vvEPA
United States
Environmental Protection
Agency
600R05043F
      Approaches for the
      Application of Physiologically
      Based Pharmacokinetic (PBPK)
      Models and Supporting Data in
      Risk Assessment
              Inhaled Air  Exhaled Air

                I	t
                  Lungs
                Dermal Contact

                 i  t
                  Skin
                Adipose Tissue
               Richly Perfused Tissues
               Poorly Perfused Tissues
                  Liver
                          , Gut
                               Ingestion
                     Metabolism

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                                               EPA/600/R-05/043F
                                                    August 2006
      Approaches for the Application of Physiologically
Based Pharmacokinetic (PBPK) Models and Supporting
                Data in Risk Assessment
              National Center for Environmental Assessment
                 Office of Research and Development
                U.S. Environmental Protection Agency
                       Washington, DC

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                                       DISCLAIMER


       This document has been reviewed in accordance with U.S. Environmental Protection

Agency policy and approved for publication. Mention of trade names or commercial products

does not constitute endorsement or recommendation for use.
Preferred citation:
U.S. Environmental Protection Agency (EPA).  (2006) Approaches for the Application of Physiologically Based
Pharmacokinetic (PBPK) Models and Supporting Data in Risk Assessment. National Center for Environmental
Assessment, Washington, DC; EPA/600/R-05/043F. Available from: National Technical Information Service,
Springfield, VA, and online at http://epa.gov/ncea.
                                              11

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                                CONTENTS
LIST OF TABLES	v
LIST OF FIGURES	vi
LIST OF ABBREVIATIONS AND ACRONYMS	vii
PREFACE 	viii
AUTHORS AND REVIEWERS	ix
EXECUTIVE SUMMARY	x

1.     INTRODUCTION	1-1
      1.1. SCOPE OF THE DOCUMENT	1-1
      1.2. INTENDED AUDIENCE	1-1
      1.3. ORGANIZATION OF THE DOCUMENT	1-2

2.     PHARMACOKINETIC DATA AND MODEL NEEDS IN RISK ASSESSMENT	2-1
      2.1. PHARMACOKINETICS AND DOSIMETRY MODELING	2-1
      2.2. DOSE-RESPONSE AND MEASURES OF DELIVERED DOSE	2-3
      2.3. PHARMACOKINETIC DATA NEEDS IN RISK ASSESSMENT	2-5
      2.4. PHARMACOKINETIC MODELS IN RISK ASSESSMENT	2-8
          2.4.1. Regulatory Needs and Considerations	2-8
          2.4.2. Use of PBPK Models in Dose-Response Assessment	2-9
          2.4.3. Use of Pharmacokinetic Data and Models in Exposure Assessment	2-11
          2.4.4. Pharmacokinetic Models in Risk Assessment: Summary	2-12

3.     EVALUATION OF PBPK MODELS INTENDED FOR USE IN RISK
      ASSESSMENT	3-1
      3.1. MODEL PURPOSE	3-1
      3.2. MODEL STRUCTURE	3-2
      3.3. MATHEMATICAL REPRESENTATION	3-5
      3.4. PARAMETER ESTIMATION	3-8
          3.4.1. Physiological Parameters	3-8
          3.4.2. Partition Coefficients	3-12
          3.4.3. Biochemical Parameters	3-13
      3.5. COMPUTER IMPLEMENTATION	3-14
      3.6. EVALUATION OF PREDICTIVE CAPACITY	3-18
          3.6.1. Model Verification	3-20
          3.6.2. Model Validation/Calibration	3-21
          3.6.3. Model Documentation	3-26
      3.7. SENSITIVITY, VARIABILITY, AND UNCERTAINTY ANALYSES	3-29
          3.7.1. Sensitivity Analysis	3-29
          3.7.2. Variability Analysis	3-32
          3.7.3. Uncertainty Analysis	3-34
      3.8. DEVELOPING PBPK MODELS FOR USE IN RISK ASSESSMENT:
         STRATEGIES FOR DEALING WITH DATA-POOR SITUATIONS	3-36
          3.8.1. Minimal Data Needs for Constructing PBPK Models	3-36
          3.8.2. Surrogate Data for Interspecies and Interchemical Extrapolations	3-37
      3.9. EVALUATION OF PBPK MODELS: SUMMARY	3-38
                                     in

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                             CONTENTS (continued)

4.  APPLICATION OF PBPK MODELS IN RISK ASSESSMENT	4-1
      4.1. CHOOSING PBPK MODELS APPROPRIATE FOR USE IN RISK
          ASSESSMENT	4-1
      4.2. EVALUATION OF DOSE METRICS FOR PBPK MODEL-BASED
          ASSESSMENTS	4-3
      4.3. REVIEW OF EXTRAPOLATIONS POSSIBLE WITH PBPK MODELS	4-11
           4.3.1.  Interspecies Extrapolation	4-11
           4.3.2.  Estimating Intraspecies Variability	4-13
           4.3.3.  Route-to-RouteExtrapolation	4-14
           4.3.4.  Duration Adjustment	4-15
           4.3.5.  High-Dose to Low-Dose Extrapolation	4-16
      4.4. ROLE OF PBPK MODELS IN REFERENCE CONCENTRATION AND
          REFERENCE DOSE DERIVATION	4-18
           4.4.1.  Reference Concentration	4-18
           4.4.2.  Reference Concentration:  Point of Departure	4-20
           4.4.3.  Reference Concentration:  Route-to-Route Extrapolation	4-20
           4.4.4.  Reference Concentration:  Duration Adjustment	4-21
           4.4.5.  Reference Concentration:  Dosimetric Adjustment Factor
                 (Interspecies Extrapolation)	4-22
           4.4.6.  Example of PBPK Model Use in Reference Concentration Derivation.... 4-23
           4.4.7.  Reference Dose	4-24
           4.4.8.  Reference Dose: Point of Departure	4-24
           4.4.9.  Reference Dose: Route-to-Route Extrapolation and Duration
                 Adjustment	4-25
           4.4.10. Reference Dose: Interspecies Extrapolation	4-25
           4.4.11. Example of PBPK Model Use in Reference Dose Derivation	4-25
           4.4.12. Uncertainty Factors: Role of PBPK Models	4-26
      4.5. ROLE OF PBPK MODELS IN CANCER RISK ASSESSMENT	4-28
           4.5.1.  Interspecies Extrapolation	4-28
           4.5.2.  Intraspecies Variability	4-29
           4.5.3.  Route-to-Route Extrapolation	4-29
           4.5.4.  High-Dose to Low-Dose Extrapolation	4-30
           4.5.5.  Example of PBPK Model Use in Cancer Risk Assessment	4-30
      4.6. MIXTURE RISK ASSESSMENT	4-33
      4.7. LINKAGE TO PHARMACODYNAMIC MODELS	4-34

GLOSSARY	G-l

REFERENCES	R-l
                                       IV

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                                  LIST OF TABLES
Table 3-1.     Equations of a four-compartment PBPK model to simulate the inhalation
             exposure of volatile organic compounds	3-6

Table 3-2.     Equations used for describing diffusion-limited uptake in PBPK models	3-7

Table 3-3.     Commonly used physiological parameters for mice, rats, and humans	3-9

Table 3-4.     Range of values of the volume and perfusion of select tissues in the mouse	3-9

Table 3-5.      Range of values of the volume and perfusion of select tissues in the rat	3-10

Table 3-6.     Range of values of perfusion of select tissues in humans	3-10

Table 3-7.     Examples of simulation software used for PBPK modeling	3-15

Table 4-1.     Dose metrics used in PBPK model-based cancer and noncancer risk
             assessments	4-6

Table 4-2.     Relationship between tumor prevalence and dichloromethane metabolites
             produced by microsomal and glutathione pathways for the bioassay
             conditions (methylene chloride-dose response in female mice)	4-31

Table 4-3.     Examples of biologically based models of endpoints and processes of
             toxicological relevance	4-36

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                                  LIST OF FIGURES


Figure 2-1.    Relationship between the exposure concentration and adverse response for a
             hypothetical chemical	2-4

Figure 2-2.    Rat-human extrapolation of exposure concentrations of toluene based on
             equivalent dose metrics (AUC [area under the curve] of toluene in blood,
             3.8mg/L/hr)	2-7

Figure 2-3.    Basic flowchart of PBPK model development	2-9

Figure 3-1.    Sample PBPK model structures	3-4

Figure 3-2.    Comparison of four PBPK model simulations (left, log scale; right, linear
             scale).  Solid lines are model simulations overlayed with experimental
             data (symbols)	3-24

Figure 3-3.    Sensitivity ratios associated with certain input parameters of a hypothetical
             PBPK model	3-30

Figure 3-4.    Monte Carlo simulation	3-33

Figure 4-1.    Flowchart for selecting PBPK models appropriate for use in risk assessment.... 4-2

Figure 4-2.    Examples of measure of tissue exposure to toxic moiety for risk assessment
             applications	4-4

Figure 4-3.    Estimation of an interindividual variability	4-14

Figure 4-4.    Oral-to-inhalation extrapolation of the pharmacokinetics of chloroform on the
             basis of same area under the curve in blood (7.06 mg/L/hr)	4-16

Figure 4-5.    Duration adjustment (4 hr to 24 hr) of toluene exposures in rats, based on
             equivalent AUC (2.4 mg/L/hr)	4-17

Figure 4-6.    High-dose to low-dose extrapolation of dose metrics using PBPK model for
             toluene	4-19

Figure 4-7.    PBPK model predictions of glutathione (GST)-pathway metabolites in mouse
             liver	4-32

Figure 4-8.    Relationship between the dose metric (|imol metabolized/g liver/hr)
             simulated by PBPK model and the cell killing inferred from
             pharmacodynamic model for chloroform	4-35
                                           VI

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                  LIST OF ABBREVIATIONS AND ACRONYMS

ADME       Absorption, distribution, metabolism, and excretion
AUC        Area under the curve
BBDR       Biologically based dose-response (model)
BMC        Benchmark concentration
BMD        Benchmark dose
Cmax        Maximal concentration
CFD         Computational fluid dynamic(s)
CSF         Cancer slope factor
DAF         Dosimetric adjustment factor
FIEC         Human equivalent concentration
IUR         Inhalation unit risk
LOAEL      Lowest-observed-adverse-effect level
MCMC       Markov chain Monte Carlo
MOA        Mode of action
NOAEL      No-observed-adverse-effect level
PBPK        Physiologically based pharmacokinetic
POD         Point of departure
QSAR       Quantitative structure-activity relationship
RfC         Reference concentration
RfD         Reference dose
UF          Uncertainty factor
UFA         interspecies uncertainty factor
UFH         intraspecies uncertainty factor
                                          vn

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                                      PREFACE

       Approaches for the Application of Physiologically Based Pharmacokinetic (PBPK)
Models and Supporting Data in Risk Assessment addresses the application and evaluation of
PBPK models for risk assessment purposes. PBPK models represent an important class of
dosimetry models that are useful for predicting internal dose at target organs for risk assessment
applications.  This report is primarily meant to serve as a learning tool for U.S. Environmental
Protection Agency (EPA) scientists and risk assessors who may be less familiar with PBPK
modeling. In addition, it can be informative to PBPK modelers within and outside EPA because
it provides an overview of the types of data and models that EPA requires for consideration of a
model for use in risk assessment. A draft of this document underwent a public comment period
and external peer review in 2005, and this final report incorporates many of the relevant
comments and suggestions received in response to the draft report.
                                          Vlll

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                           AUTHORS AND REVIEWERS
      The National Center for Environmental Assessment (NCEA), Office of Research and
Development, was responsible for the preparation of this document. It was developed under
EPA Contract No. 4W-0322-NASX, and initially prepared by Dr. Kannan Krishnan with
significant input from the authors listed below.

EPA PROJECT OFFICERS
Femi Adeshina
National Center for Environmental Assessment
Office of Research and Development
U.S. Environmental Protection Agency
Washington, DC

Chadwick Thompson
National Center for Environmental Assessment
Office of Research and Development
U.S. Environmental Protection Agency
Washington, DC

AUTHORS
Hugh Barton, National Center for Computational Toxicology, Research Triangle Park
Weihsueh Chiu, NCEA, Washington, DC
Robert DeWoskin, NCEA, Research Triangle Park
Gary Foureman, NCEA, Research Triangle Park
Kannan Krishnan, University of Montreal, Montreal, Canada
John Lipscomb, NCEA, Cincinnati
Paul Schlosser, NCEA, Research Triangle Park
Babasaheb Sonawane, NCEA, Washington, DC
Chadwick Thompson, NCEA, Washington, DC

INTERNAL EPA REVIEWERS
Jerry Blancato, National Exposure Research Laboratory, Las Vegas
Joyce Donohue, Office of Water
Hisham El-Masri, NCEA, Washington, DC
Marina Evans, National Health and Environmental Effects Research Laboratory, Research
  Triangle Park
Lynn Flowers, NCEA, Integrated Risk Information System
Karen Hammerstrom, NCEA, Washington, DC
Allen Marcus, NCEA, Integrated Risk Information System
Dierdre Murphy, Office of Air Quality Planning and Standards
Alberto Protzel, Office of Pesticide Programs, Washington, DC
Woodrow Setzer, National Center for Computational Toxicology, Research Triangle Park
                                         IX

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                               EXECUTIVE SUMMARY

       Physiologically based pharmacokinetic (PBPK) models represent an important class of
dosimetry models that are useful for predicting internal dose at target organs for risk assessment
applications. Approaches for the Application of Physiologically Based Pharmacokinetic (PBPK)
Models and Supporting Data in Risk Assessment addresses the following questions: Why are
risk assessors interested in using PBPK models? How are PBPK models evaluated for use in a
risk assessment? What are the questions or data gaps in a risk assessment that can be addressed
by PBPK models? However, this document is not meant to serve as formal U.S. Environmental
Protection Agency (EPA) guidance.
       The text is organized into four chapters. Chapter 1 outlines the scope of the document,
the intended audience, and the topics covered in the remaining chapters.  Chapter 2 presents the
rationale for using PBPK models in risk assessment and the pharmacokinetic data and models
needed to derive a reference dose (RfD), a reference concentration (RfC), and unit risk estimates
in cancer risk assessment (e.g., cancer slope factor).  Chapter 3 describes how models are
evaluated, the main model characteristics to review, and the on-going development of acceptance
criteria for model use in risk assessment.  Chapter 4 discusses applications of PBPK model
simulations within the current EPA risk assessment framework. The appendix contains a
comprehensive list of publications, current as of the end of 2005, relating to PBPK modeling and
its use in health risk assessment.
       PBPK models consist of a series of mathematical representations of biological tissues and
physiological processes in the body that simulate the absorption,  distribution, metabolism, and
excretion of chemicals that enter the body.  PBPK models are designed to estimate an internal
dose of a proposed toxic moiety to a target tissue(s) or some appropriate surrogate dose metric
for a target tissue dose. The choice of an internal dose metric is based on an understanding of the
chemical's mode of action.  The internal dose metric (sometimes called the biologically effective
dose) replaces the administered dose in the derivation of the quantitative dose-response
relationship, with the intent of reducing the uncertainty inherent in risk assessments based on an
applied dose. This reduction in uncertainty and the improved scientific basis for the dose-
response value are the main advantages of PBPK models and the reasons for the growing interest
in their use.  PBPK models also can simulate an internal dose from exposure conditions of
interest where no data are available, i.e., they can extrapolate to conditions beyond those of the

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data set used to develop the model. An important and active area of research is the
characterization of the uncertainty in risk assessments based on PBPK model results compared
with the uncertainty in results based on the administered dose.
       PBPK models exist for a wide range of chemicals with varying properties. The vast
majority of PBPK modeling efforts to date have focused on chemicals that distribute
systemically within the body and cause systemic effects, although the models'  applicability for
describing the pharmacokinetics of other chemicals, such as reactive gases, has been successfully
demonstrated.  Because this document is intended to describe some of the basic principles of
PBPK modeling and its use in risk assessment, it primarily draws upon the experience and
literature concerning chemicals with systemic distributions.
       Examples of PBPK model applications in risk assessments include interspecies
extrapolation of the dose-response relationship (based on estimates  of the internal dose), route-
to-route extrapolation, estimation of response from varying exposure condition, estimation of
human variability (within the whole population or subpopulations),  and high-to-low dose
extrapolation. PBPK models used in risk assessments would, at a minimum (1) contain a
compartment that is either identified with the target tissue,  contains the target tissue, or is
identified as a surrogate for the target tissue; (2) have defensible physiological parameter values
that are within the known plausible range; and (3) have undergone a thorough evaluation for
their structure, implementation, and predictive capability.
       Evaluation of PBPK models intended for risk assessments includes a review of the model
purpose, model structure, mathematical representation,  parameter estimation (calibration), and
computer implementation. Criteria for acceptance of a  PBPK model for use in risk assessment
include the following:  (1) the model represents the species and life stage of relevance to a
particular risk assessment, (2) it has been evaluated and peer-reviewed for the adequacy of its
structure and parameters, and (3) it provides adequate simulations of the concentration of the
toxic moiety (parent chemical or  metabolite) in the target organ (or  a surrogate compartment)
following the relevant route(s) of exposure and over the time-course for which the chemical is
present in that tissue.
       When a  PBPK model is available for the appropriate test species,  it is used to estimate the
value of internal dose metrics, which are then used to derive a given point of departure (e.g., no-
observed-adverse-effect level, lowest-observed-adverse-effect level, benchmark dose,
benchmark concentration) for use in dose-response analyses for toxicity endpoints, including
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cancer, chronic toxicity, and other toxicity endpoints.  Some risk assessment applications can be
accomplished using only a model for the test species, e.g., prediction of the toxicity in that
species by another route of exposure for purposes of route extrapolation. For most applications,
a human version of the PBPK model is also developed to estimate an administered dose to a
human that would result in the equivalent internal dose in a human that led to the observed
toxicity  in a test species or, less frequently, the biologically effective dose from a human clinical
or epidemiology study. PBPK model analysis is accepted as a scientifically sound approach to
estimating the internal dose of a chemical at a target site and as a means to evaluate and describe
the uncertainty in risk assessments.
                                           xn

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                                 1. INTRODUCTION

1.1.  SCOPE OF THE DOCUMENT
       The objective of this document is to provide a description of approaches for using
physiologically based pharmacokinetic (PBPK) data and models in human health risk
assessment.  Its primary focus is on the evaluation and use of PBPK models for predicting
internal dose at target organs in risk assessment applications. Many of the past efforts on PBPK
modeling have focused on water-insoluble gases that cause systemic toxicity (i.e., producing
effects remote from the site of exposure) and on some nonvolatile organics. This document
primarily draws on the experience and literature resulting from these efforts. These approaches
can also be applied to agents such as reactive gases and paniculate matter where the target organ
is the respiratory tract, generally in conjunction with specialized respiratory tract modeling (e.g.,
computational fluid dynamic [CFD] modeling).  Guidance concerning alternative approaches to
dosimetry modeling should also be consulted for determining a reference concentration (RfC)
value (U.S. EPA, 1994).  The discussions herein are conceptually applicable, in a broad sense, to
many kinds of dosimetry models and a wide range of substances.
       In developing this document, it was assumed that risk assessors are familiar with  some
basic concepts of pharmacokinetics and that model developers are familiar with some of the
basic concepts of risk assessment; therefore, the document serves as an overview of PBPK
modeling and its application in risk assessment.  Appropriate references to secondary review
articles and reports from which additional information can be obtained are provided.
       Finally, it is important to realize that the application of PBPK models in risk assessment
is evolving.  Thus, this document does not specify (or recommend) when the effort to construct
and apply PBPK modeling is justified; rather, it highlights some of the benefits of PBPK
modeling in  risk assessment.

1.2.  INTENDED AUDIENCE
       The document was prepared with two primary audiences in mind: (1) risk assessors who
need to know about the potential applications of PBPK models in risk assessments, and (2)
PBPK model developers who need to better understand how their efforts can help improve  health
risk assessment.
                                          1-1

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1.3.  ORGANIZATION OF THE DOCUMENT
       The remaining three chapters form the core of this document.  They describe what risk
assessors need in terms of pharmacokinetic data, and why (Chapter 2); how to evaluate PBPK
models for use in risk assessments (Chapter 3); and how to use PBPK models in risk assessments
to address specific areas of uncertainty (Chapter 4).
       Chapter 2 addresses data needs in terms of reference dose (RfD) and RfC derivation as
well as predictive estimates in cancer risk assessment. It also contains a brief discussion on the
minimal data requirements for constructing PBPK models, as well as the use of pharmacokinetic
data and PBPK models to improve exposure assessments.
       Chapter 3 presents an approach and some criteria for evaluating PBPK models intended
for use in risk assessments that will facilitate the assessor's decision regarding whether or not an
available model is adequate and scientifically defensible for use in reducing uncertainties in a
given risk assessment. The PBPK modeling issues are considered under each of the following
topic areas:  model structure, mathematical description, parameter estimation (calibration),
computer implementation, and evaluation. Current criteria as well as accepted methods are
identified and then assembled to facilitate the identification of PBPK models that meet the
requirement for use in risk assessment.
       Chapter 4 discusses how PBPK models and data can be applied within the current U.S.
Environmental Protection Agency (EPA, or the Agency) risk assessment framework to address
specific areas of uncertainty.  The following types of PBPK model applications in risk
assessment are presented in this chapter:  high-dose to low-dose, interspecies, intraspecies, route-
to-route, and scenario extrapolations; mixture risk assessment; and linkage with
pharmacodynamic models. This chapter also highlights how PBPK models are used in cancer
and noncancer assessments.
       Finally, the appendix provides a list of publications relating to PBPK modeling and its
use in health risk assessment.
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    2.  PHARMACOKINETIC DATA AND MODEL NEEDS IN RISK ASSESSMENT

2.1.  PHARMACOKINETICS AND DOSIMETRY MODELING
       Pharmacokinetics (pharmakon + kinetics; pharmakon (Greek) = drugs and poisons;
kinetics = change as a function of time) involves the study of the time course of the parent
chemical or metabolite concentrations or amounts in biological fluids, tissues, and  excreta and
the construction of mathematical models to interpret such data (Wagner, 1981). The time course
of the concentration of a chemical or its metabolite in biota is determined by the rate and extent
of absorption, distribution, metabolism, and excretion (ADME).  The pharmacokinetics or
ADME of a substance determines the delivered dose or the amount of chemical available for
interaction in the tissues. Relating adverse response observed in biota to an appropriate measure
of delivered dose (e.g., concentration of the toxic chemical in the target tissue) rather than
administered dose or exposure concentration is likely  to improve the characterization of many
dose-response relationships (see Section 2.2.).
       A range of modeling approaches is used to characterize exposures and the resulting
delivered doses.  The variety of approaches reflects differences in chemical and physical
characteristics (e.g., stable or reactive gases, particulate matter, lipophilic organics, water-soluble
compounds), differences in pharmacokinetic properties, and the ability of compounds to cause
contact site or systemic toxic effects  (U.S. EPA, 2004, 1994; Andersen and Jarabek, 2001;
Overton, 2001).
       Exposure to many drugs  and toxicants occurs via the oral route and causes systemic
effects, and many simple (e.g., one- and two-compartment) pharmacokinetic models have been
used to analyze the pharmacokinetics of such exposures (Renwick, 2001; O'Flaherty, 1981).
Generally, these compartment models contain a central compartment that represents the whole
body (or plasma) where distribution occurs nearly instantaneously (one-compartment model) or
an additional compartment (two-compartment model) where the distribution is affected by
additional processes such as metabolism or sequestration into fat. Compartment models help
characterize a chemical's kinetic behavior, and they are useful in deriving values for a chemical
or drug's distribution in the body or clearance from the blood (i.e., half-life).
       The values derived from  a compartment model analysis, however, apply only to the
conditions of the study from which the experimental data were obtained. To better represent the
biological determinants of a chemical's disposition in the body and predict the internal dose that
                                          2-1

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would result from different exposure regimens (including hypothetical exposures where no data
are available), models have evolved with multiple compartments and mathematical descriptions
of the real physiological processes and tissues most likely to affect chemical disposition (e.g.,
absorption from the gut or lung, cardiac output, metabolism in the liver, renal clearance).  These
models are called physiologically based pharmacokinetic (PBPK) models, and they are the focus
of this document.
       The need to predict behaviors of volatile anesthetics, including compounds now used
exclusively as industrial chemicals, was a driving force for the development of PBPK models
(Krishnan and Andersen, 2001). The general principles developed in these early PBPK
modeling efforts for systemically distributed compounds are also applicable to other compounds.
For example, the respiratory tract is a frequent site of both exposure and toxicity, and it has been
a particular focus for a range of modeling approaches,  including those developed to simulate the
kinetics of gases of various reactivities and solubilities, as well as parti culate matter (see U.S.
EPA, 1994).  More recently, the kinetics of reactive gases and paniculate matter within the
respiratory tract are simulated with advanced approaches such as two-dimensional and three-
dimensional CFD modeling (U.S. EPA, 2004; Martonen et al., 2001; Overton, 2001; Kimbell et
al., 1993).
       The role of metabolism is a significant factor in the development of PBPK models.
Saturable metabolism results in nonlinear relationships between the level  of administered  dose
and the levels of the internal dose for a parent or metabolite. In combination with other
physiological and chemical events, the resulting administered dose-response relationship can
quickly become difficult to resolve with simple analytical tools.  PBPK models provide an
excellent means to  account for multiple process interactions and nonlinearities and to provide
insight into the whether the parent chemical or the metabolite is the main form (or toxic moiety)
leading to adverse effects.
      Metabolism has also played an important role in the development of models for
respiratory tract toxicities. Nasal or other respiratory tract toxicities following exposure to many
volatile organic compounds has often been linked to the generation of a toxic metabolite in
respiratory tract tissues.  To simulate the kinetics and resulting toxicities for these compounds,
CFD models have been coupled with PBPK models. The CFD models describe the deposition of
the chemical in different regions of the nose, and the PBPK model then simulates the tissue
absorption, metabolic, and clearance processes (Frederick et al., 2002; Bogdanffy et al., 2001).
                                           2-2

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Other complex kinetic events in the respiratory tract are also being modeled, including the
kinetics for compounds that are relatively water soluble and that exhibit fractional absorption, or
the so-called "wash-in, wash-out" effect (Perkins et al., 1995; Medinsky et al., 1993; Johanson,
1991).
       Although the approaches detailed in the earlier RfC methodology (U.S. EPA, 1994) do
not address many of these more recent advances, there is recognition of the need for additional
approaches that address these and other challenging aspects of respiratory tract dosimetry.
       The relevant modeling approach, therefore, depends on the physical and chemical
characteristics of the material, the method and route of exposure or delivery, and the toxicities
under consideration.  All of these modeling approaches attempt to describe the dose delivered to
the relevant areas of the body, whether that is a region of the respiratory tract or skin or systemic
delivery through the blood supply to target organs. These  approaches permit estimation of some
measure of delivered dose for improved understanding of the dose-response relationship.

2.2.  DOSE-RESPONSE AND MEASURES OF DELIVERED DOSE
       Dose-response relationships that appear unclear or  confusing at the administered dose
level can become more understandable when expressed on the basis of internal dose of the
chemical. Figure 2-1 depicts the case of a hypothetical chemical for which the correlation between
dose and response is weak or complex (Panel A).  However, once the relationship is based on
internal dose, there emerges a clear and direct relationship between dose and response (Panels B
and C). The major advantage of constructing dose-response relationships on the basis of internal
or delivered dose is that it can provide a stronger biological  basis for conducting extrapolations and
for comparing responses across studies, species, routes, and dose levels (Melnick and Kohn, 2000;
Benignus et al.,  1998; Aylward  et al., 1996; Andersen et al., 1987; Clewell and Andersen, 1985).
       Relating blood and tissue concentrations with response in exposed organisms has long
been recognized in pharmacology (e.g., Wagner, 1981). In pharmacokinetics, the target tissue
dose that most closely relates to an adverse response is often referred to as the internal "dose
metric" (Andersen and Dennison, 2001). Dose metrics used in risk assessment applications,
ideally, reflect the biologically  active form of the chemical (parent chemical, metabolites, or
adducts), its level (concentration or amount), duration of internal exposure (instantaneous, daily,
lifetime, or a specific developmental period), and intensity (peak, average, or integral), as well as
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                            30 i
                                                           ,   linear
                                                            Weibull
                                      1000     2000     3000     4000
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       Figure 2-1. Relationship between the exposure concentration and adverse
       response for a hypothetical chemical. Panel A depicts the case of a chemical
       for which the correlation between dose and response is weak or complex, along
       with equally plausible curve fits (linear, Hill, and Weibull). This dose-response
       relationship is improved when it is based on an appropriate measure of internal
       dose (Panels B and C).
the appropriate biological matrix (e.g., blood, target tissue, surrogate tissues).  For assessment of

health risks related to lifetime exposure of systemically acting chemicals, in the absence of mode
of action (MO A) information to the contrary, the integrated concentration of the toxic form of

chemical expressed as the daily average (i.e., average daily area under the concentration vs. time

curve, or area under the curve [AUC]) in target tissue has been considered to be an appropriate

dose metric (Clewell et al.,  2002a; Voisin et al., 1990; Collins, 1987).
                                            2-4

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Box 2-1.  Examples of dose metrics useful for
exploring dose-response relationships
Parent chemical
    •   Peak concentration
    •   Average concentration
    •   Amount or quantity
    •   AUC (integral)
Metabolite
       Peak concentration
       Average concentration
       Amount or quantity
       Rate of production
       Cumulative rate of formed/time/L tissue
       AUC (integral)
Miscellaneous
    •   Receptor occupancy (extent/duration)
    •   Macromolecular adduct levels
    •   Depletion of cofactors
       When the toxicant is not the parent
chemical but a reactive intermediate, the
amount of metabolite produced per unit
time or the amount of metabolite in target
tissue over a period of time (e.g., mg
metabolite/L tissue during 24 hr) has been
used as the dose metric (Andersen and
Dennison, 2001).  For developmental
effects, the dose surrogate is defined in the
context of the window of exposure during a
particular gestational event (e.g., Luecke et
al., 1997;Welschetal., 1995).
       Even though the AUC and rate of
metabolite formation are among the most
commonly investigated dose metrics, other
surrogates of tissue exposure may also be appropriate for risk assessment purposes, depending on
the chemical and the MOA (Clewell  et al., 2002a). Dose metrics that may be used to derive
dose-response relationships for risk assessment are listed in Box 2-1; evaluation of dose metrics
for use in risk assessment is further discussed in Section 4.2. Finally, it should be noted that
PBPK models can also be useful for hypothesis testing, particularly with regard to  choosing
among potential dose metrics.  This is discussed further in Chapters 3 and 4, and particularly in
Section 4.5.5.

2.3.  PHARMACOKINETIC DATA NEEDS IN RISK ASSESSMENT
       The quantitative dose-response assessment portion of the risk assessment process can be
used to determine a point of departure (POD) for one or more of the most sensitive critical
effects. The POD is the dose-response point that marks the beginning of a low-dose
extrapolation, and it can be the no-observed-adverse-effect level (NOAEL) or the lowest-
observed-adverse-effect level (LOAEL) for an observed incidence or the lower bound on dose
for an estimated incidence or change in response level from a benchmark dose (BMD) analysis.
The quantitative characterization relates the administered dose to the observed responses in
laboratory or field studies. In some cases, data are available to relate an internal dose at a target
2-5

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tissue to the response, but generally the internal dose-response relationship is derived from a
model analysis. An understanding of the MOA leading to the most sensitive endpoint is used to
determine the most appropriate dose measure for deriving a POD. Noncancer and nonlinear
cancer assessments derive a POD for use in risk assessment based on the available data. This
process often requires conduct of interspecies, high-dose to low-dose, duration, and/or exposure
route extrapolations of the dose-response from available data to the likely human exposure
conditions and most sensitive human subpopulations.
      These extrapolations assume that when the value of the internal dose metric is identical in
two situations (rat vs. human, oral vs. inhalation, 6-hr exposure vs. 24-hr exposure), the two
administered doses are pharmacokinetically equivalent. For example, exposure of rats to 50 ppm
toluene for 6 hr and of humans to 17.7 ppm toluene for 24 hr yields the same blood AUC (3.8
mg/L/hr), implying that these exposure scenarios in rats and humans are pharmacokinetically
equivalent (Figure 2-2).  The example in Figure 2-2 demonstrates that pharmacokinetic
equivalence is not always linear equivalence; if one assumes that all aspects of the
pharmacokinetics of toluene in humans is identical to those in rats, an equivalent 24-hr exposure
would be 12.5 ppm (i.e., 6 hr x  50 ppm is equivalent to 24 hr x  12.5 ppm), not 17.7 ppm.
      Knowledge of the MOA supports the choice of the dose metric. For example, the most
appropriate dose metric to characterize the dose-response relationship for reactive gases that
cause contact site toxicity is the total amount of chemical in the target tissue over time, whereas
for the anesthetic effects of a volatile organic, the current (or peak) concentration in the blood is
the most appropriate dose metric. For the latter, the acute effects are more (or entirely)
dependent on concentration rather than on total amount over time, so extrapolations are best
conducted using that dose metric.
      PBPK models are often intended to estimate target tissue dose in species and under
exposure conditions for which little or no data exist.  Thus, if a complete pharmacokinetic data
set were available, then there would be no need to develop a PBPK model.  Such an optimal
pharmacokinetic data set for risk assessment would consist of the time-course data on the most
appropriate dose metric associated with exposure scenarios and doses used in the critical studies
chosen for the assessment (e.g., animal bioassays or human clinical and epidemiological studies)
and relevant human exposure conditions. An example of such a dose metric is the concentration
of a toxic metabolite in target tissue over a 24-hr period in the test species and in humans.  This
information would be obtained for the window of exposure, route and scenario of exposure
                                          2-6

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chemical, urinary metabolite levels, or fraction absorbed may be used as a surrogate for the
tissue levels.  These and other subsets of pharmacokinetic data can be used to develop a PBPK
model to estimate the level of the toxic moiety of interest, and the uncertainty in those estimates
can be formally characterized.

2.4.  PHARMACOKINETIC MODELS IN RISK ASSESSMENT
2.4.1. Regulatory Needs and Considerations
       Regulatory  agencies such as EPA derive dose-response values based on the current
understanding of a  dose-response relationship. Reference values correspond to an estimate of a
daily exposure to the human population (including sensitive subgroups) that is likely to be
without an appreciable risk of deleterious effects during a lifetime. The reference values
developed at EPA include RfC for chronic inhalation exposures and RfD for chronic oral
exposures.  For chronic oral and inhalation cancer risk assessments with an unknown or a linear
MOA (e.g., mutagenic carcinogens), EPA develops unit risk estimates, including the cancer
slope factor (CSF)  for oral exposures and the inhalation unit risk (IUR). The underlying
assumption in these derivations is that the exposure concentration (or applied dose) of a parent
chemical results in an internal exposure of the putative toxic form of the chemical in a target
organ that will be less than or equal to a level that is not associated with significant adverse
responses during a  lifetime (reference value) or that yields a likely risk at or below the estimated
lifetime risk (unit risk).
       Even though a key factor in the induction of adverse effects is the presence of the toxic
form of a chemical in the target organ, it is rare that data are available on the time course of the
toxic moiety in the target tissue(s) in humans. Even in animal studies, it is more practical to
obtain measures of blood, plasma, and urinary concentrations of toxic chemicals and their
metabolites than the actual toxic moiety level in the relevant tissue.  Pharmacokinetic models are
therefore used to estimate the tissue concentration of toxic substances.
       Among the  compartmental pharmacokinetic models, PBPK models are the most
appropriate and useful for conducting the extrapolations needed to derive reference values
because they model the underlying physiological and chemical processes that determine
chemical disposition, and they can be used to predict target organ concentrations for hypothetical
exposures (Krishnan and Andersen, 2001; Andersen,  1995; Leung, 1991; Rowland, 1985;
Himmelstein and Lutz,  1979). By simulating the kinetics and dose metric of chemicals, PBPK
                                           2-8

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models can reduce the uncertainty related to interspecies, intraspecies, route-to-route, duration,
and high-dose to low-dose extrapolations needed to derive RfC, RfD, and cancer unit risk
estimates.  The following sections discuss how the PBPK models are used in health risk
assessment. Figure 2-3 provides an overview of the development and use of PBPK models for
risk assessment; it should be noted that model development can occur within academic, industry,
and governmental bodies, and often involves collaboration or sharing of information.
      Problem
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2.4.2. Use of PBPK Models in Dose-Response Assessment
      PBPK models are useful for performing various forms of extrapolations where the data
necessary for predicting risks to humans are not available and cannot easily (or ethically) be
obtained. The primary advantage gained by using PBPK models in risk assessment is their
ability to relate toxicity responses in a test species to humans and outcomes observed in smaller
populations to likely outcomes in the general population. Thus, foremost among the
extrapolations afforded by PBPK models are inter- and intra-species extrapolations.
                                         2-9

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       In risk assessments based on nonlinear MO As (e.g., most noncancer assessments), RfC
and RfD values are derived from PODs (i.e., NOAEL, LOAEL, or benchmark concentration
[BMC]) to derive a human equivalent concentration (HEC) or dose. In RfC derivation,
pharmacokinetic adjustments, called dosimetric adjustment factors (DAFs), are applied to
account for species differences in chemical disposition.  These factors are dependent on the
nature of the inhaled toxicant and MO A, as well as the endpoint (local effects vs. systemic
effects). Dosimetry data in the test animals and humans (e.g., deposition data, region-specific
dosimetry, blood concentration of systemic toxicants), if available, can help estimate the DAF.
In the absence of such data, knowledge of critical parameters or mathematical models in the test
species and humans can be useful in estimating the DAF.  Similar methods are employed in RfD
derivation.
       An alternative to the use of DAFs is to employ models to make interspecies
extrapolations. A variety of computational tools are available for determining the uptake and
deposition of gases and parti culates in nasal pathways and the respiratory tract (U.S. EPA, 2004;
Bogdanffy and Sarangapani,  2003; Hanna and Lou, 2001; Iran et al., 1999; Bush et al., 1998;
Asgharian et al., 1995; Jarabek, 1994; Kimbell et al.,  1993). Although PBPK models have most
frequently been applied to systemically acting gases and vapors, they have also been applied, in
conjunction with other models (e.g., CFD), to more locally acting gases. Another limitation to
DAFs is that they do not account for metabolism, so PBPK modeling approaches would clearly
be preferable for metabolized compounds if adequate data are available.
       PBPK models are also useful for incorporating variability in chemical disposition into a
risk assessment.  There are numerous determinants of a chemical's disposition in the body (e.g.,
protein levels,  enzyme activity levels, tissue volumes, breathing rates, cell proliferation rates)
(e.g., Dome et al., 2002,  2001a, b; Walton et al., 2001).  Focusing on individual determinants of
disposition is useful for understanding their mechanistic basis and potential impacts on dosimetry
and response, but such an approach can easily lead to unrealistic estimates of total variability of a
chemical as well as toxic response (Lipscomb,  2004)  because the magnitude of variability
associated with such individual determinants may be neither cumulative nor additive. The net
impact of various determinants on chemical disposition is more properly evaluated by integrating
the available information with a PBPK or biologically based dose-response (BBDR) model.
       Two additional forms of extrapolation amenable to PBPK modeling include route and
duration adjustments.  The PODs in critical toxicity studies are not always obtained for exposure
                                          2-10

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scenarios of interest to risk assessment. Ideally, the POD used in the RfC process would be the
inhalation route-specific NOAEL, LOAEL, or BMC. Route-to-route extrapolation, however, can
be conducted on the basis of equivalent potential doses when information on the POD is
available only for a noninhalation route of exposure (e.g., oral route) (Pauluhn, 2003).
Historically, simplistic assumptions were used to convert the NOAEL (mg/kg/day) associated
with an oral exposure route to equivalent inhaled concentration, based on breathing rate and
body weight of the test species. Such simplistic approaches, however, incorrectly assume that
the rates of ADME and tissue dosimetry of chemicals are the same for a given total dose,
regardless of the exposure route and intake rate. PBPK modeling is useful for conducting route-
to-route extrapolation on the basis of equivalent delivered dose from PODs identified from the
NOAEL, LOAEL, or BMC (e.g., oral to inhalation).
       As mentioned above, RfC and RfD values are intended for continuous exposure of human
populations, such that the POD used in an RfC  derivation (for example) would correspond to 24
hr/day exposures (U.S. EPA, 1994). Because the PODs are frequently obtained from animal
exposures or occupational exposures that occur for 6 to 8 hr/day, 5 days/wk, adjustment to a
continuous 24-hr exposure is conducted on the  basis of hours per day and days per week (i.e.,
6/24 x 5/7), which essentially results in a lower concentration for continuous exposures (U.S.
EPA, 2002).  Depending on the dose metric identified  or hypothesized to be the most
appropriate for the chemical and endpoint, the duration-adjusted exposure values can be obtained
with PBPK models (U.S. EPA, 2002; Jarabek, 1994).  This approach is based on the expectation
that the pharmacodynamic aspect does not change between the various durations of within-day
exposures (<24 hr).
       As discussed in detail in Chapter 4, PBPK models can also be used to convert a POD in a
critical cancer study to an appropriate dose metric. Here again, simpler approaches such as body
weight scaling can be replaced with PBPK models capable of inter- and intra-species
extrapolation as well as route-to-route extrapolation. These models can also facilitate high-dose
to low-dose extrapolation by converting exposure concentrations in critical studies into predicted
dose metric values.

2.4.3. Use of Pharmacokinetic Data and Models in Exposure Assessment
       The conventional approach to exposure assessment involves the calculation of applied
dose for each route of exposure based on information about the concentration of the chemical in
                                         2-11

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the medium, frequency and duration of exposure, rate of contact with the medium, and body
weight of the individual (Paustenbach, 2000). With increased data availability, however,
absorbed dose can be calculated (U.S. EPA, 1992). In order to calculate absorbed dose,
pharmacokinetic data such as time-course data on concentration or total quantity in alveolar air,
urine, or blood are required (Paustenbach, 2000). Estimating a delivered dose from biomarker
data, absorbed dose, or applied dose, in fact, may not be straightforward. PBPK models provide
a means to improve these estimates and to fully utilize available data.
       PBPK models can be used in conjunction with an exposure assessment to improve the
quantitative characterization of the dose-response relationship and the overall risk assessment.
PBPK models can be used to identify and evaluate the relationship between an applied dose and
biomonitoring or biomarker data, or between an applied dose, biomarker level, and internal
target tissue dose (e.g., Timchalk et al., 2004, 2001; Csanady et al., 1996; Fennell et al., 1992;
Krishnan et al.,  1992). PBPK  models have also been used to establish biological exposure
indices (e.g., breath, blood, or breath concentrations) to protect workers from harmful exposures
to solvents (Droz et al., 1999;  Thomas et al., 1996a; Kumagai and Matsunaga, 1995; Leung,
1992; Perbellini et al., 1990) or in epidemiology studies to reconstruct human exposures over
time (Canuel et al., 2000; Roy and Georgopoulos, 1998; Vinegar et al., 1990). Comprehensive
PBPK models are being developed that provide estimates of an internal tissue  dose from
multiroute (oral, inhalation, dermal) or multichemical exposures (Levesque et al., 2002; Liao et
al., 2002; Corley et al., 2000; Rao and Ginsberg,  1997; Roy et al., 1996; Georgopoulos et al.,
1994). The net tissue dose associated with a multiroute  (aggregate) and/or multichemical
(cumulative) exposure are especially useful for advancing risk assessment beyond the one
chemical, one exposure route paradigm.

2.4.4. Pharmacokinetic Models in Risk Assessment:  Summary
       Adverse tissue responses are more directly and closely related to the internal target tissue
dose of the toxic moiety than to the concentration of the parent chemical in the environment.
Therefore, the scientific basis  of, and confidence in, risk assessments are enhanced when they are
supported by estimates of the internal tissue dose. Data for the internal tissue dose levels,
however, are generally not available, and the relationship between external and internal dose
may not be easily resolved.  PBPK models provide a means of estimating the internal dose for
many different exposure regimens based on what is known about the physiology of the test
                                          2-12

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species and humans and the chemical of interest. PBPK models reduce the uncertainty in dose-
response and exposure assessment and fully utilize the available data.
      In the context of dose-response assessment, PBPK models have application in:

       1.  Interspecies extrapolation of pharmacokinetically equivalent doses (RfD, RfC, CSF,
          and IUR),
      2.  Estimation of the pharmacokinetic component variability (RfC and RfD derivation),
      3.  Route-to-route extrapolation of the POD (RfC, RfD, CSF, and IUR),
      4.  Duration adjustment of the POD (RfC and RfD derivation), and
      5.  High-dose to low-dose extrapolation (CSF and IUR).

      In the context of exposure assessment, PBPK models are useful for

       1.  Converting applied dose into tissue dose,
      2.  Calculating tissue dose associated with multiroute and multimedia exposures, and
      3.  Relating biomarker data to tissue dose and potential dose by exposure reconstruction.

      PBPK models vary in their quality, transparency, and predictive capability, and they must
undergo a rigorous evaluation if the model is to be used in a risk assessment. The process and
criteria for evaluating a PBPK model are the subject of the next chapter.
                                         2-13

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            3. EVALUATION OF PBPK MODELS INTENDED FOR USE IN
                                 RISK ASSESSMENT
       PBPK models intended for risk assessment applications should be evaluated for quality
and transparency. There are no published criteria or well-defined standards for evaluating PBPK
models; however, several publications have addressed good modeling practices and approaches
for evaluating and documenting biological models intended for risk or safety assessments (Clark
et al., 2004; Andersen et al., 1995; Yates, 1978). Evaluation of PBPK models intended for risk
assessment applications includes considerations for model purpose, model structure,
mathematical representation, parameter estimation, computer implementation, and predictive
capacity as well as sensitivity, variability, and uncertainty analyses. Each of these issues is
discussed in detail in the following sections.  Although these considerations are provided in
separate sections, it is important to realize that model evaluation, from development through to
application, can be an iterative process.

3.1.  MODEL PURPOSE
       Not all PBPK models are developed to support risk assessments.  Some are developed to
be used as research tools for testing biological hypotheses or for guiding improved experimental
design.  The purpose for which a PBPK model is developed influences its structure, level of
detail, and model parameterization (e.g., species).  Thus, the structure of a PBPK model designed
for use in research may not serve the intent and purposes  of one applied in risk assessment, and
the complexities and capabilities of PBPK models vary according to their intended use. PBPK
models are generally developed to accomplish one or more of three objectives:

       •  To integrate diverse sets of pharmacokinetic data on a particular chemical;
       •  To investigate the pharmacokinetic basis of the toxicity of a chemical that appears to
          be complex at the administered dose level; and/or
       •  To predict tissue dosimetry for situations other than those directly measured in
          animals or humans (i.e., extrapolation).

       All PBPK models are simplified representations of biological systems of varying
complexities and are designed to predict the behavior and outcome of biological processes
affecting the chemical pharmacokinetics in an in vitro or  an in vivo system. Some PBPK models
                                          5-1

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are designed specifically to integrate diverse data sets in efforts to uncover mechanistic
determinants of the pharmacokinetics of a specific chemical and to aid in the interpretation of a
chemical's mode(s) of action (Haddad et al., 1998; Clewell and Andersen,  1987). However,
such PBPK models are not always intended for use in predicting the pharmacokinetic behavior of
a chemical under exposure conditions and species in animal toxicity studies that might be
important to risk assessment. Models designed for such purposes must integrate diverse sets of
pharmacokinetic data and also must be capable of predicting available in vivo pharmacokinetic
data sets.  Models with defined "predictive capabilities" are valuable for risk assessment because
they provide confidence that such models can also predict the in vivo pharmacokinetics for
chemicals under exposure conditions where little or no such data exist (e.g., the animals in the
toxicity study or the humans in risk assessment scenarios). Thus, models with this form of
predictive capacity afford risk assessors the ability to extrapolate across species, dose levels, and
exposure scenarios.  For more on model purpose, the reader is referred to Clark et al. (2004).
       For application in risk assessment, the preferred PBPK model is one that is capable of
predicting the pharmacokinetics and tissue dose of the potential toxic moiety of a chemical under
conditions applicable to critical studies in animals or humans and human environmental
exposures.

3.2. MODEL STRUCTURE
       The structure of a PBPK model in large part depends on the purpose for which the model
is developed and the philosophy of the  modeler. There is virtually no limit to the number and
complexity of compartments in a model intended to describe molecular/cellular events (see
Figure 3-1). Parsimony in selecting model structures, however, is an important and guiding
principle in developing models for use  in risk assessments. The complexity of PBPK models
used in risk assessment is often constrained by limited data available to calibrate and test the
model and the need for risk assessors to defend the model  assumptions and the values derived
from model simulations.
       The simplest conceptual model  represents the organism as a one-compartment system.
One- and two-compartment kinetic models are useful in characterizing the toxicokinetics of a
chemical for any given data set, but they are not useful for extrapolating beyond the data used to
develop the model. PBPK models differ from one- or two-compartment models by representing
many more physiological, physicochemical,  and biochemical processes in the species of interest,
                                           5-2

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and they can be used to predict internal dose levels for hypothetical exposure regimens based on
what is known about the toxicokinetics of a chemical.  In most PBPK models, tissues are
represented by specific compartments, each with a unique set of physiological (i.e., blood flows)
and physicochemical (i.e., partition coefficients) parameters.  Target tissues are generally
represented individually (e.g., brain) and nontarget tissues are lumped together (e.g., slowly
perfused tissues).  Depending on the available data, PBPK models intended for risk assessment
applications would, preferably, include the target organ as one of the compartments. More often,
a PBPK model would be capable of estimating blood concentration, which is often used as a
surrogate for tissue concentrations. Major portals of entry (e.g., lung, gastrointestinal tract),
storage organs (e.g., adipose tissue),  metabolism/transformation sites (e.g., liver, kidney) as well
as elimination routes (e.g., renal, pulmonary, fecal) would be included if at all possible.
      It is often acceptable to mathematically describe ADME of chemicals in PBPK models in
lumped or whole-body surrogate compartments without a highly resolved physically
representation in all of the tissues where these processes occur (Krishnan and Andersen, 2001),
provided that this lack of physical  representation does not interfere with a model's use as an
extrapolation tool. When data are  available to support more complex representations, the PBPK
model can be elaborated to represent more complex mechanistic and biological interactions. For
example, the liver can be divided into separate compartments depending on the localization of
enzymatic activity. Figure 3-1 provides examples of PBPK model structures that have been
commonly used to simulate the kinetics of volatile and nonvolatile substances.  Note that these
models facilitate the simulation of the concentration of chemicals or their metabolites in the
target organ or a surrogate tissue (usually blood).
      Frequently, compartments in PBPK models are assumed to be homogenously and
completely mixed reactors.  This means that the concentration of the chemical anywhere in the
tissue is the same  and related by the partition coefficient to the concentration of the chemical in
venous blood. This assumption is  typically used unless there are data to support more elaborated
descriptions, such as diffusion-limited compartments.
      Ideally, the structure of a PBPK model intended for risk assessment applications would
contain the target organ (or a surrogate tissue) as well as compartments representing tissues of
unique physiological and biochemical relevance to the pharmacokinetics of the chemical in
question.
                                           5-3

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for simulating perfusion-limited tissue uptake of inhaled chemical. Gas exchange
through lungs is indicated with arrows, and metabolism is described in liver. (B)
A model for simulating diffusion-limited tissue uptake and multi-route exposures.
Dotted lines represent the separation of cellular matrix and tissue blood
components.
                                    5-4

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3.3.  MATHEMATICAL REPRESENTATION
       Once the qualitative aspects of the model structure are deemed acceptable, the next step
in the evaluation is mathematical representation. Here the focus is on the adequacy of the
number and form of mathematical  equations used to represent the tissues and processes in the
real system being modeled.  Model code, rationale, and supporting documentation should be
readily available to the reviewer. In PBPK modeling, each tissue compartment is generally
described with a mass-balance ordinary differential equation that describes changes in the
amount of chemical in the tissue over time. These changes result from chemical distribution in
and out of the tissue and clearance processes (e.g., metabolism or excretion) in the tissue. For
chemicals distributing to tissues by passive processes, the tissue:blood partition coefficients
describe the relationship between tissue and blood concentrations. Descriptions of this blood
flow-limited uptake have been used successfully in many of the past efforts in PBPK modeling
that dealt with small-molecular-weight organics. For other compounds,  including some with
high-molecular-weight or significant protein binding, membrane diffusion can be the rate-
limiting process; for these chemicals, uptake is described with differential equations for the
tissue blood and cellular matrix subcompartments (Krishnan and Andersen, 2001; Andersen,
1995; Leung, 1991; Rowland, 1985). Tables 3-1 and 3-2 provide examples of commonly used
mathematical representations for tissue compartments and physiological processes that determine
chemical disposition. Note that mass balance differential equations have units of mass per time
(e.g., mg/hr) or sometimes concentration per time (e.g., mg/L/hr).
       The rates of metabolism in  PBPK models have typically been described as first-order,
saturable Michaelis-Menten (i.e., shifting from first order to zero order)  or second-order
processes. At low concentrations,  metabolic clearance frequently appears linear, or first order,
with respect to plasma concentration.  At higher concentrations, metabolic clearance can become
saturated and a constant amount of chemical is metabolized per unit time (i.e., zero-order
kinetics).  Second-order processes  and requisite equations are more complex and may be based
on a reversible equilibrium relationship (e.g., macromolecular binding) or the concentrations of
chemical and cofactors required for metabolism (e.g., conjugation reactions). In each case, the
reason for using a particular description should be clearly provided. PBPK models using
particular mathematical descriptions of tissue uptake, metabolism, and protein binding without
any justification cannot be used confidently for risk assessment applications. For example, if
enzyme-mediated metabolism is described as a first-order process in a PBPK model, the
                                           5-5

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      Table 3-1. Equations of a four-compartment PBPK model to simulate the

      inhalation exposure of volatile organic compounds
         Tissue compartments
                    Equations"
Arterial bloodb
                                      Ca = -
QcxCv
                Cinh
                                               Qc
                                                   Ft
Liver
JA      .       \  V  x Cv
^- = Q,x(Ca -Cv,  ——	-
dt      v       '  Km + Cvt

    dA,

 l~~dTX   + '



C< =Av~

     c,
Cv, = —
      PI
Fat
                                           dAf
                                      Af =
                                       f    dt
                                      C  =
                                      Cvr =-
     Vf

     £L
     P,
Richly perfused tissues
                                      dt
                                          dA
                                      4 =^-
                                          dt
                                      -4
                                                 -Cv
Poorly perfused tissues
    = Qsx(ca -Cv,)
                                       dt

                                          dA
                                      A = — —xdt
                                           dt
                                           P,

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        Table 3-1.  Equations of a four-compartment PBPK model to simulate the
        inhalation exposure of volatile organic compounds (continued)
Tissue compartments
Venous blood
Alveolar air
Equations"
Ql x Cv{ + Qf x Cvf +Qrx Cvr +Qsx Cvs

Cnlv —
Pb
a Equations are from Ramsey and Andersen (1984).
b The steady-state arterial blood equation in this example is used for chemicals that reach rapid equilibrium in blood,
 such as highly fat-soluble volatile chemicals. In other cases, a detailed mass-balance equation for the arterial blood
 may be needed.
A = amount (mg)
a = arterial blood
alv = alveolar air
b = blood:air
C = concentration (mg/L or mmol/L)
c = cardiac output
f=fat
inn = inhaled air
Km = Michaelis-Menten affinity constant (mg/L)
1 = liver
P = partition coefficient
p = pulmonary ventilation
Q = flow rate (L/hr"1)
r = richly perfused tissues
s = slowly perfused tissues
t = tissue :blood
V = volume (L)
v = mixed venous blood
vf = venous blood leaving fat
vl = venous blood leaving liver
Vmax = maximal velocity of enzymatic reaction (mg/hr"1)
vr = venous blood leaving richly perfused tissue
vs = venous blood leaving poorly perfused tissue
        Table 3-2.  Equations used for describing diffusion-limited uptake in PBPK
        models
Subcompartments
Tissue blood

Cellular matrix

Equations
v dCl Ac c \pi\^~c^
tl ^ Qt»( ,n out) [ < \ pt
y dC2 _\piV\Ci-C2)
n dt L ' J'x Pt
A = amount (mg)
C = concentration (mg/L or mmol/L)
in = inflow
out = outflow
PA = permeability-area coefficient
Q = flow rate (L/hr"1)
tl = tissue blood
t2 = cellular matrix
V = volume (L)
Pt = tissue :blood partition coefficient
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scientific rationale for employing such a description is needed before the model can be used for
purposes of extrapolation and prediction. Because PBPK models are simplified representations
of the real systems, the full details and actual complexity of the physiological and biochemical
processes are not incorporated in the equations used. Depending on the level of detail required
and the objective of the modeling effort, appropriate descriptions of the biochemical processes
can be included in these models.
       For use in risk assessment, the equations chosen to describe ADME should be
scientifically supported and, where possible, documented.

3.4.  PARAMETER ESTIMATION
       Chemical-specific and species-specific parameter values are required to solve the
equations constituting a PBPK model. Typically, PBPK models require the  numerical values of
physiological parameters such as alveolar ventilation rate, cardiac output, tissue blood flow rates,
and tissue volumes.  They also incorporate absorption rate parameters (e.g., for dermal or oral
uptake), clearance parameters related to metabolism, or renal and biliary excretion pathways, as
well as tissue distribution parameters such as partition coefficients (blood:air, skin:water,
skin:air, and tissue:blood), protein binding characteristics, or transporter activities. Additional
parameters (e.g., tissue DNA levels, hematocrit, number and concentration of binding proteins)
may be required in some cases. For many other purposes, knowledge of the average value or the
range of plausible values of model parameters is sufficient; however, for estimating
interindividual differences in tissue dosimetry, knowledge of the distributions of input
parameters is essential.

3.4.1.  Physiological Parameters
       The physiological parameters used in PBPK  models should either correspond to those
obtained in the experimental pharmacokinetic study or be within the range of plausible values for
the species and life stage. Peer-reviewed compilations of ranges and reference values of
physiological parameters for adult animals and humans are available (Brown et al., 1997;  Davies
and Morris, 1997; Fiserova-Bergerova,  1995; Leggett and Williams, 1991; Arms and Travis,
1988) (Tables 3-3 through 3-6), yet no such compilations exist with respect to physiological
parameters for specific subgroups of populations (e.g., developing and lactating animals,

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       Table 3-3. Commonly used physiological parameters for mice, rats, and
       humans
Physiological parameters3
Body weight (BW) (kg)
Tissue volume (fraction of BW)
Liver
Fat
Organs
Muscle and skin
Cardiac output (Qc) (L/min)
Tissue perfusion (fraction of Qc)
Liver
Fat
Organs
Muscle and skin
Minute volume (L/min)
Alveolar ventilation (L/min)
Mouse
0.025

0.055
0.1
0.05
0.7
0.017

0.25
0.09
0.51
0.15
0.037
0.025
Rat
0.25

0.04
0.07
0.05
0.75
0.083

0.25
0.09
0.51
0.15
0.174
0.117
Human
70

0.026
0.19
0.05
0.62
6.2

0.26
0.05
0.44
0.25
7.5
5
 Many PBPK models often lump certain tissues together into single compartments such as rapidly/richly and
 slowly/poorly perfused compartments.

Source: Adapted from Travis and Hattemer-Frey (1991).
       Table 3-4. Range of values of the volume and perfusion of select tissues in
       the mouse
Tissue
Adipose
Brain
Heart
Kidneys
Liver
Lungs
Muscle
Skin
Volume
(% body weight)
5-14a
1.35-2.03
0.4-0.6
1.35-1.88
4.19-7.98
0.66-0.86
35.8-39.9
15.9-20.8
Regional blood flow
(% cardiac output)

3.1-3.5
5.9-7.2
7-11.1


12.2-19.6
3.3-8.3
a Varies proportionately with body weight.

Source: Adapted from Brown et al. (1997).
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       Table 3-5. Range of values of the volume and perfusion of select tissues in
       the rat
Tissue
Adipose
Brain
Heart
Kidneys
Liver
Lungs (upper respiratory)
Muscle
Skin
Volume (% body weight)
4.6-12a
0.38-0.83
0.27-0.4
0.49-0.91
2.14-5.16
0.37-0.61
35.4-45.5
15.8-23.6
Regional blood flow
(% cardiac output)

1.5-2.6
4.5-5.1
9.5-19
13.1-22.1
11.1-17.8


a Varies proportionately with body weight.
Source: Adapted from Brown et al. (1997).
       Table 3-6. Range of values of perfusion of select tissues in humans
Tissue
Adipose
Brain
Heart
Kidneys
Liver
Muscle
Skin
Regional blood flow
(% cardiac output)
3.7-11.83
8.6-20.4
3.8-8
12.2-22.9
11-34.2
5.7-42.2
3.3-8.6
a Varies proportionately with body weight.
Source: Adapted from Brown et al. (1997).
pregnant women, children).  Physiological parameters for specific subgroups is an area of active
research, and there are some published references for some parameter values (Gentry et al.,
2004; Pelekis et al., 2003; Hattis et al., 2003; Price et al., 2003a, b; Haddad et al., 2001a;
Schoeffner et al.,  1999; Luecke et al.,  1994).
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       In PBPK models for organic chemicals, the sum total of the volumes of compartments
corresponding to soft tissues is smaller than the body weight; sometimes 85% of the body weight
(100% [body weight] - 15% [estimate of nonperfused portion based on the weight of
skeletal/structural components as percent body weight]) is used (Brown et al., 1997). Even
though the tissue volumes (expressed in liters) are needed for PBPK modeling, tissue weights
(kg) are usually used with the  assumption of unit density (L = kg).  This assumption is a
reasonable approximation because tissue densities typically range from 0.9 kg/L for fat to 1.06
kg/L for muscle (Mendez and  Keys,  1960).
       The tissue blood flow rates in the model should add up to cardiac output. Maintaining
mass balance in PBPK models requires that the sum of all flows to the compartments be equal to
the cardiac  output, although other errors in model equations can result in a lack of mass balance.
The ratio of cardiac output to alveolar ventilation rate is roughly 1 in a resting individual but
decreases with activity (Astrand and Rodahl, 1970). The specification of cardiac output
independent of the value of ventilation rate is unacceptable, particularly if the ratio
(ventilation:perfusion) is not in the normal physiological range. Frequently in PBPK models,
ventilation rate, cardiac output, and tissue perfusion rates and tissue volumes are specified for the
individual animal or human being  simulated.
       The values of common physiological parameters for a test species or human vary
depending on body weight.  To simplify the recalibration of certain parameter values when
running the model for a different species, all tissue volumes are expressed as fractions of body
weight such that, for any given body weight, the volumes in liters can be readily calculated by
multiplying the body weight by the corresponding fractional value. Similarly, because the
cardiac output and alveolar ventilation rate are related to basal metabolic rates and/or body
surface rather than to body weight, these models  can be specified as a power function of body
weight, with the exponent varying from  0.67 to 0.75 (e.g., Tardif et al., 1997; Andersen et al.,
1987). These scaling functions are based on cross-species analyses for adult animals and may
not be appropriate for all life stages.
      An acceptable PBPK model would contain tissue volumes, flow rates, and
ventilation:perfusion ratios that are within physiological limits.  The sum total of the tissue
volumes should not exceed the body weight, and the sum total of tissue blood flow rates should
equal cardiac output.
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3.4.2. Partition Coefficients
       Tissue distribution is dependent on a variety of processes, including passive diffusion,
active transport, and cellular concentrations of lipid and binding proteins, among others.
Partition coefficients describe the steady-state concentration in the tissue compared with blood or
for volatiles in blood versus air.  Calibration of PBPK models for partition coefficients has
sometimes been done by fitting model simulations to in vivo data. In such cases,
pharmacokinetic data collected following a single bolus dose or repeated doses leading to steady
state are analyzed with the PBPK model to estimate the tissue:blood partition coefficients
(Gabrielsson and Bondesson, 1987; Gallo et al., 1987; Lam et al., 1982; Chen and Gross, 1979).
Steady-state data provide the most straightforward data for model calibration; however, they
require correction for tissues in which there are significant specific binding or metabolic
processes. In tissues where there is a significant level of metabolism or binding, the calculation
of an apparent tissue:blood partition coefficient should account for the amount of chemical
consumed by such processes (Chen and Gross, 1979).
       The tissue:blood, skin:water, skin:air, and blood:air partition coefficients required for
PBPK modeling of volatile organic chemicals are conveniently determined in vitro using the vial
equilibration method (Beliveau and Krishnan, 2000; Kaneko et al., 1994; Gargas et al., 1989;
Johanson and Dynesius, 1988; Fiserova-Bergerova and Diaz, 1986; Sato and Nakajima, 1979).
Tissue:blood partition coefficients for nonvolatile chemicals may be estimated in vitro using
radioactive chemicals in ultrafiltration, equilibrium dialysis, or vial equilibration procedures
(Murphy et al., 1995; Jepson et al., 1994; Sultatos et al., 1990; Igari et al., 1983; Lin et al., 1982).
The partition coefficients estimated by these in vitro methods are acceptable, provided
equilibrium is attained  during the experimental conditions. A time-course analysis should be
conducted to choose an appropriate time point (at which equilibrium is attained) for determining
partition coefficients in vitro, and appropriate studies will help demonstrate that metabolism or
chemical reactions are  not depleting the chemical.
       Algorithms based on the consideration of solubility and binding of chemicals in
biological matrices have also been developed and applied for predicting tissue:blood, tissue:air,
and blood:air partition  coefficients of volatile organic chemicals. This approach requires
knowledge of tissue and blood composition in terms of lipid and water contents, the
octanol: water or oil: water partition coefficients of the chemical, and binding association
constants, if applicable (e.g., Poulin and Thiel, 2000;  Poulin and Krishnan,  1996a, b, 1995).  At
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the present time, there is no validated animal-replacement approach for predicting association
constants for blood or tissue protein binding of organic chemicals (Poulin and Krishnan, 1996b).
The biologically based algorithms as such are useful in providing initial estimates of tissue:blood
partition coefficients solely on the basis of the consideration of solubility in water and lipid
contents of tissues and blood. A number of other empirical or semiempirical methods relating
molecular structure or physicochemical characteristics to tissue:blood and blood:air partition
coefficients of chemicals are also available (Beliveau  et al., 2005, 2003; Payne and Kenney,
2002; Abraham and Weathersby, 1994).  Their use is acceptable, as long as the qualitative and
quantitative aspects of the  structural features and physicochemical characteristics of the new
chemical are within the range of values that were used to calibrate the algorithm.
       Partition coefficients required for PBPK models can be obtained using in vitro methods,
in vivo data obtained at steady state, or theoretical algorithms within the boundary of valid
application.

3.4.3. Biochemical Parameters
       Absorption rates, metabolic parameters (e.g., first-order or second-order rate constants,
maximal velocity, and Michaelis constant), tissue diffusion constants (for describing diffusion-
limited uptake), and transporter  activity parameters required for PBPK modeling can be
determined by fitting a model to data from in vivo studies.  In order to estimate these parameters,
pharmacokinetic data (e.g., time course of tissue or blood concentration of parent chemicals,
urinary metabolite levels) obtained following a single bolus dose or infusion may be used. For
volatile organic chemicals, data  from exhaled breath and closed chamber gas uptake studies are
frequently used with success (Gargas et al., 1986; Filser and Bolt, 1981, 1979; Andersen et al.,
1980). Descriptions of serum protein binding have important impacts on tissue distribution  and
clearance, with parameters often estimated in vitro (Himmelstein and Lutz, 1979). The rate
constants of chemical reaction with hemoglobin  and tissue proteins determined in vitro or in vivo
have been incorporated into the  PBPK model to make predictions of these phenomena in vivo
(e.g., Krishnan et al., 1992).  Biochemical parameters estimated from in vivo data using a model
are dependent on the model structure and values of other parameters (e.g., physiological), so the
application of these values in models with different structures or parameter values must be
evaluated with care.  The use of a Bayesian approach is likely to enhance the precision of
parameter estimations from in vivo data by more formally developing and  evaluating the
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uncertainty and accuracy of parameter values and by incorporating multiple data sets into their
derivation (e.g., Vicini et al., 1999).
       Appropriate methods for application of in vitro systems (e.g., freshly isolated
hepatocytes, microsomes, post-mitochondrial fractions, cytosols) to provide metabolic constants
for incorporation into PBPK models continues to be an active area of investigation. These data
may be applicable to modeling using the parallelogram approach.  For example, chemical-
specific in vitro metabolic data from cultured hepatocytes can be scaled to represent in vivo liver
clearance using in vitro data such as estimates of the number of hepatocytes present per 1 g of
liver tissue and the average liver weight (in grams) of the species and age group of interest. In
vitro data for humans can then extrapolated to in vivo by assuming that the same relationship that
successfully describes the in vitro to in vivo relationship in animals effectively converts the
human in vitro data to the in vivo situation.
       There are several examples of successful application based on appropriate in vitro-in vivo
scaling methods (Lipscomb et al., 2003, 1998; Hissink et al., 2002; Cole et al., 2001; Mortensen
and Nilsen, 1998; Mortensen et al., 1997; De Jongh and Blaauboer, 1997, 1996; Reitz et al.,
1996a, 1989; Hwang et al., 1996; Iwatsubo et al., 1996; Kedderis and Held, 1996; Gearhart et al.,
1990), although the extrapolation of in vitro data to intact animal is not clear in all cases (e.g.,
Haddad et al., 1998, 1997).  But the in vitro studies are particularly useful for evaluating the
extent of metabolism in target tissues, characterizing interindividual differences in metabolism,
and conducting animal-human extrapolation of metabolism constants based on a parallelogram
approach (Kedderis and  Lipscomb, 2001; Thrall et al., 2000; Ploemen et al., 1997; Reitz et al.,
1996b; Andersen et al., 1991).  Receptor binding and DNA-binding properties of chemicals have
also been successfully described with PBPK models on the basis of in vitro-derived data (Farris
et al.,  1988; Terasaki et al.,  1984).
       Biochemical parameters for PBPK models can be estimated using in vivo data or on  the
basis of adequate scaling of in vitro data.

3.5. COMPUTER IMPLEMENTATION
       Most PBPK models  require the use of numerical  simulation methods because they
contain differential equations and descriptions of nonlinear processes,  making exact solutions
difficult or impossible.  There are a number of integration algorithms and programming
languages currently available for coding and solving PBPK model equations (Table 3-7). Many
                                          3-14

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Table 3-7.  Examples of simulation software used for PBPK modeling
Software
Fortran compiler with
IMSL library packages,
C, Pascal, Basic
ACSL, ACSL-Tox , or
acslXtreme (Advance
Continuous Simulation
Language)
SimuSolv
Matlab
Microsoft Excel
ScoP (Simulation
Control Program)
Stella
Developer/vendor
Many vendors sell the
different compiler packages
available on the market
The Aegis Technologies
Group, Inc., Huntsville, AL
Dow Chemical Company,
Midland, MI (no longer
distributed outside the
company)
The MathWorks,
Natick, MA
Microsoft Corporation,
Redmond, WA
Simulation Resources, Inc.,
Redlands, CA
Isee Systems, Lebanon, NH
(formerly High Performance
Systems Inc.)
Salient features
Machine language compiler
packages that require certain
knowledge of computer
programming; models can be
customized to simulate
specific condition
The most commonly used
for PBPK modeling in the
toxicology community;
language designed for
modeling and evaluating the
performance of continuous
systems described by time-
dependent, nonlinear
differential equations
Makes use of ACSL
language to write the
dynamic nonlinear systems
that are translated into
FORTRAN at run time
Mathematical software with
matrix-related computations,
numerical integration
algorithms capable of
solving systems of ordinary
differential equations, and
graphical nonlinear
simulation (Simulink)
Neither translation of the
model nor the compilation
into a program is required,
but the user should specify
integration algorithm and
interval
An interactive control
program for constructing
models; when used with a C
compiler, SCoP greatly
simplifies the construction of
a simulation program
Macintosh, interactive
graphical user interface
software; enables the user to
generate models with
diagrams, where a minimal
knowledge of computer
programming is required
Examples of application
Hoang (1995); Karba et al.
(1990)
Thomas et al. (1996a); Dong
(1994)
Rey and Havranek (1996);
Ramsey and Andersen
(1984)
Easterling et al. (2000)
Haddadetal. (1996);
Johanson and Naslund
(1988)
Menzeletal. (1987)
Hoang (1995)
                               3-15

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        Table 3-7. Examples of simulation software used for PBPK modeling
        (continued)
      Software
    Developer/vendor
      Salient features
  Examples of application
Mathematica
Wolfram Research, Inc..
Champaign, IL
Mathematical software with
matrix-related computations;
numerical integration
algorithms capable of
solving systems of ordinary
differential equations	
Burmaster and Murray
(1998)
Berkely Madonna
Robert Macey and George
Oster, University of
California at Berkeley, CA
A general-purpose
differential equation solver
program developed on the
Berkeley campus under the
sponsorship of National
Science Foundation and the
National Institutes of Health;
currently used by academic
and commercial institutions
for constructing
mathematical models for
research and teaching	
Reddy et al. (2003)
SONCHES (Simulation
of Nonlinear Complex
Hierarchical Ecological
Systems)
Central Institute of
Cybernetics and Information
Processes, Academy of
Sciences of GDR, Berlin
A computer system where
connections between various
data libraries in the
preparation and post-
processing of simulation are
executed by macro
commands
Wtinscher et al. (1991)
CMATRIX
Robert Ball and Sorell L.
Schwartz, Georgetown
University, Washington, DC
A system that allows the
user to create compartmental
models based on personal
biological knowledge,
leaving the construction and
numerical solution of the
differential equations to the
software
Ball and Schwartz (1994)
BASICA
California Department of
Pesticide Regulation,
Sacramento, CA
Numerical integration
algorithms developed by the
Department for PBPK
modeling	
Dong (1994)
AVS
(Application
Visualization System)
Advanced Visual Systems,
Inc., Waltham, MA
A visualization software
package capable of
importing processed
resonance images and
combining the use of ACSL
to create three-dimensional
representations of the PBPK
of a chemical in an organism
Nichols etal. (1994)
MCSim
Drs. Bois and Maszle
Software that facilitates the
conduct of Bayesian analysis
with PBPK models but has
no graphical interface	
Jonsson and Johanson
(2003)
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of the commercially available software packages routinely make use of integration algorithms to
obtain numerical solution to differential equations (Reddy et al., 2003; Easterling et al., 2000;
Burmaster and Murray, 1998; Menzel et al., 1987) such that (for most cases) the modeler or the
risk assessor needs only to evaluate that an appropriate algorithm was used. However, if a
programming language (FORTRAN, BASIC) or spreadsheet (Lotus 1-2-3, QuattroPro, Microsoft
Excel) is used for modeling, then the modeler should write the codes for an appropriate
numerical integration algorithm (e.g., Euler, Gear, Runge-Kutta routines; predictor-corrector
methods). In such cases, the integration algorithm as well as the integration interval, i.e., the
time interval at which the calculations of the change in concentration (or amount) of chemical in
various compartments are performed, should be specified (e.g., Haddad et al., 1996; Blancato
and Saleh, 1994).
      The modeler also needs to be aware of the optimization routine offered by software
packages, particularly if parameters are to be estimated from experimental data by statistical
optimization (Holmes et al., 2000).  The personal and portable computers marketed today
possess sufficient speed, disk space, and run-time memory required for PBPK modeling and
parameter optimization; therefore, this aspect requires no formal evaluation.
      The accuracy of computational representation of PBPK models is evaluated by
"debugging," which refers to the process of error detection in computer programs. Errors  in
PBPK model code may result either from typing errors or from illogical mathematical
statements. To eliminate these errors, it is essential to carefully verify the model code  after entry
into the computer.  Commercially available simulation software, while converting the model
codes written in a source language to machine language, can detect syntax/language errors
related to incorrect writing of model codes. However, such error diagnostic features cannot
detect errors associated with incorrect mathematical representation of a process, even if the code
is written in correct programming language and without typing mistakes.
      The modeler who uses a PBPK model in risk assessment is ultimately responsible for
ensuring that the code and equations are entered correctly and that the code is subject to routine
error diagnostic checks; this may include re-coding the model.  Such verification can initially be
done by the developer,  subsequently by  individuals not involved in the model development (e.g.,
peer-reviewers and co-workers) (Clark et al., 2004), and again when used for risk assessment
purposes.
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       Solution to the differential equations in a PBPK model need not be evaluated if a highly
reputable commercial or open source simulation software has been used, although an
appropriate algorithm should have been selected. However, it is necessary to ensure that the
code and equations are entered correctly and that the code is subject to routine error diagnostic
checks.  When the modeler writes his/her own program, the appropriateness of the integration
algorithm and integration intervals should be justified; similar concerns would exist initially for
newly developed commercial or open source software.

3.6.  EVALUATION OF PREDICTIVE CAPACITY
       The purpose of model evaluation is to assess the adequacy of a model and corresponding
parameters to consistently describe the available pharmacokinetic and dose-response data of a
chemical-biological system, as well as to characterize the uncertainty associated with the
parameter values. In a risk assessment context, this also involves evaluation of the suitability
and applicability of the model for regulatory and health protection purposes. Model evaluation
includes verification and validation (or calibration). In brief, model validation deals with
building the right model, whereas model verification deals with building the model right (Balci,
1997). Model verification includes many of the topics covered in this chapter up to this point.  It
involves  an evaluation of the accuracy with which a chemical-biological system has been
transformed into a model specification (e.g., the model diagram or equations) and the accuracy to
which such a diagram or set of equations has been coded into an executable computer program.
Model validation/calibration, on the other hand, involves substantiating that the model, within its
domain of applicability, behaves with satisfactory accuracy.
       It is important to correct a common misunderstanding about what "validated model"
means. A model that has been calibrated against one data set and adequately simulates a
different  data set can be said to be "validated," but it is only validated to the extent to which
those two data sets accurately represent the larger population, not in any global sense
independent of the data used to develop and test the model.  PBPK models are used to
extrapolate to hypothetical exposure conditions or dosing regimens but, again, these
extrapolations are only valid to the extent that the data used to calibrate and test the model are of
sufficient quality to  support the extrapolations.  To avoid giving the impression that a model has
been validated to predict outcomes for which it has not been adequately tested, some modelers
will use the terms "calibrated" to describe a model containing parameters that have been
                                          3-18

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optimized to fit one (e.g., an "internal" data set and the term "having predictive utility" to
describe a model that adequately reflects another (e.g., an "external") data set. There are,
however, some advocates for using "all" of the available data to develop parameter values, and
for that approach the calibration and predictive utility distinctions no longer work. This issue of
varying methods and terms used to develop and evaluate PBPK models is a reflection of the
relative newness of the modeling discipline in risk assessment, and the research community is
actively working to advance the methodology.
       A potential complexity that may come to light during the  model evaluation process is the
existence of discrepancies between data sets or even  among different measurements within a data
set. For example, when one dosimetry study reports  that the sum of all urinary metabolites
excreted by rats is 20-30% and another study reports 40-50% urinary clearance, no PBPK model
may be able to simulate both data sets. When this occurs the modeler will need to evaluate the
data sets to identify potential sources of these differences and ultimately may need to use expert
judgment to select one over the other or accept the uncertainty implied if both are acceptable.
Obvious sources of discrepancies that a model may be able to explain would be due to dose route
and dose level. Differences that could be more difficult to explain with a single model (and a
single set of parameters) can arise from differences in dose vehicle and animal strain. In the case
of strain differences, if the modeler finds that she/he  can describe all the data from one strain of
rats but not a data set from a different strain, there is  at least a reasonable chance that some
model parameters (e.g.,  metabolic rate constants) differ for the second strain.  However, if no
potential sources of variation can be identified for discrepancies between data sets for the same
strain, vehicle, route, and dose range, then any model will fail to  fit both sets.  In such instances,
consideration of the quality of the analysis  or other features of the study, or perhaps the one that
is most consistent with all other data sets, can inform the decision of which data to utilize.
       It is also possible for a data set to be internally inconsistent.  For example, when the sum
of all  excreta does not equal the administered dose, or the sum of metabolites measured in the
blood do not equal the total blood level measured using a radiolabel, then there is a lack of mass
balance in the pharmacokinetic data. Here too, the modeler must exercise professional judgment
in determining how to simulate the data and whether some data can be excluded.  For example, a
model may be able to describe the data from three doses used in a study but not those from a
fourth dose (that is neither the highest nor the lowest dose). In this case, a classical
pharmacokinetic analysis may show that even with an unstructured model, the parameters for
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that odd dose must be quite distinct from the others, leading the modeler to conclude that there
was an error or unreported variation in the dosing or data collection. If a dosing error is
suggested, then the modeler may try varying the dose for that data set to see whether the model
can then fit the data.  In the case of a mass balance discrepancy, the modeler may choose to
normalize the data, forcing it into balance, or to introduce a "loss" term such as binding to tissue
components if that is consistent with the biochemistry.
       In the following sections, it is presumed that all such  discrepancies in the data themselves
have been dealt with.

3.6.1. Model Verification
       As mentioned above, verification of a PBPK model involves evaluation of the biological
plausibility of the model structure  and parameters, as described in the documentation, and the
mathematical correctness of the equations.  Although these topics are discussed in previous
sections, the issue of verification is being highlighted here in the  context of a risk assessor who
may have played no part in the initial development of a model. In this context, the risk
assessor(s) must, in essence, retrace the model development in order to understand the model
well enough for application in regulatory decision making. This  includes  assessing the model
from purpose and structure all the  way to examination of the model code in order to ensure that  it
mathematically implements the model as described in the documentation.  This examination
includes checking for correctness of statements and functions and correct  order of statement
execution (for languages that are not self-sorting). Although trivial, checking the mass balance is
important when evaluating errors in model  structure that could lead to erroneous increases or
decreases in the level of the chemical in tissues. Another check on model behavior is to set the
exposure level to zero; this is necessary to ensure  that the model can accurately represent steady-
state levels of the chemical and that the background level does not change with time in the
absence of exposure.
       Whether a code-based or a graphical-based software interface is used, it is preferable that
the language produce, as one output, the set of equations that constitute the PBPK model. Code-
based representations ease the task of providing sufficient documentation  demonstrating that the
model is actually constructed as may be described in prose within a peer-reviewed  publication.
To facilitate model verification, the model code would be organized and annotated in such a way
as to facilitate understanding by individuals (e.g.,  reviewers) other than the original program
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developer.  This also affords relatively easy translation into a reviewer's software of choice. In
the case of a model intended for use in a risk assessment application, it is imperative to provide
documentation of the particular parameter values and simulations that are required to reproduce
any validation runs and dose metric calculations. This usually entails the provision of step-by-
step directions, either using the language's scripting capability or in separate documentation, that
allow reproduction of the validation plots and dose-metric calculations by following specific
directions or by invoking specified program blocks.

3.6.2. Model Validation/Calibration
       Model evaluation should consider the ability of the model to predict the kinetic behavior
of the chemical under conditions that test the principal aspects of the underlying model structure.
Ideally, a PBPK model would be compared with data that are informative regarding the
parameters to which the  dose metric predictions are sensitive (this pre-supposes the use of
sensitivity and uncertainty analysis to identify the parameters of concern; see Section 3.7).  For
example, validation of a human model based solely on parent chemical data would not
necessarily provide confidence that the model could be used to predict a metabolite dose metric.
The use of parent chemical kinetic data to validate model estimates of metabolism in the human
can be highly misleading because it can be the case that the metabolism parameters have little
impact on parent chemical concentrations, whereas other uncertain parameters (e.g., ventilation
rate, blood flow, fat content) can strongly influence model predictions  of parent chemical kinetic
behavior.  However, even in such cases, sensitivity and uncertainty analyses can help to
characterize the confidence (or lack thereof) with which the model makes predictions (see
Section 3.7).
       The adequacy of model parameter values may be evaluated in different ways; no single
method has been accepted or endorsed by the modeling or regulatory community as yet.
Statistical methods required for evaluating the adequacy of model parameters are based on
comparison of simulations with experimental data  and depend on whether the objective is to
perform internal evaluation (in which all model parameters are estimated from the same data
set), external evaluation  (in which different data sets are used for model calibration and testing
the predictive capability of the model), or semi-external evaluation (in which some  of the model
parameters are based on the data set). Although no systematic research effort or guidance is
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available in this regard, there is much interest in developing consistent and acceptable evaluation
methods, and progress is being made.
       To date, PBPK model evaluation generally has not been conducted rigorously from a
statistical perspective. Although quantitative tests of goodness of fit often may be a useful aspect
of the evaluation process, they generally are not designed to test hypotheses for PBPK models,
which can be highly nonlinear and may contain a large number of parameters. None of the
classical procedures (e.g., t-, Mann-Whitney, two-sample %2, and two-sample Kolmogrov tests)
that determine whether the underlying distributions of the two data sets are similar is applicable
because the output processes of almost all real-world systems and simulations are nonstationary
and autocorrelated. Furthermore, a question exists as to whether the use of statistical hypothesis
tests is even appropriate.  Since the model is only  an approximation of the actual system, a null
hypothesis that the system and model are the same is clearly false.
       Perhaps a more important consideration may be a model's ability to accurately predict the
general behavior of the data in the intended application and whether or not the differences
between the system and the model are significant enough to affect conclusions derived from the
model.  In this regard, Haddad et al. (1995) screened various statistical procedures (correlation,
regression, confidence interval approach, lack-of-fit F-test, univariate analysis of variance, and
multivariate analysis of variance) for their potential usefulness in evaluating the degree of
agreement between PBPK model simulations and experimental data.  According to these authors,
the multivariate analysis of variance represents the most appropriate classical statistical test for
comparing PBPK model predictions with experimental data.
       For now, however, the most common (if not the most rigorous) approach to model
evaluation has involved visual inspection of the plots of model predictions (usually continuous
and represented by solid lines) with experimental values (usually discrete  and represented by
symbols) against a common independent variable (usually time). The greater the commonality
between the predicted and experimental data, the greater the  confidence in the model structure
and parameters. The correspondence between predictions and experimental data should be not
only at the level of individual values (e.g., blood concentration values) but also at the level of the
profile (i.e., bumps and valleys in the pharmacokinetic curve). In other words, the shape of the
simulated curve should correspond to that of the experimental data and also be one that would
result in a plot of the residuals (i.e., difference between the simulation and the data) without a
systematic deviation from a scatter around zero.
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       Figure 3-2 shows several examples of visual evaluations of the adequacy of PBPK model
predictions.  The models used in panels A and C could be considered adequate because they
simulate the behavior of the experimental data even though they do not accurately simulate every
single experimental datum.  On the other hand, model D would be considered less adequate, and
further work would be required to refine the model. Examination of the model simulation in
panel B suggests that this model is simulating a bolus exposure, whereas the data set (same in all
panels) appears to be from an inhalation study,  suggesting that the modeler has chosen either the
wrong exposure parameters  for the model or the wrong data set for comparison.
       This approach to model evaluation says nothing about the adequacy of the model
structure or parameters; it only reflects an individual's judgment of how closely the model
predicts the observed behavior. Evaluating the adequacy of model structure and equations is
fairly straightforward when  compared with the  evaluation of the model parameter values. For
example, inadequacies in PBPK model structures can be inferred simply by observing the
simulated and experimental  pharmacokinetic profiles (Lilly et al., 1998). If the model cannot fit
the pharmacokinetic profiles for any realistic parameter values, or it can do so only by using
values that are inconsistent with other data, then one can reasonably conclude that the structure is
inadequate.
       This evaluation of model structure provides the developer an opportunity to think about
the need for additional compartments, critical determinants  of disposition, or different
quantitative descriptions of the phenomena and to improve the capability of the model
accordingly. Again, a useful way of comparing the experimental and simulated data is to plot the
residuals (i.e., difference between experimental and simulated data) as a function of time or as a
function of various controllable variables. If two or more models fit the experimental data
equally well, new experiments may be designed to identify the model that more accurately
predicts the other attributes of the biological system (Kohn, 1995).
       One approach for determining whether the level of complexity  (number of parameters) in
a model is justified by the data is to use a nested modeling approach, where the model is reduced
to a simpler (nested) model when one or more parameters is set to zero or some other "baseline"
value (Collins et al., 1999); however, additional changes to the model may be needed in order to
maintain mass balance. The increase in goodness-of-fit obtained by allowing those parameters to
be varied can then be evaluated statistically using a j^ statistic to determine whether the
additional degrees of freedom afforded by those parameters are justified (Collins et al., 1999).
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    Figure 3-2. Comparison of four PBPK model simulations (left, log scale;
    right, linear scale). Solid lines are model simulations overlayed with
    experimental data (symbols).  Models A and C appear to simulate the data
    reasonably well. Model D seems to underpredict all points, suggesting that
    refinement is necessary.  In model B, there appears to be a mismatch between the
    exposure parameters in the model (apparently bolus) and that of the data set
    (apparently inhalation).
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       There is increasing concern about the relevance and usefulness of external evaluation in
PBPK modeling.  External evaluation requires that some of the available pharmacokinetic data
not be used during the model calibration phase, but set aside for evaluating the performance of
the model.  Not everyone is in agreement with such an approach.  Some investigators argue that
all the data used for model evaluation can be used to improve the parameter estimates, so that no
data are "wasted" toward that end.  Such an iterative approach to model evaluation and
calibration maximizes the use of the available data. Others, however, argue that this type of
modeling can become a form of self-fulfilling prophecy.
       The issue of external evaluation is particularly problematic for human data because the
actual parameters for each individual in a population might be sufficiently different,  such that a
model with a single set of parameters may not be reasonably expected to simulate the observed
kinetics in all individuals. Therefore, the process of modeling not only can take into account
existing information on parameters but also accommodate new information based on fits to
additional data sets. In this context, Bayesian analysis utilizing Markov chain Monte Carlo
(MCMC) calculations is being increasingly explored for use in PBPK modeling (Jonsson and
Johanson, 2002, 2001; Bois, 2000a, b).  In the Bayesian approach, the prior information on
parameters is updated on the basis of new pharmacokinetic data, such that the resulting posterior
estimates consistently describe all data and support better characterization of the uncertainty and
distribution in the parameter values. One continuing challenge of the Bayesian approach is how
to use important data or biological information that are not easily amenable to incorporation into
MCMC calculations, the concern being that leaving such information out gives undue priority to
the particular studies that are included.  Thus, posterior distributions always need to be
scrutinized as to their consistency with existing biological knowledge; for instance, posteriors
that are strongly inconsistent with (carefully constructed) priors may indicate problems with
model structure or errors  or inconsistencies in the data.
       Cross-validation is another potentially useful approach for model evaluation (Keys et al.,
2003). In the structure-activity relationship modeling arena (Beliveau et al., 2003), cross-
validation uses all of the available data sets by repeated subsampling. This type of a "leave-one-
out" cross-validation allows the use of available data both for estimation and evaluation of model
parameters.
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       It is likely that no single approach will be sufficient or applicable in all contexts. Each of
these approaches has its merits and limitations, and their applicability for PBPK model
evaluation depends on the purpose of the model and data availability.
       There are other important issues concerning parameters for which values are estimated by
optimizing model output to experimental data ("fitting"), including parameter values based on
posteriors from a Bayesian analysis. In such instances, the modeler must assess the
identifiability of the parameter given the data. The practical reality of modeling biological
systems is that, regardless of the complexity of the model,  there will always be some level of
"model error" in the form of inconsistencies or lack of representation of the real biological
system that can result in systematic discrepancies between the model and the experimental data.
This type of inherent structural deficiency in all models interacts with deficiencies in the
identifiability of the model parameters, potentially leading to misidentification of the parameters.
Due to the confounding effects of model error and parameter correlation, it is quite possible for
an optimization algorithm to obtain a better fit to a particular data set by changing parameters to
values that no longer have any meaningful  correspondence to the biological entity the parameter
was initially intended to represent. This problem can be ameliorated in Bayesian analyses
through appropriate prior distributions.  It is usually preferable, however, to repeatedly vary the
model parameters manually before performing an optimization to  obtain a  sense of their
identifiably and correlation under various experimental conditions. Some simulation languages
aid this process by including routines for calculating parameter covariance or for plotting joint
confidence region contours.
       Estimates of parameter uncertainty  obtained from traditional optimization routines can be
viewed as lower-bound estimates of true parameter uncertainty because only a local, linearized
variance is typically calculated. In characterizing parameter uncertainty, it is probably more
instructive to determine what ranges of parameter values are clearly inconsistent with the data
than to accept a local, linearized variance estimate provided by the optimization algorithm. The
Bayesian approach, in principle, gives a more global characterization of parameter uncertainty
(see Section 3.7.3).

3.6.3. Model Documentation
       Adequate documentation is critical  in the evaluation of a model.  The level of
documentation for a PBPK model depends on its intended  use. For models developed for
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research or hypothesis testing, the documentation need only include sufficient information about
the model so that an experienced modeler can accurately reproduce its structure and
parameterization.  Usually this documentation would include a combination of one or more "box
and arrow" model diagrams together with any equations that cannot be unequivocally derived
from the diagrams. For simple models, a well-constructed model diagram, together with a table
of the input parameter values and their definitions, may be all that an accomplished modeler
would need to create the mathematical equations defining a PBPK model.
       For models submitted in support of a risk assessment, the level of documentation is
considerably greater. These models will be subjected to internal and external peer review, and
their structure, supporting data, simulations, and use in the derivation of reference values must be
completely transparent and reproducible. In addition to graphical representations of the model,
this level of documentation would likely include well-annotated and complete documentation of
the model code, all data (fully referenced) that were used to calibrate and/or test the model, a
description of the calibration and testing procedures used, fully referenced sources for all
parameter values (or the optimization  methods, results, and data used in optimizing parameters),
sensitivity analysis or other rationale that guided the choice of which parameters were optimized,
simulation run conditions, any additional analyses that help characterize or support the quality of
the model, and all supporting documentation that would be needed by an experienced modeler to
run the model and accurately reproduce any simulations used (or submitted for use) in deriving
reference values.
       The model diagram should be labeled with the names of the key variables associated with
the compartment or process represented by  each box and arrow.  All tissue compartments,
metabolism pathways, routes of exposure, and routes of elimination must be clearly and
accurately presented. The model diagram should also clearly differentiate blood flow from other
transport (e.g., biliary excretion) or metabolism, and arrows should be used where the direction
of transport could be ambiguous.
       In general, there would be a one-to-one correspondence of the boxes in the diagram to the
mass balance equations (or steady-state approximations) in the model. Similarly, the arrows in
the diagram would correspond to the clearance (transport or metabolism processes) in the model.
Each of the arrows connecting the boxes in  the diagram should correspond to one of the terms in
the mass balance equations for both of the compartments it connects, with the direction of the
arrow pointing from the compartment in which the term is negative to the compartment in which
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it is positive. Arrows connected only to a single compartment, which represent uptake and
excretion processes, are interpreted similarly.
       Interpretation of the model diagram is supplemented by the definition of the model input
parameters in the corresponding table. The definition and units of the parameters can indicate
the nature of the process being modeled (e.g., diffusion-limited vs. flow-limited transport,
binding vs. partitioning, saturable vs. first-order metabolism). The values used for all model
parameters are to be provided, with units. If any of the listed parameter values are based on
allometric scaling, the scaling method should be fully described with body weights used to
obtain the allometric constant and the power of body weight used in the scaling. Any equations
included to supplement the diagram should be dimensionally consistent and in a standard
mathematical notation.
       Model documentation plays a critical role in effective transfer of complex biological
models between model developers and potential users, particularly those who will evaluate the
model and implement it in risk assessment applications. Approaches for model documentation
are still evolving, but adequate documentation is essential to the transparency and reproducibility
of risk assessments. One approach that can be implemented in many modeling programs that
have scripting capabilities is to create computer code that reproduces all the key results, although
not necessarily the full procedure to obtain these results (e.g., optimization, Monte Carlo
analysis, etc., which sometimes involve multiple software). The key results are (1) fits to data
used for parameter estimation, (2) calculation of dose metrics for critical studies (e.g., animal
toxicology or occupational epidemiological  studies) to be used in developing dose-response
values (e.g., RfC, RfD, CSF, or unit risk), and (3) calculation of human dose metrics used in
developing dose-response values.  Such scripts help to quickly recreate critical numerical values
used in the risk assessment and facilitate working with a new model for evaluation or application
in risk assessment. However, that also means that these scripts need to be evaluated carefully to
ensure that they are correct in terms of the computer implementation and the situation they are
modeling. Finally, if model development and implementation in risk assessment are carried out
by different people, not all of these scripts would be expected upon completion of model
development; others would be created during its application in the risk assessment.
       PBPK models intended for use in risk assessment should be evaluated to ensure that they
provide simulations of pharmacokinetic profiles consistent with the experimental data and that
the parameters (point estimates, range of values, or distributions) are appropriate for the
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intended application. Scripts facilitate transparency and reproducibility in modeling by
recreating fits to kinetic data, estimation of dose metrics in critical studies, and calculation of
human dose metrics for development of dose-response values (e.g., RfD, CSFs).

3.7.  SENSITIVITY, VARIABILITY, AND UNCERTAINTY ANALYSES
       In models of biological systems, estimates of the values of model parameters will always
have some variance, due both to biological variation and experimental or model errors. The
interest in having a PBPK model that describes a variety of data with a consistent set of
parameters prevents a model from providing an optimal fit to all  sets of experimental data.  For
example, a PBPK model of a compound with saturable metabolism is required to reproduce both
the high and low concentration behaviors, which  appear qualitatively different, using the same
parameter values. If one were independently fitting single curves with a model, different
parameter values might provide better fits at each concentration,  but they would be relatively
uninformative for extrapolation.
       Where only some aspects of the model can be  evaluated, it is particularly important to
assess the uncertainty associated with the aspects that are untested. For example, a model  of a
chemical and its metabolites that is intended for use in cross-species extrapolation to humans
would preferably be verified using data in different species, including humans,  for both the
parent chemical and the metabolites.  If only parent chemical data are available in the human, the
correspondence of metabolite predictions with data in several animal species could be used as a
surrogate, but this deficiency needs to be carefully considered when applying the model to
predict human metabolism.
       One of the values of biologically based modeling is the identification of specific data that
would improve the quantitative prediction of toxicity in humans from animal experiments.  The
variability, uncertainty, and sensitivity of parameters constituting the PBPK models can also be
evaluated, which is desirable for models that are used to derive dose-response values.

3.7.1. Sensitivity Analysis
       Sensitivity analysis provides a quantitative evaluation of how parameters in input
functions influence the dose metric or outcome.  Such an analysis provides insight into how each
parameter influences estimates of the dose metric and the subsequent dose-response value, and
which parameter(s) have the greatest impact on the dose-response value estimate. Sensitivity
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analysis facilitates a focused use of resources for more detailed analysis and for further data
gathering to reduce uncertainty and to better characterize pharmacokinetic variability (Clewell et
al., 1994; Bois et al., 1991; Hetrick et al., 1991).
       Sensitivity analysis for PBPK models typically compares the magnitude of change in
output for a defined change in each input parameter. This process of single changes in one
parameter while all others are held constant is called "local" parameter sensitivity analysis. This
analysis yields sensitivity ratios that correspond to the ratio of change in simulation output (e.g.,
tissue dose) to change in parameter value. Figure 3-3 depicts hypothetical sensitivity ratios
associated with some input parameters of a PBPK model.  The greater the absolute value of the
sensitivity ratio, the more important the parameter.  In this example, the sensitivity ratio for
breathing rate is the highest of all input parameters, indicating that it is the most sensitive model
parameter for the dose metric.  The sensitivity ratio of 2 for breathing rate signifies that a 1%
change in the numerical value of this parameter will result in a 2% change in the dose metric.
Sensitivity Ratio
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       Figure 3-3. Sensitivity ratios associated with certain input parameters of a
       hypothetical PBPK model.
       In practice, sensitivity ratios greater than 1 (in absolute value) are of concern because this
results in the amplification of input error (Allen et al., 1996).  It is critical that fractional blood
flows sum to cardiac output when they are varied in sensitivity analyses or else mass balance will
be violated and normalized sensitivity ratios much larger than 1 may be obtained for blood flow
parameters.
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       There are several caveats when conducting local parameter sensitivity analyses (such as
described above). One is that they only show the sensitivity of the model predictions to a change
in the single parameter when all other parameters are held constant.  For example, consider the
sensitivity to breathing rate depicted in Figure 3-3. What would have happened if one had
known, before starting the modeling process, that the breathing rate was 20% higher than the
default value actually used?  Would the predicted dose metric have then turned out to be 40%
higher? Only if none of the other parameters were calibrated to the model data during the
modeling process.  If in each case  (default breathing rate vs. 20% higher) one had started with
that value of the breathing rate and then calibrated the Vmax and other parameters to the data, the
result would be different values of Vmax, etc., that would compensate to some extent  for the
change in breathing rate.
       As a simple analogy, consider the fit of a straight line to some data, where the intercept is
a "known"  parameter and the slope is fitted. After fitting the line, one might determine that the
fit is very sensitive to the intercept by showing that if the intercept is changed while holding the
slope constant (i.e.,  standard sensitivity analysis), the value of the line equation changes a lot.
But if one had started with a larger value of the intercept at the beginning of the modeling
process, fitting the line to the data would have resulted in a lower value for the slope, such that
the value of the line equation would not change as much as when only the intercept is increased.
In short, the parameter estimation process leads to certain correlations between the values of
parameters that are fixed as inputs and those that are fitted. Thus, standard sensitivity analysis,
although very informative about the importance of individual parameters, can overestimate the
actual impact of changes in individual parameters because it does not account for correlations.
       In the case of Figure 3-3, it might be that starting with a different breathing rate and then
calibrating  Vmax, etc., would have yielded almost identical values for the dose metric and that the
overall modeling process is insensitive to breathing rate, even though the model predictions are
sensitive to changes in breathing rate when none of the other parameters are changed. Another
example would be that blood concentrations can be highly sensitive to oral absorption rate
constants until steady state is achieved; if the risk assessment is estimating steady-state
concentrations in humans, estimates of the oral absorption rate constants may be essentially
irrelevant.  On the other hand, depending on the data at hand, "local" sensitivity analyses may
underestimate the impact of changing individual parameters due to the nonlinear!ty of the model.
For instance, if all the data were obtained at doses where metabolism was saturated, then the
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model fit will be insensitive to the "Km" over a wide range of values, but for making low-dose
predictions, the Km may be a very sensitive parameter.  Thus, it is important to carry out
sensitivity analyses under conditions reflecting the studies providing data for model calibration
(i.e., pharmacokinetic studies), under conditions appropriate for estimating dose metrics in
critical studies, and finally under conditions appropriate to the risk assessment. These analyses
help identify the key parameters under the conditions relevant for the various steps in a
dosimetry-based risk assessment.

3.7.2. Variability Analysis
       The focus of a variability analysis is to evaluate the range of values that a parameter
expected to be present in individuals may have in a population and the impact of that variability
on variability in the dose metric.  PBPK models can account for interindividual differences in
specific parameters (e.g., enzyme levels, tissue volumes, body weights, workload) and simulate
tissue dose variability in populations (Dankovic and Bailer, 1994; Sato et al., 1991).
Alternatively, PBPK models can simulate an average individual representing a specific subgroup
of the population (e.g., adult women,  pregnant women, lactating women, children), and thus
evaluate subgroup-specific tissue dose (Corley et al., 2003; Gentry et al., 2003; Price et al.,
2003b; Sarangapani et al.,  2003; Krishnan and Andersen, 1998; Fisher et al., 1997), although this
latter approach would not provide the probability or likelihood of a particular output for a
population.
       The magnitude of interindividual variability can be characterized using information such
as the estimated tissue dose corresponding to the 95th percentile and 50th percentile. To derive
this information, Monte Carlo simulations based on distributions of input parameters
(physiological parameters, enzyme content/activity with or without the consideration of
polymorphism) have frequently been used (Lipscomb et al., 2003; Gentry et al., 2002; Haber et
al., 2002; Lipscomb and Kedderis, 2002; Timchalk et al., 2002; Bogaards et al., 2001; El-Masri
et al., 1999; Thomas et al., 1996a, b).  The Monte Carlo method consists of repeated
computations using inputs selected at random from statistical distributions for each parameter to
generate a statistical distribution for the output, i.e., dose metric (Figure 3-4).  The Monte Carlo
approach to variability analysis has been used to evaluate the net impact of the variability of
critical biochemical and physiological parameters (e.g.,  Clewell and Andersen, 1996; Portier and
Kaplan, 1989).
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                Blood flows

              Body weights

             Metabolic Enzymes
            Partition coefficients
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       Figure 3-4. Monte Carlo simulation. In this approach, the distribution of
       internal concentration versus time is simulated by repeatedly (often as many as
       10,000 iterations) sampling input values based on the distributions of individual
       parameters in a population.
      When conducting variability analysis, it is important to identify correlations in model
parameters. For example, cardiac output (Qc) and breathing rate (QA) are expected to vary in
proportion to each other, so using independent distributions that might give a very high value of
Qc with a very low value of QA would be unrealistic. On the other hand, one could consider the
distributions of Qc and the distribution of the f\c = QA/QC and multiply the value selected from
the fAc distribution by the value selected from the Qc distribution to obtain the value of QA to be
used.
      Conceptually, the Bayesian framework is particularly well suited for variability analyses
because it allows a "hierarchical" structure in which parameters can be specified at the
"population" (e.g., mean and variance, with uncertainty) and "individual" (i.e., drawn from the
population) levels (Jonsson and Johanson, 2002, 2001), thereby conducting a simultaneous
analysis of variability and uncertainty. Moreover, Bayesian analyses combine prior knowledge
about parameters and their variability and uncertainty with data from new experimental studies
generating "posterior" distributions of the parameters for both the population and individuals
(along with uncertainty) that reflect both preexisting knowledge and the new data (Bernillon and
Bois, 2000; Johanson et al., 1999; Bois, 1999). However, care also must be taken in
implementing these analyses to account for biologically supported correlations among
                                         3-33

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parameters, which is as important for Bayesian analyses as it is for "traditional" Monte Carlo
simulation. In addition, because the posteriors from Bayesian analyses are calibrated to a
particular data set, care must be taken when deciding when and how the posterior distributions
for the PBPK parameters are used to make predictions. Consideration must be given as to
whether the subject populations in the data sets represent the population(s) of interest. For
example, data from subjects in a controlled human exposure may be only representative of a
population at rest. Although the Bayesian analysis may correctly estimate a relatively low
ventilation rate for this group, that ventilation rate may not be appropriate for the activity level in
the general population. Thus, one must chose data sets and parameter values carefully to reflect
the population of interest in the risk assessment.  In the above example, an additional traditional
Monte Carlo simulation could be performed in which some posterior distributions would be
replaced with distributions considered more representative of the population of interest.
       A variability analysis for a PBPK model is not a prerequisite for its use in risk assessment
applications.  The assessment of the impact of parameter variability on tissue dose, however, is a
prerequisite for a PBPK model intended for use in estimating the interindividual variability
(pharmacokinetic component).

3.7.3.  Uncertainty Analysis
       Uncertainty analysis for PBPK models characterizes the impact that a lack of precise
knowledge about the numerical value of a parameter or model structure itself has on estimates of
the dose metric.  Uncertainty regarding  model structure or parameter values may contribute to
uncertainty in the predicted dose metric, particularly for low-dose exposure situations (Hattis et
al., 1990). Uncertainty analysis is particularly useful when a PBPK model does not adequately
simulate the experimental data. Such a  situation may arise due to either lack of precise estimates
of parameter values or inadequacies in the model structure. In such cases, either a quantitative
uncertainty analysis or model-directed mechanistic studies might improve the predictive ability
and robustness of the PBPK model  (Haddad et al., 1998; Clewell and Andersen, 1987).
       Quantitative uncertainty analyses for specific dose metrics (e.g., amount metabolized,
tissue concentration of parent chemical  at a specific time, cancer estimates) have been conducted
using a traditional Monte Carlo approach, a Bayesian MCMC analysis (Elder, 1999; Gelman et
al., 1996; Krewski et al., 1995; Farrar et al., 1989), a stochastic response surface method, or a
fuzzy simulation approach (Nestorov, 2001; Isukapalli et al., 1998).  The latter method is
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particularly useful when statistical distributions of parameters cannot be reliably defined and
only semiquantitative, qualitative, and vague information is available.
       If there is a lack of confidence regarding the numerical value of a parameter (e.g.,
imprecision due to the method used for parameter estimation), a quantitative analysis of the
uncertainty associated with a parameter(s) of the PBPK model will help characterize the impact
on the dose metric of interest.  Uncertainty analysis will be of limited utility if the available data
directly inform the dose metrics of interest, such as the case where a model adequately fits
multiple data sets that directly measure the relevant internal dose following exposure by the
routes and  in species of interest.  However, even predictions from such "well-calibrated" models
may benefit from uncertainty analysis, particularly if the dose metrics of interest are indirectly
inferred (e.g., total metabolism when only blood concentrations are measured).  In addition,
where possible and relevant, uncertainty analysis can be performed to strengthen credibility of
the PBPK model and guide resource allocation for risk assessment-oriented research.
       Sensitivity, uncertainty, and variability analyses should be conducted using acceptable
statistical methods.  EPA has published guiding principles for Monte Carlo analysis (U.S. EPA,
1997), but  no such guidance for Bayesian methods has been released, although active research
and development are ongoing. When using the Bayesian approach, care should be taken to
ensure that the resulting PBPK model simulations respect the following basic conditions:

       •   The numerical values of physiological parameters (representing prior or posterior
           distributions) are within known, plausible limits;
       •   The sum of tissue volumes is lower than the body weight;
       •   The sum of tissue blood flows is equal to cardiac output;
       •   The mass balance is respected (chemical absorbed = chemical in body + chemical
           eliminated); and
       •   The covariant nature of the parameters is appropriately respected (e.g., the person
           with lowest breathing rate cannot be the one receiving the highest cardiac  output)

       While taking advantage of the sophisticated statistical approaches, it is important to
ensure that the resulting model and parameters are within plausible range or representative of the
reality.
       Sensitivity, uncertainty, and variability analyses can help improve the credibility of
PBPK models as well as prioritize research needs to improve the model for risk assessment
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applications.  However, such analyses may not be required for all PBPK models intended for
risk assessment applications.

3.8. DEVELOPING PBPK MODELS FOR USE IN RISK ASSESSMENT:
STRATEGIES FOR DEALING WITH DATA-POOR SITUATIONS
3.8.1. Minimal Data Needs for Constructing PBPK Models
       When an adequately evaluated PBPK model is not available for the species, life stage,
and route relevant to a risk assessment application, significant resources may be needed to
develop such a model, depending on the chemical, the availability of prior information, and the
complexity of disposition mechanisms being modeled.  The minimal data required for
developing such models for a chemical in any given species are

       •  Partition coefficients,
       •  Biochemical constants,
       •  Route-specific absorption parameters, and
       •  In vivo pharmacokinetic data for model evaluation.

       As outlined in this chapter,  the partition coefficients required for PBPK modeling may be
estimated using the theoretical algorithms found in the literature. Their use,  however, should be
limited to the domain of validity and the families of chemicals for which such algorithms have
been developed and validated. Biochemical constants such as metabolism rates or binding
association constants may be obtained using in vitro systems.  Other biochemical parameters
may be required, such as renal clearance, which currently can only be determined from in vivo
data. Additionally, route-specific absorption parameters such as the rate of oral absorption and
the skin permeability constant are required to describe oral absorption and dermal absorption,
respectively, prior to achieving steady state.  Of these, the skin permeability  coefficient can be
obtained using available quantitative structure-activity relationships (QSARs). Such absorption
parameters are not required for simulating intravenous administration and inhalation exposures.
Finally, some in vivo pharmacokinetic data (at a minimum blood concentration time-course data
at two dose levels) are required for evaluating the PBPK model for a particular route of
exposure.
       The minimal data set identified above should be available for the species used in the
critical study. Human models, however, may be constructed with knowledge of species-specific
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blood solubility/binding characteristics. Other model parameters, including metabolism rates,
may be either scaled or kept species-invariant, according to the current state of knowledge
(Section 4.5). Of course, the availability of a data set for external evaluation in humans may be a
limiting factor.  In such cases, surrogate data sets may be used for model evaluation purposes.

3.8.2. Surrogate Data for Interspecies and Interchemical Extrapolations
       In the absence of human data for model evaluation purposes, surrogate data have been
used successfully, although it must be noted that surrogate data may add additional uncertainty to
a risk assessment. A parallelogram approach can be used to generate surrogate data. This
approach uses two data sets:  one demonstrating the relationship between in vitro and in vivo
findings in a test species, and the  other demonstrating the relationship between in vitro human
and in vitro test species findings;  these data are used to predict the in vivo effects in humans.
Accordingly, if human data either cannot be collected or is not available for a chemical of
interest, it may suffice to evaluate a related chemical for which such data are available. Jarabek
et al. (1994) used this parallelogram approach for model development and interspecies
extrapolation of the pharmacokinetics of HCFC-123 (2,2-dichloro-l,l,l-trifluoroethane). In this
case, the  authors developed rat PBPK models for HCFC-123 as well as a structural analog
(halothane) by estimating partition coefficients and metabolic constants. Following the
evaluation of the rat PBPK model for each of these chemicals, human models were constructed.
The adequacy of the human model for halothane was evaluated using available human in vivo
data; the  model for HCFC-123 was assumed to reasonably simulate the in vivo pharmacokinetics
in humans due to the structural and metabolic similarities between the two chemicals, despite the
absence of in vivo human HCFC-123 pharmacokinetic data (Williams et al., 1996; Jarabek et al.,
1994). This is one practical way of getting around the lack of human data for model evaluation,
particularly when external evaluation is intended.
       To deal with situations where there is a lack of data to determine PODs for closely related
chemicals, a family approach has been suggested.  This approach, proposed by Barton  et  al.
(2000), is based on the principle that the acceptable concentrations for related chemicals,
particularly metabolites, can be derived using data on the parent chemical.  Thus, if the NOAEL
for the parent chemical is established, there would also have been internal systemic exposures to
its metabolites.  By determining the external exposure levels for these compounds that result in
the same  systemic exposure, the NOAELs for these compounds can be established. The
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determination of the internal dose and systemic exposures for the parent chemical and
metabolites is accomplished using PBPK models, thus facilitating the derivation and
establishment of the RfD/RfC with a poor database.
       QSAR approaches are also available for constructing inhalation PBPK models for
volatile organic chemicals in the rat (Beliveau et al., 2003).  Accordingly, the contributions of
various molecular fragments (CH3, CH2, CH, C, C=C, H, Cl, Br, F, benzene ring, and H in
benzene ring) toward the parameters of PBPK models have been determined. With the
knowledge of the number of the fragments occurring in a given molecule, the partition
coefficients and the metabolic constants can be  obtained and a first-generation PBPK model can
be constructed.  This QSAR approach is useful to initially develop PBPK models for other
chemicals, as long as the number and nature of fragments in the chemical do not differ from the
ones in the calibration set used in the  study (Beliveau et al., 2003).

3.9.  EVALUATION OF PBPK MODELS: SUMMARY
       The basic criteria for evaluation of PBPK models intended for risk assessment
applications, as outlined in Sections 3.1 through 3.7, are summarized below.

       •   The PBPK model would predict the pharmacokinetics and tissue dose of the toxic
          form of a chemical or a surrogate such as parent compound.
       •   The structure of a PBPK model would contain the target organ or a surrogate tissue,
          such as blood.
       •   The equations chosen to describe ADME would be justified on the basis of known
          mechanisms of such processes  for the chemical of interest or by analogy with other
          chemicals.
       •   The tissue volumes, flow rates, and ventilation:perfusion ratios specified in the model
          would be within reasonable physiological limits.
       •   The power function frequently  assumed for scaling of physiological flows on the
          basis of body weight ranges between 0.67 and 0.75 unless species- or individual-
          specific data are available.
       •   Maximal velocities of metabolism may also be scaled on the basis of body weight,
          typically raised to the 0.75 power, but measured values for specific enzymes in
          humans do not generally correlate with body weight, so the choice of whether and
          how to scale metabolism is at the discretion of the modeler.
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•  Partition coefficients required for PBPK models can be obtained from steady-state in
   vivo or in vitro data or theoretical algorithms in the application domain.

•  Biochemical parameters for PBPK models can be estimated using in vivo data or
   valid in vitro methods.

•  A PBPK model is frequently implemented using  commercially available software
   requiring that the model code (but not the coding of integration algorithms) be
   checked.  If the modeler chooses to write his/her own program, then the
   appropriateness of the integration algorithm and integration interval should be
   justified.  The PBPK model code is checked for accuracy of units, mass balance,
   blood flow balance, and behavior at zero dose.

•  Evaluation of the PBPK model structure and parameters should be conducted to
   ensure that the model adequately predicts the pharmacokinetic behavior (i.e., bumps
   and valleys in the concentration vs.  time plot) of the chemical and that the parameters
   (point estimates, range of values or  distributions) consistently describe available data.

•  A model used in a risk assessment would be accompanied by sufficient
   documentation to support an independent evaluation and reconstruction of the model
   and simulation results. Scripts facilitate transparency and reproducibility in modeling
   by providing computer code to recreate fits to kinetic data, estimation of dose metrics
   in critical studies, and calculation of human dose metrics for development of dose-
   response values (e.g., RfD, CSFs).  A more rigorous verification that may be
   considered by the risk assessor is to independently re-code the model to ensure that
   the documentation is thorough and that there are no bugs in the code.

•  Sensitivity, variability, and uncertainty analyses can help improve the credibility of
   PBPK models by identifying the parameters that  have the greatest impact on a model
   output. In addition, these analyses are useful in prioritizing research needs to improve
   a model for risk assessment application.  Such analyses, however, may not be
   required  for all PBPK models intended for risk assessment applications.
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            4.  APPLICATION OF PBPK MODELS IN RISK ASSESSMENT

4.1.  CHOOSING PBPK MODELS APPROPRIATE FOR USE IN RISK ASSESSMENT
       PBPK models are most often used in risk assessments to simulate tissue and blood
concentrations of a toxic moiety (parent chemical or metabolite) resulting from the dosing
regimens in the animal toxicity or human studies that are the basis for deriving dose-response
values (e.g., RfC, RfD, CSFs). Specifically, the model would be able to simulate the dose
metrics in the test species and/or in humans for the exposure route and exposure scenario of
relevance. For most applications in risk assessment, a PBPK model

       •   Would have been developed or calibrated for the species and life stages of relevance
          to the risk assessment,
       •   Would be structured and adequately parameterized to simulate uptake via routes
          associated with human exposures as well as the critical study chosen for the
          assessment,
       •   Would be able to provide predictions of the time-course of concentration of the toxic
          moiety or appropriate surrogate (parent chemical or metabolite) in the target organ of
          interest or a suitable surrogate compartment, and
       •   Must have been peer-reviewed and evaluated for its quality and predictive capability.

      Figure 4-1 depicts how the above criteria can be applied for selecting appropriate PBPK
models. Basically, a peer-reviewed PBPK model for the relevant species and life stage
consisting of parameters for simulating relevant routes of exposure and potentially relevant dose
metrics is appropriate for use in risk assessment.
       The first criterion, though appearing self-evident, is quite fundamental, because the
models available in the literature sometimes were not parameterized for the specific species and
life stage used in the critical toxicological study forming the basis of a risk assessment. For
example, PBPK models for volatile organic compounds may have been developed in rats, yet
one of the critical studies in the assessment is in mice. When the PBPK model has not been
developed for the species or life stage used in a critical study, additional work may be needed to
further elaborate the model.
       PBPK models chosen for risk assessment applications would be able to provide
simulations of the tissue dose of the toxic moiety or an appropriate dose metric for exposure
scenarios and routes associated with the critical study as well as human exposures.  Finally,

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                                    Is the PBP
                                   model available
                                   for the test
                                    species and
                                     humans?
                                     Are the
                                  parameters tor
                                    simulating
                                  relevant routes
                                    available?
Experimental
   Data
 Collection
                                  Does the model
                                   simulate dose
                                metrics of relevance
                                   risk assessmen
                                   Has the model
                                 been evaluated and
                                   peer-re viewed?*
Undertake
evaluation and

peer review





Use in
risk assessment

       Figure 4-1.  Flowchart for selecting PBPK models appropriate for use in risk
       assessment.   In this context, the model should be evaluated as described in
       Chapter 3.

the PBPK model for the relevant species and life stage and exposures corresponding to the
critical study and risk assessment needs should be peer-reviewed; if it has not been, then efforts
may be directed towards such a review (see Chapter 3).
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       Peer-reviewed PBPK models that facilitate the prediction of dose metrics for a chemical
through relevant routes of exposure for the life stage and species used in critical studies are a
prerequisite for their use in risk assessments.  Most risk assessment applications also require a
model parameterized for humans if the critical studies were in animals.

4.2.  EVALUATION OF DOSE METRICS FOR PBPK MODEL-BASED ASSESSMENTS
       When using PBPK models in risk assessment (RfD, RfC, and unit risk estimates), the
basic data needed are

       1.  POD and  critical effect from one or more key studies,
       2.  Peer-reviewed PBPK model for the relevant test species and humans, and
       3.  Dose metric appropriate for the risk assessment and supported by the MOA (if
          known).

       The methods  and challenges associated with the identification of critical effects and
PODs for an assessment remain the same regardless of whether one uses PBPK models or not.
The approaches for identifying PODs can be found elsewhere (U.S. EPA, 2005a, 1994). The
criteria and issues associated with the selection of PBPK models useful  for risk assessment were
considered in the previous section. It is worth noting that although a human model is typically
needed, route extrapolation and some other limited applications can be undertaken with only a
model for the relevant test species. The third data need noted above, i.e., the identification of the
appropriate dose metric, is a key aspect determining the use of PBPK models in risk assessment.
       The dose metric, or the appropriate form of chemical most closely associated with the
toxicity, varies from chemical to chemical, depending on the MOA and critical effect. It has two
basic properties: the  moiety and the measure thereof. The dose metric for PBPK-based risk
assessment is chosen following the identification of the potential toxic moiety and evaluation of
the relationship with  the endpoint of concern.  A useful framework for evaluating hypothesized
MO As is included in Guidelines for Carcinogen Risk Assessment (U.S.  EPA, 2005b). Although
the framework specifically deals with carcinogens, the concepts are broadly applicable to
noncancer MO As. The framework provides useful discussion related to evaluating multiple
MO As (particularly over dose ranges) and for assessing relevance to humans.  Furthermore,
available data on closely related chemicals may be used to infer the likely toxic moiety.
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Similarly, the toxicity data for various exposure routes and modes of administration may be
compared to infer the potential toxic moiety (IPCS, 2005).
       After the potential toxic moiety has been identified, the appropriate measure of tissue
exposure to the toxic moiety can be selected (Figure 4-2).  For example, peak concentration has
been related to some neurotoxic effects of solvents (e.g., MacDonald et al., 2002; Benignus et al.,
1998; Pierce et al., 1998; Bushnell, 1997), such as the correlation of concentration of
trichloroethylene at the time of testing with observed effects on behavioural and visual functions
(Boyes et al., 2000). For tetrachlorodibenzodioxin, tissue concentrations of the chemical
measured during a critical period of gestation have been reported to predict the intensity of
developmental responses (Hurst et al., 2000).  The gender-specific genotoxic effects of benzene
in mice are related to differences in the rate of oxidative metabolism (Kenyon et al., 1996).
                                                  Potential
                                                 Toxic Moiety

(
»
Maximum
1
Parent Chemical
Z^
Concentration
Metabolite Unknown*
^>^
i

Rate of production
7\ TV
Integrated
1
Average
Integrated
1 1 J
r

Cmax
(mg/L. Tissi

AUC
je) (mg/L tissue
xtime)

mg formed
per unit time
(e.g. mg/hr/L tissue)
mg formed AUC
over time specified mg/L tissue x time
(e.g. mg/hr/Ltissue) (p are nt o f me tab o lit e)
Devaluate correlations
DOSE METRICS to toxic responses
       Figure 4-2.  Examples of measure of tissue exposure to toxic moiety for risk
       assessment applications.
                                        4-4

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       For chronic effects of chemicals, the integrated concentration of the toxic form of
chemical in target tissue over time (i.e., AUC), typically determined as the daily average, is often
considered a reasonable dose metric (Clewell et al., 2002a; Voisin et al., 1990; Andersen et al.,
1987; Collins, 1987). For carcinogens producing reactive intermediates, the amount of
metabolite produced per unit time and the amount of metabolite in target tissue over a period of
time (e.g., mg metabolite/L tissue during 24 hr) have been used as dose metrics (Andersen and
Dennison, 2001; Andersen et al., 1987). For developmental effects, the dose surrogate is defined
in the context of the window of exposure for a particular gestational event (e.g., Welsch et al.,
1995). Although the AUC and rate of metabolite formation figure among the most commonly
investigated dose metrics, other surrogates of tissue exposure may also be appropriate for risk
assessment purposes, depending on the chemical and its MOA (e.g., maximal concentration
[Cmax] of the toxic moiety, duration and extent of receptor occupancy, macromolecular adduct
formation, or depletion of glutathione) (Clewell et  al.,  2002a).  Table 4-1 lists the dose metrics
used in a number of PBPK-based cancer and noncancer risk assessments described in the peer-
reviewed literature.
       When the appropriate dose metric cannot readily be identified, evaluation of the
relationship with the endpoint of concern can be undertaken with each of the dose metrics to
identify the one that exhibits the best association (e.g., Andersen et al., 1987; Kirman et al.,
2000). This becomes particularly important when there are limited or confusing data on the
plausible MOA of the chemical. At a minimum, the appropriate dose metric can be identified as
the one that demonstrates a consistent relationship  with positive and negative responses  observed
at various dose levels, routes, and scenarios in a given species. In other words, the level of the
dose metric would be lower for exposure conditions that elicit no effect and higher for conditions
that elicit toxic responses, regardless of the route and exposure scenario (Clewell et al., 2002a).
       Where there is an inadequate basis for prioritizing one dose metric over another, some
suggest using the most conservative one (the dose metric estimating the highest risk or lowest
acceptable exposure level) to be health protective (Clewell et al., 2002a).  The use of appropriate
dose metric can help to reconcile route and species differences in cancer responses, provided
there are no pharmacodynamic differences.  There  has been at least one instance in which PBPK
model-derived dose measures could not reconcile rat and mouse kidney tumor data (Smith et al.,
1995), indicating the significant role of factors other than the target tissue exposure to toxic
moiety.
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Table 4-1. Dose metrics used in PBPK model-based cancer and noncancer
risk assessments
Chemical
Acrylonitrile
Bromotrifluoromethane
Butoxyethanol (2-)
Chloroform
Chloropentafluorobenzene
1,4-Dioxane
Ethyl acrylate
Ethylene glycol ethers
Formaldehyde
Heptafluoropropane
Isopropanol
Methoxyacetic acid
Methyl chloroform
Methyl mercury
Endpoint
Brain tumors
Cardiac sensitization
Forestomach lesions and
tumors
Liver cancer
Hepatic effects and
kidney tumor
Liver toxicity
Liver tumors
Forestomach tumors
Developmental toxicity
Cancer
Cardiac sensitization
Neurobehavioral effects
Developmental/
reproductive effects
Developmental effects
Hepatic effects
Neurological effects
Dose metric
Peak metabolite
concentration in target
tissue
Concentration of parent
chemical at the end of
exposure
Concentration of
butoxyethanol/ butoxy
acetic acid in forestomach
Amount of metabolites
covalently bound to
biological macromolecules
L liver per day; % cell
kill/day
Maximal rate of
metabolism per unit kidney
cortex volume
AUC of parent chemical in
liver
Time-weighted average
concentration in liver over
lifetime
Liver AUC
Tissue-specific glutathione
depletion
Peak concentration and
average daily AUC of the
alkoxyacetic acid
(metabolite) in blood
DNA-protein crosslinks
Concentration of parent
chemical at the end of
exposure
Peak blood concentration
AUC of isopropanol and
its metabolite (acetone)
AUC of parent chemical
(gestational day 11)
Maximal concentration of
parent chemical
(gestational day 8)
Area under the liver
concentration vs. time
curve
Fetal brain concentrations
Reference
Kirman et al. (2000)
Vinegar and Jepson (1996)
Poet et al. (2003)
Reitzetal. (1990a)
Meek et al. (2002)
Clewell and Jarnot (1994)
Leung and Paustenbach
(1990)
Reitzetal. (1990b)
Frederick etal. (1992)
Sweeney etal. (2001)
Schlosser et al. (2003);
Casanova et al. (1996)
Vinegar and Jepson (1996)
Gentry et al. (2002)
Gentry et al. (2002)
Clarke etal. (1993, 1992)
Welsch etal. (1995)
Reitzetal. (1988a)
Gearhart etal. (1995)
                                4-6

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      Table 4-1.  Dose metrics used in PBPK model-based cancer and noncancer
      risk assessments (continued)
Chemical
Methyl methacrylate
Methylene chloride
Styrene
Tetrachlorodibenzodioxin
Toluene
Trichloroethylene
Vinyl acetate
Vinyl chloride
Endpoint
Nasal lesions
Cancer
Lung tumors (mouse)
Biochemical responses
Cancer risk
Behavioral effects
Renal toxicity
Neurotoxicity
Cancer (liver lung and
kidney)
Olfactory degeneration
and tumor development
Angiosarcoma
Dose metric
Amount
metabolized/time/volume
nasal tissue
Rate of glutathione
transferase metabolites
produced/L liver/time
Steady-state concentration
of ring oxidation
metabolite mediated by
CYP2F
Body burden
Time-weighted receptor
occupancy
Up/down regulation of
receptor occupancy
Fraction of cells induced
Brain concentrations at the
time of testing
Metabolite production/L
kidney/day
Blood concentration of
metabolite
(trichloroethanol)
Amount
metabolized/kg/day; AUC
for trichloroacetic acid or
dichloroacetic acid/L
plasma; production of
thioacetylating
intermediate from
dichlorovinylcysteine in
kidney
Intracellular pH change
associated with the
production of acetic acid;
proton concentration in
olfactory tissue
mg metabolized/L liver;
mg metabolite produced/L
liver/day
Reference
Andersen et al. (2002,
1999)
Andersen etal. (1987)
Cruzen et al. (2002)
Kim et al. (2002)
Andersen etal. (1993)
Portier etal. (1993)
Conolly and Andersen
(1997)
Van Asperen et al. (2003)
Barton and Clewell (2000)
Barton and Clewell (2000)
Clewell et al. (2000);
Fisher and Allen (1993)
Bogdanffy etal. (2001,
1999)
Clewell etal. (2001);
Reitzetal. (1996b)
AUC = area under the curve
      An important consideration in risk assessments conducted with a PBPK model is that the

critical study (i.e., the study upon which the RfC, RfD, or CSF is based) cannot always be
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selected on the basis of administered dose or exposure concentration. This is because the
relationship of the HEC or human equivalent dose to the administered animal dose depends on
the selected dose metric, which may vary from one endpoint to another and with the nature of the
exposure (species, route of administration, vehicle, duration, etc.). Instead, the pharmacokinetic
model is used to calculate the appropriate dose metrics for each of the endpoints of concern in
each study (Barton and Clewell, 2000).  To calculate the dose metrics, the model parameters are
set to those for the species in the toxicity study, whether an experimental animal study or a
human study. In the case of developmental studies, it may be necessary to estimate parameters
for a pregnant female or neonate rather than for an average adult, and physiological and
biochemical parameters may have to be time dependent. To the extent possible, it is best to use
study-specific data on animal strain, body weights, age, and activity when selecting parameters
for the model. The experimental parameters in the model are then set to reproduce the exposure
scenario performed in the study, and the model is run for a sufficient period of time to
characterize the animal exposure to the chemical and, if necessary, its metabolites.
       There are often a number of options regarding the way in which the model can be run to
characterize the dose metric (Clewell et al., 2002a).  The choices made will depend on the dose
metric(s) selected (e.g., peak vs. average), the nature of the chemical (e.g., volatile vs.
persistent), and the nature of the risk assessment (acute vs. chronic, cancer vs.  noncancer).
Frequently, an average daily dose metric such as the average daily AUC is estimated (note that
the average daily AUC is the same metric as the time-weighted average concentration, differing
by only a factor of 24 if the daily AUC was expressed in terms of hours).  In general, the
averaging period in the case of cancer is typically taken to be the lifetime, whereas the averaging
period in the case of noncancer risk assessment is usually considered to be the duration of the
exposure or, perhaps, a critical window of exposure.
       For short-term exposures, the model must be run for an appropriate period, which
depends on the dose metric being used and the timing of the measurement of toxicity in relation
to the period of exposure.  For short exposure, this is easily done by running the model for the
total duration of the exposure (or exposures, for repeated exposure studies) to obtain dose
metrics. If the animals were held for a postexposure period  before toxicity was evaluated, the
model must be run either until the end of the postexposure period or for a sufficient duration to
ensure that the parent chemical or metabolite, depending on dose metric,  has been completely
cleared from the body.  On the other hand, if toxicological evaluations, e.g., neurological tests,
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were performed during or immediately at the end of the exposure period, then the dose metric
might be determined at the time of evaluation.  The resulting dose metric obtained for the total
duration of the exposure (including any postexposure period) may need to be divided by the
number of days over which the experiment was conducted to derive the average daily value for
an integrated measure such as AUG.
       The same approach (running the model for the total duration of the study) can be used to
calculate dose metrics for longer-term exposures.  This approach would typically be necessary
for models that describe changes in physiology or biochemistry during different life stages (e.g.,
children, elderly). An alternative approach, which is often attractive for modeling of chronic
exposures with time-invariant model parameters, is to estimate the steady-state dose metric.
       There are two principal methods for calculating a steady-state estimate. In the first, the
model is run until steady state is reached and then the dose metric is calculated by subtraction.
For example, in the case of a chronic oral or inhalation exposure conducted 5 days per week, the
model can be run consecutively for 1 week, 2 weeks,  3 weeks, and so on. To calculate the
average daily AUC for a given week, the value at the end of the previous week is subtracted
from the value at the end of the current week and the result is divided by 7.  This process is
repeated until the change in the dose metric from one week to the next is insignificant. For
continuous exposures, the comparison can be made on a daily basis rather than weekly.
       The other method for estimating the steady-state dose metric is to estimate it from a
single-day exposure. The model is run for a single-day exposure plus an adequate postexposure
period to capture clearance of the parent compound or relevant metabolite.  This value of the
single-day dose metric is then modified by the  necessary factors to obtain an average daily value
(e.g., by multiplying by five-sevenths in the case of the 5-day-per-week exposure just described).
This method is faster, but is only approximate if the system  is not linear. Typically, it is
sufficiently accurate for estimating average daily AUC when exposures are below the onset of
any nonlinearities.  It can be checked against the first method described to determine its accuracy
in a particular case.
       The dose metric calculations needed are determined  by the method to be used for the
noncancer or cancer analysis.  If the NOAEL/uncertainty factor (UF) method is being used in an
assessment, a dose metric needs to be calculated only for the NOAEL or LOAEL exposure for a
particular study and endpoint.  On the other hand, if dose-response modeling is going to be
performed, such as in the BMD approach, dose metrics generally would be  calculated for all
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exposure groups.  The dose metrics are then used in the dose-response model in place of the
usual exposure concentrations or administered doses. It is important to remember that when this
is done, the result of the dose-response modeling will also be in terms of a value of the dose
metric rather than an exposure concentration or administered dose. Dose-response modeling is
more properly conducted on the dose metrics because it is expected that the observed effects of a
chemical will be more simply and directly related to a measure of target tissue exposure than to a
measure of administered dose.
       To convert an animal dose metric (e.g., at the BMD) to an equivalent exposure
concentration or administered dose, the pharmacokinetic model must be run repeatedly, varying
the exposure concentration or administered dose, until the dose metric value is obtained. In the
case of calculating the acceptable human exposure  corresponding to a given toxicity study, the
physiological, biochemical, and exposure parameters in the model are set to appropriate human
values and the model is iterated until the dose metric obtained for the human exposure of concern
(often continuous or daily lifetime exposure) is equal to the dose metric obtained for the toxicity
study. One effective way to do this is to run the model  at regular dose intervals (e.g., log or half-
log)  over a wide dose range.  These results can be used  to generate a regression  line describing
the relationship between the internal dose metric and the exposure dose or concentration.  This
regression line can be used to accurately estimate the exposure giving a particular internal dose
metric, as can be confirmed by  running the model for that exposure.  Plotting the relationship
between exposure and the internal dose metric is also valuable because it demonstrates where
nonlinearities occur.
       The human dose metrics used for deriving dose-response values can be calculated in an
analogous way to the dose metric for the toxicity study; i.e., if the dose metric in the toxicity
study was expressed in terms of an average daily value, the dose metric used for calculating the
associated human exposure should also represent an average daily value. However, it should be
remembered that the exposure scenarios may be different, e.g., continuous human inhalation in
contrast to a 6-hr/day exposure in the animal toxicity study.  When a steady-state dose metric is
used in both an  experimental animal and the human, the calculation of a steady-state dose metric
in the human generally requires running the model  for a much longer period of time than in the
animal.  For short-term exposures, where the model has been run for the total duration of the
toxicity study and the average dose metric value has been calculated, the dose metric used to
calculate associated human exposure is usually obtained for an exposure over the same time
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period.  An exception to this rule is the case where it is anticipated that the short-term exposure
of concern for the human may represent a short-term excursion against a background of chronic
exposure. In this case, a more conservative approach may be preferred, in which a steady-state
dose metric calculation is used for the human.
       The following section describes applications of PBPK models in risk assessment.  These
applications relate to high-dose to low-dose extrapolation, interspecies extrapolation, estimating
intraspecies variability, route-to-route extrapolation, and duration extrapolation as required for
RfD derivation, RfC derivation, and cancer risk assessment.

4.3.  REVIEW OF EXTRAPOLATIONS POSSIBLE WITH PBPK MODELS
       Risk assessment applications typically require that extrapolations be made from the
critical studies (i.e., animal toxicology or human epidemiology studies) to the human exposure
situation.  These extrapolations of the critical studies are the focus of pharmacokinetic modeling.
To a significant extent, the models utilize in vitro or in vivo data to enable the model to address
these extrapolations (e.g., characterize pharmacokinetics at high and low doses, parameterize
models for test species and humans).  To a more limited degree, extrapolations are made in the
course of model development, most typically due to limitations on available data for humans,
such that it is assumed parameters scale in some manner from animals to humans. As
pharmacokinetic modeling strives to become increasingly predictive in nature, it is likely that
predictive tools (e.g., methods to predict partition coefficients) will play larger roles in model
development.

4.3.1. Interspecies Extrapolation
       The application of PBPK models for interspecies extrapolation of tissue dosimetry is
performed in several steps.  First, a model for the appropriate species in potential critical toxicity
studies is developed. Increasingly, a priori predictions of the PBPK model are compared with
experimental observations to evaluate the adequacy of the structure and the parameter estimates
of the rodent model. This sometimes involves refining some or all of the parameters by allowing
modeling software to estimate the best value for these parameters. The  next step involves using
species-specific or allometrically scaled physiological parameters in  the model and replacement
of the chemical-specific parameters (e.g., metabolic rates, protein binding  constants) with
appropriate estimates for the species of interest (e.g., humans).  Thus, in this approach, the
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qualitative determinants of pharmacokinetics are considered to be invariant among the various
mammalian species.  Qualitative differences between species, if any, can also be factored into
the existing structure of PBPK models (e.g., if different metabolic pathways existed among
species) but, obviously, data describing these species differences are required.
       For conducting interspecies extrapolation of pharmacokinetic behavior of a chemical,
quantitative estimates of model parameter values (i.e., partition coefficients, physiological
parameters, and metabolic rate constants) in the second species are required.  The tissue:air
partition coefficients of chemicals appear to be relatively constant across species, whereas
blood:air partition coefficients show some species-dependent variability. Therefore, the
tissue:blood partition coefficients for human PBPK models have been calculated by dividing the
rodent tissue:air partition coefficients by the human blood:air partition values (Krishnan and
Andersen, 2001).  The tissue:air and blood:air partition coefficients for volatile organic
chemicals may also be predicted using appropriate data on the content of lipids and water in
human tissues and blood (Poulin and Krishnan, 1996a, b).
       Whereas the adult physiological parameters vary coherently across species, the kinetic
constants for metabolizing enzymes do not necessarily follow any type of readily predictable
pattern, making the interspecies extrapolation of xenobiotic metabolism difficult.  Therefore, the
metabolic rate constants for xenobiotics are best obtained in the species of interest.  In vivo
approaches for determining metabolic rate constants  are not always feasible for application in
humans. The alternative is to obtain such data under in vitro conditions (e.g., Lipscomb et al.,
1998, 2003).  A parallelogram approach may also be used to predict values for the human PBPK
model on the basis of metabolic rate constants obtained in vivo in rodents as well as in vitro
using rodent and human tissue fractions (Lipscomb et al., 1998; Reitz et al., 1988b).
Alternatively, for chemicals exhibiting high affinity (low Km) for metabolizing enzymes, Vmax
has been scaled to the 0.75 power of body weight, keeping the Km species invariant.  This
approach may be useful as a crude approximation, but it may be used only  when other direct
measurements of metabolic parameters are not available or feasible.
       An example of rat-human extrapolation of the kinetics of toluene using a PBPK model is
presented in Figure 2-2 (Chapter 2). Here the structure of the PBPK model developed in rats was
kept unchanged, but the species-specific parameters were determined either by scaling or
experimentally, as described above (Tardif et al., 1997). The model was then able to predict
accurately the kinetics of toluene in humans.  Whenever the human data for a particular chemical
                                          4-12

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are not available for evaluation purposes, a corollary approach permitting the use of human data
on similar chemicals may be attempted (Jarabek et al., 1994).
       There are some instances where PBPK models can be used for interspecies extrapolation
of toxicity studies without the need of an animal PBPK model. For example, an RfC for
methanol has been proposed (Starr and Festa, 2003) using a mice developmental toxicity study
(Rogers et al., 1993) where blood methanol levels were also reported. By using the blood
methanol level at the POD from the mice study, a previously published human methanol PBPK
model (Bouchard et al., 2001) was used to predict the inhalation concentration associated with
the same internal blood methanol level in humans. This example highlights the advantage
afforded by toxicity studies that also include pharmacokinetic measurements.

4.3.2. Estimating Intraspecies Variability
       Intraspecies variability for the dose metric can be assessed using PBPK models to
estimate the magnitude of interindividual variability (pharmacokinetic component) for RfC and
RfD derivations. For this purpose, population distributions of parameters, particularly those
relating to physiology and metabolizing enzymes (i.e. genetic  polymorphisms), are specified in a
Monte Carlo approach, such that the PBPK model output corresponds to distributions of dose
metric in a population. Using the Monte Carlo approach, repeated computations based on inputs
selected at random from statistical distributions for each input parameter (e.g., physiological
parameters, enzyme content/activity with or without the consideration of polymorphism) are
conducted to provide a statistical distribution of the output, i.e., tissue dose.  Using the
information on the dose metric corresponding to a high percentile (e.g., 95th) and the 50th
percentile, the magnitude of interindividual variability can be  computed for risk assessment
purposes (Figure 4-3).
       Even though past efforts largely have characterized the impact of the distributions of
parameters in the adult population, variability analyses also need to address different life stages
(e.g., pregnancy, children, aged). Generally, age-specific changes in physiology, tissue
composition,  and metabolic activity (reviewed in O'Flaherty,  1994) can be incorporated into the
same model structure used for adults (Corley et al., 2003). Published examples of modeling
different ages describe predictions for a range of chemicals with different properties (Clewell et
al., 2004, 2002b; Ginsberg et al., 2004; Sarangapani et al., 2003). However, some life stages,
notably pregnancy and lactation, require different model structures (i.e., describing the mother
                                          4-13

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        .a
        re
        .a
        o
                                50th percentile
                                                                   95th percentile
                                         I   interindividual variability  i

                                 Concentration
       Figure 4-3. Estimation of an interindividual variability. In this example,
       interindividual variability describes the variation between the 50th (median) and
       95th percentile values of a dose metric simulated with a probabilistic PBPK
       model.
and the offspring) (Corley et al., 2003; Gentry et al., 2003, 2002).  Characterization of population
variability across ages and life stages as well as adult variability is an ongoing area of
development. PBPK models represent a powerful tool for quantitatively characterizing
population pharmacokinetic variability for application to risk assessment.  For more information,
the reader is referred to Use of PBPK Models to Quantify the Impact of Human Age and
Interindividual Differences in Physiology and Biochemistry Pertinent to Risk (U.S. EPA, 2006).

4.3.3. Route-to-Route Extrapolation
       There are two different approaches to route extrapolation involving PBPK models.  The
first one is to use an animal model to extrapolate a POD for one route to a POD by another route
on the basis of equivalent dose metric. The second approach would involve the estimation of the
human POD for one route from the available animal POD for another route on the basis of
equivalent dose metric.
       The extrapolation of the kinetic behavior of a chemical from one exposure route to
another is performed by including appropriate equations to represent each exposure pathway.
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For simulating the intravenous administration of a chemical, a single input representing the dose
administered to the animal can be included in the equation for mixed venous concentration.  Oral
gavage of a chemical dissolved in a carrier solvent may be modeled by introducing a first-order
or a zero-order uptake rate constant, and dermal absorption has been modeled by including a
diffusion-limited compartment to represent skin as a portal of entry (Krishnan and Andersen,
2001). After the equations describing the route-specific entry of chemicals into systemic
circulation are included in the model, it is possible to conduct extrapolations of pharmacokinetics
and dose metrics. This approach is illustrated in Figure 4-4 for oral-to-inhalation extrapolation
of the kinetics of chloroform in rats. For simulating the inhalation pharmacokinetics, the oral
dose was set to zero, whereas for simulating  chloroform kinetics following oral dosing the
inhaled concentration was set to zero (Figure 4-4).  Accordingly, 4-hr inhalation exposure to 83.4
ppm chloroform is equal to an oral dose of 1  mg/kg, as determined with PBPK models on the
basis of equivalent dose metric (i.e., parent chemical AUC in blood) (Figure 4-4).  Note that the
peak concentrations differ by about 10-fold;  thus, if peak concentration was thought to be the
appropriate dose metric, higher inhalation  exposures would be required to produce the  same peak
as a 1-mg/kg oral dose.

4.3.4. Duration Adjustment
      On the basis of equivalent dose metric, the duration-adjusted exposure values can be
obtained with PBPK models (Simmons et al., 2005; Bruckner, 2004; Brodeur et al., 1990;
Andersen et al., 1987). For example, if the appropriate dose metric were the AUC of a chemical,
it would initially be determined for the exposure duration  of the critical study using the PBPK
model and then the atmospheric concentration for a continuous exposure (during a day, window
of exposure, or lifetime) yielding the same AUC is determined by iterative simulation.  Figure
4-5 depicts an example of 4-hr to 24-hr extrapolation of the pharmacokinetics of toluene in rats,
based on equivalent 24-hr AUC (2.4 mg/L/hr). The rats exposed to 50 ppm for 4 hr and 9.7 ppm
for 24 hr of toluene would receive the same dose metric. Again, it should be noted that
extrapolations across long durations may not be warranted, as life stage changes and
pharmacodynamic adaptations (e.g., sensitization and desensitization) may be operational
(Clewell et al., 2002a).
                                          4-15

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                                          Oral
                          100 -|
                           10
                            1 -
                           0.1 -
                          0.01 -
                     e
                     ID
                     >   0.001
                                        2345
                                            Time (hours)
                                        Inhalation
c    100 n
o
1
ID
S
35
•° ?
o g.
o
J2
£
(D
                          10 -
                           1  -
                          0.1
                         0.01
                             01     234567
                                            Time (hours)

       Figure 4-4. Oral-to-inhalation extrapolation of the pharmacokinetics of
       chloroform on the basis of same area under the curve in blood (7.06
       mg/L/hr). The oral dose was 1 mg/kg and the inhaled concentration was 83.4
       ppm (4 hr).

       Source:  Adapted from Corley et al. (1990).
4.3.5. High-Dose to Low-Dose Extrapolation
       PBPK models facilitate high-dose to low-dose extrapolation of tissue dosimetry by
accounting for the dose-dependency of relevant processes (e.g., saturable metabolism, enzyme
induction, enzyme inactivation, protein binding, and depletion of glutathione reserves) (Clewell
and Andersen, 1987). The description of metabolism in PBPK models has frequently included a
capacity-limited metabolic process that becomes saturated at high doses. Nonlinearity arising
from mechanisms other than saturable metabolism, such as enzyme induction, enzyme
                                          4-16

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                      o E
  100-
   10-
   1 -
  0.1 -
  0.01 -
 0.001 -
0.0001
                                        8    12    16
                                          Time (hours)
                                                       20
                                                            24
                      c
                      o
                      I
                      I
                      8-§
   10-1
    1 -
                            0.1 -
                           0.01 -
                          0.001 -
                         0.0001
                                         16   24   32
                                           Time (hours)
                               40
48
       Figure 4-5. Duration adjustment (4 hr to 24 hr) of toluene exposures in rats,
       based on equivalent AUC (2.4 mg/L/hr). The rats were exposed to 50 ppm
       toluene for 4 hr and 9.7 ppm for 24 hr.

       Source:  Adapted from Tardif et al. (1997).
inactivation, depletion of glutathione reserves, and binding to macromolecules, have also been
described with PBPK models (e.g., Krishnan et al., 1992; Clewell and Andersen, 1987).  A
PBPK model intended for use in high-dose to low-dose extrapolation needs equations and
parameters describing dose-dependent phenomena if they occur in the range of interest for the
assessment. Because the determinants of nonlinear behavior may not be identical across species
and age groups (e.g., maximal velocity for metabolism, glutathione concentrations), these
parameters are required for each species/age group.  During the conduct of high-dose to low-
                                          4-17

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dose extrapolation, no change in the parameters of the PBPK model is required except for the
administered dose or exposure concentration.
       An example of high-dose to low-dose extrapolation is presented in Figure 4-6.  In this
figure, both the blood AUC and the amount metabolized over a period of time (12 hr) are plotted
as a function of exposure concentrations of toluene.  For conducting high-dose to low-dose
simulation in this particular example, only the numerical value of the exposure concentration
(which is an input parameter for the PBPK model) was changed during every model run. All
other model parameters remained the same.  The model simulations shown in Figure 4-6 indicate
the nonlinear nature of blood AUC as well as the amount of toluene metabolized per unit time in
the exposure concentration range simulated.  In such cases, the high-dose to low-dose
extrapolation of tissue dosimetry should not be conducted assuming linearity but, rather, should
be performed using tools such as the PBPK models.

4.4.  ROLE OF PBPK MODELS IN REFERENCE CONCENTRATION AND
REFERENCE DOSE DERIVATION
4.4.1. Reference Concentration
       The RfC corresponds to an estimate (with uncertainty spanning perhaps an order of
magnitude) of continuous inhalation exposure (mg/m3) for a human population, including
sensitive subgroups, that is likely to be without an appreciable risk of deleterious effects during a
lifetime (U.S. EPA, 1994). Notationally, RfC is defined as:

                          RJC=POD[HEC]/UF

where:
       POD[HEc] = POD (NOAEL, LOAEL, or BMC) dosimetrically adjusted to an HEC
       UF = uncertainty factors to account for the extrapolations associated with the POD (i.e.,
            interspecies differences in sensitivity, human intraspecies variability, subchronic-
            to-chronic extrapolation, LOAEL-to-NOAEL extrapolation, and incompleteness of
            database)

       The starting point for an RfC derivation is the identification of the POD for the critical
effect in a key study.  Subsequent steps involve (a) adjustment for the difference in duration
between experimental exposure (e.g., 6 hr) and expected human exposure (24 hr), (b) calculation
                                         4-18

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of the HEC, and (c) application of uncertainty factors (UFs).  The benefit of using PBPK models

in the RfC process is discussed below. Specifically, the role of PBPK models in determining the
POD, duration adjustment factor, and HEC is presented in Sections 4.4.2 through 4.4.6. It
                      o
                      h-
                      QJ
                      m

                      <
                           300 n
                           200 -
                           100 -
                                           500          1000
                                       Exposure Concentration (ppm)
1500
                      o
                      _Q
                      ro
                      "S
                      E
                           15 -,
                           10 -
                      o _l
                      E O
                        K

                            5 -
                                          500           1000
                                       Exposure Concentration (ppm)
1500
       Figure 4-6. High-dose to low-dose extrapolation of dose metrics using PBPK
       model for toluene. Inhalation exposures were for 4 hr, and areas under the curve
       and amount metabolized were calculated for 12 hr.  Note that there is a slight
       curve in the top graph around 125 ppm.

       Source:  Adapted from Tardif et al. (1997).
should be noted that although the various extrapolations were presented in a hierarchical fashion
earlier in this document (e.g., interspecies, intraspecies, route, duration, and high-dose to low-
                                          4-19

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dose), the order of extrapolations is changed in this section to more closely parallel the RfC and
RfD derivation processes.

4.4.2. Reference Concentration: Point of Departure
       It is important to realize that currently the POD for RfC derivation cannot be identified or
established with only pharmacokinetic data or PBPK models in the absence of dose-response
data. Integrated pharmacokinetic-pharmacodynamic models (e.g., Timchalk et al., 2002;
Gearhart et al., 1994, 1990) may be capable of predicting response and thus estimating a POD in
the future, but this is a research effort that is not yet ready for risk assessment applications. At
present, PBPK modeling can be useful for conducting route-to-route extrapolation, duration
adjustments, inter- and intraspecies extrapolations on the basis of equivalent delivered dose from
PODs identified in toxicity, epidemiology, or clinical studies.

4.4.3. Reference Concentration: Route-to-Route Extrapolation
       Typically, the POD used in the RfC process would be the inhalation route-specific
NOAEL, LOAEL, or BMC.  These PODs essentially correspond to exposure concentrations in
an experimental or field study (NOAEL, LOAEL) or to the lower confidence limit (95th
percentile) of the exposure concentration (BMCL) associated with a specified response level
(generally in the range of 1 to 10% above background; e.g., BMCLio%) derived from statistical
analysis of experimental dose-response data (U.S. EPA, 2000a, 1994).
       When information on the POD is available only for a noninhalation route of exposure
(e.g., oral route), route-to-route extrapolation can be conducted (Pauluhn, 2003).  Historically,
the NOAEL (mg/kg/day) associated with an oral exposure route was converted to  milligrams per
day and then to the equivalent inhaled concentration on the basis of human breathing rate and
body weight.  Data on the route-specific fraction absorbed, when available, are used to determine
the equivalent inhalation concentration on the basis of equivalent absorbed doses (U.S. EPA,
1999a). Such  simplistic approaches, however, assume that the rates of ADME and tissue
dosimetry of chemicals are the same for a given total dose, regardless of the exposure route and
intake rate. These approaches essentially neglect the route-specific differences in
pharmacokinetics, such as first-pass clearance. First-pass clearance can arise when chemicals
undergo extensive metabolism in tissues at portals of entry; this may include the intestines and
liver for orally absorbed compounds or the lungs for inhaled compounds (Benet et al., 1996).
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Therefore, route-to-route extrapolation using a more complete pharmacokinetic modeling
approach, such as PBPK modeling, is preferable, as described in Section 4.3.3.

4.4.4. Reference Concentration: Duration Adjustment
       An RfC addresses continuous exposure of human populations, so the POD used in its
derivation should correspond to 24-hr/day exposures (U.S. EPA, 1994). PODs are frequently
obtained from animal exposures or occupational exposures that occur for 6 to 8 hr/day, 5
days/wk, so an adjustment to a continuous 24-hr exposure, resulting in a lower concentration for
continuous exposures, is conducted on the basis of hours per day and days per week (i.e., 6/24 x
5/7) (U.S. EPA, 2002).  This simple adjustment assumes that "Haber's Rule" applies, i.e., that
for a given chemical  C x t = k, where C and t are the concentration (mass per unit volume) and
time needed (at that concentration) to produce some toxic effect, and k is a constant  associated
with that toxic effect. The rule leads to the conclusion, for example, that doubling the
concentration will halve the time needed to produce a comparable effect level. In
pharmacokinetics, the integration of C x t over the exposure-response time frame of interest is
also referred to as the AUG.  If the AUC is not the dose metric most associated with the adverse
effect (e.g., sometimes peak concentration is more critical) or various C x t = k regimens do not
result in a comparable effect level, then "Haber's Rule" is not applicable (U.S. EPA, 2002).
When data indicate that a given toxicity is more dependent on concentration than on duration
(time), this adjustment would not be used.  If the appropriate measure of internal dose is
uncertain, the Agency uses adjustment to a continuous inhalation exposure based on the C x t
relationship as a matter of health-protective policy (U.S. EPA, 2002).  For additional insights
into "Haber's Rule" (as one in a family of power functions) and its use in risk assessment, the
reader is referred to Miller et al. (2000).
       PBPK models can be used to estimate the value of a proposed internal dose metric that
would result from various administered doses (U.S. EPA, 2002; Jarabek, 1994).  PBPK models
do not address pharmacodynamic events and assume that these events do not alter the kinetics
for within-day exposures (<24 hr). Consistent with the Agency's policy (U.S. EPA, 2002), the
dose metric of a chemical for the exposure scenario of the critical study is initially determined
using the PBPK model (e.g., 6 hr/day, 5 days/wk); then the atmospheric concentration for a
                                          4-21

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continuous exposure (24 hr/day) during a lifetime or a particular window of exposure that yields
the same dose metric is determined by iterative simulation.

4.4.5. Reference Concentration: Dosimetric Adjustment Factor (Interspecies
Extrapolation)
       In the RfC process, a DAF is applied to the duration-adjusted POD to account for
pharmacokinetic differences between test species and humans to derive an HEC (U.S. EPA,
1994). The DAF depends on the nature of the inhaled toxicant and the MOA as well as the
endpoint (local effects vs. systemic effects). Dosimetry data, if available, in the test animals and
humans (including deposition data, region-specific dosimetry, blood concentration of systemic
toxicants) are used to estimate the DAF. In the absence of such data, knowledge of critical
parameters or mathematical models in the test species and humans can be useful in estimating
the DAF.
       For highly reactive or water-soluble gases that do not  significantly accumulate in blood
(e.g., hydrogen fluoride, chlorine, formaldehyde, volatile organic esters), the DAF is derived for
estimates of the delivery of chemical to different regions of the respiratory tract, based on
regional mass transfer coefficients and differences in surface area and ventilation rates (U.S.
EPA,  1994).  For poorly water-soluble gases that cause remote effects (e.g., xylene, toluene,
styrene), PBPK models are identified as the preferred approach. Absent a PBPK model, the
DAF is determined on the basis of the ratio of blood:air partition coefficients in animals and
humans (U.S. EPA, 1994). For gases that are water soluble with some blood accumulation (e.g.,
acetone, ethyl acetate, ozone, sulfur dioxide, propanol, isoamyl  alcohol) and have the potential
for both respiratory and remote effects, some combination of the above approaches may be used.
       An alternative to the use of DAFs, discussed in the RfC guidance (U.S.  EPA, 1994) is to
employ more elaborate or chemical-specific models to make interspecies extrapolations.  A
variety of computational tools are available to determine the uptake and deposition of gases and
particulates in nasal pathways and the respiratory tract (U.S. EPA, 2004; Bogdanffy and
Sarangapani,  2003; Hanna and Lou, 2001; Iran  et al., 1999; Bush et al., 1998; Asgharian et al.,
1995; Jarabek, 1994; Kimbell et al., 1993).  PBPK models are frequently used for systemically
distributed gases and vapors, but in conjunction  with other models (e.g., CFD), they can be used
for locally acting gases with contact site effects.  A limitation of DAFs is that they do not
account for metabolism of the more reactive gases, so PBPK modeling approaches would clearly
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be preferable for these compounds if adequate data are available. Further applications of PBPK
models to the more reactive gases and agents are expected to continue to be developed in the
near future.
       Intraspecies extrapolations and the application of UFs in RfC derivation are addressed in
Section 4.4.12.

4.4.6. Example of PBPK Model Use in Reference Concentration Derivation
       The RfC derivations for m-xylene and vinyl chloride exemplify the application of PBPK
models. In the case of m-xylene, using the adjusted NOAEL of 39 mg/m3 as input to the rat
PBPK model, the steady-state blood concentration was established (0.144 mg/L) (Tardif et al.,
1997). The human model was then run to determine the exposure concentration yielding that
same dose metric (HEC = 41  mg/m3) (U.S. EPA, 2003). In an alternative approach, the dose
metric associated with the unadjusted NOAEL (217 mg/m3, 6 hr/day, 5 days/wk, 13 wks) in the
rat was determined using the  PBPK model (time-weighted average blood concentration = 0.198
mg/L). Then, the human PBPK model was used to determine the 24-hr exposure concentration
that would produce this target dose metric (39 mg/m3). Dividing this value by the appropriate
UFs (3 for interspecies pharmacodynamic differences,  10 for interindividual variability, 3 for
subchronic to chronic extrapolation, and 3 for database deficiency), the RfC was determined (0.1
mg/m3).
       In the case of vinyl chloride, the RfC was derived from the NOAEL for the oral route
(U.S. EPA, 2000b).  The PBPK model was initially used to derive the dose metric associated
with the rat NOAEL (0.13 mg/kg/day). Because systemic toxicity resulted in the same endpoint
regardless of exposure route,  a human PBPK model was exercised to determine the continuous
inhalation exposure concentration associated with the same dose metric (2.5 mg/m3) (Clewell et
al., 1995). Using a total UF of 30 (3 for toxicodynamic component of interspecies UF and 10 for
intraspecies variability), the RfC was established (0.1 mg/m3).
       If the available human PBPK
                                      Box 4-1. Role of PBPK models in the RfC process
model is probabilistic in nature,
                                      •   Route-to-route extrapolation of the point of departure
accounting for the population
distribution of parameters
Duration adjustment calculation
Dosimetric adjustment factor (i.e., interspecies)
                                         Pharmacokinetic component of human variability
(biochemical, physiological, and
physicochemical), the magnitude of the interindividual variability can be estimated (Delic et al.,
                                          4-23

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2000). In that case, the intraspecies uncertainty factor might be set to 3 (to account only for
pharmacodynamic differences). The potential role of the PBPK model in the RfC process is
summarized in Box 4-1.

4.4.7. Reference Dose
       An RfD is an estimate (with uncertainty spanning perhaps an order of magnitude) of a
daily exposure to the human population (including sensitive subgroups) that is likely to be
without an appreciable risk of deleterious effects during a lifetime (Dourson et al., 1992; Barnes
and Dourson 1988). It is expressed in units of milligrams per kilogram per day.  An RfD is
calculated as follows:

                          RfD = POD/UF
where:
       POD = NOAEL, LOAEL, or BMD
       UF = uncertainty factors related to extrapolations associated with the POD (i.e.,
       interspecies extrapolation, human variability, subchronic-to-chronic extrapolation,
       LOAEL-to-NOAEL extrapolation) or incompleteness of the database.

       An RfD derivation begins with the identification of the POD for the critical effect.
Subsequently, the UFs are applied as appropriate.  PBPK models are potentially useful in
deriving the RfD by estimating the POD and extrapolation factors,  as described in Sections 4.4.8
through 4.4.11.

4.4.8. Reference Dose: Point of Departure
       As with RfC derivation, PBPK models are not able to establish a POD in the absence of
experimental dose-response data. Development of a BBDR model linked with a PBPK model
could potentially improve the quantification of the dose-response and POD for RfD derivation.
There has been some success in developing BBDR models for simple adverse effects (e.g.,
cholinesterase inhibition, cytotoxicity, hematoxicity) (Ashani and Pistinner, 2004; Cox, 1996;
Gearhart et al., 1994, 1990; Reitz et al., 1990a), but these models are not routinely used to
estimate PODs for RfD derivation, partly due to limitations on data needed to calibrate and test
the models.  New technologies (e.g., toxicogenomics) may offer the potential for generating
                                          4-24

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needed data, and more integrated PBPK and BBDR models may be an attainable goal in the near
future.

4.4.9. Reference Dose: Route-to-Route Extrapolation and Duration Adjustment
       The RfD derivation generally uses an oral NOAEL, LOAEL, or BMD as the POD.  The
oral route-specific NOAEL and LOAEL correspond to experimentally tested doses, whereas the
BMD is obtained from statistical modeling of dose-response data (U.S. EPA, 2000a).
       When an oral POD is unavailable, PBPK models can be useful in deriving such values on
the basis of results obtained for other dosing routes (e.g., inhalation, intravenous, dermal), as
previously described.  Extrapolation of inhalation data using simple assumptions about
ventilation rate, chemical concentration, and body weight will be inaccurate due to
pharmacokinetic factors such as first-pass clearance, discussed above for route-to-route
extrapolation in RfC derivation. In addition, comparisons of oral PODs with dosimetry based
route extrapolation of inhalation results can be valuable because the vehicle (e.g., corn oil) in
oral gavage studies sometimes alters the toxicity response.
       As with RfCs, chronic RfDs are intended for continuous exposure of human populations.
For PODs derived from gavage studies, typically administered 5 days/wk, it has been standard
practice to adjust for continuous exposure using a 5/7 adjustment. Alternatively, PBPK models
can be used to model human 7-day/wk exposures and thus estimate a dose metric corresponding
to a POD determined in experimental animal bioassays.

4.4.10. Reference Dose: Interspecies Extrapolation
       As with RfC derivation, PBPK models can be employed to account  for pharmacokinetic
differences between test species and humans and covert a POD to a human  equivalent dose (U.S.
EPA, 2002). Estimation of human pharmacokinetic variability and the application of UFs in RfD
derivation are discussed in Section 4.4.12.

4.4.11. Example of PBPK Model  Use in Reference Dose Derivation
       The RfD derivation for ethylene glycol monobutyl ether exemplifies the current approach
of PBPK model application (U.S. EPA, 1999b).  In this case, the LOAEL identified in an animal
study (59 mg/kg/day)  was provided as input to the PBPK model to determine the Cmax of the
metabolite butoxy acetic acid in blood (BAAmax) (Corley et al., 1997). The dose metric
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(BAAmax) associated with the LOAEL was established in the test species (103 uM). The human
PBPK model was then run to determine the exposure dose that would give the target dose metric
(103 uM) (Corley et al., 1997). The resulting human equivalent dose of 7.6 mg/kg/day was
divided by the appropriate UFs (30; 10 for interindividual differences and 3 for LOAEL-to-
NOAEL  extrapolation) to establish the RfD (0.3 mg/kg/day). In this particular case, the
interspecies pharmacodynamic factor was set to 1 because in vitro studies suggested that humans
are less sensitive than rats to the hematologic effects of ethylene glycol monobutyl ether (U.S.
EPA, 1999b).
       When the BMD is available, a similar approach is used to establish the RfD. In the case
of ethylene glycol monobutyl ether, initially the dose metric associated with the BMD was
established (BAAmax = 64 uM) and then the human PBPK model was used to back-calculate the
equivalent dose (5.1 mg/kg/day). Using the appropriate UF (10 for interindividual variability),
the RfD was derived (0.5 mg/kg/day) (U.S. EPA, 1999a).  If the human PBPK model accounted
for the population distribution of
                                           Box 4-2. Role of PBPK models in the RfD process
parameters, the pharmacokmetic
                                           •   Route-to-route extrapolation
component of the interindividual variability
could be addressed as illustrated in the
dose-response analysis with methyl
mercury (Clewell et al., 1999). PBPK            variability
Duration adjustment
Pharmacokinetic component of interspecies
extrapolations
Pharmacokinetic component of human
models, by facilitating the simulation of tissue dose of the toxic moiety of chemicals, address
specific areas of uncertainty associated with derivation of the RfD, as shown in Box 4-2.

4.4.12.  Uncertainty Factors:  Role of PBPK Models
       The UFs and variability factors used in RfC and RfD derivation account for
extrapolations from test animals to humans (interspecies, UFA), across duration of exposure
(subchronic to chronic), from LOAEL to NOAEL, for variability within the human population to
protect the most sensitive population (intraspecies variability, UFH), and for poor quality or
missing data in the database (database deficiency) (U.S. EPA, 1994; Jarabek, 1994). The total of
all UFs generally should not exceed 3,000 (U.S. EPA, 2002). If the NOAEL for a chemical with
an adequate database has been identified in a chronic study, only the UFA and UFn are used in
the assessment.  The conventional default value for UFA of 10 is used in RfC and RfD derivation
as an approximation of cross-species scaling resulting in equivalent effects. Similarly, the
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default value for UFn of 10 is presumed adequate to account for variability in the human kinetic
and dynamic processes following exposure and to protect potentially sensitive human
subpopulations.
       The values for UFA and UFH are based on empirical information for pharmacokinetics
and pharmacodynamics (e.g., isoenzyme levels, enzyme activity levels, tissue volumes, breathing
rates, cell proliferation rates) (Dome et al., 2002, 2001a, b; Walton et al., 2001) and science
policy and historical use. Extrapolations across species or estimates of interindividual variability
(e.g., differences arising from genetic polymorphisms), however, are best done on the basis of
chemical specific determinants of disposition and effects. Initially, evaluation of specific
determinants of interspecies differences or human variability is useful,  but simple pooling of
these specific determinants without accounting for covariance or nonlinear interactions can lead
to unrealistic estimates for either UFA or UFH (Lipscomb, 2004). The net impact of various
determinants on the UFA and UFH is more properly evaluated within the integrated and
physiologically based context of a PBPK or BBDR model.
       When data are available to go beyond default uncertainty values, these UFs can be
subdivided into their toxicokinetic and toxicodynamic components (IPCS, 2005; U.S. EPA,
2005b). The World Health Organization's International Programme on Chemical Safely (IPCS)
has produced guidance on the development of chemical-specific adjustment factors (CSAFs)
(IPCS, 2005).  Although the principles of using chemical-specific data  in developing values for
UFs has long been endorsed by EPA (e.g., U.S. EPA, 1994), and many of the guiding principles
in the IPCS document are also components of EPA's risk assessment approach, the Agency does
not use CSAFs per se, due in part to differences in calculation methods. For instance, the Agency
often separates the pharmacokinetic and pharmacodynamic components of interspecies
variability equally (i.e., 1005 or 3.16, generally rounded to 3 each), whereas the IPCS advocates
10°'6 (4.0) and 10°'4 (2.5), respectively (IPCS, 2005).
       When sufficient chemical-specific data are available for PBPK  modeling, such models
are useful for characterizing the magnitude of the pharmacokinetic component of the UFA as well
as the UFH used in the RfC and RfD processes. When using PBPK models to adjust for
pharmacokinetic differences between species,  a factor of 3 (one-half order of magnitude) is
generally retained to account for remaining uncertainties (U.S. EPA, 2003, 1994; Clewell et al.,
2002a; Jarabek, 1995a). However, chemical-specific information on the pharmacodynamic
aspect of inter- and intraspecies differences may inform a further reduction or increase of these
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UFs from default values.  It should be recognized that PBPK and BBDR models are not currently
suitable for characterizing the magnitude of LOAEL-NOAEL, subchronic-chronic, or database
UFs, although research in these areas is ongoing (Thomas et al.,  1996a).

4.5. ROLE OF PBPK MODELS IN CANCER RISK ASSESSMENT
       The dose-response assessment portion of cancer risk assessment may vary, depending on
MOA considerations.  A CSF can be based on a linear extrapolation from the POD (i.e., high-
dose to low-dose extrapolation), or a nonlinear analysis may be applied (U.S. EPA, 2005b).
Either approach may also require interspecies or route-to-route extrapolations for the POD. The
role of PBPK models in conducting these extrapolations is discussed in Sections 4.5.1 through
4.5.5.

4.5.1. Interspecies Extrapolation
       For gases and particulates, the default procedure for interspecies extrapolation involves
the derivation of an HEC, as described in Section 2.5.4 (Jarabek, 1995a, b; U.S. EPA, 1994).  For
oral exposures, when a PBPK model is not available, the EPA endorsed scaling of doses for
carcinogens between species (e.g., rat to humans) according to body mass raised to the three-
fourths power (BW0-75) (U.S. EPA, 2005b, 2002, 1992b).  This procedure presumes that equal
doses in these units (i.e., in mg/kg°'75/day), when administered daily over a lifetime, will result in
equal lifetime cancer risks across mammalian species. The three-fourths power scaling
relationship  (sometimes called "Kleiber's law" from his original  proposition in a 1932 article) is
generally attributed to differences in metabolic rate. The leading biological rationale for a less-
than-full-power relationship for general metabolic processes (i.e., < BW1) is that exchange
surfaces and distribution networks constrain the concentration and flux of metabolic reactants
(Enquist et al., 1998; West et al., 1997). There remains considerable dissent as to the generality
of the BW°75 scaling factor, the underlying biological rationale, and the value of the exponent
(i.e., many proponents advocate a BW0'67 scaling based solely on surface area differences),
particularly for toxicological effects of xenobiotic chemicals in contrast to endogenous anabolic
and catabolic processes (Agutter and Wheatley, 2004). Nonetheless, BW0'75 scaling remains the
current EPA default approach (U.S. EPA, 1992b).
       The nature and slope of the dose-response relationship for carcinogens may not be
identical in test species and humans due to pharmacokinetic and pharmacodynamic differences
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(Monro, 1994). If appropriate data are available in both the test species and humans (e.g., tissue
or blood concentrations), then interspecies extrapolations of an equivalent carcinogenic or safe
dose can be conducted. In the absence of a complete data set, PBPK models provide a means to
characterize the relationship between the applied dose and the internal dose of a carcinogen in
the species of interest for subsequent extrapolation to humans (Andersen et al., 1987).

4.5.2. Intraspecies Variability
       Intraspecies variability in pharmacokinetics or pharmacodynamics has not usually been
considered in cancer risk assessment. CSFs have been used without further adjustment to
account for susceptible populations.  The recent supplemental guidance, however, suggests that
an additional adjustment factor to the cancer slope or unit risk value be considered to account for
enhanced susceptibility in early life (i.e., to neonates and young children) from exposure to
carcinogens exhibiting a mutagenic MOA (U.S. EPA, 2005a). Furthermore, when assessing the
less-than-lifetime exposures occurring in childhood, the guidelines stipulate consideration of
adult-children differences in key exposure factors (e.g., skin surface area, drinking water
ingestion rates) (U.S. EPA, 2005c).
       PBPK models can be useful in evaluating pharmacokinetic differences among adults and
children and their impact on the internal disposition of chemical carcinogens (Ginsberg et al.,
2004; Clewell et al., 2004; Price et al., 2003b; Gentry et al., 2003; Clewell et al., 2002b).
However, the quantitation of differences in tissue dose between adults and children would not be
account for pharmacodynamic differences related to early-life exposures of neonates and
children.

4.5.3. Route-to-Route Extrapolation
       As with RfC and RfD derivation, PBPK models can facilitate the conduct of route-to-
route extrapolation by accounting for the route-specific rate and magnitude of absorption, first-
pass effect, and metabolism (Clewell and Andersen, 1994).  The slope factor or the POD
associated with one exposure route can be translated into applied dose for another exposure route
by simulating the tissue dose of toxic moiety associated with the exposures by each route (U.S.
EPA, 2000b; Gerrity et al., 1990).
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4.5.4. High-Dose to Low-Dose Extrapolation
       The oral CSF or the IUR can be determined by modeling the relationship between the
cancer response and the administered dose or exposure concentration (U.S. EPA, 2005a).
According to the revised cancer guidelines, either a nonlinear (i.e., RfC or RfD) or linear (i.e.,
unit risk estimate) extrapolation based on the POD can be conducted, as appropriate for the
MOA of the carcinogen (U.S. EPA, 2005a).  The use of internal dose or delivered dose in such
analysis has been encouraged.
       Because high doses of chemicals are often administered in rodent cancer bioassays, the
number of tumors observed in such studies is not always directly proportional to the exposure
dose.  Thus, the dose-response relationships can appear complex, in part due to nonlinearity in
the pharmacokinetic processes occurring at high exposure doses. In other words, the target tissue
dose of the toxic moiety may be disproportional to the administered doses used in animal
bioassays (Figure 2-1, Chapter 2).  Therefore, dose-response analysis based on an appropriate
dose metric may result in linearization of the relationship (Clewell et al., 2002a, 1995; Andersen
et al., 1987). The slope factor derived using the dose metric-response curve has units of (dose
metric)"1. For nonlinear analyses, a POD can be converted using a PBPK  model to the dose
metric at which no significant incidence of cancer is expected on the basis of MOA of the
chemical and dose-response data.
       An integrated PBPK-BBDR model would improve the characterization of a chemical
carcinogen dose-response relationships (e.g., a PBPK model coupled to a clonal expansion and
progression model); however, most such coupled models are still in the development stage (U.S.
EPA, 2005b). PBPK models improve
estimation of the internal dose metric for a
chemical carcinogen and play an important
role in reducing the uncertainties associated
  . .        ,, .         .   .        1-1      •»   High-dose to low-dose extrapolation
with some of the extrapolations used in the       T °     .     •.•,•._.    +  +
                                           »   mtraspecies variability to protect sensitive
cancer risk assessment process (Box 4-3).
Box 4-3. Role of PBPK models in cancer risk
assessment
•  Interspecies extrapolations of pharmacokinetically
   equivalent doses
•  Route-to-route extrapolation
   subpopulations
4.5.5. Example of PBPK Model Use in Cancer Risk Assessment
       For assessing the cancer risk associated with human exposures, the exposure
concentration is used as input to human PBPK models to estimate the dose metric, which is then
multiplied with the dose metric-based slope factor.  In the cancer risk assessments using PBPK
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models, it is assumed that the tissue response associated with a given level of dose metric in the
target tissue is the same in test animals and in humans (e.g., Andersen et al.,  1987). It is a
reasonable assumption that can be revised as a function of species-specific mechanistic
information available for a given chemical.
       The demonstration of the applicability of PBPK models in cancer risk assessment was
first accomplished with dichloromethane, which caused liver and lung tumors in mice exposed to
2,000 or 4,000 ppm 6 hr/day, 5 days/wk for lifetime (Andersen et al., 1987).  In this case, the
mouse PBPK model was used to calculate the tissue dose of metabolites and parent chemical
arising from exposure scenarios comparable to those of the cancer bioassay study, and their
relationship to the observed tumor incidence was then examined. Because the parent chemical
was nonreactive, Andersen et al. (1987) considered it an unlikely candidate responsible for the
tumorigenicity.  Hence, the relationship between the tissue exposure to its metabolites and tumor
incidence was examined (Table 4-2).  Whereas the dose metric based on oxidative pathway
varied little between 2,000 and 4,000 ppm, the flux through the glutathione pathway increased
with increasing dose of dichloromethane and corresponded well  with the degree of
dichloromethane-induced tumors at these exposure concentrations.
       Table 4-2.  Relationship between tumor prevalence and dichloromethane
       metabolites produced by microsomal and glutathione pathways for the
       bioassay conditions (methylene chloride-dose response in female mice)
Exposure
(ppm)
0
2,000
4,000
Microsomal pathway
dose3
Liver
—
3,575
3,701
(Lung)
—
(1,531)
(1,583)
Glutathione pathway
dose8
Liver
—
851
1,811
(Lung)
—
(123)
(256)
Tumor number
Liver
6
33
83
(Lung)
(60)
(63)
(85)
1 Tissue dose is cumulative daily exposure (mg metabolized/volume tissue/day). Reprinted from Toxicology &
 Applied Pharmacology, vol. 87, Andersen et al., Physiologically based pharmacokinetics and the risk assessment
 process for methylene chloride, pp. 185-205, 1987, with permission from Elsevier.
       The model prediction of the target tissue dose of the glutathione conjugate resulting from
6-hr inhalation exposures to 1-4,000 ppm dichloromethane is presented in Figure 4-7.  The
                                          4-31

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estimation of target tissue dose of dichloromethane-glutathione conjugate by linear back-
extrapolation gives rise to a 21-fold higher estimate than that obtained by the PBPK modeling
approach.  This discrepancy arises from the nonlinear behavior of dichloromethane metabolism
at high-exposure concentrations. At exposure concentrations exceeding 300 ppm, the
                    10000
                     0.01
                         1         10        100       1000       10000
                                         PPM in air

       Figure 4-7. PBPK model predictions of glutathione (GST)-pathway
       metabolites in mouse liver. The three curves are for a linear extrapolation from
       the bioassay exposures of 2,000 and 4,000 ppm (upper curve), the expected tissue
       dose, based on model parameters for the mouse (middle line), and the expected
       dose expected in humans, based on human model parameters (bottom line). The
       curvature occurs because oxidation reactions that are favored at low inhaled
       concentrations become saturated as inhaled concentration increases above several
       hundred ppm.  Reprinted from Toxicology & Applied Pharmacology., vol. 87,
       Andersen et al., Physiologically based pharmacokinetics and the risk assessment
       process for methylene chloride, pp. 185-205, 1987, with permission from
       Elsevier.
cytochrome P-450-mediated oxidation pathway is saturated, giving rise to a corresponding
disproportionate increase in the flux through glutathione conjugation pathway. By accounting
for the species-specific differences in metabolism rates and physiology in the PBPK model, the
target tissue dose for humans was estimated to be some 2.7 times lower than that for the mouse.
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The target tissue dose-based slope factor has subsequently been used for characterizing the
cancer risk associated with human exposures (Haddad et al., 2001a; Reitz et al., 1989; Andersen
et al., 1987). The case of dichloromethane exemplifies how PBPK models can be used to
improve the dose-response relationship on the basis of appropriate dose metrics, thus leading to
scientifically sound conduct of interspecies and high-dose to low-dose extrapolations essential
for cancer risk assessments.

4.6.  MIXTURE RISK ASSESSMENT
      PBPK models facilitate risk assessment of chemical mixtures by estimating the change in
dose metrics due to multichemical interactions (Haddad et al., 2001b).  For conducting tissue
dosimetry-based assessments for mixtures, adequately evaluated PBPK models for the mixture in
the test species and in humans are required and the dose-response values for the individual
chemicals (e.g., CSF, RfD, RfC) known. The approach for using PBPK models in risk
assessment of mixtures of systemic toxicants or carcinogens exhibiting threshold mechanism of
action, would consist of (Haddad et al., 2001b)

       1.  Characterizing the dose metrics associated with dose-response values for the mixture
          components,
      2.  Obtaining predictions of dose metrics of each mixture component in humans, based
          on information on exposure levels provided as input to the mixture PBPK model; and
      3.  Determining the sum total of the ratios of the results of steps (1) and (2) for each
          component during mixed exposures.

       Similarly, for carcinogens with slope factor (Haddad et al., 2001b),

       1.  The dose metric-based slope factor can be established for each component using the
          animal PBPK model,
      2.  The dose metric associated with human exposure concentrations can be established
          using mixture PBPK models, and
      3.  The results  of steps (1) and (2) can be combined to determine the potentially altered
          cancer response during mixed exposures.

      Risk assessments based on the use of PBPK models for single chemicals and mixtures, as
detailed in previous sections, account for only the pharmacokinetic aspect or, more specifically,
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target tissue exposure to toxic moiety. If these tissue exposure simulations are combined with
pharmacodynamic models, then better characterization of dose-response relationships and
prediction of PODs (NOAEL, BMD, BMC) may become possible.

4.7. LINKAGE TO PHARMACODYNAMIC MODELS
       The identification of PODs by simulation may become possible with the use of BBDR
models. These models would require the linkage of quantitative descriptions of
pharmacokinetics and pharmacodynamics via mechanism of action.  Accordingly, the output of
PBPK models is linked to the pharmacodynamic model using an equation that reflects the
researcher's hypothesis of how the toxic chemical participates in the initiation of cellular
changes leading to measurable toxic responses.  For example, certain DNA adducts cause
mutations, cytotoxic metabolites kill individual cells, and expression of growth factors can act as
a direct proliferation stimulus. In each of these cases, the temporal change in the dose metric
simulated by the PBPK model is linked with mathematical descriptions of the process of adduct
formation, cytotoxicity, or proliferation in the BBDR models to simulate the quantitative
influence of these processes on tumor outcome.  Figure 4-8 presents an example of the
relationship between dose metric (simulated by the PBPK model) and fraction of liver cells
killed (simulated by pharmacodynamic model) for chloroform. In this case, the
pharmacodynamic model consisted of differential equations to simulate time-dependent changes
in the number of hepatocytes in the liver as a function of basal rates of cell division and death,
chloroform-induced cytolethality, and regenerative replications (Page et al., 1997; Conolly and
Butterworth, 1995).
       Table  4-3 presents a list of pharmacodynamic models for cancer and noncancer
endpoints.  A characteristic of several of these pharmacodynamic models is that they are able to
simulate the normal physiological processes (e.g., cell proliferation rates, hormonal cycle) and
additionally account for the ways in which chemicals perturbate such phenomena, leading to the
onset  and progression of injury.  Pharmacodynamic models that can be linked with PBPK
models are not available for a number of toxic effects  and modes of action. This situation is a
result, in part, of the complex nature of these models and the extensive data requirements for
development and evaluation of these models for various exposure and physiological conditions.
       With the availability of integrated pharmacokinetic-pharmacodynamic models, the
scientific basis of the process of estimating PODs and characterizing the dose-response curve
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will be significantly enhanced. Additionally, such a modeling framework will facilitate a
quantitative analysis of the impact of pharmacodynamic determinants on the toxicity outcome,
such that the magnitude of the pharmacodynamic component of the interspecies and intraspecies
factors can be characterized more confidently. Even though some PBPK models have been used
in RfD, RfC, and unit risk estimate derivation for a number of substances (Table 4-1),  the need
for applying such models (where possible) should be continuously  explored.
            0.30
            0.25 - -
          1
            §.1S  •
            0,10  -
            0.05 - -
            0.00
               0,00
1.00
2.00
3.00
4.00
i.OO
6.00
                Liver dose surrogate ({iittol metabolized/g liver/60 min)
       Figure 4-8. Relationship between the dose metric (|Jmol metabolized/g
       liver/hr) simulated by PBPK model and the cell killing inferred from
       pharmacodynamic model for chloroform. Reprinted from Fundamentals of
       Applied Toxicology., vol. 37, Page et al., Implementation of EPA revised cancer
       assessment guidelines:  incorporation of mechanistic and pharmacokinetic data,
       pp. 16-36, 1997, with permission from Oxford University Press.
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Table 4-3. Examples of biologically based models of endpoints and processes
of toxicological relevance
Toxicity endpoint
or process
Cancer
Cholinesterase
inhibition
Developmental
toxicity
Estrus cycle
Gene expression
Granulopoiesis
Nephrotoxicity
Teratogenic effect
Features
Simulation of relative roles of
initiation, promotion,
cytolethality, and proliferation
Simulation of dose-dependent
inhibition of plasma
cholinesterase, red blood cell
acetyl cholinesterase and brain
acetyl cholinesterase, and
nontarget B-esterase
Simulation of altered cell
kinetics as the biological basis
of developmental toxicity
Simulation of interactions of
estradiol and lutenizing
hormone
Simulation of induction of
CYP1A1/2 protein expression
in multiple tissues
Simulation of loss of
proliferating cells and loss of
functional cells
Simulation of induction of
renal 2\i globulin in male rat
kidney as a function of
proteolytic degradation and
hepatic production
Sensitivity distribution of
embryo as a function of age
and stage of development
Chemical studied
2-acetylamino fluorine
Chloroform
Dimethylnitrosamine
Formaldehyde
Polychlorinated biphenyls
Pentachlorobenzene
Saccharin
Organophophates
Methyl mercury
Endocrine-modulating
substances
Tetrachlorodibenzodioxin
Cyclophosphamide
2,2,4-Trimethyl-2 -phenol
Hydroxyurea
References
Conolly et al. (2003); Tan et
al. (2003); Thomas et al.
(2000); Conolly and Andersen
(1997); Conolly and Kimbell
(1994); Chen (1993); Luebeck
etal. (1991); Cohen and
Ellwein (1990); Moolgavkar
and Luebeck (1990);
Moolgavkar and Knudson
(1981); Moolgavkar and
Verizon (1979); Armitage and
Doll (1957)
Timchalk et al. (2002);
Gearhart et al. (1994, 1990)
Faustman et al. (1999); Leroux
etal. (1996)
Andersen etal. (1997)
Santostefano etal. (1998)
Steinbach etal. (1980)
Kohn and Melnick (1999)
Luecke etal. (1997)
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                                      GLOSSARY
Absorbed dose: The amount crossing a specific absorption barrier (e.g., the exchange
boundaries of the skin, lung, and digestive tract) through uptake processes.

Applied dose:  The amount presented to an absorption barrier and available for absorption
(although not necessarily having yet crossed the outer boundary of the organism).

Area under the curve (AUC):  The concentration of a chemical in tissues or blood integrated
over time.  It is a measure of tissue exposure to chemicals over a period of time.

Bayesian statistics:  An approach that considers a model's parameters as random variables with
a probability distribution for describing each parameter.  The distribution based only on prior
information and assumptions is called the prior distribution. Analysis of new data yields a
posterior distribution that reconciles the prior information and assumptions with the new data.

Benchmark dose (BMD) or benchmark concentration (BMC): A dose or concentration that
produces a predetermined change in response rate of an adverse effect (called the benchmark
response) compared to background.

Biologically based dose-response (BBDR) model:  A predictive model that describes biological
processes at the cellular and molecular level linking the target organ dose to the adverse effect.

Cancer slope factor (CSF): An estimate of the increased cancer risk from a lifetime exposure
to an agent. This estimate, usually expressed in units of proportion (of a population) affected, is
generally reserved for use in the low-dose region of the dose-response relationship. It is often an
upper bound, approximating a 95% confidence limit.

Clearance: Volume containing the amount of drug eliminated per unit time by a specified
organ; it has the dimension  of a flow per unit time.

Critical effect:  The first adverse effect, or its known precursor, that occurs to the most sensitive
species as the dose rate of an agent increases.

Delivered dose: The amount of a substance available for biologically significant interactions in
the target organ.

Diffusion limited uptake:  Compounds (typically high molecular weight and those with
significant protein binding) where membrane diffusion is often the rate-limiting process.

Dose metric:  The target tissue dose that is closely related to ensuing adverse responses. Dose
metrics used for risk assessment applications  should reflect the biologically active form of
chemical, its level, and duration of internal  exposure, as well as intensity.

Dose-response assessment: The process of determining the relationship between the magnitude
of administered, applied, or internal doses and biological responses.  Response can be expressed
as measured or observed incidence or change in level of response, percent response in groups of
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subjects (or populations), or the probability of occurrence or change in level of response within a
population.

Exposure assessment: The process of identifying and evaluating the human population exposed
to a toxic agent by describing its composition and size as well as the type, magnitude, frequency,
route, and duration of exposure.

First-order process: A linear metabolic process where a constant fraction of chemical is
metabolized per unit time.

First-pass effects: Metabolism that occurs before a compound can enter the general circulation.
For example,  an orally administered compound may undergo metabolism in the intestines and/or
liver prior to systemic distribution.

Flow-limited diffusion:  The chemical diffuses readily between blood and tissue compartments
and exchange is limited primarily by blood flow.

Half-life:  Interval of time required for one-half of a given substance present in an organ to leave
it through processes other than physical decay. It is a constant only for mono-exponential
functions.

Human equivalent concentration (HEC):  The human concentration (for inhalation exposure)
of an agent that is believed to induce the same magnitude of toxic effect as the exposure
concentration in experimental  animal species.  This adjustment may incorporate pharmacokinetic
information on the particular agent, if available, or use a default procedure.

Integration interval: The time interval at which the calculations of the change in concentration
or amount of chemical in various compartments of the model are performed.

Internal dose: A more general term denoting the amount absorbed without respect to specific
absorption barriers or exchange boundaries.  The amount of the chemical available for
interaction by any particular organ or cell is termed the delivered or biologically effective dose
for that organ or cell.

Markov-chain Monte-Carlo  simulation: An approach that has frequently been used within a
Bayesian statistical framework to (a) sample each model's parameters from their prior
distributions,  (b) fit the model with the sampled parameters to several additional experimental
data sets, and (c) compare the model's predictions with the experimental results to obtain
posterior distributions for the model's parameters that improve the model's fit. These steps are
repeated thousands of times until each parameter's posterior distribution converges to a more
robust distribution that reflects a wider database.

Pharmacokinetic models: Mathematical descriptions simulating the relationship between
external exposure levels and the biologically effective dose at a target tissue over time.
Pharmacokinetic models take into account absorption, distribution, metabolism,  and elimination
of the administered chemical and its metabolites.
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Pharmacodynamic models:  Mathematical descriptions simulating the relationship between a
biologically effective dose and the occurrence of a tissue response over time.

Physiologically based pharmacokinetic (PBPK) model: A model that estimates the dose to
target tissue by taking into account the rate of absorption into the body, distribution and storage
in tissues, metabolism, and excretion on the basis of interplay among critical physiological,
physicochemical, and biochemical determinants.

Point of departure (POD):  The dose-response point that marks the beginning of a low-dose
extrapolation.  This point can be the lower bound on dose for an estimated incidence or a change
in response level from a dose-response model (BMD, BMC), or a no-observed-adverse-effect
level or lowest-observed-adverse-effect level for an observed incidence or change in level or
response.

Potential dose:  The amount ingested, inhaled,  or applied to the skin.

Reference concentration (RfC):  An estimate (with uncertainty spanning perhaps an order of
magnitude) of a continuous inhalation exposure to the human population (including sensitive
subgroups) that is likely to be without an appreciable risk of deleterious effects during a lifetime.
It can be derived from a NOAEL, LOAEL, or benchmark concentration, with uncertainty factors
generally applied to reflect limitations of the data used. Generally used in EPA's noncancer
health assessments. [Durations include acute, short-term, subchronic, and chronic].

Reference dose (RfD): An estimate (with uncertainty spanning perhaps an order of magnitude)
of a daily oral  exposure to the human population (including sensitive subgroups) that is likely  to
be without an appreciable risk of deleterious effects during a lifetime. It can be derived from a
NOAEL, LOAEL,  or benchmark dose, with uncertainty factors generally applied to reflect
limitations of the data used. Generally used in EPA's noncancer health assessments. [Durations
include acute,  short-term, subchronic, and chronic].

Steady state:  A variable is said to have attained steady state when its value stays constant in a
given interval  of time, i.e., when its derivative is zero.

Target organ: The biological organ(s) most adversely affected by exposure to a chemical or
physical agent.

Terminal half-life: The  terminal half-life is the interval of time for the concentration of the
drug in a compartment to decrease 50% in its final phase.

Uncertainty:  Uncertainty occurs because of lack of knowledge. Uncertainty can often be
reduced with greater knowledge of the system or by collecting more and better experimental or
simulation data.

Uncertainty factors (UFs)/variability factors:  Generally, 10-fold default factors used in
operationally deriving the reference dose and reference concentration from experimental data.
The factors are intended to account for (a) variation in sensitivity among the members of the
human population (i.e., interindividual variability), (b) uncertainty in extrapolating animal data
to humans (i.e., interspecies uncertainty), (c) uncertainty in extrapolating from data obtained in a
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study with less-than-lifetime exposure to lifetime exposure (i.e., extrapolating from subchronic to
chronic exposure), (d) uncertainty in extrapolating from a lowest-observed-adverse-effect level
rather than from a no-observed-adverse-effect level, and (e) uncertainty associated with
extrapolation when the database is incomplete.

Variability:  Variability refers to true heterogeneity or diversity. Differences among individuals
in a population are referred to as interindividual variability; differences for one individual over
time are referred to as intraindividual variability.

Volume of distribution: The volume of distribution is the ratio between the administered dose
and plasma or blood concentration of a chemical.

Zero-order process:  A saturated metabolic process where a constant amount of chemical is
eliminated per unit time.
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Thomas, RS; Conolly, RB; Gustafson, DL; et al. (2000) A physiologically based pharmacodynamic analysis of
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                    APPENDIX

LIST OF PUBLICATIONS RELEVANT TO PBPK MODELING OF
      ENVIRONMENTAL CHEMICALS AND ITS USE

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 1.  Abbas, R., and Fisher, J. W. (1997). A physiologically based pharmacokinetic
    model for trichloroethylene and its metabolites, chloral hydrate, trichloroacetate,
    dichloroacetate, trichloroethanol, and trichloroethanol glucuronide in B6C3F1 mice.
    Toxicology and Applied Pharmacology 137, 15-30.

 2.  Abbas, R., and Hayton, W. L. (1997). A physiologically based pharmacokinetic and
    pharmacodynamic model for paraxon in rainbow trout.  Toxicology and Applied
    Pharmacology 145, 192-201.

 3.  Abraham, M. H., Kamlet, M. J., Taft, R. W., Doherty, R. M., and Weathershy, P. K.
    (1985). Solubility properties in polymers and biological media. 2. The correlation
    and prediction of the solubilities of nonelectrolytes in biological tissues and fluids.
    Journal of Medicinal Chemistry 28, 865-870.

 4.  Aggarwal, G., Kohn, M. C., and Melnick, R. L. Development of a physiologically
    based pharmacokinetic model for isoprene. Isoprene, NTP TR 486, H -l-H-17.
    2000. National Institute of Environmental Health Sciences., North Carolina.
    Ref Type: Report

 5.  Albanese, R. A., Banks, H. T., Evans, M. V., and Potter, L. K. (2002).
    Physiologically based pharmacokinetic models for the transport of trichloroethylene
    in adipose tissue. Bulletin of Mathematical Biology 64, 97-131.

 6.  Ali.N, T. R. (1999). Toxicokinetic modeling of the combined exposure to Toluene
    and N-Hexane in Rats and Humans. J Occup Health 41, 95-103.

 7.  Allen, B. C., and Fisher, J. W. (1993). Pharmacokinetic modeling of
    trichloroethylene and trichloroacetic acid in humans. Risk Analysis 13, 71-86.

 8.  Allen, B. C., Covington, T. R., and Clewell, H. J. I. (1996). Investigation of the
    impact of pharmacokinetic variability and uncertainty on risks predicted with a
    pharmacokinetic model for chloroform. Toxicology 111, 289-303.

 9.  Altman, P. L., and Dittmer, D. S. (1961). Blood and other body fluids. Federation of
    American Society for Experimental Biology, Bethesda.

10.  Andersen, M. E., Krewski, D., and Withey, J. R. (1993). Physiological
    pharmacokinetics and cancer risk assessment. Cancer.Lett. 69, 1-14.

11.  Andersen, M. E., and Clewell, H. J. I. (1994). Gas uptake studies of deuterium
    isotope effects on dichloromethane metabolism in female B6C3F1 mice in vivo.
    Toxicology and Applied Pharmacology 128, 158-165.

12.  Andersen, M. E. (1995). Development of physiologically  based pharmacokinetic
    and physiologically based pharmacodynamic models for applications in toxicology
    and risk assessment. Toxicol Lett. 79, 35-44.

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13. Andersen, M. E., Clewell, H. J. I, and Frederick, C. B. (1995). Applying si,ulation
    modeling to problems in toxicology and risk assessment-a short perspective.
    Toxicology and Applied Pharmacology 133, 181-187.

14. Andersen, M. E., Clewell, H. J. I, Gearhart, J., Allen, B. C., and arton, H. A.
    (1997). Pharmacodynamic model of the rat estrus cycle in relation to endocrine
    disrupters. Journal of Toxicology and Environmental Health 189-209.

15. Andersen, M. E., Eklund,  C. R., Mills, J. J., Barton, H. A., and Birnbaum, L. S.
    (1997). A multicompartment geometric model of the liver in relation to regional
    induction of cytochrome P450s. Toxicol.Appl.Pharmacol. 144, 135-144.

16. Andersen, M. E., and Barton, H. A.  (1999). Biological regulation of receptor-
    hormone complex concentrations in relation to dose-response assessments for
    endocrine-active compounds. Toxicol.Sci. 48, 38-50.

17. Andersen, M. E., and Jarabek, A. M. (2001). Nasal tissue dosimetry-issues and
    approaches for "Category 1" gases: a report on a meeting held in Research Triangle
    Park, NC, February 11-12, 1998. Inhal.Toxicol 13, 415-435.

18. Andersen, M. E., and Sarangapani, R. (2001). Physiologically based
    clearance/Extraction models for compounds metabolized in the Nose:  An example
    with Methyl Methacrylate. Inhal.Toxicol. 13, 397-414.

19. Andersen, M. E., Green, T., Frederick, C. B., and Bogdanffy,  M.  S. (2002).
    Physiologically based pharmacokinetic (PBPK) models for nasal  tissue dosimetry of
    organic esters: assessing the state-of-knowledge and risk assessment applications
    with methyl methacrylate  and vinyl  acetate. Regulatory Toxicology and
    Pharmacology 36, 234-245.

20. Andersen, M. E. (2003). Toxicokinetic modeling and its applications in chemical
    risk assessment. Toxicol Lett. 138, 9-27.

21. Andersen, M. E. (2004). Computer demonstration of physiological-toxicokinetic
    models: demonstrating a computer model that simulates the estradiol (E2)-primed
    LH surge during proestrus in the rat. Toxicol.Lett. 138, 179-182.

22. Andersen, M. E., Gargas, M. L., Jones, R. A., and Jenkins, L.  J. (1980).
    Determination of the kinetic constants for metabolism of inhaled toxicants in vivo
    by gas uptake measurements. Toxicology and Applied Pharmacology 54, 100-116.

23. Andersen, M. E. (1981). Pharmacokinetics of inhaled gases and vapors.
    Neurobehavioral Toxicol.and Teratol. 3, 383-389.

24. Andersen, M. E. (1981). A physiologically based toxicokinetic description of the
    metabolism of inhaled gases and vapors: analysis at steady state. Toxicology and
    Applied Pharmacology 60, 509-526.

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25. Andersen, M. E. and Clewell, H. J. III. Pharmacokinetic interaction of mixtures.
    Dayton, O. H. Proceedings of the 14th Annual Conference on Environmental
    Toxicology , 221-238. 1983. AFAMRL-TR-83-099.
    Ref Type: Abstract

26. Andersen, M. E., and Keller, W. C. (1984). Toxicokinetic principles in relation to
    percutaneous absorption and cutaneous toxicity. In Cutaneous Toxicity (V. A. Drill,
    and P. Lazar, Eds.), pp. 9-27. Raven Press, New York.

27. Andersen, M. E., Clewell, H. J. I, Gargas, M. L.,  Smith, F. A., and Reitz, R. H.
    (1987). Physiologically-based pharmacokinetics and risk assessment process for
    methylene chloride. Toxicology and Applied Pharmacology 87, 185-205.

28. Andersen, M. E., Gargas, M. L., Clewell, H. J. L,  and Severin, K. M. (1987).
    Quantitative evaluation of the metabolic interaction between trichloroethylene and
    1,1-dichloroethylene in vivo using gas uptake methods. Toxicology and Applied
    Pharmacology 89, 149-157.

29. Andersen, M. E., MacNaughton, M. G., Clewell, H. J. L, and Paustenbach, D. J.
    (1987). Adjusting exposure limits for long and short exposure period using a
    physiological pharmacokinetic model. American Industrial Hygiene Association
    JournaUS, 335-343.

30. Andersen, M. E. (1988). Quantitative risk assessment and occupational carcinogens.
    Applied Industrial Hygiene 3, 267-273.

31. Andersen, M. E. (1988). Quantitative risk assessment and occupational carcinogens.
    Applied Industrial Hygiene 3, 267-273.

32. Andersen, M. E. (1991). Physiological modeling of organic chemicals. Annals of
    Occupational Medecine 35, 305-321.

33. Andersen, M. E., Clewell, H. J. L, and Gargas, M. L. (1991). Physiologically-based
    pharmacokinetic modeling with dichloromethane, its metabolite carbon monoxide
    and blood carboxyhemoglobin in rats and humans. Toxicology and Applied
    Pharmacology 108, 14-27.

34. Andersen, M. E., Krishnan, K., Conolly, R. B., and McClellan, R. O. (1992).
    Biologically based modeling in toxicology research. Arch.Toxicol Suppl 15, 217-
    227.

35. Andersen, M. E., Krishnan, K., Conolly, R. B., and McClellan, R. O. (1992).
    Mechanistic toxicology research and biologically-based modeling: partners for
    improving quantitative risk assessments. Chemical Industry Institute of Toxicology
    12, 1-8.

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36. Andersen, M. E., Mills, J. J., and Gargas, M. L. (1993). Modeling receptor-mediated
    processes with dioxin: Implications for pharmacokinetics and risk assessment. Risk
    Analysis 13, 25-36.

37. Andersen, M. E., and Krishnan, K. (1994). Physiologically based pharmacokinetics
    and cancer risk assessment. Environ.Health Perspect. 102 Suppl 1,  103-108.

38. Andersen, M. E., and Krishnan, K. (1995). Relating In Vitro to In Vivo Exposures
    with Physiologically Based Tissue Dosimetry and Tissue Response Models. In
    Animal Test Alternatives: Refinement, Reduction, Replacement (H. Salem, Ed.), pp.
    9-25. Marcel Dekker, Inc., New York.

39. Andersen, M. E., Clewell, H. J. L, and Frederick, C. B. (1995). Contemporary issues
    in toxicology. Applying simulation modeling to problems in toxicology and risk
    assessment - a short perspective. Toxicology and Applied Pharmacology 133, 181-
    187.

40. Andersen, M. E. (1995). Physiologically based pharmacokinetic (PB-PK) models in
    the study of the disposition and biological effects of xenobiotics and drugs.
    Toxicology Letters 82-83, 341-348.

41. Andersen, M. E., Clewell, H., Ill, and Krishnan, K. (1995).  Tissue dosimetry,
    pharmacokinetic modeling, and interspecies scaling factors. Risk Anal. 15, 533-537.

42. Andersen, M. E., and Krishnan, K. (1995). Relating in vitro to in vivo exposures
    with physiologically-based models of tissue dosimetry and tissue response. In
    Animal test alternatives:refinement, reduction and replacement. (H. Salem, Ed.), pp.
    9-25. Marcel Dekker, Inc., New York, Basel, Hong Kong.

43. Andersen, M. E., Birnbaum, L. S., Barton, H. A., and Eklund, C.  R. (1997).
    Regional hepatic CYP1A1 and CYP1A2 induction with 2,3,7,8-tetrachlorodibenzo-
    p-dioxin evaluated with a multicompartment geometric model of hepatic zonation.
    Toxicology and Applied Pharmacology 144, 145-155.

44. Andersen, M. E., Sarangapani, R.,  Gentry, P. R., Clewell, H. J. I, Covington, T. R.,
    and Frederick, C. B. (1999). Application of a hybrid CFD-PBPK nasal dosimetry
    model in an inhalation risk assessment: an example with acrylic acid. Toxicological
    Sciences 57, 312-325.

45. Andersen, M. E., and Sarangapani, R. (1999). Clearance concepts applied to the
    metabolism of inhaled vapors in tissues lining the nasal cavity. Inhalation
    Toxicology 11, 873-897.

46. Andersen, M. E., Sarangapani, R., Frederick, C. B., and Kimbell, J. S. (2000).
    Dosimetric adjustment factors for methyl methacrylate derived from a steady-state
    analysis of a physiologically based clearance-extrapolation model. Inhalation
    Toxicology 11, 899-926.

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47. Andersen, M. E., Sarangapani, R., Reitz, R. H., Gallavan, R. H., Dobrev, I. D., and
    Plotzke, K. P. (2001). Physiological modeling reveals novel pharmacokinetic
    behavior for inhaled octamethylcyclotetrasiloxane in rats. Toxicol Sci. 60, 214-231.

48. Andersen, M. E., and Dennison, J. E. (2001). Mode of action and tissue dosimetry in
    current and future risk assessments.  Science of the Total Environment 274, 3-14.

49. Andersen, M.E., Scimeca, J., Olin, S.S. (2005). Kinetic and mechanistic data needs
    for a human phsiologically based pharmacokinetic (PBPK) model for acrylamide:
    pharmacokinetic model for acrylamide. Adv Exp Med Biol 561,117-25. Review.
    PMID: 16438294  [PubMed - indexed for MEDLINE]

50. Anderson, M. W., Eling, T. E., Lutz, R. L., and Mattews, H. B. (1977). The
    construction of a pharmacokinetic model for the disposition of PCBs in the rat.
    Clinical Pharmacology and Therapeutics 22, 765-773.

51. Angelo, M. J., and Pritchard, A. B. (1987). Route to route extrapolation of
    dichloromethane exposures using a physiological  pharmacokinetic model. Drinking
    Water and Health  8, 254-264.

52. Apostolou, A. (1998). What's in a name: toxicokinetics, pharmacokinetics, or just
    kinetics? Regulatory Toxicology and Pharmacology 27, 82-83.

53. Arms, A. D. and Travis, C. C. Reference Physiological Parameters in
    Pharmacokinetic Modeling. Office of Health and Environmental Assessment. EPA.
    EPA/600/6-88/004,  1-1-7.16. 1988. Washington, DC., US EPA ( United State
    Environmental Protection Agency).
    Ref Type: Report

54. Asgharian, B., Wood, R., and Schlesinger, R. B. (1995). Empirical modeling of
    particle deposition in the alveolar region of the lungs: A basis for interspecies
    extrapolation. Fundamental and Applied Toxicology  27, 232-238.

55. Auton, M. J., and Woollen, B. H. (1991). A physiologically based mathematical
    model for the human inhalation pharmacokinetics of 1,1,2-trichloro-1,2,2-
    trifluoroethane. International Archives of Occupational and Environmental Health
    63, 133-138.

56. Auton, T. R., Ramsey, J. D., and Wollen, B. H. (1993). Modelling dermal
    pharmacokinetics  using in vitro data. Part II. Fluazifop-butyl in man. Human &
    Experimental Toxicology 12, 207-213.

57. Auton, T. R., Ramsey, J. D., and Woollen, B. H. (1993). Modelling dermal
    pharmacokinetics  using in vitro data. Part I. Fluazifop-butyl in the rat. Human &
    Experimental Toxicology 12, 199-206.

58. Aylward, L. L., Hays, S. M., Karch, N. J., and Paustenbach, D. J. (1996). Relative
    susceptibility of animals and humans to the cancer hazard posed by 2,3,7,8-

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    tetrachlorodibenzo-p-dioxin using internal measures of dose. Environmental Science
    and Technology 30, 3534-3543.

59.  Balaz, S., and Lukacova, V. (2000). A model-based dependence of the human
    tissue/blood partition coefficients of chemicals on lipophilicity and tissue
    composition. Quantitative Structure-Activity Relationships 18, 361-368.

60.  Ball, R., and Schwartz, S. L. (1994). Cmatrix: software for physiologically based
    pharmacokinetic modeling using a symbolic matrix representation system.
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61.  Banks, H.  T., Musante, C. J., and Tran, H. T. (1997). A dispersion model for the
    hepatic uptake and elimination of 2,3,7,8-tetrachlorodibenzo-p-dioxin. CRSC-
    TR97-29 1-24.

62.  Barton, H. A., Creech, J. R., Godin, C. S., Randall, G. M., and Seckel, C. S. (1995).
    Chloroethylene mixtures: pharmacokinetic modeling and in vitro metabolism of
    vinyl chloride, trichloroethylene, and trans-1,2-dichloroethylene in rat. Toxicology
    and Applied Pharmacology 130, 237-247.

63.  Barton, H. A., and Andersen, M. E. (1998). A model for pharmacokinetics and
    physiological feedback among hormones of the testicular-pituitary axis in adult
    male rats:  a framework for evaluating effects of endocrine active compounds.
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64.  Barton, H. A., and Clewell, H. J., Ill (2000). Evaluating noncancer effects of
    trichloroethylene:  dosimetry, mode of action, and risk assessment. Environ.Health
    Perspect. 108 Suppl 2, 323-334.

65.  Basak, S. C., Mills, D., Hawkins, D. M., and El-Marsi, H. A. (2002). Prediction of
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66.  Basak, S. C., Mills, D., Hawkins, D. M., and El-Marsi, H. A. (2003). Prediction of
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67.  Bass, L., and Keiding, S. (1988). Physiologically based models and strategic
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68.  Batterman, S., Zhang, L., Wang, S., and Franzblau, A. (2002). Partition coefficients
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69.  Baxter, L. T., Zhu, H., Mackensen, D. G., and Jain, R. K. (1994). Physiologically
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70.  Baxter, L. T., Zhu, H., Mackensen, D. G., Butler, W. F., and Jain, R. K. (1995).
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71.  Beck, B. D., Mattuck, R. L., Bowers, T. S., Cohen, J.  T., and OTlaherty, E. (2001).
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72.  Beliles,  R. P., and Totman, L. C. (1989). Pharmacokinetically based risk assessment
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73.  Beliveau, M., and Krishnan, K. (2000). Estimation of rat blood: air partition
    coefficients of volatile organic chemicals using reconstituted mixtures of blood
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74.  Beliveau, M., Tardif, R., and Krishnan, K. (2003). Quantitative structure-property
    relationships for physiologically based pharmacokinetic modeling of volatile
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75.  Benignus, V. A., Boyes, W. K., and Bussnell, P. J. (1998). A dosimetric analysis of
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76.  Bernillon, P., and Bois, F. Y. (2000). Statistical issues in toxicokinetic modeling: a
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78.  Birnbaum, L., Bischoff, K., Blancato, J., Clewell, H.,  Dedrick, R., Delp, M.,
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    Physiological parameter values for PBPK models. A report prepared by the
    international life sciences institute risk science institute. 1-137. 1994.  U.S.
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                                        88

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           APPENDIX A
LIST OF REVIEWERS AND OBSERVERS

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   Panel Peer Review of the Draft NCEA Document "Approaches for the Application of
 Physiologically Based Pharmacokinetic Models and Supporting Data in Risk Assessment"

                                   Arlington, VA
                               November 10-11, 2005

                                 List of Participants
Gregory M. Blumenthal, Ph.D.
GMB Consulting
Chapel Hill, NC

James V. Bruckner, Ph.D.
University of Georgia
Athens, GA

Janusz Z. Byczkowski, Ph.D., D.Sc., D.A.B.T.
Consultant
Fairborn, OH

Harvey Clewell
CUT Centers for Health Research
RTF, NC

Gary L. Ginsberg, Ph.D.
Connecticut Department of Public Health
Hartford CT, 06134
                                     A-l

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   Panel Peer Review of the Draft NCEA Document "Approaches for the
Application of Physiologically Based Pharmacokinetic Models and Supporting
                      Data in Risk Assessment"

                        November 10-11, 2005
Observer Registration
Name
Tammie Covington
George Cruzan
Rob DeWoskin
Paul Dugard
Jane Eickhoff
Kate Z. Guy ton
C. Eric Hack
Douglas Johns
Russ Keenan
Trevor Knowblich
Thomas McDonald
Robert McGaughy
Gary Mihlan
Beth E. Mileson
Pat Phibbs
Micah Reynolds
Bob Sonawane
Chadwick Thompson
David Bottimore
Amanda Jacob
Organization
ENVIRON International Corp
ToxWorks
US EPA/NCEA
HSIA
TOXCEL LLC
US EPA
TERA
US EPA/NCEA
AMEC Earth & Environmental, Inc.
Inside EPA News
Arysta LifeScience North America Corporation
US EPA/NCEA
Bayer CropScience
Technology Sciences Group, Inc.
BNA, Inc.
TOXCEL LLC
US EPA/NCEA
US EPA/NCEA
Versar, Inc.
Versar, Inc.
Nov. 10
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
                              A-2

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APPENDIX B
 AGENDA

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United States
Environmental Protection Agency
Panel Peer Review of the Draft NCEA Document "Approaches for
the Application of Physiologically Based Pharmacokinetic Models
and Supporting Data in Risk Assessment"
Hyatt Arlington
1325 Wilson Boulevard
Arlington, VA 22209
Agenda
THURSDAY, NOVEMBER 10, 2005

      8:30AM      Registration Begins

      9:OOAM      Welcome, Goals of Meeting, and Introductions
                  David Bottimore, Versar, Inc.

      9:10AM      Welcome
                  Bob Sonawane, EPA/NCEA

      9:15AM      Background on "Approaches for the Application of Physiologically Based
                  Pharmacokinetic Models and Supporting Data in Risk Assessment"
                  Chad Thompson, EPA/NCEA

      9:30AM      Chair's Introduction and Review of Charge
                  Gary Ginsberg, Chair

      9:40AM      Reviewer Roundtable of Overview Comments
                  Gary Ginsberg, Chair

      10:OOAM     Observer Comment Period

      10:20AM     Discussion Session  and Responses to Charge Questions (with break as
                  appropriate)

      12:00PM     Lunch

      1:OOPM      Discussion Session  and Responses to Charge Questions (continues, with
                  break as appropriate)

      4:15PM      Discussion of Public Comments

      4:30PM      Recap of Comments/Recommendations and Plans for Writing

      5:00PM      Adjourn
                                     B-l

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United States
Environmental Protection Agency
Panel Peer Review of the Draft NCEA Document "Approaches for
the Application of Physiologically Based Pharmacokinetic Models
and Supporting Data in Risk Assessment"
Hyatt Arlington
1325 Wilson Boulevard
Arlington, VA 22209
Agenda


FRIDAY, NOVEMBER 11, 2005

      9:OOAM     Welcome and Goals of Panel Writing Session
                David Bottimore, Versar, Inc.

      9:15AM     Panel Writing Session
                Gary Ginsberg, Chair

      11:45AM    Closing Remarks and Next Steps

      12:00PM    Adjourn
                                 B-2

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   APPENDIX C
CHARGE QUESTIONS

-------
   Panel Peer Review of the Draft NCEA Document "Approaches for the Application of
 Physiologically Based Pharmacokinetic Models and Supporting Data in Risk Assessment"

                                 November 10-11, 2005

                External Peer Review Panel Workshop Charge Questions

Purpose of the Document:
The  purpose  of the  draft document  is  to  describe  some  approaches for the  use of
physiologically-based pharmacokinetic (PBPK)  models  in risk assessment.   PBPK  models
represent an important class of dosimetry models that  are useful for predicting internal dose at
target organs for risk assessment applications.  Dose-response relationships that appear unclear
or confusing at the administered dose level can become more understandable when expressed on
the basis of internal dose of the chemical.  To predict internal dose level,  PBPK models use
pharmacokinetic  data  to  construct  mathematical representations  of biological  processes
associated with the absorption, distribution, metabolism, and elimination of compounds. With
the appropriate data, these models can  be  used to extrapolate across species and exposure
scenarios, and address various sources of uncertainty in risk assessments. This report addresses
the following questions: (1) Why do risk assessors need PBPK models; (2) How  can these
models be used in risk assessments; and (3) What are the characteristics of acceptable PBPK
models for use in risk assessment?

Workshop Purpose:
The purpose  of the workshop is to carry out an independent external peer review of the draft
framework document entitled,  "Approaches for the Application  of  Physiologically  Based
Pharmacokinetic Models and  Supporting Data in Risk Assessment."  Independent external
experts in PBPK modeling and risk assessment have been invited as panelists to provide review
and comment on the document, as well as address the particular charge questions (see below).
Further, we ask that you consider and provide remarks on the public comments. We hope your
feedback will improve the usefulness and clarity of the final document.

Questions:
1. What is the panel's overall view of the thoroughness, clarity, and applicability of this report?

2. Are the graphical examples explaining various concepts clear and helpful? If not, do you have
suggestions for improving clarity?

3. Does this document  reasonably describe the major  potential uses and advantages of PBPK
modeling in risk assessment, are there risk assessment applications of PBPK modeling that have
not been addressed?

4. Are there improvements to the document that would substantially help risk assessors who are
less familiar with PBPK modeling better understand the  potential strengths and limitations of
PBPK modeling?
                                          C-l

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5.  Do you think that PBPK modelers  outside the EPA, and those less  familiar with risk
assessment practices, would find this document useful as far as fostering the kinds  of research
and model development useful for risk assessment?

6.  Are there  current research needs and data gaps not highlighted in this report  that would
improve the utilization of PBPK models in risk assessment?

7. Are there future reports that you could envision which would compliment or expand upon the
topics covered in the current document? For example,  would a report focused on dosimetry
models for reactive gases be helpful?  Or a report focused on extrapolation across life stages
using PBPK modeling?

8. Do you have additional comments/suggestions that were not covered in the above questions?
                                        C-2

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        APPENDIX D
POWERPOINT PRESENTATIONS

-------
            David Bottimore
Welcome, Goals of Meeting, and Introductions
                 D-l

-------
                          Chad Thompson, EPA/NCEA
Background on "Approaches for the Application of Physiologically Based Pharmacokinetic
                 Models and Supporting Data in Risk Assessment"
                                  D-2

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            APPENDIX E
WRITTEN COMMENTS FROM REVIEWERS

-------
                 PRE-MEETING COMMENTS SUMMARY REPORT
  Panel Peer Review of the Draft NCEA Document "Approaches for the Application of
Physiologically Based Pharmacokinetic Models and Supporting Data in Risk Assessment'
                                  Prepared for:
                       U.S. Environmental Protection Agency
                    National Center for Environmental Assessment
                               808 17th Street, N.W.
                              Washington, DC 20074
                                  Prepared by:
                                   Versar, Inc.
                                6850 Versar Center
                            Springfield, Virginia 22151

                            Contract No. C68-C02-061
                                  Task Order 89
                                   Reviewers:
                           Gregory M. Blumenthal, Ph.D.
                             James V. Bruckner, Ph.D.
                     Janusz Z. Byczkowski, Ph.D.,D.Sc.,D.A.B.T.
                                Harvey J. Clewell
                              Gary L. Ginsberg, Ph.D.
                                November 9, 2005

        Specific Comments Section Revised with Additions on November 16, 2005
                                       E-l

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                        TABLE OF CONTENTS


I.   INTRODUCTION	3
II.   CHARGE TO THE PEER REVIEWERS	4
III.  GENERAL COMMENTS	6
IV.  RESPONSE TO CHARGE QUESTIONS	9
V.   SPECIFIC OBSERVATIONS	25
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I.  INTRODUCTION

The objective of this Task Order is to perform a panel peer review of the draft EPA document,
developed by the National Center for Environmental Assessment (NCEA), entitled "Approaches
for the Application of Physiologically Based Pharmacokinetic Data and Models in Risk
Assessment." Pharmacokinetics is the study of the biological processes that affect the
absorption, distribution, metabolism and excretion of a substance, such as a drug or toxicant.
Pharmacokinetic data and models have important applications in risk assessment. Given
sufficient physiological and pharmacokinetic data, physiologically based pharmacokinetic
(PBPK) models, which mathematically represent pharmacokinetic processes based on known
biological properties, can be developed. Such models can then predict an internal dose (generally
blood level or target tissue level) that would result from different exposure regimens or in
different species. Pharmacokinetic data and PBPK models can also support quantitative
estimates of intraspecies internal dose variability.  Examples include the variability in
physiological values (e.g., tissue volumes or fluid flows), or in metabolic capacity associated
with the presence of enzyme polymorphisms.  Predicted internal dosimetry from PBPK models
can also be used with benchmark dose or other empirical approaches for dose-response analysis.

The objective of this document is to provide a description of approaches for using PBPK data
and models in human health risk assessment. The document primarily focuses on the evaluation
and use of these models in predicting internal doses at target organs for risk assessment
applications, based on EPA guidelines. The document assumes that risk assessors are familiar
with the basic concepts of PBPK modeling, and that model developers are familiar with basic
concepts of risk assessment. Hence, exhaustive descriptions of PBPK modeling and/or risk
assessment methods are not presented. However, brief descriptions of both disciplines, as well
as appropriate references to secondary review articles and reports, are included in the document.
                                          E-3

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II.     CHARGE TO THE PEER REVIEWERS

Purpose of the Document:
The purpose of the draft document is to describe some approaches for the use of physiologically-
based pharmacokinetic (PBPK) models in risk assessment. PBPK models represent an important
class of dosimetry models that are useful for predicting internal dose at target organs for risk
assessment applications.  Dose-response relationships that  appear unclear or confusing  at the
administered dose level can  become  more understandable when expressed on the basis  of
internal dose of the chemical.  To predict internal dose level, PBPK models use pharmacokinetic
data  to construct mathematical  representations of  biological  processes associated  with the
absorption, distribution, metabolism, and elimination of compounds.  With the appropriate data,
these  models can be used to extrapolate  across species and exposure scenarios, and address
various sources  of uncertainty  in  risk assessments.   This report addresses  the following
questions: (1) Why do risk assessors need PBPK models; (2) How can these models be used in
risk assessments; and (3) What are the characteristics of acceptable PBPK models for use in risk
assessment?

Workshop Purpose:
The purpose of the workshop is to carry out an independent external peer review of the draft
framework document entitled,  "Approaches for the Application of Physiologically Based
Pharmacokinetic Models and Supporting Data in Risk Assessment." Independent external
experts in PBPK modeling and risk assessment have been invited as panelists to provide review
and comment on the document, as well as address the particular charge questions (see below).
Further, we ask that you consider and provide remarks on the public comments. We hope your
feedback will improve the usefulness and clarity of the final document.

Questions:
1. What is the panel's overall view of the thoroughness, clarity, and applicability of this report?

2. Are the graphical examples  explaining various concepts clear and helpful? If not, do you have
suggestions for improving clarity?

3. Does this document reasonably describe the major potential uses and advantages of PBPK
modeling in risk assessment, are there risk assessment applications of PBPK modeling that have
not been  addressed?

4. Are there improvements to the document that would substantially help risk assessors who are
less familiar with PBPK modeling better understand the potential strengths and limitations of
PBPK modeling?

5. Do you think that PBPK modelers outside the EPA, and those less familiar with risk
assessment practices, would find this document useful as far  as fostering the kinds of research
and model development useful for risk assessment?

6. Are there current research needs and data gaps not highlighted in this report that would
improve the utilization of PBPK models in risk assessment?
                                          E-4

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7. Are there future reports that you could envision which would compliment or expand upon the
topics covered in the current document? For example, would a report focused on dosimetry
models for reactive gases be helpful? Or a report focused on extrapolation across life stages
using PBPK modeling?

8. Do you have additional comments/suggestions that were not covered in the above questions?
                                          E-5

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III.    GENERAL COMMENTS

Gregory M. Blumenthal
The report is relatively thorough and applicable, although it presupposes that the readers already
have a good grasp of such pharmacokinetic concepts as "first-pass effect"; zero-order, first-order,
and second-order metabolic processes; and metabolic saturation. The clarity of this report to EPA
scientists and risk assessors without a thorough background in these pharmacokinetic concepts
may be severely limited.

An additional minor improvement could be made by heavily emphasizing the term "dose
metric". This massively useful concept is the key to the applicability and utility of PBPK models
in risk assessment and its importance cannot be overstated.

In general, the graphical examples are appropriate and useful. However, the authors should
provide text for each figure, even if it repeats material in the main text.

Innovation in computational biology and its application to risk assessment is an ongoing process.
This report should be envisioned as a living document, with room to expand as novel methods
and applications arise. Key among the areas with explosive growth occurring are acute
dosimetry, point-of-contact dosimetry, whole-life and developmental modeling,  maternal-fetal
dosimetry, and metabolic network modeling to identify sensitive subpopulations.

James V. Bruckner

Janusz Z. Byczkowski
The   reviewed   document "Approaches  for the  Application of  Physiologically  Based
Pharmacokinetic (PBPK) Models and Supporting Data in Risk Assessment" seems to be the first
comprehensive publication that systematically  reviews application of PBPK modeling in risk
assessment.  The  authors of this document should be commanded for preparing thorough, clear
and well organized report.

This document reads smoothly. It clearly states the scope and intent of the report in the
introductory section. The PBPK model applications, issues and potential pitfalls are presented
transparently and discussed appropriately. The "boxes", tables and figures are easily readable
and informative. The schematic diagrams are appropriate and well designed.  The rest of the
figures adequately illustrate the issues discussed in the text.  However, because the mathematical
equations in the text are kept to the absolute minimum, it would be informative if an example of
the computer codes, for instance of the "classic" Ramsey and Andersen's PBPK  model, was
provided in an appendix to the document. The extent of literature review, supplemented by the
list of all pertinent references in the Appendix 2, seems to be adequate and complete - up to the
beginning of the year 2003. An exhaustive list of partition coefficients and metabolic constants
for PBPK modeling of many classes of chemical compounds is provided in the Appendix 3.

While this document is addressed to risk assessors rather than pharmacokineticists, it contains
many clarifications and suggestions that may be useful in developing both PBPK and
                                          E-6

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pharmacokinetic models in general. For example, the Appendices provide extremely useful for
pharmacokineticist compilation of references and parameters.

A public discussion, initiated over the Internet, proved that there is a genuine interest in this
report among the international experts from both fields - pharmacokinetics and risk analysis
(involved were members from three mailing lists: PharmPK < http://www.boomer.org/pkin/ >,
Risk Anal , and DRSG
). The participants of this discussion emphasized that in addition to
physiological modeling of pharmacokinetics, there is a need for "...pharmacodynamic and
disease progress modelling to get the full picture..."

This is also this reviewer's belief, that although this document represents an opportunity for the
Agency and a good beginning of the process to depart from defaults in order to base its chemical
risk assessment paradigm on physiologically realistic and scientifically defensible methodology,
much more work needs to be done. Particularly, linking the internal dosimetry with the effects of
environmental contaminants represents a real challenge as it needs  further research. Even though,
the section 4.4 of this report attempts to address the issue of linkage of PBPK to
pharmacodynamic models, it also demonstrates that still additional science is needed to be able
to predict and quantify the health effects of many classes of chemical compounds.

If the U.S. EPA chose to continue exploring this trend, this reviewer would suggest that the
future report by the Agency, perhaps entitled "Approaches for the Application of Physiologically
Based Pharmacodynamic (PBPD) Models and Supporting Data in Risk Assessment", may be
essential in order to stimulate research in the PBPD, to summarize the endeavor so far, and to
support progress in this field.

Harvey J. Clewell

Gary L. Ginsberg
This is a well written document, primarily of use to those experienced in pharmacokinetics,
PBPK modeling and risk assessment.  It makes many cogent points, describing both general
principles and special considerations needed to successfully develop, evaluate and  apply PBPK
models.  It does not provide a great deal of detail in any area which makes the document easier to
read cover to cover, and get an overview of the subject matter. However, the lack of details and
specific case examples prevents this from being a PBPK "cookbook" which one could use as a
stand alone resource to actually construct a PBPK analysis. One would already have to know
about modeling software, model structure, mathematical relationships, optimization/backfitting
techniques, evaluation techniques (e.g., residuals calculations, mass balance calculations), and
probabilistic techniques (Monte Carlo, Bayesian) to really make use of this document. However,
for those in the field or at EPA who are applying PBPK to risk assessment, this should be a
helpful set of principles. To some extent, the document has the potential to standardize modeling
practice,  not in terms of which parameters to use, but in terms of basic approaches and
applications.

The document focuses upon the use of PBPK modeling to address certain extrapolation issues in
the setting of reference values and slope factors: cross-species, dose route, high dose to low dose,
                                          E-7

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temporal adjustments, and degree of variability. However, it doesn't provide anything of
substance on several other uses of PBPK modeling: across age group extrapolations; in utero
modeling; variability due to genetic polymorphisms, lactational models, etc. Additionally, the
document does not put PBPK modeling into an overall context of pharmacokinetic analysis in
which classical one and two compartment models have been used for many years to provide
adequate description of chemical fate, and which have been applied to risk assessment (e.g.,
methyl mercury, dioxin).

The appendices are a useful compilation of equations that can be used to derive parameter inputs
if empirical data are not available. It is also helpful to have parameter data sheets for a variety of
xenobiotics. However,  these parameter data sheets are not optimally useful because the model
structure for which these values were derived is not specified. In some cases, references are
provided so that the reader has a head start if he/she needs to develop a model for that analyte.
However, in many cases references are not provided.

In spite of the aforementioned, the document does a good job of introducing and providing
perspective on many important topics. In a number of cases, it doesn't go far enough. For
example, it introduces the concept that PBPK modeling can be used to help interpret
biomonitoring data.  This is an emerging and essential application for PBPK modeling because it
offers the opportunity to convert a urinary or blood biomarker level into an exposure dose from
which key questions about population and individual risk may begin to be assessed. The
document may be enhanced by  a more complete description of this application including its
methodological and interpretative issues.

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IV.    RESPONSE TO CHARGE QUESTIONS
 1.  What is the panel's overall view of the thoroughness, clarity, and applicability of
     this report?
Gregory M. Blumenthal
The report is relatively thorough and applicable, although it presupposes that the readers already
have a good grasp of such pharmacokinetic concepts as "first-pass effect"; zero-order, first-order,
and second-order metabolic processes; and metabolic saturation. The clarity of this report to EPA
scientists and risk assessors without a thorough background in these pharmacokinetic concepts
may be severely limited.

James V. Bruckner

Janusz Z. Byczkowski
From this reviewer's point of view, this is the first comprehensive publication that systematically
reviews application  of PBPK modeling in risk assessment. The authors of this document should
be commanded for preparing thorough, clear and well organized report.

Harvey J. Clewell
In general, I was very impressed with the thoroughness and clarity of the report.  It is well
written, easy to read, and covers most of the important issues for applying PBPK modeling in
risk assessment. There are, however, a few additional areas that should be discussed in the
report:

- Sections 2.5 and 2.6 should include multiple references to the IPCS document on chemical
specific adjustment factors (CSAFs) in order to clarify the relationship between the model
applications discussed in these sections with the description of the CSAF approach in the IPCS
document.

- Section 2.5.5 (p. 2-11) incorrectly states that "The IVF of 10 conventionally used in RfC
dereivation implies that for the same level of response or nonresponse, the potential doses among
individuals may differ by as much as - but not more than - an order of magnitude." This is a
common misunderstanding. In fact, the IVF of 10 is associated with the potential ratio of the
equitoxic doses for an average individual as compared to a sensitive individual. Therefore, an
IVF of 10 is consistent of a range of equitoxic doses across the population of about two orders of
magnitude.

- The first paragraph in Section 3.3 is incorrect: a mass-balance differential equation consists of a
series of rate terms (not clearance terms), and the units are mass per time (not volume per time).
These rate terms are often calculated as the product of a clearance (in units of volume per time)
and a concentration (in units of mass per volume). Also, the uptake of a chemical in systemic
circulation by a tissue is proportional to its activity gradient, where the tissue: blood relationship
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of activities is related to the concentration difference by the partition coefficient. It just confuses
things to mention Pick's law of diffusion since the transport is generally blood-flow limited, not
diffusion limited.

- Section 3.5 should include a description of the process of internal verification of the model
code. I disagree completely with the suggestion in the document that the risk assessor is not
responsible for ensuring that the computer implementation of the model is free from error.
Curiously, the summary (Section 3.9) actually includes considerations relevant to internal
verification (in the second to last bullet) that are not mentioned at all in this section.

- Section 3.6 should include a discussion of the necessity of evaluating the model specifically for
the dose metric that will be used in the risk assessment. For example, if the validation of the
human model is based solely on parent chemical kinetic data, it may not be valid at all for a
metabolism dose metric.

- Section 4.3 should include (perhaps between sub-sections 4.3.5 and 4.3.6,  a much more
detailed explanation of the alternative approaches for calculating a dose metric for  a repeated
exposure, as discussed in Clewell et al. (2002):

       - Calculation of total  dose metric over entire study divided by length of study
       - Single dose estimate (total AUC for single dose adjusted for exposure frequency)
       - Steady-state estimate (subtraction of consecutive periods after steady state or periodicity
       is achieved)

Gary L. Ginsberg
For the most part, this is a clear presentation of how PBPK modeling can be used in cancer and
non-cancer risk assessment, building a logical progression from basic uses and of PBPK
modeling in risk assessment (Chapter 2) to the ingredients, design and implementation of PBPK
models (Chapter 3), to evaluation of PBPK models once constructed (later in Chapter 3), and
finally to briefcase examples of PBPK model use in risk assessment  (Chapter 4).  The report
provides especially useful sections on parameter estimation (Section 3.4), model evaluation
(Section 3.6), constructing models in data-poor situations (Section 3.8).   Any risk assessment
document is likely to leave out some application or question. In the case of this document there
are several important cases which are largely unexplored but which are topics of considerable
interest to risk assessors:  1) Extrapolation across age groups and for in utero and lactational
exposure; 2) Extrapolation to those with genetic polymorphisms; 3) Use of PBPK modeling for
interpreting human biomonitoring data; 4) Use of simpler compartmental models to address risk
assessment questions. Further, other topics are treated incompletely such as chemical mixtures
(covered to some extent in Section 4.3.9) and how models differ for different types of
xenobiotics (most of discussion is based upon non-reactive volatile organics; Figure 3-1 shows
different models for different chemicals but doesn't explain whats going on).

While the document provides excellent background information and general principles, it is not
detailed enough to constitute a cookbook or user's manual for PBPK modeling. As such, it is
most useful for those already in the field to ensure consistency of approach.  It is also perhaps a
way  for non-modeler risk assessors to become better able to understand and interpret the output
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of PBPK models.  On the last point, it may be very useful to include a section on "Interpreting
the Output of PBPK Models." This could help the generalist and the modeler alike.

As described in the ES and Introduction, this document relies on experience with water-insoluble
gases and some non-volatile organics. The explanation given is that PBPK modeling has thus far
focused on these types of chemicals. There is a wide range of PBPK models from dioxins/PCBs
to pesticides, to inorganics (metals, perchlorate) to VOCs.  It would be good to start the
document off with a broad rather than narrow description of PBPK uses thus far and provide
descriptions of how PBPK modeling may differ for chemicals with very different properties
(e.g., metals, bone or binding sites may be important to disposition; lipid binding and metabolism
less important; lipophilic slowly metabolized organics (PCBs) - lipid partitioning important
determinant of fate; perchlorate - transport via symporter, etc. etc.).
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 2.  Are the graphical examples explaining various concepts clear and helpful? If not, do
     you have suggestions for improving clarity?
Gregory M. Blumenthal
In general, the graphical examples are appropriate and useful. However, several minor changes
might be made to improve the clarity of some of the examples:

Figure 2-1 - Use bold type for the axis labels of the graphs in order to highlight the role of the
dose metric (rate of amount metabolized, in this case) in linearizing the dose-response function.

Figure 2-2 - Shade the area under the curves to emphasize the AUC as dose metric.

Figure 3-1 - More closely associate each diagram (A, B, C, D) with its respective literature
citation.

Figure 3-2 - Provide text for the figure, even if it repeats material in the main text.

Figure 3-3 - Provide text for the figure, even if it repeats material in the main text. Additionally,
note that this is just an illustration and not real data from any particular model.

Figure 3-4 - Provide text for the figure, even if it repeats material in the main text. Additionally,
some indication of how many Monte Carlo iterations are involved may be useful.

Figure 4-1 - If the parameters are not available, you want benchwork to precede model
development, if at all possible.

Figure 4-2 - Use the phrase "dose metric" whenever possible.

Figure 4-4 - Shade the area under the curves to emphasize the AUC as dose metric.

Figure 4-5 - Shade the area under the curves to emphasize the AUC as dose metric.

Figure 4-6 - Replace the diagonally-oriented curly brackets for the interindividual variability
factor with horizontally-oriented  square brackets at the x-axis.

Figure 4-8 - Add a note that this  is an illustration, not actual data from a specific chemical.

James V. Bruckner

Janusz Z. Byczkowski
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The "boxes", tables and figures are easily readable and informative. The schematic diagrams are
appropriate and well designed. The rest of the figures adequately illustrate the issues discussed in
the text.

Harvey J. Clewell
Figures 2-2 and 4-5 give a misleading illustration of a human equivalent exposure calculation or
temporal adjustment. The comparison shown, which appears to accumulate the AUC over just
24 hours, would only be appropriate if the animals/subjects were exposed only for a single day
and were sacrificed/tested at exactly 24 hours.  The comparison that appears to be intended, i.e.,
adjustment to continuous  exposure, should either continue to accumulate the AUC after the 24-
hour exposure until the chemical is completely cleared, or should calculate an AUC for
consecutive 24 hour time-points after steady-state is achieved.

Figure 3-2, panel B should show an inhalation profile of the correct duration rather than an oral
profile. I would suggest a case where the end-exposure concentration is overpredicted by an
order of magnitude and the predicted post-exposure concentrations decrease much too rapidly so
they cross through the data.

Figure 3-3 should not include a parameter sensitivity as high as 2 without some additional
discussion explaining that, in actual practice, it is unusual for a PBPK model to have a parameter
sensitivity much greater than zero in  absolute value, and that such a condition is a cause for
concern since it indicates  amplification of input error (Allen and Clewell 1996).

Figure 4-2 should be revised to eliminate any extensive variables (amounts/quantities).  Only
intensive variables (concentrations, AUCs, amounts produced per unit volume) should be
considered for use as dose metrics.

On p. 4-12, there is a reference to Figure 2-2 indicating that the model accurately predicts the
observed kinetics  in the human, but there is no data shown in the Figure.

Figure 4-5 shows  rat and human panels, but the caption and text refers to both panels as being for
rats.

Gary L. Ginsberg
The figures have good content and purpose and are generally simple enough for the casual reader
to learn from. The following are some points for improving the figures:

Figure 2-2 (pg 2-6)- For direct interspecies comparison of kinetics, it would be good to show the
human 6 hr exposure curve at 50 ppm and then show in legend the  concentration needed in
humans for 6 hrs to match the rodent AUC from 50 ppm.  Then the use of PBPK models to
simulate different scenarios (continuous exposure) with the bottom chart, along with different
species, would be clearer.

Section 2.5.1 - a graphic from the RfC document or elsewhere showing different modeling
approaches for different types of gases/particles would be helpful.
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 Figure 3-1 - this is a potentially important figure and can set the stage for comparison of PBPK
modeling approaches for different types of chemicals.  However, the text and legend fall short of
this treatment and it makes one wonder about the point of the figure. Also, the "D" part of the
figure is cramped and difficult to read.

Section 3.4.2 - Partition coefficients - a graphic of vial equilibration technique and how one gets
to tissue:blood from separate measurement of tissue:air and blood:air. In fact the text does not
talk about this common approach for deriving tissue:blood.

Figure 3-2-pg 3-18- can the figures be represented on a linear scale to more clearly see
goodness of fit or at least discuss the issue of log vs linear y axis.  The text that goes with this
figure (3-18 bottom) promises to show how adequacy of model structure can be judged from the
graph.  However, the text states that the poor fit in Fig 3-2B may be due to either inadequate
structure or problems with model parameters. So this example falls short of teaching us how to
judge structural issues from the data. On top of that, it appears that the data and  models in A,B,
and D are describing  a steady state situation in which chemical is continuously taken up and
eliminated, followed by a break point wherein chemical is no longer taken up but just eliminated.
Figure B appears to show a much different uptake pattern (bolus) and may be off not because of
model  structure but because the exposure parameters are wrong.

Figure 3-4 - it's a good figure.  An enhancement would be to show how an input distribution
(e.g., bimodality in metabolic enzymes) can be transmitted thru to the distribution of AUC
results.

Figure 4-2 - very busy, not easy to follow. Perhaps remove the Amount-^quantity in tissue
boxes under parent and metabolite, and the Average  -^ mg formed boxes under rate of
production.  Also need a new box under Unknown-^AUC--^ "Evaluate Correlations to Tox
Response".  Also the bottom right box should be in units of per tissue volume.

Figure 4-3 - should the toluene parent compound plot have more of an upward bend to it to
match saturation above 500 ppm?

Page 4-12 - 2nd para - discussion of Figure 2-2 which allegedly demonstrates predictiveness of
a toluene rat model for humans. However, Figure 2-2 has no data points, only simulated lines, so
one cannot tell good the fit is or the predictiveness of the model.

Figure 4-5 - heading for lower figure should be rat and break point in upper figure when
concentration starts decending should be 4 hr, not later.  Also, the conversion from 4 hr to 24 hr
dose for equivalent AUC is not quite linear - it would be helpful to point out why the lower dose
over longer time is somewhat less efficient (is there saturation at the higher dose?).
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Figure 4-6, Page 4-15 - nicely laid out figure.  However, its important to indicate that 99th to
50th can also be used to indicate size of variability factor.  The figure represents the degree of
intraspecies variability as being determined on the basis of the 95th to 50% comparison.
However, some have used 99th % as another upper bound for evaluating population variability.
This may be important to ensure that low percentage subgroups which have distinct
pharmacokinetics are not diluted out of the analysis. (Ginsberg, et al. 2001 - ALDH analysis
which showed that a metabolic polymorphism in an ethnic minority (Asians)  that leads to much
less acetaldehyde detoxification and greater risk of ethanol toxicity could be overlooked when
that population is averaged in the general pop. To see this subgroup in variability statistics, one
needed to compare 99th to 50th, not 95th.)
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   3.  Does this document reasonably describe the major potential uses and advantages of
      PBPK modeling in risk assessment, are there risk assessment applications of PBPK
      modeling that have not been addressed?
Gregory M. Blumenthal
The use of PBPK models in quantifying age-dependent pharmacokinetic adjustments, allowing
departure from ADAFs for mutagenic carcinogens, should also be addressed.

James V. Bruckner

Janusz Z. Byczkowski
Yes. This document seems to be reasonable, thorough and complete.

Harvey J. Clewell
I think the document adequately describes the major potential uses and advantages of PBPK
modeling in risk assessment.

Gary  L. Ginsberg
Overall, the answer is yes. See answer to #1 for comments on what applications have not been
fully covered.
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 4.  Are there improvements to the document that would substantially help risk
     assessors who are less familiar with PBPK modeling better understand the
     potential strengths and limitations of PBPK modeling?
Gregory M. Blumenthal
A chapter with a basic introduction to critical pharmacokinetic concepts is necessary.

James V. Bruckner

Janusz Z. Byczkowski
Yes. This reviewer would suggest to include an example of source codes for a PBPK model, for
instance, codes of the "classic" Ramsey and Andersen (1984) PBPK model for styrene.

Harvey J. Clewell
Perhaps a few case-studies where the strengths and limitations of a particular model used in a
risk assessment were evaluated.

Gary L. Ginsberg
As mentioned above, a section on interpretation of model output could be helpful for non-
modeling risk assessors in reviewing the results of a modeling exercise. Areas of interpretation
can be confidence in the model (extent to which it is calibrated and tested against external
datasets, goodness of fit, number of parameters needing back-fit), more on sensitivity analysis
(what is level of confidence and key uncertainties in the most sensitive parameters; what are
reasonable bounds for these parameters; how much might they influence the assessment), more
on non-linearities and how they affect results, etc.

The document could do a better job of educating the reader on the source of toxicokinetic non-
linearities. Michaelis-Menten kinetics are not described, perhaps because this is too technical a
subject? There are numerous opportunities to provide background on non-linear kinetics,
whether due to saturable absorption, binding, metabolism, or excretion (e.g., Section 3.4.3 -
biochemical parameters).

The RfC (1994) methodology comes up in several locations.  One clear presentation of the role
of PBPK modeling within the RfC approach would be useful, especially in terms of
simplications taken that are not normally used in full PBPK modeling assessments.
Additionally, it would be good to explain some of the differences between reactive gas and non-
reactive gas models (local vs. systemic effect).

Other improvements would be to consolidate and clarify some aspects of Section 2. Specifically:
Page 2-12 to 2-15 - RfD Development Section - much of this material is redundant with RfC
section. It would be more efficient to combine the bulk of the RfC and RfD sections into one
general principles  section and then have subsections that discuss any techniques specific to the
inhalation or oral dose route.
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Also: Page 2-15 - the box - has essentially the same rules as in the RfD box, but here they are
worded differently - any reason for this? It can confuse the reader. Also, left out of Box 2-3 is
PBPK use in duration adjustment. There are needs for duration adjustment in oral studies (e.g., 5
day a week gavage dosing to 7 day per week continuous exposure in drinking water). The RfD
section should discuss the utility of PBPK models to extrapolate from one exposure scenario in
animals (e.g., bolus dosing which may involve saturation  of activation or detoxification systems)
to a more continuous exposure scenario in humans to achieve the same AUC dose.

Also, Page 2-18 - Section 2.8 - This section should come before the RfD/RfC sections.  PBPK
models, at their most basic and primary level, are an advanced form of exposure assessment.
The improved exposure metric is then more effectively used in non-cancer and cancer risk
assessment. Therefore, the exposure assessment application should come before the risk
assessment discussion.  This section brings up an important and evolving use of PBPK modeling
- conversion of biomonitoring data to exposure doses and application to risk assessment. This
merits considerably more attention in this document. There are several case studies (dioxin,
mercury, PFOA, phthalates) where this approach is used.

The differences between flow-limited and diffusion-limited kinetics as introduced on Page 3-3,
bottom should be spelled out more fully.

Page 3-17, 2nd full para - near the end - "PBPK modeling is not a fitting exercise" - this is
debatable since some parameters are fitted to an initial dataset.  Better to state that since  many
parameters are not fitted,  can't expect perfect match to the underlying PK dataset.

There can be more discussion of limitations of fitting procedures (e.g., metabolic constants)
wherein one may have a fairly insensitive parameter and so the parameter estimate is still fairly
uncertain.  This may  affect the predictiveness of the model since the uncertain parameter may not
be very reliable for different conditions of exposure.  It would be good to describe a bit more the
iterative approach and use of multiple datasets to optimize the fit.  Finally, the situation where
there are multiple backfitted parameters (typically an absorption coefficient and metabolic
constants)  should be described as being particularly uncertain in terms of the optimal value of
the individual parameters.

Same para on page 3-17 - where does the 2 SD rule for evaluating results come from?What other
choices are there? An option is to use best model fit when considering multiple underlying
datasets and iterative recalibration.

Issue of model calibration vs. validation (e.g., Page 3-19) - its confusing to say that a model
which has been cross-checked against external datasets isn't really "validated" but is only
"calibrated".  Calibration signifies the adjustment of a model to match an underlying
observation, not an independent test of the model predictiveness (without adjustment) against a
new dataset. A different term is needed to described this  activity and the confidence it provides.
Perhaps "confirmation of predictive ability" for certain types of data.

More on model calibration - Page  3-21 - top section - should discuss case where underlying PK
datasets disagree with one another. A single model will not be able to simulate both; must
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decide which underlying dataset to trust more or consider 2 different versions of the model - one
that fits one dataset optimally and the other fits the 2nd dataset.

Need for peer-reviewed model: Page 4-1 - 2nd bullet and page 4-3 - requirement that a PBPK
model must be peer-reviewed before being used in risk assessment seems excessive, or at least
should be caveated to state that the applications for which a model must be peer-reviewed to be
considered for risk assessment. The point of this guidance is to describe the principles for
developing and evaluating a model to enable it to be used in risk assessment. If one follows
these principles the need for external peer review prior to the risk assessment is diminished.
Perhaps it is USEPA policy that the model must first be peer reviewed to be used in deriving any
value that goes onto IRIS. The best approach for this document may be to say that the policy at
certain agencies or for certain risk applications may be to peer review a model prior to use.

Description of PBPK for Mixtures - Page 4-21 - this section would be helped by citing
examples where mixtures were analyzed with PBPK models and how this was accomplished
(cite work by Ray Yang), and by expanding the description of the HI approach. This appears to
be a simple addition approach to His for multiple contaminants in a mixture in which the PBPK
model is used to adjust the ingredient concentration as influenced by the other chemicals. The
description should include how chemicals may interact (at metabolic enzymes or binding sites)
and how this can be simulated in a model. Further, the description at the top of Page 4-22 is
confusing due to the word "POD". I recommend replacing it with "environmental exposure
concentration".

As described above, it would be good to relate PBPK to the classical PK frame of reference.
This is only done in passing in this document.  However, risk assessors will come across one
compartment models from time to time (e.g., mercury, dioxin, chlorpyrifos) and will want to be
able to distinguish these from pBPK and why is PBPK preferable (or are there cases where one
compartment is just fine for RA?).
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    5.  Do you think that PBPK modelers outside the EPA, and those less familiar with risk
       assessment practices, would find this document useful as far as fostering the kinds of
       research and model development useful for risk assessment?
Gregory M. Blumenthal
This document excels at describing the role that PBPK modeling plays in EPA risk assessment
practices.  This should greatly assist  non-EPA PBPK modelers  in developing and  presenting
models that serve EPA risk assessment purposes.

James V. Bruckner

Janusz Z. Byczkowski
Yes. While  this document is  addressed to risk assessors rather than pharmacokineticists,  it
contains  many  clarifications  and suggestions  that may be useful  in developing PBPK  and
pharmacokinetic models in general. For example, the Appendices provide extremely useful for
pharmacokineticists compilation of references and parameters. A public discussion, initiated over
the Internet,  proved that there is a genuine interest in this report among the international experts
from both fields - pharmacokinetics and risk analysis.

Harvey J. Clewell
Yes, I think the document is particularly valuable for those who would like to develop  a PBPK
description for a chemical that would be of value to the agency for a risk assessment.

Gary L. Ginsberg
As stated above, the document is technical but fairly readable and gives risk assessors the whys
and some of the hows for doing PBPK modeling. Without actually having an operative model in
front of you to work with, one cannot fully appreciate what is involved. It is a very hands on
activity. Perhaps a section that takes apart a case example could make this all more concrete. It
could show the construction of a real world  model from choice of structure, through
parameterization (showing sources of parameter values), different simulations with different
exposure inputs, matches to key datasets, and how the model is affected by sensitive parameters.
The document may also describe how  one learns how to do it (attending workshops; working
with other modelers).
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    6.  Are there current research needs and data gaps not highlighted in this report that
       would improve the utilization of PBPK models in risk assessment?
Gregory M. Blumenthal
Innovation in computational biology and its application to risk assessment is an ongoing process.
This report should be envisioned as a living document, with room to expand as novel methods
and  applications  arise.  Key among the  areas  with explosive growth  occurring  are  acute
dosimetry, point-of-contact dosimetry,  whole-life and developmental modeling, maternal-fetal
dosimetry, and metabolic network modeling to identify sensitive subpopulations.

James V. Bruckner

Janusz Z. Byczkowski
No. This report represents the current state- of-the-art in the PBPK modeling.

Harvey J. Clewell
Not that I can think of.

Gary L. Ginsberg
This document doesn't really address research needs and data gaps, as it is more of an
informational rather than an analytical document.  Many of the research needs are chemical
specific or host specific (age groups, polymorphisms, etc.), or have to do with chemical
mixtures.  I suppose a section that outlines these key areas of data needs would be helpful.

A related issue is where does the PK data come from to construct and calibrate models.  The
discussion in section 2.3 doesn't really cover this.  There could be a discussion that this is not a
regulatory-driven activity but the data are developed for specific risk assessment needs. It would
be helpful to describe the PK data gathering that is required for FIFRA and TSCA and discuss
the limitations for its use in PBPK modeling. Risk assessors familiar with these programs may
wonder about the utility of these data for modeling.
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    7.  Are there future reports that you could envision which would compliment or expand
       upon the topics covered in the current document? For example, would a report
       focused on dosimetry models for reactive gases be helpful? Or a report focused on
       extrapolation across life stages using PBPK modeling?
Gregory M. Blumenthal
See answer to #6.

James V. Bruckner

Janusz Z. Byczkowski
Yes. A report focused on PBPK modeling of gestational and lactational transfers of chemicals
would be helpful in addressing unique problems of assessing risk from exposures of children to
environmental pollutants.

Moreover,   this reviewer can  envision the future  report by  the  Agency, perhaps entitled
"Approaches for the Application of Physiologically Based Pharmacodynamic (PBPD) Models
and Supporting Data in Risk Assessment".

Harvey J. Clewell
Both of the suggested reports would be of value.

Gary L. Ginsberg
As stated above, there are various areas which are not fully covered in this document.  These
could conceivably form the material of other in depth PBPK / risk reports. Even if this were the
case, consideration should be given to providing more information on these areas in this report to
make it more complete and representative of the field. In addition to the above, a  document that
is more  of a "How To", providing a step-by-step methodology for conducting PBPK modeling
and explains how some of the simulation software works might encourage more people  to use
the                                                                          technology.
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    8.  Do you have additional comments/suggestions that were not covered in the above
       questions?
Gregory M. Blumenthal
Appendix 1 requires  significant explanation and discussion.  Those formulas should not be
published without appropriate descriptions and caveats.

James V. Bruckner

Janusz Z. Byczkowski
Yes. Because numerous typing errors were spotted in the Appendices (see below), this reviewer
would suggest a thorough "quality control" of the Appendices (at least, a "quality reading" by
the professional technical proofreader).

Harvey J. Clewell
Table 3-1: I would remove the subscripts for current and previous simulation time.  These
subscripts are only accurate for explicit integration algorithms such as the Euler method.  They
are not correct for the case of implicit algorithms such as the Gear (backward differentiation)
method.

Similarly, specifying the "integration interval" is only relevant to constant step-size algorithms.
For variable step-size algorithms, the appropriate element is the "error criteria". There are a
number of places in the document where this oversight should be corrected.

P. 3-17:1 would suggest also mentioning an alternative rule of thumb often used by modelers:
that a model is successful if it is within a fator of two to three of the data more than  half the time.

I don't understand, and probably don't agree with, the 6th bullet in section 3.9.  I could agree
with scaling metabolism by tissue weight, but not by body weight.

I have made a number of minor suggested edits to my copy of the document, which I will
provide to the peer review organizers.

I have also suggested a number of additional references at various places in main document.
They are listed here:

Abraham, MH; Weathersby, PK. JPharm Sci. 1994, 83, 1450-1456.

Allen BC, Covington TR, Clewell HJ.  1996.  Investigation of the impact of pharmacokinetic
variability and uncertainty on risks predicted with a pharmacokinetic model for chloroform.
Toxicology 111:289-303.
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Astrand, P., and Rodahl, K.  Textbook of Work Physiology.  McGraw-Hill, New York, 1970.

Beliveau, M; Lipscomb, J; Tardif, R; Krishnan, K. Chem Res Toxicol. 2005, 18, 475-485.

Clewell HJ, Andersen ME.  1985. Risk assessment extrapolations and physiological modeling.
Toxicol Ind Health 1:111-131.

Clewell HJ, Andersen ME.  1996. Use of physiologically-based pharmacokinetic modeling to
investigate individual versus population risk.  Toxicology 111:315-329.

Clewell, H.J., Gentry, PR., Covington, T.R., Sarangapani, R., and Teeguarden, J.G  2004.
Evaluation of the potential impact of age- and gender-specific pharmacokinetic differences on
tissue dosimetry. Toxicol. Sci. 79:381-393.

Gentry, PR., Hack, C.E., Haber, L., Maier, A., and Clewell, III, HJ. 2002. An Approach for the
Quantitative Consideration of Genetic Polymorphism Data in Chemical Risk Assessment:
Examples with Warfarin and Parathion. Toxicological Sciences 70:120-139.

Lilly, P.O., Thornton-Manning, J.R., Gargas, M.L., Clewell, H.J., and Andersen, M.E.  1998.
Kinetic characteristics of CYP2E1 inhibition in vivo and in vitro by the chloroethylenes. Arch
Toxicol 72:609-621.

Sarangapani R, Teeguarden J, Andersen ME, Reitz RH, Plotzke KP. 2003a. Route-specific
differences in distribution characteristics of octamethylcyclotetrasiloxane in rats: analysis using
PBPK models. Toxicol Sci.  71(l):41-52.

Sarangapani, R., Gentry, PR., Covington, T.R., Teeguarden, J.G, and Clewell, HJ.  2003b.
Evaluation of the potential impact of age- and gender-specific lung morphology and ventilation
rate on the dosimetry of vapors. Inhal Toxicol 15(10):987-1016.

Gary L. Ginsberg
Yes, see below for a variety of broad and specific comments.
                                          E-24

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V.     SPECIFIC OBSERVATIONS

Gregory M. Blumenthal

James V. Bruckner
p. xi, pgr. 3, line 7; p. xii, pgr. 1, line 7; and p. xiii, line 3:  Replace the word "applied" with
"administered".

p. xii, pgr. 4, lines 1 & 2: What is meant by the term "value" in the phrase "it is used to estimate
the value of internal dose metrics"?

p.  1-1, pgr. 1, line 8:  It should be noted here for less familiar readers that RfC methodology
applies to inhalation exposures.

p. 2-1, pgrs. 1 & 2:  It might be useful to include a short, transitional paragraph that clarifies the
difference(s) between classical pharmacokinetic (PK) analysis (of data) and PK modeling.

p. 2-2, lines 25-28:  I assume that Fig. 2-1  illustrates (is an example of) a chemical that is
metabolically activated. If this is the case, it should be mentioned in the text and noted that the
modeling provides evidence of this phenomenon.

p. 2-3, pgr. 1:  It may be useful here to note the importance of being able to relate the mode of
action to the biologically-active form of the chemical.

p. 2-5, pgr. 1:  It would be worthwhile to point  out that PK equivalence may not equate to
toxicity equivalence, due to the potential existence of thresholds and toxicodynamic differences.

p. 2-5, line 21:  The term "window of susceptibility" should be succinctly defined.

p. 2-7, line 11:  Substitute "administered" for "applied" dose.

p. 2-9, pgr. 1:  It should be recognized (and pointed out) here that estimation of equivalent
absorbed doses (by inhalation and ingestion) does not take into account an important factor;
namely the frequent differences in the duration of the oral (usually bolus) and inhalation
(frequently hours) exposures.  Bruckner and his colleagues have assessed the influence of first-
pass effect with equivalent inhalation and oral exposures to VOCs by:  (1) measuring the total
absorbed dose for 2- to 3-hour inhalation exposures in rats; (2) administering this total dose by
constant gastric infusion over the same time-frame; and (3) monitoring blood and tissue
concentrations of the compound of interest during and post exposure [e.g., see Sanzgiri et al.
Toxicol. Appl. Pharmacol. 134: 148-154 (1995)].

p. 2-9, lines 26 - 30:  The magnitude of CNS depression is an example of an effect that is
dependent upon the momentary concentration of a VOC in the blood/brain. PBPK models and
objective measurements of trichloroethylene-induced CNS dysfunction in rats have been utilized
to demonstrate that Haber's Rule and ten Berge et al's. J. Hazard. Mater. JJ: 301-309 (1986) Cn
                                          E-25

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X t  approaches to time scaling result in overestimation of risks when extrapolating from shorter
to longer exposure times and underestimation when extrapolating from longer to shorter
exposures [Boyes et al. Environ. Health Per spec. 108 (Suppl 2.): 317-322, 2000; Bruckner et al.
J. Toxicol. Environ. Health 67 (Part A}: 621-634, 2004].

p. 2-12, Box 2-2:   Should "Interspecies uncertainty factor" be added?

p. 2-14, lines 26-29:  This sentence is a bit unclear. I assume the authors intend to state that
default uncertainty factors of 3 are used for potential interspecies and intraspecies
pharmacodynamic differences in conjunction with PBPK modeling.  See suggested editorial
changes.

p. 2-15, line 26:  Has the meaning of the abbreviation "IUR" been stated previously?

p. 2-17. lines 11-13:  The paper of Lee et al. Toxicol.  Appl. Pharmacol. 139: 262-271 (1996)
might be cited here as an example of the influence of dose on the extent of first-pass hepatic and
of first-pass pulmonary elimination of orally-administered trichloroethylene.

p. 2-18. line 1:  Should drinking water "rate" be "volume"?

p. 2-18, lines 3 - 17:   The authors seem unnecessarily tentative in stating that "PBPK models are
potentially useful in evaluating the pharmacokinetic basis ...".  Furthermore, it has been clearly
established a number of times in this document that potential pharmacokinetic and
pharmacodynamic differences are separate/different entities.

p. 2-18, Box 2-4:   Can't PBPK models be useful in certain intraspecies pharmacokinetic
extrapolations (e.g., child to adult)?

p. 3-2, line 15:  What is meant by the statement that there is no limitation to the size of a
compartment? Doesn't a compartment's size have to be physiologically realistic?

p. 3-3, line 10:  Is use of the term "reactors" necessary? It may not be familiar to the general
reader.

p. 3-3, lines 25 & 26:  Concentration gradient is, of course, just one factor in  Pick's law of
diffusion. See suggested editorial change in the text.

p. 3-8, lines 7-9:  An ILSI committee is currently finalizing a series of manuscripts that include
a compilation of some physiological values for immature rodents and humans.
p. 3-10, Table 3-5:  The range of values given for pulmonary blood flow (as a % of cardiac
output) is 11.1-17.8%.  Doesn't 100% of the cardiac output pass through the pulmonary
circulation?

p. 3-11, lines 14:  The phrase "model validation" might be utilized rather than "external
evaluation".
                                          E-26

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p. 3-13, lines 11 & 12:  What do the authors mean when they state that in vitro to in vivo
extrapolations are not clear?

p. 3-19, pgr. 2: It would be useful to briefly address the question of the quality of experimental
PK data sets. Many factors can influence the accuracy of experimental measurements in animals
and humans, from stress on the subjects to analytical chemistry problems. My primary role in
PBPK model development has been to provide quality empirical time-course data, so I am aware
of many of the potential problems.

p. 3-27, line 27:  I assume that in vivo kinetic data may also be useful for model calibration.

p. 3-29, lines 1-3:  Should the words "The model for" be inserted at the beginning of this
sentence? It is problematic as presently written.

p. 3-29, lines 32:  Some sort of disclaimer sentence should probably be added at the end of this
section, emphasizing that a relatively high degree of uncertainty is usually inherent in the use of
surrogate data.

p. 3-30, line 25:  The term "steady-state" can be inserted between the words "/« vivo" and
"data".

p. 3-31, lines 3-6:  Another bullet/point should be added addressing the use of kinetic data for
model construction/calibration and the need for additional  data sets for model validation.

p. 3-31, line 7: Still another bullet/point should be added at or near the beginning of this section.
It should point that the model should include/focus on the proximate toxic moiety, if it and/or the
MOA is/are  understood.

p. 4-1, lines  6& 7:  Types of human  studies, that may serve as the critical study, should be
expanded to include clinical and experimental studies.  See the recommended change in the text.

p. 4-3. Box 4-1. 2—bullet:   "Binding" should be included  with storage.

p. 4-4, lines  24-26: Treatment with an inhibitor of the metabolism of a toxic parent compound
may enhance its toxicity by decreasing its rate of metabolic clearance.

p. 4-5, pgr. 1:  It would be worthwhile pointing out that the concentration of ligand at a
particular point in time is often considered to be the most appropriate dose metric for adverse
effects associated with receptor interactions.

p. 4-12, lines 26 & 27:  The words "oral" and "gavage" are redundant.

p. 4-13, Fig. 4-4:  Obviously, as shown here, exposure conditions that yield equivalent AUCs
can be forecast, but the oral Cmax is about 10-fold higher in the oral group.  This relatively high
concentration may exceed a toxicity threshold. Alternatively, the adverse effect may depend
upon the momentary concentration.
                                           E-27

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p. 4-14, pgr. 1:  It would be worthwhile to point out that PBPK models are now being used to
make duration adjustments for derivation of acute exposure guideline levels (AEGLs) for a
number of chemicals. AEGLs are established for 10- and 30-minute inhalation exposures, as
well as 1-, 4- and 8-hour exposures. Typically, a critical study with a single duration of exposure
serves as the basis for derivation of AEGLs for the other exposure durations. A PBPK model is
used to forecast the inhaled concentration required for each time-period to produce the same dose
metric as that associated with an adverse effect in the critical study.  Bruckner et al. (2004)
(referenced previously) described the AEGLs program and illustrated the use of PBPK for time
scaling with trichloroethylene.

p. 4-20, Table 4-2:  How is tumor prevalence expressed here? No units are given.

p. 4-23. line 11:  Shouldn't the word "difference" be "differential"?

Janusz Z. Byczkowski
P. xii Line 29 -       Quote: "...which are then use to derive..."
                    Change to: "...which  are then used to derive..."

P. 2-2 Line 21 -      please add a short paragraph on modeling of dermal exposures. Some of
                    the following references, listed in the Appendix 2, may be used:

Auton, T. R., Ramsey, J. D., and Wollen, B. H. (1993). Modelling dermal
pharmacokinetics using in vitro data.  Part II. Fluazifop-butyl in man. Human &
Experimental Toxicology 12, 207-213.

Auton, T. R., Ramsey, J. D., and Woollen, B. H. (1993). Modelling dermal
pharmacokinetics using in vitro data.  Part I. Fluazifop-butyl in the rat. Human &
Experimental Toxicology 12, 199-206.

Blancato, J. N.,  and Bischoff, K. B. (1993). The application of pharmacokinetic
models to predict target dose. In Dermal risk assessment. Dermal and inhalation
exposure and absorption of toxicants. (R. G. M. Wang, J. B. Knaak, and H. I.
Macbach, Eds.), pp. 31-46. CRC Press Inc.

Bookout, R. L. J., McDaniel,  C. R., and Quinn, D. W. M. J. H. (1996).
Multilayered dermal subcompartments for modeling chemical absorption. SAR
QSAR Environ  Res. 5, 133-150.

Corley, R. A., Markham, D. A., Banks,  C., Delorme, P., Masterman, A., and
Houle, J. M. (1997). Physiologically based pharmacokinetics and the dermal
absorption of 2-butoxyethanol vapor by humans. Fundamental and Applied
Toxicology 39,  120-130.

Corley, R. A., Gordon, S. M., and Wallace, L. A. (2000). Physiologically based
pharmacokinetic modeling of the temperature-dependent dermal absorption of
                                         E-28

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chloroform by humans following bath water exposures. Toxicological Sciences
53, 13-23.

Jepson, G. W., and McDougal, J. N. (1999). Predicting vehicle effects on the
dermal absorption of halogenated methanes using physiologically based
modeling. Toxicological Sciences 48, 180-188.

Loizou, G. D., Jones, K., Akrill, P., Dyne, D., and Cocker, J. (1999). Estimation
of the dermal absorption of m-xylene vapor in humans using breath sampling and
physiologically based pharmacokinetic analysis. Toxicological Sciences 48, 170179.

McDougal, J. N., Jepson, G. W., Clewell, H. J., MacNaughton, M. G., and
Andersen, M. E. (1986). A physiological pharmacokinetic model for dermal
absorption of vapors in the rat. Toxicology and Applied Pharmacology 85, 286294.

McKone, T. E. (1993). Linking a PBPK model for chloroform with measured
breath concentrations in showers: implications for dermal exposure models.
Journal of Exposure Analysis and Environmental Epidemiology  3, 339-365.

Nichols, J. W., McKim, J. M., Lien, G. J., Hoffman, A. D., Bertelsen,  S. L., and
Elswick, B. A. (1996). A physiologically based toxicokinetic model for dermal
absorption of organic chemicals by fish. Fundamental and Applied Toxicology
31,229-242.

Roy, A., Weisel, C. P., Lioy, P. J., and Georgopoulos, P. G. (1996). A distributed
parameter physiologically-based pharmacokinetic model for dermal and
inhalation exposure to volatie organic compounds. Risk Analysis 16, 147-160.

Shatkin, J. A., and Brown, H. S. (1991). Pharmacokinetics of the dermal route of
exposure to volatile organic chemicals in water: A computer simulation model.
Environmental Research 56, 90-108.

Thrall, K. D., and Woodstock, A. D. (2002). Evaluation of the dermal absorption
of aqueous toluene in F344 rats using real-time breath analysis and
physiologically based pharmacokinetic modeling. Journal of Toxicology and
Environmental Health 65, 2087-2100.

P. 2-14 Line 24 -     Please add a sentence or two, explaining that Monte Carlo modeling
                    coupled with PBPK represents a useful approach to quantify impact of
                    parameter variability on simulated dose metrics (e.g., excerpt from page 3-
                    24).

P. 2-15 Line 28 -     Quote: " ...either a nonlinear (i.e., RJC or RfD) or linear..''
                    Please delete "(i.e., RfC or RfD)"

P. 2-16 Line 1 -      Quote: " ...the tumors observed in such studies are..''
                                         E-29

-------
                    Please add "the number of tumors observed in such studies is"

P. 3-2 Line 24 -      Quote: "...biochemicalparameters (i.e., partition coefficients)...'"
                    Please change to "physicochemical parameters (i.e., partition
                    coefficients)"

P. 3-6 Line 12 -      Please change in the equation for Tissue blood expression "(Ci+C2)" to
                    "(C, - C,/PH,)"
                    and in the equation for Cellular matrix "(Ci-C2)" to "(Ci - C2/P_tb)"
                    Add below the table 3-2:  "PH,_= partition coefficient tissue:blood"

P. 3-7 Line 18 -      Quote: "...(mg/L-hf1)..?
                    This expression of unit, mathematically, does not make sense.  Please
                    change either to exponential "(ma x L— x hr^-)"  or proportional
                    "(mg/L/hr)" expression.

P. 3-17 Line 28 -     Quote: "...every single data..."
                    Please change to "every single datum"

P. 3-29 Line 28 -     Quote: "...  a web-basedresource for PBPK modeling
                    (http://www.capkr.man.ac.uk). The site provides instant access to
                    resources such as data, methodology, and tools necessary to start PBPK
                    modeling effort..."
                    Unfortunately, the provided URL, points to the password-protected
                    "members  only" university web site, without public access to any
                    resources.
                    Please either, provide URL to publicly accessible web site (for example,
                    http://www.pbpk.org/ ) or delete this information.

P. 4-13 Line 4; 4-14 Lines 8 and  14 -       Quote: "...mg/L-hr..."
                    This expression of unit, mathematically, does not make sense.  Please
                    change either to exponential "(mg x L- x hr1)"  or proportional
                    "(mg/L/hr)"  expression.

P. 4-16 Lines 23 - 26 -       Quote: "...Because the Agency has traditionally applied the
                    uncertainty factors to the external dose and not to the internal dose, it may
                    be useful to undertake a systematic evaluation of the outcome of applying
                    the uncertainty factors to the external and internal doses for various
                    chemicals and situations..."
                    The Agency traditionally applied the uncertainty factors to the external
                    dose because before accepting PBPK models it could not calculate
                    realistically internal doses,  delivered to the target. The very goal of
                    applying PBPK models in risk assessment is to determine the internal dose
                    metrics under relevant exposures, and thus, reverting to "external dose
                    divided by uncertainty factor"  as a basis for calculation of RfD and/or RfC
                    would nix most of the advantage from using the  PBPK model. Even
                                          E-30

-------
                     though, as already noted in the document, for the linear range of PK, the
                     result is numerically the same, no matter whether uncertainty factors are
                     applied to internal or external dose, the right method is to divide internal
                     dose metrics by uncertainty factor(s), and then, to calculate human
                     exposure (external) dose. Undertaking the "systematic evaluation", as
                     suggested in the document, would just waste time and resources as its
                     outcome can be easily predicted right now: it is always appropriate to
                     divide internal dose metrics by uncertainty factor(s); while it is only
                     sometimes appropriate to divide external dose by uncertainty factor(s) -
                     only when dealing with linear pharmacokinetics.

                     This reviewer suggests to substitute the above quoted sentence with the
                     recommendation to appropriately apply uncertainty factor(s) to internal
                     dose metrics, before calculating human exposure (external) dose for RfD
                     and/or RfC, applicable for both linear and nonlinear pharmacokinetics.

P. 4-17 Lines 7 and 15; 4-18 Line 15 -       Quote: "...mg/kg-d..."
                     This expression of unit, mathematically,  does not make sense. Please
                     change either to exponential "(mg x  kgr^-x d—)" or proportional
                     "(mg/kg/d)" expression.

P. 4-23 Line 11 -     Quote: "...difference equations..''
                     Please change to: "differential equations"

P. G-l Line 23 -      Quote: "...Cancer scope factor..''
                     Please change to: "Cancer slope factor"

P. G-l Line 34 -      Quote: "...Delivered dose: The amount of a substance available for
                     interactions with biologically significant receptors in the target
                     organ..''
                     Although this definition is correct, risk assessors usually use the term
                     "receptors" differently than pharmacologists. For the risk assessor,
                     "receptor" often means the individual (human subject) exposed to a
                     potentially harmful chemical compound.
                     To avoid confusion, this reviewer would suggests changing the definition
                     of Delivered dose, to:  "The amount of a substance available for
                     interactions with biologically significant targets in the affected tissues".

P. G-2 Line 11 -      Quote: "...This adjustment may incorporate..."
                     Please change to: "The adjustment of concentration from animal to human
                     may incorporate".

P. G-2 Line 27 -      Quote: "...the relationship between external exposure level and the
                     biologically effective dose at a target tissue..."
                     Please add: "the relationship between external exposure level and the
                     biologically effective dose at a target tissue overtime".
                                           E-31

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P. G-2 Line 27 -      Quote: "...the relationship between a biologically effective dose and the
                     occurrence of a tissue response..''
                     Please add: "the relationship between a biologically effective dose and the
                     occurrence of a tissue response overtime".

P. G-2 Line 42 -      "Reference concentration (RfCf:
                     Please change to revised IRIS definition (effective July 2005           <
                     http://www.epa.gov/iris/gloss8.htm >: "An estimate of a continuous
                     inhalation exposure for a given duration to the human population
                     (including susceptible subgroups) that is likely to be without an
                     appreciable risk of adverse health effects over a lifetime. It is derived from
                     a BMCL, a NOAEL,  a LOAEL, or another suitable point of departure,
                     with uncertainty/variability factors applied to reflect limitations of the data
                     used."

P. G-3 Line 5 -       "Reference dose (R/Df:
                     Please change to revised IRIS definition (effective July 2005
                     < http://www.epa.gov/iris/gloss8.htm >: "An estimate of a daily oral
                     exposure for a given duration to the human population (including
                     susceptible subgroups) that is likely to be without an appreciable risk of
                     adverse health effects over a lifetime. It is derived from a BMDL, a
                     NOAEL, a LOAEL, or another suitable point of departure, with
                     uncertainty/variability factors  applied to reflect limitations of the data
                     used."

P. G-3 Line 22 -      Please explain the term "window of susceptibility".

P. R-12 ref. Price et al. (2003a) - Change "Conelly" to "Conolly"

P. R-12 ref. Price et al. (2003b) - Add in "J Toxicol Environ Health A66:"

Appendix 3, P. 6 Line 13 -   Quote: "...Oxydation..."
                     Please correct to "Oxidation"

Appendix 3, P. 6 Line 16 and P. 7 Line 22 - Quote: "...conjugaison..."
                     Please change to "conjugation"

Appendix 3, P. 8 Lines 24, 25 -     Quote: "...Oxydation..."
                     Please correct to "Oxidation"

Appendix 3, P. 19 Lines 33,  34, 35 37, 39, 40, 41, 43 -     Quote: "...Oxydation..."
                     Please correct to "Oxidation"

Appendix 3, P. 20 Lines 18,  20, 22 - Quote: "...Oxydation..."
                     Please correct to "Oxidation"
                                           E-32

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Appendix 3, P. 22 -   Please correct illegible fonts

Appendix 3, Pp. 25, 36 and 51 Line 5 -      Quote: "...coumpound..."
                    Please change to "compound"

Appendix 3, P. 28 Line 17 - Quote: "...conjugaison..."
                    Please change to "conjugation"

Appendix 3, P. 46 Line 1 -   Quote: "...CHLOROFLUOROHYDROCARBONE..."
                    Please change to "CHLOROFLUOROHYDROCARBON"

Appendix 3, P. 57 Line 14 - Quote: "...(yountK).."
                    Please change to "(youth)"

Appendix 3, P. 81 Line 15 - Quote: "...disapearance ..."
                    Please change to "disappearance"

Appendix 3, P. 83 Lines 36 and 39 - Quote: "...conjugaison..."
                    Please change to "conjugation"

Appendix 3, Pp. 100,  103 and 106 Line 19 - Quote: "...caracteristics..."
                    Please change to "characteristics"

Appendix 3, Pp. 119 and 120 Line 2 - Please translate into English.
Harvey J. Clewell
p. 1-2, lines 26-27: change "a compilation... environmental chemicals." to "and a case study
based on the evaluation of a PBPK model for isopropanol (Clark et al. 2004)"

p. 2-2, line 31: Clewell and Andersen 1997 should be 1985

p. 2-4, lines 5 and 35; p. 2-14, line 29p. 2-16, line 7: Clewell et al., 2002 should be 2002a
(Clewell Andersen and Barton)

p. 2-7, line 12: add "exposure" at beginning of line

p. 2-9, line 2: change was to could be

p. 2-13, line 8: change "overly" to "highly"

p. 2-18, line 4: add Clewell et al. 2004

p. 3-1, line 31: Clewell and Andersen 1997 should be 1987
                                         E-33

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p. 3-2, line 15: change "size" to "complexity"

p. 3-3, line 11: change "equal" to "related by the partition coefficient"

p. 3-3, line 22: delete "clearance" and change "volume" to "mass"

p. 3-3, line 23: change "liters" to "mg" and "milliliters" to "mg" and delete "clearance"

p. 3-3, line 25-26: delete "is described according to Pick's law of simple diffusion, which states
that the flux of a chemical" and change "concentration" to "activity (concentration adjusted by
partition coefficient"

p. 3-3, line 27: delete "passive and"

p. 3-5, table: remove all subscripts "n" and "n-1" and related definitions in footmote

p. 3-6, table 3-1, footnote b: add "steady-state" before "arterial"

p. 3-6, table 3-2: correct equations (should be Cl  - C2/P2)

p. 3-7, line 1: add "a" after "by"

p. 3-7, line 2: add "a" after "on"

p. 3-7, line 3: add "typically" before "been"

p. 3-7, line 4: delete "second order"

p. 3-7, lines 4-7: delete from "Conjugation" to "successfully"

p. 3-7, line 28: after "volumes", add "absorption rate parameters (e.g., for dermal or oral
uptake),"

p. 3-8, line 12: add Gentry et al. 2004; Gentry et al. 2006 (ILSI human perinatal parameters)

p. 3-8, line 23: delete "(e.g., Andersen et al., 1987)." and add "but decreases with activity
(Astrand and Rodahl, 1970)."

p. 3-8, lines 14-16: change 91% to 85% and 9% to 15% and add reference to Brown et al. 1997.

p. 3-8, lines 18-19 change "which may seem questionable...in risk assessment." to "is a
reasonable approximation since tissue densities typically range from 0.9 kg/L for muscle to 1.06
kg/L for fat (Ross et al. 1991, Mendez and Keys,  1960)

p. 3-9, table 3-3 title: change "Reference" to "Typical"
                                           E-34

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p. 3-10, Table 3-5: add "upper respiratory tract" as footnote for Lungs

p. 3-10, Table 3-6: add volumes

p. 3-11, line 11: delete "or binding"

p. 3-12, line 6: add Beliveau et al. 2005 and Abraham and Weathersby  1994.

p. 3-14, table: move Ramsey and Andersen (1984) from ACSL row, last column to SimuSolv
row, last column.  Add Clewell et al. 2000 to ACSL row, last column.

p. 3-17, line 5: change "levels" to "amounts" in three places

p.3-18, line 17:  after "profiles", add (Lilly et al.1998)"

p. 3-20, line 23: after "zero", add (Sarangapani et al. 2003a)

p. 3-22, line 4: change "the" to "hypothetical"

p.3-22, line 11: add "In actual practice, it is a matter of concern for sensitivity ratios for be
greater than one in absolute value, since this results in the amplification of input error (Allen et
al. 1996).

p. 3-22, Figure 3-3 caption:  add "hypothetical" before "PBPK"

p. 3-24, line 6: add Sarangapani et al. 2003b, Gentry et al. 2003.

p. 3-24, line 14: add Gentry et al. 2002.

p. 3-24, line 18: add Clewell and Andersen 1996.

p. 3-24, line 23: change "/Q" to "/Qc"

p. 3-25, line 24: change Clewell and Andersen 1997 to 1987.

p. 3-28, line 26: change "suffices" to "may suffice"

p. 3-30, lines 29-31: delete

p. 4-1, line 7: delete "epidemiological"

p. 4-1, line 9: change "as well  as" to "and/or"

p. 4-5, line 15: add Andersen et al. 1987.

p. 4-7, table: add acrylic acid ; nasal lesions ; average nasal concentration ; Andersen et al. 1999.
                                          E-35

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p. 4-7, table, butoxyethanol row: change "Levels" to "Concentration"

p. 4-7, table, methylmethacrylate row: change "amount metabolized/time" to "amount
metabolized/time/volume nasal tissue" and delete 1999 reference

p. 4-8, table, top row: add "transferase" after "glutathioine

p. 4-8, table, TCDD row: change "Number" to "Fraction"

p. 4-8, table, TCE row: change "in" to "per L"

p. 4-8, table, VC row: delete "mg metabolite produced/L liver"

p. 4-9, lines 22 and 26: change Clewell and Andersen 1997 to 1987.

p. 4-12, line 26: change "is" to "can be"

p. 4-15, lines 11-12: delete "for unimodel, normal distribution (Naumann et al. 2001)"

p. 4-17, line 32: delete "Subsequently" and change "conventional" to "case of the RfD"

p. 4-19, line  11: change "simulate" to "estimate"

References:

Abraham, MH; Weathersby, PK. JPharm Sci. 1994, 83, 1450-1456.

Allen BC, Covington TR, Clewell HJ. 1996. Investigation of the impact of pharmacokinetic
variability and uncertainty on risks predicted with a pharmacokinetic model for chloroform.
Toxicology 111:289-303.

Astrand, P., and Rodahl, K. Textbook of Work Physiology. McGraw-Hill, New York, 1970.

Beliveau, M; Lipscomb, J; Tardif, R; Krishnan, K. Chem Res Toxicol. 2005,  18, 475-485.

Clark, LH, Setzer RW, and Barton, HA. 2004. Framework for evaluation of physiologically-
based pharmacokinetic models for use in safety or risk assessment. Risk Analysis, 24(6): 1697-
1717.

Clewell HJ, Andersen ME.  1985. Risk assessment extrapolations and physiological modeling.
Toxicol Ind Health  1:111 131.

Clewell HJ, Andersen ME.  1996. Use of physiologically-based pharmacokinetic modeling to
investigate individual versus population risk. Toxicology 111:315-329.
                                         E-36

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Clewell, H.J., Gentry, P.R., Covington, T.R., Sarangapani, R., and Teeguarden, J.G.  2004.
Evaluation of the potential impact of age- and gender-specific pharmacokinetic differences on
tissue dosimetry. Toxicol. Sci. 79:381-393.

Gentry, P.R., Hack, C.E., Haber, L., Maier, A., and Clewell, III, HJ.  2002.  An Approach for the
Quantitative Consideration of Genetic Polymorphism Data in Chemical Risk Assessment:
Examples with Warfarin and Parathion. Toxicological Sciences 70:120-139.

Gentry, PR. et al.  2004. Data for physiologically based pharmacokinetic modeling in neonatal
animals: physiological parameters in mice and Sprague-Dawley rats. J. of Children's Health 2(3-
4):363-411.

Gentry, PR. et al.  2006.  Physiological parameters for early life stages. Report of an ILSI
working group.  In preparation.

Lilly, P.O., Thornton-Manning, J.R., Gargas, M.L., Clewell, H.J., and Andersen, M.E. 1998.
Kinetic characteristics of CYP2E1 inhibition in vivo  and in vitro by the chloroethylenes. Arch
Toxicol 72:609-621.

Mendez J, Keys A, 1960. Density and composition of mammalian muscle. Metabolism 9:184-
188.

Ross R, Leger L, Guardo R, De Guise J, Pike BG 1991 Adipose tissue volume measured by
magnetic resonance imaging and computerized tomography in rats. J Appl Physiol 70: 2164-
2172

Sarangapani R, Teeguarden J, Andersen ME, Reitz RH, Plotzke KP 2003a. Route-specific
differences in distribution characteristics of octamethylcyclotetrasiloxane in rats: analysis using
PBPK models. Toxicol Sci. 71(l):41-52.

Sarangapani, R., Gentry, PR., Covington, T.R., Teeguarden, J.G, and Clewell, HJ.  2003b.
Evaluation of the potential impact of age- and gender-specific lung morphology and ventilation
rate on the dosimetry of vapors. Inhal Toxicol 15(10):987-1016.

Gary L. Ginsberg
ES, 2nd Page (2nd para) and later in the document - 3 aspects of PBPK models are called out as
being essential to include. However, there are others. For example, PBPK model structure be
must be appropriate to the exposure route (oral vs. dermal vs. inhalation vs. lactation vs. trans-
placental) and MOA (only parent compound simulated or both  parent compound and
metabolites;  GSH depletion or other defense mechanisms simulated?).  Further, a good general
principle is that the PBPK model must include all major elimination pathways (renal,  exhalation,
liver metabolism, as appropriate).

ES- same para as last entry, last sentence - "available animal-alternative algorithms" - the word
animal seems out of place given that many of the algorithms in the appendix are for humans as
well as animals.
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Page 2-1, last sentence of 1st para and Page 2-2 to 2-3: assertion is made that internal dose
metric provides a better relationship to toxic effect than does external dose.  While this is
typically true and may be self-evident to some, the text needs to say why this should be so. For
example, it can be stated that internal dose is obviously closer to biologically effective dose than
is the applied dose, and that internal dose and applied dose may not be directly proportional due
to saturable processes, distributional phenomena, secondary clearance pathways that are active at
higher doses, etc.

Page 2-1, 2nd para - 3rd sentence - seems illogical - I think what it is trying to say is that orally
absorbed compounds tend to  exert their effects at systemic rather than local  sites so PBPK
models have focused on modeling systemic compartments.  However, the sentence is poorly
written. The next sentence appears to be referring to classical one and two compartment models
in the first clause, with the more highly evolved modeling referring to PBPK. This sentence
should be unpacked into one  or several paragraphs which gives appropriate background for the
more basic models and their potential utility in risk assessment (e.g., mercury, dioxin), and why
the more complex PBPK models are needed in other applications.

Page 2-1 - last para - obviously the document is focusing on modeling of systemic sites and
steering clear of local dosimetry at portal  of entry. It would probably be best to state this more
clearly and then refer to the RfC methodology for particles and gases, the more refined CFD
models, and the oral models of g.i. dosimetry (e.g., Frederick, et al., 1992) as important
applications for chemicals which produce contact site toxicity but will not be the focus of this
document.  Then state whether certain principles developed in this document would tend to apply
to the contact site modeling approaches.

Page 2-4 - top - states that default approach is to use lifetime AUC in target tissue as the most
appropriate dose metric for chronic exposure.  However, how is the lifetime AUC derived -
running the model for 2 years for a rat or 70 years for a human? That would be require large
time steps that may miss important periods of greater exposure when  there may also be windows
of susceptibility that affect chronic risk.  Therefore, the concept of windows of vulnerability
should be included when considering a lifetime AUC approach.

Page 2-5, 2nd para - replace the word "current" with peak or Cmax??
Last 2 paras of 2-5: appears to be describing optimal dataset vs. limited dataset with need for
PBPK modeling. It would be helpful to set up  discussion this way. Lead in phrase "the  most
robust PK dataset needed for RA would consist of..." is awkward and indirect.

Page 2-7, 2nd para, last line - what is a non-compartmental model??  Even one compartment
models are "compartmental".  This sentence appears to, once again, gloss over the important
distinctions between non-physiological compartmental models vs. PBPK models.

Page 2-12 - Box of bullet points - consider changing "dosimetric adjustment factor" to "cross-
species" AF to be more specific and contrast this bullet from the one that follows.
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Page 2-10, last para - a more complete discussion of how the default RfC methodology
addresses cross-species dosimetric adjustments via PBPK modeling is needed. That
methodology relies upon a steady state equation in which the HEC calculation is simplified down
to a ratio of the animal to human blood/air partition coefficient. The current document should
present this and describe whether there are situations in which RfC derivation should involve
more complete PBPK modeling.

Page 2-16 - Interspecies Extrapolation for carcinogens - this section should make the point that
there are no uncertainty factors in carcinogen toxicity assessment with the interspecies scaling
factor the only factor used to modify the slope factor derived from animal studies.  Therefore,
PBPK models are valuable to extend the dose response analysis to human receptors that may
have unusual exposure and pharmacokinetics (e.g., children, elderly) to address intraspecies
variability, and to use PBPK models to improve upon the interspecies scaling factor approach.
The existing text does not make these points.

Page 2-18, top para, 2nd sentence - "However ..."  This  sentence is unnecessary - PK is not
expected to adjust for PD differences across species or individuals under any circumstances.
This does not diminish the value of PBPK model adjustment of cancer risk assessments for
dosimetry differences at different life stages.

Page 2-20 -first sentence - very broad statement about circumstances under which PBPK models
wouldn't be needed. Should add the caveat:  and if the same relationships between external and
internal  dose exist across species, age groups, dose routes, etc., then wouldn't need PBPK
modeling.

Page 2-20 - second set of numbered points - consider changing "potential dose" to "intake
dose".

Page 3-1 to 3-2 - model purpose - should include the use of PBPK models to help  interpret
MOA by distinguishing between parent compound and metabolite as active toxicant.  Ginsberg
and Rao 2000 publication is a good example of this for MTBE.  Discussion in Section 4 (page 4-
5) gets at this but this purpose or utility should also be stated up front.

Page 3-1, end of first para - need to include another step  in PBPK model evaluation: "evaluation
of model predictiveness against external datasets".

Page 3-7, top para - general principles are described for a variety of important topics - binding,
metabolism. However, much more can be stated, especially  with regards to how metabolism is
represented.  No mention is made of Km or Vmax or possible involvement of multiple CYPS
having different activity. Ping-pong mechanism needs definition.

Page 3-9, Table 3-3. Should include rapidly perfused tissues as a line in the table since many
models have a  simplified lumped compartment of this nature.

Page 3-12, Section 3.4.3 - Biochemical Parameters - should describe how in vivo data are used
to derive metabolic constants - how backfitting  (optimization) techniques are iteratively used.
                                          E-39

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Should also discuss issue where multiple parameters need backfitting (e.g., absorption
coefficient, metabolic constants) and how this can lead to uncertain parameter estimates (Getting
the right answer for the wrong reason).

Page 3-18 - "structure may be inadequate" not "is inadequate". Figure 3-2 uses log scale.  Text
should make the point that linear scale highlights data to model differences more clearly and
should be used over log scale if possible.

Page 3-20, end of 1st full para - while visual inspection is a convenient evaluation procedure
commonly used, the method  of residuals is a relatively easy approach that is also used and
should be described.

Page 3-20, next para - level of complexity evaluation - set one parameter to zero and see if it
impacts model outcome - this isn't so simple as removing one parameter (e.g., a tissue
compartment) may require adjusting the size of another compartment to maintain physiological
sense; in this way would be  changing more than one parameter.

Page 3-23 - bottom - should spell out what is meant by "individual-specific" parameters - are
these values for actual people or values picked from a random distribution.

This section (Variability Analysis) should describe possible form of M-C results - normal,
lognormal, multimodal.

Page 3-26 - should describe how uncertainty analysis  is run - how is M-C analysis used
differently here than in  variability analysis?

Page 3-29, top - description of parallelogram approach for CFC and halothane a bit confused -
needs rewording and clarification (e.g., The human CFC model was assumed to behave as well
as the human halothane model because they were similarly developed and calibrated from in
vitro data.

Page 3-30, 4th and 5th bullets - there is no apparent difference between them.
6th bullet is a new rule not stated previously in Section 3 and is not well developed.

Page 3-31 - there is no  final bullet for variability, sensitivity, uncertainty.  For completeness, one
(or several) should be provided.

Page 4-1 - should add another bullet stating that the PBPK model should be reflective of the
MO A in terms of simulating  key activation/detoxi cation steps, stores of key factors such as GSH
or metallothionen, and estimating concentrations in lexicologically  important tissues.

Page 4-3 - the list of bullets should include one evaluating the fit to external datasets to
determine predictive nature of the model. This listing overlaps with the information presented in
Section  3 and may not be needed or just be merged into Section 3.
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Page 4-9 - 1st full para, last sentence - what chemical is referered to in this example where rat
and mouse kidney tumor data could not be reconciled? Is this simply a matter of species
differences in pharmacodynamics?  This is what is implied on the basis that PK evaluation using
various dose metrics couldn't resolve the difference.

Page 4-9, last para - the term dose-dependence used in a confusing manner.  I think they are
referring to non-linearities - better to use that term if this is what is meant. Dose dependence
often implies something else.

Page 4-10, 1st para under Interspecies Extrap - the protocol described leaves out the iterative
model fitting step that is often needed to "tweak" parameters to obtain optimum fit to the
calibration dataset.  That should come before the 4th sentence.  Also, in the next step, it would
be good to clarify what is meant by chemical-specific parameters (biochemical parameters such
as metabolic and transport rates, partition coefficients).
                                          E-41

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     APPENDIX F
OBSERVER COMMENTS

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                                 Comments by Eric Hack

Toxicology Excellence for Risk Assessment (TERA) was sponsored by the Department of
Defense to prepare oral comments for this peer review meeting. The comments provided are
those of TERA.

General comments

This document gives a good description of PBPK modeling, and covers the basics of how it can
be used to reduce uncertainty in risk assessment.  The compilations of existing models for
kinetics and dynamics are also useful. The document will have merit in that it will help increase
the understanding and acceptance of the need for quantitative risk analysis methods among
qualitative risk assessors.  EPA should be applauded for undertaking this effort.

Addressing the issues highlighted below will add to the value of the document.

Significant Issues:

There were a number of issues (such as the application of PBPK models to use data to replace
uncertainty factors) that were addressed briefly in Chapter 2, but much more thoroughly in
Chapters 3 and 4. It would be useful to note in Chapter 2 that these issues are addressed in more
detail later. It would also be useful to include one integrated discussion of some topics, such as
the use of PBPK models for interspecies and intraspecies extrapolation or variability and
uncertainty analysis, since some people may use the document more as a lookup document.

While the document does mention the term chemical-specific adjustment factors (CSAFs) in
Section 2.6.3, it would be useful to use this term, and to cite the IPCS (2005) guidance when the
specific examples are provided in Chapters 3 and 4.  This discussion should note that one may
be able to obtain in vivo data (e.g., blood concentration) to address interspecies differences in
pharmacokinetics, it is very unlikely that one could obtain enough samples to adequately
characterize human variability in kinetics, and so the PBPK model is essentially the only way to
do so (as discussed in IPCS, 2005).  The Gentry et al. (2002) article cited in the detailed
comments carried the calculations for dose variability resulting from polymorphisms through to
the calculation of CSAFs. I was glad to see the IPCS 2001 citation, but it would be useful to
include the citation in the text (e.g., rather than only citing the Naumann paper), in the context of
the discussion of uncertainty factors. In addition, the 2001 document has been superseded by the
finalized (2005) document, at
http://www.who.int/ipcs/methods/harmonization/areas/uncertainty/en/index.html

In the model evaluation section, the discussion of assessing model fit is oversimplified. Visual
fitting and a criterion that the predictions should be within 2 standard deviations of the mean is
described, but other goodness of fit metrics also exist. For example, Krishnan et al. (1995)
proposed a PBPK index based on root mean square of the error between predictions and data.
The description of the 2 standard deviations rule should be offered as perhaps one measure of
goodness of fit, but it is too simplistic to be relied upon to evaluate all PBPK models under all
circumstances.
                                       F-l

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The sections on uncertainty and variability analysis needs more detail. More description of the
methods and especially the issues associated with the interpretation of the results of these
analyses and their use in risk assessment would be helpful.  For example, the importance of
accounting for parameter correlations in MC or MCMC analyses, issues with the direct use of
MCMC results in estimating dose metric distributions, the impact of model error on the results of
MCMC analyses, or the proper handling of mixed group and individual observations in MCMC
analysis.

More discussion of the use of surrogates for target doses should be included.  Using surrogates,
such as blood concentrations rather than target tissue concentrations, the use of parent chemical
concentrations or flux through a metabolic pathway instead of toxic metabolite concentrations, is
sometimes necessary when the knowledge of the mode of action is more detailed than the kinetic
knowledge, or when the toxic moiety cannot be measured directly.

Discussion of fetal or neonatal modeling should be included in the document.  This is an
important contribution of PBPK modeling to the assessment of developmental toxicity.

There is a list of possible dose metrics is given in Box 2-1.  This choice is critical for dose metric
estimation, and more discussion of when each choice is appropriate would be helpful.

Although it is mentioned later in the document, the description of the uses of PBPK models in
chapter 2 should include mode of action hypothesis formulation and testing.

Editorial and minor comments:

Using PBPK for duration adjustment may also be useful for the oral route, not just inhalation. It
can be used to account for gavage vs. drinking water dosing, or dosing 5 days/week vs. 7
days/week.

P. 2-4, line 5. There  are multiple Clewell et al.  2002 papers in the references.  Which one is
cited?

P 2-7, line 9.  Should mutagenic be replaced with genotoxic?

P 2-8, line 32.  Specify excess risk above background in the BMDL definition.

P 2-10, line 29. Define flow-limited perfusion.

Section 2.5.5.  Should use standard notation for interspecies UF (i.e. UFA) and the intraspecies
variability factor (i.e. UFH).

P 3-6, Table 3-2. The equations are incorrect.  The rate of change in the cellular matrix should
be [PA]*(C1/V1 - C2/PtiSSue:biood), and this term is subtracted in the equation for the change in
blood.
                                       F-2

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Section 3.4.1.  Consider adding a citation for compilation of rodent neonatal physiological
parameters:
Gentry, P.R., Haber, L.T., McDonald, T.B., Zhao, Q. Covington, T., Nance, P., Clewell III, H.J.,
Lipscomb, J.C., and Barton, H.A. 2004. Data for physiologically based pharmacokinetic
modeling in neonatal animals: physiological parameters in mice and sprague-dawley rats. Journal
of Children's Health.  2(3-4): 363-412.
ILSI also has a major project underway for compiling human and rodent neonatal physiological
parameters.

Section 3.5.  Since this section includes ways to verify that the model is coded properly, this is a
good section for saying that a mass balance calculation should be included and checked.

Table 3-7. I believe there is an X-windows graphical user interface for MCSim. I was surprised
to see no mention of the EPA software (is it under development). Even if under development, it
would be useful to mention it.

P 3-18.  There are some inconsistencies with the discussion of model evaluation. On line 12, the
document says that the visual evaluation approach says nothing about the adequacy of the model
structure or parameters. I disagree with this statement. On lines 16-17, it correctly says that
inadequacies in the model structure can be inferred using this approach. Later, on page 3-20,
line 19, the document says that visual inspection is the best approach to model evaluation.

Figure 3-3. It should be emphasized that one should also consider the uncertainty  in the different
parameters.  For example, even though the model is sensitive to blood:air PC, if this parameter is
very well known, then it will be changed very little in an uncertainty analysis, and will result in
little uncertainty about the dose metric calculations.  On the other hand, VMax is often known
with little certainty, and although the model is less sensitive to this parameter, it will be very
much more widely in an uncertainty analysis and contribute much more to the uncertainty in the
dose metrics.

P. 3-23, lines 3 to 27.  This is a very good point, and it is nice to see it given some discussion.

P. 3-23, line 12. Should this be "compensate to some degree for the change in breathing rate"?

P. 3-24, line 13. While we appreciate the citation of Haber et al. 2002,  this paper only provided
the background information about the polymorphisms. The PBPK/Monte Carlo simulation was
published as
Gentry, P.R., C.E. Hack, L. Haber, A. Maier and H.J. Clewell, 3rd. 2002. An Approach for the
Quantitative Consideration of Genetic Polymorphism Data in Chemical Risk Assessment:
Examples with Warfarin and Parathion. Toxicol Sci. Nov, 70(1): 120-39.

P. 3-24, line 31. Point out that one of the advanatages of the MCMC approach is that the
posterior parameter distribution obtained is a joint, multivariate distributions that accounts for
correlations between  the parameters.
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P. 3-27, line 24.  Include physiological parameters in the bulleted list of minimal data required to
build a model.

P. 3-28, line 13.  Expand that the critical study is the critical study used for development of the
risk value (RfC, RfD, or cancer unit risk).

P. 4-1, lines 21-23.  This is very simplified.  I guess the peer review is expected to capture all of
the model evaluation criteria described earlier? Bullet 2 above includes 'and evaluated for its
structure and parameters'.

Box 4-1. There are bullets in this box that were not in the chapter 3 summary (e.g., major sites
of storage).

Figure 4-4.  A description  of how the 4-hour inhalation exposure duration was selected is needed
in the text describing this figure, or in a footnote.

Section 4.3.4.  Add a caveat regarding extrapolation over very long durations and
pharmacodynamic factors  that may dominate (see Clewell, Andersen, and Barton,  2002).

Section 4.3.5.  Consistent with other language in the document, intraspecies variability sounds
more appropriate as a header than intraspecies extrapolation.

P. 4-15, line 12.  Why does the distribution have to be a unimodel normal distribution?  I
understand why you would want a unimodel distribution, but it does not have to be normal.

P. 4-18.  It would be useful to use vinyl chloride as a case example for the requirements and
capabilities of PBPK for route-to-route extrapolation (mentioned earlier, but not with an
example.) First, VC met the requirement that systemic toxicity was the concern, and that the
same endpoint was applicable for the oral and inhalation routes.  Second, use of route-to-route
allowed the use of a better study for the derivation of the RfC. A NOAEL was available for the
oral route, but not for the inhalation route.
                                       F-4

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              APPENDIX G
ADDITIONAL REFERENCES AND SUGGESTIONS

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PBPK Modeling Process Flowchart:
     Mechanisms
      of ToxJcity
     Refine Model
                                Problem
                               Identification
                                Literature
                               Evaluation
Physiological
 Constants
                            Model Formulation
                               Simulation
Compare to
Kinetic Data
                             Des%n/Conduct
                           Critical Experiments
 Biochemical
   Constants
Vatidate Model
                                                           I
                         Extrapolation
                          to Humans
                                   G-l

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Proposed Figure 4-1 Modification:
                                  Is the PBP
                                model available
                                  for the test
                                  species and
                                   humans?
                                   Are the
                                parameters tor
                                  simulating
                                relevant routes
                                  available?
Experimental
    Data
 Collection
                               Does the model
                                simulate dose
                             metrics of relevance
                               o risk assessmen
                                Has the model
                              been evaluated and
                                peer-reviewed?
                                           risk assessment
                                                 G-2

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Validation of Dose Metric Prediction:

Ideally, a PBPK model should be compared with data that is informative regarding the parameters
to which the dose metric predictions are sensitive. This pre-supposes the use of sensitivity and
uncertainty analysis to identify the parameters of concern (those that have the most influence on
the dose metric estimate and are the least certain). For example, validation of a human model
based solely on parent chemical data would not necessarily provide confidence that the model
could be used to predict a metabolite dose metric. The use of parent chemical kinetic data to
validate model estimates of metabolism in the human can be highly misleading, because it is
often the case that the metabolism parameters have little impact on parent chemical
concentrations, while other uncertain parameters (e.g., ventilation rate, blood flow, fat content)
can strongly influence model predictions of parent chemical kinetic behavior. Time-dependent
sensitivity analysis could be conducted with the model under the conditions of the "validation"
exposure to determine whether the metabolic parameter values are identifiable from the data.
                                           G-3

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Calculation of Dose Metrics:

       An important consideration in risk assessments conducted with a PBPK model is
that the critical study (the study showing effects at the lowest exposure) cannot always be
selected on the basis of administered dose or exposure concentration.  This is because the
relationship of the HEC or HED to the administered animal dose depends on the selected
dose metric, which may vary from one endpoint to another, and the nature of the
exposure (species, route of administration, vehicle, duration, etc.). Instead, the
pharmacokinetic model is used to calculate the appropriate dose metrics for each of the
endpoints of concern in each study (Barton and Clewell, 2000).  To calculate the dose
metrics, the model parameters are  set to those for the species in the toxicity study,
whether an experimental animal study or a human study. In the case of developmental
studies, it will be necessary to estimate parameters for a pregnant female or neonate
rather than  an average adult, and physiological and biochemical parameters may have to
be time-dependent.  To the extent possible, study-specific data on animal strain, body
weights, age, and activity should be used in selecting parameters for the model. The
experimental parameters in the model are then set to reproduce the exposure scenario
performed in the study, and the model is run for a sufficient period of time to characterize
the animal exposure to the chemical and, if necessary, its metabolites.

       There are often a number of options regarding the way in which the model should
be run to characterize the dose metric Clewell et  al. 2002a). These will depend upon the
dose metric(s) selected (e.g., peak  vs, average), the nature of the chemical (e.g., volatile
vs. persistent), and the nature of the risk assessment (acute vs. chronic, cancer vs.
noncancer). Usually, the desire is  to estimate an  average daily dose metric, such as the
average daily AUG. (Note that the average daily AUC is the same metric as the time-
weighted average concentration, differing  only by a factor of 24.) In general, the
averaging period in the case of cancer is typically taken to be the lifetime, while the
averaging period in the case of noncancer risk assessment is usually considered to be the
duration of the exposure or, perhaps, a critical window of susceptibility.

       For short-term exposures, the model must be run for an appropriate period, which
depends on the dose metric being used and the timing of the measurement of toxicity  in
relation to the period of exposure.  For short exposure, this is easily done by running the
model for the total duration of the  exposure (or exposures, for repeated exposure studies)
to obtain dose metrics.  If the animals were held for a post-exposure period before
toxicity was evaluated, the model must be run either till the end of the post-exposure
period or for a sufficient duration to ensure that the parent chemical has been completely
cleared from the body or, for a dose metric based on a metabolite, a long enough time to
ensure the complete clearance of the metabolite.  On the other hand, if neurological tests
were performed immediately at the end  of the exposure period, then the dose metric
should be determined at, or up to, that time.  The resulting dose metric obtained for the
total duration of the exposure (including any post-exposure period) can then be divided
by the number of days over which  the experiment was conducted in order to  derive the
average daily value.
                                       G-4

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       The same approach (running the model for the total duration of the study) can be
used to calculate dose metrics for longer-term exposures.  This approach would typically
be necessary for models that describe changes in physiology or biochemistry during
different lifestages (e.g., children, elderly).  However, an alternative approach, which is
often attractive for modeling of chronic exposures with time-invariant model parameters,
is to estimate the steady-state dose metric. There are two principal methods for
calculating a steady-state estimate.  In the first, the model is run until steady state is
reached and then the dose metric is calculated by subtraction.  For example, in the case of
a chronic oral or inhalation exposure conducted 5 days per week, the model can be run
consecutively for 1 week, 2 weeks, 3 weeks, and so on. To calculate the average daily
AUC for a given week, the value at the end of the previous week is subtracted from the
value at the end of the current week and the result is divided by 7. This process is
repeated until the change in the dose metric from one week to the next is insignificant.
For continuous exposures, the comparison can be made on a daily basis instead of
weekly. The other method for estimating the steady-state dose metric is to estimate it
from a single day exposure. The model is run for a single-day exposure plus an adequate
post-exposure period to capture clearance of the parent compound or relevant metabolite.
This value of the single-day dose metric is then modified by the necessary factors to
obtain an average daily value (e.g., by multiplying by five-sevenths in the case of the 5-
day per week exposure just described).  This method is faster, but is only approximate if
the system is not linear.  Typically, it is sufficiently accurate for estimating  average daily
AUC when exposures are below the onset of any nonlinearities.  It can be checked
against the first method described to determine its accuracy in a particular case.

       The dose metric calculations needed are determined by the method to be used for
the noncancer or cancer analysis. If the NOAEL/UF method is being used in  a noncancer
risk assessment, a dose metric only needs to be calculated for the NOAEL or LOAEL
exposure for a particular study and endpoint. On the other hand, if dose-response
modeling is going to be performed, such as in the Benchmark Dose approach, dose-
metrics must be calculated for all exposure groups. The dose metrics are then used in the
dose-response  model in place of the usual exposure concentrations or administered doses.
It is important  to remember that when this is done, the result of the dose-response
modeling will also be in terms of a value of the dose metric rather than an exposure
concentration or administered dose. Dose-response modeling is more properly conducted
on the dose metrics, since it is expected that the observed effects of a chemical will be
more simply and directly related to a measure of target tissue exposure than to a measure
of administered dose.

       In  order to convert an animal dose metric (e.g., at the Benchmark dose) to an
equivalent exposure concentration or administered dose, the pharmacokinetic model must
be either run repeatedly, varying the exposure concentration or administered dose until
the dose metric value is obtained.  In the case of calculating the acceptable human
exposure corresponding to a given toxicity study, the physiological, biochemical, and
exposure parameters in the model are set to appropriate human values and the model is
iterated until the dose metric obtained for the human exposure of concern, often
continuous or daily lifetime exposure, is equal to the  dose metric obtained for the toxicity
                                       G-5

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study, or, once again by dose estimation by a line-search regression. The dose metric
should be calculated in an analogous way to the dose metric for the toxicity study; that is,
if the dose metric in the toxicity study was expressed in terms of an average daily value,
the dose metric used for calculating the associated human exposure should also represent
an average daily value. When a steady-state dose metric is used in both an experimental
animal and the human, it should be noted that the calculation of a steady-state dose metric
in the human generally requires running the model for a much longer period of time than
in the animal.  For short-term exposures, where the model has been run for the total
duration of the toxicity study and the average dose metric value has been calculated, the
dose metric used for calculating the associated human exposure should usually be
obtained for an exposure over the same time period.  An exception to this rule is the case
where it is anticipated that the short-term exposure of concern for the human may
represent a short-term excursion against a background of chronic exposure. In this case,
a more conservative approach may be preferred,  in which a steady-state dose metric
calculation is used for the human.
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Model Evaluation:

       Model evaluation should consider the ability of the model to predict the kinetic
behavior of the chemical under conditions which test the principal aspects of the
underlying model structure. While quantitative tests of goodness of fit may often be a
useful aspect of the evaluation process, the more important consideration may be the
ability of the model to provide an accurate prediction of the general behavior of the data
in the intended application.

       In models of biological  systems, estimates of the values of model parameters will
always have uncertainty, due both to biological variation and experimental error. The
demand that the PBPK fit a variety of data with a consistent set of parameters limits its
ability to provide an optimal fit to a specific set of experimental data.  For example, a
PBPK model of a compound with saturable metabolism is required to reproduce both the
high and low concentration behaviors, which appear qualitatively different, using the
same parameter values. If one were independently fitting single curves with a model,
different parameter value might provide better fits at each concentration, but would be
relatively uninformative for extrapolation.

       Where only some aspects of the model  can be evaluated, it is particularly
important to assess the uncertainty associated with the aspects which are untested. For
example, a model of a chemical and its metabolites which is intended for use in cross-
species extrapolation to humans would preferably be verified using data in different
species, including humans, for both the parent  chemical and the metabolites. If only
parent chemical data is available in the human, the correspondence of metabolite
predictions with data in several animal species could be used as a surrogate, but this
deficiency should be carefully considered when applying the model to predict human
metabolism.  One of the values of biologically based modeling is the identification of
specific data which would improve the quantitative prediction of toxicity in humans from
animal experiments.

       In some cases it may be considered necessary or preferable to use all of the
available data to support model development and parameterization. Unfortunately, this
type of modeling can easily become a form of  self-fulfilling prophecy: models are
logically strongest when they fail, but psychologically most appealing when they succeed
(Yates, 1978). Under these conditions, model  evaluation can be particularly difficult,
putting an additional burden on the investigators to substantiate the trustworthiness of the
model for its intended purpose. Nevertheless,  a combined  model development and
verification can often be successfully performed, particularly for models intended for
interpolation, integration, and comparison of data rather than for true extrapolation.
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Parameter "Fitting":

When parameter estimation has been performed by optimizing model output to
experimental data ("fitting"), the investigator must assure that the parameter is adequately
identifiable from the data (Carson et al., 1983). Moreover, the practical reality of
modeling biological systems is that regardless of the complexity of the model there will
always be some level of "model error" (lack of homomorphism with the biological
system) which can result in systematic discrepancies between the model and
experimental data. This model structural deficiency interacts with deficiencies in the
identifiability of the model parameters, potentially leading to mis-identification of the
parameters. Due to the confounding effects of model error and parameter correlation, it
is quite possible for an optimization algorithm to obtain a better fit to a particular data set
by changing parameters to values that no longer correspond to the biological entity the
parameter was intended to represent.  It is usually preferable, prior to performing an
optimization, to repeatedly vary the model parameters manually to obtain a sense of their
identifiability and correlation under various experimental conditions, although some
simulation languages include routines for calculating parameter covariance or for plotting
joint confidence region contours. Estimates of parameter uncertainty obtained from
optimization routines should be viewed as lower bound estimates of true parameter
uncertainty since only a local, linearized variance is typically calculated.  In
characterizing parameter uncertainty, it is probably more instructive to determine what
ranges of parameter values are clearly inconsistent with the data than to accept a local,
linearized variance estimate provided by the optimization algorithm. Although MCMC
parameter estimation may lead to systematic errors, it might be useful in calculating
parameter uncertainty.
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Model Verification:

       It is important to differentiate model verification and model validation. In brief,
model validation deals with building the right model, while model verification deals with
building the model right (Balci 1997). The accuracy of transforming the chemical-
biological system into a model specification (e.g. the model diagram or equations), and
the accuracy of converting the model representation from a diagram or equations into an
executable computer program is evaluated in model verification.  Model validation, on
the other hand, is  substantiating that the model, within its domain of applicability,
behaves with satisfactory accuracy.

        Verification of a PBPK model involves evaluation of the biological plausibility
of the model structure and parameters as described in the documentation, and the
mathematical correctness of the equations. PBPK model verification also involves
examination of the model code to assure that it mathematically implements the model as
described in the documentation. This examination includes checking for correctness of
statements and functions, and correct order of statement execution (for languages that are
not self-sorting).  Improper statement order in a numerical integration code can result in a
model that appears to run normally but gives the wrong results. A problem common to
some graphic model representations is the inadvertent mis-specification of a parameter as
local vs. global in one of the compartments, again resulting in a model that appears to run
normally but gives the wrong results.

       Whether a code- or graphical-based model is used, it is preferable that the
language produce as one possible output the set of equations that constitute the PBPK
model.  Code-based representations ease the task of insuring that the model is actually
constructed  as described in the documentation.  To facilitate model verification, the
model code  should be organized and commented in such a way as to facilitate
understanding by  individuals other than the original program developer. In the case of a
model intended for use  in a risk assessment application,  it is imperative to provide
documentation of the particular parameter values and simulations that are required to
reproduce any validation runs and dose metric calculations. This usually entails the
provision of step-by-step directions, either using the language's scripting capability or in
separate documentation, that allow reproduction of the validation plots and dose-metric
calculations by following specific  directions or by invoking specified program blocks.
                                       G-9

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Model Documentation:

       Adequate documentation is critical for evaluation of a model. The documentation
for a PBPK model should include sufficient information about the model so that an
experienced modeler could accurately reproduce its structure and parameterization.
Usually the suitable documentation of a model will require a combination of one or more
"box and arrow" model diagrams together with any equations which cannot be
unequivocably derived from the diagrams. In fact, for simple models a well-constructed
model diagram, together with a table of the input parameter values and their definitions,
is all that an accomplished modeler should need in order to create the mathematical
equations defining a PBPK model. The model diagram should be labeled with the names
of the key variables associated with the compartment or process represented by each box
and arrow.  All tissue compartments, metabolism pathways, routes of exposure, and
routes of elimination should be clearly and accurately presented. The model diagram
should also clearly  differentiate blood flow from other transport (e.g., biliary excretion)
or metabolism, and arrows should be used where the direction of transport could be
ambiguous.

       In general, there should be a one-to-one correspondence of the boxes in the
diagram to the mass balance equations (or steady-state approximations) in the model.
Similarly, the arrows in the diagram correspond to the clearance (transport or metabolism
processes) in the model. Each of the arrows connecting the boxes in the diagram should
correspond to one of the terms in the mass balance equations for both of the
compartments it connects, with the direction of the arrow pointing from the compartment
in which the term is negative to the compartment in which it is positive. Arrows only
connected to a single compartment, which represent uptake and excretion processes, are
interpreted similarly.

       Interpretation of the model  diagram is supplemented by the definition of the
model input parameters in the corresponding table.  The definition and units of the
parameters can indicate the nature of the process being modeled (e.g.,  diffusion-limited
vs. flow-limited transport, binding vs. partitioning, saturable vs. first-order metabolism,
etc.).  The values used for all model parameters should be provided,  with units. If any of
the listed parameter values are based on allometric scaling, a footnote should provide the
body weight used to obtain the allometric constant as well as the power of body weight
used in the scaling. Any equations included to supplement the diagram should be
dimensionally consistent and in a standard mathematical notation. Generic equations
(e.g., for tissue "i") can help to keep the description brief but complete.
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Model Calibration:

       A critical issue in the use of Bayesian approaches, such as Markov Chain Monte
Carlo (MCMC) analysis, for the "calibration" of PBPK models in risk assessment
applications is whether the posterior distributions for the PBPK parameters should be
used to estimate dose metrics in place of the prior estimates based on the scientific
judgment of the model developers.  One concern is that the Bayesian approach may give
undue priority to the particular studies included in the Bayesian analysis (as compared to
potentially more appropriate studies that may have been used to inform the various
parameters in the model, but which were not amenable to incorporation in the MCMC
analysis.

       Another consideration is whether the subject population in the data sets included
in the MCMC analysis is representative of the population for which the  risk assessment is
being performed.  For example, the subjects in controlled human exposures may be at
rest, and the MCMC my correctly estimate a relatively low ventilation rate; however, this
ventilation rate may not not be appropriate for the activity level in the general population.
Therefore, calculations of dose metrics and uncertainty/variability analyses performed in
support of an environmental risk assessment would more properly use a ventilation rate
suitable for the general  population, not the posterior obtained from the experimental
subjects.

       The greatest value of MCMC analysis is its ability to characterize the variability
and uncertainty in the model predictions, and as such is most appropriately used in the
risk characterization segment of a risk assessment. Its use in the dose-response
assessment is more problematic.
                                       G-ll

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