21
COMPUTER SIMULATIONS IN
PHARMACOKINETICS AND
PHARMACODYNAMICS:
REDISCOVERING SYSTEMS
PHYSIOLOGY IN THE 21ST
CENTURY
Paolo Vicini
Contents
21.1 Introduction
21.2 Level 1: Computer Simulation of the Whole Organism
21.3 Level 2: Computer Simulation of Isolated Tissues and Organs
21.4 Level 3: Computer Simulations of the Cell
21.5 Level 4: Proteins and Genes
21.6 Conclusion
Acknowledgments
References
21.1 INTRODUCTION
Perhaps no technology in human history has radically changed so many dis-
ciplines as the introduction of personal computing and the now-ubiquitous
presence of the World Wide Web. What the joint application of these enabling
technologies allows us to do is to instantaneously and effi ciently exchange
Computer Applications in Pharmaceutical Research and Development, Edited by Sean Ekins.
ISBN 0-471-73779-8 Copyright © 2006 John Wiley & Sons, Inc.
513
514 REDISCOVERING SYSTEMS PHYSIOLOGY IN THE 21ST CENTURY
robust, verifi able, and consistent information. An area that has benefi ted
enormously from this is what is sometimes termed as “biocomputation,” or
the revolutionary transformation of biological and biomedical research from
a painstaking endeavor often reserved for bench and fi eld researchers to
a discipline based on prompt availability of information and data mining
(Fig. 21.1). However, clearly outlining what is exactly entailed by “biocompu-
tation,” or “biomedical simulations,” is more often than not a challenge.
Terms like “systems biology” and “bioinformatics” are increasingly used in
multiple settings, but the multiple meanings behind them and especially the
expectations associated with these technologies are not always clear. Some
even draw a distinction between “biomedical informatics” and “bioinformat-
ics,” not unlike those who distinguish between “bioengineering” and “bio-
medical engineering.” The very fact that biomedical computation has become
so pervasive has made it diffi cult to draw clear boundaries between areas and
to unambiguously defi ne areas of expertise and/or infl uence for practitioners
that are now extending computer modeling to virtually every aspect of the
biomedical enterprise “from bench to bedside”[1], all the way from clinical
record management to computer-aided drug design, through clinical trial
simulation, therapeutic drug monitoring, pharmacogenomics, and molecular
engineering.
The information revolution in biology has been facilitated, and in a very
real sense motivated, by the emphasis placed on “discovery science”[2]
projects such as the Human Genome Project and the various databasing
efforts needed to somehow coordinate and manage the increasing amount
of bioinformation being generated by thousands of laboratories worldwide.
This has coincided with a scientifi c change of emphasis that is best tracked
through the different interpretations and meanings associated with the
phrase “systems biology” nowadays and a few decades ago. According to
Guyton [3] and other holistic physiologists, a living homeostatic system was
thought of as being comprised of a series of interacting parts, or subsystems,
an understanding of which was deemed essential to comprehension of the
complex dynamics of the whole. However, the starting point at that time was
the intact system, as it was believed that only through information gathered
on the macroscopic behavior of the whole could one understand the inner
workings of the parts. Since Aristotle’s proposal that “the whole is more
than the sum of the parts,” direct investigation of the living system was
essential. The approach was “top to bottom.” This point of view shifted with
the advent of molecular biology, which brought within reach the possibility
of looking directly at the parts themselves at an unprecedented level of bio-
physical detail. A clear, unambiguous, and validated understanding of the
parts would in time, researchers argued, lead to an understanding of how
they interact and how they conspire to shape the dynamic performance of
the intact, living system. This in turn motivated a paradigm shift from clini-
cal sciences to basic sciences, and in pharmaceutical sciences from clinical
pharmacology to molecular pharmacology. This is the “bottom to top”
INTRODUCTION 515
NCBI PubMed Articles on “Computer Simulation”, 1994-2004 NCBI PubMed Articles on “Computer” and “Drug
Development”, 1994-2004
7000 35
6000 30
5000 25
4000 20
3000 15
2000 10
1000 5
0 0
19941995 199619971998 19992000 200120022003 2004 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
Publication Year Publication Year
Figure 21.1 The emergence of computer simulation in the peer-reviewed biomedical literature as represented in NCBI’s
PubMed. The database is available at http://www.pubmed.org, and the searches were carried out on September 17,
2005.
Number of Articles
Number of Articles
516 REDISCOVERING SYSTEMS PHYSIOLOGY IN THE 21ST CENTURY
approach to biomedical research. Clearly, with so much information at their
fi ngertips, modern biologists should have more than enough ammunition to
build comprehensive, testable models of biosystems: Possunt quia posse
videntur. However, what could not be anticipated is that unexpected com-
plexity lurked in the modalities of interactions of the ingredients that make
up a living system, so that mathematical and computer representations of
comparatively simple subsystems tend to be almost invariably much more
complex than the whole, living system of which they are a part [4]. This has
turned into a somewhat unsatisfactory situation for modern biological
research, where the need to refocus is periodically felt, for example, through
initiatives such as the NIH Roadmap [5] and changes to NIH peer review
criteria [6].
The drug development process was also infl uenced by these changes in
perspective, but in a slightly different way. Because drug development must
remain focused on the clinical outcome, or, in other words, it has to generate
drugs that are safe and effective, the shift to molecular pharmacology has,
at least in the private sector, been accompanied by a continued presence of
the tenets of clinical pharmacology, in a benefi cial synergy that includes the
best of both worlds [7]. This has not necessarily been the case in academia,
where training programs in clinical pharmacology have become few and far
between and the emphasis is on basic science, sometimes at the expense of
traditional disciplines such as pharmacokinetics and pharmacodynamics
[8].
What happens in drug development these days is a recasting of Guyton’s
all-encompassing, whole-system quantifi cation approach, balanced by an
increased awareness of the “parts list” that comes from molecular biology [9].
Thanks to the pragmatism that characterizes the drug development process,
these two different emphases are both used to lead to the creation of better
therapeutics. The FDA, for example, has been rather well positioned to take
advantage of advances in biocomputation and has introduced recent develop-
ments in computational modeling in the development process through the
issue of guidances and consensus documents [10]. The same is happening at
other federal agencies. The EPA is becoming increasingly aware [11] of the
potential advantage [12] of aggressively using computational representations
of complex systems to predict likely system behavior, or at least narrow down
the fi eld of possibilities. DARPA has started a project, termed Virtual Soldier,
to achieve the rather ambitious goal of creating physiological, mathematical,
and software representations of individual soldiers [13].
In this chapter, we describe some of the advances in biocomputation that
have impacted or potentially will impact pharmaceutical research and devel-
opment. We list them by “biological size,” going from the most to the least
organized, or from the most complex to the least complex. We focus on clini-
cal sciences in particular, because we feel that simplifi ed, but useful repre-
sentations of pharmacological interventions have the greatest potential for
LEVEL 1: COMPUTER SIMULATION OF THE WHOLE ORGANISM 517
shortening the development process and weeding out potentially unsatisfac-
tory candidates. The discussion is articulated along four levels, roughly fol-
lowing the idea of “biological size.” which will carry us from whole organism
to genetic networks through the analysis of biocomputation applications to
isolated organs, cells, and molecules.
21.2 LEVEL 1: COMPUTER SIMULATION OF THE
WHOLE ORGANISM
In a sense, being able to model the whole organism is the essential goal of
biocomputing. In drug development, it provides the obligatory handle to lead
to response from exposure (Fig. 21.2). Provided the intact organism can be
mathematically represented, a whole series of possibilities can be brought into
practice, such as the simulation of clinical trials and of the prospective behav-
ior of entire populations. In drug development, whole body systems are usually
represented in one of two ways. The fi rst approach is through the formaliza-
tion of a lumped-parameter PK-PD model [14], often coupled with a model
of the disease process [15], whose parameters can be estimated from data. A
relatively small number of differential equations, between one and ten, is used
to predict the system’s behavior over time [16]. Often, but not always, some
variation of population PK-PD [17], predicated on nonlinear regression and
nonlinear mixed-effects models [18], is used to estimate both the population
parameter values and their statistical distribution. The same approach can be
taken in reverse [19] by using models to generate synthetic data, ultimately
performing a full clinical trial simulation from fi rst principles [20]. The other
approach to whole organism models is based on physiological modeling [21],
brought into practice by physiologically based pharmacokinetic (PBPK)
models [22]. These models are still based on ordinary differential equations,
but they attempt to describe the organism and especially the interacting
organs with more detail, often by increasing the number of differential equa-
tions (from 10 to perhaps 30) and building appropriate interactions between
Exposure Kinetics Dynamics Response
•Dosage Regimen •Route and absorption •Effect and toxicity •Continuous/discrete
•Chronic exposure •Demographics •Receptor interaction •Clinical endpoints
•Environmental factors •Serum concentrations •Biomarkers •Surrogate endpoints
Figure 21.2 The exposure-response road map passes through pharmacokinetics and
pharmacodynamics. This sequence of events is essentially the same as that which
informs computer simulation of clinical trials, with the addition of complicating, but
important, factors such as protocol adherence and dropouts.
518 REDISCOVERING SYSTEMS PHYSIOLOGY IN THE 21ST CENTURY
the organs that resemble their physical arrangement in the organism being
studied.
Although the representation of the intact organism provided by PK-PD
and PBPK models is simplifi ed, it does pose nontraditional challenges. For
PK-PD, the purpose consists in fi nding the best (simplest?) model that can
explain the observations [23]. Formally speaking, the concept of “best” is
diffi cult to defi ne unambiguously. More often than not, model selection is
driven by some kind of parsimony criterion that balances model complexity
with the actual information content provided by the measurements. A con-
sensus workshop developed some time ago a set of “good practices” that can
serve as guidance to model development, selection, and application [24].
PBPK models come at the problem from a different angle [25]. Because they
embed previous knowledge about the organ kinetics, their arrangements, and
their specifi c parameter values, the process of tailoring the model to the spe-
cifi c measurements at hand is not as crucial. On the other hand, PBPK models
can suffer greatly in their predictive power if their parameterization is inac-
curate, poorly specifi ed, or not well tailored to the particular drug. Many
researchers split PBPK model parameters and structures into “drug specifi c”
and “not drug specifi c,” thus implying that the model can indeed capture
some underlying dynamics that are general for all drugs, and that further
specifi cation can be limited to the exclusive characteristics of a certain mole-
cule. It is also very important to specify parameter and structure uncertainty
when dealing with model-based predictions [26]. More detail on how these
parameters can be specifi ed is also provided below. The approach taken by
PBPK modeling is not very dissimilar from the recently proposed Physiome
Project [27], a “parts list” of the human organism whose development follows
the broad strokes of the Human Genome Project. More often than not, the
rate-limiting step for development of PBPK models is the availability of infor-
mation on single-organ parameters, such as clearance rates and partition
coeffi cients [28]. An exhaustive list of these such as the one that the Physiome
Project may provide could certainly be of use to the biomedical investigator.
As we have mentioned above, the EPA is also showing interest in computer-
based prediction of individual pharmacokinetics and has recently released a
document detailing the technology for public comment. Finally, it is worth-
while to note that there have been recent advances in the understanding of
the mechanistic underpinnings of whole organism homeostasis [29] that have
not yet been aggressively applied in drug development (where they would be
most useful, one would expect, for between- and within-species scaling).
It is interesting to note that the foremost challenges for the detailed model-
ing of the intact organism (computing time, complexity of interactions, model
selection) are very similar to those entailed by the analysis of proteomic or
genomic data. In the clinical case, complexity shifts from the richness of the
data set to the model formulation, whereas in the proteomic-genomic case the
main source of diffi culties is the sheer size of the data set; however, at least
at present, interpretative tools are rather uncomplicated.
LEVEL 2: COMPUTER SIMULATION OF ISOLATED TISSUES AND ORGANS 519
21.3 LEVEL 2: COMPUTER SIMULATION OF ISOLATED
TISSUES AND ORGANS
The behavior of molecules in isolated organs has been the subject of
extensive investigation. The heart [30] and the liver [31] were historically
the organs most extensively investigated [32], although the kidney [33] and
brain [34] have also been the subjects of mathematical modeling research.
The liver in particular has been extensively researched both in the bio-
medical [35] and pharmaceutical [36] literature. Many of the computer
simulations for the heart and liver were carried out with distributed blood-
tissue exchange (BTEX) models [37], because the increased level of detail
and temporal resolution certainly makes the good mixing and uniformity
hypotheses at the basis of lumped parameter models less tenable [38]. The
work of Goresky, Bassingthwaighte, and others has spearheaded this area
of development for mathematical modeling, and in recent times drug
development has rediscovered some of the analytical tools proposed by
this research community [39]. It can be speculated that the integration of
organ-specifi c modeling with the above whole-organism models would
result in improvements for the PBPK approach through “better” (i.e.,
more physiologically sensible and plausible) models of individual organs.
The main challenge in doing so is the required shift from lumped to dis-
tributed parameter models. The jump to partial differential equations is
fraught with diffi culties, especially because the average bench biologist
often has a lot of trouble grasping the concepts behind ordinary differen-
tial equations as well. This motivates the question of which is the audience
for these technologies, or who is expected to be a user for the various
software and a reader for the papers. There is an enormous variety of
software for pharmacokinetic and pharmacodynamic simulations, with
a partial list available in Table 21.1 and more updated lists available
elsewhere [40].
As an example of infrastructure endeavors, a new project funded by the
National Institute for General Medical Sciences at the NIH, the Center
for Modeling Integrated Metabolic Systems (MIMS) [41], has as its mission
the development and integration of in vivo, organ-specifi c mathematical
models that can successfully predict behaviors for a range of parameters,
including rest and exercise and various pathophysiological conditions. The
Microcirculation Physiome [42] and the Cardiome [43] are other multi-
center projects focused on particular aspects of the Physiome undertaking.
One prevalent concept that seems to emerge in these large-scale projects
is that of interdisciplinary collaboration, and especially of the need to tap
many areas of expertise for the solution of these problems. It seems widely
accepted that the development of integrated computational representa-
tions of biological systems has to borrow from many fi elds, if nothing else
because of the multidisciplinary complexity that some of these endeavors
imply.
520 REDISCOVERING SYSTEMS PHYSIOLOGY IN THE 21ST CENTURYTABLE 21.1
Name Manufacturer/Distributor Web Site
acslXtreme Xcellon and AEgis Technologies Group http://www.aegisxcellon.com/
ADAPT II Biomedical Simulations Resource (USC) http://bmsr.usc.edu/
Berkeley Madonna University of California-Berkeley http://www.berkeleymadonna.com/
GastroPlus Simulations Plus http://www.simulations-plus.com
GNU Octave University of Wisconsin http://www.octave.org/
JSim National Simulation Resource http://nsr.bioeng.washington.edu/PLN/
Kinetica Thermo Electron Corporation http://www.thermo.com
MATLAB-Simulink The MathWorks http://www.mathworks.com/
MLAB Civilized Software Inc: http://www.civilized.com/
ModelMaker ModelKinetix http://www.modelkinetix.com/
NONMEM University of California at San Francisco and Globomax ICON http://www.globomaxservice.com
PhysioLab Entelos http://www.entelos.com/
PKBUGS Imperial College at St Mary’s Hospital London http://www.mrc-bsu.cam.ac.uk/bugs/
PopKinetics SAAM Institute http://www.saam.com
R The R Project Group http://www.r-project.org/
SAAM II SAAM Institute http://www.saam.com
S-PLUS Insightful http://www.insightful.com/
Stella isee Systems (formerly High Performance Systems) http://www.hps-inc.com/
Trial Simulator Pharsight Corporation http://www.pharsight.com
USC*PACK Laboratory of Applied Pharmacokinetics USC http://www.lapk.org
WinNonlin Pharsight Corporation http://www.pharsight.com
WinNonMix Pharsight Corporation http://www.pharsight.com
XDA Teranode http://www.teranode.com
This table lists some currently available software tools, both academic and commercial, that can and have been used for pharmacokinetic and pharma-
codynamic simulations, sometimes together with data integration and analysis results management. These tools run the gamut from very general model-
ing and data analysis tools to highly specialized population pharmacokinetic and pharmacodynamic programs. The reader should be aware that the
list is not exhaustive, and the capabilities of most of these products, as well as their availability, are expected to change over time. No endorsement of
these particular products is implied.
LEVEL 3: COMPUTER SIMULATIONS OF THE CELL 521
21.4 LEVEL 3: COMPUTER SIMULATIONS OF THE CELL
Cellular level computer simulations are complicated by the fact that there is
no universal accord as to how several of the intracellular and membrane
processes actually take place. Although the use of competing computer
models would be an effi cient way to select the best hypothesis among a slew
of competing ones, this approach is rarely taken in cell biology, where experi-
mental verifi cation dominates the literature by and large [44]. At the same
time, although understanding the cell, its receptors and channels, and the
modalities of membrane transport may be a worthwhile endeavor from the
scientifi c point of view, in drug development this has to be balanced against
the constructive role of this information in accelerating the development
process. Because many of these models await independent scientifi c valida-
tion, their use in drug development is perhaps not as widespread. These
modeling paradigms are more aggressively used in the biomedical research
arena. The Virtual Cell [45] is an online [46] repository of some of these
models, which also makes available a computer simulation of the whole cell
to its users’ network [47]. Another online repository of biophysical models is
at the CellML website [48].
The idea of “network” is very widespread in the models that focus on the
cellular environment. Clearly, interactions between cells, or also within the
intracellular milieu, can be viewed as complex networks of signals, and thus
the computer implementation of oriented networks is a straightforward
approach to modeling this kind of systems. Some very interesting work has
been done in this regard in bacterial systems through a very creative approach
based on the exhaustive enumeration of the biochemical reactions taking
place within the cell [49]. The system is then studied at steady state, because
the dynamic parameters determining the time-varying biochemistry are
largely unknown and the stoichiometry of the reactions, in contrast, is reason-
ably well identifi ed. However, far from being limiting, the study of the (struc-
turally constrained) universe of possibilities [50] related to all steady states
in such a system has allowed us to learn a great deal about the long-term
behavior of simple organisms exposed to variable environmental conditions
and has provided new avenues of investigation for the optimal design of bio-
reactors and, more in general, for how biological systems may choose to adapt
in the face of changing environments [51] by redistributing energy to various
sublocations of the overall reaction network. This has been described for
simple organisms by models that integrate data at many levels, from gene to
biochemistry to physiology [52].
A whole new level of complexity is provided by the investigation of
signals within the cell. Signaling networks are increasingly complex with
respect to the networks we have discussed that deal with material fl uxes
because the precise signaling modalities are largely unknown, and this is a
signifi cant source of diffi culties. New tools are being developed for this
purpose [53].
522 REDISCOVERING SYSTEMS PHYSIOLOGY IN THE 21ST CENTURY
In the pharmacokinetics literature, there are still not that many exam-
ples of tight integration between cellular, in vitro information and whole
system prediction. One example regarding a mechanistic model of the
intracellular metabolism of methotrexate [54], which was then merged in
an integrated model of in vitro and in vivo information [55], may serve as
a possible case in point for the gains that can be reaped from the synergistic
amalgamation (with predictive purposes) of cellular and whole-body
models.
21.5 LEVEL 4: PROTEINS AND GENES
Computational protein design is an area of ever-increasing interest [56]. Its
most intriguing feature is that it can lead to the design and laboratory creation
of structures that are not present in nature [57]. From the standpoint of phar-
macokinetics and pharmacodynamics computer simulations, the challenge is
once again to achieve the blending of very heterogeneous information at
many structural levels. There is no doubt that drug design can be accom-
plished through computer simulation of the expected behavior of new mole-
cules designed to have specifi c physicochemical properties. The success story
of antiretrovirals [58] testifi es to that concept. At the same time, one of the
most interesting contributions of computer simulation to pharmacotherapy
was also in the fi eld of HIV/AIDS treatment, through the development of
models of HIV viral load [59] based on clinical data [60] that shed consider-
able light on the disease mechanism. One wonders how much stronger the
impact would have been if such models could have been augmented with cel-
lular and molecular quantitative information. As it often happens, the precise
modalities of the interaction in question are not that clear. It seems, however,
that tight collaboration between clinical and preclinical departments in indus-
try, or between clinicians and bench biologists in academia, is essential to
make signifi cant progress in the development and applications of in silico
biomedicine.
One example of such constructive cross talk can be found in the growing
literature on quantitative structure-pharmacokinetic relationships (QSPKR).
Reports on how to predict pharmacokinetics from molecular information, or
how to link pharmacokinetic parameters with molecular features, have
appeared in both the pharmacokinetic [61] and the toxicological [62] litera-
ture. Others are extending this to pharmacodynamics as well [63], and the
approaches look promising.
Perhaps a common feature to these examples is that there does not seem
to be an overarching, well-defi ned method for approaching the integration
problem at the basis of preclinical to clinical simulations. It can also be
said, however, that many different methodological developments are being
ACKNOWLEDGMENTS 523
aggressively tried. For example, information theory approaches are being
tried to identify genes that lead to disease susceptibility [64], in a sense
merging the smallest with the largest information items. Some recent con-
tributions allow the mapping of genetic data onto a queryable network
based on ordinary differential equations [65]. Which of these numerous
methodological approaches will become the gold standard of tomorrow?
This is hard to say as of now. Could it be that some of the new fi elds in
the “new biology” are just not mature enough? By way of example, a
PubMed search of “pharmacogenomics” reveals a research paper to review
ratio of 2.40 (two and a half research papers for every review, 3128/1301);
compare that with the 8.91 ratio obtained with “pharmacokinetics” (about
nine research papers for every review, 246683/27691), or with the even
higher ratio of a more established discipline such as “simulation” (22.12,
or 71269/3222). This present “state of the literature” may be the hallmark
of fi elds that are still trying to defi ne themselves and their untapped
potential.
21.6 CONCLUSION
We have attempted to provide a brief review of recent developments in
biocomputation that are of (potential) relevance to drug development.
The major challenge that seems to emerge is the need for quantitative, test-
able, and validated frameworks for the joint analysis of large data sets
available in disparate formats and focused on different biological scales
(Fig. 21.3). Clearly, the solution(s) to this problem will have to borrow from
many disciplines, undoubtedly biology and pharmacology, but also (bio)-
engineering, computer science, (applied) mathematics and physics, and
(bio)statistics. It seems that biology is currently at a crossroads, where the
“best” approaches to analyze and synthesize this rapidly growing corpus of
information have not been developed yet. For drug development, the chal-
lenge is to formalize testable models of intact systems that would allow, for
example, simulation and testing of all development steps of various thera-
peutic targets against the ever-changing landscape of human physiology.
This will in turn require rapidly changing professional expertise that can
quickly and effi ciently adapt to the shifting objectives of modern biomedi-
cal investigation.
ACKNOWLEDGMENTS
This work was partially supported by Grant NIH P41-001975, “Resource
Facility for Population Kinetics.”
524 REDISCOVERING SYSTEMS PHYSIOLOGY IN THE 21ST CENTURY
Regulatory Mechanisms Dosage and Route
Cellular Networks
Pharmacokinetics Pharmacodynamics
2.5 1
0.9
2 0.8
0.7
1.5 0.6
0.5
1 0.4
0.3
0.5 0.2
0.1
0 0
0 6 12 18 24 0 6 12 18 24
Time (hours) Concentration (mg/dl)
DemograpHhistoigrcam ofC heighot variates Clinical Response
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
125 130 135 140 145 150 155 160 0 6 12 18 24
Gene Expression height
Covariate Values Time (years)
Figure 21.3 Modeling and simulation in the general context of the study of xenobiot-
ics. The network of signals and regulatory pathways, sources of variability, and mul-
tistep regulation that are involved in this problem is shown together with its main
components. It is important to realize how between-subject and between-event varia-
tion must be addressed in a model of the system that is not purely structural, but also
statistical. The power of model-based data analysis is to elucidate the (main) subsys-
tems and their putative role in overall regulation, at a variety of life stages, species,
and functional (cell to organismal) levels. Images have been selected for illustrative
purposes only. See color plate.
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