APPENDIX A 

A GENERAL REFERENCE ON PHYSIOLOGICALLY-BASED 

PHARMACOKINETIC/PHARMACODYNAMIC (PBPK/PD) MODELING 

Yang, R.S.H., M.E. Andersen, J.E. Dennison, Y.C. Ou, K.H. Liao and B. Reisfeld. 2004. 

Physiologically based pharmacokinetic and pharmacodynamic modeling. Chapter 23. 

In: Mouse Models of Cancer, E.C. Holland, Ed. Wiley Inc., New York, NY. p. 391-405. 

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23

PHYSIOLOGICALLY BASED PHARMACOKINETIC

AND PHARMACODYNAMIC MODELING

RAYMOND S. H. YANG AND JAMES E. DENNISON

Quantitative and Computational Toxicology Group, Center for Environmental Toxicology and Technology, Department of

Environmental and Radiological Health Sciences, Colorado State University, Fort Collins, Colorado

MELVIN E. ANDERSEN

Department of Biomathematics and Physical Sciences, CIIT Centers for Health Research, Research Triangle Park, North Carolina

YING C. OU

Human Genome Sciences, Inc., Rockville, Maryland

KAI H. LIAO AND BRAD REISFELD

Quantitative and Computational Toxicology Group, Center for Environmental Toxicology and Technology, Department of Chemical

Engineering, Colorado State University, Fort Collins, Colorado

INTRODUCTION

At first glance, the topic of physiologically based

pharmacokinetic/pharmacodynamic (PBPK/PD) modeling

appears to be outside the central theme of this book.

However, with the advances of modern biology and

computational technology, it is just a matter of time

for any area of biomedical sciences to be integrated

with computer science. Two aspects are particularly

important for the application of PBPK/PD modeling in

cancer research, thus underscoring the relevance for the

inclusion of this chapter in the book: (1) incorporation of

PBPK/PD modeling in any biomedical research can avoid

unnecessary experiments, thereby conserving precious

resources, and (2) computer simulations (i.e., in silico

experimentation) using validated PBPK/PD models will

minimize animal usage.

The intent of this chapter is to (1) introduce the general concept and background knowledge of PBPK/PD

modeling; (2) provide some examples of application

of PBPK/PD modeling; (3) illustrate the utility of

PBPK/PD modeling, particularly in the pharmaceutical

drug development process; and (4) project future development on “second-generation” PBPK/PD modeling and

In silico toxicology. An emphasis was given to introducing the concepts of PBPK/PD modeling rather than

the details of its techniques and processes. For more

detailed background and conceptual information on PBPK

modeling, the readers are referred to our earlier introductory discussion (Yang and Andersen, 1994) and the

two “timeless papers” by Bischoff and Brown (1966)

and Dedrick (1973). For more extensive information, particularly regarding modeling techniques, the reader should

consult the two future books from our laboratories (Reddy

ž Q2 et al.,• 2004; Yang et al., 2004).

WHAT IS PHYSIOLOGICALLY BASED

PHARMACOKINETICS? WHAT ARE THE

DIFFERENCES BETWEEN PBPK AND

CLASSICAL PHARMACOKINETICS?

Physiologically based pharmacokinetics (PBPK), as the

name implies, is a special branch of pharmacokinetics

Mouse Models of Human Cancer, edited by Eric C. Holland

ISBN 0-471-44460-X Copyright  2004 John Wiley & Sons, Inc.

391

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392 PHYSIOLOGICALLY BASED PHARMACOKINETIC AND PHARMACODYNAMIC MODELING

where physiology and anatomy of the animal or human

body as well as the biochemistry of the chemical or chemicals of interest are incorporated into the conceptual model

for computer simulation. Classical pharmacokinetics refer

to those empirical noncompartmental or compartmental

pharmacokinetic studies routinely practiced in the pharmaceutical industry (van de Waterbeemd and Gifford, 2003).

As will be illustrated later, the compartments of a PBPK

model have anatomic and physiologic significance. This

is a major difference from empirical noncompartmental

or compartmental pharmacokinetic modeling approaches.

PBPK models can be used to describe concentration–time

profiles in individual tissue/organ and in the plasma or

blood. When the concentration of a certain target tissue,

rather than the plasma concentration, is highly related to a

compound’s efficacy or toxicity, PBPK modeling will be

a more useful tool than classical pharmacokinetic models

for describing PBPK/PD relationships and thus make a

better prediction of the time course of drug effects resulting from a certain dose regimen for the compound of

interest. Furthermore, PBPK models in combination with

absorption simulation and quantitative structure–activity

relationship (QSAR) approaches will bring us closer to

a full prediction of drug disposition for pharmaceutical

new entities and help streamline the selection of lead

drug candidates in the drug discovery process (van de

Waterbeemd and Gifford, 2003). Lastly, unlike empirical

noncompartmental and compartmental pharmacokinetics,

PBPK modeling is a powerful tool for extrapolation, be

it for interspecies, interroutes, interdoses, interlife stages,

and so on.

The concept of PBPK had its embryonic development

in the 1920s and 1940s; for a more detailed early

history, readers are referred to two books which are in

preparation (Reddy et al., 2004; Yang et al., 2004). PBPK

modeling blossomed and flourished in the late 1960s and

early 1970s in the chemotherapeutic area mainly due to

the efforts of investigators with expertise in chemical

engineering process design and control. Two notable

pioneers in this development are Kenneth B. Bischoff,

then at the University of Texas, Austin, Texas, and Robert

Dedrick of Biomedical Engineering and Instrumentation

Branch, Division of Research Services, National Institutes

of Health, Bethesda, Mariland. Two timeless publications

by these investigators are, respectively, “Drug Distribution

in Mammals” (Bischoff and Brown, 1966) and “Animal

Scale-Up” (Dedrick, 1973); these articles are highly

recommended to those who are interested in PBPK

modeling. In the mid-1980s, two articles on PBPK

modeling of styrene and methylene chloride (Andersen

et al., 1987; Ramsey and Andersen, 1984) started yet

another “revolution” in the toxicology and risk assessment

arena. Today, there are more than 700 publications directly

related to PBPK modeling on industrial chemicals,

drugs, environmental pollutants, and simple and complex

chemical mixtures (Reddy et al., 2004).

A PBPK model, graphically illustrated in Figure 23.1,

reflects the incorporation of basic physiology and

anatomy. The compartments actually correspond to

anatomic entities such as liver, lung, and so on, and

the blood circulation conforms to the basic mammalian

physiology. In this specific model, a published example on

methylene chloride, it is quite obvious that the exposure

route of interest is inhalation because the lung and gas

exchange compartments are prominently displayed with

intake (CI) and exhalation (CX) vapor concentrations

indicated. Oral and/or dermal exposures may be added

easily to the gastrointestinal tract compartment or general

venous circulation, respectively. Some tissues (e.g., richly

or slowly perfused tissues in Fig. 23.1) are “lumped”

together because there is insufficient evidence to conclude

that each of these tissues is kinetically distinct enough for

the specific chemical to warrant a separate compartment.

If one draws an analogy of the “scale-up” from a

laboratory chemical engineering process to a chemical

plant to the scale-up of a mouse to a human, one finds

that both situations are governed by a great number

of physical and chemical processes. In mammals, the

physical processes (i.e., mass balance, thermodynamics,

transport, and flow) often vary in a predictable way.

However, chemical processes such as metabolic reactions

may vary greatly and are less predictable among species.

These physical and chemical processes interact in the body

such that the pharmacokinetics of any given chemical

between one species and another may be more (or less)

predictable depending on the amount of background

information available.

HOW DOES A PHYSIOLOGICALLY BASED

PHARMACOKINETIC MODEL WORK?

A PBPK model applies fundamental physiologic, biochemical, and engineering principles to describe the distribution and disposition of chemicals in the body at any

given time. The process and approach may be summarized

in a flowchart (Fig. 23.2). Once the chemical of interest

and the problems needing to be addressed are identified,

a thorough literature evaluation is conducted.

The fundamentals of PBPK modeling are to identify

the principal organs or tissues involved in the disposition

of the chemical of interest and to correlate the chemical

absorption, distribution, metabolism, and excretion within

and among these organs and tissues in an integrated and

biologically plausible manner. A scheme is usually formed

where the normal physiology is followed in a graphical manner (i.e., a conceptual model as in Fig. 23.1).

Within the boundary of the identified compartment (e.g.,

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HOW DOES A PHYSIOLOGICALLY BASED PHARMACOKINETIC MODEL WORK? 393

Richly perfused

Fat

Slowly perfused

Liver

Lung

metabolism

Gas

exchange

G.I. TRACT

KZER

CI QP CX

QC

CA1

QC

CV CA

QC

Km,

Vmax

Km,

Vmax

KF

AM1LU AM2LU

KF

AM2L AM1L

QR QR

CA

CA

CA

CA

QF QF

QS QS

QL QL

CVL

CVS

CVF

CVR

Figure 23.1. Graphical representation of a PBPK model for methylene chloride. (Andersen

et al., 1987).

an organ or tissue or a group of organs or tissues), whatever “comes” in must be accounted for via whatever

“goes out” or whatever is transformed into something

else. This “mass balance” is expressed as a mathematical equation with appropriate parameters carrying biologic

significance. A series of such equations representing all of

the interlinked compartments are formulated to express a

mathematical representation, or model, of the biologic system. This model can then be used for computer simulation

to predict the time course behavior of any given parameter. Three sets of parameters are needed for PBPK model

building: physiologic parameters (e.g., ventilation rates,

cardiac output, organs as percent body weight), thermodynamic parameters (e.g., tissue partition coefficients, flow

rates), and biochemical parameters (e.g., Km and Vmax).

Most, if not all, of the parameters for laboratory animals

are available in relevant literature, such as the Biological Data Book and the special report by the International

Life Sciences Institute (ILSI) on the compilation of physiologic parameters for PBPK models (Brown et al., 1997).

When information gaps exist, the solution is either an

empirical one via experimentation or through allometric

extrapolation, usually based on a power function of the

body weight (Lindstedt, 1987).

The U.S. Environmental Protection Agency (EPA)

guidance document (2002) includes a very nice discussion

on “modeling the data.” Although it is not necessarily for

PBPK modeling, the discussion reflects some “dos” and

“don’ts” on computer modeling. We quote some of the

passages below:

The• selection of a mathematical model structure to fit ž Q3

the data being analyzed should be guided by the biology

of the common mechanism of toxicity, the toxicokinetics of the chemicals, and the observed shapes of their

dose-response curves and the experimental designs used

to generate the data. If available, pharmacodynamic and

pharmacokinetic data should be considered in order to

account for tissue concentrations and to aid in defining dose-response relationships across different species,

routes and time-frames of exposure ... .

... Although it is not possible to recommend the use

of specific models, a few points that should be considered

in modeling the data follow:

ž Modeling of individual animal data is desirable; however, if this is not practical, then use

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394 PHYSIOLOGICALLY BASED PHARMACOKINETIC AND PHARMACODYNAMIC MODELING

Design/conduct

critical experiments

Simulation

Compare to

kinetic data

Refine

model

Validate

model

Extrapolate

to humans

Model

formulation

Mechanisms

of toxicity

Physiological

constants

Biochemical

constants

Literature

evaluation

Problem

identification

Figure 23.2. Flowchart illustrating processes involved in PBPK. (From M. E. Andersen,

Pharmacokinetics in Risk Assessment, Drinking Water and Health, National Academy Press,

Washington, D.C., 1987, pp. 8–23.)

of summary data such as means and standard

deviations can be alternatives

ž Care should be taken with modeling high-dose

data (particularly extreme doses) because the

model shape in the low-dose region can be

influenced by high-dose data

ž Log transformation of data should be justified

because such a transformation may distort the

dose-response curve

ž Data variability should be described by appropriate statistical techniques and reflected in the

potency estimate (e.g., by weighting the data

in the fitting procedure)

ž Confidence intervals or limits should be

included in the analysis because they can

be valuable for evaluating the influence of

variability on the potency estimates

ž An estimate for the uncertainty of the model

used in the analysis should be included

ž The statistical fitting method used must be

clearly described.

For the most well-studied chemicals or drugs, it is likely

that the biochemical constants such as Km’s and Vmax’s

are known and readily retrievable from the information

data base. However, it must be made clear here that

the Km, Vmax, and KF (first-order rate constant) in a

PBPK model (known as in vivo Km, Vmax, KF for a

given chemical) such as the ones given in Figure 23.1 are

hybrid constants of all the saturable or linear metabolic

pathways, respectively, for the chemical of interest in

the organ and/or body. They are different from the

in vitro Km, Vmax, or KF of a given pure enzyme.

While they are not directly interchangeable, the in vitro

constants in the literature may be used to estimate

in vivo constants for modeling purposes (Kedderis and

Lipscomb, 2001; Lipscomb et al., 1998). Also, for most

well-known chemicals, it is likely that enough is known

about the mechanism of toxicity to be incorporated

into the model for computer simulation. Physiologic

constants such as organ volumes and blood flow rates

are usually available in the literature for the common

laboratory animals as well as humans. Therefore, at

least in those instances of “well-known” chemicals, a

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PHYSIOLOGICALLY BASED PHARMACODYNAMIC MODELING 395

model may be conceptually illustrated as in Figure 23.1

and mathematically represented by a number of mass

balance differential equations. Computer simulations may

be made for any number of desired time course endpoints

such as the blood levels of the parent compound, liver

level of a reactive metabolite, and similar information

on different species, at lower or higher dose levels,

and/or via a different route of exposure. The experimental

pharmacokinetic data may then be compared with PBPK

model simulation to see if they are superimposable upon

each other. If this is indeed the case, the model is

consistent with actual results. Validation of the PBPK

model with data sets other than the working set (or training

set) to develop the model is necessary. Once validated, the

PBPK model is ready for extrapolation to other animal

species, including humans. However, if the experimental

data and PBPK model simulation are not consistent,

the model might be deficient because critical scientific

information might be missing or certain assumptions

are incorrect. The investigator, with knowledge of the

chemical and a general understanding of the physiology

and biochemistry of the animal species, can design and

conduct critical experiments for refining the model to

reach consistency with experimentation (Fig. 23.2). This

refinement process may be repeated again and again

when necessary; such an iterative process is critically

important for the development of a PBPK model. There

is always the possibility that a good model may not

be obtained at the time because of the limitation of

our knowledge on the chemical. An emphasis must

be made here that the investigator and the knowledge

possessed are the single most important determinant of

the outcome of the results; mathematical modeling and

advanced computational capabilities are nothing more

than good tools.

MYTHS ABOUT PHYSIOLOGICALLY BASED

PHARMACOKINETICS; ARE THEY REAL?

Common belief is that PBPK modeling is highly resource

intensive and very difficult to do, particularly involving

interactive pharmacokinetics or pharmacodynamics. This

warrants some special discussion: First, by the time

chemicals such as drugs or pesticides reach the stage of

commercialism, many types of studies have already been

conducted, including pharmacokinetic studies. Thus, they

are already resource intensive during the developmental

stage to become successful chemicals in commerce. The

important point is how may quantitative, time course

data useful for PBPK model development be generated

during the product development phase? The data required

for PBPK modeling are really not too much different

from those required for the classical pharmacokinetics

in the present IND/NDA (investigational new drug

application/new drug application) process. A slight new

orientation to the existing battery of studies would

generate adequate quantitative time course data for PBPK

modeling. Thus, it is definitely not any more resource

intensive from the existing requirements. Furthermore, if

the incentive (e.g., regulatory guideline-driven scientific

studies) is there, such quantitative, time course data would

have been automatically generated during the product

development phase. In fact, PBPK modeling, being a

hypothesis testing tool in toxicology, may be utilized

to conduct many different kinds of experiments on a

computer (i.e., in silico toxicology).

A great deal of research effort has been devoted to

the development of simple, high-throughput, and in vitro

predictive tools in the pharmaceutical industry (van de

Waterbeemd and Gifford, 2003). While these short-term,

rapid assays certainly offer some utility, particularly in

the early drug development process, an inherent danger

of such tools is the “by-pass” of integrated mammalian

physiology and architecture of the body. In that regard,

development of in silico toxicology such as PBPK/PD

modeling and other biologically based computer modeling has the advantage of integrating whole-body pharmacokinetics and pharmacodynamics with computational

technology. The resulting predictive tools will minimize

unnecessary experiments and improve the attrition rate of

drug or chemical product development with much more

scientific validity and confidence. In that sense, PBPK/PD

modeling, once integrated as a part of the product development plan, will actually save expenses and resources as

well as minimize unnecessary animal experiments.

Second, while PBPK modeling is by no means a

very easy technology, it is not any more difficult than

some of the classical pharmacokinetic and statistical modeling carried out in the routine product development

process. Furthermore, excellent training opportunities

(e.g., www.cvmbs.colostate.edu/enhealth/cett/) are available, and the development of software is such that more

and more user-friendly tools are going to be available.

PHYSIOLOGICALLY BASED

PHARMACODYNAMIC MODELING

Using plain English, pharmacokinetics can be considered

as “What the body does to the chemicals,” and pharmacodynamics can thus be considered as “What the chemicals do to the body.” Physiologically based pharmacodynamic (PBPD) modeling is therefore computer simulation

of pharmacologic or toxicologic effects of chemicals or

drugs based on the biology of chemical/drug– receptor

interactions. From the point at which a chemical or a

drug enters into the body to the point of pharmacologic or

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396 PHYSIOLOGICALLY BASED PHARMACOKINETIC AND PHARMACODYNAMIC MODELING

toxicologic effect, it is a continuum of pharmacokinetics

and pharmacodynamics. It is difficult to distinguish where

pharmacokinetics end and pharmacodynamics start. When

we consider the pharmacology or toxicology of a chemical or a drug, we must consider both pharmacokinetics

and pharmacodynamics to have a full understanding. To

consider either area alone is to understand only part of

the picture.

PBPK modeling preceded PBPD modeling by many

years because of the slower and later advances of mechanistic understanding of modes of action of chemicals and

drugs. It is a natural course of evolution that PBPK blossomed and flourished first because it was developed based

on the fundamentals of mammalian physiology, analytical

chemistry, engineering principles of mass transport and

mass balance, and desk-top computer hardware and software development. These were all well-developed areas

in the earlier days. PBPD modeling is dependent upon the

mechanistic basis of chemical/drug– receptor interactions,

and the biology associated with it took time to mature. The

recent trend is such that more and more PBPD modeling

work is evident. PBPK modeling has matured to the point

that research endeavors are centered around more complex systems (e.g., multichemical interactions, subcompartmentalization of organs) or special problem-driven

models (e.g., dermal uptake of chemicals from showers,

exposure dose reconstruction). As will be discussed later,

the “delumping” of organ and tissue compartments and

the linkage of PBPK models with other types of biologically based models may lead us to second-generation

PBPK/PD modeling.

DATA REQUIREMENTS FOR PBPK OR PBPD

MODELING

What are the specific data needed for building PBPK models? Obviously, well-conducted in vivo pharmacokinetic

data are essential, and usually the more the data sets (e.g.,

different doses, routes, species), the better. In each study,

time course blood and tissue concentration data are essential. These time course data should include at least the

following tissues and organs: blood (or plasma if blood

cell binding is not an issue), liver (organ of metabolism),

kidney (representing well-perfused organs/tissues), muscle

(representing slowly perfused organs/tissues), and target

organ(s)/tissue(s). We also need other PBPK-modeling

specific information, such as (1) physiologic constants,

including body size, organ and tissue volumes, blood flow,

and ventilation rates; (2) biochemical constants, including the chemical-specific metabolic rate constants such

as Vmax and Km, partition coefficients for tissues; and

(3) mechanistic factors such as target tissues, metabolic

pathways, and receptor interactions. Enzyme kinetic data,

particularly human data, of at least the key metabolic processes will be important for the PBPK model. In vitro

determination of tissue partition coefficients and enzyme

kinetic data is relatively straightforward and inexpensive. With modern genetic engineering technologies, many

human enzymes are available commercially. Thus, heretofore unavailable human enzyme kinetic information for

many of the environmentally important chemicals are

within easy reach for many laboratories. These experiments should be performed.

For PBPD modeling, the data requirement is much

more variable because of the many different types of

chemical/drug– receptor interactions. Thus, it is much

more of a compound-specific nature. However, as a rule

of thumb, quality time course data on the key biologic

processes to be modeled are essential.

PBPK OR PBPK/PD MODELS FOR CHEMICAL

INTERACTIONS (INTERACTIVE PBPK

OR PBPK/PD MODELS)

Human exposure to chemicals is rarely, if ever, to single

chemicals. In the area of clinical pharmacology, adverse

drug interactions are undoubtedly serious concerns. For

instance, Lazarou et al. (1998) estimated that there were

over 2.2 million cases of serious adverse drug reactions

(ADRs) in hospital patients in 1994 in the United States

and among these cases 106,000 were fatal. During their

hospital stay, the patients in the survey statistics were

given an average of eight drugs. Comparing with other

statistics of causes of death, these investigators (Lazarou

et al., 1998) indicated that ADRs became the fourth to the

sixth leading cause of death for that year in the United

States. Thus, it is important to discuss the issues related

to the development of interactive PBPK/PD modeling

(see particularly the example given later on the work

of Kanamitsu et al., 2000).

From the perspective of interactive PBPK/PD modeling, two aspects need to be addressed: pharmacokinetic

interactions and pharmacodynamic interactions. Because

PBPD modeling is a relatively recent effort and few

such models are available for even single chemicals, we

will concentrate all our discussion on interactive PBPK

models. The most ideal and scientifically defensible data

requirement for establishing an interactive PBPK model

is that each component chemical in the mixture already

have its respective established PBPK model and that there

are many pharmacokinetic data sets in laboratory animals

as well as in humans available for each of these component chemicals. The interactive PBPK model is then built

on the basis of known pharmacokinetic interactions. For

instance, the component chemicals may inhibit each others’ biotransformation. The individual PBPK models may

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APPLICATION OF PBPK/PD MODELING 397

then be linked together at the liver compartment by introducing competitive inhibition (or other types of inhibition)

terms in the mass balance differential equation.

In some cases, even more specific and stringent data

requirements are needed; an example may be the ultralowdose pharmacokinetic data in perinatal developmental

stages of laboratory animals for extrapolation to human

fetuses and babies using PBPK modeling. This area is

still in its infancy and further development is anticipated.

APPLICATION OF PBPK/PD MODELING

Dosing Schedule of a Chemotherapeutic Agent

Methotrexate is a folate analogue and a well-known

cancer chemotherapeutic agent. This is one of the

chemotherapeutic agents which was studied extensively

with PBPK modeling. The mechanism of toxicity is

due to the binding of methotrexate to dihydrofolate

reductase, a key enzyme in DNA synthesis, leading to

cessation of DNA synthesis and cell death. In some

organs (liver, kidney, intestine, and marrow) and many

tumors, methotrexate undergoes metabolism to active

polyglutamate derivatives (even more potent inhibitors for

dihydrofolate reductase). Because these polyglutamates

are retained in some tissues far longer than the parent

compound, it has been suggested that this effect is

of great importance for the antineoplastic property of

methotrexate.

Table 23.1 shows the toxicity of methotrexate to mice

under a variety of dosing schedules (Morrison et al.,

1987). Obviously, toxicity does not directly correlate

with total dose. Decreasing total dose by a factor of

117 (350/3) led to an increase, rather than a substantial

decrease, in toxicity. In addition, the area under the

plasma concentration–time curve (AUC), a frequently

used pharmacokinetic parameter for bioavailability, did

not correlate with toxicity. For instance, the AUC for a

bolus dose of 350 mg/kg is about two orders of magnitude

greater than that of the 96-h infusion at 0.8 μg/h•, yet ž Q4

toxicity is higher with infusion.

The reason for the above phenomenon turned out to

be intimately associated with the pharmacokinetics of

methotrexate (and its polyglutamate metabolites) and the

threshold and length of time that dihydrofolate reductase

is inhibited (thus inhibition of DNA synthesis). At a bolus

dose of 350 mg/kg, even though there is a short period of

very high blood and tissue concentration, the inhibition

of DNA synthesis did not persist long enough to cause

lethality in at least some of the mice. At an infusion

rate of 0.8 μg/h• for 96 h, even though the blood and ž Q5

tissue levels were low, they were nevertheless high enough

to cause sustained inhibition of DNA synthesis, which

ultimately translated into higher lethality in the animals.

These scientific discoveries eventually led to the revision

of the methotrexate PBPK model by incorporating the

inhibition of DNA synthesis into the model.

From the modeling perspective, the iterative process

of making new scientific discoveries and then refining the

PBPK model by incorporating such new information into

the model is a wonderful illustration of what we discussed

in relation to Figure 23.2. An even more significant

illustration is the fact that a validated methotrexate PBPK

model can be used to conduct all the experiments in

Table 23.1 on a computer. With such complicated dosing

schedules, it is apparent how the lives of hundreds of mice

may be saved and how much time and resources may be

diverted to other more efficient usages.

“Electronic Rats”

One of our earlier examples was the PBPK/PD modeling

of a toxicologic interaction between kepone (also known

as chlordecone) and carbon tetrachloride (CCl4) based on

mechanisms of interactive toxicity and the application

of computer technology in acute toxicity studies. This

was a collaboration among three research groups: Melvin

E. Andersen, CIIT (presently CIIT Centers for Health

Research); Harihara M. Mehendale, Northeast Louisiana

Table 23.1. Dosing Schedule Dependence of Methotrexate Toxicity in Mice

Dose

(mg/kg) Schedule

Total Dose

(mg/kg)

Peak Plasma

Concentration (M) Effect

350 Single dose 350 10−3 LD50

25 Twice daily 50 10−4 LD50

3 Every 3 h, 5 times, rest 8 h,

then every 3 h, 3 times

24 10−5 >LD50a

0.5 Every 3 h, 20 times 10 10−6 >LD50a

0.8 μg/h Infusion 96 h 3 10−8 >LD50a

aHigher toxicity than LD50.

Source: Morrison et al., 1987.

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398 PHYSIOLOGICALLY BASED PHARMACOKINETIC AND PHARMACODYNAMIC MODELING

Mitotic

cells

Cells

(G0 phase)

KMIT

KBIR

Injured

cells

Dead

cells

CCl4 alone or

CCl4 + kepone

Animal

death

Estimate

LD50

Phago

cytosis

KDIEI

KINJ KDIE1 KPH

≥50% Cellular

death 

KREP

Figure 23.3. A conceptual PBPD model for CCl4 and Kepone interaction. KMIT = rate

constant for mitosis; KBIR = rate constant for cell birth; KINJ = rate constant for cell injury;

KDIEI = rate constant for general cell death; KDIE1 = rate constant for cell death due to injury;

KPH = rate constant for phagocytosis (El-masri et al., 1996).

University (presently University of Louisiana at Monroe);

and our Quantitative and Computational Toxicology group

at Colorado State University. The details of this study

may be found elsewhere (El-masri et al., 1996). Briefly,

CCl4 is a well-known hepatotoxin. Following free-radical

formation through the P450 enzyme system, the toxicity

of CCl4 can be an accumulation of lipids (steatosis,

fatty liver) and degenerative processes leading to cell

death (necrosis). Kepone is found in the environment

as a result of photolytic oxidation of Mirex, a pesticide

used for the control of fire ants, or as a pollutant from

careless and irresponsible discharge. At relatively low

levels (e.g., 10 ppm in the diet), even repeated dosing

of kepone in the diet up to 15 days caused no apparent

toxicity to the liver. The toxicologic interaction between

kepone and CCl4 was reported by Curtis et al. (1979).

They illustrated that a 15-day dietary exposure of male

rats to kepone at 10 ppm, an environmentally realistic

level, markedly enhanced liver toxicity produced by

an i.p. injection of a marginally toxic dose of CCl4

(100 μL/kg). This toxicologic interaction is unique in

that (1) unlike many other toxicologic interaction studies

which were usually dealing with acute toxicity at very

high doses, kepone in this instance was administered at

a very low environmental level; (2) CCl4 was also dosed

at a low, marginally toxic level; and (3) the magnitude

of toxicologic interaction, 67-fold, is very large. The

mechanism of this toxicologic interaction was elucidated

by Mehendale’s group through a series of studies to be the

impairment, by kepone, of the liver’s regeneration process.

These mechanistic studies were summarized in a number

of publications (Mehendale, 1984, 1991, 1994).

As shown in Figure 23.3, a PBPD model was constructed by El-masri et al. (1996) based on the mechanism

of toxicologic interaction between kepone and CCl4. This

PBPD model was verified by literature information, and

it was capable of providing time course computer simulations of mitotic, injured, and pyknotic (dead) cells after

treatment with CCl4 alone or with kepone pretreatment.

This PBPD model was further linked with Monte Carlo

simulation to provide predictability of the acute lethality

of CCl4 alone and in combination with kepone. As shown

in Table 23.2, the a priori predictions of lethality were in

very good agreement with experimentally derived values

except at very high CCl4 levels. In this latter case, the

underprediction of lethality was due to toxicity other than

in the liver, that is, the neurotoxic effects of CCl4 on the

central nervous system. When this study was first presented at the International Congress of Toxicology Symposium in 1995, a reporter for Food and Chemical News

wrote a section titled “Colorado Researchers Use Electronic Rats.” Although it was somewhat amusing at the

time, the term “electronic rats” nevertheless reflects our

ultimate goal of in silico toxicology.

Clonal Growth in Relation to Carcinogenesis

The U.S. National Toxicology Program (NTP) and its

predecessor, the National Cancer Institute’s Carcinogenesis Bioassay Program, collectively, form the world’s

largest toxicology program (NTP, 2002). In its nearly 40

years of operation, fewer than 600 chemicals have been

studied for carcinogenicity and other chronic toxicities

A-9
APPLICATION OF PBPK/PD MODELING 399

Table 23.2. PBPK/PD Modeling and Monte Carlo

Simulation of Kepone/CCl4 Toxicologic Interaction

Dose Observedb ž Model Predictiona

Kepone %

(ppm)

Dead

CCl4

(μL/kg)

Dead

Rats

Percent

Dead

Deadž

Rats

0 100 0 0.0 0

0.0

0 1000 1–2 13.2 1

11.1

0 3000 3 32.8 4

44.4

0 6000 4–5 47.8 8

88.8

10 10 0 0.0 0

0.0

10 50 4–5 47.5 4

44.4

10 100 8–9 84.0 8

88.8

aMortalities in 48 h, given a hypothetical condition of n = 9; Monte

Carlo simulation, n = 1000. bActual lethality studies (n = 9).

Source: Modified after Yang et al., Toxicol. Lett., 82/82 : 497–504, 1995.

(NTP, 2002, 2003). These “gold standard” chronic toxž Q6

ž Q7

icity/carcinogenicity studies are extremely expensive (i.e.,

up to several million dollars per chemical), require large

number of animals (i.e., about 2000 animals per chemical),

and are lengthy (i.e., 5–12 years per chemical). Thus, considering the approximately 80,000 chemicals in commerce

(NTP, 2002), the number of compounds for which we

have adequate toxicology information for risk assessment

so far is miniscule. With the mode and rate of studying these chemicals as indicated above, it is unlikely that

our society will ever have thorough toxicology information on the majority of the chemicals that we use now or

may use in the future. Considering further the “real-world”

issue of the health effects of chemical mixtures, it would

be impossible to obtain adequate information on most of

the chemicals or chemical mixtures that humans might be

exposed to using the conventional approach (Yang, 1994,

1997). Thus, the PBPK/PD modeling approach described

below represents a possible alternative to the expensive

and time-consuming cancer bioassays.

We have used a modification of the medium-term

bioassay of Ito and co-workers (1989a,b) to study the carcinogenicity of chlorobenzenes. The Ito assay involves

the sequential administration of a potent initiator, diethylnitrosamine (DEN), followed by chemical treatment and

mitogenic stimulation of hepatocyte growth via partial

hepatectomy. As shown in Figure 23.4, this protocol

allows the evaluation of carcinogenic potential within

DEN+corn oil

s s

DEN+HCB, PECB, TECB, or DCB

s s s s s

s s s

HCB, PECB, TECB or DCB

Sacrifice s

DEN

PH

(Days)1 23 26 28 47 56 14

Figure 23.4. Experimental design for initiation–promotion

study and estimated parameters for clonal growth model. The

initiation agent, DEN, was administered i.p. (200 mg/kg) at

week 0. HCB, PECB, TECB, or DCB was delivered by gavage

starting week 2 at dose of 0.1 mmol/kg per day, 7 days/week. A

two-thirds partial hepatectomy was performed on all animals on

week 3. Liver tissues were collected 23, 26, 28, 47, and 56 days

following initial DEN dosing. Concurrent controls without DEN

initiation were also performed for all groups (Ou et al., 2003).

eight weeks by identification of glutathione S-transferase

placental form (GST-P) positive preneoplastic foci as endpoint marker lesions. A large number of chemicals have

been tested using this protocol. When compared with the

two-year chronic bioassay, results from the Ito mediumterm bioassay have correctly identified 97% of genotoxic

hepatocarcinogens and 86% of the known nongenotoxic

hepatococarcinogens (Ogiso et al., 1990). The principal

modification of this protocol in our laboratory is the incorporation of pharmacokinetics and pharmacodynamics by

conducting time course studies on tissue dosimetry, cell

division rates, cell death rates, and GST-P foci formation.

To collect experimental data, briefly, as shown in

Figure 23.4, male Fisher 344 rats, 8 weeks of age,

were initiated with a single dose (200 mg/kg i.p.)

of diethylnitrosamine. Two weeks later, animals were

exposed to daily gavage consisting of 0.1 mmol/kg 1,4-

dichlorobenzene (DCB), 1,2,4,5-tetrachlorobenzene

(TECB), pentachlorobenzene (PECB), or hexachlorobenzene (HCB) in corn oil vehicle for 6 weeks. Partial hepatectomy was performed 3 weeks after initiation. Liver

weight, 5-bromo-2

-deoxyuridine labeling index for analysis of cell division rate, and number and volume of GST-P

positive foci were measured at 23, 26, 28, 47, or 56 days

after initiation•. ž Q8

We then used a clonal growth stochastic model (Ou

et al., 2001, 2003; Thomas et al., 2000) to describe the

dynamic growth of preneoplastic foci during the Ito

medium-term bioassay. The clonal growth model is based

A-10
400 PHYSIOLOGICALLY BASED PHARMACOKINETIC AND PHARMACODYNAMIC MODELING

Portion of two-stage model applicable

to GST-P data

μa

αa, αb

βa, βb

A μb

Normal

cells

α

β

Initiated

cells

B

Malignant

cells

Figure 23.5. Simple two-stage model of carcinogenesis. The

analysis presented here focuses on normal and initiated

states (Ou et al., 2003).

on the two-stage model of carcinogenesis (Moolgavkar

and Luebeck, 1990; Moolgavkar and Venzon, 2000),

where the carcinogenesis process is described by the

two critical rate-limiting steps: (a) from normal to initiated cells and (2) from initiated cells to malignant states

(Fig. 23.5). The model allows the incorporation of relevant biologic information such as the kinetics of tissue

growth and differentiation and mutation rates. The clonal

growth stochastic model adopts a discrete-time numerical

approach, where the time axis is decomposed into a series

of time intervals, where parameters are allowed to change

between but not with segments. To represent the multiplicity of the cellular states and the time-varying nature of

the numerous cell behavior variables, the numerical model

resorts to a recursive simulation. The growth of normal

liver is described deterministically, whereas other cellular

events use stochastic simulation. This approach facilitates

description of the complex biologic process with timedependent values.

A combination of experimental toxicology and computer simulation described above was used to analyze

clonal growth of GST-P enzyme-altered foci during

liver carcinogenesis in an initiation–promotion regimen

for DCB, TECB, PECB, and HCB. The clonal growth

stochastic model (Ou et al., 2001, 2003; Thomas et al.,

2000) incorporating the hypothesis of two initiated cell

populations (referred to as A and B cells) (Fig. 23.5)

was successfully used to describe the foci development

data for four chlorobenzenes (Fig. 23.6 presented as an

example for HCB and PECB). The B cells are initiated

cells that display selective growth advantage under conditions that inhibit the growth of initiated A cells and normal

hepatocytes. A sensitivity analysis of model parameters

indicated that the net growth rate of B cells during the twoweek regenerative period following partial hepatectomy

is among the most sensitive parameters for determining

the final foci volume. Furthermore, the estimated values of this model parameter among four chlorobenzenes

appear to be positively correlated with the induction of

CYP2B1/2, CYP1A2, c-fos, enlarged liver, and final foci

volume, indicating that examining effects of chemicals

on regenerative responses following partial hepatectomy

may be a way to understand the carcinogenicity potential

of chlorobenzene compounds. While TECB, PECB, and

HCB all increased significant foci volume, only HCB had

effects on normal hepatocyte proliferation. The use of a

two-cell hypothesis for the description of DEN control

data (with partial hepatectomy) also indicated the presence of multiple phenotypes of initiated clones following

DEN treatment, with resistant phenotypes arising during

early carcinogenesis.

As initiation–promotion protocols are widely used in

the study of carcinogenesis, the clonal simulation of foci

growth, in combination with PBPK modeling, will be a

useful quantitative tool for examining the time course of

a dose–concentration relationship at critical target tissues

and concentration-dependent pharmacodynamic changes

at cellular levels during carcinogenesis.

HOW ARE PBPK/PD MODELS VALIDATED?

HOW CAN THEY BE USEFUL PREDICTIVE

TOOLS?

To develop a PBPK/PD model, quantitative time course

experimental data sets are essential for comparisons with

computer simulations. As indicated earlier, the goal and

the hope are that computer simulations are superimposable

with experimental data. The data sets used for model

building are working sets (or training sets). For model

validation, it is very important that data sets other than

the working sets are used to compare with the model

simulation results. For instance, assume• a PBPK/PD ž Q9

model was developed using PK and PD data sets from

intravenous dosing of two dose levels of drug A reported

by laboratory X. The validation of this PBPK/PD model

for drug A should be carried out using different data sets

such as PK and PD following oral and dermal dosing

of drug A reported, respectively, by laboratories Y and

Z. Generally, the more different data sets used in the

validation process, the more robust the PBPK/PD model.

Once a PBPK/PD model is validated, it may be used

for predictive purposes. However, the present state-of-theart is such that the predictive capability is limited to the

very compound for which the PBPK/PD model is developed, or at the very least to close analogues with the

same mechanism of action. For example, Kanamitsu et al.

(2000), using a PBPK model, predicted in vivo drug–drug

interaction between triazolam and erythromycin based on

in vitro enzyme kinetic studies using human liver microsomes and recombinant human cytochrome P450 3A4

A-11
FUTURE PERSPECTIVES: IN SILICO TOXICOLOGY AND SECOND-GENERATION PBPK/PD MODELING 401

Time (days)

Foci volume (%)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Foci number/cm3 1000

3000

5000

7000

9000

DEN DEN+PECB DEN+HCB

0 20 40 60 80 100 120 0 20 40 60 80 100120 0 20 40 60 80 100120

PH PH PH

PH PH PH

Figure 23.6. Comparison of the clonal model outputs with experimental measurements of foci

growth for PECB and HCB congeners. Time-dependent changes in foci growth were measured

in animals subjected to an initiation/promotion protocol using DEN as an initiator and PECB or

HCB as a promoting agent. Using the standard stereologic methods, two-dimensional transection

data of GST-P foci were converted to three-dimensional foci number (foci number/cm3) and foci

volume (volume percentage of foci) in the liver. To illustrate the stochastic nature of foci growth,

the figures here show results from five runs of simulation. For comparison, experimental data

ž Q1 of Jang et al. (1993)• (triangle symbols) and simulation results for the DEN controls without

partial hepatectomy (lower solid gray lines) are shown along with those of the DEN controls (Ou

et al., 2003).

(CYP3A4). The mechanistic basis for this drug–drug

interaction which involved 15 fatalities in Japan in 1993

is a mechanism-based inhibition (or “suicide inhibition,” meaning the enzyme metabolizes a chemical to

a reactive metabolite which, in turn, irreversibly inactivates the enzyme) for macrolide antibiotics, such as

erythromycin. Once the enzyme is permanently inactivated, its metabolism of the other coadministered drug

is impaired, leading to a scenario of “drug overdose.”

With the present state-of-the-art, Kanamitsu et al. (2000)

should be able to use their PBPK model to predict potential serious dose-limiting toxicities for combination therapies involving macrolide antibiotics and coadministered

drugs metabolized by CYP3A4 provided certain basic

PK parameters are known for the drugs involved as

well as in vitro enzyme kinetic information using human

CYP3A4. When more and more such mechanistic information is available for classes of chemicals, it is likely that

reaction rules may be established for certain molecular

attributes, and reaction network modeling (see the following section on second-generation PBPK/PD modeling) may be linked with PBPK/PD modeling such that

more generalized prediction of toxicities might become

a reality.

FUTURE PERSPECTIVES: IN SILICO

TOXICOLOGY AND SECOND-GENERATION

PBPK/PD MODELING

In essence, in silico toxicology means integrating computer modeling with focused, mechanistic animal experimentation such that experiments which are impractical

(e.g., too large, too expensive) or impossible (e.g., human

experiments with carcinogens) to perform are conducted

on a computer. We believe that utilization of computer

A-12
402 PHYSIOLOGICALLY BASED PHARMACOKINETIC AND PHARMACODYNAMIC MODELING

modeling is essential in the studies of toxicology of chemicals/drugs, chemical/drug mixtures, and their risk/safety

assessment. The area of biology, in general, will be well

served by the application of computer technology as an

alternative research method to conserve resources and

minimize the killing of laboratory animals. Looking into

the future, we believe that the linkage of PBPK modeling

and “reaction network modeling,” described briefly in the

following two subsections, has the potential of providing

a computer simulation platform for complex biologic systems involving chemicals/drugs, chemical/drug mixtures,

and/or multiple stressors. For a more detailed discussion,

the readers are referred to three publications (Liao et al.,

2002; Yang et al., 2003a,b) from our laboratory.

BUILDING A SECOND-GENERATION PBPK/PD

MODEL

In classical pharmacokinetics and physiologically based

pharmacokinetics, human or animal bodies were often

described by a few compartments. By second-generation

PBPK/PD modeling, we refer to integrating PBPK with

reaction network modeling, thus including many more

compartments (i.e., a delumping process). Our thoughts

may best be explained in this way: If one draws a parallel

between an oil refinery, where application of the reaction

network modeling approach has been very successful,

and a human body, the individual processing units in the

oil refinery may be considered as equivalent to the vital

organs of the human body. Even though the cell or organ

may be much more complicated, the complex biochemical

reaction networks in each organ may be modeled and

linked much the same way as the modeling of the entire oil

refinery through linkage of the individual processing units.

REACTION NETWORK MODELING

From the perspective of its original application in

petroleum engineering, a Reaction Network Model is a

tool for predicting the amounts of reactants, intermediates,

and products as a function of time for a series of

coupled chemical reactions (potentially numbering in the

tens of thousands of reactions for some systems). It is

usually a mathematical or symbolic formulation suitable

for solution on the computer. A reaction network model

builder is a tool for the computer generation of a reaction

network model. The model builder can thus be used not

only to solve the kinetic equations of interest but also

to generate the reaction mechanisms, rate constants, and

reaction equations themselves.

Essentially, the model builder works as follows:

1. The concentrations of the species to be reacted or

metabolized are input to the model builder.

2. For each species in turn, the model builder performs

a test against each of a set of “reaction rules” to

determine whether or not the species is susceptible

to a particular chemical reaction.

3. If it is not susceptible to any reactions, no further

action is taken on this species.

4. If it is susceptible, a transformation of the species

into one or more product species is performed based

on the particular chemical reaction.

5. Each of these product species then undergoes the

same susceptibility tests and a similar transformation sequence. This leads to a linking of all reactants

with intermediates and, ultimately, with final products. This linking forms the structure of the chemical

“reaction network.”

6. After the reaction network is established, the

rate constants for the reactions are retrieved or

are computed.

7. The coupled differential equations governing the

reaction kinetics for the network are then formulated

by the model builder.

8. Finally, the kinetic equations, that is, the model

equations, are solved numerically, leading to the

concentrations of all species as a function of time.

More details on reaction network modeling, particularly

the initial application to biomedical research, are available in a number of recent publications (Klein et al.,

2002; Liao et al., 2002; Reisfeld and Yang, 2003; Yang

et al., 2003a,b).

CONCLUSION

It is fitting to conclude with some recent testimonials from

reputable scientists for the importance of the integration

of different fields and the central role computer modeling

will play in biology:

In an AAAS Plenary Lecture on February 13, 1998,

Dr. Harold Varmus, then Director of the National

Institutes of Health, emphasized, among others,

two specific themes: “Discoveries in biology and

medicine depend on progress in many fields of

science” and “Methods that dramatically expand

biological data also demand new modes of analysis

and new ways to ask scientific questions.” He said,

“In short, biology is not only for biologists.”• ž Q10

Craig Venter of the human genome fame stated, “If we

hope to understand biology, instead of looking at

one little protein at a time, which is not how biology

works, we will need to understand the integration

of thousands of proteins in a dynamically changing

A-13
REFERENCES 403

environment. A computer will be the biologist’s

ž Q11 number one tool.”• (Bulter, 1999).

Tyson and colleagues (2001) indicated, “Many prominent molecular biologists have pointed out the pressing need for theoretical and computational tools to

show the spatial and temporal organization implicit

in the way the macromolecules are ‘wired together’

ž Q12 to create a living cell.”•

PBPK models have proven useful in uncovering determinants of disposition of carcinogens and other compounds in the body; PBPD cancer models have shown the

role of mutation and cell proliferation in the time course of

tumor development. Both of these types of models initially

lacked considerable biologic detail due to limitations of

our knowledge of fundamentals of cell and molecular biology. The revolution in genomic technologies in the past

decade has revolutionized the database to support mechanistic modeling of chemical disposition and of biologic

responses and these technologies now provide a basis for

expansion of these models with increasing biologic detail.

Reaction network models of cell constituents and genetic

regulatory networks of cellular controls appear particularly attractive candidates for approaches to uncover the

interactions and perturbations controlling neoplastic transformations and growth.

Another contemporary extension of PBPK/PD models

is closely tied to current attempts to unravel the circuitry

of living cells and to discover the manner in which these

circuits lead to biologic function and health. Mathematical models of gene networks and their perturbation by

disease or by chemical exposures are now being developed (Andersen and Barton, 1999). In some cases, simple

prokaryotic cells with specific circuit elements (e.g., biologic oscillators, switches, amplifiers) have been produced

and examined by laboratory experiments and by computation (Guet et al., 2002; Hasty et al., 2002; McMillen

et al., 2002). These computational models evaluate the

protein networks within cells, the genetic control of these

networks, and the logic of cellular responses affected by

these networks (Alm and Arkin, 2003; Davidson et al.,

2002; Ferrell, 2002).

Gene network modeling in intact animals will

inevitably draw on PBPK and reaction network models

to track concentrations of endogenous and exogenous

signaling compounds and on PBPD models to simulate

consequences of the interactions of these compounds

with signaling pathways within cells. Reverse engineering

approaches attempt to uncover the circuitry of working

cells (Csete and Doyle, 2002). Large-scale simulation

modeling that has formed the major core of PBPK/PD

models remains important in examining these genetic

regulatory networks. However, these types of models are

being augmented by Boolean approaches using on–off

logic to increase the scope of genomic coverage (Bolouri

and Davidson, 2002). Efforts in understanding genetic

networks may be especially important in providing

insights into neoplastic diseases in which cell signaling

networks become impaired or deranged (Hahn and

Weinberg, 2002; Hanahan and Weinberg, 2000).

ACKNOWLEDGMENTS

The concepts and work discussed in this presentation were

partially contributed by many colleagues associated or collaborating with the Quantitative and Computational Toxicology group at Colorado State University; we are grateful to

their contribution and intellectual stimulation. Any advances

in science require funding support from many agencies. We

thank NIEHS (Superfund Basic Research Program Project P42

ES05949; research grants RO1 ES09655 and RO3 ES10116

ZES1; training grant T32 ES 07321; and Career Development Award K25 ES11146), ATSDR (Cooperative Agreement U61/ATU881475), and U.S. Air Force (research grants

F33615-91-C-0538; F49620-94-1-0304). Without the generous support of these agencies, the development of research

described herein could have never been possible.

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