For example,
ual variability for PK parameters is estimated using compartmental models can evaluate whether demo-
estimates of the population mean and variance in a graphic factors (weight, age, laboratory values, drug
post hoc step, while in the latter, interindividual vari- polymorphism), drug-related factors (formulation,
ability is estimated simultaneously with the popula- manufacturer), or other potential variables (disease
tion mean and variance (Beal and Sheiner, 1998). In variables, use of concomitant medication) contribute
other words, within NONMEM the FO algorithm to interindividual variability in certain parameters.
uses a linearization technique that first assumes h = 0, Not only does compartmental modeling allow the
contrary to the FOCE algorithm which uses the pos- identification of important covariates, but it can also
terior mode of h (that relies on conditional esti- quantify their relative importance.
mates) (Bonate, 2011). A modification of the FOCE Compartmental models are often used to relate a
algorithm, known as the Laplacian FOCE method, drug’s PK to its response (PD), whether it be efficacy,
exists also within NONMEM whereby a second- toxicity, or both. PK-PD modeling can also be used to
order Taylor series is performed instead of the first- link preclinical (animal) data to data collected from
order expansion (Beal and Sheiner, 1998). human subjects by providing a common framework
The MLEM algorithm is different from the previ- for understanding the data. A well-constructed com-
ous methods because it does not rely on any lineariza- partmental model can also be used to answer a wide
tion techniques (D’Argenio et al, 2009). This algorithm variety of questions through simulations. Throughout
involves maximizing a likelihood function through an drug development, questions arise at various stages,
iterative series of two steps that are repeated until con- and compartmental models can be used at all stages
vergence. In the first step, termed the expectation step to answer these questions. For instance, in Phase 1,
or “E-step,” the conditional mean and covariance for questions regarding optimal dosing for Phase 2 can
each individual’s data are computed and the expected be answered using PK/PD modeling. Among other
likelihood function associated with these parameters is uses, compartmental modeling can be used to support
obtained. In the second step, the maximization step or proof-of-concept claims, select optimal dosing regi-
“M-step,” the population mean, covariance, and error mens, optimize dosing schedule, and refine study
variance parameters are updated to maximize the designs (FDA guidance; Chien et al, 2005).
likelihood from the previous step (Bonate, 2011; An example of how PK/PD modeling was helpful
D’Argenio et al, 2009). This algorithm is available in making key decisions surrounding the development
within ADAPT 5, as mentioned in Appendix A. of a drug is described by Neiforth and colleagues.
Interferons are used to treat various viral infections
Frequently Asked Questions and malignancies. Despite their therapeutic benefits,
their short half-life requires frequent administration
»»How can we tell if we are using the right model to
describe our data? (three times per week) and they can be highly anti-
genic. PEGylation of interferons is thought to increase
»»Are certain algorithms better than others? the circulating half-life as well as decrease immuno-
»»When should individual compartmental analysis be genicity. In this example a PK/PD model was con-
used rather than population analysis? structed to relate the exposure to PEG-modified
interferon alfa-2a to its effect on the induction of the
production of MX protein (Neiforth et al, 1996).
Applications of Compartmental Modeling Because of their many effects MX proteins were
Compartmental modeling is an extremely versatile considered to be a useful PD probe. The goal of
tool that allows researchers to do much more than model development was to provide information to
simply estimate pharmacokinetic and/or pharmaco- improve dosing strategies as well as guide the drug
dynamic parameters and quantify their variability. development of future modified molecules.
828 Chapter 25
The PK/PD model was based on data from a substances, such as hormones, nutrients, and oxygen,
randomized single ascending dose study that are transported to the organs by the same network of
included 45 healthy adult male subjects receiving 1 blood vessels (arteries). The drug concentration
of 4 subcutaneous doses of PEG-modified interferon within a target organ depends on plasma drug con-
alfa-2a or interferon alfa-2a. The PK of the inter- centration, plasma versus tissue protein binding, the
feron products, described by a one-compartment rate of blood flow to an organ, and the rate of drug
model with first-order absorption and elimination, uptake into the tissue. Physiologically, uptake (accu-
was related to the PD through an indirect model. The mulation) of drug by organ tissues occurs from the
drug stimulated the production of MX protein (stim- extracellular fluid, which equilibrates rapidly with
ulation of kin) via an Emax function. the capillary blood in the organ. Some drugs cross the
The simulations obtained from the PK/PD model- plasma membrane into the interior fluid (intracellular
ing exercise indicated that, although the addition of a water) of the cell (Fig. 25-4).
PEG moiety to interferon alfa-2a did indeed prolong In addition to drug accumulation, some organs of
the half-life of the drug, the PD properties associated the body are involved in drug elimination, either by
with the PEG-modified interferon alfa-2a would still excretion (eg, kidney) or by metabolism (eg, liver).
necessitate a twice-weekly dosing regimen in order to The elimination of drug by an organ may be described
attain a comparable response to the unmodified prod- by drug clearance in the organ (see Chapters 7 and 12).
uct. This was a far cry from the anticipated once- The liver is an example of an organ with drug metabo-
weekly dosing for the PEG-modified product and these lism and drug uptake (accumulation). Physiologically
predictions were confirmed by two Phase II trials. based pharmacokinetic (PBPK) modeling aims to
In conclusion, PK/PD modeling demonstrated consider as much as possible all processes of drug
that the PEG-modified interferon alfa-2a provided uptake, distribution, and elimination.
little therapeutic benefit over its unmodified counter- In physiological PK models, drugs are carried
part, which proved to be consistent with Phase II by blood flow from the administration (input) site to
findings. These findings contributed to the decision various body organs, where the drug rapidly equili-
to discontinue the development of this product for brates with the interstitial water in the organ.
this indication. Physiological pharmacokinetic models are mathe-
Modeling and simulations are not only being used matical models describing drug movement and dis-
and further developed by the pharmaceutical industry position in the body based on organ blood flow and
or academia but, from a regulatory perspective, have the organ spaces penetrated by the drug. In its sim-
also been used to enhance decision making and con- plest form, a physiologic pharmacokinetic model
tribute to product labeling (pertaining to dosage and considers the drug to be blood flow limited. Drugs
administration, safety, or clinical pharmacology) are carried to organs by arterial blood and leave
(Bhattaram et al, 2007). In some submissions to the organs by venous blood (Fig. 25-5).
FDA, drug companies benefitted from modeling and In such a model, transmembrane movement of
simulations performed by reviewers, who were able to drug is rapid, and the capillary membrane does not
extract information from the data that had not other- offer any resistance to drug permeation. Uptake of
wise been presented (Bhattaram et al, 2005, 2007).
Lee et al (2011) found that over an 8 year period
(2000 to 2008), modeling and simulations contrib- Q, Cart Blood Q, Cven
uted to the approval of 64% of products while it
influenced the labeling of 67% of products. Extracellular water
Physiologic Pharmacokinetic Models Intracellular water
The human body is composed of organ systems con- FIGURE 254 In describing drug transfer, the physiologic
taining living cells bathed in an extracellular aqueous pharmacokinetic model divides a body organ into three parts:
fluid (see Chapter 11). Both drugs and endogenous capillary vessels, extracellular space, and intracellular space.
Empirical Models, Mechanistic Models, Statistical Moments, and Noncompartmental Analysis 829
Equation 25.9. Substituting in Equation 25.11 with
Tissue compartment
Cven = Ctissue/Ptissue yields
Cart, Q t Cven
Blood d(VtissueCtissue ) C
Q C tissue
=
dt t art − (25.12)
Ptissue
FIGURE 255 Noneliminating tissue organ. The extra-
cellular water is merged with the plasma water in the blood. Equation 25.12 describes drug distribution in a none-
liminating organ or tissue group. For example, drug
distribution to muscle, adipose tissue, and skin can be
drug into the tissues is rapid, and a constant ratio of
represented in a similar manner by Equations 25.13,
drug concentrations between the organ and the
25.14, and 25.15, respectively, as shown below. For
venous blood is quickly established. This ratio is the
tissue organs in which drug is eliminated (Fig. 25-6),
tissue/blood partition coefficient:
parameters representing drug elimination from the
C liver (kLIV) and kidney (kKID) are added to account for
tissue
P (25.
tissue = 9)
C drug removal through metabolism or excretion.
blood
Equations 25.16 and 25.17 are derived similarly to
where P is the partition coefficient. those for the noneliminating organs above.
The magnitude of the partition coefficient can Removal of drug from any organ is described by
vary depending on the drug and on the type of tissue. drug clearance (Cl) from that organ. The rate of drug
Adipose tissue, for example, has a high partition for elimination is the product of the drug concentration
lipophilic drugs. The rate of drug carried to a tissue in the organ and the organ clearance.
organ and tissue drug uptake depend on the rate of
blood flow to the organ and the tissue/blood partition V dC
Rate of drug elimination tissue tissue
=
coefficient, respectively. dt
The rate of blood flow to the tissue is expressed = Ctissue ×Cltissue
as Qt (mL/min), and the rate of change in the drug
concentration with respect to time within a given tis- The rate of drug elimination may be described for
sue organ is expressed as each organ or tissue (Fig. 25-7).
d(V
tissueCtissue )
=Qt (Cin −Cout ) (25.10) d(V C ) C
Muscle: MUS MUS MUS
dt =Q C
dt MUS MUS −
P
MUS
d(V C
tissue tissue )
=Qt (Cart −C
d ven ) (25.11)
t (25.13)
where Cart is the arterial blood drug concentration and d(VFA CF T ) C
: T A FAT
Adipose tissue =Q
Cven is the venous blood drug concentration. Qt is FAT
CFAT −
dt PFAT
blood flow and represents the volume of blood flow-
ing through a typical tissue organ per unit of time. (25.14)
If drug uptake occurs in the tissue, the incoming
concentration, Cart, is higher than the outgoing venous
concentration, Cven. The rate of change in the tissue Tissue compartment
C
drug concentration is equal to the rate of blood flow art Cven
Q t
multiplied by the difference between the blood drug Blood
concentrations entering and leaving the tissue organ.
In the blood flow–limited model, drug concentration in Drug
the blood leaving the tissue and the drug concentration eliminated
within the tissue are in equilibrium, and Cven may be
estimated from the tissue/blood partition coefficient in FIGURE 256 A typical eliminating tissue organ.
830 Chapter 25
QBR d(V CKID )
Brain Kidney: KID
dt
QLU
Lung CKID Cl
Q KID
= KID CKID − C
P −
KID
KID P
KID
QH
Heart (25.17)
QMUS
Muscle d(VLUCLU ) C
Lung: =Q LU
QKID dt LU (25.18)
PLU
Urine Kidney
where LIV = liver, SP = spleen, GI = gastrointestinal
tract, KID = kidney, LU = lung, FAT = adipose,
QSP SKIN = skin, and MUS = muscle.
Spleen The mass balance for the rate of change in drug
Q concentration in the blood pool is
LIV QGI
Liver GI
d(VbCb ) CMUS CLIV C
=Q Q Q KID
dt MUS P
+ LIV
+
P KID
Q MUS LIV PKID
BO
Bone
(muscle) (liver) (kidney)
QA
Adipose C
+ SKIN C C
QSKIN +
Q FAT LU
Q FAT Q Q C
P
SK SKIN P
+ LU −
P b b
FAT LU
Skin
(skin) (adipose) (lung) (blood)
FIGURE 257 Example of blood flow to organs in a physi-
ologic pharmacokinetic model. (25.19)
Lung perfusion is unique because the pulmonary
artery returns venous blood flow to the lung, where
carbon dioxide is exchanged for oxygen and the
d(V blood becomes oxygenated. The blood from the
NCSKIN ) C
Skin: SKI QSKIN C
SKIN
=
dt SKIN −
P lungs flows back to the heart (into the left atrium)
SKIN
through the pulmonary vein, and the quantity of
(25.15) blood that perfuses the pulmonary system ultimately
passes through the remainder of the body. In describ-
ing drug clearance through the lung, perfusion from
d(V C ) the heart (right ventricle) to the lung is considered
Liver: LIV LIV = C
t LIV (QLIV −QGI −QSP )d venous blood (Fig. 25-7). Therefore, the terms in
Equation 25.19 describing lung perfusion are
C I CSP C
+
Q G
+Q reversed compared to those for the perfusion of other
SP −
Q LIV
GI P
I P LIV
G SP PLIV tissues. With some drugs, the lung is a clearing organ
besides serving as a merging pool for venous blood.
Cl
−
C int In those cases, a lung clearance term could be
LIV P (25.16)
LIV included in the general model.
Venous blood
Arterial blood
Empirical Models, Mechanistic Models, Statistical Moments, and Noncompartmental Analysis 831
After intravenous drug administration, drug uptake [Cb]f = fb[Cb] (25.21)
in the lungs may be very significant if the drug has high
affinity for lung tissue. If actual drug clearance is at a [Ct]f = ft[Ct] (25.22)
much higher rate than the drug clearance accounted for
by renal and hepatic clearance, then lung clearance of where fb is the blood free drug fraction, ft is the tissue
the drug should be suspected, and a lung clearance term free drug fraction, Ct is the total drug concentration in
should be included in the equation in addition to lung tissue, and Cb is the total drug concentration in blood.
tissue distribution. Therefore, the partition ratio, Pt, of the tissue
The system of differential equations used to drug concentration to that of the plasma drug con-
describe the blood flow–limited model is usually solved centration is
through computer programs, in an analogous manner to
what is used with compartmental modeling. Because of fb [Ct ] = = P (25.23)
the large number of parameters involved in the mass ft [Cb ]
t
balance, and because “true” solutions to a set of differ-
ential equations may not solely exist, more than one set By assuming linear drug binding and rapid drug
of parameters often fit the experimental data. This is equilibration, the free drug fraction in tissue and
common with human data, in which many of the organ blood may be incorporated into the partition ratio
tissue data items are not available. The lack of sufficient and the differential equations. These equations are
tissue data sometimes leads to unconstrained models. similar to those above except that free drug concen-
As additional data become available, new or refined trations are substituted for Cb. Drug clearance in the
models are adopted. For example, methotrexate was liver is assumed to occur only with the free drug. The
initially described by a flow-limited model, but later inherent capacity for drug metabolism (and elimina-
work described the model as a diffusion-limited model. tion) is described by the term Clint (see Chapter 12).
Because invasive methods are available for ani- General mass balance of various tissues is described
mals, tissue/blood ratios or partition coefficients can by Equation 25.24:
be determined accurately by direct measurement.
Using experimental pharmacokinetic data from ani- d(VtissueCtissue )
=Qt (Cart −Cven )mals, physiologic pharmacokinetic models may dt
yield more reliable predictions. (25.24)
d(VtissueCtissue ) Ct
=Qt C −
dt art P
t
Physiologic Pharmacokinetic Model
with Binding
or
The physiologic pharmacokinetic model described
above assumed flow-limited drug distribution without
d(VtissueCtissue ) Ct fQ C t
drug binding to either plasma or tissues. In reality, = −
dt t art f b
many drugs are bound to a variable extent in either
plasma or tissues. With most physiologic models,
For liver metabolism,
drug binding is assumed to be linear (not saturable or
concentration dependent). Moreover, bound and free
d(VLIVCLIV ) C
= C (Q −Q −Q ) −
Q LIV
drug in both tissue and plasma are in equilibrium.
dt b LIV GI SP LIV PFurther, the free drug in the plasma and in the tissue LIV
equilibrates rapidly. Therefore, the free drug concen- (hepatic drug elimination)
tration in the tissue and the free drug concentration in
the emerging blood are equal: C C
+
Q GI
Q SP
GI P
+ SP GI PSP (25.25)
[Cb]f = [Ct]f (25.20)
832 Chapter 25
The mass balance for the drug in the blood pool is offers no barrier to drug permeation. If no drug bind-
ing is involved, the tissue drug concentration is the
d(VbCb ) C same as that of the venous blood leaving the tissue.
=Q C +
Q LIV
dt MUS MUS LIV P This assumption greatly simplifies the mathematics
LIV
involved. Table 25-5 lists some of the drugs that
(muscle) (liver) have been described by a flow-limited model. This
model is also referred to as the perfusion model.
C C
+
Q KID +
Q SKIN
KID P
A more complex type of physiologic pharmacoki-
SKIN P (25.26)
KID SKIN netic model is called the diffusion-limited model or
(kidney) (skin) the membrane-limited model. In the diffusion-limited
model, the cell membrane acts as a barrier for the
C C drug, which gradually permeates by diffusion.
+
Q FAT LU
FAT
+QLU Q C
P
−
P b b Because blood flow is very rapid and drug perme-
FAT LU
ation is slow, a drug concentration gradient is estab-
(adipose) (lung) (blood) lished between the tissue and the venous blood (Lutz
and Dedrick, 1985). The rate-limiting step of drug
diffusion into the tissue depends on the permeation
The influence of binding on drug distribution is an
across the cell membrane rather than blood flow.
important factor in interspecies differences in pharma-
Because of the time lag in equilibration between
cokinetics. In some instances, animal data may predict
blood and tissue, the pharmacokinetic equation for
drug distribution in humans by taking into account the
the diffusion-limited model is very complicated.
differences in drug binding. For the most part, extra-
polations from animals to humans or between species
are rough estimates only, and there are many instances Physiologic Pharmacokinetic Model
in which species differences are not entirely attribut- Incorporating Hepatic Transporter-Mediated
able to drug binding and metabolism. Clearance
It is now well recognized that drug transporters play
Blood Flow–Limited Versus important roles in the processes of absorption, distri-
Diffusion-Limited Model bution, and excretion and should be accounted for in
Most physiologic pharmacokinetic models assume PBPK models. Predicting human drug disposition,
rapid drug distribution between tissue and venous especially when involving hepatic transport, is difficult
blood. Rapid drug equilibrium assumes that drug dif- during drug development. However, drug transport
fusion is extremely fast and that the cell membrane may be a critical process in overall drug disposition in
TABLE 255 Drugs Described by Physiologic Pharmacokinetic Model
Drug Category Comment Reference
Thiopental Anesthetic Blood, flow limited Chen and Andrade (1976)
BSP Diagnostic Plasma, flow limited Luecke and Thomason (1980)
Nicotine Stimulant Blood, flow limited Gabrielsson and Bondesson (1987)
Lidocaine Antiarrhythmic Blood, flow limited Benowitz et al (1974)
Methotrexate Antineoplastic Plasma, flow limited Bischoff et al (1970)
Biperiden Anticholinergic Blood, flow limited Nakashima and Benet (1988)
Cisplatin Antineoplastic Plasma, multiple metabolite, binding King et al (1986)
Empirical Models, Mechanistic Models, Statistical Moments, and Noncompartmental Analysis 833
the body such that without a realistic description of mechanisms in microstructures such as interior cellular
transport processes in the body, model accuracy may structures, membrane transporters, surface receptors,
be deficient. Watanabe et al (2009) describe a model genomes, and enzymes. The liver is a complex organ
with hepatobiliary excretion mediated by transporters, intimately connected to drug transport and bile move-
organic anion-transporting polypeptide (OATP) 1B1 ment. Compartment concepts are needed to track the
and multidrug resistance–associated protein (MRP) 2, mass of drug transfer in and out of those fine struc-
for the HMG-CoA reductase inhibitor drug, pravas- tures as shown by the example in Fig. 25-8. Human
tatin. While the classical blood flow–based physiologic liver microsomes are used to help predict the meta-
pharmacokinetic models developed 40 years ago using bolic clearance of drugs in the body.
systems of differential equations are still useful in The PBPK model with pravastatin (Watanabe et al,
describing the mass balance and transfer of drug within 2009) is used to evaluate the concentration–time
major organs, the models are inadequate in light of new profiles for drugs in the plasma and peripheral organs
discoveries in molecular biology and pharmacogenom- in humans using physiological parameters, sub-
ics. Drug disposition and drug targeting are better cellular fractions (cells lysed and contents fraction-
understood based upon using influx/efflux and binding ated based on density), and drug-related parameters
IV
Qtotal
Lung Rapid equilibrium
compartment Urine
QBrain
Brain
QMuscle
Muscle
QKidney
Kidney
QLiver
Inlet Inlet Inlet Inlet Inlet
PSinf PSdif
k PO (H)
a or
ID (R)
CLmet, int
(H)
GI
PSbile
(R)
Bile
FIGURE 258 Schematic diagram of the PBPK model predicting the concentration–time profiles of pravastatin. The liver
compartment was divided into five compartments to mimic the dispersion model. Indicated are blood flow (Q), the active hepatic
uptake clearance (PSinf), the passive diffusion clearance (PSdif), the biliary clearance (PSbile), and the metabolic clearance (Clmet, int),
human (H), and rat (R). The enterohepatic circulation was incorporated in the case of humans. (From Watanabe et al, 2009, with
permission.)
Liver
Liver
Liver
Liver
Liver
834 Chapter 25
(unbound fraction and metabolic and membrane trans- be used. St-Pierre et al (1988) developed a simple
port clearances extrapolated from in vitro experiments). one-compartment open model, based on the liver as
The principle of the prediction was as follows. First, the only organ of drug disappearance and metabolite
subcellular fractions were obtained by comparing in formation. The model was used to illustrate the metab-
vitro and in vivo parameters in rats. Then, the in vitro olism of a drug to its primary, secondary, and tertiary
human parameters were extrapolated in vivo using metabolites. The model encompassed the cascading
the subcellular fractions obtained in rats. Pravastatin effects of sequential metabolism (Fig. 25-9).
was selected as the model compound because many The concentration–time profiles of the drug and
studies have investigated the mechanisms involved in metabolites were examined for both oral and intrave-
the drug disposition in rodents, and clinical data after nous drug administration. Formation of the primary
intravenous and oral administration are available. metabolite from drug in the gut lumen, with or with-
When multiple drug metabolites are involved, out further absorption, and metabolite formation
the physiologic model of the cascade events can be arising from first-pass metabolism of the drug and
quite complicated and an abbreviated approach may the primary metabolite during oral absorption were
IV
k E|mi| E|mii|
k E|mi| F|mii|
k|mi| E|mii|
k F|mi| k|mi| F|mii| k|mii| k|miii|
D MI MII MIII
PO
k E|mi| E|mii|
k E|mi| F|mii|
k|mi| E|mii|
k F|mi| k|mi| F|mii| k|mii| k|miii|
D MI MII MIII
mii|ka|mi| F|mi|
mi| E|
E|
k a E
ka F
|
mi E
|m
i| F|
mii| |m
ii|
E
E mi| E|
k a k |
a
k
D G
Gut MIGut
FIGURE 259 A schematic representation of the one-compartment open model for drug (D) and its primary (MI), secondary
(MII), and tertiary (MIII) metabolites after intravenous (IV) and (po) drug dosing (scheme II) The effective rate constants contributing
to the appearance of the metabolites in the systemic circulation are presented. The solid lines denote sources pertaining to drug
or metabolite species in the circulation; the uneven dashed lines represent sources arising from absorption of drug or the primary
metabolite from the gut lumen; and the stippled lines denote sources arising from first-pass metabolism of the drug or primary
metabolite. See the glossary for definition of the terms. (From St-Pierre et al, 1988, with permission.)
k
a E F|mi|
k
a |mi| E|mi| F|mii|
Empirical Models, Mechanistic Models, Statistical Moments, and Noncompartmental Analysis 835
considered. Mass balance equations, incorporating when differences in drug concentrations in arterial
modifications of the various absorption and conver- and venous are considered (see Chapter 11). The
sion rate constants, were integrated to provide the implication of venous versus arterial sampling is
explicit solutions. hard to estimate and may be more drug dependent.
Most pharmacokinetic models are based on sampling
of venous data. In theory, mixing occurs quickly
when venous blood returns to the heart and becomes
Frequently Asked Questions reoxygenated again in the lung. Chiou (1989) has
»»Why are differential equations used to describe estimated that for drugs that are highly extracted, the
physiologic models? discrepancies may be substantial between actual
»»Why do we assume that drug concentrations concentration and concentration estimated from
in venous and arterial blood are the same in well-stirred pharmaco kinetic models.
pharmacokinetics?
»»Why should transporters be considered in
physiological models? NONCOMPARTMENTAL ANALYSIS
Noncompartmental analyses provide an alternative
method for describing drug pharmacokinetics
without having to assign a particular compartmen-
Application and Limitations of Physiologic tal model to the drug. Although this method is
Pharmacokinetic Models often considered to be model independent, there
The physiologic pharmacokinetic model is related are still a few assumptions and key considerations
to drug concentration and tissue distribution using that must not be overlooked. This approach is,
physiologic and anatomic information. For exam- therefore, better referred to as “noncompartmen-
ple, the effect of a change in blood flow on the drug tal” as it does assume a “model” in that, among
concentration in a given tissue may be estimated other things that will be reviewed below, the PK
once the model is characterized. Similarly, the effect needs to be linear and the terminal phase must be
of a change in mass size of different tissue organs on log-linear.
the redistribution of drug may also be evaluated The first assumption is that the drug in question
using the system of physiologic model differential displays linear pharmacokinetics (DiStefano and
equations generated. When several species are Landaw, 1984; Gibaldi and Perrier, 2007). In other
involved, the physiologic model may predict the words, exposure increases in proportion with
pharmacokinetics of a drug in humans when only increasing dose and PK parameters are stable
animal data are available. Changes in drug–protein through time. A second important assumption is that
binding, tissue organ drug partition ratios, and intrin- the drug is eliminated from the body strictly from
sic hepatic clearance may be inserted into the physi- the pool in which it is being measured, the plasma,
ologic pharmacokinetic model. for example (Benet and Ronfeld, 1969; DiStefano
Most pharmacokinetic studies are modeled and Landaw, 1984). Finally, this approach assumes
based on blood samples drawn from various venous that all sources of the drug are direct and unique to
sites after either IV or oral dosing. Physiologists the measured pool (DiStefano and Landaw, 1984).
have long recognized the unique difference between If these assumptions hold true, noncompartmental
arterial and venous blood. For example, arterial ten- analyses can be conducted if sufficient concentra-
sion (pressure) of oxygen drives the distribution of tion–time data are available (eg, if there are rich
oxygen to vital organs. Chiou (1989) and Mather data). In most circumstances “rich data” are consid-
(2001) have discussed the pharmacokinetic issues ered to be a minimum of 12 different concentration
836 Chapter 25
time points (eg, includes the predose concentration) (Equation 25.27). The moment curve shows the
associated with a single-dose administration. Any characteristics of the distribution.
less data may provide inaccurate estimations of
pharmacokinetic parameters using the noncompart- ∞
mental approach. µ or mt m m n = tmm h o e t ∫ f (t)dt (25.27)
0
where f(t) is the probability density function, t is
Statistical Moment Theory time, and m is the mth moment.
Noncompartmental analyses are based on statistical For example, when m = 0, substituting for m = 0
moment theory, which provides a unique way to study yields Equation 25.28, called the zero moment, m0:
time-related changes in macroscopic events. A mac-
∞
roscopic event is considered the overall event brought µ0 = ∫ f (t)dt (25.28)
about by the constitutive elements involved. For 0
example, in chemical processing, a dose of tracer
If the distribution is a true probability function, the
molecules may be injected into a reactor tank to track
area under the zero moment curve is 1. When f (t)
the transit time (residence time) of materials that stay
represents drug concentration that is a function of
in the tank. The constitutive elements in this example
time, the zero moment is referred to as area under the
are the tracer molecules, and the macroscopic events
curve (AUC). The AUC can be obtained through
are the residence times shared by groups of tracer
integration of f (t) or using the trapezoidal method, as
molecules. Each tracer molecule is well mixed and
described in Chapter 2.
distributes noninteractively and randomly in the tank.
Substituting into Equation 25.27 with m = 1,
D0
In the case of all the molecules (∫ dDe = D ) Equation 25.29 gives the first moment m1:0 0 that
exit from the tank, the rate of exit of tracer molecules
∞
(–dDe/dt) divided by D0 yields the probability of a µ1 = ∫ t1 f (t)dt (25.29)
0
molecule having a given residence time t. A mathe-
matical formula describing the probability of a tracer The area under the curve f(t) times t is called the
molecule exited at any time is a probability density AUMC, or the area under the first moment curve.
function. Mean residence time (MRT) is the expected The first moment, m1, defines the mean of the
value or mean of the distribution. distribution.
MRT provides a fundamentally different approach Similarly, when m = 2, Equation 25.27 becomes
than classical pharmacokinetic models, which involve the second moment, m2:
the concept of dose, half-life, clearance, volume, and
concentration. The classical approach does not account
∞
for the observation that molecules in a cluster move µ = t22 ∫ f (t) dt (25.30)
0
individually through space and are more appropri-
ately tracked as statistical distribution based on where m2 defines the variance of the distribution.
residence-time considerations. Consistent with the Higher moments, such as m3 or m4, represent skewness
concept of mass and the dynamic movement of mol- and kurtosis of the distribution. Equation 25.27 is
ecules within a region or “space,” MRT is an alterna- therefore useful in characterizing families of moment
tive concept to describe how drug molecules move in curves of a distribution.
and out of a system. The concept is well established The principal use of the moment curve is the
in chemical kinetics, where the relationships between calculation of the MRT of a drug in the body. The
MRT and rate constants for different systems are elements of the distribution curve describe the dis-
known. tribution of drug molecules after administration and
A probability density function f(t) multiplied by the residence time of the drug molecules in the
tm and integrated over time yields the moment curve body.
Empirical Models, Mechanistic Models, Statistical Moments, and Noncompartmental Analysis 837
Mean Residence Time
EXAMPLE »» »
According to statistical moment theory, MRT is the
expected value or mean of the distribution of a prob- An antibiotic was given to two subjects by an
ability density function. However, MRT can also be IV bolus dose of 1000 mg. Let’s assume that the
viewed from the perspective of the disposition of drug’s pharmacokinetics is well described by a
drug molecules. After an intravenous bolus drug one-compartment model. The drug has a volume of
dose (D0), the drug molecules distribute throughout distribution of 10 L and follows a one-compartment
the body. These molecules stay (reside) in the body model with an elimination constant (lz) of (1) 0.1 h–1
for various time periods. Some drug molecules leave and (2) 0.2 h–1 in the two subjects. Let’s assume
the body almost immediately after entering, whereas that the concentration at time zero was 100 mg/L
other drug molecules leave the body at a much later in each subject. Determine the Cl and the MRT for
time period. The term MRT describes the average each subject based on the concentrations listed in
time that drug molecules stay in the body or in a Table 25-6 using the noncompartmental approach.
kinetic space.
The equation to calculate the MRT following Solution
intravenous bolus or constant infusion administra- Noncompartmental Approach
tions is described in Equation 25.31:
1. From Table 25-6, multiply each time point with
AUMC∞
MR 0 Duration the corresponding plasma Cp to obtain points
T = − (25.31)
AUC∞ 2 for the moment curve. Use the linear trapezoidal
0
rule and sum the area to obtain the area under
where AUMCt
0 is the area under the (first) moment- the concentration–time curve (AUCt ) and the
0
versus-time curve from t = 0 to infinity, AUC∞ (or zero area under the moment curve (AUMCt
0 ) for each
0
moment curve) is the area under the concentration- subject, as demonstrated in Table 25-7.
versus-time curve from t = 0 to infinity, and Duration The AUCt (area from time zero to 30 hours) for
0
is the duration of the drug infusion. subject 1 is 961.6 mg · h/L while it is 509.2 mg ⋅ h/L
for subject 2. We can then calculate the AUC∞
The AUMC can be extrapolated to infinity from :
0
AUMCt
0 using the following equation and assuming A C∞ t
U 0 = AUC0 +Ct /λz
a log-linear terminal phase:
so AUC∞ = 961.605 + 4.979/0.1 = 1011.395 mg ⋅ h/L
0
(C × t) C (subject 1)
AUMC∞
0 = AUMCt t t
0 + λ + (25.32)
2
z λ AUC∞ = 509.243 + 0.248/0.2 = 510.483 mg ⋅ h/L
0
z (subject 2)
One major limitation of the AUMC∞
0 calculation is The Cl is therefore: Cl = Dose/AUC∞
0 .
that it can only be calculated after a single-dose So Cl = 1000/1011.395 = 0.99 L/h (subject 1)
administration, and not at steady-state conditions Cl = 1000/510.483 = 1.96 L/h (subject 2)
like the AUC∞. This is because the superposition
0 We now calculate the AUMCt
0 using Equation 25.32:
principle of the AUC (eg, that the AUC∞ after a sin-
0
gle dose is exactly equal to the AUCt AUMCt
0 = 1383.135 + 149.37/0.1 + 4.979/0.12 =
0 (ss) for a drug
product exhibiting linear pharmacokinetics, see 9963.4 (subject 1)
Chapter 7 for additional details) does not apply to AUMCt
0 = 525.308 + 7.44/0.2 + 0.248/0.22 =
the AUMC calculation. So the AUMC cannot be 2526.9 (subject 2)
calculated easily at steady state over a dosing inter- And, finally the MRT:
val like the AUC. In practical terms, it means that the
MRT = AUMC∞
0 /AUC∞
0 − (Duration infusion/2)
AUMC, and therefore the MRT, can only be calcu-
lated readily with the noncompartmental approach So MRT = 9963.4/1011. 395 = 9.85 h (subject 1)
after a drug is administered as a single dose. MRT = 2526.9/510.483 = 4.95 h (subject 2)
838 Chapter 25
TABLE 256 Simulated Plasma Data after an properties. In addition, it creates confusion when
IV Bolus Dose, Illustrating Calculation of MRT other parameters need to be calculated, such as the
Vss, as we will see later. So although it is not incor-
Cp (mg/L)
rect to label the ratio of AUMC/AUC by calling it an
Time (h) Subject 1 Subject 2 MRT with specification of the administration route,
0 100 100 it is recommended to avoid confusion by referring to
this ratio as mean transit time (MTT):
1 90.484 81.873
2 81.873 67.032 MTT = AUMC∞ ∞
0 /AUC0 after extravascular
3 74.082 54.881 administration (25.33)
4 67.032 44.933
and as we have seen earlier,
6 54.881 30.119
8 44.933 20.19 MRT AUMC∞ / ∞
= 0 AUC0 − (duration infusion/2)
after IV administration
12 30.119 9.072
16 20.19 4.076
such that
24 9.072 0.823
30 4.979 0.248 MTT = MAT + MRT (25.34)
where MAT is the mean absorption time, or the aver-
age time it takes for drug molecules to be absorbed
Mean Transit Time (MTT), Mean into the systemic circulation.
Absorption Time (MAT), and Mean With this nomenclature, the MRT is always
Dissolution Time (MDT) obtained after IV administration, and the MTT
always represents the total transit time, which is the
After IV administration, the rate of systemic drug
sum of the MAT and the MRT. With this nomencla-
absorption is zero, because the drug is placed
ture, the route of administration will dictate what the
directly into the bloodstream. The MRT calculated
MAT will be and will therefore influence the MTT,
for a drug after IV administration basically reflects
but the MRT will stay constant regardless of the
the elimination processes in the body, and therefore
route of administration.
the MRT that molecules stay in the systemic circula-
So after oral administration MTT
tion. When drugs are administered extravascularly, PO = MATPO +
MRT, after IM administration MTTIM = MATIM +
such as after oral administration, the ratio of AUMC
MRT, and so on.
to AUC does reflect not only the residence time of
In some cases, IV data are not available and an
molecule once they are in the systemic circulation
MTT for a solution may be calculated. The mean
(MRT) but also the duration of time during which
dissolution time (MDT), or in vivo mean dissolution
they are absorbed. The AUMC/AUC ratio therefore
time, for an immediate-release (IR) solid drug prod-
changes depending on how the drug is administered;
uct would be:
hence many refer to this ratio as MRTPO when the
drug is orally administered, MRTinh when the drug is MDTPO(IR) = MTTPO(IR) – MTTPO(solution) (25.35)
administered via inhalation, MRTIM when the drug is
administered intramuscularly, and so on. This method MDT reflects the time for the drug to dissolve in
of reporting the MRT does suggest that the duration vivo. Equation 25.35 calculates the in vivo dissolu-
of time that molecules stay in the systemic circulation tion time for an immediate-release solid drug prod-
changes with the method of administration, which is uct (tablet, capsule) given orally. MDT has been
incorrect if the drug displays linear pharmacokinetic evaluated for a number of drug products. MDT is
TABLE 257 Example of Calculation of MRT
Subject 1 Subject 2
Time (h) Cp (mg/L) AUC (mg/L*h) Cp x t (mg/L*h) AUMC (mg/L*h2) Cp (mg/L) AUC (mg/L*h) Cp x t (mg/L*h) AUMC (mg/L*h2)
0 100 0 100 0
1 90.484 95.242 90.484 45.242 81.873 90.9365 81.873 40.9365
2 81.873 86.1785 163.746 127.115 67.032 74.4525 134.064 107.9685
3 74.082 77.9775 222.246 192.996 54.881 60.9565 164.643 149.3535
4 67.032 70.557 268.128 245.187 44.933 49.907 179.732 172.1875
6 54.881 121.913 329.286 597.414 30.119 75.052 180.714 360.446
8 44.933 99.814 359.464 688.75 20.19 50.309 161.52 342.234
12 30.119 150.104 361.428 1441.784 9.072 58.524 108.864 540.768
16 20.19 100.618 323.04 1368.936 4.076 26.296 65.216 348.16
24 9.072 117.048 217.728 2163.072 0.823 19.596 19.752 339.872
30 4.979 42.153 149.37 1101.294 0.248 3.213 7.44 81.576
Sum 961.605 7971.79 509.2425 2483.502
839
840 Chapter 25
most readily estimated for immediate-release-type Other Pharmacokinetic Parameters
products, because the absorption process (or MAT) Calculated by the Noncompartmental
may be influenced by certain types of modified- Analysis
release drug products.
The reader is referred to Chapter 7, where it is speci-
fied in detail how to estimate drug clearance (Cl) using
EXAMPLE »» » the noncompartmental approach. Using the AUC value
(zero moment curve) obtained with the trapezoidal
Data for ibuprofen (Gillespie et al, 1982) are shown method, total clearance (Cl/F) can be determined as
in Tables 25-8 and 25-9. Serum concentrations for follows:
ibuprofen after administration of a capsule and
a solution are tabulated as a function of time in Dose
Tables 25-8 and 25-9, respectively. Cl /F =
AUC∞
0
As listed in Table 25-10, the MTT for the solution
was 2.65 hours and for the product was 4.04 hours.
Therefore, MDT for the product is 4.04 – 2.65 = In addition, bioavailability (F) can also be deter-
1.39 hours. mined using concentration data obtained follow-
ing intravenous (IV) and oral administration of a
TABLE 258 Serum Concentrations for Capsule lbuprofen
Time (h) Cp Cpt tCp Dt
0 0 0
0.167 0.06 0.01002 0.000836
0.333 3.59 1.195 0.1000
0.50 7.79 3.895 0.425
1 13.3 13.300 4.298
1.5 14.5 21.750 8.762
2 16.9 33.80 13.887
3 16.6 49.80 41.80
4 11.9 47.60 48.70
6 6.31 37.86 85.46
8 3.54 28.32 66.18
10 1.36 13.60 41.92
12 0.63 7.56 21.16
Total AUMC = 332.695
k = 0.347 h-1, AUC∞
= 89.1
0
Cp ⋅ t Cp 0.63 ⋅12 0.63
AUMC of tail piece (extrapolation to ∞) = + = + = 27.02
k k2 0.347 0.3472
AUMC∞
0 = 332.695+ 27.02 = 359.715
359.715
MTTcapsule = = 4.04 h
89.1
Data adapted from Gillespie et al (1982).
Empirical Models, Mechanistic Models, Statistical Moments, and Noncompartmental Analysis 841
TABLE 259 Serum Concentrations for Solution lbuprofen
Time (h) Cp Cpt tCp Dt
0 0 0
0.167 17.8 2.973 0.248
0.333 29.0 9.657 1.048
0.5 29.7 14.85 2.046
1 25.7 25.7 10.14
1.5 19.7 29.55 13.81
2 17.0 34.0 15.88
3 11.0 33.0 33.50
4 7.1 28.4 30.70
6 3.82 22.92 51.33
8 1.44 11.52 34.45
10 0.57 5.70 17.22
12 0.38 4.56 10.26
Total AUMC = 220.64
k = 0.455 h-1, AUC∞
0 = 87.7
Cp ⋅ t Cp 0.38 ⋅12 0.38
AUMC of tail piece (extrapolation to ∞) = + = + = 11.86
k k2 0.455 0.4552
AUMC∞
0 = 220.64 +11.86 = 232.478
232.478
MTTsolution = 2.65 h
87.7
Data adapted from Gillespie et al (1982).
drug (Gibaldi and Perrier, 2007). MRT is useful in calculating other pharmacokinetic
Dose parameters, particularly the total volume of distribu-
IV ⋅AUC
oral
F = (25.36) tion (V
Dose ss).
oral ⋅AUCIV
Vss = Cl × MRT (25.37)
TABLE 2510 Parameters for Capsule and
Solution lbuprofen We have previously seen that the AUMC cannot be
readily calculated, unless it is after a single-dose
Parameter Units Capsule Solution
administration. In addition, the MRT can only be cal-
∞
AUC (mg/mL)h 89.1 87.7
0 culated after IV administration, as otherwise the MTT
is calculated (when an extravascular administration is
AUMC∞
0 (mg/mL)h2 359.7 232.5
used) and this parameter includes the MAT in addition
ka h−1 0.46 4.90 to the MRT. So what it means is that the total volume
K h−1 0.347 0.455 of distribution (Vss) can, therefore, only be readily
calculated after a single-dose IV administration.
MTT Hours 4.04 2.65 This is a major limitation of the noncompartmental
Parameters were calculated from data of Gillespie et al (1982). approach, compared to the compartmental approach
842 Chapter 25
when the total volume of distribution can always be between all tissue and the circulatory system (plasma
calculated, but obviously only if a valid compartmen- compartment). However, extrapolation to a specific
tal model is used. tissue drug concentration is inaccurate and analogous
to making predictions without experimental data.
Although specific tissue drug concentration data are
COMPARISON OF DIFFERENT missing, many investigators may make general predic-
APPROACHES tions about average tissue drug levels.
The compartmental model is particularly useful
Physiological Versus Compartmental for comparing the pharmacokinetics of related thera-
Approach peutic agents. In the clinical pharmacokinetic litera-
Both physiological and compartmental models aim ture, drug data comparisons are based on compartmental
to incorporate as much information as possible about models. Though alternative pharmacokinetic models
the system (biological or other) that encompasses the have been available for approximately 20 years, the
data being modeled. Both approaches rely on dif- simplicity of the compartment model allows easy tabu-
ferential equations or partial differential equations to lation of parameters such as Vss, the distribution t1/2,
ensure that laws of mass balance are respected. and the terminal t1/2. The PBPK approach is used much
While physiological models take into consider- less frequently, even though a substantial body of data
ation biological processes at very specific molecular has been generated using these types of models.
levels, compartmental models may lump various Because the PBPK model is more detailed,
organs or tissues into groups. For example, a one- accounting for processes of drug distribution, drug
compartment model “groups” together all compo- binding, metabolism, and drug flow to the body
nents of the human body such that they are represented organs, disease-related changes in physiologic pro-
by a single box. Thus, compartmental models can be cesses are more readily related to changes in the
viewed as more simplistic in comparison with their pharmacokinetics of the drug. Furthermore, organ
physiologic counterparts. mass, volumes, and blood perfusion rates are often
The major advantage of compartmental models scalable, based on size, among different individuals,
is that the time course of drug in the body may be and even among different species. This allows a per-
monitored quantitatively with a limited amount of turbation in one parameter and the prediction of the
data. Generally, only plasma drug concentrations effect of changing physiology on drug distribution
and limited urinary drug excretion data are available. and elimination. The physiological pharmacokinetic
Compartmental models have been applied success- model can also be modified to include a specific
fully for the prediction of drug pharmacokinetics and feature of a drug. For example, for an antitumor
the development of dosage regimens. Moreover, agent that penetrates into the cell, both the drug level
compartmental models are very useful in relating in the interstitial water and the intracellular water
plasma drug levels to pharmacodynamic and toxic may be considered in the model. Blood flow and
effects in the body. tumor size may even be included in the model to
The simplicity and flexibility of the compartmen- study any change in the drug uptake at that site.
tal model is the principal reason for its wide applica- The physiological pharmacokinetic model can
tion. In many cases, the compartmental model may be calculate the amount of drug in the blood and in any
used to extract some information about the underlying tissues for any time period if the initial amount of
physiologic mechanism through model testing of the drug in the blood is known and the dose is given by
data. Thus, compartmental analysis may lead to a more IV bolus. In contrast, the tissue compartment in the
accurate description of the underlying physiological compartmental model is not related to any actual
processes and the kinetics involved. In this regard, anatomic tissue groups. The tissue compartment is
compartmental models are sometimes misunderstood, needed when the plasma drug concentration data are
overstretched, and even abused. For example, the tis- fitted to a multicompartment model. In theory, when
sue drug levels predicted by a compartmental model tissue drug concentration data are available, the
represent only a composite pool for drug equilibration multiple-compartment models may be used to fit
Empirical Models, Mechanistic Models, Statistical Moments, and Noncompartmental Analysis 843
both tissue and plasma drug data together, including model may be created before actual data are obtained,
the drug concentration in a specific tissue. in order to predict what concentration time profiles
While both types of analyses can be challenging, may look like. It is with this simple comparison,
there are also difficulties specific to each method. In “top-down” versus “bottom-up,” that it is easier to
PBPK modeling, obtaining the necessary rates and reconcile both methods and see when it may be useful
constants to describe molecular processes is not always to use one more than the other. When a lot of data are
obvious or easy. Those who perform compartmental available, compartmental modeling may be priori-
modeling must deal with the challenges of noisy data, tized. In contrast, when no data are available yet for a
or data whose behavior is not easily described by drug product, then PBPK may be extremely useful to
simple models, making the determination of the “best potentially predict what may happen. For scenarios
model” more difficult and time consuming. that are somewhere between these two extreme situ-
The compartmental approach is all about “identi- ations (no data or a lot of data), then both models
fiability,” which means that a process should not be may coexist and be useful. It is important to note as
fitted if it cannot be “identified” or supported by the well that a mixture of the two approaches can be
data, while in the PBPK approach most of the param- used. For example, compartmental modeling can use
eters are not identifiable and will be “fixed.” For “physiological” parameters to predict or explain
example, a compartmental model will not predict CYP enzyme activity when drug–drug interaction
what an oral bioavailability parameter may be if con- data are being modeled (Pasternyk et al, 2000).
centration data are only available following IV admin-
istration. Predicting an oral bioavailability parameter
would then be “unidentifiable.” This is in direct con- Noncompartmental Versus Compartmental
trast to the PBPK modeling approach in which a bio- Approach
availability parameter may still be in the model, even Noncompartmental and compartmental analyses are
though there is no data to support it. both excellent methods that can be used to characterize
A common descriptor of the compartmental the PK and/or PD of a drug, when used in their appro-
versus the physiological approach is to describe the priate context. The disadvantages of each method
former as a “top-down” approach, while the later is highlight the advantages of the other method, but when
a “bottom-up” approach. A “top-down” approach utilized correctly, each approach has its own merits.
means that the compartmental model is created from Table 25-11 summarizes the key advantages and dis-
the data, and the model will therefore need to be iden- advantages of each approach (Ette and Williams, 2004;
tifiable from these data, and ideally will be shown Tett et al, 1998).
to be perfectly capable of explaining these data. For additional information, the reader is also
A “bottom-up” approach means that the PBPK referred to a section in Chapter 7 that describes the
TABLE 2511 Advantages and Disadvantages of Noncompartmental Versus Compartmental
Population Analyses
Advantages Disadvantages
– Easy and quick to perform – Requires rich sampling
Noncompartmental Analysis – No special software is needed – Makes assumptions regarding
– Robust and easily reproducible linearity
– Can be performed with rich or – Requires experienced analyst
sparse data – Time-consuming and labour
– Can be performed using data from intensive
Compartmental Population Analysis heterogeneous sources or special – Software is not user-friendly
populations
– Can deal with both linearity and
nonlinearity
844 Chapter 25
relationships between clearance, volume of distribu-
tion, and rate constants between the noncompart-
mental and compartmental approaches.
A
SELECTION OF PHARMACOKINETIC
B
MODELS
C
Many factors should be considered when using
mathematical models to study rate processes (eg,
pharmacokinetics of a drug). Ultimately, the type of
model that is used will depend on the questions that Time
need to be answered, as well as the nature of the data FIGURE 2511 Plasma drug concentration profiles due
available. Indeed, adequate experimental design and to distribution and metabolic process. (See text for description
the availability of valid data are important consider- of A, B, and C.)
ations in model selection and testing. For example,
the experimental design should determine whether a nonlinear metabolism. Finally, a combination of A
drug is being eliminated by saturable (dose-dependent) and C may approximate a rough overall linear decline
or simple linear kinetics. A plot of metabolic rate (curve B). Notice that the drug concentration–time
versus drug concentration can be used to determine profile is shared by many different processes and that
dose dependence, as in Fig. 25-10. the goodness-of-fit is not an adequate criterion for
Metabolic rate can be measured at various drug adopting a model. For example, concluding linear
concentrations using an in vitro system (see Chapter 12). metabolism based only on curve B would be incor-
In Fig. 25-10, curve B, saturation occurs at higher rect. Contrary to common belief, complex models
drug concentration. tend to mask opposing variables that must be isolated
For illustration, consider the drug concentra- and tested through better experimental designs. In
tion–time profile for a drug given by IV bolus. The this case, a constant infusion until steady-state exper-
combined metabolic and distribution processes may iment would yield information on saturation without
result in profiles like those in Fig. 25-11. the influence of initial drug distribution.
Curve A represents a slow initial decline due The use of pharmacokinetic models has been
to saturation and a faster terminal decline as drug critically reviewed by Rescigno and Beck (1987) and
concentration decreases. Curve C represents a domi- by Riggs (1963). These authors emphasize the dif-
nating distributive phase masking the effect of ference between model building and simulation. A
model is a secondary system designed to test the
primary system (real and unknown). The assump-
tions in a model must be realistic and consistent with
A
physical observations. On the other hand, a simula-
tion may emulate the phenomenon without resem-
bling the true physical process. A simulation without
B
identifiable support of the physical system does little
to aid understanding of the basic mechanism. The
computation has only hypothetical meaning.
Drug concentration Frequently Asked Questions
»»Why is statistical moment used in pharmacokinetics?
FIGURE 2510 Metabolic rate versus drug concentra-
tion. Drug A follows first-order pharmacokinetics, whereas drug »»Why is MRT used in pharmacokinetics? How is MRT
B follows nonlinear pharmacokinetics and saturation occurs at related to the total volume of distribution (Vss)?
higher drug concentrations.
Metabolic rate
Log concentration
Empirical Models, Mechanistic Models, Statistical Moments, and Noncompartmental Analysis 845
CHAPTER SUMMARY
Various types of models can be used to describe PK subjects. Model-dependent pharmacokinetic param-
data. These include empirical, data-driven models eters can thus be determined with different
such as allometric scaling. The latter is used to pre- approaches. Pharmacokinetic parameters can also be
dict pharmacokinetic parameter values for humans determined using noncompartmental analyses based
based on animal data. Another model category is the on statistical moment theory. MRT (mean residence
mechanistic one, in which models aim to include as time) is a statistical approach that treats drug mole-
much information as possible about the system that cules as individual units that move through organ
surrounds the data being studied. Physiologically and body spaces according to kinetic principles, and
based PK models are mechanistic models that use a allows independent development of many equations
system of differential equations to describe drug that are familiar to classical kineticists. MRT allows
transfer and accumulation in various tissues or the determination of the time for mean residence of
organs in the body. Published data in the physiology the molecules (eg, dose administered) in the body
literature regarding size (mass) of organs and blood according to the route of administration. The vari-
flow to each organ and body mass are used. ance of the residence time can also be determined
Compartmental models are also mechanistic models using statistical moment theory based on probability
that use a system of differential equations to describe density function. The MRT approach allows another
drug disposition. In contrast with PBPK models, way of computing the volume of distribution of a
molecular processes are not specifically modeled; drug through the derived equations. While the non-
thus a compartment does not usually represent one compartmental approach does not make any assump-
specific actual organ or tissue. Because they do not tions regarding a compartmental model, this
include physiological data (organ size, blood flow, approach is not without its own assumptions (linear
etc), compartmental models can be applied to sparse PK, elimination, and sampling from the same
data obtained from individual subjects or groups of compartment).
LEARNING QUESTIONS
1. After an intravenous bolus dose (500 mg) of is found to be 0.25 h–1, MRT may be calcu-
an antibiotic, plasma–time concentration data lated compartmentally simply as 1/k. What
were collected and the area under the curve different assumptions are used in here versus
was computed to be 25 mg/L·h. The area under Question 1?
the first moment-versus-time curve was found 3. What are the principal considerations in inter-
to be 100 mg/L·h2. species scaling?
a. What is the mean residence time of this drug? 4. What are the key considerations in fit-
b. What is the clearance of this drug? ting plasma drug data to a pharmacokinetic
c. What is the total volume of distribution of model?
this drug? 5. What assumptions must hold true in order to
2. If the data in Question 1 are fit to a one- conduct noncompartmental analyses?
compartment model with an elimination k that
846 Chapter 25
ANSWERS
Frequently Asked Questions Why do we assume that drug concentrations in venous
and arterial blood are the same in pharmacokinetics?
How can we tell if we are using the right model to
describe our data? • After an IV bolus drug injection, a drug is diluted
rapidly in the venous pool. The venous blood is oxy-
• In reality, there is no “right model” because dif- genated in the lung and becomes arterial blood. The
ferent combinations of pharmacokinetic parameter arterial blood containing the diluted drug then per-
estimates can often describe the same set of data fuses all the body organs through the systemic circu-
using a given model. There can be a model that is lation. Some drug diffuses into the tissue and others
superior to another according to predefined crite- are eliminated. In cycling through the body, the blood
ria, but it is not necessarily the “right” model. The leaving a tissue (venous) generally has a lower drug
most appropriate model also depends on the objec- concentration than the perfusing blood (arterial). In
tives of the modeling exercise, as well as the nature practice, only venous blood is sampled and assayed.
of the data that were collected. Drug concentration in the venous blood rapidly equil-
Are certain algorithms better than others? ibrates with the tissue and will become arterial blood
in the next perfusion cycle (seconds later) through the
• Each algorithm has its strengths and weaknesses, body. In pharmacokinetics, the drug concentration is
and depending on the nature of the data being fitted, assumed to decline smoothly and continuously. The
some algorithms may present certain advantages difference in drug concentration between arterial and
over others. For example, some of the algorithms venous blood reflects drug uptake by the tissue, and
that employ linearization may converge more this difference may have important consequences in
quickly than those that perform no linearization; drug therapy, such as tumor treatment.
therefore, results could possibly be obtained more
quickly. Why should transporters be considered in physiolog-
ical models?
When should individual compartmental analysis be
used rather than population analysis? • Drug transporters play important roles in the pro-
cesses of absorption, distribution, and excretion, and
• Besides being used when data are only available if they are not considered in physiological models,
from one subject, individual compartmental analysis the models may not be as accurate as they should be.
can be used to perform naïve pooled data analysis
Why is statistical moment used in pharmacokinetics?
with data from a larger population. For example,
data from a group of subjects can be pooled together • Statistical moment is adaptable to mean residence
such that a mean concentration–time profile is cre- time calculation and is widely used in pharmaco-
ated from this group. The mean profile can then kinetics because of its simplicity and robustness.
be fitted using a compartmental PK model, and the
Why is MRT used in pharmacokinetics?
results can be used as initial estimates to perform
population PK analyses if desired. • Mean residence time (MRT) represents the aver-
age staying time of the drug in a body organ or
Why are differential equations used to describe
compartment as the molecules diffuse in and out.
physiologic models?
MRT is an alternative concept used to describe how
• Differential equations are used to describe the rate long a drug stays in the body. The main advantage
of drug transfer between different tissues and the of MRT is that it is based on probability and is
blood. Differential equations have the advantage consistent with how drug molecules behave in the
of being very adaptable to computer simulation physical world. Concentration in a heterogeneous
without a lot of mathematical manipulations. region of the body may be hard to pinpoint.
Empirical Models, Mechanistic Models, Statistical Moments, and Noncompartmental Analysis 847
How is MRT related to the total volume of distribu- 2. MRT = 1/0.25 = 4 hours. In this case, the one-
tion (Vss)? compartment model must be assumed.
• 3. The principal considerations are size, drug-
The Vss can be determined from MRT according to
protein binding, and maximum life span poten-
the following equation: Vss = Cl × MRT, using data
tial of the species.
obtained following single-dose, intravenous drug
4. The objectives of the modeling must always be
administration.
kept in mind, and the simplest model that best
Learning Questions explains the data should always be retained.
1. a. MRT = AUMC/AUC = 100/25 = 4 hours 5. Linear kinetics are assumed, and it is also
b. Cl = Dose/AUC = 500/25 = 20 L/h assumed that drug loss (elimination) only
c. Vss = Cl × MRT = 20 × 4 = 80 L occurs from the compartment from which
samples are being collected.
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Appendix A: Applications of
Software Packages in
Pharmacokinetics
Philippe Colucci and Murray P. Ducharme
The term “pharmacokinetics” (PK) is relatively young new approaches to data analysis and pharmacokinetic
and was first introduced in 1953 (Wagner 1981). modeling. In addition, computer software is also used
Although some of the concepts associated with phar- for the development of experimental study designs,
macokinetics are much older (eg, Michaelis–Menten statistical data treatment, data manipulation, graphical
equation in 1913, Hill equation in 1908), the study of representation of data, pharmacokinetic model simu-
pharmacokinetics and pharmacodynamics (PD) has lation, and projection or prediction of drug action.
only been popularized over the last 60 years. Since The improvements in computing have allowed
the early conceptions of compartmental PK analysis for the estimation of pharmacokinetic (PK) and phar-
in the 1960s and noncompartmental analysis in the macodynamic (PD) parameters from increasingly
1970s, the studies of PK and/or PD in drug develop- complex PK/PD models. Complex PK/PD and PBPK
ment have advanced rapidly. These advancements are models are being elaborated today, where they would
strongly correlated with the explosion of computers, have been impossible to apply 30 years ago due to the
especially personal computers (PCs). Computer speed slow computation time (months) in order to obtain
and storage capacity have doubled approximately parameters. Consequently, these improvements in
every 2 years over the last 40 years (Keyes 2006). conjunction with improvements in the analytical
Therefore, mathematical computation time has dra- analysis of systemic drug concentrations and the cap-
matically shortened over the same period of time. turing of pharmacodynamic parameters have led to a
The increased speed of computers as well as their much better understanding of the pharmacokinetics
storage capacity has led to the development of numer- and pharmacodynamics of drugs during drug develop-
ous computer software programs that now allow ment. Furthermore, the increased speed of the com-
for the rapid solution of complicated pharmaco kinetic puter’s processors has allowed many more scientists
equations and rapid modeling of pharmaco kinetic the freedom to simultaneously analyze concentration
processes. At its core, a software program is a set of data (PK) as well as response data (PD) on their per-
instructions written in a computer language. The com- sonal computers, as most PCs are fast enough to run
puter’s operating system must support the computer PK software packages compared to 30 years ago
language of the software in order for this software to when these PK software packages were often installed
function properly. Accordingly, some software may on dedicated PK computers or mainframes.
only work in a Windows-based operating system (OS)
while others may have been designed to work in
Windows, Apple OS, or Linux. It is important to know COMPARTMENTAL AND
the software requirements in order to properly choose NONCOMPARTMENTAL ANALYSES
the software that is most appropriate for the computer
that will run the software packages. In order for the user to decide which PK software
These software programs simplify tedious calcu- package to use, it is important for the user to under-
lations and allow more time for the development of stand which type of analysis is required. Not all
851
852 Appendix A
computer programs satisfy all of the user’s full It can be used after single dose or steady-state condi-
requirements. Therefore, the choice of a software tions, and can explain and characterize all different
package will depend on the objective of the analysis routes of administration. Compartmental analyses
and the PK methodology required. try to explain observed concentrations, whether they
There are three main PK and PK/PD analysis are PK or PD in nature, or whether they are support-
methodologies. These are the noncompartmental, the ing the data as in the case of clinical covariates.
individual compartmental, and the population com- Compartmental analyses use compartment models
partmental approaches. that have both a mathematical and a statistical basis,
As the name implies, the noncompartmental and for this the use of specialized PK software pack-
approach does not need the specification of the num- ages is mandatory.
ber of compartments or exponentials that character- There are two main methodological approaches
ize the shape of the concentration-versus-time curve. to compartmental analyses, individual or population
This method is described in Chapters 7 and 25. This based. With individual PK analysis, a model is writ-
methodology became popular in the early 1980s and ten to explain the observed concentrations in an
is based on the theory of statistical moments, which individual. The model minimizes the error between
is a mathematical concept explaining the distribution the predicted and observed concentrations to provide
of data (Gibaldi et al, 2007; Riegelman et al, 1980; PK parameters that best explain the observed data of
Yamaoka et al, 1978). This methodology requires the individual. As we have seen in Chapter 25, phar-
many concentration samples over a period of time macokinetic models often use nonlinear equations
per patient in order to correctly estimate the PK that often have no definite numerical solutions.
parameters (Gabrielsson et al, 2012). The method Models are therefore often written mathematically
utilizes simple analyses that require very little com- with differential equations, and these have to be
puter power if any. In most cases, a simple spread- solved by the software algorithms. With individual
sheet such as EXCEL® can be used to calculate all of compartmental analysis, the data from one individ-
the required PK parameters associated with this ual is analyzed without any influence from the data
analysis. Nevertheless many scientists will still use a collected from other individuals who may be in the
dedicated software program to perform this type of same study. Multiple functions/algorithms have been
analysis. One reason is that the management of the proposed to best minimize the error between the
input data as well as the output tables and profiles is observed and predicted concentrations or the “least
simplified, especially if numerous subjects/patients squares.” Most softwares give the user the opportu-
are analyzed. Another reason can be that some nity to utilize ordinary least squares, weighted least
parameters are more tedious to calculate, such as squares, maximum likelihood, and/or Bayesian
calculating the concentration at time 0 for a bolus methods. The Bayesian method requires prior infor-
administration or determining the optimal elimina- mation on the parameters being predicted or fitted.
tion rate constant (Kel) for all subjects. Furthermore, As the model does not attempt to determine the
the use of programs can allow the user to perform population PK parameters but just the individual’s
curve stripping in a simple manner. An example of a PK parameters, this type of analysis is relatively
popular program to perform noncompartmental quick to perform, although much longer than the
analysis is Certara Phoenix WinNonlin®. noncompartmental analysis.
The compartmental approach can be considered An example of a Microsoft Excel worksheet to
the classical PK approach, although it started in time generate time–concentration data after n doses of a
more as an individual graphical stripping technique drug given orally according to a one-compartment
than a true compartmental method due to the absence model is given in Fig. A-1. The parameter inputs are
of computing power and the availability of semilog in column B, time is in column D, and concentration
graph paper. The compartmental approach is still the is in column E.
gold standard since it can be used for any types of drugs, The population compartmental approach involves
whether they exhibit linear or nonlinear characteristics. the “simultaneous” analysis of data from all individuals.
Applications of Software Packages in Pharmacokinetics 853
A B C D E F
1 D 100000 0 0.00
2 KA 2 0.1 1.78
3 K 0.4 0.2 3.16
4 V 10000 0.3 4.23
5 TAU 4 0.4 5.04
6 F 1 0.5 5.64
7 N 1 0.6 6.07
8 EXP(-KA∗TAU) 0.000335463 0.7 6.36
9 EXP(-K∗TAU) 0.201896518 0.8 6.55
10 FKAD 200000 0.9 6.65
11 V(K-KA) −16000 1 6.69
12 AA 1 1.1 6.67
13 BB 1 1.2 6.60
14 1.3 6.5
15 FD/VK 25 AUC 1.4 6.38
16 1.5 6.24
17 FD/V… 8.86435343 Cmax-ss 1.6 6.08
18 1.7 5.92
19 1.8 5.74
20 TMAX 1.0058987 tmax-1 1.9 5.57
21 2 5.39
22 2.1 5.21
23 TMAX-SS 0.86516026 tmax-ss 2.2 5.03
24 2.3 4.86
25 2.4 4.68
26 2.5 4.51
27 2.6 4.35
28 2.7 4.19
29 2.8 4.03
30 2.9 3.88
31 3 3.73
32 3.1 3.59
33 3.2 3.45
34 3.3 3.32
35 3.4 3.19
36 3.5 3.07
37 3.6 2.95
38 3.7 2.84
39 3.8 2.73
40 3.9 2.62
41 tmin 4 2.52 Cmin
42 PARAMETER PARAM. Value PARAM-TERM TIME (hrs) CONC (mcg/mL)
FIGURE A-1 Example of a Microsoft Excel spreadsheet used to calculate time–concentration data according to an oral one-
compartment model after n doses.
854 Appendix A
This analysis has been shown to be vastly superior best describes the data statistically: Typi-
to the individual compartmental analysis in terms of cally, a least-squares program is employed, in
robustness and is therefore the preferred approach which the sum of squared differences between
when performing compartmental analyses nowa- observed data points and theoretic prediction is
days, now that computing power is no more a limit- minimized. Usually, a mathematical procedure
ing factor. Contrary to individual compartmental is used iteratively (repetitively) to achieve a
analyses where PK parameters are estimated for minimum in the sum of squares (convergence).
each individual, population compartmental analyses Some data may allow easier convergence with
estimate the typical average PK parameters for the one procedure rather than another. The math-
population, along with their interindividual vari- ematical method employed should be reviewed
ability, as well as the overall residual variability, before use.
which includes the intraindividual variability. It is 2. Fitting data into a pharmacokinetic or phar-
these population parameter estimates (PK parameters macodynamic model defined by the user: This
and variability parameters) that allow inferences to method is by far the most useful, because any
be made for other populations, as well as provide the list of prepared models is often limited. This is
possibility to perform simulations of expected con- where much progress has been made over the
centration–time profiles under different conditions last 20 years. The increased speed and storage
(eg, different dosing regimens, different subpopula- with computers including PCs have allowed
tions such as renally impaired patients). Numerous new algorithms and new software packages
algorithms have been proposed to perform popula- to be developed or updated that provide the
tion compartmental analysis. These include paramet- user with more than the one or two alternative
ric and nonparametric approaches. softwares/algorithms that were previously the
Numerous methods and software packages exist only available. The flexibility of user-defined
to perform population PK analyses. Scientists should models allows continuous refinement of models
possess the skills and experience to perform com- as new experimental information becomes
partmental analyses, as it is easy to make an error available. This is synonymous with the “Learn
and there are many steps involved in performing this and Confirm” approach established by Sheiner
type of analysis. Many have proposed this to be an (1997). Some software merely provides a util-
“art,” not just a “science,” as intuition, experience, ity program for fitting the data to a series of
and collaborative brainstorming sessions are all an polynomials. This utility program provides a
essential part of a successful analysis. simple, quantitative way of relating the vari-
The reader is referred to Chapters 7 and 25 for ables, but offers little insight into the underly-
additional details regarding noncompartmental and ing pharmacokinetic processes.
compartmental approaches. For more in-depth 3. Simulation: Some software programs generate
explanations and techniques regarding population data based on a model with parameter input by
compartmental analyses and the “art” of modeling, the user. When the parameters are varied, new
the fabulous book by Bonate is essential reading data are generated based on the model chosen.
(Bonate, 2011). The user is able to observe how the simulated
model data matches the experimental observed
data. Another purpose for simulations is to
SOFTWARE USES allow the user to answer hypothetical questions.
Using simulations, numerous different clinical
Computer programs allow the user to perform one or
trials can be simulated to determine the impact
more of the following analyses:
of modifying certain clinical characteristics.
1. Fitting drug concentration–time data to a series For example, simulations could determine
of built-in pharmacokinetic models provided the predicted concentration profiles in renally
by the software, and choosing the one that impaired patients versus normal subjects.
Applications of Software Packages in Pharmacokinetics 855
This could be done for hundreds of different Some software packages are free while others
scenarios, whereas it would be impossible in are commercially available at a cost. The quality of
reality to dose all these studies to obtain such the software does not necessarily correlate with its
information. price tag, though, and it is important to research the
4. Experimental design: To estimate the param- program’s specifications to ensure it will fit the
eters of any model, the experimental design needs of the scientist. Some programs may be free
of the study must have points appropriately but they may require additional programs in order to
spaced to allow curve description and model- work or compile PK and PD models (eg, Fortran
ing. Although statisticians stress the need for compilers), or to perform even basic graphical rela-
proper experimental design, little information tionships or summary analyses.
is generally available for experimental design It is also important to note that all software
in pharmacokinetics when a study is performed packages should be validated for proper installation
for the first time. For the first pharmacokinetic in order to ensure the accuracy of the results.
study, an empirical or a statistical experiment Software used for data analyses that depend on sta-
design is necessarily based on assumptions tistical and pharmacokinetic calculations should be
that may later prove to be wrong. However, for validated with respect to the accuracy, quality, integ-
subsequent studies, certain software packages rity, and security of the data. One approach for deter-
allow the user to optimize the sampling scheme mining the accuracy of the data analysis is to
for upcoming studies to maximize the utility of compare the results obtained from two different
the data collected. software packages using the same set of data
5. Clinical pharmacokinetic applications: Some (Heatherington et al, 1998). Because software pack-
software programs are available for the clinical ages may have different functionalities, different
monitoring of narrow-therapeutic-index drugs results (eg, pharmacokinetic parameter estimates)
(ie, critical-dose drugs) such as the amino- may be obtained. Some PK software packages pro-
glycosides, other antibiotics, theophylline, vide built-in template studies (and results) that can
phenytoin, cyclosporine, tacrolimus, lithium, be compared with results from the same model
or others. These programs may include cal- obtained by the user to ensure the accuracy of the
culations for creatinine clearance using the installation.
Cockcroft–Gault method or other equations Table A-1 and the following text list some of the
(see Chapter 21), dosage estimation, pharmaco- popular PK softwares available. Listing of a soft-
kinetic parameter estimation for the individual ware package within this text does not mean that it
patient, and pharmacokinetic simulations. has been endorsed by the authors. The descriptions
6. Computer programs for teaching: Software may not represent the latest versions as features are
applications for teaching have been reviewed often added or improved. The user should contact
by Charles and Duffull (2001). the program vendors directly for more information.
The software packages are listed in alphabetical
order without regard to personal preferences or
SOFTWARE PACKAGES ranking.
No PK software package is perfect and each soft-
ware package will have advantages and disadvan- ADAPT 5
tages that can favor the use of different packages at Since 1985, ADAPT-II followed by ADAPT 5 has
different times or for specific situations. Thus, been developed and supported by the Biomedical
before deciding on a software, it is imperative to Simulations Resource (BMSR) in the Department
understand the objectives of the PK analyses, the of Biomedical Engineering at the University of
available data, and past experiences of users with Southern California, under support from the National
certain software packages. Institute for Biomedical Imaging and Bioengineering
TABLE A-1 List of Popular PK Software Packages
Version Approximate
Software Reviewed Analysis Type Operating System Price∗ URL
ADAPT 5® 5.0.048 Individual compartmental; Windows Free (requires http://bmsr.usc.edu/software/adapt/
population compartmental; Fortran)
optimal sampling scheme
Bear (to be used with R) 2.6.3 Noncompartmental Windows Free http://pkpd.kmu.edu.tw/bear/
Berkeley Madonna® 8.3.18 Population compartmental Windows; Apple $ http://www.berkeleymadonna.com/
GastroPlus® SimCYP® 8.5 Simulation package Windows $$$$$$ http://www.simulations-plus.com
/Products.aspx?pID=11
Kinetica® 5 Noncompartmental; Windows $$$ http://www.adeptscience.co.uk
individual compartmental; /products/lab/kinetica
population compartmental
Monolix® 4.3.1 Population compartmental Windows; Linux $$ http://www.lixoft.eu/
NLINMIX (used with SAS) NA Population compartmental SAS Macro Free (requires SAS) http://support.sas.com/kb/25/032
.html#pur
NONMEM® 7.3.0 Individual compartmental, Windows; Linux; $$$$ http://www.iconplc.com/technology
population compartmental Apple Solaris /products/nonmem/
Phoenix NLME® 1.2 Population PK/PD Windows (Start-up $$$$$) http://www.certara.com/products
then $$$$ yearly /pkpd/phx-nlme
Phoenix WinNonlin® 6.3 Noncompartmental; indi- Windows (Start-up $$$$$) http://www.certara.com/products
vidual compartmental then $$$ yearly /pkpd/phx-wnl
Pmetrics® (to be used 1.2 Individual compartmental; Windows; Apple Free http://www.lapk.org/pmetrics.php
with R) population compartmental
PK-Sim® 5.2.1 Individual compartmental; Windows $$$$$ http://www.systems-biology.com
population compartmental /products/pk-sim.html
PK Solution® 2 Noncompartmental Windows; Linux; $ http://www.summitpk.com
Apple /pksolutions/pksolutions.htm
Scientist/PK Analyst® 3.0 Curve stripping Windows $ http://www.micromath.com/
∗ $ ≤1000$; $$>1000$ and ≤2.5k; $$$ >2.5k and ≤5k; $$$$ >5k and ≤10k; $$$$$ >10k and ≤20k; $$$$$$>20k.
856
Applications of Software Packages in Pharmacokinetics 857
and the National Center for Research Resources of intervals for the ratio of the test to reference products
the National Institutes of Health (NIH). With support for common pivotal BE parameters such as AUC0-t,
from the NIH, ADAPT 5 is a software package that AUC0-inf, and Cmax. One limitation of this software is
has been tested, upgraded, and well published over that data must be obtained according to a typical
the last 30 years. ADAPT 5 is a free computational study design established by Bear, and entered in a
modeling platform (requires user to have a valid very specific manner; otherwise, the software cannot
Fortran 95 compiler) developed for pharmacokinetic perform the necessary calculations.
and pharmacodynamic applications. It is intended
for basic and advanced clinical research and is Berkeley Madonna
designed to facilitate the discovery, exploration, and
Berkeley Madonna is a commercially available gen-
application of the underlying pharmacokinetic and
eral purpose differential equation solver for con-
pharmacodynamic properties of drugs. ADAPT 5
structing mathematical models developed on the
has been developed under the direction of David Z.
Berkeley campus under the sponsorship of the NSF
D’Argenio in collaboration with Alan Schumitzky
(National Science Foundation) and the NIH. It has a
and Xiaoning Wang (D’Argenio et al, 2009). It
relatively user-friendly graphical interface that
allows the user to choose from numerous algorithms
allows the user to modify the model by modifying a
both for individual and for population compartmen-
diagram. The software’s powerful algorithms allow
tal analyses such as weighted least squares, maxi-
for quick convergence and it has been used exten-
mum likelihood (ML), generalized least squares
sively in the development of multicompartment
(GLS), maximum a posteriori Bayesian estimation
models such as physiologically based pharmacoki-
(MAP), maximum likelihood estimation via the EM
netic models (PBPK) (Amrite et al, 2008). It also
algorithm with sampling (MLEM), iterative two-
allows for easy simulations of profiles at steady state
stage (ITS), standard two-stage (STS), and naive-
and can determine the impact when the value for
pooled data (NPD) modeling, each with WLS, ML,
one parameter is modified. Although this software
and MAP estimators. Other features include a simu-
package has been widely used in other fields, in
lation module (SIM) that includes capabilities for
pharmacometrics it is mostly used to find prelimi-
single and multisubject Monte Carlo simulations and
nary results (priors), which are then used in another
an optimal sample schedule design module
software package.
(SAMPLE) that provides the ability to calculate D-
and C-optimal samples. The SAMPLE module
allows the user to determine the minimum number of GastroPlus, SimCYP
sparse samples that should be taken in a future study GastroPlus and SimCYP are mechanistically based
as well as the optimal timing of these samples. simulation software programs that can predict the
rate and extent of drug exposure for drugs adminis-
tered via intravenous, oral, ocular, intranasal, and
Bear pulmonary routes in human and preclinical species.
This software is an example of a software package The underlying model within these softwares is the
written to work with R (see description of the R Advanced Compartmental Absorption and Transit
software). It stands for BE/BA for R. It is a free (ACAT) model. Features include a variety of dosage
package created by Hsin-ya Lee and Yung-jin Lee. It forms: intravenous (bolus or infusion), immediate
is designed to analyze average bioequivalence (ABE) release (tablet, capsule, suspension, solution, lingual
data from a study using noncompartmental PK analy- spray, and sublingual tablet) and controlled release
sis (NCA) with an analysis of variance (crossover, (gastric retention, dispersed release, integral tablet,
replicated crossover, parallel designs for single- or enteric-coated tablet and capsule, and buccal patch),
multiple-dose studies). Typical noncompartmental and in vitro–in vivo correlation for immediate- or
PK parameters for a bioequivalence study can be controlled-release formulations. It allows the user
estimated with the calculation of 90% confidence to perform in vitro–in vivo extrapolation (IVIVE).
858 Appendix A
These software packages have gained in popularity coupled with Monte Carlo and Markov Chains
with scientists who develop new drugs, who use them (MCMC) for maximum likelihood estimation.
to predict the expected PK parameter values in humans.
Nlinmix (SAS)
Kinetica SAS is an all-purpose data analysis system with
a flexible application-development language. Over
Kinetica, from Thermo Scientific, allows users to
5000 SAS products are reported to be available
perform a range of analyses, from noncompart-
including various “PROC” (subroutines) available
mental analysis to population pharmacokinetic–
for statistical as well as general linear and nonlinear
pharmacodynamic analyses. This software also has
regression models. One such subroutine is the
built-in templates for use with noncompartmental
NLINMIX macro to fit nonlinear mixed models. It
and PK and PD compartmental analyses. Kinetica
uses PROC NLIN and PROC MIXED and can only
has a graphical interface that facilitates data analy-
be used with SAS version 8 or higher. This subrou-
sis, reporting, and file storage. For its population
tine uses a Taylor series expansion point to deter-
compartmental analysis, Kinetica incorporates the
mine the fixed and random parameters specified in
EM algorithm that was originally in P-Pharm.
the model. When set to zero, this analysis is similar,
Kinetica has a visual model designer that allows
but not identical, to Sheiner and Beal’s first-order
the user to create a model without having to write
method (Beal and Sheiner, 1982) in NONMEM. The
their own code; a model that is created graphically
analysis can also be estimated by expanding the non-
is converted by the software into the basic code
linear function about random effects parameters set
that represents the visual model. Although a vari-
equal to their current empirical best linear unbiased
ety of analyses can be performed with this soft-
predictor (EBLUP), which is Lindstrom and Bates’
ware, it is not very user friendly.
approximate second-order method (Lindstrom et al,
1990). Although the subroutine is freely accessible,
Monolix the user requires SAS, which is not free. This limits
its popular usage and most modeling scientists turn
Monolix (MOdèles Non LInéaires à effets miXtes) is
to other software programs.
a software package that was developed based on
research in statistics and modeling, led by INRIA
(Institut National de la Recherche en Informatique et Nonmem
Automatique). Monolix is free of charge for academics, NONMEM (Nonlinear Mixed Effects Model), devel-
students, and regulatory agencies, but charges a yearly oped originally by S. L. Beal and L. B. Sheiner and
license fee for commercial uses. Like ADAPTs, the NONMEM Project Group at the University of
Monolix has been supported by an agency helping with California, is a program used for estimating parame-
its development, testing, and use. Although it has not ters in population PK/PD. It was one of the first PK/PD
existed for as long as ADAPT, publications with modeling software and is considered by many scien-
Monolix are becoming more prevalent. This software tists as the gold standard for population compartmental
allows users to apply nonlinear mixed-effect models for PK and PK/PD analyses. The program first appeared
advanced population analysis, PK/PD, and preclinical in 1979 and numerous papers featuring NONMEM
and clinical trial modeling and simulation. Monolix is have been published since then. NONMEM versions
based on the Matlab scientific environment; however, a up through VI are the property of the Regents of
stand-alone version is available, and therefore, Matlab the University of California, but ICON Development
does not need to be purchased. This package has Solutions has exclusive rights to license their use.
numerous built-in and compiled PK and PD models. NONMEM 7 up to the current version 7.3 have been
The primary algorithm utilized by this software is the updated by ICON (Beal et al, 1989–2009). In addition
Stochastic Approximation of EM (SAEM) algorithm to its basic applications in population PK and/or PD
Applications of Software Packages in Pharmacokinetics 859
analysis, NONMEM is useful for evaluating relation- from those associated with NONMEM and can pro-
ships between pharmacokinetic parameters and demo- vide different results. Scientists can construct their
graphic data (often referred as covariates) such as age, models by selecting through a wide library of mod-
weight, and disease state. els, or by coding them graphically and/or manually.
Different algorithms are available in NONMEM This software is also relatively user-friendly com-
to perform population compartmental analyses. pared to some other programs available. Although
With version 7, ITS, and Monte Carlo expectation- the software contains some interesting features, its
maximization and Markov Chain Monte Carlo cost is prohibitive, which is why many scientists
Bayesian methods have been added to the classical continue to rely on software packages such as
likelihood methods available in previous versions. NONMEM and ADAPT 5, which arguably continue
These included first-order (FO) estimation method, to be academic and industry standards.
first-order conditional estimation (FOCE), and
Laplace conditional estimation algorithms. NONMEM Pmetrics
can be used to simulate data as well as fit data.
Pmetrics is a free software package developed by the
NONMEM requires Fortran; however, NONMEM
Laboratory of Applied Pharmacokinetics at the
works also with free Fortran programs that can easily
University of Southern California to be used within
be downloaded over the Internet.
R. Contrary to most other compartmental PK soft-
Phoenix WinNonlin and NLME ware packages discussed in this chapter, this pro-
gram provides a nonparametric approach to
These software packages are available from Certara.
determine PK and PD parameters. The available
Phoenix WinNonlin provides a relatively easy-to-use
algorithms include the ITS Bayesian parametric
interface for data management, plotting, noncompart-
population PK modeling (IT2B), nonparametric
mental analysis including bioequivalence testing, as
adaptive grid (NPAG), and a semi-parametric Monte
well as individual compartmental PK/PD analysis. It
Carlo simulator. IT2B is generally used to obtain
can handle large numbers of subjects or profiles.
initial parameter range estimates to be used with
WinNonlin’s input and output data may be managed
NPAG and assumes a normal or transformed to nor-
via Excel (Microsoft)-compatible spreadsheet files.
mal distribution of the PK parameters. NPAG creates
WinNonlin is a powerful least-squares program for
a nonparametric population model consisting of
parameter estimation. Both a user-defined model and a
discrete support points, each with a set of estimates
library of over 20 compartmental models are available
for all parameters in the model plus an associated
to be used for analysis. The program accepts both dif-
probability (weight) of that set of estimates. Pmetrics
ferential and regular (analytical) equations. Users may
was previously known as USC Pack from Roger
select the Hartley-modified or Levenberg-type Gauss–
Jelliffe and has been around for decades.
Newton algorithm or the (Nelder and Mead) simplex
algorithm for minimizing the sum of squared residu-
als. Compartmental models, curve fitting, and simula- PK-Sim
tions are specially designed for pharmacokinetics. PK-Sim is a comprehensive software tool for PBPK
Phoenix NLME replaced WinNonMix and is a modeling. It allows access to relevant anatomical and
software package for population PK and PK/PD physiological parameters for humans and the most
analyses. Phoenix NLME includes a wide set of common laboratory animals (mouse, rat, minipig,
optimization engines for nonlinear mixed-effects dog, and monkey) that are contained in an integrated
modeling, including a new EM (expectation maximi- database. Further, it provides access to different
zation) method (QRPEM). Other algorithms include PBPK calculation methods to allow model building
FO, extended least-squares FOCEI, Lindstron–Bates and parameterization. PK-Sim uses both relevant
FOCE, naive-pooled, ITS, and nonparametric algo- generic passive processes automatically provided
rithm. The FO and FOCE algorithms are different (eg, distribution through the blood flow) and specific
860 Appendix A
active processes (eg, metabolization by a certain Scientist/PKAnalyst
enzyme) that are specified by the user. PK-Sim is Scientist is specifically designed to fit model equa-
designed for use by nonmodeling experts and only tions to experimental data. Scientist is a general
allows minor structural model modifications to be mathematical modeling application that can perform
made. However, more experienced modellers can use nonlinear least-squares minimization and simula-
MoBi, which allows the user full access to all model tion. Scientist can fit almost any mathematical model
details including the option for extensive model from the simplest linear functions to complex sys-
modifications. tems of differential equations, nonlinear algebraic
equations, or models expressed as Laplace trans-
PK Solutions forms. A statistics menu is available for AUC, Cmax,
PK Solutions is an automated Excel-based pro- tmax, and mean residence time parameter calcula-
gram that provides noncompartmental single- and tions. However, the program does not handle differ-
multiple-dose pharmacokinetic data analysis of ential equations or user-defined models. Plot outputs
concentration-time data following intravenous or are available, as are pharmacokinetic curve strip-
extravascular routes of administration. The pro- ping, and least-squares parameter optimization.
gram provides comprehensive tables of the most PKAnalyst for Windows is designed to simulate
widely used and published pharmacokinetic and perform parameter estimation for pharmacoki-
parameters (up to 75 parameters can be obtained) netic models. Built-in models can calculate micro
and graphs. Multiple dose and steady-state param- rate constants for compartmental models, analyze
eters are automatically projected from single-dose saturable (Michaelis–Menten) kinetics, handle bolus
results using exponential terms (no modeling or and zero-/first-order input for finite and infinite time
differential equations are involved). This allows periods, and produce concentration/effect Sigmoid-
easy determination of steady-state profiles when Emax diagrams, including parameter estimation and
certain dosing parameters are changed such as statistical data analysis.
changing the dosing interval. The last version was released in 2005. Therefore,
no changes have been made or supported since then.
Other software packages exist that are more recent
R
and more flexible.
R (http://www.r-project.org/) is a language and envi-
ronment within which statistical computing and
graphics are implemented. R is available as free SPECIALIZED THERAPEUTIC DRUG
software under the terms of the Free Software MONITORING SOFTWARE
Foundation’s GNU General Public License in source
code form. It compiles and runs on a wide variety of Therapeutic drug monitoring (TDM) is the practice
platforms such as UNIX, Linux, Windows, and of taking some blood concentrations from an indi-
Apple OS. R is not a PK software per se but provides vidual in order to optimize the dosing for that
a wide variety of statistical (linear and nonlinear individual to ensure that the concentrations of a nar-
modeling, classical statistical tests, time-series anal- row therapeutic drug remain within a safe and effica-
ysis, classification, clustering, etc) and graphical cious range. Only limited, sparse samples (one or two)
techniques for data handling and model analysis. It are taken at strategic times. With these limited sam-
originated in Bell Laboratories and is now main- ples and the patient’s characteristics, a Bayesian
tained as a nonprofit software by a private founda- analysis is performed to predict the expected con-
tion. It is highly applicable to PK applications. The centration profile. Many software packages are
commercially available S language is often the available with built-in models for the most common
vehicle of choice for research in statistical methodol- narrow therapeutic drugs that are clinically adminis-
ogy, and R provides an open source route to partici- tered. A thorough review of these available software
pation in that activity. packages is provided by Fuchs et al (2013).
Applications of Software Packages in Pharmacokinetics 861
EXAMPLE 1 • • • EXAMPLE 2 • • •
From a series of time–concentration data (Fig. A-2, Generate some data for a two-compartment model
columns A and B), determine the elimination rate using two differential equations. Initial conditions
constant using the regression feature of MS Excel. are dose = 1, V = 1, k12 = 0.2, k21 = 1, and k = 3.
Solution Solution
a. Type in the time and concentration data The data may be generated with ADAPT 5 (Fig. A-3).
shown in columns A and B (see Fig. A-2).
b. Convert in column C all concentration data
to ln concentration. Data point #1 may EXAMPLE 3 • • •
be omitted because ln of zero cannot be
determined. After a drug is administered orally, plasma drug
c. From the main menu, select Insert: concentration–time data may be fitted to a one- or
Select function two-compartment model, to estimate the absorp-
SLOPE tion rate constant, elimination rate constant, and
Y data range (select last 4 value) volume of distribution. Based on the results of
X data range (select last 4 value) these models, it is possible to determine which
model best explains the results using the minimum
The slope, given in Fig. A-2, is –0.1. In this case,
objective function (MOF). Results from NONMEM
the ln concentration is plotted versus time, and the
(one-, two-compartment models) are shown in
slope is simply the elimination rate constant.
Fig A-4A and A-4B. In this case, the plasma concen-
Note: To check this result, students may be
trations were better fitted using a two-compartment
interested in simulating the data with dose =
model than a one-compartment model. The MOF
10,000 μg/kg, VD = 1000 mL/kg, ka = 0.8 h–1, and
was significantly lower with the two-compartment
k = 0.1 h–1.
model versus a one-compartment model.
A B C
1 Time (hrs) Conc Ln (Conc)
2 0 0
3 2 7049.53 8.86
4 4 7194.95 8.88
5 6 6178.08 8.73
6 8 5116.2 8.54
7 10 4200.5 8.34
8 12 3441.45 8.14 Slope −0.1
9 14 2818.09 7.94
10 16 2307.36 7.74
FIGURE A-2 Example of a Microsoft Excel spreadsheet used to calculate time–concentration data according to an oral
one-compartment model after n doses.
862 Appendix A
ADAPT 5 SIM — MODEL SIMULATION
Enter file name for storing session run (∗.run): Run1.run
—– MODEL INPUT INFORMATION —–
Data file name (∗.dat): C:pt1.csv
∗∗ This is a population data file: C:pt1.csv
Will analyze 1st subject
The number of model inputs: 0
The number of bolus inputs: 1
Enter the compartment number for each bolus input (e.g. 1,3,…): 1
The number of input event times: 1
Input Event Information
Time Value for all Inputs
Event Units, B(1)
1. 0.000 1.000
—– MODEL OUTPUT INFORMATION —–
The number of model output equations: 2
The number of observations: 15
—– SIMULATION SELECTION —–
The following simulation options are available:
1. Individual simulation
2. Individual simulation with output error
3. Population simulation
4. Population simulation with output error
Enter option number: 1
—– ENTER PARAMETER INFORMATION —–
Parameter file name: C:Priors1.prm
Enter values for indicated parameters:
Parameter Old Value New Value (<Enter> if no change)
k 3.000
k12 .2000
k21 1.000
Vc 1.000
Vp 1.000
Enter Initial Conditions:
Parameter Old Value New Value (<Enter> if no change)
IC( 1) 0.000
IC( 2) 0.000
—– RESULTS —–
— A. Parameter Summary —
Individual simulation
Parameter Value
k 3.000
k12 0.2000
k21 1.000
Vc 1.000
Vp 1.000
IC( 1) 0.000
IC( 2) 0.000
FIGURE A-3 A sample of the ADAPT 5 application program used to solve the two-differential equation for a two-compartment
model after IV bolus dose. (The first 15 data points are shown. Time is in hours.)
Applications of Software Packages in Pharmacokinetics 863
— B. Simulation Summary —
Model: 2-cpt model; example 2
Individual simulation
Obs.Num. Time Y(1), … ,Y( 2)
1 0.000 0.000 0.000
2 0.1700E-01 0.9471 0.3281E-02
3 0.3300E-01 0.8999 0.6160E-02
4 0.5000E-01 0.8524 0.9008E-02
5 0.6700E-01 0.8074 0.1165E-01
6 0.8300E-01 0.7673 0.1397E-01
7 0.1000 0.7269 0.1625E-01
8 0.1170 0.6887 0.1836E-01
9 0.1330 0.6547 0.2020E-01
10 0.1500 0.6203 0.2201E-01
11 0.1670 0.5879 0.2367E-01
12 1.000 0.5076E-01 0.3067E-01
13 2.000 0.7278E-02 0.1346E-01
14 3.000 0.2433E-02 0.5446E-02
15 4.000 0.9586E-03 0.2188E-02
FIGURE A-3 (Continued )
$PROBLEM Run1; Book Chapter 1CPT Oral plasma
$INPUT ID, TIME, RATE, DOSE=AMT, DV, EVID, MDV
$DATA NM1.CSV
$SUBROUTINES ADVAN2 TRANS2
$PK
ALAG1 = THETA(1)∗EXP(ETA(1))
KA = THETA(2)∗EXP(ETA(2))
CL = THETA(3)∗EXP(ETA(3))
V = THETA(4)∗EXP(ETA(4))
SC = V
K10 = CL/V
HALF=LOG(2)/K10
$THETA
(0 0.3 ) ; ALAG
(0 10 ) ; KA
(0 1 ) ; CL
(0 4 ) ; VC
$OMEGA 0.05 ; ALAG
0.05 ; KA
0.05 ; CL
0.05 ; VC
$ERROR
IPRED = F
IF(F.GT.0)THEN
W = F
FIGURE A-4A Sample output from NONMEM showing oral data fitted to (ADVAN 2, TRANS2) a one-compartment model with
first-order absorption and first-order elimination.
864 Appendix A
ELSE
W = 1
END IF
IRES = DV – IPRED
IWRES = IRES/W
Y = F + F∗EPS(1) + EPS(2)
$SIGMA 0.05 0.05
$ESTIMATION METHOD=1 NOABORT SIGDIGITS=3 MAXEVAL=9999 PRINT=0 POSTHOC
NM-TRAN MESSAGES
WARNINGS AND ERRORS (IF ANY) FOR PROBLEM 1
(WARNING 2) NM-TRAN INFERS THAT THE DATA ARE POPULATION.
CREATING MUMODEL ROUTINE…
PROBLEM NO.: 1
Run1; Book Chapter 1CPT Oral plasma
0DATA CHECKOUT RUN: NO
DATA SET LOCATED ON UNIT NO.: 2
THIS UNIT TO BE REWOUND: NO
NO. OF DATA RECS IN DATA SET: 378
NO. OF DATA ITEMS IN DATA SET: 7
ID DATA ITEM IS DATA ITEM NO.: 1
DEP VARIABLE IS DATA ITEM NO.: 5
MDV DATA ITEM IS DATA ITEM NO.: 7
0INDICES PASSED TO SUBROUTINE PRED:
6 2 4 3 0 0 0 0 0 0 0
0LABELS FOR DATA ITEMS:
ID TIME RATE DOSE DV EVID MDV
0FORMAT FOR DATA:
(7E7.0)
TOT. NO. OF OBS RECS: 340
TOT. NO. OF INDIVIDUALS: 18
0LENGTH OF THETA: 4
0DEFAULT THETA BOUNDARY TEST OMITTED: NO
0OMEGA HAS SIMPLE DIAGONAL FORM WITH DIMENSION: 4
0DEFAULT OMEGA BOUNDARY TEST OMITTED: NO
0SIGMA HAS SIMPLE DIAGONAL FORM WITH DIMENSION: 2
0DEFAULT SIGMA BOUNDARY TEST OMITTED: NO
0INITIAL ESTIMATE OF THETA:
LOWER BOUND INITIAL EST UPPER BOUND
0.0000E+00 0.3000E+00 0.1000E+07
0.0000E+00 0.1000E+02 0.1000E+07
0.0000E+00 0.1000E+01 0.1000E+07
0.0000E+00 0.4000E+01 0.1000E+07
0INITIAL ESTIMATE OF OMEGA:
0.5000E-01
0.0000E+00 0.5000E-01
0.0000E+00 0.0000E+00 0.5000E-01
0.0000E+00 0.0000E+00 0.0000E+00 0.5000E-01
FIGURE A-4A (Continued )
Applications of Software Packages in Pharmacokinetics 865
0INITIAL ESTIMATE OF SIGMA:
0.5000E-01
0.0000E+00 0.5000E-01
0ESTIMATION STEP OMITTED: NO
CONDITIONAL ESTIMATES USED: YES
CENTERED ETA: NO
EPS-ETA INTERACTION: NO
LAPLACIAN OBJ. FUNC.: NO
NO. OF FUNCT. EVALS. ALLOWED: 9999
NO. OF SIG. FIGURES REQUIRED: 3
INTERMEDIATE PRINTOUT: NO
ESTIMATE OUTPUT TO MSF: NO
ABORT WITH PRED EXIT CODE 1: NO
IND. OBJ. FUNC. VALUES SORTED: NO
THE FOLLOWING LABELS ARE EQUIVALENT
PRED=NPRED
RES=NRES
WRES=NWRES
1DOUBLE PRECISION PREDPP VERSION 7.2.0
ONE COMPARTMENT MODEL WITH FIRST-ORDER ABSORPTION (ADVAN2)
0MAXIMUM NO. OF BASIC PK PARAMETERS: 3
0BASIC PK PARAMETERS (AFTER TRANSLATION):
ELIMINATION RATE (K) IS BASIC PK PARAMETER NO.: 1
ABSORPTION RATE (KA) IS BASIC PK PARAMETER NO.: 3
TRANSLATOR WILL CONVERT PARAMETERS
CLEARANCE (CL) AND VOLUME (V) TO K (TRANS2)
0COMPARTMENT ATTRIBUTES
COMPT. NO. FUNCTION INITIAL ON/OFF DOSE DEFAULT DEFAULT
STATUS ALLOWED ALLOWED FOR DOSE FOR OBS.
1 DEPOT OFF YES YES YES NO
2 CENTRAL ON NO YES NO YES
3 OUTPUT OFF YES NO NO NO
1
ADDITIONAL PK PARAMETERS – ASSIGNMENT OF ROWS IN GG
COMPT. NO. INDICES
SCALE BIOAVAIL. ZERO-ORDER ZERO-ORDER ABSORB
FRACTION RATE DURATION LAG
1 ∗ ∗ ∗ ∗ 4
2 5 ∗ ∗ ∗ ∗
3 ∗ – – – –
– PARAMETER IS NOT ALLOWED FOR THIS MODEL
∗ PARAMETER IS NOT SUPPLIED BY PK SUBROUTINE;
WILL DEFAULT TO ONE IF APPLICABLE
0DATA ITEM INDICES USED BY PRED ARE:
EVENT ID DATA ITEM IS DATA ITEM NO.: 6
TIME DATA ITEM IS DATA ITEM NO.: 2
DOSE AMOUNT DATA ITEM IS DATA ITEM NO.: 4
DOSE RATE DATA ITEM IS DATA ITEM NO.: 3
0PK SUBROUTINE CALLED WITH EVERY EVENT RECORD.
PK SUBROUTINE NOT CALLED AT NONEVENT (ADDITIONAL OR LAGGED) DOSE TIMES.
0ERROR SUBROUTINE CALLED WITH EVERY EVENT RECORD.
1
FIGURE A-4A (Continued )
866 Appendix A
#TBLN: 1
#METH: First Order Conditional Estimation
#TERM:
0MINIMIZATION SUCCESSFUL
NO. OF FUNCTION EVALUATIONS USED: 359
NO. OF SIG. DIGITS IN FINAL EST.: 3.4
0PARAMETER ESTIMATE IS NEAR ITS BOUNDARY
THIS MUST BE ADDRESSED BEFORE THE COVARIANCE STEP CAN BE IMPLEMENTED
ETABAR IS THE ARITHMETIC MEAN OF THE ETA-ESTIMATES,
AND THE P-VALUE IS GIVEN FOR THE NULL HYPOTHESIS THAT THE TRUE MEAN IS 0.
ETABAR: -2.4682E-06 1.3091E-06 -9.0175E-03 1.6093E-03
SE: 9.5606E-06 5.0353E-06 3.3000E-02 1.8596E-02
P VAL.: 7.9628E-01 7.9487E-01 7.8465E-01 9.3104E-01
ETAshrink(%): 9.8133E+01 9.9017E+01 -2.1777E-01 7.8698E+00
EPSshrink(%): 5.9519E+00 4.7599E+00
#TERE:
Elapsed estimation time in seconds: 1.68
1
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ FIRST ORDER CONDITIONAL ESTIMATION
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
#OBJT:∗∗∗∗∗∗∗∗∗∗∗∗∗∗ MINIMUM VALUE OF OBJECTIVE FUNCTION
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
#OBJV:∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ 1497.827 ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
1
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ FIRST ORDER CONDITIONAL ESTIMATION
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ FINAL PARAMETER ESTIMATE
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
FIGURE A-4A (Continued )
Applications of Software Packages in Pharmacokinetics 867
THETA – VECTOR OF FIXED EFFECTS PARAMETERS ∗∗∗∗∗∗∗∗∗
TH 1 TH 2 TH 3 TH 4
3.36E-01 5.56E+00 1.28E+00 4.30E+00
OMEGA – COV MATRIX FOR RANDOM EFFECTS – ETAS ∗∗∗∗∗∗∗∗
ETA1 ETA2 ETA3 ETA4
ETA1
+ 5.00E-06
ETA2
+ 0.00E+00 5.00E-06
ETA3
+ 0.00E+00 0.00E+00 2.07E-02
ETA4
+ 0.00E+00 0.00E+00 0.00E+00 7.76E-03
SIGMA – COV MATRIX FOR RANDOM EFFECTS – EPSILONS ∗∗∗∗
EPS1 EPS2
EPS1
+ 1.13E-02
EPS2
+ 0.00E+00 1.80E+00
1
OMEGA – CORR MATRIX FOR RANDOM EFFECTS – ETAS ∗∗∗∗∗∗∗
ETA1 ETA2 ETA3 ETA4
ETA1
+ 2.24E-03
ETA2
+ 0.00E+00 2.24E-03
ETA3
+ 0.00E+00 0.00E+00 1.44E-01
FIGURE A-4A (Continued )
868 Appendix A
ETA4
+ 0.00E+00 0.00E+00 0.00E+00 8.81E-02
SIGMA – CORR MATRIX FOR RANDOM EFFECTS – EPSILONS ∗∗∗
EPS1 EPS2
EPS1
+ 1.06E-01
EPS2
+ 0.00E+00 1.34E+00
FIGURE A-4A (Continued )
$PROBLEM Run1; Book Chapter 2CPT Oral plasma
$INPUT ID, TIME, RATE, DOSE=AMT, DV, EVID, MDV
$DATA NM1.CSV
$SUBROUTINES ADVAN4 TRANS4
$PK
ALAG1 = THETA(1)∗EXP(ETA(1))
KA = THETA(2)∗EXP(ETA(2))
CL = THETA(3)∗EXP(ETA(3))
V2 = THETA(4)∗EXP(ETA(4))
Q = THETA(5)∗EXP(ETA(5))
V3 = THETA(6)∗EXP(ETA(6))
SC = V2
K12 = Q/V2
K21 = Q/V3
K10 = CL/V2
C1 = K12 + K21 + K10
C2 = K21∗K10
Lambda = 0.5∗(C1 – SQRT(C1∗C1 – 4∗C2))
HALF=LOG(2)/Lambda
$THETA
(0 0.3 ) ; ALAG
(0 10 ) ; KA
(0 1 ) ; CL
(0 4 ) ; VC
(0 0.2 ) ; CLD
(0 5 ) ; VP
FIGURE A-4B Sample output from NONMEM showing oral data fitted to (ADVAN 4, TRANS4), a two-compartment model with
first-order absorption and first-order elimination.
Applications of Software Packages in Pharmacokinetics 869
$OMEGA 0.05 ; ALAG
0.05 ; KA
0.05 ; CL
0.05 ; VC
0.05 ; CLD
0.05 ; VP
$ERROR
IPRED = F
IF(F.GT.0)THEN
W = F
ELSE
W = 1
END IF
IRES = DV – IPRED
IWRES = IRES/W
Y = F + F∗EPS(1) + EPS(2)
$SIGMA 0.05 0.05
$ESTIMATION METHOD=1 NOABORT SIGDIGITS=3 MAXEVAL=9999 PRINT=0 POSTHOC
NM-TRAN MESSAGES
WARNINGS AND ERRORS (IF ANY) FOR PROBLEM 1
(WARNING 2) NM-TRAN INFERS THAT THE DATA ARE POPULATION.
CREATING MUMODEL ROUTINE…
PROBLEM NO.: 1
Run1; Book Chapter 2CPT Oral plasma
0DATA CHECKOUT RUN: NO
DATA SET LOCATED ON UNIT NO.: 2
THIS UNIT TO BE REWOUND: NO
NO. OF DATA RECS IN DATA SET: 378
NO. OF DATA ITEMS IN DATA SET: 7
ID DATA ITEM IS DATA ITEM NO.: 1
DEP VARIABLE IS DATA ITEM NO.: 5
MDV DATA ITEM IS DATA ITEM NO.: 7
0INDICES PASSED TO SUBROUTINE PRED:
6 2 4 3 0 0 0 0 0 0 0
0LABELS FOR DATA ITEMS:
ID TIME RATE DOSE DV EVID MDV
0FORMAT FOR DATA:
(7E7.0)
TOT. NO. OF OBS RECS: 340
TOT. NO. OF INDIVIDUALS: 18
0LENGTH OF THETA: 6
0DEFAULT THETA BOUNDARY TEST OMITTED: NO
0OMEGA HAS SIMPLE DIAGONAL FORM WITH DIMENSION: 6
0DEFAULT OMEGA BOUNDARY TEST OMITTED: NO
0SIGMA HAS SIMPLE DIAGONAL FORM WITH DIMENSION: 2
FIGURE A-4B (Continued )
870 Appendix A
0DEFAULT SIGMA BOUNDARY TEST OMITTED: NO
0INITIAL ESTIMATE OF THETA:
LOWER BOUND INITIAL EST UPPER BOUND
0.0000E+00 0.3000E+00 0.1000E+07
0.0000E+00 0.1000E+02 0.1000E+07
0.0000E+00 0.1000E+01 0.1000E+07
0.0000E+00 0.4000E+01 0.1000E+07
0.0000E+00 0.2000E+00 0.1000E+07
0.0000E+00 0.5000E+01 0.1000E+07
0INITIAL ESTIMATE OF OMEGA:
0.5000E-01
0.0000E+00 0.5000E-01
0.0000E+00 0.0000E+00 0.5000E-01
0.0000E+00 0.0000E+00 0.0000E+00 0.5000E-01
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.5000E-01
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.5000E-01
0INITIAL ESTIMATE OF SIGMA:
0.5000E-01
0.0000E+00 0.5000E-01
0ESTIMATION STEP OMITTED: NO
CONDITIONAL ESTIMATES USED: YES
CENTERED ETA: NO
EPS-ETA INTERACTION: NO
LAPLACIAN OBJ. FUNC.: NO
NO. OF FUNCT. EVALS. ALLOWED: 9999
NO. OF SIG. FIGURES REQUIRED: 3
INTERMEDIATE PRINTOUT: NO
ESTIMATE OUTPUT TO MSF: NO
ABORT WITH PRED EXIT CODE 1: NO
IND. OBJ. FUNC. VALUES SORTED: NO
THE FOLLOWING LABELS ARE EQUIVALENT
PRED=NPRED
RES=NRES
WRES=NWRES
1DOUBLE PRECISION PREDPP VERSION 7.2.0
TWO COMPARTMENT MODEL WITH FIRST-ORDER ABSORPTION (ADVAN4)
0MAXIMUM NO. OF BASIC PK PARAMETERS: 5
0BASIC PK PARAMETERS (AFTER TRANSLATION):
BASIC PK PARAMETER NO. 1: ELIMINATION RATE (K)
BASIC PK PARAMETER NO. 2: CENTRAL-TO-PERIPH. RATE (K23)
BASIC PK PARAMETER NO. 3: PERIPH.-TO-CENTRAL RATE (K32)
BASIC PK PARAMETER NO. 5: ABSORPTION RATE (KA)
TRANSLATOR WILL CONVERT PARAMETERS
CL, V2, Q, V3 TO K, K23, K32 (TRANS4)
0COMPARTMENT ATTRIBUTES
COMPT. NO. FUNCTION INITIAL ON/OFF DOSE DEFAULT DEFAULT
STATUS ALLOWED ALLOWED FOR DOSE FOR OBS.
1 DEPOT OFF YES YES YES NO
2 CENTRAL ON NO YES NO YES
3 PERIPH. ON NO YES NO NO
4 OUTPUT OFF YES NO NO NO
1
FIGURE A-4B (Continued )
Applications of Software Packages in Pharmacokinetics 871
ADDITIONAL PK PARAMETERS – ASSIGNMENT OF ROWS IN GG
COMPT. NO. INDICES
SCALE BIOAVAIL. ZERO-ORDER ZERO-ORDER ABSORB
FRACTION RATE DURATION LAG
1 ∗ ∗ ∗ ∗ 6
2 7 ∗ ∗ ∗ ∗
3 ∗ ∗ ∗ ∗ ∗
4 ∗ – – – –
– PARAMETER IS NOT ALLOWED FOR THIS MODEL
∗ PARAMETER IS NOT SUPPLIED BY PK SUBROUTINE;
WILL DEFAULT TO ONE IF APPLICABLE
0DATA ITEM INDICES USED BY PRED ARE:
EVENT ID DATA ITEM IS DATA ITEM NO.: 6
TIME DATA ITEM IS DATA ITEM NO.: 2
DOSE AMOUNT DATA ITEM IS DATA ITEM NO.: 4
DOSE RATE DATA ITEM IS DATA ITEM NO.: 3
0PK SUBROUTINE CALLED WITH EVERY EVENT RECORD.
PK SUBROUTINE NOT CALLED AT NONEVENT (ADDITIONAL OR LAGGED) DOSE TIMES.
0ERROR SUBROUTINE CALLED WITH EVERY EVENT RECORD.
1
#TBLN: 1
#METH: First Order Conditional Estimation
#TERM:
0MINIMIZATION SUCCESSFUL
NO. OF FUNCTION EVALUATIONS USED: 462
NO. OF SIG. DIGITS IN FINAL EST.: 3.2
0PARAMETER ESTIMATE IS NEAR ITS BOUNDARY
THIS MUST BE ADDRESSED BEFORE THE COVARIANCE STEP CAN BE IMPLEMENTED
ETABAR IS THE ARITHMETIC MEAN OF THE ETA-ESTIMATES,
AND THE P-VALUE IS GIVEN FOR THE NULL HYPOTHESIS THAT THE TRUE MEAN IS 0.
ETABAR: -1.8435E-06 1.5359E-06 -1.9829E-02 2.6382E-03 1.0060E-06 -6.2575E-07
SE: 8.2275E-06 6.3126E-06 3.7159E-02 1.8238E-02 7.1168E-06 2.5343E-06
P VAL.: 8.2271E-01 8.0777E-01 5.9361E-01 8.8498E-01 8.8758E-01 8.0497E-01
ETAshrink(%): 9.8394E+01 9.8768E+01 -4.3824E-01 7.8343E+00 9.8611E+01 9.9505E+01
EPSshrink(%): 1.6718E+01 4.8067E+00
#TERE:
Elapsed estimation time in seconds: 3.38
1
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ FIRST ORDER CONDITIONAL ESTIMATION
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
FIGURE A-4B (Continued )
872 Appendix A
#OBJT:∗∗∗∗∗∗∗∗∗∗∗∗∗∗ MINIMUM VALUE OF OBJECTIVE FUNCTION
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
#OBJV:∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ 1260.882 ∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
1
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ FIRST ORDER CONDITIONAL ESTIMATION
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ FINAL PARAMETER ESTIMATE
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
THETA – VECTOR OF FIXED EFFECTS PARAMETERS ∗∗∗∗∗∗∗∗∗
TH 1 TH 2 TH 3 TH 4 TH 5 TH 6
3.00E-01 4.25E+00 1.17E+00 4.06E+00 1.60E-01 4.61E+00
OMEGA – COV MATRIX FOR RANDOM EFFECTS – ETAS ∗∗∗∗∗∗∗∗
ETA1 ETA2 ETA3 ETA4 ETA5 ETA6
ETA1
+ 5.00E-06
ETA2
+ 0.00E+00 5.00E-06
ETA3
+ 0.00E+00 0.00E+00 2.61E-02
ETA4
+ 0.00E+00 0.00E+00 0.00E+00 7.46E-03
ETA5
+ 0.00E+00 0.00E+00 0.00E+00 0.00E+00 5.00E-06
ETA6
+ 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 5.00E-06
FIGURE A-4B (Continued )
Applications of Software Packages in Pharmacokinetics 873
SIGMA – COV MATRIX FOR RANDOM EFFECTS – EPSILONS ∗∗∗∗
EPS1 EPS2
EPS1
+ 1.06E-02
EPS2
+ 0.00E+00 2.50E-01
1
OMEGA – CORR MATRIX FOR RANDOM EFFECTS – ETAS ∗∗∗∗∗∗∗
ETA1 ETA2 ETA3 ETA4 ETA5 ETA6
ETA1
+ 2.24E-03
ETA2
+ 0.00E+00 2.24E-03
ETA3
+ 0.00E+00 0.00E+00 1.62E-01
ETA4
+ 0.00E+00 0.00E+00 0.00E+00 8.64E-02
ETA5
+ 0.00E+00 0.00E+00 0.00E+00 0.00E+00 2.24E-03
ETA6
+ 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 2.24E-03
SIGMA – CORR MATRIX FOR RANDOM EFFECTS – EPSILONS ∗∗∗
EPS1 EPS2
EPS1
+ 1.03E-01
EPS2
+ 0.00E+00 5.00E-01
FIGURE A-4B (Continued )
874 Appendix A
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Appendix B: Glossary1
A, B, C Preexponential constants for ANDA Abbreviated New Drug Application;
three-compartment model equation see also NDA
a, b, c Exponents for three-compartment ANOVA Analysis of variance
model equation
API Active pharmaceutical ingredient
a Probability of making a type 1 error
AR Absolute risk
b Probability of making a type 2 error
ARI Absolute risk increase
a, b, g Exponents for three-compartment
AUC Area under the plasma level–time curve
model equation (equivalent to a, b, c
above) [AUC]∞
0 Area under the plasma level–time
curve extrapolated to infinite time
l1, l2, l3 Exponents for three-compartment-
type exponential equation (equivalent [AUC]t0 Area under the plasma level–time
to a, b, c above; more terms may be curve from t = 0 to last measurable
added and indexed numerically with plasma drug concentration at time t
l subscripts for multiexponential
models) AUMC Area under the (first) moment–time
curve
Delta (∆) Delta is sometimes referred to as the
BA Bioavailability
“effect size” and is a measure of the
degree of difference between tested BCS Biopharmaceutics Classification
population samples System
m0 The null hypothesis value for the BDDCS Drug disposition classification system
mean
BE Bioequivalence
ma ma is the alternative hypothesis value
BioRAM Biopharmaceutics Risk Assessment
expected for the mean
Roadmap
c2 Chi-square test
BLA Biologic license application
A or Ab Amount of drug in the body of time t; BM Biomarker
see also DB
BMI Body mass index
Ab∞ Total amount of drug in the body
BRCP Breast cancer-resistance protein
ABC ABC transport protein (an ABC transporter)
ABW Average body weight BUN Blood urea nitrogen
AE Adverse event C Concentration (mass/volume)
ANCOVA Analyses of covariance Ca Drug concentration in arterial plasma
1The FDA maintains a list of acronyms and abbreviations at www.accessdata.fda.gov/scripts/cder/acronyms/index.cfm.
875
876 Appendix B
∞ Average steady-state plasma drug Clint Intrinsic clearance
C
av
concentration
Cl′int Intrinsic clearance (unbound or
Cc or Cp Concentration of drug in the central free drug)
compartment or in plasma
Clnr Nonrenal clearance
Ccr Serum creatinine concentration,
ClR Renal clearance
usually expressed as mg%
CE Clinical endpoint CluR Renal clearance of uremic patient
Ceff Minimum effective drug
ClT Total body clearance
concentration
COX-1 Cyclo-oxygenase-1
CGI Concentration of drug in gastrointestinal
tract CQA Critical quality attribute
CI Confidence interval CMC Chemistry, manufacturing, and control
Cm Metabolite plasma concentration CRF Case report form
Cmax Maximum concentration of drug CRFA Cumulative relative fraction absorbed
C∞
max Maximum steady-state drug Cv Drug concentration in venous plasma
concentration; see also Cssmax
%CV Percent coefficient of variation
Cmin Minimum concentration of drug
CYP Cytochrome P-450
C∞
max Minimum steady-state drug
concentration; see also C D Amount of drug (mass, eg, mg)
ssmin
Cp Concentration of drug in plasma DA Amount of drug absorbed
C 0 DB Amount of drug in body
p Concentration of drug in plasma at
zero time (t = 0) (equivalent to C0) DE Drug eliminated
C∞
p Steady-state plasma drug DGI Amount of drug in gastrointestinal tract
concentration (equivalent to Css) DL Loading (initial) dose
Cp Last measured plasma drug
n Dm Maintenance dose
concentration
DNA Deoxyribonucleic acid
Css Concentration of drug at steady state
DN Normal dose
Cssav Average concentration at steady state
DP Drug in central compartment
Cssmax Maximum concentration at steady
state Dt Amount of drug in tissue
Cssmin Minimum concentration at steady Du Amount of drug in urine
state
D0 Dose of drug
Ct Concentration of drug in tissue
D0 Amount of drug at zero time (t = 0)
cGMP Current Good Manufacturing Practices
E Extraction (extraction ratio)
CKD Chronic kidney disease E Pharmacologic effect
CL Total body clearance; see also ClT E Intercept on y axis of graph relating
ClCr Creatinine clearance pharmacologic response to log drug
concentration
ClD Dialysis clearance
eGFR Estimate of GFR based on an MDRD
Clh Hepatic clearance equation
Glossary 877
Emax Maximum pharmacologic effect kel Excretion rate constant (first order)
E0 Pharmacologic effect at zero drug ke0 Transfer rate constant out of the effect
concentration compartment
EC50 Drug concentration that produces kI Inhibition constant: = k-I/kI+
50% maximum pharmacologic effect
KM Michaelis–Menten constant
ELS Extended least square
km Metabolism rate constant (first order)
EMA European Medicines Agency
k
(http://www.ema.europa.eu/ema/) N Normal elimination rate constant
(first order)
ER Extraction ratio (constant equivalent
to E kN Nonrenal elimination constant of
h) nr
normal patient
F Fraction of dose absorbed
(bioavailability factor) kU
nr Renal elimination constant of uremic
patient
f Fraction of dose remaining in the
body ku Uremic elimination rate constant
(first order)
fe Fraction of drug excreted unchanged
in urine kon First-order association rate constant
fu Unbound fraction of drug koff First-order dissociation constant
FDA US Food and Drug Administration k0 Zero-order absorption rate constant
f(t) Function representing drug elimina- kle Transfer rate constant from the central
tion over time (time is the indepen- to the effect compartment
dent variable)
k21 Transfer rate constant (from the
f ′(t) Derivative of f(t) tissue to the central compartment);
first-order transfer rate constant from
GFR Glomerular filtration rate
compartment 2 to compartment 1
GI Gastrointestinal tract
LBW Lean body weight
GMP Good Manufacturing Practice
m Slope (also slope of E vs log C)
Ho The null hypothesis
Mu Amount of metabolite excreted in urine
H1 The alternative hypothesis
mAbs Monoclonal antibodies
[ I ] [ I ] is the inhibitor concentration in an
MAT Mean absorption time
enzymatic reaction
MDR1 p-Glycoprotein, ABCB1
IBW Ideal body weight
MDRD MDRD equation used to estimate GFR
ICH International Conference on
Harmonisation (http://ich.org/) MDT Mean dissolution time
IVIVC In vitro–in vivo correlation MEC Minimum effective concentration
K Overall drug elimination rate constant miRNA MicroRNA
(k = ke + km); first-order rate constant,
MLP Maximum life-span potential
similar to ke1
MRP Multidrug resistance-associated
Ka Association binding constant
proteins
ka First-order absorption rate constant
MRT Mean residence time
Kd Dissociation binding constant
MRTc Mean residence time from the central
ke Excretion rate constant (first order) compartment
878 Appendix B
MRTp Mean residence time from the Rmax Maximum pharmacologic response
peripheral compartment
RLD Reference-listed drug
MRTt Mean residence time from the tissue
RNA Ribonucleic acid
compartment (same as MRTp)
RNAi RNA interference
MTC Minimum toxic concentration
RRR/RRI Relative risk reductions/increases
m0 Area under the zero moment curve
(same as AUC) SD Standard deviation
m1 Area under the first moment curve SEM Standard error of the mean
(same as AUMC)
SM Starting material
NDA New Drug Application
siRNA Small inhibitory RNA
NNH Numbers-needed-to-harm
SNP Single-nucleotide polymorphism
NONMEN Nonlinear mixed-effect model
t Time (hours or minutes); denotes tissue
NTI Narrow therapeutic index; see also when used as a subscript
critical dose drug
TE Therapeutic equivalent
OTC Over-the-counter drugs
teff Duration of pharmacologic response
OATP Organic anion transporting to drug
polypeptide
tinf Infusion period
OAT Organic anion transporter
tlag Lag time
P Amount of protein
tmax Time of occurrence for maximum
PAT Process analytical technology (peak) drug concentration
PA Pharmaceutical alternative t0 Initial or zero time
PE Pharmaceutical equivalent t1/2 Half-life
PD Pharmacodynamics T Time interval between doses
PEG Polyethylene glycol USP United States Pharmacopeia
P-gp p-Glycoprotein, MDR1, ABCB1 V Volume (L or mL)
PGt Pharmacogenetics V Velocity
PK Pharmacokinetics Vapp Apparent volume of distribution
(binding)
PPI Patient package insert
VC Volume of central compartment
Q Blood flow
VD Volume of distribution
QA Quality assurance
Ve Volume of the effect compartment
QbD Quality by design
Vi Vi and V are the reaction velocity with
QC Quality control
and without inhibitor, respectively
QTPP Quality target product profile
Vmax Maximum metabolic rate
R Infusion rate; ratio of Cmax after n dose
Vp Volume of plasma (central compartment)
to Cmax after one dose (see Chapter 9)
(accumulation ratio); pharmacologic Vt Volume of tissue compartment
response (see Chapter 19)
(VD)exp Extrapolated volume of distribution
r Ratio of mole of drug bound to total
moles of protein (VD)SS or VDSS Steady-state volume of distribution
Index
Page numbers followed by f indicate figures; page numbers followed by t indicate tables.
A in GI tract, 393–394, 393f clinical application, 185, 185f
AAGP. See Alpha-acid double-peak phenomenon, nonlinear elimination with,
glycoprotein 400–401, 401t 244
Abatacept, 669–670, 670f emptying time, 394–395, 395f Absorption data
Abbreviated New Drug food effects on, 396–398, determination of
Application (ANDA), 397t, 398f, 399f with Wagner–Nelson
235f, 471, 529–530, 560 GI motility, 394, 394f, 395t method, 190–191, 191f
bioequivalence studies for, 469, GI perfusion, 396 maximum concentration time,
491, 503, 503t, 504f inhibition of, 712–713 and AUC response to,
bioequivalence study waiver, of lipid-soluble drugs, 451–452 191–195, 192t, 194f
503–504 lubricant effect on, 425, 425f signicance of, 184
NDA compared with, 503, 503t via lymphatic system, 396 Absorption enhancers, 425, 462
review of, 502–503, 505f method for studying, 402–405 Absorption kinetics, 182f
ABC transporters. See ATP- models for estimation of Absorption phase, of plasma
binding cassette CRFA, 195–199 drug concentration-
Abilify. See Aripiprazole Loo–Riegelman method, time curve, 182, 183,
Absence of drug, 663 195–196, 197t 183f–184f
Absolute bioavailability, 339–341, nonlinear elimination with, Absorption rate constants
472–473, 473f 243–244 determination of
Absorption in obesity, 756 elimination rate constant
absorption and elimination particle size and, 421–422 ip-op with, 190,
rate constant effects on pharmacokinetics of, 182–183, 190f
maximum concentration 183f lag time and, 189f, 189t
time to maximum con- polymorphism, solvates, and with method of residuals,
centration, and AUC, drug, 422–423, 422f, 188–189, 188f
193–194, 194f, 194t 423f with modied Wagner–
administration route and, 374, rate constant determination, Nelson method, 195
375t–376t, 376 188–191, 188f, 189f, with two-compartment oral
disintegration compared 190f, 192t, 193t, 196f, absorption data,
with dissolution and, 197f, 197t, 198f, 198t 195–210, 196f, 197t,
418–419, 418f rate of, dissolution rate com- 198f
in drug product design, pared with, 431–440, practice problem, 191–193,
373–374 439f, 440f 193t
in elderly, 703, 737–739 solubility, pH and, 421 Absorption window, 450
first-order, 185–188, 185f, stability, pH and, 421 Absorptive pressure, 262
186f, 187f zero-order, 184–185, 184f Acceptance criteria, 556, 559
879
880 INDEX
Accumulation, 205–209, 206f, with pseudoephedrine, Anhydrous state, 422
207f, 207t, 209t 184–185 Animal studies
clinical example, 209–210 in TDM, 691–692 interspecies scaling in, 819,
in tissues, 264–265 with theophyline, 225 822, 822f
Accumulation half-life, 208–209, viral, 714 valproic acid in pigs, 242–243
209t Adverse effect, 560 ANOVA. See Analysis of variance
Accuracy, 64, 68 Adverse event. See Adverse drug Antacids, 406
Acetaminophen, metabolism of, reaction Antibiotic therapy, probenecid
329 Adverse response, 646 for prolonging duration
Acetylation, 329 Aerosol therapy, 459 of activity, 644
Achlorhydric patients, 405 Afnity, 262, 265, 280 Antibiotics. See also specic
Achromycin V. See Tetracycline Aging. See Elderly drugs
Acids. See Weak acids Alanine aminotransferases (ALT), in elderly, 702–704
Activated charcoal, 801 803 elimination half-life, 135
Active Pharmaceutical Ingredient Albumin, 274–275, 274t, 281, elimination rate constant and,
(ADI) equivalence, 529, 626, 804 87, 134–135
532t, 560 Albuterol, 683 in infants and children, 700
Active targeting, 628 Alendronate sodium (Fosamax®), Anticancer drugs, 113. See also
Active transport, 382, 382f 400 specic drugs
Active tubular secretion, 166–167, Alfentanil, 285–286 Anticholinergic drugs, 406
166t Alkaline phosphatase, 808 Antiepileptic drugs, 450, 538
clearance by, 160 Allegra. See Fexofenadine Antihypertensive drugs. See
ADAPT5 Allergic response, 646–647 specic drugs
SAMPLE module, 857 Allometry, 818 Antilogarithm, 38
simulation module in, 857 Allopurinol, 324 Antimicrobials, PK-PD indices
Adaptive method for dosing with Alpha-acid glycoprotein for, 653t
feedback, 716–717 (AAGP), 274t, 275, Antipsychotic drugs, 445, 450, 538
Adaptive model, 693 277–279, 804 Antisense oligonucleotide drugs,
Additive effect model, 656–658, ALT. See Alanine 623
657f, 658f aminotransferases Apparent volume of distribution.
Adherence, in elderly, 745–746 Alternative testing, 56 See also Clearance and
Adiponectin, 71 Amberline resins, 801–802 volume of distribution
Adipose tissue. See Fat Ambien. See Zolpidem tartrate of aminoglycosides, 217–218
Adjustment. See Dosage Aminoglycosides calculation of, 78–79, 78f
adjustment dialysis removal of, 800 clearance relationship with,
Administration route. See also in elderly, 703–704 156, 170, 170t
specic routes elimination rate constant elimination half-life relation-
absorption and, 374–375, and apparent volume ship with, 170, 170t
375t–376t of distribution of, IV infusion for determination
determination of, 697–700, 217–218 of, 131, 132f
700t renal dose adjustment for, 800 in multicompartment models,
ADR. See Adverse drug reaction Aminophylline, 695 111–112
Adrenal tissue, 261f, 263–264, Aminotransferases, 808 in noncompartmental models,
263f Amobarbital, 276 84
Adverse drug reaction (ADR) Amorphous forms, 422 in one-compartment open
absorption pharmacokinetics Amphetamine, 162, 265, 330 model, 76, 77–88, 78f,
and, 184–185 Amprenavir (Agenerase), 299–300 80t
in elderly, 744–745 Analysis of variance (ANOVA), in physiologic drug distribution
with lidocaine, 122–123 60–62, 498 model, 267–273, 269t
nonlinear pharmacokinetics ANDA. See Abbreviated New calculation of, 267–270,
causing, 247 Drug Application 268f, 269t
INDEX 881
in complex biological partial bioequivalencce and, comparison of Bayes, least-
systems, 270–272, 272f 498–400, 499f squares, steady-state,
practice problem, 270 examples of, 499–500 and Chiou methods,
protein binding of drugs and, of plasma drug concentration 719–720, 719t, 720t
276–277, 277f curve, 131, 132f, Beads, 586–588
clinical example, 270 498–499, 499f Bear software, 857
effect of changing plasma Area under the rst moment Bell-shaped curve. See Normal
protein, 277–279 curve (AUIMC), 836, distribution
electrolyte balance effects, 837, 838 Benzodiazepines, 285
281 Area, volume of distribution by, Benzpyrene, 332
practice problem, 279–280, 109–110 Berkeley Madonna software, 857
280t Aripiprazole (Abilify), 809 Beta phase. See Elimination phase
significance of, 79–80, 80t Arterial drug concentrations, 301 Beta-adrenergic receptors
at steady state, 272, 273f Articial membrane in elderly, 743–744
in two-compartment model, permeability, 404–405 Bias, 65–66
100–105, 101f Asacol. See Mesalamine Biexponential proles, 103, 121,
central compartment Aspartate aminotransferase (AST), 121f
volume, 107–109 803 Biliary clearance, 347
extrapolated volume, Aspirin, 409 Biliary ducts, 323f
109–110 absorption of, 398, 399f Biliary excretion, 346–347, 347f
practical focus, 113–114 dissolution rate compared with biliary clearance estimation,
practice problem, 110–111, absorption rate of, 424 347–348
111f enteric coated, 570 clinical example, 348
signicance of, 111–112 rate of release of, 35, 36f enterohepatic circulation, 348
steady-state volume, 272, Assays, in TDM, 699–689 inhibition of, 713
273f AST. See Aspartate significance of, 308
tissue compartment volume, aminotransferase (AST) Bilirubin, 673, 808
112–113 ATP-binding cassette (ABC), Bimodal distribution, 52–53
volume by area, 109–110 384, 384t, 387t Binding. See Protein binding of
Approved Drug Products AUC. See Area under the curve drugs
with Therapeutic Augmentin (amoxicillin–clavulinic allosteric, 291
Equivalence acid), 644 Binding constants, 286–287
Evaluations (Orange AUIMC. See Area under the rst graphic determination of
Book), 515–516, 515t moment curve in vitro methods, 287–288,
Area under the curve (AUC), 13, Auto-induction, 336 287f, 288f
13f, 28–29, 28f Autoregulation, 159, 159f in vivo methods, 288–290
absorption rate constants Azithromycin (Zithromax), Binding sites, 287–288, 287f
determined with, 119–120, 143, 252–253, drug interactions due to
191–195, 192t, 194f 252t, 280 competition for, 291,
apparent volume of Azo drugs, 325 295
distribution calculated graphic determination of
from, 78–79, 78f B in vitro methods, 287–288,
clearance determined from, 84 Bactrim. See Sulfamethoxazole/ 287f, 288f
elimination and absorption trimethoprim in vivo methods, 288–290
rate constant effects Balsalazide, 374, 374t Bioavailability, 539–540
on, 193–194, 194f, Base. See Weak base absolute, 339–340, 472–473,
194t Bayesian theory, 714–715 473f
in linearity determination, adaptive method for dosing age and, 489
249–250, 250f with feedback, 716–717 blood flow effects on, 340–341
MRT calculations, 837, Bayes estimator, 717–719, drug design considerations,
851f–853f 718f, 718t 448
882 INDEX
Bioavailability (Cont.): clinical endpoints, 476t, 479, study designs
drug products with issue, 480t–481t, 481, 481t, fasting, 490
532t–533t 494–495 food intervention, 490–491
drug–drug interaction effects examples of, 496–497 waivers of, 503–505, 509t
on, 448 clinical examples, 496–497 Bioequivalent drug products, 531
drug–drug interactions, 488 clinical significance, 511–512 Biologic drugs, 535–540, 618
examples of, 341 crossover study designs for, Biologic Price Competition and
factors influencing, 486–489 491–496 Innovation Act, 539
food effects on, 397t, 398, clinical endpoint, 479, Biologic specimen sampling, 11
398f, 467–468 480t–481t, 485, Biological systems, volume of
nonlinear pharmacokinetics 494–495 distribution in, 270–271,
and, 247–248 Latin-square cross over 271f
relative, 473–474 design, 491–492, 492t Biomarkers
transporter role in, 348–349, multiple-dose, 493–494, clinical considerations for,
349f 495f, 497 647–649
Bioavailability studies nonreplicate, parallel, 493 clinical endpoints,
methods for assessing, 475–482, in patients maintained on pharmacodynamics
476t therapeutic regimen, 495 and, 647, 648t
in vitro, 481–482 replicated, 492 pharmacogenomic, 357
in vivo, 475, 490 scaled average, 493 surrogate, 514, 514t
plasma drug concentration, data evaluation, 497–498 Biopharmaceutical Classication
475–477, 476t, 477f ANOVA, 498 System (BCS), 349,
urinary drug excretion data, for NDA, 469–471, 470f 419, 507–509, 509t
476t, 477–478, 477f partial AUC, 499–500 disintegration test for, 418–419,
of MR drug products, 570, pharmacokinetic, 497–498 418f
606–607, 607f purpose of, 471–72 dissolution, 508
MRT, 840 statistical, 497–498 drug products where
MRT and, 840 two one-sided tests bioavailability or
practice problem, new procedure, 497–498 bioequivalence may be
investigational drug, design and evaluation of, self-evident, 508–509
474–475 484–489 permeability, 508
purpose of, 471–472 analytical methods, 490 solubility, 507–508
relative and absolute, 472–475, objectives, 484 Biopharmaceutical Drug
473f RLD, 485 Disposition
special concerns, 512–514, study considerations, Classication System
513t, 514t 484–485, 485t (BDDCS), 508
special considerations in, determination of, 482–484, Biopharmaceuticals, 1–4, 2f, 3t.
512–514, 513t, 514t 495–496 See also Biotechnology
transit time in, 573 examples of, 500–502, 501f, pharmacokinetics of, 630–631,
Biochemical markers, 673 501t, 502f, 502t 635–636
Bioequivalence in vitro, 476t, 481–482 Biopharmaceutics
average, Bear software in vitro approaches, 482 basis of, 2
analysis of, 857 methods for assessing, 475 bioavailabilitiy and, 446–448
bases for determining, 495–496 of MR drug products, 516, 608 dissolution and drug release
issues in, 513t multiple endpoints, 482, 482t, testing, 446–448
multiple-dose, 493–494 483, 483t dissolution profile
pharmaceutical and therapeutic pharmacodynamic endpoints, comparisons, 434–435,
equivalence relationship 478–479, 480t 434f
and, 530–531, 531f possible surrogate markers for, drug design considerations,
Bioequivalence studies, 530, 540 514, 514t 416–418, 420t, 618
for ANDA, 471, 471f, 502–503, special concerns in, 512–514, formulation factors, 423–425,
505t, 506t 513t, 514t 423t, 424t
INDEX 883
of MR drug products, 572–575 Blood ow models. See practice problems, 233–235
large intestine, 574–575 Physiologic CAPD. See Continuous
small intestine transit time, pharmacokinetic models ambulatory peritoneal
573–574 Blood urea nitrogen (BUN), 730 dialysis
stomach, 572–573 Blood–brain barrier, 266 Capillary membranes, 265–266
physicochemical properties, Blood-ow-limited model. See Carprofen, 330
420–421, 420t, 447–448 Perfusion-limited Carrier-mediated GI absorption,
QbD integration with, 551 models 382–386, 382f, 384,
Biopharmaceutics Classication BMI. See Body mass index 384t, 385f
System, 507–509, 509t Body clearance. See Clearance Carriers. See Drug carriers
Biosimilar drug products, 530–540, Body mass index (BMI), Cartesian coordinate, 30, 30f
631–632 705–706, 754–755, 755t Carvedilol, biostatics in
Biosimilarity, interchangeability Bonfessoni correction, 60 interpretation of FDA,
vs., 511, 539 Bovine spongiform 69–70
Biotechnology, 631–632 encephalopathy (BSE), Catenary model, 18, 18f
gene therapy, 619, 622–623 554 CAVH. See Continuous
monoclonal antibodies, Bowman’s capsule, 158 arteriovenous
618–619, 619t, 620f, Brain, 266 hemoltration
621t–622t Brand name, 529 Cefamandole, 91
oligonucleotide drugs, 523 Buffering agents, 452 Cefazolin, 281t
protein drugs, 615, 616t–617t, BUN. See Blood urea nitrogen Cefoperazone, 207, 276–277,
618 Bupropion hydrochloride 281t, 805
Biotransformation, 49. See (Wellbutrin), 222 Cefotaxime, 226
Metabolism Cefotetan, 276, 281t
Biowaiver, 503–505, 506–507 C Cefuroxime, generic vs. brand, 533
Black box approach, 20 Caco-2 cells, 404 Celiac disease, 406
Bleomycin, 452 CAD. See Cyclic antidepressant Cell, drug distribution within,
Blinding, 60 drugs 266
Blood Caffeine, 819, 822, 822f Cell membranes, drug passage
drug concentration Calcium, 406, 452 across
measurement of, 11, 12t Calculus, 27 carrier-mediated transport,
units of expression for, 34 differential, 27 382–386, 382f, 384t,
Blood ow integral, 28–29, 28f 385f
bioavailability relationship with, Capacity-limited elimination, passive diffusion, 378–382,
340–341 233–236, 234f, 235t 379f, 383f
enterohepatic, 348 Capacity-limited metabolism, permeability, 265–266
to GI tract, 396 229–231, 231f, 237f, Central compartment, 98–99,
hepatic and intrinsic clearance 237t 269, 269t
relationships with, Capacity-limited pharmacokinetics, distribution in, 266
345–346 233–236, 234f elimination from, 154
hepatic clearance of clearance in, 241–242, 242f renal clearance in, 154
protein-bound drugs clinical focus, 242–243 volume of distribution in,
relationship with, determination of Michaelis 107–109, 369
342–345, 343f constant and maximum Cephalexin, 406
hepatic, in hepatic disease, 806 elimination rate, Cephalosporins, 276–277, 277f,
to liver, 321, 322f, 323f 236–238, 237f, 237t, 281–282, 281t
in obesity, 757–758 238–240, 238f, 239f anaphylactic reaction to, 66
physiologic drug distribution elimination half-life in, 233–235 hypersensitivity, 646
and, 261–263, 262f, interpretation of Michaelis protein binding of, 277, 281,
263t constant and maximum 281t, 282
renal, 158–159, 159f elimination rate, Cephalothin, 320–321, 321f
to tissues, 99, 100t 240–241, 241f Cerebral spinal uid (CSF), 266
884 INDEX
CFR. See Code of Federal of protein-bound drugs, metabolism inhibition,
Regulations 344–346, 346f 710–712
cGMP. See Current Good variation in, 331t nomograms and tabulations,
Manufacturing IV infusion for determination 694
Controls (CMC) of, 140–141 in obese patient, 705–706
Changes to an Approved NDA or models of partial pharmacokinetic
ANDA, 559 model-independent, 153–154 parameter regimens,
Chemistry, Manufacturing, and physiologic, 153, 153f 694
Controls (CMC), 2, MRT and, 840 pharmacokinetics of,
557, 557t in multicompartment models, 706–707, 708t–709t, 709
Cheng–Prusoff equation, 318 110–111, 111f, 114 population based, 693
CHF. See Congestive heart failure in one-compartment model, practice problem, 696-697
Child-Pugh classication, 806, 80–85 drug assay, 688
806t in one-compartment open elderly dosing, 702–703, 707
Children, dosage determination model, 84, 153–154 clinical example, 704f
in, 700–703, 701t of protein-bound drugs, 283 practice problems, 703–704
Chiou method, 719–720, 720t, in three-compartment model, renal function and, 704–705
729t 114–115, 115f food interactions in, 713–714
Chirality, 535 in two-compartment open individualization of dosage
Chloramphenicol, 422, 422f model, 110–111, 111f regimens, 682
Cholestyramine, 377t, 406 See also Creatinine clearance; MTM, 681
Chronic Kidney Disease Hepatic clearance; pediatric dosing, 700–702, 701t
Epidemiology Renal clearance plasma drug concentration
Collaboration (CKD- Clearance and volume of in response to dose
EPI) equations, 784 distribution ratio, 156 and dosage intervals,
Chronopharmacokinetics, Clindamycin, 696–697 697–698
245–246, 246t Clinical endpoint bioequivalence PopPK in
Circadian rhythms and drug crossover study, 479, adaptive method for dosing
exposure, 246–247 480t–481t, 494–495 with feedback, 715–717
clinical focus, 247 Clinical endpoints, 647, 648t analysis of population
Cimetidine (Tagamet), 332, Clinical pharmacokinetics, 5, 5t pharmacokinetic data,
400–401, 406, 711, 742 administration route 720–722
Ciprooxacin, 247 determination, 699, 700t Bayes estimator, 717–718,
Circadian rhythms, 246, 247 adverse viral interactions in, 714 718f, 718t
Circadian rhythms and drug conversion from IV infusion to clinical example of, 715–716
exposure, 246–247 oral dosing, 694–695 comparison of Bayes, least-
Clearance, 150–152, 152f design of dosage regimens, squares, steady-state,
biliary, 347–348 692–693 and Chiou methods,
dialysis, 799 dose and dosage interval in, 719–720, 719t, 720t
of capacity-limited drug, 698–699 decision analysis involving
241–242, 242f dose determination, 696 diagnostic test, 722–723,
from drug-eliminating tissues, dosing frequency in 698 723t, 724t
83–85 drug interactions in practical focus, 10, 10f
elimination half-life and absorption inhibition, regional pharmacokinetics in,
volume of distribution altered renal 724
relationship with, 170, reabsorption, 706–707, TDM in, 5
170t 707t, 708t, 708t–709t ADRs and, 691–692
intrinsic empirical regimens, 694 clinical example, 690–692
blood ow and hepatic individualized regimens, dosage adjustment in, 689
clearance relationship 693 dosage regimen design for,
with, 342–344 MAO inhibition, 710–712 684–685
in hepatic disease, 806 metabolism induction, 712 drug assay, 688–689
INDEX 885
drug concentration Compliance, 576, 686 Continuous variable, 51
measurement in, Computers, 31–32. See also Continuous veno-venous
686–687, 689 Software hemoltration
drug pharmacokinetics in, Concentration. See also Plasma (CVVH), 802
685 drug concentration Controlled vs. noncontrolled
drug product in, 684 drug response relationship studies, 66
patient compliance, 686 with, 10, 10f Controlled-release drug product,
patient response evaluation, measurement of, 8, 14 568, 569t, 591
686 biologic specimen Convective transport, 388
pharmacokinetic evaluation sampling, 11 Coordinates
in, 689, 690t blood, plasma, or serum rectangular, 30, 30f, 35, 35f
serum drug concentration concentrations, 11–12, semilog, 30, 30f, 688, 723
monitoring in, 689–690 12f, 14–15 Core tablets, 589–590
Clinical toxicology, 11 forensic measurements, 14 Corticosteroids, 407
Clinically signicant differences, plasma drug concentration CPKS. See Clinical
58–59 time curve, 12–15, 12f, pharmacokinetic
Clobazam, 285 13f CPP. See Critical process
Clopidogrel (Plavix), 389, 693 saliva concentration, 13 parameters
Clotrimazole, 458 signicance of, 14–15 Creatinine, 779–780. See also
CMC. See Chemistry, in TDM, 686–687, 687f Serum creatinine
Manufacturing, and tissue concentration, 13–14 concentration
Controls units for expressing, 34 Creatinine clearance, 166
CMVs. See Critical monitoring of, 689–690 dose adjustment based on
manufacturing units of expression in, 33–34, in adults, 781, 782f
variables 34t in children, 781–782, 782f
Cocaine, 118t in urine and feces, 13–14 eGFR measurements for,
Cocaine alkaloid, 645 Concerta. See Methylphenidate 783–784, 783t
Cockcroft–Gault method, 741, Concomitant medicine, in general, 794–795
783, 784, 785 793 elderly, 747–748 GFR measurements for,
Code of Federal Regulations Conditional probability curves, 783–784, 783t–784t
(CFR), 419, 534 716, 716f practice problems, 782–783,
Codeine, 333, 391 Condence interval approach, 782f, 792–794
Coefcient of variation, 54 54–55 in elderly, 705
Colon, 392 See also Two one-sided tests elimination rate constant
Colonic drug delivery, 454 procedure relationship with,
Combination drug products, 644 zero, 55 786–787, 786f
Compartment models, 16–18, Condence intervals, 54, 55 factors affecting, 778–789, 784t
16f, 18f, 823f, 824t, Conformance to specication, 559 in obese patient, 759
882–885 Confounding, 66–67 renal function classification
application of, 827–828 Congestive heart failure, 405 based on, 783t
of bolus IV administration Conjugation reactions. See software calculations for
determination, 97–99, Phase II reactions Cockcroft–Gault or
98f Constant IV infusion, 131, 132f other equations, 855
PK-PF, 827 Continuous ambulatory CRFA. See Cumulative relative
Compartmental Absorption and peritoneal dialysis fraction absorbed
Transit Models, 195 (CAPD), 797 Critical dose drugs. See Narrow
Compartmental pharmacokinetic Continuous arteriovenous therapeutic index drugs
analysis hemoltration Critical manufacturing variables
EXCEL® spreadsheet in, (CAVH), 802 (CMVs), 542, 560
852852. 853f Continuous renal replacement Critical Process Parameters, 442,
Competitive enzyme inhibition, therapy (CRRT), 552
316, 316f 802–803 Critical quality attributes, 441
886 INDEX
Crohn’s disease, 405, 454 parametric vs. nonparametric, Diffusion-limited models, 262,
Cross-sensitivity, 647 51–52 262f, 265
Cross-tolerance, 646 Data analysis Diunisal, 705
Crossover control, 66 for linearity determination, Digestive phase, 573
Crossover study designs for 249–250, 250f, 251t Digit Symbol Substitution Test
bioequivalence Death rates, age-adjusted, 5, 5t (DSST), 662
clinical endpoint, 494–495 Denite integral, 28 Digoxin
Latin-square cross over Delayed release drug products, loading dose, 113–114
designs, 491–492, 568, 569t Digoxin (Lanoxin), 19
491t, 492t DELS. See Difference-extended accumulation of, 264
multiple-dose, 493–494 least-squares affinity of, 780
nonreplicate parallel, 493 Delta effect size, 57 distribution and elimination
in patients maintained on Demeclocycline, 282t half-lives of, 118t
reference, 495 Dental implant, 598 distribution of, 113, 264
replicated, 492 Deoxyribonucleic acid (DNA) drug interactions of, 338
scaled average, 493 delivery of, 622, 630 serum concentration, 691
CSF. See Cerebral spinal uid in drug delivery, 334 TDM of, 690–692
Cumulative relative fraction Depakene. See Valproic acid two-compartment model for
absorbed (CRFA), Dependent variable, 15, 51 distribution of, 105–107,
196–199, 198f, 199f Dermaex, 596 105f, 105t, 106t
Current Good Manufacturing Design space, 441, 552 in uremic patients, 105
Practices (cGMPs), Desipramine, 334 Dihydropyrimidine dehydrogenase,
555, 556t Desolvated solvates, 422 365–366
Curve tting, 30 Dexmedetomidine hydrochloride Dipyridamole, 400, 401
CVVH. See Continuous injection (Precedex®), Direct effect model, 660, 660f
veno-venous 275 Dirithromycin, 282
hemoltration Dextroamphetamine, 588 Discriminating dissolution test,
Cyclic antidepressant drugs Dextromethorphan, 333, 589 433–434
(CAD), 333, 334 Dialysance, 799 Disease states. See specic states
Cyclosporine A, 20, 21f Dialysis, 797–799 absorption in, 405–406
Cylinder method, 427, 431 clinical examples, 800–801 bioavailability in, 489
CYP enzymes, 159 practice problem, 799–800, Disintegration
Cytochrome P-450 (CYP450), 800f, 800t dissolution and absorption
321, 324, 335–336, 362t Dialysis clearance, 799 compared with,
CYP1A2, 357, 362t, 364, 757 Diazepam, 662 418–419, 418f
CYP2C19, 362t, 364–365, 757 Diazepam (Valium) testing of, 418–419, 418f
CYP2C9, 362t, 364, 757 drug interactions of, 711–712 Displacement
CYP2D6, 362t, 363–365, 757 elimination of, 284–285 drug interactions arising from,
CYP2E1, 756–757 protein binding of, 275–276 297–298, 297f
CYP3A4, 365, 756 Diazoxide, 296, 296f protein binding of drugs and,
drug interactions of, 246 Diet. See Food 295–297, 296f, 297t
induction of, 334–335, 334t, Difference-extended least-squares Dissolution, 419
712 (DELS), 722 BCS and, 508
in elderly, 740 Differential calculus, 27 clinical performance and,
in obese patient, 756 Differential equations, 824t 441–442
polymorphisms of, 332, 333t, Diffusion disintegration compared
365 across cell membranes, 378–382, with absorption and,
379f, 381f, 381t 418–419, 418f
D facilitated, 384 excipients and, 424–425, 424t
Dapsone, 405 protein binding and, 280t lubricant effect on, 425, 425t
Data Diffusion cells system, 432, 432f of MR drug products, 571,
ordinal, 52 Diffusion coefcient, 380 571f
INDEX 887
plasma concentration compared drug interaction and, 708t pharmacokinetic
with, 440–441, 440f in elderly, 739 considerations, 775–776
profile comparisons, 434–435, nonlinear elimination serum creatinine
435f combined with, 253 concentration and
rate of, absorption rate in obese patient, 756 creatinine clearance,
compared with, statistical, 52–53 780–785, 782f, 783t,
439–440, 439f, 440f Distribution equilibrium, 98, 784t
serum concentration compared 52–53, 101, 687 in TDM, 689, 697–698
with, 441, 441f Distribution half-life, 107, 118t, in uremic patients, 785–796,
solubility and, 419–420, 419f 262–263 788t–789t, 789f,
Dissolution in a reactive Distribution phase 790t–791t
medium, 424 length of, 120–121, 121f Dosage form
Dissolution test significance of, 122 for MR drug products, 575
apparatus for, 427, 427t, 430f in two-compartment open pharmaceutically equivalent,
development and validation of, model, 101, 108 532t–533t
426–429 Divalproex sodium in TDM, 686
discriminating, 433–434 (Depakote®ER), 581 Dosage interval, 210–211, 210t,
of enteric-coated products, DNA. See Deoxyribonucleic acid 211t
432–433 Dosage determination of, 698
of ER drug products, 571, biopharmaceutic plasma drug concentration
571f, 604, 604f considerations for, 446 response to, 697–698
mechanical calibration for, 433 determination of, 696, 698 Dosage regimen. See also
medium for, 428–429 in elderly, 702–703 Multiple-dosage
meeting requirements for, in infants and children, regimens
436–437 700–702, 701t design of, 684–685
methods for, 427, 429–431 in obese patients, 705–705 empirical regimens, 694
cylinder, 427t, 431 drug design considerations, individualized, 693
diffusion cell, 427t, 432, 432f 448–449, 692–693 nomograms and tabulations
ow-through cell, 427t, 431 duration of activity and in, 694
intrinsic dissolution, 432 elimination half-life population based, 693
paddle, 427t, 429–430, 430f relationships, 644, regimens based on partial
paddle-over disk, 427t, 431 645t, 646f pharmacokinetic
peristalsis, 332 duration of activity parameters, 694
reciprocating cylinder, 427t, relationship with, 643 individualization of, 682–683
430–431 response relationship with, schedules for, 220–223, 221f,
reciprocating disk, 427t, 431 634f–642f, 640–642, 2224t
rotating basket, 427t, 429 643–644 clinical example, 222
rotating bottle, 427t, 431–432 in uremic patient, 776 practice problem, 222–223
for novel/special dosage Dosage adjustment in uremic patient, 786–787, 786f
forms, 433 in elderly, 744 Dose determination, 696
performance verification test, in hepatic disease, 809 Dose-dumping, 576, 603
433 in renal impairment, 776, 777t Dosing frequency, 449, 698
variable control problems in, clearance-based, 778 Dosing in infant studies, 700–703,
437 elimination rate constant- 701t
Distribution, 52–53. See also based, 778–779 Double-peak phenomenon,
Apparent volume extracorporeal removal of 400–401, 400t
of distribution; drugs, 796–803, 798t, Doxorubicin, 266
Physiologic drug 800f, 800t Doxycycline, 282t
distribution general approaches to, 777, Drug accumulation. See
within cells, 266 777t Accumulation
to CNS and blood-brain GFR measurement, 779–780, Drug approval and labeling
barrier, 266 783–784 PK-PD models role in, 671
888 INDEX
Drug carriers Drug in body biopharmaceutics for, 446,
albumin, 626 absorption and, 182–184, 182f 446t, 459t
liposomes, 626–627, 627f for capacity-limited drug after colonic drug delivery, 454
polymeric delivery systems, IV bolus infusion, combination drug/medical
585–586, 588, 600–601, 233–235, 235f device, 417
602t, 625–626, 625f in multiple-dosage regimens, dose considerations for,
protein drugs, 618, 626, 210–212, 211t 448–449
626t–617t in one-compartment open dosing frequency
Drug clearance. See Clearance model, 76, 76f considerations for, 449
Drug concentration. See physiologic drug distribution GI side effects, 452
Concentration and, 259t, 267–273 inhalation drug products,
Drug concentration-time curve, Drug interactions 457–459, 458t
12–13, 12f, 13f in clinical pharmacokinetics IR and MR drug products,
Drug delivery absorption inhibition, 452–453
albumin, 626 712–713 nasal drug products, 457
colonic, 454 altered renal reabsorption oral drugs, 449
floating, 593 due to urinary pH parenteral drugs, 455, 455f
of genes, 622–623 changes, 713 patient considerations in, 449
lipoproteins, 626 biliary excretion inhibition, pharmaceutical equivalence
liposomes, 626–629 713 issues, 532t–533t
oral, 449 food effect on, 713–714 pharmacodynamics for,
osmotic, 590–592, 591f, 592f MAO inhibition, 712 446–447
polymeric systems, 585–586, metabolism induction, 712 pharmacokinetics for, 447–448
588f, 600–601, metabolism inhibition, phases in, 637–639, 637f, 638f
625–626, 625f 710–712 physicochemical
of protein drugs, 615, pharmacokinetics of, considerations for,
616t–617t, 618 706– 707, 708t–709t 420–423, 420t
rectal, 454–455 of CYP450 enzymes, 246, 710 PK-PD information flow in,
targeted in GI tract, 389–390, 390f 637–639
agents for, 629 during hepatic metabolism, rectal and vaginal drug
drugs for, 629 336–338, 337t delivery, 454–455
oral immunization, 629–630 auto-induction and route of administration in,
site-specic carrier, 628–629 time-dependent 449–450, 450f
target site, 628 pharmacokinetics, 336 SUPAC, 460
transdermal, 185, 185f, 316t, clinical example, 338 transdermal products, 459–460
408 enzyme variations, 334 Drug product development
vaginal, 455 genetic variations, 332–333 process, 637–638, 637f
Drug disposition, 4 transporter-based, 336–338, Drug product performance
Drug distribution. See 337t dissolution and, 441–442
Distribution protein binding causing drug product quality and, 418,
Drug effect vs. drug response, competition for 547, 548t
638–639 binding sites, 300–301 excipient effect on, 423–425,
Drug elimination. See displacement, 295–298 423t, 424t
Elimination Drug markers, 808 BSE in gelatin, 554
Drug excretion. See Excretion Drug metabolism. See Metabolism gelatin capsules stability, 554
Drug exposure Drug product design in vitro, 425–426, 426t
Circadian rhythms and, absorption during, 401–402 in vivo, 437–441, 438f, 439f,
246–247 absorption in, 373–374 440f, 441f
drug response and, 10 enhancers, 460 Drug product quality
protein binding and, 298–299 bioavailability for, 448, drug product performance and,
response relationship with, 638 473–474, 486–490, 487t 418, 547, 548t
INDEX 889
Drug products. See also specic Efux transporters, 383f, extrahepatic metabolism,
products 385–386, 489 312–313
bioequivalent, 531 eGFR. See Estimated GFR rst-pass effects, 338–341,
with possible bioavailability Elderly, 702–704 340t, 343f
and bioequivalence adherence in, 745–746 liver anatomy and physiology,
issues, 532t–533t pharmacology in, 746–747 321–323, 322f, 323f
risks from, 545–546, 546f transporters in, 742–743 Michaelis-Menton kinetics
Drug recalls, 555, 558t Electrolyte balance, 281 of, 312–321, 313f,
Drug response. See Response Electronic spreadsheets, 852, 853f 314f, 315f–316f
Drug review process, 502–503, Elimination, 249–250. See also clinical example, 317–318
504t Clearance of protein-bound drugs,
bioequivalence study waiver, biliary excretion, 346–347, 347f 344–346, 346f
502–503, 504t, 509t biliary clearance estimation, transporter role in, 337t,
dissolution profile comparison, 347–348 348–349, 349f
506–507 clinical example, 348 nonlinear, 243–244
Drug selection, 684 enterohepatic circulation, 348 in one-compartment open model
Drug withdrawals, 558 signicance of, 348 as amount per time unit, 81
Drug–drug interactions, 747 biliary excretion, 346–347, 347f as fraction eliminated per
Drug–macromolecule complex, capacity-limited, 233–242, time unit, 81f, 82
273 234f, 235f, 235t, 237f, as volume per time unit,
Drug–protein binding. See Protein 237t, 238f, 241f, 242f 81, 81f
binding of drugs from central compartment, 153 by organs/tissue, 83–84
Drug-specic transporters. See dialysis effects on, 796–803, of protein-bound drugs,
Transporters 800t 281–282, 281t, 282t
Duodenum, 392 enzymatic, 231–232, 232t clinical example, 285–286
Duration of drug action, 13 extrahepatic drug metabolism, restrictive and
dose and elimination half-life 312–313 nonrestrictive, 283–284
effects on, 643, 644f rst-order elimination, volume of distribution
dose relationship with, 643–644 309–310 relationship with,
elimination half-life effect on, fraction of drug excreted 282–283
644, 645f, 645t unchanged, 310–311, properties of, 162t
Dynamic range, 688 311f rate of, 231–232, 232t
fraction of drug metabolized, renal drug excretion, 159–162,
E 310–311, 311f 162t
Early dose administration, 214 practical focus, 311 clinical application, 162–163
Efavirenz, 488 first-order, 41, 41t, 309–310, practice problem, 163
Effect. See Response 426 renal clearance and, 163–167,
Effect compartment hepatic clearance, 311 166f, 166t
pharmacodynamic models, biotransformation pathways, zero-order, 40–41, 43
660–664, 660f 326–331, 327f, 328f, Elimination half-life
PK-PD models with, 660, 328t, 329f, 330t of capacity-limited drug,
664f, 665f biotransformation reactions, 233–235
Effect compartment model, 325–326, 325t, 326t dialysis effects on, 800, 800t
660–662, 662f blood ow and intrinsic distribution half-life
application, 662–663 clearance relationships relationship with, 107,
Effective concentration. See with, 345 117–118, 118f
Minimum effective drug interactions during, dose and duration of activity
concentration 331–338, 333t, 334t, relationships with,
Effective renal plasma ow 335t, 337t 643–644, 644f
(ERPF), 160 enzymes involved in, duration of activity response
Efcacy studies, 10, 602–603 313–317, 315f–316f to, 643–644, 644f, 645t
890 INDEX
Elimination half-life (Cont.): Enterocytes, 382 Excipients. See also Absorption
in infants, 701t Enterohepatic circulation, 348, enhancers
infusion method for calculation 400 bioavailability and
of, 135–136 Enzyme kinetics. See Michaelis– bioequivalence
in multiple-dosage regimens, Menten kinetics problems, 533
209–210, 209t, 210t Enzymes. See also BSE in gelatin, 554
for various drugs, 790t–791t Capacity-limited drug product performance
Elimination phase pharmacokinetics effect of, 423–425,
of plasma drug concentration genetic polymorphs, 362t, 363f 423t, 553–554, 553t
time curve, 183, 183f hepatic drug product performance with
in two-compartment open CYP450 genetic variations, gelatin capsules stability, 554
model, 114 331t, 361 factors with, 423–425, 423t,
clearance and, 110–111, 111f species differences in, 425t, 553–554, 553t
of plasma drug 330–331, 331t qualitative changes to, 561, 561t
concentration-time induction of, 334–335, 335t Excretion, 149. See also Renal
curve, 98, 98f, 100–101 inhibition of drug excretion
Elimination rate constants in drug interactions, 316–317, biliary, 346–347, 347f
absorption rate constant flip- 316f, 334, 334t biliary clearance estimation,
flop with, 190, 190f kinetics in, 315–317, 315f, 347–348
of aminoglycosides, 217–218 316f clinical example, 348
clinical application, 89, 89f kinetics of, 313–321, 313f, enterohepatic circulation,
in noncompartmental model, 79 314f 347f, 348
in one-compartment open model, phase I, 365–366 signicance of, 348
77, 77f, 81–82, 81f phase II, 366–367 Excretion rate method. See Rate
example of, 82 saturation of, 231–233, 232t method
practice problems, 87f, 88–89, ER/MR drug products. See Exocytosis, 387, 388f
88f Extended/modied Exponential functions, 38
in two-compartment open release (EM/MR) Exponents, 38–40
model, 76–77 products Exposure. See Drug exposure
urinary excretion data for Ergometrine, 118t Extended least-squares (ELS)
calculation of, 86–89, ERPF. See Effective renal plasma method, 717, 818–819,
86f, 87f ow 819f, 820t
for various drugs, 788t–789t Error, 65–66 Extended/modied release
ELS. See Extended least-squares Erythrocytes, 276 (EM/MR) products
method dissolution testing of, 372, pharmacokinetic simulation of,
Empirical models, 16, 817 423, 423f 578–580, 579f
Emptying, gastric, 422–423 Erythromycin, 398, 399f, 422f, 423 plasma drug concentration of,
Enantiomers, metabolism of, Erythropoietin, 389 579, 579f
330, 330t Esomeprazole (Nexium), 6, 7t–8t, statistical evaluation of, 608
End-stage renal disease (ESRD) 9t, 389 types of, 581–601
extracorporeal removal of Esophagus, 391 combination products, 597
drugs in, 796, 797 Estimates GFR, 782-785, 783t core tablets, 589–590
protein binding of drugs in, 294t ESRD. See End-stage renal disease drug release from matrix,
Endocytosis, 387, 388f Estraderm, 460 584, 584f
Endoplasmic reticulum, 324 Etoposide, 120–121 gastroretentive system, 593
Endpoints Etretinate, 264 gum-type matrix tablets, 585
clinical, 479, 480t–481t Eulexin. See Flutamide implants and inserts, 593
surrogate, 648, 648t EXCEL® spreadsheet, 852 ion-exchange products, 589
Enteral administration routes, 376t application examples, 861 liposomes, 600t, 699–600
Enteral system, 390 calculation of oral one- microencapsulation, 590
Enteric-coated products, 570 compartment model nanotechnology derived,
dissolution test of, 432–433 dosage, 861f 598–599
INDEX 891
osmotic drug delivery Extracorporeal removal of drugs, concentration, and
system, 590–592, 590f, 796–803 AUC, 185–188,
591t, 592t dialysis, 797–801, 798t 193–194, 193f, 194t
parenteral dosage forms, clinical example, 800–801 nonlinear elimination with, 244
597–598 practice problem, 799–800, rate constant determination
polymeric matrix tables, 800f, 800t elimination rate constant
585–586, 588, 602t hemofiltration, 802–803 ip-op, 190, 190f
prolonged-action tablets, 588 hemoperfusion, 800–801 lag time and, 189, 189f
slow-release pellets, beads, or Extraction ratio, 340, 340t, 345 with method of residuals,
granules, 586–587, 588t Extrahepatic drug metabolism, 188–190, 188f
transdermal drug delivery 309, 312–313 practice problem, 191–192,
system, 593–597, 594t in elderly, 740–741 192t
Extended/modied release first-order elimination, 309–310 with two-compartment
(ER/MR) products, 436, fraction of drug excreted oral absorption data,
436f, 453, 568, 569t unchanged, 310–311, 185–188, 186f, 187f
advantages and disadvantages 311f with urinary data, 193
of, 575–576 fraction of drug metabolized, with Wagner–Nelson
bioavailability study for, 570 310–311, 311f method, 190–191
occupancy time and, 573 practical focus, 311 First-order conditional estimate
pharmacokinetic prole, Extrapolation, 33 (FOCE), 721
606–607 Extrinsic factors, 735 First-order elimination, 39–42,
rate of drug absorption, 607, Extrusion-spheronization, 587 41t, 42f, 309–310
607f First-order half-life, 41–42, 41t,
steady-state plasma drug F 42f
concentration, 607 Facilitated diffusion, 384 First-order process, 41–42, 41t, 42f
bioavailability study of Famotidine, 400 First-pass effects, 338
transit time in, 573 Fasting study, for bioequivalence, absolute bioavailability,
bioequivalence study for, 608 490–491, 500–502, 339–340, 486–489
biopharmaceutic factors of, 501f, 501t, 502f, 502t blood flow, intrinsic clearance,
572–575 Fat and hepatic clearance
large intestine, 574–575 distribution to, 263, 263f relationships, 342–344
small intestine, 573–574 drug absorption and, 410 evidence of, 338–339
stomach, 572–573 FDA. See Food and Drug liver extraction ratio, 339, 340t
clinical efficacy and safety of, Administration Fisher’s exact test, 63
601–602 FDA Modernization Act Fixed model, 693
clinical example of, 580–581 (FDAMA), 700 Flecainide, 333
dissolution rates of, 571, 571f Feces, 13–14 Flip-op, of absorption and
dosage form selection, 575 Felodipine (Plendil), 704, 704f elimination rate
evaluation of, 601 Fenobrate, 456 constant, 190, 190f
clinical considerations, Fentanyl, 453 Floating drug delivery system, 593
605–606 Fexofenadine, 354, 355t, 401, Flow model. See Physiologic
dissolution studies, 571, 571f 387t, 711 pharmacokinetic model
IVIC, 604–605 Fick’s law of diffusion, 33, 252, Flow-dependent metabolism, 323
pharmacodynamic and 379–381 Flow-through-cell method, 427t,
safety considerations, Filtration pressure. See 430
602–603 Hydrostatic pressure Fluconazole, 455
pharmacokinetic studies, 605 First-order absorption, 185–188, Fluid mosaic model, 378
examples of, 570–571 185f, 186f, 187f Fluid-bed coating, 586
generic substitution of, 606 absorption and elimination Flunitrazepam, 285
kinetics of, 577–578 rate constant effects on Fluorouracil (FU), 245, 382
with immediate release maximum concentration Fluoxetine, 334
component, 580 time, time to maximum Flutamide (Eulexin), 264
892 INDEX
Fluvastatin sodium (Lescol®), 342 double-peak phenomenon, Global two-stage approach, 826
Fluvoxamine, 247, 711 400–401, 401t Globulins, 275
FOCE. See First-order conditional emptying time, 402–403 Glomerular ltration, 159–160,
estimate food effects on, 396, 397t, 160t, 758
Food 398–400, 398f–399f clearance by, 165–166, 166t
drug interactions with, 396, GI motility and, 394–396, urine formation and, 159, 160t
397t, 398–400, 398f, 394f Glomerular ltration rate (GFR),
399f, 759 GI perfusion, 396 158–159, 160t
Food and Drug Administration intestinal motility, 396 in elderly, 704–705
(FDA) and, 2 anatomic and physiologic MDRD or CKD-EPI equations
GI absorption and, 396, considerations, for estimation of,
398–300, 398f, 399f 370–373, 390, 390f 783–785
Food and Drug Administration drug interactions in, 389–390, measurement of, 779–780,
(FDA). See also 390f 784–785, 784t
Abbreviated New Drug side effects involving, 452 renal drug excretion and, 309
Application; New Drug GastroPlus software, 179, 181f, Glomerulus, 158
Application 857–858 Glutathione, 329, 330f
bioavailability study guidance, Gastroretentive system, 593 Good Manufacturing Practices
485–486 Gaussian distribution. See (GMPs), 555, 556t
bioequivalence study Normal distribution Goodness of t, 63
guidance, 485–486 Gelatin capsules, 418, 554 Gradumet, 585
generic biologics guidance, 511 Gelatin, BSE in, 554 Granules, 586–587
Food intervention study, 490–491 Gene delivery Grapefruit juice, 334, 335t,
Forensic drug measurements, 14 DNA technology, 622, 630 406–407
Fosamax®. See Alendronate viral, 622, 630 Graphic determination
sodium Gene therapy, 619, 622–623 in vitro methods, 287–288, 287f
Fraction of dose in body, 210–211, General clearance method, in vivo methods, 288–290
211t 794–795 of renal clearance, 168, 168If
Fraction of drug excreted, 169–170 Generic biologics, 510–511 Graphs, 28, 28f, 29–31
Fraction of drug excreted Generic drugs curve fitting, 30, 32, 32f
unchanged, 310–311, bioequivalence studies, 491 fitting patients to, 32–33, 32f
311f physical attributes of, 536–537 practice problems, 31–33
dose adjustment based on, Generic substitution, 531, 606 slope determination, 30,
787, 790t–791t Genetic polymorphism, 329, 32–33, 32f
Fraction of drug metabolized, 332, 358–359 Griseofulvin, 301, 398, 398f,
310–311, 311f CYP450 isozymes, 332–333, 422, 451
Free drug concentration, 284 333t, 361–365, 362t Gum-type matrix tablets, 585
FU. See Fluorouracil in pharmacogenetics,
Furosemide (Lasix), 277, 405 358–359 H
in metabolism, 359, 360t–361t Haldol. See Haloperidol
G of transporters, 360t–361t Half-life. See also Elimination
Gamma scintigraphy, 402 Genetics. See Pharmacogenetics half-life
Gantrisin. See Sulsoxazole Gentamicin accumulation, 208–209, 209t
Garamycin. See Gentamicin intermittent IV infusion of, distribution, 117–118, 118t,
sulfate 216–217 262–263
Gastric emptying time, 573–574 in uremic patients, 792–793 first-order, 41–42, 41t, 42f
Gastrointestinal therapeutic Gentamicin sulfate (Garamycin), time to reach steady-state drug
systems (GITs), 216–217, 793–794 concentration and,
590–591, 590f, 591t GFR. See Glomerular ltration rate 132–134, 132f
Gastrointestinal tract GI tract. See Gastrointestinal tract zero-order, 40–41, 41t
absorption in, 180f, 181, 377t, Giusti-Hayton method, 792 Haloperidol (Haldol), 685
572 Glial cells, 265–266 Haptens, 619
INDEX 893
Hazard ratio, 69 blood ow, intrinsic Hill equation, 454–455, 555f
Hematocrit, 158 clearance, and hepatic HIV-AIDS, 299
Hemodialysis, drug elimination clearance relationships Housekeeper contractions, 573
during, 797–799, 798t, in, 342–344, 343f Human follicle-stimulating
800t evidence of, 338–339 hormone (hFSH),
Hemoltration, 802–803 liver extraction ratio, 80–81, 81t
Hemoperfusion, 800–01 339–340, 340t Human growth hormone, 374
Henderson–Hasselbalch equation, liver anatomy and physiology, Hybridoma, 619
161–162 321–323, 321t, 322f, Hydrates, 423
Heparin, caution, 534 323f Hydromorphone (Dilaudid) ER,
Hepatic clearance, 311–313 Michaelis–Menten kinetics of, 115–116, 116t, 590f
biotransformation pathways, 312–313, 313f, 314f, distribution and elimination half-
326–331, 330t 315f, 316f, 317–318 life of, 117–118, 118t
acetylation, 329 clinical example, 317–318 Hydrophilic polymers, 586
enantiomer metabolism, 330, enzyme inhibition kinetics, Hydrostatic pressure, 261–262
330t 315–318, 315f, 316f Hypersensitivity, 646
mercapturic acid conjugation, metabolite kinetics for one- Hypothesis testing, 56–58
329, 329f compartment model with nonparametric data, 63–66
phase I reactions, 326, 327f drugs, 318–319, 318f with parametric data, 57–58
phase II reactions, 326–328, metabolite kinetics for two- software in, 854–855
328f, 328t compartment model Hysteresis loop, 661, 662f
regioselectivity, 330 drugs, 320–321, 321f Hysteresis plots
species differences in, practice problem, 319–320, in PK-DSST relationship, 663,
330–331, 331t 320f 664f, 665f
biotransformation reactions, of protein-bound drugs,
325–326, 326t 344–345 I
blood flow and intrinsic blood ow changes, 345–346 Ibuprofen, 840–841, 840t
clearance relationships, intrinsic clearance changes, IBW. See Ideal body weight
342–344 342–343 IC , 318
50
drug interactions during, transporter role in, 348–349, ICH. See International
336–338, 337t, 708 349f Conference on
auto-induction and Hepatic disease Harmonization
time-dependent classification of, 806, 806t, 807t Ideal body weight (IBW), 755,
pharmacokinetics, 336 metabolites in, 805–806 755t
clinical example, 338 pharmacokinetics in, 803 Ileum, 392
enzyme variations, 332, 334 for active drugs with IM injection. See Intramuscular
example, 331–332 metabolites, 805–806 injection
genetic variations, 332–333, dosage adjustment in, Imipramine, 277, 333, 334
333t 803–804, 804t, 809 Immediate-release (IR) drug
transporter-based interactions, fraction of drug products, 452
336–338, 337t metabolized, 804–805 bioavailability of, 506, 509t
enzymes involved in, 330–331, hepatic blood ow and Implants, 598
331t intrinsic clearance, 806 In vitro graphic determination of
extrahepatic metabolism, 309, liver function tests and blinding constants and
312–313 hepatic markers, 808 sites, 287–288, 287f
first-pass effects, 338 pathophysiologic assessment In vitro–in vivo correlation, 437
absolute bioavailability, of, 806–807, 806t, 807t BCS, 441
339–341 practice problem, 805 discriminating dissolution test,
blood ow effects on Hepatic extraction ratios, 284 441
bioavailability and liver Hepatitis, 805 dissolution and clinical
metabolism, 340, 340t, High-extraction ratio drugs, 343 performance, 442–444,
341 Higuchi equation, 584 443f
894 INDEX
In vitro–in vivo correlation (Cont.): Inhalation drug delivery, 408 design considerations for, 373,
failure of, 444–445, 445f Inhalation drug products, 375f, 455f
level A correlation, 438, 438f 457–459, 618, 735 Intravenous (IV) bolus
level B correlation, 439 Inhibition administration, 375t
level C correlation, 439 of absorption, 712–713 ADRs with, 85
dissolution rate compared of biliary excretion, 713 clinical application, 85
with absorption rate, of enzymes design considerations for,
439, 439f in drug interactions, 710–712 455–456, 455f
percent of drug dissolved kinetics of, 318 MRT of, 837–838, 838t
compared with percent MAO inhibition, 712 multicompartment models,
absorbed, 439–440, of response and degradation 97–98, 98–99, 98f,
439f, 440f of response, 645f, 105–107, 121–122
plasma concentration 663–664, 666 clinical application of,
compared with percent of production of response k 85–86, 113–114
in
of drug dissolved, (model I) and degrada- determination of, 116–117,
440–441, 440f, 441f tion of response k 117f
out
serum concentration (model II), 663–664, practical application of, 89,
compared with percent 666, 666f 89f
of drug dissolved, 441, Inserts, 598 practice problem, 87–88
441f Institutional Review Board (IRB), one-compartment open model,
In vitro–in vivo relationship 484 75–78, 76f, 78f, 80t,
(IVIVR), 441 Insulin, 618 236–240, 237f, 238f,
In vivo perfusion studies, of GI inhalation, 618 239t
tract, 403 oral delivery of, 374 apparent volume of
In-vivo bioequivalence studies, Integral calculus, 28–29, 28f distribution in, 77–80,
504t Interchangeability, biosimilarity 78f, 80t, 81f
In-vivo graphic determination of vs., 511 calculation of elimination
binding constants and Interdigestive phase, 573 rate constant from
sites, 288–290 Interferon, 618 urinary excretion data,
In-vivo permeability studies, 404 Interferon-b, 711 86–89, 86f, 88f
Independent variable, 15, 51 Interleukin 6 (IL-6) capacity-limited drug
Indirect response models, average serum concentrations elimination, 233–236,
663–670, 665f, 666f, vs. time by abatacept 234f, 235f
667f, 668f–669f, 670 dose, 670f clearance in, 80–85, 81f
application, 668–669, Intermittent IV infusion, clinical application, 85–86,
668f–669f 214–215, 216t 89
models I and II clinical example, 217–218 elimination rate constant in,
diagram for basic, 665f superposition of several IV 76–77, 77f
response proles for models infusion doses, 214–216 relationship between dose and
I and II after three IV International Conference on duration of activity,
doses, 666f Harmonization (ICH), 643
models III and IV, 665f 540–541, 555, 556–557 three-compartment open model,
Individualization, of dosage Interpolation, 32–33 114–116, 115f, 115t
regimens, 682–683 Interspecies scaling, 818–819, three-compartment open
Individualized regimens, design 819f, 820t, 821t, 822 model of
of, 693 Intestinal absorption, 737 clinical applications,
Induction, in drug interactions, 712 transporters in, 383–386, 383f 115–116, 115t
Infants, 700–702, 701t Intestinal motility, 396 two-compartment open model
dosing studies, 700–703, 701t Intestinal permeability, 400–405 of, 76–77, 80, 100–105,
Infusion. See Intravenous (IV) Intramuscular (IM) injection 101f, 104f, 104t,
infusion clinical example, 456–457 110–112, 117–118
INDEX 895
apparent volume of loading dose combined K
distribution in, 107, with, 141–142, 141f Kanamycin, 703
109, 112–113 practical focus, 142–142 Kernicterus, 267
clearance in, 114 Intravenous (IV) injections, Ketoconazole, 335, 398, 405
clinical application, 105–107, repetitive, 210-213, 211t Kidney, 157. See also renal
105f, 105t, 106t early or late dose administration entries
elimination rate constant in, during, 214 anatomic considerations of,
114 missed dose during, 213–214 157, 157f, 158f
method of residuals, Intrinsic clearance blood supply to, 157–158
103–105, 104f, 104t blood flow and hepatic clearance drug distribution to, 263–264,
practical focus, 113–114 relationships witih, 337, 264f
practice problems, 117–118, 342–344, 343f glomerular filtration and urine
118t in hepatic disease, 806 formation, 159–160,
relation between distribution of protein-bound drugs, 345 160t
and elimination Intrinsic dissolution method, 432 regulation of blood flow,
half-life, 117–118, 118t Inulin, 166, 166t 158–159, 159f
Intravenous (IV) infusion, 131 Invirase®. See Saquinavir Kidney disease. See Renal
clearance estimated from, mesylate impairment
140–141 Ion-exchange products, 589 Killing
constant, 132 Ion-pair formation, 388–390 concentration-dependent, 651
conversion between oral Iontophoresis, 460, 596 time-dependent, 652–653
dosing and, 694–696 IR drug products. See Kinetica software, 858
elimination half-life calculated Immediate-release Kupffer cells, 323
from, 135–136 drug products Kurtosis, 53
example of, 135 IRB. See Institutional Review
intermittent, 214, 216t Board L
clinical example of, 217–218 Irreversible drug-protein binding, Labels, 5–6
superposition of several 265, 273 black box section, 20
IV infusion doses, Isoenzymes, 246 geriatric subsection in, 746
214–216 Isoniazid, 329 pharmacogenomic biomarkers
loading dose Isoproterenol, 330 on, 357
one-compartment open metabolism of, 325 PK-PD models role in, 671
model, 136–138, 137f rate constant flip-flop with, Lag time, for drug absorption,
two-compartment model, 190 189, 189f
141–142, 141f Isotretinoin, 488 Lanoxin. See Digoxin
one-compartment model of, Itraconazole, 405 Lansoprazole (Prevacid), 406
131–134 IV bolus administration. See Large intestine, 573–575
loading dose combined Intravenous (IV) bolus Lasix. See Furosemide
with, 136–138, 137f administration Late dose administration, 214
steady-state drug IV infusion. See Intravenous Latin-square crossover designs,
concentration in, infusion 491–492, 491t, 492t
132–135, 132f, 133f IV injections. See Intravenous Law of parsimony, 32
plasma drug concentration– injections Lean body weight (LBW), 706
time curve for, 98, 98f IVIVC. See In vitro–in vivo Least-squares method, 31–32,
practice problems, 136–140 correlation 53–54, 700, 719–720,
total body clearance after, IVIVR. See In vitro–in vivo 719t, 720t, 824, 825t
241–242, 242f relationship Leunomide, 348–349
two-compartment model of, Levothyroxine sodium
141–142 J (Levothyroxine,
apparent volume of Jaundice, 267 Synthroid), 496
distribution in, 142 Jejunum, 392, 404 Librium. See Chlordiazepoxide
896 INDEX
Lidocaine, 19–20, 20f Loperamide (Imodium), 116, 406 gum-type, 585
ADRs involving, 122–123 Lovastatin (Mevacor®), 331–332 polymeric, 585–586
distribution and elimination Low-extraction ratio drugs, Maximum effect model, 653–654,
half-lives of, 118, 118t 343–344 654f, 655f
IV infusion of, 141 Lubricant Maximum life-span potential,
perfusion model of, 20 absorption effect of, 423, 425f 819, 822, 822f
protein binding of, 296, 296f, dissolution effect of, 423, Maximum plasma concentration,
300 424t, 425f 13, 183, 183f
Lincomycin, 787 Lung perfusion and elimination, elimination and absorption
Linear concentration effect 830 rate constant effects of,
model, 655–656, 656f Lupron® Depot, 601 188–191, 188f, 189f,
Linear log dose-pharmacologic Lymphatic system 191f
response absorption by, 396 Maximum reaction rate
one-compartment model, 642 in hepatic clearance, 313, 326,
Linear regression, 31–32, 32f M 327f, 328–329, 328t
Linearity, 688 mABs. See Monoclonal enzyme inhibition, 313–314
determination of, 249–250, antibodies Maximum recommended starting
250f, 251t Macrolide-binding inhibition dose, 638
Lineweaver–Burk equation, 315 in vitro, 318 MDL. See Minimum detectable
Linezolid (Zyvox), 712 Macroscopic events, 836 limit
Link model, 660–663, 660f. See Maintenance dose, 759–759 MDR1. See P-g transporter
Effect compartment Mammillary model, 17–18 MDT. See Mean dissolution
model MAO. See Monoamine oxidase time; Mean dissolution
Lipid bilayer, 372–378 MAOIs. See Monoamine oxidase time
Lipid formulation classication inhibitors Mean, 63
system, 450 Markers. See also Biomarkers Mean absorption time (MAT),
Lipid-soluble drug absorption, biochemical, 673 838, 839t, 840
450–451 hepatic, 803 Mean dissolution time (MDT),
Lipoproteins, 274t, 275–276, 626 surrogate, 514, 514t 838, 839t, 840
Liposomes, 500t, 579, 599–500, MAT. See Mean absorption time Mean residence time (MRT), 837
626–629, 631 Mathematical fundamentals, 27 calculation of, 838, 839t, 840
Lithium, 118t calculus calculation of drug in body,
Liver anatomy and physiology, differential, 27 836, 838, 838t, 843
321–323, 322f, 323f integral, 28–29, 28f of IV bolus dose, 837, 838,
Liver disease. See Hepatic exponents, 38–40 838t
disease graphs, 28f, 29–31 model-independent nature of,
Liver extraction ratio, 339–340, curve tting, 30 835–836
340t, 341t practice problems, 36–38, 38f noncompartmental approach
Loading dose, 758 slope determination, 30, using, 835–840
of digoxin, 113–114 32–33, 32If example of, 837
IV infusion plus logarithms, 38–40 statistical moment theory and,
one-compartment open rates and orders of, 40 836
model of, 136–138, 137f rst-order reactions, 41–42, Mean transit time (MTT),
practice problem, 138–140 41t, 42f 838–839t, 840
two-compartment model of, rate constant, 39–40 Measurement
141–142, 141f zero-order, 40–41, 41t, 42f significance of, 34–35
in multiple-dosage regimens, significant figures, 34–35 significant figures, 34–35
219–230 spreadsheet use, 31 Measures of central tendency,
Local anesthetics, 300 units, 33–34, 34t 53–54
Loo–Riegelman method, 195–196, Matrix, drug release from, 584 MEC. See Minimum effective
197t Matrix tablets, 584–586, 584f concentration
Loops of Henle, 157, 158f drug release from, 584, 584f Median, 53
INDEX 897
Medical device, drug designed enzymes involved in, determination of, 236–238,
for use with, 417 322–324, 330–331, 237f, 237t, 238f, 240
Medication adherence, in elderly, 331t, 335t interpretation of, 240–242,
745–746 extrahepatic metabolism 240f
Medication therapy management and, 309–311, Michaelis–Menten kinetics,
(MTM), 681 312–314 231–233
Membrane-limited models. See rst-pass effects, 338–344, of hepatic clearance, 313–321,
Diffusion-limited 340t, 342t 313f, 314f, 315f–316f
models liver anatomy and clinical example, 317–318
Membranes. See also Cell physiology, 321–323, enzyme inhibition kinetics
membranes 322f, 323f in, 315–317, 315f, 316f
permeability of, 265–266 Michaelis–Menten kinetics, metabolite kinetics for one-
Mephenytoin, 330, 331f 313–321, 313f, 314f, compartment model
Mepivacaine, 300 315f–316f, 316f drugs, 318–319, 318f,
Mercaptopurine (Purinethol), of protein-bound drugs, 320f
oral, 496–497 345–346, 346f metabolite kinetics for two-
Mercaptopurine acid transporter role in, 336–338, compartment model
conjugation, 329, 329f 337t, 348–349 drugs, 320–321, 320f
Mesalamine (Asacol), 329, 329f, induction of, 712 practice problem, 317–318
374, 377t, 454, 500t, in obese patient, 767–768 in one-compartment model
574, 579 inhibition of, 710–712 with IV bolus injection,
Mesalamine delayed-R, 573–574 Metabolites 233–235, 234f, 235t
Metabolism, 149, 325 in hepatic disease, 805–806 clearance in, 241–242, 242f
biotransformation reactions in, kinetics of clinical focus, 242–243
325, 325t for one-compartmental determination of Michaelis
blood flow relationship with, model drugs, 318–319, constant and maximum
340–341 318f, 319f elimination rate,
capacity-limited, 229–231, 231f for two-compartment model 236–238, 237f, 237t,
CYP450 polymorphisms drugs, 320–321, 320f, 238f
affecting, 332, 333t, 321f interpretation of Michaelis
365 Metazalone, 398 constant and maximum
extrahepatic, 312–314, 740–741 Method of residuals, 103–105, elimination rate, 240,
rst-order elimination, 104f, 104t 240f
309–310 absorption rate constants practice problems, 235–242
fraction of drug excreted determined with, Micro needles, 595
unchanged, 310–311, 188–189, 188f Microencapsulation, 590
311f Methylphenidate (Concerta), Microsoft EXCEL®. See EXCEL®
fraction of drug 580, 591 Microsome, 324, 324f, 326f
metabolized, 310–311, Metoclopramide, 406 Microvilli, 393, 393f, 406
311f Metoprolol, 71, 242, 242f, 454 Midazolam, 285, 336
hepatic, 311–312, 807, 807t Mevacor®. See Lovastatin plasma concentration vs. effect
biotransformation pathways, Mexiletine, 300–301 in, 664
326–331, 326t, 327f, MFOs. See Mixed-function Milrinone, 118t
328f, 328t, 329f, 331f, oxidases Minimum detectable limit (MDL),
339f Micafungin, 672–673 688
biotransformation reactions, Michaelis constant Minimum effective concentration
325–326, 326t in hepatic clearance, 315–317, (MEC), 12–13
blood ow and intrinsic 315f, 316f during multiple-stage
clearance relationships in one-compartment model regimens, 205
with, 342, 343f with IV bolus on plasma drug concentration–
drug interactions during, injection, 233–235, time curve, 12–13, 12f,
331–335 334t 234f, 235t 13f
898 INDEX
Minimum inhibitory Motility missed dose during, 213–214
concentration (MIC), GI, 394, 394t schedules of, 220–223, 221f,
221, 651, 651f intestinal, 396 224t
Minimum quantiable level Moxalactam, 108t, 118, 118f Multiple-dose bioequivalence,
(MQL), 688 MQL. See Minimum quantiable 220–223, 221f, 224t,
Minimum toxic concentration level 493–494
(MTC), 5, 12 MR drug products. See Muscle, drug distribution to,
during multiple-dosage Modied-release 33–34
regimens, 205 products Mutations, 358
on plasma drug concentration- MRT. See Mean residence time
time curve, 12–13, 12f, MTC. See Minimum toxic N
13f concentration N-acetyltransferase, 367
Missed dose, 213–214 MTM. See Medication therapy N-acetylcysteine (Mucomyst),
Mixed drug elimination, 243–244 management 367
Mixed function oxidases MTT. See Mean transit time Nanotechnology, 598–599
(MFOs), 323–324, (MTT) Narrow therapeutic index (NTI)
324f, 334t Multicompartment models. drugs, 492, 682
Mixed-effect statistical model, 721 See also Three software programs for
MLEM algorithm, 827 compartment monitoring, 855
MLP. See Maximum life-span open model; Two- Nasal drug delivery, 407
potential compartment open Nasal drug products, 407
Mode, 53 model Natural logarithm, 38
Model-independent clearance for IV bolus administration, NDA. See New Drug Application
estimation, 153–154 98–99 Negative skew, 53
Model-independent nature of clinical application, Negatively skewed data, 54
MRT, 835–836 105–107, 122 Negativity predictability, 723
Modication of Diet in Renal determination of, 120 Nelnavir, 63
Disease (MDRD), practical application, Neonates, elimination half-life in,
367–368, 742, 121–122, 122f 701–702
783–785 renal clearance in, 154–155 Nephrons, 157, 158f
Modied, Wagner–Nelson Multifactorial ANOVA, 61 Nephrotic syndrome, 294t
method, 195 Multiple comparison methods, 62 Nesiritide, 671–672
Modied-release (MR) drug Multiple-dosage regimens, 205 Neutraceuticals, 707
products, 452–453, clinical example, 209–210, 222 New Drug Application (NDA), 2,
500t, 567–568, 569t. drug accumulation in, 205–209, 503–504, 507
See also Extended/ 206f, 207t, 209t ANDA compared with, 503,
modied release intermittent IV infusion, 503t
(EM/MR) products 214–216, 216t changes to, 537–538, 537t
Modied-release parenteral clinical example, 216–217 bioequivalence studies in,
dosage forms, 456 superposition of several 469–470
Moments. See Statistical moment IV infusion doses, changes to, 537, 537t
theory 214–216, 216t chemistry, manufacturing, and
Monoamine oxidase (MAO), loading dose in, 219–220 controls section of, 557t
324, 712 oral regimens, 218–219 New drug development process,
Monoamine oxidase inhibitors practice problems, 222–223, 637–638, 637f
(MAOs), 243 224t New molecular entry, 638
Monoclonal antibodies (mAbs), repetitive IV injections, 210, Nexium. See Esomeprazole
618–619, 619t, 620f, 211t Niacin (Niaspan), 244–245
621t–622t early or late dose Nicotinic acid, 244
Monolix software, 858 administration during, Nifedipine (Procardia XL), 516,
Morphine, 312, 448 214 517f
INDEX 899
Nimix (SAS) software, 858 rst-order absorption and absorption of, 398–399
Nitrates, 645–646 nonlinear elimination, elimination of, 284
Nitrofurantoin, 422 244 Norepinephrine, 265
Nitroglycerin, 301, 453, 595–596 mixed drug elimination, Normal distribution, 52–53
Nomograms, for dose adjustment 243–244 Noyes–Whitney equation, 27
in uremic patients, two-compartment model NSAIDs. See Nonsteroid anti-
786–787, 786f, with nonlinear inammatory drugs
788t–789t elimination, 244–245 NTI drugs. See Narrow
Non-zero order, 42 zero-order input and therapeutic index
Noncompartmental model, 84, 651 nonlinear elimination, (NTI) drugs
compartmental model 244 Null hypothesis, 56
comparison with, in one-compartment model Numerical problem-solving
843–844, 843t with IV bolus algorithms, 826
MRT calculations in, 837, injection, 233–235, Nutraceuticals, 684
838t, 841–842 234f, 235f Nutrients, drug absorption
PK-PD in, 651, 651f–653f clinical focus, 242 affected by, 389,
Noncompartmental interpretation of Michaelis 406–407
pharmacokinetic constant and maximum
analysis elimination rate, 240, O
EXCEL® spreadsheet in, 852 241f OATP. See Organic anion-
Noncompetitive inhibition, practice problems, 232–233, transporting
316–317 235–242 polypeptide
Nonlinear mixed-effect model protein-bound drugs with, Obese patients, dose adjustment
(NONMEM), 248–249, 248f, 249f for renal impairment
720–721, 858–859, one-compartment model in, 705–706
863f–867f drugs, 249, 249f Occupancy concept, 653–655
Nonlinear mixed-effects saturable enzyme elimination Occupancy theory, 653–655,
modeling processes, 229–231, 654f. See also Transit
Phoenix NLME software for, 231f, 232t time in absorption
859 NONMEM. See also Nonlinear Odds ratio, 69
Nonlinear pharmacokinetics, 11, mixed-effect model Older adults. See Elderly
827–828 minimum objective function in Oligonucleotide drugs, 623
adverse reactions and toxicity calculation of plasma OLS. See Ordinary least-square
due to, 247 concentration, 861 method
bioavailability of drugs with, oral data fitted to one- Omeprazole (Prilosec), 336, 339,
247–248 compartment model 406
chronopharmacokinetics with first-order One-compartment open model,
and time-dependent absorption and 16, 16f, 18f
pharmacokinetics, elimination, 863f–867f absorption rate constant
245–247, 246t oral data fitted to two- determination from,
Circadian rhythms and drug compartment model 190, 190f
exposure, 246–247 with first-order for distribution, nonlinear
clinical focus, 246 absorption and elimination, combined
determination of linearity, elimination, 868f–873f with, 243–244
249–251, 250f Nonreplicate, parallel elimination in
dose-dependent, 252–253, 252t bioequivalence study, as amount per time unit,
in one-compartment model 493 81
distribution with Nonrestrictive clearance, as fraction eliminated per
nonlinear elimination, 283–284 time unit, 81f, 82
243–244 Nonsteroid anti-inammatory as volume per time unit,
clinical focus, 244–245 drugs (NSAIDs) 81, 81f
900 INDEX
One-compartment open model prediction of, 401–402 Oxazepam, 285
(Cont.): rate constants for Oxicams, 284
for IV bolus administration, determination of, 188–191, Oxymorphone ER (Opana ER),
75–76, 76f 190f, 191f, 192t, 194t, 580–581
apparent volume of 195f Oxytetracycline, 282t
distribution in, 77–78, signicance of, 184 Oxytocin, 407
78f, 80t zero-order model of, 184–185
capacity-limited drug Oral cavity, 391 P
elimination, 236–240, Oral delivery P-glycoprotein, 159, 266, 279, 337
237f, 238f, 239t clinical example, 456–457 bioavailability and, 386, 387t
clearance in, 80–85 drug product considerations P-glycoprotein transporters, 159,
clinical application, 35–36, for, 374, 456, 456f 367–368, 383, 385, 386
89, 89f of insulin, 374 gender differences in, 276
elimination rate constant in, Oral dosage regimens genetic polymorphism of,
76–77, 77f, 78f conversion between IV 367–368
urinary excretion data infusion and, 694–696 Paclitaxel (Taxol), 113, 808
for elimination rate multiple doses, 218–219 Paddle method, 427f, 429–430,
constant calculation, Oral drug absorption 430f
86–89 prediction of, 401–402 Paddle-over-disk method, 427t,
for IV infusion, 131–134 during product development, 431
loading dose combined 390–401 Pan coating, 586
with, 136–138, 137f Oral immunization, 629–630 Panoderm patch (Ela), 596–597
steady-state drug Orange book. See Approved Panodermal patch (Ela), 596–597
concentration in, Drug Products Pantoprazole (Pontinex), 406
131–134, 132f, 133f with Therapeutic Para-aminohippuric acid, 283
of metabolite IV infusion, Equivalence Paracellular drug diffusion, 377,
318–319, 318f, 319f Evaluations 378f, 382
of protein-bound drugs, 249, Order of reactions, 42 Parametric data, 52, 57–58
249f Ordinal data, 52 Parametric tests, 59
One-way ANOVA, 60–61 Ordinary least-squares (OLS) Parenteral administration routes,
Onset time, 13, 1889 method, 824, 825t 374, 375–376t
Open system, 17 Organ clearance, 152, 153 Parenteral drug products,
Oral absorption Organic anion-transporting 455–456, 455f, 462
anatomic and physiologic polypeptide (OATP), clinical example, 456–457
considerations, 337–338, 833 modified-release, 456,
290–294, 290f Organic cation transporter, 160 597–598
during drug product Organs Paroxetine (Prozac), 209–210,
development, 376f, blood flow to, 262, 262t 245, 386, 388f
401–402 drug accumulation in, 264–265 Parsimony, 105
first-order model of, 185–188, drug uptake by, 261–263, Partial pharmacokinetic
185f, 186f, 187f 262f, 262t parameters, dosage
rate constant determination, elimination by, 83–84 regimens based on, 694
188–191, 190f, 191f, OrosSoftcap (Alza), 592, 592f Particle size
194f, 194t, 195f, 197t Ortho Evra, 185, 185f bioavailability and
GI tract absorption, 390–401, Osmotic drug delivery system, bioequivalence
390f, 393f, 394f, 395f, 590–592, 590f, 591f, problems, 535
395t 592f, 592t drug absorption and, 408,
models for estimation of, 195 Osmotic pump systems, 402, 403 421–422
CRFA, 196–199, 197t, 198t OTC drugs. See Over-the-counter Partition coefcient, drug, 263
Loo–Riegelman method, drugs 263f, 264
195–196, 196f, 197t Over-the-counter (OTC) drugs, 682 Passive diffusion, 260–261,
pharmacokinetics of, 182–184 Oxacillin, 538 378–382, 379f, 383f
INDEX 901
Passive targeting, 628 Permeation enhancers. See dose and duration of activity
PAT. See Process analytical Absorption enhancers relationship, 643–644,
technology pH, 3 646f
Patient renal excretion and, 161–162, dose–response relationship,
compliance, in TDM, 686 161t 640–642, 641f, 642f,
determination of K and V solubility, drug absorption 653–655, 654f
km max
Michaelis constant and and, 421 drug tolerance and physical
maximum elimination stability and drug absorption, dependency, 645–646
rate in, 238 421 drug-receptor theory,
Patient response, in TDM, 686 pH–partition hypothesis, 381–382 639–640, 639t, 640f
Paxil. See Paroxetine Phagocytosis, 387 elimination half-life effect
hydrochloride Pharmaceutical alternatives, on duration of activity,
PDF. See Probability density 533–534, 540 644, 645f, 645t
function Pharmaceutical development, hypersensitivity and adverse
Peak plasma concentration. See 547–550 response, 646
Maximum plasma CMV and, 542, 569 PF-PD model development,
concentration CPP and, 552 82, 647f, 649–650,
Pediatric Research Equity Act PAT and, 552–553 827–828
(PREA), 448 QbD, 441–442 practice problem, 643
Peeling. See Method of residuals biopharmaceutics integration pharmacogenomic biomarkers
Pellets, 586–588, 587f with, 550–551, 550t in drug labels, 357
Penicillin Pharmaceutical equivalence, 531, practice problem, 643
absorption of, 398 532t–533t, 540 receptor occupancy concept,
clearance of, 151 future of, 538–539 653–655
in elderly, 703 practice problem, 534–535 receptors for drugs, 655
hypersensitivity to, 646–647 Pharmaceutical substitution, 531 protein-binding of drugs,
in infants and children, 702 Pharmacodynamic models, 295–297, 296f, 297t
protein binding of, 782 649–650, 649f Pharmacogenetics, 6, 332,
renal excretion of, 276 exposure-response 357–358, 357f
Pentobarbital, 276 relationships, 638 polymorphisms and, 358–361,
Pepcid. See Famotidine maximum effect model, 360t–361t, 362t
Percent of drug dissolved, 653–654, 653f, 654f transporter, 360t–360t
439–441, 440f noncompartment PK-PD, 651 Pharmacogenomics, 357
Perfusion models, 18–19, 19f software for data fitting, 854 Pharmacokinetic evaluation, in
Perfusion of GI tract, 396 systems, 670–671, 671f, 672f TDM, 685
Perfusion pressure, 158 Pharmacodynamic tolerance, Pharmacokinetic models, 15–21,
Perfusion-limited models, 262, 645–646 16f
262f, 829–831, 829f Pharmacodynamics MLP for, 819–820
vs. diffusion, 832 confounders in elderly, 744 physiologic
Peripheral compartment. See dose–response relationship in, application and limitations
Tissue compartment 640–642, 641f, 642f of, 835
Peristalsis method, 432 drug design considerations, with binding, 831–832
Peritoneal dialysis, 797 446–447 compartment approaches
Peritubular capillaries, 158 of ER drug products, 602–603, compared with, 823,
Permeability 603f 824t
BCS and, 508 pharmacokinetics and, 635 diffusion-limited model,
of cell and capillary biomarker considerations, 262, 262f, 265
membranes, 265–266 647–648 ow-limited model, 262,
intestinal, 400–405 biomarkers, 262f, 829–831, 829f
Permeability-limited models. pharmacodynamics with hepatic transporter-
See Diffusion-limited and clinical endpoints, mediated clearance,
models 647–648, 648t 348–349, 349f, 832–835
902 INDEX
Pharmacokinetic models, dosage adjustment in, Phase II reactions, 326–329, 326t,
physiologic (Cont.): 803–804, 804t, 809 328, 328f, 328f, 328t
interspecies scaling in, fraction of drug Phenobarbital
818–819, 819f, 820t, metabolized, 804–805 excretion of, 347
821t, 822, 827 hepatic blood ow and metabolism of, 332
software for data fitting, 854 intrinsic clearance, 806 pharmacokinetic study,
Pharmacokinetic parameters, 15 liver function tests and parametric testing,
Pharmacokinetic parameters of hepatic markers, 808 62–63
various drugs, 832t pathophysiologic Phenobarbitone, 448
Pharmacokinetic- assessment of, Phenothiazine, 265, 406
pharmacodynamic 806–807, 806t, 807t Phenytoin
(PK-PD) models, practice problem, 805 metabolism of, 332
652–670 in obese patient, 756–759 nonlinear pharmacokinetics of,
with binding, 831–832, 834 pharmacodynamics and 238–240, 239f, 242
with effect compartment, biomarker considerations, oral, 451
643–644 647–649 protein binding of, 236
components of, 649–650, 649f dose and duration of activity Phoenix WinNonlin and NLME
linear concentration effect, relationship, 643–644 software, 858
655–656, 656f dose and elimination half- Phospholipid bilayer, 377–378
maximum drug concentration life effects on duration Physical dependency, 645–646
effect in, 653–654, 654f of activity, 644, 645f, Physiochemical properties, 447
noncompartmental, 651–653, 645t drug design considerations,
651f dose elimination half-life 420t, 447
receptors in development of, on duration of activity, particle size and drug
639–640 644, 645f, 645t absorption, 420t,
Pharmacokinetics, 152, 161–162, dose-response relationship, 421–422
165t. See also Clinical 638–639, 640–642, solubility, pH, an drug
pharmacokinetics; 640f, 642f absorption, 420t, 421
Nonlinear drug tolerance and, 645–646 Physiologic absorption
pharmacokinetics drug-receptor theory, administration route and, 374,
of absorption, 182–184, 182f, 639–640, 639t, 640t 375f, 376, 376t–377t
183f hypersensitivity and adverse cell membranes in
basics of, 15–21, 16f, 18f, 20f, response, 646 drug passage across,
21f PK-PD model development, 378–386, 380t, 382f,
biomarkers, 637–638, 637f, 638f, 383f 385f
pharmacodynamics 640–650, 649f nature of, 377–378, 378f
and clinical endpoints, practice problem, 643 clinical examples, 386–387,
647, 648t receptor occupancy concept, 387t
of biopharmaceuticals, 630–631 653–655 disease states affecting,
capacity-limited, 233–235, receptors for drugs, 639, 639t 405–406
234f, 235t in TDM, 689 drug interactions affecting, 406
clinical focus, 242–243 units in, 33–34, 34f drug interactions in GI tract,
elimination half-life in, Pharmacologic effect 389–390, 390f
240–241 linear decline as function of drug product design and,
practice problems, 232–233 time, 642, 642f 401–402
dose-dependent, 252 log drug concentration vs., 641f inhalation drug delivery, 408
clinical example, 253–254, Pharmacologic response vs. methods for studying
253t dose on linear scale, gamma scintigraphy, 402
drug design considerations, 640–641, 641f in vivo GI perfusion studies,
447–448 Pharmacodynamic response. See 403–404
in elderly, 737–743, 744 Response intestinal permeability,
in hepatic disease, 803–804 Phase I reactions, 326. 327f 404–405
INDEX 903
markers, 402–403 with binding, 831–832 percent of drug dissolved
osmotic pump systems, 403 compartment approach compared with,
RDDCs, 403 compared with, 439–441, 440f
nasal drug delivery, 407 822–823 physiologic drug distribution,
nutrients affecting, 389, diffusion-limited model, 274, 274t, 275
406–407 260–261, 260f, 832 in saturable enzymatic
oral, 390 ow-limited model, 262, elimination processes,
anatomic and physiologic 262f, 262t 231–232, 231f, 232t
considerations, with hepatic transporter- of sustained-release drugs,
390–393, 390f mediated clearance, 570–571
GI tract absorption, 377t, 832–825, 833f, 834f in TDM, 681, 687t
384–401, 384t, 390f, interspecies scaling, units of expression for, 34
393f, 394–395, 396t, 818–822, 819f, 821t, Plasma drug concentration–time
397t, 399f 822f curve, 12–13, 12f, 13f
topical and transdermal drug signicance of, 20 absorption phase of, 182–183,
delivery, 408 Physiologic pharmacokinetic 182f, 183f
Physiologic drug distribution, model (ow model), AUC of, 498–500, 500f
259–260, 261f, 261t 18–19 clearance determined from, 84
apparent volume of, 267–273, Physiologically based absorption distribution phase length on,
271f, 272f kinetics (PBPK), 108
calculation of, 267–270, 178–179, 180f elimination phase of, 183, 183f
267f, 269t Pinocytosis, 387, 388 enduring saturation, 229–231
in complex biological Piroxicam, 284 for IV infusion, 132–134,
systems, 270–271, 271f PK solutions software, 860 132f, 133f, 133t
practice problem, 270 PK-DSST relationship, 662–664, measurements using, 11–12,
cell and capillary membrane 665f 12f, 12t
permeability, 265–266 PK-PD mode of multiple-dosage regimens,
within cells and tissues, 266 of antimicrobial efficacy, 653 218–219
clinical focus, 267 PK–PD models. See for oral dosing, 185–186, 185f,
to CSF and brain, 266 Pharmacokinetic– 186f
distribution half-life, blood pharmacodynamic postabsorption phase of, 183,
flow, and drug uptake (PK-PD) models 183f
by organs, 262–264, PK-Sim software of protein-bound drugs
262f, 262t, 263f for PBPK modeling, 859–860 with nonlinear
drug accumulation, 264–265 Plasma drug concentration, 8, pharmacokinetics,
gender differences, 276 10, 10f, 13f, 475–477, 248–249, 248f, 249f,
hydrostatic pressure, 260–262 476f, 477f. See also 300
of protein-bound drugs, Steady-state, drug for transdermal delivery, 185,
273–275, 274f, 274t, concentration 186f
281–282, 281t, 282f in bioavailability and in two-compartment open
Physiologic models, 16, 16f, bioequivalence studies, model, 100–105, 101f,
18–19, 18f, 19f 475–478 104f, 104t
of clearance, 153, 153f during multiple-dosage Plasma ow, renal, 152
compartment models compared regimens, 206–209, Plavix. See Clopidogrel
with, 822–823, 842–843 207t, 210t Pmetrics software, 859
compartmental models intermittent IV infusion, Polyclonal antibodies, 619
compared with, 14–16, 215–217, 215f Polymeric delivery systems,
842–843 oral regimens, 211–217 585–586, 588,
pharmacokinetic, 828–831, repetitive IV injections, 600–601, 602t,
828f, 829f 210–211, 211t 625–626, 625f
application and limitations after oral dosing, 183, 183f Polymeric matrix tables,
of, 827 peak plasma, 183, 183f 585–586, 599, 612t
904 INDEX
Polymorphism. See Genetic Precision, 688 clinical examples of,
polymorphism Predictability, 713t 282–285, 299–301
Polymorphs, 422–423. 423t Predicted plasma drug distribution, binding,
PopPK. See Population concentration, during displacement, and
pharmacokinetics multiple dosage pharmacodynamics
(PopPK) regimens, 206, 207t relationships, 281–282,
Population analysis, 825–826 Predilution, 802 282t
Population averages, dosage Prilosec. See Omeprazole drug exposure, 298–299
regimens based on, 693 Probability. See also Bayesian effects of change in protein
Population compartmental theory binding, 277–279, 295
pharmacokinetic conditional, 716, 716f interactions due to
analysis, 852, 854 Probability theory, 715, 716f competition for
Population pharmacokinetics Procainamide binding sites, 291, 295
(PopPK), 5, 714–716, distribution and elimination considerations in, 274t
735 half-lives of, 188t, 301 determinants of, 285
adaptive method for dosing multiple-dosage regimens of, distribution and, 278–279,
with feedback, 221, 221f 281–282, 282t
716–717 population data on, 721, 742 elimination and, 281–282,
analysis method for dosing Procardia XL. See Nifedipine 281t, 282t, 283–284
with feedback, Process analytical technology, clinical example, 284–285
720–722 552–553 restrictive and nonrestrictive
analysis of data in, 720–722 Process validation, 557–558 elimination, 283–284,
analysis of population Prodrugs, 361, 487 344–345
pharmacokinetic data Product inhibition, 245 gender differences in, 276
Bayes estimator, 717–719 Prolonged-action drug product, hepatic clearance and, 345–346
Bayesian theory introduction, 570, 588 blood ow changes, 345
714–715 Propantheline bromide, 406 changes in, 345–346, 346f
comparison of Bayes, least- Proportional drug effect model, intrinsic clearance changes,
squares, steady-state, 658–660, 659f 345
and Chiou methods, Propranolol kinetics of, 286–287
719–720, 719f, 720f absorption, 405 effects of change in protein
decision analysis involving elimination, 283 binding, 279–299, 295
diagnostic test, 722, metabolism, 332, 333, 342 graphic determination of
723t Protein binding of drugs, binding constants and
model selection criteria, 722 273–276, 274f, 274t sites, 287–289, 287f,
noncompartment compared apparent volume of 288f, 289f, 290f
with compartment, distribution and, practical focus, 287
843–844, 843t 276–277, 277f renal function and, 294t
Pore transport, 388 clinical example, 280 methods for, 274, 274t
Portal veins, 332f effect of changing plasma nonlinear pharmacokinetics
Positive predictability, 723 protein, 277–279 due to, 248–249, 248f,
Positively skewed data, 54 electrolyte balance effects 300
Postabsorption phase, 183, 183f on, 281 one-compartment model
Postapproval changes, 460, practice problem, 279–280, drugs, 249, 249f
558–559, 599t 280t protein concentration–
Postmarketing surveillance clearance and, 283 drug concentration
program, 562 clinical examples, 275–276, relationship, 290–291,
Power test, 52–58 280–281 290f, 292t, 293t, 295
Pravastatin sodium (Pravachol®), clinical significance of, Protein drugs, 615, 616t–617t,
317–318, 833–834, 290–291, 292t, 618–624, 618f–620f,
833f 293t–294t 621t, 624–626
INDEX 905
Prothrombin time, 808 Randomization, 65 Regioselectivity, 330
Proton pump inhibitors, 406 Range, 53 Regression coefcient, 64–65
Prozac. See Paroxetine Ranitidine (Zantac®), 338, 400 midpoint method, 168–169
Pseudoephedrine, 184–185 Rate Regression line, 31–32
PT. See Prothrombin time dissolution rate compared Relative availability, 422–423
Pulmonary absorption, 738–739 with, 439–440, 439f, Release test, 425–426, 426f
Pulsatic drug development, 165 440f development and validation of,
Purine drugs, accumulation of, of elimination, 231–232, 232t 426–429, 427t
265 Rate constants, 17, 156. See Remote drug delivery capsules
Purinethol. See Mercaptopurine also Absorption rate (RDDCs), 403
Pyrimidine drugs, accumulation constants Renal blood ow, 158–159, 159f
of, 265 Rate method, for elimination rate Renal clearance, 163–168
constant calculation, in adult, 701t
Q 86–88, 87f, 89f from central compartment, 154
QA. See Quality assurance Rate of drug excretion, 478, 478f determination of fraction of
QbD. See Quality-by-design Rate-limiting steps in absorption, drug excreted and,
(QbD) 418–420, 418f, 419f 168–170
QC. See Quality control Ratio scale data, 52 graphical methods, 168, 168f
Quality. See Drug product RBF. See Renal blood ow in multicompartment
quality RDDCs. See Remote drug models, 153–155
Quality assurance, 554–555 delivery capsules practice problem, 163,
practical focus, 554 Reabsorption, 161–162, 162t 168–170
GMPs, 555, 556t clearance by, 165 model-independent methods,
guidance for industry, 555 urinary pH changes and, 713 153–154
quality standards, 556–557 Reabsorption fraction, 161, 713 in newborn, 701t
Quality control (QC) Reaction order. See Order of renal drug excretion and
practical focus, 555 reaction glomerular filtration
GMPs, 555 Recalls, 558, 558t and active secretion,
guidance for industry, 555 Receptor occupancy concept, 160
quality standards, 555 653–655 glomerular ltration only,
Quality risk, 547, 548, 549–550, Receptors 160, 165
549f PK–PD model development glomerular ltration
Quality target prole (QTPP), and, 639–640, 640f reabsorption, 160t, 161
441, 551 polymorphism affecting, 362t Renal drug excretion, 159–161,
Quality-by-design (QbD), Reciprocating disk method, 427t, 162f
441–442, 534, 551, 557 431 clinical application, 162
biopharmaceutics integration Recombinant drugs, approved, in elderly, 309, 741–742
with, 550–551, 550t 616t–617t practice problems, 163,
Quinidine Recombinant human insulin for 169–170
distribution and elimination inhalation (Exubera), renal clearance and
half-lives of, 118t 408 examples, 167
drug interactions of, 338, 711 Rectal drug delivery, 376t, glomerular ltration and
hepatic clearance, 344 454–455 active secretion,
pharmaceutical alternatives, 533 Rectangular coordinates, 30, 30f, 166–167, 167f
35, 36f glomerular ltration and
R Rectum, 392–393, 574 reabsorption, 160t, 161
R Foundation for Statistic Red blood cells. See glomerular ltration only,
Computing Erythrocytes 165–166, 166t
R software for PK applications, Reduced drug clearance, 110–111, Renal impairment
860 111f dose adjustment in, 777t
Random variable, 51 Regional pharmacokinetics, 724 clearance based, 778
906 INDEX
Renal impairment, dose adjustment exposure relationship with, 638 Saturable enzymatic elimination,
in (Cont.): inhibition of, 663–664, 666 231–232, 231f,
elimination rate constant pharmacodynamic, 649, 686 231t. See also
based, 778–779 stimulation of, 66f, 666–667 Capacity-limited
extracorporeal removal of variability in, 684t pharmacokinetics
drugs, 796–803, 798t, Restrictive clearance, 344–345 Saturation, 229–231. See also
800f, 800t Restrictive elimination, 283–284 Capacity-limited
fraction of drug excreted Reticuloendothelial system pharmacokinetics
unchanged, 787, 283–284, 323, 422 Scale-up and postapproval
790t–791t Reversible drug-protein binding, changes (SUPAC), 460,
GFR measurement, 783–784 273–274, 274f, 536, 558–561, 559t
pharmacokinetic 295–297 adverse effect, 560
considerations, 775–776 Rifampin, 335 assessment of effects of
serum creatinine Risk assessment, 546, 548f, 549f change, 559–560
concentration and Risk calculations, 68–70 CMVs, 559
creatine clearance, Risk management, 545–546 equivalence, 560
779–785, 782f, 783t, drug manufacturing practical focus, 561
784t requirements, 557, 557t changes in batch size, 561
for uremic patients, 785–796, drug recalls and withdrawals, quantitative change in
788t–789t, 789, 555, 558t excipients, 561, 561t
790t–791t process validation, 557–558 Scaled average bioequivalence,
general approach in, 777–779, regulatory and scientific 493
777t considerations, 557 Schedules, dosing, 220–223,
moxalactam disodium Risks from medications, 221f, 224t
response to, 118, 118f 545–546, 546f Scientist/PKAnalyst software,
protein binding of drugs in, 275 Ritonavir, 338, 448 860
with aging, 704–705 Rotating basket method, 427t, SD. See Standard deviation
Renal plasma ow (RPf), 158 429 Selection bias, 684
Repeat-action tablet, 570 Rotating bottle method, 427t, Selective serotonin reuptake
Repeated measures regression 431–432 inhibitors (SSRIs),
analysis, 61–62 Route of administration drug interactions with,
Repetitive IV injections, determination of, 699–700 243, 334
210–213, 211t drug design considerations, Semilog coordinates, 30, 30f,
early or late dose 449–450, 450f 688, 723
administration during, extravascular considerations Sensitivity, 688, 723
214 for, 417 Sepsis, moxalactam disodium
missed dose during, 213–214 RPF. See Renal plasma ow pharmacokinetics in
Replicated crossover Ruggedness, 689 patients with, 118,
bioequivalence study, 518
492 S Serotonin syndrome, 243, 712
RES. See Reticuloendothelial Safety considerations in ER/MR Serum
system drug products, 601–603 creatinine concentration dose
Residence time. See Mean Safety information, PK in rst adjustment based on
residence time in-human doses, 638 in elderly, 742
Response, 8, 10 Salicylic acid digoxin concentration in, 691
degradation of, 66f, 666–667 absorption of, 326, 327f drug concentrations in, 11,
dose relationship with, 607– biotransformation of, 326, 12t, 687t, 689–690
608, 640–642, 641f 327f, 328 units of expression for, 33
drug concentration pH of, 381t Serum creatinine concentration,
relationship with, 8, renal excretion of, 162 dose adjustment based
10, 10f Saquinavir mesylate (Invirase®), on
drug exposure and, 10, 638 278, 334–335 in adults, 742
INDEX 907
eGFR using MDRD or PK-Sim, 859–860 Statins, 317–318
CKD-ELI equations, R, implementation of Statistical evaluation
741–742 statistical computing of bioequivalence, 497, 498t
GFR measurements for, and graphics, 860 of ER drug products, 608
741–742 Scientist/PKAnalyst, 860 Statistical inference study, 63
in infants, 701, 701t SimCYP, 857–858 Statistical moment theory,
in obesity, 759 Solubility, 419 836–837, 838t
Side effect. See Adverse drug BCS and, 507–508 MAT, MDT, and MTT, 838
reaction pH drug absorption and, 421 model-independent and
Sieving coefcient, 802–803 Solubility–pH prole, 421 model-dependent
Sigma-minus method, 86–89, 88f Solute carrier transporters, 368 nature of MRT,
Signicant differences, 58–59 Solvates, 422–423 835–836
Signicant gures, 34–35 absorption and, 422–423, Statistics
SimCYP software, 857–858 422f, 423f distributions, 52–53
Similarity factor, 435, 435f Sonophoresis, 596 hypothesis testing, 56–58,
Simulation, software data SOP. See Standard Operating 63–66
generation for, 864–866 Procedures predictability, 713t, 723
Single-nucleotide polymorphism Sorbitrate, 453 probability, 715
(SNP), 358–359, 3389 Species probability testing, 715
Sink conditions, 428 hepatic biotransformation Steady state
Site-dependent metabolism, 323 enzyme variation with, apparent volume of
Site-specic drug delivery. See 330–331, 331t distribution at, 109
Targeted drug delivery scaling among, 818–819, 819f, clearance relationship with,
Skewed data, 54 820t, 821t, 822 134–135
Skewed distribution, 53 Specications, 556, 558 drug concentration, 132,
Skin, drug distribution to, 262, clinically relevant, 441–445 132f
262f Specicity, 688, 723 during IV infusion, 100–103,
Slope determination, 30, 30f, Spray dry coating, 586 101f
32–33, 32f Spreadsheets apparent volume of
Slow release pellets, beads or electronic, 852, 853f distribution at, 101f,
granules, 586–587, EXCEL®, 852 117–118
588t pharmacokinetic calculations one-compartment model of,
Slow-erosion core tablet, 89–90 using, 31 132–134, 132f, 133f,
Small intestine, 573–574, 574t SSRIs. See Selective serotonin 133t
SNP. See Single-nucleotide reuptake inhibitors two-compartment model of,
polymorphism St. John’s wort, 707 141–142, 141f
Sodium ferric gluconate complex Stability, 445–446, 689 during loading dose plus IV
model, 823, 824t bioavailability and infusion
Software packages bioequivalence one-compartment model,
ADAPT5, 855, 857, 857t, 862 problems, 486, 533 136–138, 137f
Bear, 857 determination of, 445–446 two-compartment model,
Berkley Madonna, 857 pH, drug absorption and, 100–103, 101f
GastroPlus, 857–858 421 in multiple-dosage regimens,
Kinetica, 858 Stability–pH prole, 421 206, 206f, 208, 210t
list of popular PK packages, Standard deviation (SD), 54, Steady-state plasma drug
856t 57–58 concentration, of ER/
Monolix, 858 Standard error of the mean MR drug products,
Nimmix (SAS), 858 (SEM), 55 132–1314, 133f
Nonmem, 858–859, 863f–867f Standard Operating Procedures Stimulation of degradation of
Phoenix WinNonlin and (SOPs), 555 response, 666–667
NLME, 858, 859 Standard two-stage (STS) Stimulation of production of
PK solutions, 860 method, 721, 826 response, 666–667
908 INDEX
Stimulation of production of T clinical example, 690–692
response k (model III) Tachyphylaxis, 646 dosage adjustment in, 683,
in
and simulation of Tagamet. See Cimetidine 683f, 683t
degradation of response Tamoxifen, 368 dosage regimen design,
k (model IV), 667f Target drug concentration, 634–635
out
Stomach, 391 684–685 drug assay in, 688–689
STS method. See Standard during multiple-dosage drug concentration
two-stage method regimens, 205 measurements in,
Student’s t-test, 59, 64 steady-state, 133 686–687, 687t
Study submission, 502–506, Targeted drug delivery, 627–630 drug interactions, 748
503t, 504t, 505f, 505t agents for, 629 drug pharmacokinetics in, 685
bioequivalence study waiver, drugs for, 629 drug product in, 684
503–504 general considerations in, 627 drug selection for, 684, 684t
dissolution profile comparison, oral immunization, 629–640 patient compliance in, 686
506–507 site-specific carrier, 628–629 patient response evaluation in,
Subcutaneous absorption, 738 target side, 628 686
Subcutaneous injection, 374, 375t targeting agents, 628 pharmacokinetic evaluation in,
Sublingual tablets, 453–454 Targeted-release products, 568, 685, 689, 690t
Substance abuse, potential for, 569t, 570 serum drug concentration
644, 645 Taxol. See Paclitaxel monitoring in, 689–690
Substitution, generic, 514–516, TBW. See Total body weight software for, 860
515t TCAs. See Tricyclic Therapeutic equivalence, 515–516,
Sulfadiazine, 329 antidepressants 515t, 530
Sulfamethoxazole/trimethoprim Tenoxicam, 283 future, 538–539
(Bactrim), 162 Tetracycline Therapeutic equivalence
Sulfanilamide, 329 absorption, 398 evaluation codes,
Sulsoxazole (Gantrisin), 277, accumulation of, 265 515–516, 515t
308, 329 multiple oral-dose regimens, for nifedipine extended-release
renal excretion of, 162 219 tablets, 516, 517t
Sumatriptan nasal spray, 162 protein binding of, 281–282, Therapeutic index, 13
Sumatriptan, 226 282t Therapeutic nonequivalence of
SUPAC. See Scale-up and Theophylline, 573, 695 generic drugs, 538
postapproval changes absorption of, 399, 399f Therapeutic window, 13
Superiority trials, 56–57, 57t Bayesian methods applied to, Thiopurine S-methyltransferase,
Superposition principle, 206, 207t 718 366
for several IV infusion doses, clearance of, 171 Three-compartment open model
214–216, 216t distribution and elimination for IV bolus administration,
Suppositories, 455 half-lives of, 118t 114–116, 115f, 115t
Surfactants, dissolution effect, 424 dosage regimen of, 695 MRT calculations i, 838, 839t,
Surrogate endpoints, 648, 648t drug interactions of, 711 840
Surrogate markers, 514, 514t food interaction with, 713 Ticlopidine (Ticlid®), 400, 406
Sustained-release products, IV infusion of, 141 Time for peak plasma
570–571 metabolism of, 324 concentration, 185–186
Synthetic reactions. See Phase II multiple-dosage regimens of, elimination and absorption
reactions 221, 221t, 225 rate constant effects
Synthroid. See Levothyroxine Theophylline extended-release on, 191–195, 192t,
sodium capsules, 436, 436t 194f
Systemic clearance. See Therapeutic drug monitoring Time to reach steady-state drug
Clearance (TDM), 683–684, 683f, concentrations
Systems pharmacodynamic 683t, 691 in multiple-dosage regimens,
model, 670–671, 671f ADRs and, 691–692 210t
INDEX 909
in one-compartment model, Transdermal drug delivery, 185, Tubular reabsorption, 161–162,
132–134, 132f, 133f, 185f, 376t, 459–460 162t
133t absorption in, 737–738 Tubular secretion, 160, 758
Time-dependent drug product considerations Two one-sided tests procedure,
pharmacokinetics, for, 459–460, 459t 497–498
245–246, 246t Transdermal Therapeutic Two-compartment open model,
Circadian rhythms and drug Systems (TTS), 17–18, 18f, 100–114
exposure, 246–247 594–597, 594t absorption rate constants
clinical focus, 247 Transfer constants, 103 determined from,
drug interactions and, 336 Transgene, 622 190–191, 190f,
Timolol, 242, 242f Transit time in absorption. See 196t–197t, 198f
Tissue compartment, 99 also Occupancy theory curve, 98, 98f
distribution in, 269, 269t GI, 573–574, 574t elimination phase in, 76–77
Tissues large intestine, 574–575 of plasma drug
accumulation in, 264–265 Transporters concentration-time
blood flow to, 100t, 262, ABC, 367 curve, 98, 98f
262t in carrier-mediated intestinal for IV bolus administration,
concentration in, 13, 101–102, absorption, 382, 383t, 100, 103–107, 105f,
687t 384–386, 384f 105t, 106t
distribution to, 263–267, 263f, dose-dependent clearance, 80
264f pharmacokinetics, 252, clinical application, 105–107,
distribution within, 266 252t 105f, 105t, 106t
elimination by, 83–85 drug interactions based on, elimination rate constant,
TMP/SMX. See Trimethoprim/ 337t, 366–368 76–77
sulfamethoxazole efflux, 385–386, 385f method of residuals,
Tobramycin, in uremic patients, in elderly, 742–743 103–105, 104f, 104t
795, 800–801 genetic polymorphism of, practical focus, 107–108
Tolazamide, 198–199, 199f, 360t–361t practice problems, 110–112,
523–525, 524t in GI tract, 404 111f
Tolbutamide, 277–344 in hepatic clearance and relation between
Tolerance, 645–646 bioavailability, distribution and
Topical drug delivery, 468 348–349, 349f impact elimination half-life,
Torsades de pointes, 711 of, 386–387 107, 117–118, 118f
Total body clearance, 33, 163 P-gp, 159, 385–386, 387t of IV infusion, 141–142
after IV bolus infusion, drug internations involving, apparent volume of
241–242, 242f 336–338, 337t distribution in, 142
Total body weight (TBW), 755, gender differences in, 276 loading dose combined
755t genetic polymorphism of, with, 141–142, 141f
Total predictability, 723 360t–361t practical focus, 142–143
Total time for drug to be physiologic models of metabolites, 320–321, 320f,
excreted, 478, 478f incorporating, 832 321f
Toxic concentration. See physiologic pharmacokinetic with nonlinear elimination,
Minimum toxic models incorporating, 244
concentration 732–835, 822f, 834f Type I error, 56–57, 57t
Toxicity, in drug development, uptake of, 386–387 Type II error, 56–57
638f Trapezoid rule, 282
Toxicokinetics, 10–11, 818 Tricyclic antidepressants (TCAs) U
Toxicology, 6, 11 absorption of, 405, 406 United States Pharmacopeia
Transcellular absorption, distribution of, 272 National Formulary
377–378, 378f TTS. See Transdermal (USP-NF), 556
Transcytosis, 387–388 Therapeutic Systems Units of measurement, 32–33, 34t
910 INDEX
Uremia, 775–777, 777t V Waivers, of bioequivalence,
dose adjustment for, 785–796 Vaginal drug delivery, 455 studies, 503–505
fraction of drug excreted Valacyclovir, 487 Warfarin
unchanged methods, Validation, of release test, distribution of, 277
787, 790t–791t 426–429, 427t in elderly, 744
general clearance method, Validity, 67 elimination of, 284
794–795 of urinary excretion, 89–90, 89f TDM of, 683
method comparison, 784–786 Valium. See Diazepam Weak acids
nomograms for, 786–787, Valproic acid (Depakene), diffusion of, 381
789, 789f 242–243, 248–249 renal excretion of, 161–162
practice problems, 782–783, Vancomycin, 538, 692, 798–799 Weighted least-squares (WLS)
782f, 792–794, 794t Variables, 15, 57 approach, 717, 719–720
Wagner method, 795–796 Critical Manufacturing Well-stirred models, 76, 268,
pharmacokinetics of, 775–776 Variables, 542, 560 284, 295, 301
Urinary excretion data, 476t, nominal-scale type, 52 Wellbutrin. See Bupropion
477–478, 478f Variance, 54 hydrochloride
absorption rate constants Vasopressin, 407 Withdrawal symptoms, 616
determination with, 193 Veins, hepatic and portal, 332f WLS approach. See Weighted
cumulative amount of drug Velosef. See Cephradine least-squares approach
excreted in urine, 477, Venous drug concentrations,
477f 301 X
elimination rate constant Verapamil, 344 Xanthine oxidase, 324, 757
calculated from, Vesicular transport, 387–388 Xenobiotics, 723–724, 822
86–89, 86f, 88f Viagra. See Sildenal
clinical application, 89, 89f Vinblastine, 113, 333 Z
practice problem, 87–89, Vinca alkaloids, 333 Zantac®. See Ranitidine
88f Vincristine, 113 Zero-order absorption, 184–185,
rate of drug excretion, 478, Vindesine, 333 184f
478f Viral ADRs, 714 clinical application, 185, 185f
total time for drug to be Vitamin C, 70–71 nonlinear elimination with,
excreted, 478, 478f Vitamin E, 404 244–245
validity of, 89–90, 89f Volume of distribution. See Zero-order absorption model,
Urine Apparent volume of 184–185, 184f
drug concentration in, 13 distribution Zero-order elimination, 40–41,
formation of, 159, 160t VPA. See Sodium valproate 43
pH of Zero-order half-life, 40–410, 41t
renal excretion and, 161–162, W Zero-order process, 40–44
162f Wagner method, 995–996 Zero-order reactions, 40–410,
renal reabsorption and, 713 Wagner–Nelson method, 41t, 42f
USP-NF. See United States 190–191, 191f, 198f. Zithromax. See Azithromycin
Pharmacopeia National See also Modied Zolpidem tartrate (Ambien), 581
Formulary Wagner–Nelson method Zyvox. See Linezolid