Pharmacokinetics

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Contents

Basic considerations

Pharmacokinetics models

Compartment modeling

One compartment model- IV bolus, IV infusion, extra

vascular

Multi compartment model

Two compartment model

Non- linear pharmacokinetics

Cause of non- linearity

Michaelis- Menten equation

Estimation of Kmax and Vmax

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Pharmacokinetics

Refers on how the human body acts on the drug.

Definition:

• Pharmacokinetics is the study of the kinetics of drug

absorption, distribution, metabolism and elimination and

their relationship with the pharmacological, therapeutic or

toxicological response in man and animals.

➢ Now Pharmacokinetics can be better described as LADME.

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Pharmacokinetic Process

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Clinical Pharmacokinetics:

The application of pharmacokinetic principles in the safe

and effective management of individual patient.

Population pharmacokinetics:

The study of pharmacokinetic differences of drugs in

various population groups.

Toxicokinetics:

the application of principle to the design, conduct and

interpretation of drug safety evaluation studies.

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Plasma Drug Concentration–Time Curve

Two categorizes of parameters can be evaluated from a plasma

concentration time profile.

Pharmacokinetic

Pharmacodynamic

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Pharmacokinetic Parameters

❖Peak plasma concentration (cmax)

❖Time of peak concentration(tmax)

❖Area under curve (AUC)

Peak Plasma Concentration(cmax):

The point at which, maximum concentration of drug in

plasma.

Units : µg/ml

Peak conc. Related to the intensity of pharmacological

response, it should be above MEC but less than MSC.

The peak level depends on administered dose and rate of

absorption and elimination.

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Time of peak concentration (tmax):

The time for the drug to reach peak concentration in plasma

(after extra vascular administration).

Units : hrs

Useful in estimating onset of action and rate of absorption.

Important in assessing the efficacy of single dose drugs

used to treat acute conditions (pain, insomnia ).

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Area under curve (AUC):

It represents the total integrated area under the plasma level-

time profile and expresses the total amount of the drug

that comes into systemic circulation after its

administration.

Units : µg/ml x hrs

Represents extent of absorption – evaluating the

bioavailability of drug from its dosage form.

Important for drugs administered repetitively for treatment

of chronic conditions (asthma or epilepsy).

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PHARMACODYNAMICS

Pharmacodynamics is the study of the biochemical and

physiological effects of drugs on the body;

Includes the mechanisms of drug action and the

relationship between drug concentration and effect.

Typical example of pharmacodynamics is how a drug

interacts quantitatively with a drug receptor to produce a

response (effect).

Receptors are the molecules that interact with specific

drugs to produce a pharmacological effect in the body.

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PHARMACODYNAMIC PARAMETERS

1.Minimum effective concentration (MEC)

Minimum concentration of drug in plasma/receptor site is

required to produce therapeutic effect.

Concentration of drug below MEC – sub therapeutic level

2.Maximum safe concentration (MSC)

Concentration in plasma above which adverse or unwanted

effects are precipitated.

Concentration above MSC – toxic level

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3.Onset time

Time required to start producing pharmacological response.

Time for plasma concentration to reach MEC after

administrating drug.

4.Onset of action

The beginning of pharmacologic response.

It occurs when plasma drug concentration just exceeds the

required mec.

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5.Duration of action

The time period for which the plasma concentration of

drug remains above MEC level.

6.Intensity of action

It is the minimum pharmacologic response produced by the

peak plasma conc. Of drug.

7.Therapeutic range

the drug conc. Between MEC and MSC

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Pharmacokinetic models

Pharmacokinetic modeling is a mathematical modeling

technique.

Predicting the absorption, distribution, metabolism and

excretion (ADME) of synthetic or natural chemical substances

in humans and other animal species.

Why model the data ?

There are three main reasons

1. Descriptive: to describe the drug kinetics in a simple way.

2. Predictive: to predict the time course of the drug after

multiple dosing based on single dose data, to predict the

absorption profile of the drug from the iv data.

3. Explanatory: to explain unclear observations

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Applications

Characterizing the behaviour of drugs in patients.

Calculating the optimum dosage regimens for individual

patients.

Evaluating the bioequivalence between different

formulations of same drug.

Determining the influence of altered physiology or disease

state on drug ADME.

Prediction of drug concentration in various body fluids with

any dosage regimen.

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Estimation of the possible accumulation of drugs/

metabolites.

Correlating plasma drug concentration with

pharmacological response.

Explaining the drug interactions.

Evaluating the risk of toxicity with certain dosage

regimens.

Predicting the multiple dose concentration curves from

single dose experiments.

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Pharmacokinetic Model Approach

Pharmacokinetic models are hypothetical structures used to

describe the fate of a drug in a biological system following

its administration.

The two major approaches in the quantitative study of

various kinetic processes of drug disposition in body are

1. Model approach

2. Model independent approach

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Pharmacokinetic Modelling

Compartment Models Non-compartment Models Physiologic Models

AUC, MRT, MAT, Cl, VSS

Caternary Mamillary Model

Model

One compt Multi compt Two compt

i v bolus

i v bolus

Single oral Dose

i v infusion

Oral drug

Intermittent i v infusion

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Multiple doses

Types of pharmacokinetic models

Compartment models ; are also called empirical models.

Physiological models ; are realistic models.

Distributed parameter models ; are also realistic models.

A Compartment is a group of tissues with similar blood

flow and drug affinity.

A compartment is not a real physiologic or anatomic region.

A Model is a mathematic description of a biologic system

and is used to express quantitative relationships.

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Compartment model

Traditional and most widely used approach to

pharmacokinetic characterization of drug.

simply interpolate the experimental data and allow on

empirical formula to estimate drug concentration with time.

Assumptions of Compartmental Models

The body is represented as a series of compartment

arranged in series or parallel to each other.

Each compartment is not a real physiological or anatomical

region but fictitious or virtual one.

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Considered as a tissue or group of tissue that have similar

drug distribution characteristics

Within each compartments the drugs is considered to be

rapidly and uniformly distributed.

The rate of drug movement between compartment (entry

into and exit)is described by first order kinetics.

Rate constants are used to represent rate of entry into and

exit from compartment.

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Types of Compartment model

Two categories

Mammillary model

Catenary model

❖Mammillary model

Most common compartment model used in

pharmacokinetics.

It consists of one or more peripheral compartments

connected to the central compartment in a manner similar

to connection of satellites to a planet .

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They are joined parallel to the central compartment.

The central compartment( or compartment 1) comprises of

plasma and highly perfused tissues such as lungs, liver,

kidney etc. which rapidly equilibrate with drugs.

The peripheral compartments or tissue compartments (

denoted by numbers 2,3 etc) are those with low vascularity

and poor perfusion.

Distribution of drugs to these compartments is through

blood.

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Movement of drug can be defined by first-order kinetics.

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Catenary model

The compartments are joined to one another in a series like

compartments of a train.

It is rarely used because it is not observed that anatomicaly

or physiologically various organs are directly linked to the

blood compartment.

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Applications of Compartment Modeling

Simple and flexible approach and is widely used

Gives a visual representation of various rate process

involved in drug disposition.

Shows how many rate constants are necessary to describe

these processes.

To describe drug concentration changes in each

compartment.

Monitoring of drug concentration change with time a

limited amount of data( plasma concentration or urinary

excretion data is sufficient.)

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Important in the development of dosage regimens.

Useful in predicting drug concentration time profile in both

normal and pathological conditions.

Useful in relating plasma drug levels in therapeutic and

toxic effects in body.

Clinically, drug data comparisons are based on

compartment models.

Its simplicity allows for easy tabulation of volume of

distribution, half life etc.

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Disadvantages

Several assumptions have to be facilitate data

interpretation, since the compartments and parameters bear

no relationship with the physiological function.

Extensive efforts are required in the development of an

exact model.

Model may vary within a study population.

Can be applied only to a specific drug under study.

Difficulties generally arise when using models to interpret

the differences between results from human and animal

experiments.

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Physiological Models

Also known as physiologically – based pharmacokinetic

models (PB-PK Models)

drawn on the basis of known anatomical and physiological

data

present more realistic picture of drug disposition in various

organs and tissues.

The number of compartments to be included in the model

depends upon the disposition characteristic of the drug.

Tissues with similar perfusion properties are grouped into a

single compartment

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Types of Physiological method

Two types

Blood flow rate limited models

Membrane permeation rate limited models

Blood flow rate limited models:

More popular and commonly used

Assumption that the drug movement within a body region is

much more rapid than its rate of delivery to that region by the

perfusing blood.

Also called as perfusion rate limited models.

Applicable only to the highly membrane permeable drugs.

(low molecular weight, poorly ionised & highly lipophilic

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drugs- thiopental, lidocaine)

Membrane Permeation Rate Limited Models

More complex

Applicable to highly polar, ionised and charged drugs.

Cell membrane act as a barrier for the drug that gradually

permeates by diffusion.

Also called as diffusion limited models

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Advantages

Mathematical treatment is straightforward.

Realistic approach.

Data filling is not required.

Gives exact description of drug concentration –time profile

in any organ or tissue,

The influence of altered physiology or pathology on drug

disposition can be easily predicted from changes in the

various pharmacokinetic parameters.

Frequently used in animals.

Mechanism of ADME of drug can be easily explained.

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Disadvantages

Obtaining the experimental data is a very exhaustive

process.

Prediction of individualized dosing is difficult.

Less number of data point is to be assessed.

Monitoring of drug concentration in body is difficult.

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Distributed Parameter Model

Analogous to physiological model but has been designed to

take into account

Variations in blood flow to an organ.

Variations in drug diffusion in an organ.

Specially useful for assessing regional difference in drug

concentration in tumours or narcotic tissues.

Mathematical equations are more complex and collection of

drug concentration data is more difficult.

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Non Compartmental Analysis

Also called as model independent methods

It does not require the assumption of specific compartment

model.

Based on the assumption that the drugs or metabolites

follow linear kinetics.

Can be applied to any compartment model.

Approach based on statistical moments theory.

It involves collection of experimental data following a

single dose of drug

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If one consider the time course of drug concentration in

plasma as a statistical distribution curve, then

MRT = AUMC/AUC

Where

MRT= mean residence time

AUMC= area under the first moment curve

AUC= Area under the zero moment curve

MRT= is defined as the average amount of time spent by

the drug in the body before being eliminated.

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Applications

Used to estimate the important Pk parameters-

bioavailability, clearance and apparent volume of

distribution.

Also useful in determining half life, rate of absorption and

first order absorption rate constant.

Advantages:

Ease of derivation of Pk parameters by simple algebraic

equations

Same mathematical treatment can be applied almost any

drug or metabolite if they follow first order kinetics.

Detailed description of drug disposition characteristic is not

required.

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Disadvantages

Provides limited information regarding the plasma drug

concentration- time profile.

Does not adequately treat non- linear cases.

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One Compartment Open Model

Simplest model.

The body is considered as a single , kinetically

homogenous unit.

This model applies only to those drugs that distributes

rapidly throughout the body.

Drugs move dynamically in an out of this compartment

Elimination is first order (monoexponential) process with

first order rate constant

Rate of input(absorption)> rate of output(elimination).

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• Any change in plasma concentration reflects a proportional

change in drug concentration throughout the body.

• Open model indicates that the input (availability) and

output(elimination) are unidirectional and that the drug can

be eliminated from the body.

Ka KE

Metabolism

Drug

Blood and other

Input body tissues output

(Absorption) (Elimination) Excretion

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One Compartment Open Model

Intravenous Bolus Administration

When drug is given in the form of rapid i.v. injection it takes

about one to three Minutes for complete circulation.

Hence, the rate of absorption is neglected in calculations.

Blood and other body KE

tissues

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General expression of rate of drug presentation to the body

is

dX= Rate In –Rate Out

dt

If, Rate in absorption is absent,

dX= Rate Out

dt

If, the rate out or elimination follows first –order kinetics

dX= -KEX

dt

KE=first order elimination rate constant

X= amount of drug in body at any time t

remaining to be implemented.

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Estimation of Pharmacokinetic Parameters- IV

bolus Administration

A drug that follows one compartment kinetics and

administered as rapid I.V. Injection , the decline in plasma

drug concentration is only due to elimination of drug from

the body, the phase being called as elimination phase.

Elimination phase can be characterized by 3 parameters

❖Elimination rate constant

❖Elimination half- life

❖Clearance

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Elimination Rate Constant

dX = – KEX

dt

Integrating above equation yields

ln X = ln X0 – KEt

where Xo = amount of drug at time t=0 (initial amount of

drug injected)

Equation can be written in exponential form as

X= Xo e‐KEt

The above equation shows the disposition of a drug that

follows one compartmental kinetics is monoexponential.

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Transforming equation into logarithm form we get,

Log X = Log X0 –‐ KEt

2.303

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X=Vd C

X= amount of drug in the body

C= drug concentration in plasma

Vd = Apparent volume of distribution

Log C = Log C0 KEt

2.303

Overall elimination rate Constant:

The elimination or removal of drug from the body is the sum

of urinary excretion, metabolism, biliary excretion,

pulmonary excretion and other mechanism involved therein.

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Elimination half life

Also called as biological half life.

Defined as the time taken for the amount of drug in the

body as well as plasma concentration to decline by one-half

or 50% its initial value.

t1/2 = 0.693/KE

t1/2 = 0.693Vd/ClT

Apparent volume of distribution:

Two separate and independent pharmacokinetic

characteristic of drugs are

1. Apparent volume of distribution

2. clearance

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For drugs given as i.v. bolus ,

Vd(area) = X0

KEAUC

For drugs administered extravascularly,

Vd= FX0

KEAUC

where,X0= dose administered

F=fraction of drug absorbed in

systemic circulation.

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Clearance

Clearance is defined as the theoretical volume of body fluid

containing drug from which the drug is completely

removed in a given period of time.

Cl = Rate of elimination

Plasma drug concentration

Cl = dX/dt

C

Total body clearance : elimination of drug from the body

involves processes occurring in kidney, liver, lungs and

other eliminating organs.

Also called as total systemic clearance.

ClT = ClR+ ClH+ Cl others

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ClT= KEX

C

X/C = Vd

ClT=KEVd ; ClH=KmVd;ClR=KeVd

ClT= 0.693Vd

t1/2

for drugs given as IV bolus

ClT = X 0

AUC

for drugs given as EV

ClT = FX 0

AUC

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Organ clearance

Rate of Elimination = Rate of Presentation to the organ –

Rate of exit from the organ

Rate of Presentation (input)= organ blood flow x Entering

concentration = (QCin)

Rate of exit (output)= organ blood flow x Exiting

concentration= (QCout)

Rate of elimination ( rate of extraction) = QCin- Qcout

Extraction Ratio(ER)=Cin- Cout/ Cin

Based on ER values drugs can be

classified as:

Drugs with high ER=above0.7

Drugs with intermediate ER=between 0.7‐0.3

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D.DruulogMsix .cwomith low ER = below 0.3

Hepatic clearance

ClH= ClT- ClR

ClH =QHERH

QH = hepatic blood flow(about 1.5l/min)

ERH = hepatic extraction ratio

Divided into 2 groups

Drugs with hepatic blood flow rate limited clearance

Drugs with intrinsic capacity limited clearance.

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One Compartment Open Model – Intravenous

Infusion

Rapid i.v. injection is unsuitable when the drug has

potential to precipitate toxicity or when maintenance of a

stable concentration or amount of the drug in body desired.

In such a situation, the drug is administered at a constant

rate (zero ordered) by i.v. infusion.

Advantages of zero order infusion of drug include

1. Ease of control of rate of infusion.

2. Prevents fluctuating maxima and minima (peak and

valley) plasma level. This is desired especially when the

drug has a narrow therapeutic index.

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Other drugs, electrolytes and nutrients can be conveniently

administered simultaneously by the same infusion line in critically ill

patients.

The model can be represented as follows

During infusion, the rate of change in amt. of drug in the body, dx/dt is

the difference between the zero order rate of drug infusion Ro and first

order rate elimination, ‐KEx:

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Integration and rearrangement of above equation yields

Since X=Vd C the above equation can be transformed into

concentration terms as follows

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One Compartment Open Model- Extravascular

Administration

When a drug is administered by extravascular route (e.g.

oral, i.m., rectal, etc.), absorption is a prerequisite for its

therapeutic activity.

The rate of absorption may be described mathematically as

a zero-order or first-order process.

A large number of plasma concentration time profiles can

be described by a one compartment model with first-order

absorption and elimination.

However, under certain conditions, the absorption of some

drugs may be better described by assuming zero-order

(constant rate) kinetics.

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Distinction between zero-order and first-order absorption

processes. Figure a is regular plot, and Figure b a semi log

plot of amount of drug remaining to be absorbed (ARA)

versus time t.

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Zero-order absorption is characterized by a

constant rate of absorption

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During absorption phase, the rate of absorption is greater than

elimination phase.

At plasma concentration, the rate of absorption equals the rate of

elimination and the change in amount of drug in the body is zero

During post absorption phase, the rate of elimination is greater than the

absorption rate

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Zero Order Absorption Model – EV

Administration

This model is similar that for constant rate infusion.

In controlled drug delivery systems, the rate of drug

absorption is constant and continues until the amount of

drug at the absorption site (GIT) is depleted.

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First Order Absorption Model – EV

Administration

For a drug that enters the body by a first order absorption

process, gets distributed in the body according to one-

compartment kinetics and is eliminated by a first order

process

Differential form of the equation

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Ka = first order absorption rate constant

Xa = amount of drug at the absorption site remaining to be

absorbed.

integration of above equation yields

Transforming into concentration terms,

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Assessment of Pharmacokinetic Parameters – EV

Administration

Cmax and tmax:

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Elimination Rate Constant:

Absorption rate is significantly greater than the elimination

rate Kat >>Ket

Absorption rate constant:

Calculated by method of residuals

Te technique also known as feathering, peeling and

stripping

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Wagner- Nelson Method for Estimation of Ka

Determination of Ka from unabsorbed amount of drug at

any time plots.

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Determination of KE from urinary excretion data

Rate of excretion method

Sigma-minus method

Rate of excretion method:

Advantage:

Drugs that having long half- lives, urine may be collected

for only 3-4 half lives.

No need to collect all urine samples.

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Sigma- Minus method

(X ∞

u – Xu)=amount remaining to be excreted ARE

Disadvantage: Total urine has to be carried out until no

unchanged drug can be detected in the urine (upto 7-half-

lives)

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Multicompartment models

One compartment is described by mono‐exponential term i.e

.elimination.

For large class of drugs this terms is not sufficient to descr

ibe its disposition.

It needs a bi‐or multi‐exponential terms

This is because the body is composed of a heterogeneous g

roup of tissues each with different degree of blood flow an

d affinity or drug and therefore different rates of eliminatio

n.

Ideally a true pharmacokinetic model should be the one wit

h a rate constant for each tissue undergoing equilibrium.

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Multicompartment Model

( delayed distribution methods)

Multicompartment models provide answers to such

questions as:

(1) How much of a dose is eliminated?

(2) How much drug remains in the plasma compartment at

any given time? And

(3) How much drug accumulates in the tissue

compartment?

The latter information is particularly useful for drug safety

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Multicompartment models are based on following assumptions

Central compartment-comprising of blood/plasma and

highly perfused tissues such as brain, heart, lung, liver and

kidney.

Peripheral compartment comprising of poorly perfused

tissues such as muscles, skin & adipose etc.

IV administered medications are introduced directly into

the central compartment

Irreversible drug elimination (hepatic or renal excretion )

take place only from the central compartment

Reversible distribution occurs between central and

peripheral compartment.

Elimination of drug follows first order kinetics

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Two Compartment Open Model

All multicomponent models is a two compartment model.

Body tissues are broadly classified into 2 categories.

Central compartment or Compartment1:

Comprises of blood and highly perfused tissues like liver

,lungs, kidneys, etc that equilibrate with the body rapidly.

Peripheral or Tissue Compartmen or Compartment2:

Comprises of poorly perfused and slow

equilibrating tissues such as muscles,

skin, adipose, etc.

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Considered as a hybrid of several

functional physiologic units.

Based on the drug elimination, two compartment model

can be categorized in to 3 types

1. With elimination from Central

compartment

1. With elimination from peripheral

compartment

1. With elimination from both the

compartments

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Two Compartment Open Model –IV bolus

Administration

The rate constants k12 and k21 represent the first-order rate

transfer constants for the movement of drug from

compartment 1 to compartment 2

(k12) and (k21) represents from compartment 2 to

compartment 1.

Most two-compartment models assume that elimination

occurs from the central compartment model.

The plasma level–time curve for a drug that follows a two-

compartment model may be divided into two parts,

(a) a distribution phase

b) an elimination phase

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Distribution Phase:

The initial, more rapid decline of drug from the central

compartment into the tissue compartment.(line a).

• Elimination phase:

The drug concentrations in both the central and tissue

compartments decline in parallel and more slowlycompared

to the distribution phase. This decline is a first-order

process and is called the elimination phase or the beta (ß)

phase (line b) or post‐distributive phase.

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During the distribution phase, Drug elimination and

distribution occur concurrently.

Net transfer of drug from the central compartment to the

tissue compartment because the rate of distribution is faster

than the rate of elimination.

• The fraction of drug in the tissue compartment is

equilibrium with the fraction of drug in the central

compartment.

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In contrast to this compartment, the

conc of drug in the peripheral compartment firs

t increases and reaches its max.

Following peak, the drug conc declines

which corresponds to the post‐distributiv phase.

dCc = K21Cp–K12Cc–KECc

dt

Extending the relationship X= VdC

dCc = K21Xp – K12Xc – KEXc

dt Vp Vc Vc

Xc & Xp= amount of drug in the central and peripheral

compartment,

Vc & Vp= apparent volume of drug in the central &

peripheral compartment.

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The rate of change in drug conc in the peripheral component is given

by:

On integration equation gives conc of drug in central and peripheral

compartments at any given time t :

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α andβ are hybrid first order constants for rapid dissolution

phase and slow elimination phase, which depend entirely

on 1st order constants K12, K21, KE

The constants K12, and K21 that depict the reversible

transfer of drug between the compartments are called micro

or transfer constants.

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Simplification of the equation as

Cc = distribution exponent + elimination exponent.

A and B are hybrid constants for two exponents and can be

resolved by graph by method of residuals.

Co = plasma drug conc immediately after i.v. injection

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Method of residuals :

The biexponential disposition curve obtained after i. v. bolus of a drug

that fits two compartment model can be resolved into its individual

exponents by the method of residuals

From graph the initial decline due to distribution is more rapid than the

terminal decline due to elimination i.e. the rate constant a >> b and

hence the term e‐at approaches zero much faster than e –βt

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In log form, the equation becomes

C = back extrapolated plasma concentration

values

A semilog plot of C vs t yields the terminal linear

phase of the curve having slope –b/2.303 and

when back extrapolated to time zero, yields

y‐intercept log B. The t1/2 for the elimination

phase can be obtained from equation

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www = 0.693/b.

Residual conc values can be found as‐

Cr = C – C = Ae‐αt

log Cr = log A – αt

2.303

A semilog plot

Cr vs t gives a

straight line.

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Assessment of Pharmacokinetic Parameters – IV

Bolus Administration

Parametres of the model viz K12, K21, KE etc can be derived by

proper substitution of the values

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For two compartment model, KE is the rate constant for

elimination of drug from the central compartment and β is

the rate constant for elimination from the entire body.

Overall elimination t1/2 can be calculated from β.

Area under the plasma concentration –time curve can be

obtained by

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The apparent volume of central compartment Vc is given as

The apparent volume of peripheral compartment can be

obtained from the equation

The apparent volume of distribution at steady state or

equilibriumcan be defined as

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It is also given as

Total systemic clearance is given as

The pharmacokinetic parameters can also be calculated by

using urinary excretion data

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Rate of excretion of unchanged drug in urine

Renal clearance is given as

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Two Compartment Open Model – IV Infusion

The model can be depicted as shown as

The plasma or central compartment concentration of a drug

that fits two compartment model when administered as

constant rate (zero order) IV infusion, is given by equation:

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At steady state, the second and third term in the bracket becomes zero

and equation reduces to

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Now VcKE = Vdß substituting this in equation

The loading dose Xo,L to obtain Css immediately at the

start of infusion can be calculated from the equation

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Two Compartment Open Model- Extravascular

Administration – First Order Absorption

This model can de depicted as follows

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The rate of change in drug concentration in the central

compartment is described by 3 exponents that describe drug

disposition.

C=absorption exponent + distribution exponent +

elimination exponent

The 3 exponents can be resolved by stepwise application of

method of residuals assuming Ka>α>β

Ka can also be estimated by Loo- Riegelman method.

It requires plasma concentration-time data both after oral

and IV administration of the drug to the same subject at

different times.

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Non linear Pharmacokinetics

It is a Dose Dependent Pharmacokinetics.

Nonlinear pharmacokinetic models imply that some aspect

of the pharmacokinetic behaviour of the drug is saturable.

It is also called as mixed –order and capacity limited

kinetics.

Detection of Non linear pharmacokinetics:

Determination of steady state plasma concentration at

different doses.-

if the steady state concentrations are directly proportional

to the dose is not observable.

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Determination of some important pharmacokinetic

parameters such as fraction bioavailable, elimination half

life or total systemic clearance at different doses of drug.

Any change in these parameters is indicative to non-

linearity which are usually constant.

Causes of non-linearity:

Drug absorption

Distribution

Metabolism

Excretion

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Drug Absorption

Three causes:-

1. Solubility / dissolution of drug is rate-limited;

Griseofulvin – at high concentration in intestine.

2. Carrier – mediated transport system; Ascorbic acid,

Riboflavin & Cyanocobalamin – saturation of transport

system at higher doses results in non linearity.

3. Presystemic gut wall / hepatic metabolism attains

saturation; Propranolol, hydralazine andverapamil-

saturation of presymetic metabolism of these drugs at

high doses leads to increased bioavailability.

These parameters affected F, Ka, Cmax and AUC.

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Drug Distribution

Non linearity in distribution of drugs administered at high

doses may be due to

1. Saturation of binding sites on plasma proteins. ex:

Phenylbutazone and naproxen

2. Saturation of tissue binding sites. Ex: thiopental, fentanyl.

In both cases free plasma drug concentration increases.

Vd Increase only in (1)

Clearance with high ER get increased due to saturation of

binding sites.

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Drug Metabolism

Non-linearity occurs due to capacity limited metabolism,

Small changes in dose administration can produce large

variations in plasma concentration at steady state- major

source of large intersubject variability in pharmacological

response..

• Two important causes

1.Capacity – limited metabolism due to enzyme

&/cofactor saturation; Phenytoin, Alcohol, theophylline

Saturation of enzymes results in – decrease in ClH –

increase in Css.

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2.Enzyme induction–Ex. Carbamazepine.

decrease in peak plasma concentration- on repetitive

administration over a period of time.

Common cause of both dose and time dependent kinetics.

Enzyme induction results in increase ClH – decrease in

Css.

Other reasons of non linearity includes saturation of

binding sites, inhibitory effects of the metabolites on

enzymes and pathological situations (hepatotoxicity and

changes in hepatic blood flow).

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Drug Excretion

Two active processes in renal excretion of a drug which are

saturable,

1. Active tubular secretion – Penicillin G after saturation of

carrier systems – decrease in renal clearance.

2. Active tubular reabsorption – Water soluble vitamins &

Glucose.- after saturation of carrier systems – increase in

renal clearance.

Other reasons like forced diuresis, change in urine pH,

nephrotoxicity & saturation of binding sites.

In case of biliary excretion non – linearity due to saturation

– Tetracycline & Indomethacin.

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Michaelis Menten Equation

The kinetics of capacity limited or saturable processes is

best described by Michaelis-Menten equation.

-dc = Vmax C (I)

dt Km+C

-dC/dt = rate of decline of drug conc. with time

Vmax = theoretical maximum rate of the process

KM = Michaelis constant

Three situation can now be considered depending upon the

value of Km and C.

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1.When KM = C:

under this situation , eq I reduces to,

-dC/dt = Vmax/2 ……………….II

The rate of process is equal to half of its maximum rate.

2.When Km >>C

Here Km +C = Km and the equation I reduces to

-dc/dt = Vmax C/ Km

above eq. is identical to the one that describe first order

elimination of drug, where Vmax/KM= KE.

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3. When Km<< C

under this condition, Km+C= C and the equation (I)

-dc/dt= Vmax

above equation is identical to the one that describe a zero

order process i.e. the rate process occurs at constant rate

Vmax and is independent of drug conc.

E.g. Metabolism of ethanol

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Determination of Km and Vmax

The parameters Kmand Vmax can be assessed from the

plasma concentration –time data collected after IV bolus

administration of a drug with nin linear characteristics.

Rewriting the equation (I)

-dc = Vmax C

dt Km+C

Integration of above equation followed by conversion to

log base 10 yields

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Km and Vmax from Steady State Concentration

If drug is administered for constant rate IV infusion/ in a

multiple dosage regimen, the steady-state conc. is given in

terms of dosing rate (DR):

(1)

If the steady-state is reached, then the dosing rate = the rate

of decline in plasma drug conc. & if the decline occurs due

to a

single capacity-limited process then above equation

become as:

(2)

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Estimation of Km and Cmax

Three methods are used

1. Lineweaver-Burk/Klotz Plot

2. Direct linear plot

3. Graphical method

Lineweaver-Burk/Klotz Plot:

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Direct linear plot

A pair of Css1 and

Css2 obtained with

two different dosing

rates DR1and DR2 is

plotted.

The points Css1 and

DR1 are joined to form

a line and a second line

is obtained similarly

by joining Css2 and

DR2.

DR axis to obtain V

max and on x axis to

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Graphical Method

In this method by rearranging eq. (2) we get

KM & Vmax can be estimated by simultaneous eq. As

Combination of the above 2 equation yields

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