DRAFT EPA/600/R-05/043A
DO NOT CITE OR QUOTE June 2005
External Review Draft
Approaches for the Application of Physiologically
Based Pharmacokinetic (PBPK) Models and Supporting
Data in Risk Assessment
NOTICE
THIS DOCUMENT IS A PRELIMINARY DRAFT. It has not been formally
released by the U.S. Environmental Protection Agency and should not at this
stage be construed to represent Agency policy. It is being circulated for comment
on its technical accuracy and policy implications.
National Center for Environmental Assessment
Office of Research and Development
U.S. Environmental Protection Agency
Washington DC
-------
DISCLAIMER
This document is a draft for review purposes only and does not constitute U.S.
Environmental Protection Agency policy. Mention of trade names or commercial products does
not constitute endorsement or recommendation for use.
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CONTENTS
LIST OF BOXES v
LIST OF TABLES vi
LIST OF FIGURES vii
LIST OF ABBREVIATIONS AND ACRONYMS viii
PREFACE ix
AUTHORS AND REVIEWERS x
EXECUTIVE SUMMARY xi
1. INTRODUCTION 1-1
1.1. SCOPE OF 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 2-2
2.3. PHARMACOKINETIC DATA NEEDS IN RISK ASSESSMENTS 2-4
2.4. PHARMACOKINETIC MODELS IN RISK ASSESSMENT 2-7
2.5. ROLE OF PBPK MODELS IN RfC DERIVATION 2-8
2.5.1. Reference Concentration 2-8
2.5.2. Point of Departure 2-8
2.5.3. Duration Adjustment 2-9
2.5.4. Dosimetric Adjustment Factor 2-10
2.5.5. Uncertainty Factors: Role of PBPK Models 2-11
2.5.6. Summary 2-12
2.6. ROLE OF PBPK MODELS IN RfD DERIVATION 2-12
2.6.1. Reference Dose 2-12
2.6.2. Point of Departure 2-13
2.6.3. Uncertainty Factors ; 2-14
2.6.4. Summary 2-15
2.7. ROLE OF PBPK MODELS IN CANCER RISK ASSESSMENT 2-15
2.7.1. High-Dose to Low-Dose Extrapolation 2-15
2.7.2. Interspecies Extrapolation 2-16
2.7.3. Route-to-Route Extrapolation 2-17
2.7.4. Intraspecies Variability 2-17
2.7.5. Summary 2-18
2.8. USE OF PHARMACOKINETIC DATA AND MODELS IN EXPOSURE
ASSESSMENT 2-18
2.8.1. Conventional Approaches 2-18
2.8.2. Role of PBPK Models 2-19
2.8.3. Summary 2-19
2.9. PHARMACOKINETIC DATA NEEDS IN RISK ASSESSMENT:
SUMMARY 2-19
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CONTENTS (continued)
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 3-3
3.4. PARAMETER ESTIMATION 3-7
3.4.1. Physiological Parameters 3-8
3.4.2. Partition Coefficients 3-11
3.4.3. Biochemical Parameters 3-12
3.5. COMPUTER IMPLEMENTATION 3-13
3.6. MODEL EVALUATION 3-16
3.7. SENSITIVITY, UNCERTAINTY, AND VARIABILITY ANALYSES 3-21
3.7.1. Sensitivity Analysis 3-21
3.7.2. Variability Analysis 3-23
3.7.3. Uncertainty Analysis 3-25
3.8. DEVELOPING PBPK MODELS FOR USE IN RISK ASSESSMENT:
STRATEGIES FOR DEALING WITH DATA-POOR SITUATIONS 3-27
3.8.1. Minimal Data Needs for Constructing PBPK Models 3-27
3.8.2. Surrogate Data for Interspecies and Interchemical Extrapolations 3-28
3.9. EVALUATION OF PBPK MODELS: SUMMARY 3-30
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 4-4
4.3. EXAMPLES OF THE USE OF PBPK MODELS IN RISK ASSESSMENT .... 4-9
4.3.1. High-Dose to Low-Dose Extrapolation 4-9
4.3.2. Interspecies Extrapolation 4-10
4.3.3. Route-to-Route Extrapolation 4-12
4.3.4. Duration Adjustment 4-14
4.3.5. Intraspecies Extrapolation 4-15
4.3.6. RfD Derivation 4-16
4.3.7. RfC Derivation 4-17
4.3.8. Cancer Risk Assessment (unit risk estimates, RfC, and RfD) 4-18
4.3.9. Mixture Risk Assessment 4-21
4.4. LINKAGE TO PHARMACODYNAMIC MODELS 4-22
GLOSSARY G-l
REFERENCES R-l
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LIST OF BOXES
Box 2-1. Examples of dose metrics useful for exploring dose-response relationships 2-4
Box 2-2. Role of PBPK models in the RfC process 2-12
Box 2-3. Role of PBPK models in the RfD process 2-15
Box 2-4. Role of PBPK models in cancer risk assessment 2-18
Box 2-5. Role of PBPK models in exposure assessment 2-19
Box 4-1. Questions and issues to be considered while evaluating the adequacy of
a PBPK model 4-3
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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 3-5
Table 3-2. Equations used for describing diffusion-limited uptake in PBPK models 3-6
Table 3-3. Reference 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 3-14
Table 4-1. Dose metrics used in PBPK model-based cancer and noncancer risk
assessments 4-7
Table 4-2. Relationship between tumor prevalence and dichloromethane metabolites
produced by microsomal and glutathione pathway for the bioassay conditions
(methylene chloride-dose response in female mice) 4-20
Table 4-3. Examples of biologically based models of endpoints and processes of
toxicological relevance 4-25
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LIST OF FIGURES
Figure 2-1. Relationship between the exposure concentration and adverse response for a
hypothetical chemical 2-3
Figure 2-2. Rat-human extrapolation of exposure concentrations of toluene on the basis
of equivalent dose metrics (AUC of toluene in blood; 3.8 mg/L-hr) 2-6
Figure 3-1. Conceptual representations of PBPK models for (A) toluene, (B) ethylene
oxide, (C) 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD), and (D) vinyl acetate. 3-4
Figure 3-2. Comparison of PBPK model simulations (solid lines) with experimental
data (symbols) 3-18
Figure 3-3. Sensitivity ratios associated with certain input parameters of a PBPK model.. 3-22
Figure 3-4. Illustration of the use of the Monte Carlo approach for simulating the
distribution of internal concentration versus time on the basis of population
distributions of PBPK model parameters 3-25
Figure 4-1. Decision tree 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 4-6
Figure 4-3. High-dose to low-dose extrapolation of dose metrics using PBPK model for
toluene 4-11
Figure 4-4. Oral-to-inhalation extrapolation of the pharmacokinetics of chloroform on the
basis of same AUC in blood (7.06 mg/L-hr) 4-13
Figure 4-5. Duration adjustment (4 hr to 24 hr) of toluene exposures in rats, based on
equivalent AUC (2.4 mg/L-hr) 4-14
Figure 4-6. Estimation of the interindividual factor from the 50th (median) and 95th
percentile values of a dose metric simulated with a probabilistic PBPK
model 4-15
Figure 4-7. PBPK model predictions of glutathi one-path way metabolites in liver
in mice 4-20
Figure 4-8. Relationship between the dose metric ((irnol metabolized/g liver/hr)
simulated by PBPK model and the cell killing inferred from
pharmacodynamic model for chloroform 4-23
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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)
BMD benchmark dose
BMC benchmark concentration
Cmax maximal concentration
CSF cancer slope factor
DAF dosimetric adjustment factor
HEC human equivalent concentration
HI hazard index
IUF interspecies uncertainty factor
IUR inhalation unit risk
IVF intraspecies variability factor
LOAEL lowest-observed-adverse-effect level
NOAEL no-observed-adverse-effect level
MBDE mass balance differential equation
MO A mode of action
MVK Moolgavkar-Venzon-Knudson
OSF oral slope factor
PK pharmacokinetic
PBPK physiologically based pharmacokinetic
POD point of departure
QSAR quantitative structure-activity relationship
RfD reference dose
RfC reference concentration
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PREFACE
This draft report, 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. These 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 EPA scientists and risk assessors who may be less familiar with the field. In
addition, this report can be informative to PBPK modelers within and outside the Agency, as it
provides an assessment of the types of data and models that the EPA requires for consideration
of a model for use in risk assessment. This draft report will be externally peer-reviewed by an
independent panel of experts prior to making the report final.
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AUTHORS AND REVIEWERS
The National Center for Environmental Assessment, Office of Research and
Development, was responsible for the preparation of this document. It was developed under
EPA Contract No. 4W-0322-NASX.
EPA PROJECT OFFICERS
Femi Adeshina
National Center for Environmental Assessment
Office of Research and Development
U.S. Environmental Protection Agency
Washington, DC
Chad wick Thompson
National Center for Environmental Assessment
Office of Research and Development
U.S. Environmental Protection Agency
Washington, DC
AUTHORS
Kannan Krishnan, University of Montreal, Alberta, Canada
Hugh Barton, NHEERL-RTP
Rob DeWoskin, NCEA-RTP
Bob Sonawane, NCEA-W
Chadwick Thompson, NCEA-W
INTERNAL EPA REVIEWERS
Jerry Blancato, NERL-LV
Weihsueh Chiu, NCEA-W
Joyce Donohue, OW
Hisham El-Masri, NCEA-W
Marina Evans, NHEERL-RTP
Lynn Flowers, NCEA-IRIS
Karen Hammerstrom, NCEA-W
John Lipscomb, NCEA-Cin
Allen Marcus, NCEA-IRIS
Dierdre Murphy, OAQPS
Alberto Protzel, OPP-W
Paul Schlosser, NCEA-RTP
Woodrow Setzer, NHEERL-RTP
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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?
Because PBPK modeling efforts to date have largely focused on chemicals that cause
systemic effects (i.e., water-insoluble gases and some nonvolatile organics), this document draws
upon the experience and literature on these efforts.
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 U.S. Environmental Protection Agency risk assessment
framework. Useful resources are provided as appendices, including (1) a list of publications
relating to PBPK modeling and its use in health risk assessment, (2) a compilation of parameters
of several published PBPK models, and (3) a list of published algorithms for estimating
parameters for PBPK models of environmental chemicals.
PBPK models consist of a series of equations for compartments, fluid flows, and
chemical reactions that represent real biological tissues and physiological processes in the body
and 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 applied dose
in a quantitative dose-response assessment, with the intent of reducing the uncertainty inherent in
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using the applied dose to derive risk values. This reduction in uncertainty and improved
scientific basis for the risk 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., to extrapolate to conditions beyond those
of the 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 applied dose.
Examples of PBPK model applications in risk assessments include interspecies
extrapolation of the dose-response (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 should, 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. As a resource, appendices to this document provide a
compilation of parameters of several published PBPK models, a list of available animal-
alternative algorithms for parameter estimation, and key references.
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) the model has been evaluated and peer-reviewed for the adequacy
of its structure and parameters, and (3) the model 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 use to derive a given point of departure (e.g.,
NOAEL, LOAEL, BMD, BMC) for use in dose-response analyses for toxicity endpoints,
including 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
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toxicity in that species by another route of exposure for purposes of route extrapolation. For
most applications, a version of the PBPK model is also developed to simulate kinetics in humans
for estimating the applied dose to a human needed to achieve the relevant internal dose predicted
from the animal toxicity or, less frequently, 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.
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1 1. INTRODUCTION
2
3 1.1. SCOPE OF DOCUMENT
4 The objective of this document is to provide a description of approaches for using
5 physiologically based pharmacokinetic (PBPK) data and models in human health risk
6 assessment. The document focuses primarily on the evaluation and use of PBPK models for
7 predicting internal dose at target organs in risk assessment applications. Many of the past efforts
8 on PBPK modeling have focused on water-insoluble gases that cause systemic toxicity (i.e.,
9 producing effects remote from the site of exposure), as well as some nonvolatile organics. This
10 document primarily draws on the experience and literature on these efforts. The approaches are
11 not intended, for example, to apply directly to agents, gaseous or particulate, where the target
12 organ is the respiratory tract; the reference concentration (RfC) methodology (U.S. EPA, 1994)
13 should be consulted for these circumstances. However, the elements of discussion found in this
14 document are also conceptually applicable, in a broader sense, to other kinds of dosimetry
15 models and a wider range of substances.
16 In developing this document, it was assumed that risk assessors are familiar with the
17 basic concepts of PBPK modeling and that model developers are familiar with the basic concepts
18 of risk assessment; therefore, the document contains only brief descriptions of PBPK modeling
19 and risk assessment methods. Appropriate references to secondary review articles and reports
20 from which readers can obtain additional information are provided.
21 Finally, it is important to realize that the application of PBPK models in risk assessment
22 is evolving. Thus, this document does not specify (or recommend) when the effort to construct
23 and apply PBPK modeling is justified by the additional insight it provides; rather it highlights
24 some of the benefits of PBPK modeling in risk assessment.
25
26 1.2. INTENDED AUDIENCE
27 The document was prepared with two primary audiences in mind: (1) risk assessors who
28 need to know about the potential applications of PBPK models in risk assessments, and (2)
29 PBPK model developers who need to be familiar with potential applications in health risk
30 assessment.
31
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1 1.3. ORGANIZATION OF THE DOCUMENT
2 Three key chapters form the main core of this document. They describe what risk
3 assessors need in terms of pharmacokinetic data, and why (Chapter 2); how to evaluate PBPK
4 models for use in risk assessments (Chapter 3); and how to use PBPK models in risk assessments
5 to address specific areas of uncertainty (Chapter 4).
6 Chapter 2 addresses data needs in terms of reference dose (RfD) and RfC derivation, as
7 well as predictive estimates in cancer risk assessment. This chapter also contains a brief
8 discussion on the minimal data requirements for constructing PBPK models, as well as the use of
9 pharmacokinetic data and PBPK models to improve exposure assessments.
10 Chapter 3 presents an approach and some criteria for evaluating PBPK models intended
11 for use in risk assessments. The issues relating to the evaluation of PBPK models that are
12 discussed in this chapter will facilitate the assessor's decision on whether or not an available
13 model is adequate and scientifically defensible for use in reducing uncertainties in a given risk
14 assessment. In this regard, the PBPK modeling issues are considered under each of the
15 following topic areas: model structure, mathematical description, parameter estimation
16 (calibration), computer implementation, and evaluation. Current criteria as well as accepted
17 methods are identified and then assembled to facilitate the identification of PBPK models that
18 meet the requirement for use in risk assessment.
19 Chapter 4 discusses how PBPK models and data can be applied within the current
20 Agency risk assessment framework to address specific areas of uncertainty. The following types
21 of PBPK model applications in risk assessment are presented in this chapter: high-dose to low-
22 dose extrapolation, interspecies extrapolation, intraspecies extrapolation, route-to-route and
23 scenario extrapolation, mixture risk assessment, and linkage with pharmacodynamic models.
24 This chapter also highlights how PBPK models are used in cancer and noncancer assessments.
25 The appendices provide a list of publications relating to PBPK modeling and its use in
26 health risk assessment, a compilation of parameters of several published PBPK models, and a list
27 of published algorithms for estimating parameters for PBPK models of environmental chemicals.
28
29
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1 2. PHARMACOKINETIC DATA AND MODEL NEEDS IN RISK ASSESSMENT
2
3 2.1. PHARMACOKINETICS AND DOSIMETRY MODELING
4 Pharmacokinetics (pharmakon + kinetics; pharmakon (Greek) = drugs and poisons;
5 kinetics = change as a function of time) involves the study of the time course of the parent
6 chemical or metabolite concentrations or amounts in biological fluids, tissues, and excreta and
7 the construction of mathematical models to interpret such data (Wagner, 1981). The time course
8 of the concentration of a chemical or its metabolite in biota is determined by the rate and extent
9 of absorption, distribution, metabolism, and excretion (ADME). The pharmacokinetics or
10 ADME of a substance determines the delivered dose or the amount of chemical available for
11 interaction in the tissues. Relating adverse response observed in biota to an appropriate measure
12 of delivered dose (e.g., concentration of the toxic chemical in the target tissue) rather than
13 administered dose or exposure concentration is likely to improve the characterization of many
14 dose-response relationships.
15 A range of modeling approaches is used to characterize exposures and resulting delivered
16 doses. This variety of approaches reflects differences in chemical and physical characteristics
17 (e.g., stable or reactive gases, particulate matter, lipophilic organics, water-soluble compounds)
18 and their ability to cause contact site or systemic toxic effects (Andersen and Jarabek, 2001;
+
19 Overton, 2001; U.S. EPA, 1994; 2004). Many drugs and toxic chemicals that cause systemic
20 effects are absorbed following oral exposures, so compartmental and noncompartmental
21 pharmacokinetic modeling has focused on these characteristics (O'Flaherty 1981; Renwick
22 2001). Compartmental modeling, generally described as a set of mathematical equations that
23 describe empirical pharmacokinetic data concerning a chemical, evolved to include mathematical
24 descriptions of biological processes (e.g., partition coefficients, tissue volumes), which is the
25 focus of this document.
26 Because the respiratory tract is a frequent site of both exposure and toxiciry, it has been a
27 particular focus for a range of modeling approaches. These approaches include those developed
28 for gases of various reactivity and solubility, as well as for particulate matter (see U.S. EPA,
29 1994). More refined approaches are available and useful for reactive gases and particulate
30 matter, including two-dimensional and three-dimensional modeling such as computational fluid
31 dynamics models (Kimbell et al., 1993; Martonen et al., 2001; Overton, 2001, U.S. EPA, 2004).
32 Predicting behaviors of volatile anesthetics, including compounds now used exclusively as
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1 industrial chemicals, was a driving force for the development of PBPK models (Krishnan and
2 Andersen, 2001).
3 Another significant factor influencing modeling approaches is the role of metabolism.
4 For example, a range of volatile compounds can cause nasal or other respiratory toxicities that
5 require metabolism of the chemical in respiratory tract tissue. These kinds of chemicals have
6 been modeled using elaborate PBPK models of the nose (with or without representation of the
7 rest of the body) that have been linked with computational fluid dynamic models to describe the
8 deposition of chemical in different regions of the nose (Frederick et al., 2002; Bogdanffy et al.,
9 2001). Similarly, compounds that are relatively water soluble require specific approaches that
10 address aspects such as fractional absorption or "wash-in, wash-out" effects (Johanson, 1991;
11 Medinsky et al., 1993; Perkins et al., 1995).
12 Although the approaches detailed in the RfC methodology do not address all of these
13 aspects, there is recognition of the need for additional approaches that address these and other
14 challenging aspects of respiratory tract dosimetry (U.S. EPA, 1994).
15 The relevant modeling approach, therefore, depends on the physical and chemical
16 characteristics of the material, the method and route of exposure or delivery, and the toxicities
17 under consideration. All of these modeling approaches attempt to describe the dose delivered to
18 the relevant areas of the body, whether that is a region of the respiratory tract or skin, or systemic
19 delivery through the blood supply to target organs. These approaches permit estimation of some
20 measure of delivered dose for improved understanding of the dose-response relationship.
21
22 2.2. DOSE-RESPONSE AND MEASURES OF DELIVERED DOSE
23 Dose-response relationships that appear unclear or confusing at the administered dose
24 level can become more understandable when expressed on the basis of internal dose of the
25 chemical. Figure 2-1 depicts the case of a hypothetical chemical for which the correlation between
26 dose and response is weak or complex (Panel A). However, once the relationship is based on
27 internal dose, there emerges a clear and direct relationship between dose and response (Panels B
28 and C). The major advantage of constructing dose-response relationships on the basis of internal
29 or delivered dose is that it can provide a stronger biological basis for conducting extrapolations and
30 for comparing responses across studies, species, routes, and dose levels (Andersen et al., 1987;
31 Clewell and Andersen, 1997; Aylward et al., 1996; Benignus et al., 1998; Melnick and Kohn,
32 2000).
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Hill.
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linear
Weibull
60-|
TJ
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!_ 40-\
||> 30-
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*o
£ 10 -
(0
a:
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B
1000 2000 3000
Exposure concentration (ppm)
30 -
25 •
§ 20
o
t 15-
CL
£ 10-
4000
1 10 100 1000
Exposure concentration (ppm)
10000
10 20 30 40 50
Rate of amount metabolized (mg/hr)
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 use of blood and tissue concentrations for relating dose and response in exposed
organisms has long been recognized in pharmacology (e.g., Wagner, 1981). The target tissue
dose closely related to ensuing adverse responses is often referred to as the "dose metric"
(Andersen and Dennison, 2001). Dose metrics used for risk assessment applications should
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
specific window of susceptibility), and intensity (peak, average, or integral), as well as 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
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of action (MO A) information to the contrary, the integrated concentration of the toxic form of
chemical over lifetime (i.e., area under the concentration versus time curve [AUC]) in target
tissue has been considered to be the appropriate dose metric (Collins, 1987; Voisin et al., 1990;
Clewell et al., 2002).
When the carcinogen 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 window of
susceptibility for a particular gestational
event (e.g., Welsch et al., 1995; Luecke et
al., 1997).
Even though the AUC and rate of
metabolite formation are among the most
Box 2-1. Examples of dose metrics useful for
exploring dose-response relationships
Parent chemical
• Peak concentration
• Average concentration
• Amount or quantity
• AUC
Metabolite
• Peak concentration
• Average concentration
• Amount or quantity
• Rate of production
• Cumulative rate of formed/time/L tissue
• AUC
Miscellaneous
• Receptor occupancy (extent/duration)
• Macromolecular adduct levels
• Depletion of cofactors
commonly investigated dose metrics, other surrogates of tissue exposure may also be appropriate
for risk assessment purposes, depending on the chemical and its MOA (Clewell et al., 2002).
Box 2-1 lists dose metrics that can be used to derive dose-response relationships for risk
assessment.
2.3. PHARMACOKINETIC DATA NEEDS IN RISK ASSESSMENTS
The 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, based
on the relationship between administered dose and observed responses in laboratory or field
studies. For noncancer and nonlinear cancer assessments, adjustments to the POD are then made
to account for uncertainties in the estimate of a POD for humans and to protect the most sensitive
human subpopulation exposed by specific routes (e.g., inhalation, oral). This process frequently
requires conducting interspecies, intraspecies, high-dose to low-dose, duration, and exposure
route extrapolations of responses. Based on information about the MOA of the compound, an
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1 appropriate approach for the extrapolation can be identified. Such an approach implies that
2 when the value of the dose metric is identical in two situations (rat vs. human, oral vs. inhalation,
3 6-hr exposure vs. 24-hr exposure), the two administered doses are pharmacokinetically
4 equivalent For example, exposure of rats to 50 ppm toluene for 6 hr and of humans to 17.7 ppm
5 toluene for 24 hr yields the same blood AUC (3.8 mg/L-hr), implying that these exposure
6 scenarios in rats and humans are pharmacokinetically equivalent (Figure 2-2). Alternatively, if
7 one were to assume that the pharmacokinetics in humans were identical to those in rats, an
8 equivalent 24 hr exposure would be calculated to be 12.5 ppm (i.e., 6 hr x 50 ppm is equivalent
9 to24hr x 12.5 ppm).
10 For reactive gases that cause contact site toxicity, the concentration of chemical or its
1.1 delivery rate to the target may be the relevant dose metric, whereas for anesthetic effects of
12 volatile organics, the current concentration in the blood has been an effective dose metric. In
13 these cases, the acute effects are more —or entirely— dependent upon concentration than on
14 time, so the extrapolations would be dependent upon that dose metric, potentially without
15 adj ustments for duration of exposure.
16 The most robust pharrnacokinetic data set needed for risk assessment would consist of the
17 time-course data on the dose metric associated with exposure scenarios and doses used in the
18 critical studies chosen for the assessment (e.g., animal bioassays or human epidemiological
19 studies) and relevant human exposure conditions. An example of such a dose metric is the
20 concentration of a toxic metabolite in target tissue over a 24 hr period in the test species and in
21 humans. This information should be obtained for the window of susceptibility, route and
22 scenario of exposure associated with the critical study as well as for the window of susceptibility,
23 appropriate route, and exposure scenarios in humans. If such a pharmacokinetic data set is
24 available for each scenario of interest, then there is no real need for any pharmacokinetic models,
25 even though their availability can facilitate simulation of other potential scenarios of interest and
26 critical determinants of tissue dose.
27 In almost all cases, dose metric measurements associated with human exposures to
28 environmental chemicals will not be available. Even the available animal pharmacokinetic data
29 may not correspond to the active toxic moiety, relevant route, or appropriate dose levels. In the
30 absence of experimental data on the biologically active form of the chemical in target tissues,
31 data on blood concentration of the parent chemical, urinary metabolite levels, or fraction
32
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RAT
I
I
100-
10-
1 -
0.1 -
0.01 -
0.001 -
0.0001
8 12 16
Time (hours)
20
24
HUMAN
Venous blood concentration
10 -
1 -
i °"
•§ 0.01 -
0.001 -
n nnm .
/•"^
0 4 8 12 16 20 24
Time (hours)
2
3
4
5
6
7
8
9
10
11
12
13
14
Figure 2-2. Rat-human extrapolation of exposure concentrations of toluene
on the basis of equivalent dose metrics (AUC of toluene in blood; 3.8 mg/L-
hr). Rat exposures are for 6 hr to 50 ppm; human exposures are for 24 hr to 17.7
ppm. Both exposures yield the same AUC, as determined using species-specific
PBPK models published by Tardif et al. (1997). Similar exercises can be done to
determine the exposure concentrations that yield equivalent peak concentrations
(Cmax) in rats and humans.
absorbed may be used as a surrogate of dose metrics. These 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.
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1 2.4. PHARMACOKINETIC MODELS IN RISK ASSESSMENT
2 Regulatory agencies have a mandate to develop guidelines for toxicity testing and
3 formulate risk values based on the current understanding of the dose-response relationship.
4 Reference values correspond to an estimate of an exposure level for a given duration that is
5 likely to be without an appreciable risk of adverse effects over the lifetime in humans, including
6 sensitive subpopulations. The reference values developed at EPA include reference
7 concentration (RfC) for chronic inhalation exposures and reference dose (RfD) for chronic oral
8 exposures. For chronic oral and inhalation cancer risk assessments with an unknown or a linear
9 MOA (e.g., mutagenic carcinogens), EPA develops unit risk estimates, such as cancer slope
10 factor (CSF) and inhalation unit risk (IUR) estimates. The underlying assumption in these
11 processes is that the exposure concentration (or applied dose) results in a toxic chemical moiety
12 in a target organ that will be less than or equal to a level not associated with significant adverse
13 responses during a lifetime (reference value) or that yields a likely risk at or below the estimated
14 lifetime risk (unit risk).
15 Even though a key factor in the induction of adverse effects is the presence of the toxic
16 form of a chemical in the target organ, it is rare that data are available on the time course of the
17 toxic moiety of chemicals in the target tissue(s) in humans. Even in animal studies, it is more
18 practical to get measures of blood, plasma, and urinary concentrations of toxic chemicals and
19 their metabolites than to get data on the time course on the actual tissue dose of a toxic moiety
20 relevant for use in risk assessment. Pharmacokinetic models are therefore used to simulate the
21 tissue concentration of toxic substances. There are both noncompartmental and compartmental
22 pharmacokinetic models (Renwick, 2001); however, we will focus on compartmental models.
23 Among the compartmental pharmacokinetic models, those that allow for prediction of
24 target organ concentration are most appropriate and useful for conducting extrapolations
25 essential for risk assessment. These models are commonly referred to as PBPK. models
26 (Himmelstein and Lutz, 1979; Rowland, 1985; Leung, 1991; Andersen, 1995; Krishnan and
27 Andersen, 2001). By simulating the kinetics and dose metric of chemicals, they attempt to
28 reduce the uncertainty related to the interspecies, intraspecies, high-dose to low-dose, route-to-
29 route, and exposure scenario extrapolations essential in the context of RfC, RfD, and cancer unit
30 risk estimate processes. The following sections discuss how the PBPK models are used in the
31 context of health risk assessment.
32
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1 2.5. ROLE OF PBPK MODELS IN RfC DERIVATION
2 2.5.1. Reference Concentration
3 The RfC corresponds to an estimate of continuous inhalation exposure (mg/m3) for a
4 human population, including sensitive subgroups, that is likely to be without an appreciable risk
5 of adverse health effects during a lifetime (U.S. EPA, 1994). Notationally, RfC is defined as:
6
7 RJC = POD[HEC]/UF
8
9 where:
10 POD[HEC] = POD (no-observed-adverse-effect level [NOAEL], lowest-observed-adverse-
11 effect level [LOAEL], or benchmark concentration [BMC]) dosimetrically
12 adjusted to a human equivalent concentration (HEC)
13
14 UF = uncertainty factors to account for the extrapolations associated with the POD (i.e.,
15 interspecies differences in sensitivity, intraspecies extrapolation, subchronic-to-
16 chronic extrapolation, LOAEL-to-NOAEL extrapolation, and incompleteness of
17 database)
18
19 The starting point for an RfC derivation is the identification of the POD for the critical
20 effect in a key study. Subsequent steps involve (1) adjustment for the difference in duration
21 between experimental exposure (e.g., 6 hr) and expected human exposure (24 hr); (2) calculation
22 of the HEC, based on dosimetric adjustments; and (3) application of uncertainty factors. The
23 benefit of using PBPK models in the RfC process is discussed below. Specifically, the role of
24 PBPK models in determining the POD, duration adjustment factor, HEC, and uncertainty factors
25 is presented in Sections 2.5.2 through 2.5.5.
26
27 2.5.2. Point of Departure
28 Ideally, the POD used in the RfC process should be the inhalation route-specific NOAEL,
29 LOAEL, or BMC. These PODs essentially correspond to exposure concentrations of an
30 experimental or field study (NOAEL, LOAEL) or to the lower confidence limit (95th percentile)
31 of the exposure concentration (BMCL) associated with a specified response level (generally in
32 the range of 1 to 10 %; e.g., BMCLio%) derived from statistical analysis of experimental dose-
33 response data (U.S. EPA, 1994, 2000a).
34 Route-to-route extrapolation can be conducted on the basis of equivalent potential doses
35 when information on the POD was available only for a noninhalation route of exposure (e.g., oral
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1 route) (Pauluhn, 2003). For example, the NOAEL (mg/kg/day) associated with a particular
2 exposure route (e.g., oral) was converted to milligrams per day and then to equivalent inhaled
3 concentration, based on breathing rate and body weight of the test species. This simplistic
4 approach assumes that the rates of absorption, distribution, metabolism, excretion, and tissue
5 dosimetry of chemicals are the same for a given total dose, regardless of the exposure route and
6 intake rate. Such an approach essentially neglects the route-specific differences in
7 pharmacokinetics—more specifically, absorption, clearance, and first-pass effects. When data
8 on the route-specific fraction absorbed are available, they are used to determine the equivalent
9 inhalation concentration on the basis of equivalent absorbed doses (U.S. EPA, 1999a), but
10 preference would be given to more complete pharmacokinetic modeling.
11 The POD for RfC derivation cannot be identified or established with only
12 pharmacokinetic data or PBPK models, independent of the dose-response data. On the other
13 hand, better characterization of dose-response relationships has been demonstrated by the use of
14 integrated pharmacokinetic-pharmacodynamic models (e.g., Gearhart et al., 1990,1994;
15 Timchalk et al., 2002). Such models might be capable of predicting response and thus
16 determining a POD if sufficient data are available. More commonly, however, PBPK modeling
17 will be useful for conducting route-to-route extrapolation on the basis of equivalent delivered
18 dose from PODs identified from NOAEL, LOAEL, or BMC (e.g., oral to inhalation).
19
20 2.5.3. Duration Adjustment
21 RfCs are intended for continuous exposure of human populations, such that the POD used
22 in its derivation should correspond to 24 hr/day exposures (U.S. EPA, 1994). Because the PODs
23 are frequently obtained from animal exposures or occupational exposures that occur for 6 to 8
24 hr/d, 5 d/wk, adjustment to a continuous 24 hr exposure is conducted on the basis of hours per
25 day and days per week (i.e., 6/24 x 5/7), which essentially results in a lower concentration for
26 continuous exposures (U.S. EPA, 2002). This simple adjustment, generally referred to as
27 Haber's Rule, implies that the AUC (i.e., concentration x time [C x t]) and not peak
28 concentration is the dose metric associated with the toxicity endpoints (U.S. EPA, 2002). When
29 data indicate that a given toxicity is more dependent on concentration than on duration (time),
30 this adjustment would not be used. If neither dose metric is demonstrable experimentally to be
31 the appropriate measure of internal dose, the Agency uses adjustment to a continuous inhalation
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1 exposure based on the C x t relationship as a matter of health-protective policy (U.S. EPA,
2 2002).
3 Depending on the dose metric identified or hypothesized to be the most appropriate for
4 the chemical and endpoint, the duration-adjusted exposure values can be obtained with PBPK
5 models (Jarabek, 1994; U.S. EPA, 2002). This approach is based on the expectation that the
6 pharmacodynamic aspect does not change between the various durations of within-day exposures
7 (<24 hr). Consistent with the Agency's policy (U.S. EPA, 2002), the AUC of a chemical for the
8 exposure scenario of the critical study should be determined initially using the PBPK model
9 (e.g., 6 hr/d, 5 d/wk); then the atmospheric concentration for continuous exposures (24 hr/d)
10 during lifetime or particular window of susceptibility yielding the same AUC or Cmax can be
11 determined by iterative simulation.
12
13 2.5.4. Dosimetric Adjustment Factor
14 In the RfC process, a dosimetric adjustment factor (DAF), intended to account for
15 pharmacokinetic differences between test species and humans, is applied to the duration-adjusted
16 POD (NOAEL, LOAEL, or BMC) to derive HECs (U.S. EPA, 1994). The DAF depends on the
17 nature of the inhaled toxicant and MOA as well as the endpoint (local effects vs. systemic
18 effects). The dosimetry data in the test animals and humans (e.g., deposition data, region-
19 specific dosimetry, blood concentration of systemic toxicants), if available, can help estimate the
20 DAF. In the absence of such data, knowledge of critical parameters or mathematical models in
21 the test species and humans can be useful in estimating the DAF.
22 For highly reactive or water-soluble gases that do not significantly accumulate in blood
23 (e.g., hydrogen fluoride, chlorine, formaldehyde, volatile organic acids, and esters), the DAF is
24 derived using simulated delivery of chemical to different regions of the respiratory tract, based
25 on regional mass transfer coefficients, as well as differences in surface area and ventilation rates
26 (U.S. EPA, 1994). For gases that are water soluble with some blood accumulation (e.g., acetone,
27 ethyl acetate, ozone, sulfur dioxide, propanol, isoamyl alcohol) and potential for both respiratory
28 and remote effects, the DAF could be calculated on the basis of uptake, defined by overall mass
29 transfer coefficient, as well as flow-limited perfusion distribution models. The DAF for poorly
30 water-soluble gases that cause remote effects (e.g., xylene, toluene, styrene) is determined on the
31 basis of blood:air partition coefficients and flow-limited perfusion models (U.S. EPA, 1994).
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1 A variety of computational tools are available for determining the uptake and deposition
2 of gases and particulates in nasal pathways and the respiratory tract (Kimbell et al., 1993;
3 Jarabek, 1994; Asgharian et al., 1995; Tran et al., 1997; Bush et al., 1998; Hanna et al., 2001,
4 Bogdanffy and Sarangapani, 2003; U.S. EPA, 2004). PBPK models have most frequently been
5 applied to systemically acting gases and vapors. They have also been applied, in conjunction
6 with other models (e.g., computational fluid dynamics), to more locally acting gases. Their use
7 (discussed above) in estimating dose metrics over time allows for a more refined duration
8 adjustment. Also, the other RfC approaches do not account for metabolism of the more reactive
9 gases, so PBPK modeling approaches would clearly be preferable for these compounds if
10 adequate data are available. There is little doubt that further applications of PBPK models to the
11 more reactive gases and agents will be developed and realized in the near future.
12
13 2.5.5. Uncertainty Factors: Role of PBPK Models
14 The uncertainty/variability factors used in RfC derivation include one or more of the
15 following: an interspecies uncertainty factor (IUF) of 3 to account for possible pharmacodynamic
16 differences; an intraspecies variability factor (IVF) of 10 for variability in kinetics and dynamics
17 among humans; subchronic-to-chronic extrapolation factor of 10; a LOAEL-to-NOAEL factor of
18 10; and a database deficiency factor of 1 to 10 (U. S. EPA, 1994; Jarabek, 1994). The total of all
19 uncertainty factors generally should not exceed 3,000 (U.S. EPA, 2002). With the exception of
20 the IVF, the magnitude of the factors listed above cannot be estimated using pharmacokinetic
21 data or PBPK models alone, although they can be determined either by conducting appropriate
22 experiments or by using integrated pharmacokinetic-pharmacodynamic models. Experiments to
23 estimate the IVF for each toxic chemical in each population of interest is neither plausible nor
24 ethical. It has been possible, however, to estimate the IVF by analyzing available data on
25 pharmaceutical products collected in human volunteers and patients over the years (Ham's et al.,
26 1999; Silverman et al., 1999).
27 The IVF of 10 conventionally used in RfC derivation implies that for the same level of
28 response or nonresponse, the potential doses among individuals may differ by as much as—but
29 not more than—an order of magnitude. The factor of 10 is a composite of the interindividual
30 differences in pharmacokinetics and pharmacodynamics (Renwick and Lazarus, 1998). The
31 magnitude of the pharmacokinetic component of the IVF can be estimated with the use of PBPK
32 models and applied in conjunction with the remaining interindividual pharmacodynamic
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1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
variability factor of 3, and this is entirely consistent with what is done under the RfC process to
account for dosimetry and pharmacodynamic differences between species (Jarabek, 1994; U.S.
EPA, 2002). The PBPK models are also potentially useful for estimating the magnitude of the
pharmacokinetic component of the uncertainty factors for LOAEL-to-NOAEL and subchronic-
to-chronic extrapolations, but the feasibility of such estimations has not yet been explored
systematically (Thomas et al., 1996b).
2.5.6. Summary
The potential role of the PBPK
model in the RfC process is summarized
in Box 2-2.
Box 2-2. Role of PBPK models in the RfC process
• Route-to-route extrapolation of the POD
• Duration adjustment calculation
• Dosimetric adjustment factor
• Intraspecies variability factor (PK component)
2.6. ROLE OF PBPK MODELS IN RfD DERIVATION
2.6.1. Reference Dose
An RfD is 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
(Barnes and Dourson 1988; Dourson et al., 1992). 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, intraspecies extrapolation, 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 uncertainty factors are applied as appropriate. Regarding the RfD process,
PBPK models are potentially useful in determining the POD as well as the extrapolation factors,
as described in Sections 2.6.2 and 2.6.3.
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1 2.6.2. Point of Departure
2 Where possible, the RfD derivation uses an oral NOAEL, LOAEL, or BMD as the POD.
3 The oral route-specific NOAEL and LOAEL correspond to experimentally tested doses, whereas
4 the BMD is obtained from statistical modeling of dose-response data (U.S. EPA, 2000a). When
5 the LOAEL or NOAEL has not been identified in an oral dosing study but has been obtained for
6 another route of exposure, the route-to-route dose conversion in the past assumed that absorption
7 by both routes is 100% and that equal potential doses administered via inhalation and oral route
8 are equitoxic (Pauluhn, 2003). In other words, this overly simplistic approach assumed that the
9 rates of absorption, distribution, metabolism, excretion, and tissue dose of toxic moiety of
10 chemicals are identical, regardless of the exposure route, particularly if the same dose (mg/kg/d)
11 is administered by both routes. The data on route-specific fraction absorbed, when available,
12 have been used to improve the scientific basis of the route-to-route extrapolation process (e.g.,
13 U.S. EPA, 1999a).
14 When the oral NOAEL, LOAEL, or BMD is unavailable for a given route of exposure,
15 PBPK models can be particularly useful in deriving such values on the basis of results obtained
16 for other dosing routes (e.g., inhalation, intravenous, dermal). PBPK models facilitate the
17 conduct of route-to-route extrapolation (e.g., inhalation to oral) to establish the oral route-
18 specific POD (NOAEL, LOAEL, BMD), based on equivalent internal dose. The use of PBPK
19 models represents a significant improvement in the scientific basis of the conventional route-to-
20 route extrapolation approach, because it takes into account the route-specific rates and magnitude
21 of absorption, clearance, and first-pass effects.
22 PBPK models, however, are not able to establish an oral POD in the absence of some
23 route-specific experimental dose-response and kinetic data. Development of a biologically based
24 dose-response (BBDR) model linked with a PBPK model could potentially improve the
25 quantification of the dose-response and POD for RfD derivation. There has been some success
26 in developing BBDR models for simple adverse effects (e.g., cholinesterase inhibition,
27 cytotoxicity, hematoxicity) (Gearhart et al., 1990, 1994; Reitz et al., 1990a; Cox, 1996; Ashani
28 and Pistinner, 2004), but these models are not routinely used to estimate PODs for RfD
29 derivation because of the lack of data needed to calibrate and test the models. New technologies
30 (e.g., toxicogenomics) offer the potential for generating the needed data, and more integrated
31 PBPK and BBDR models may be an attainable goal in the near future.
32
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1 2.6.3. Uncertainty Factors
2 The uncertainty factors used in RfD derivation include extrapolations across species
3 (interspecies) and across duration of exposure (subchronic to chronic), degree of response (e.g.,
4 LOAEL-to-NOAEL), variability within a population (intraspecies variability), and to account for
5 poor or absent data in the database (database deficiency). If the NOAEL for a chemical with an
6 adequate database has been identified in a chronic study, only the IUF and IVF are used in the
7 assessment. The IUF of 10 conventionally used in RfD derivation addresses the possibility that
8 the same level of response or nonresponse is associated with a HED that is 10 times lower than
9 the dose administered to animals. Similarly, the FVF of 10 is presumed to account for both the
10 differences in tissue dosimetry and tissue response within a human population.
11 If in vivo pharmacokinetic and pharmacodynamic data are available for humans and the
12 test species as well as for the various subgroups of the population, chemical-specific adjustment
13 factors can be derived to replace the default uncertainty factors. The IUF and IVF may also be
14 estimated from an understanding of the key pharmacokinetic and pharmacodynamic
15 determinants of a chemical's disposition in the body (e.g., isoenzyme levels, enzyme activity
16 levels, tissue volumes, breathing rates, cell proliferation rates) (e.g., Dome et al., 2001a, b, 2002;
17 Walton et al., 2001). Extrapolating among species or estimating interindividual variability must
18 be performed carefully because the magnitude of variability associated with individual
19 determinants is neither cumulative nor additive. A one-by-one evaluation of the determinants of
20 interspecies differences or interindividual variability is useful for understanding the mechanistic
21 basis and their relative importance, but such an isolated approach can easily lead to unrealistic
22 estimates of the overall magnitude of an FVF or IUF. The net impact of various determinants on
23 the IVF and IUF is more properly evaluated by integrating the available information with a
24 PBPK or BBDR model.
25 PBPK models are useful for characterizing the magnitude of the pharmacokinetic
26 component of the IUF as well as the IVF used in the RfD process. When using PBPK models to
27 adjust for pharmacokinetic differences, a factor of 3 is generally used to account for the potential
28 interspecies differences and interindividual variability in pharmacodynamics, as with the RfC
29 process (Jarabek et al., 1995; Clewell et al., 2002; U.S. EPA, 2003). However, chemical-specific
30 information on the pharmacodynamic aspect of inter- and intraspecies differences may inform on
31 further reduction of these uncertainty factors. It should be recognized that in their current state
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1 of advancement, PBPK and BBDR models are not suitable for characterizing the magnitude of
2 LOAEL-NOAEL and subchronic-chronic factors.
3 Although a thoroughly characterized BBDR model might address the LOAEL-NOAEL
4 issue, it is unlikely that such models will be capable of extrapolating from subchronic to chronic
5 effects because of the multiplicity of feedback systems and plasticity within organisms, nor will
6 such models be capable of accounting for the potential for different adverse effects over the
7 lifespan.
8
9 2.6.4. Summary
10 PBPK models, by facilitating the
Box 2-3. Role of PBPK models in the RfD process
11 simulation of tissue dose of the toxic
Route-to-route extrapolation
Interspecies uncertainty factor (PK component)
Intraspecies variability factor (PK component)
12 moiety of chemicals, address specific areas
13 of uncertainty associated with derivation of
14 the RfD, as shown in Box 2-3.
15
16 2.7. ROLE OF PBPK MODELS IN CANCER RISK ASSESSMENT
17 The dose-response assessment portion of cancer risk assessment may vary, depending on
18 MO A considerations. It can involve the determination of a slope factor based on linear
19 extrapolation from the POD (i.e., high-dose to low-dose extrapolation) or it may involve the use
20 of the POD for nonlinear analysis (U.S. EPA, 2005a). Either approach may also require
21 extrapolation of animal data to humans, hi addition, some of the assessments may require route-
22 to-route extrapolations. The role of PBPK models in conducting these extrapolations is
23 discussed in the following sections (2.7.1 through 2.7.4).
24
25 2.7.1. High-Dose to Low-Dose Extrapolation
26 The oral slope factor or IUR has frequently been determined by modeling the relationship
27 between the cancer response and the administered dose (or exposure concentration) (U.S. EPA,
28 2005a). According to the revised cancer guidelines, however, either a nonlinear (i.e., RfC or
29 RfD) or linear (i.e., unit risk estimate) extrapolation based on the POD can be conducted, as
30 justified by the MOA of the carcinogen (U.S. EPA, 2005a). Further, the use of internal dose or
31 delivered dose in such analysis has been encouraged.
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1 Because high doses of chemicals are often administered in rodent cancer bioassays, the
2 tumors observed in such studies are not always directly proportional to the exposure dose.
3 Rather, the cancer dose-response relationships appear complex, in part due to nonlinearity in the
4 pharmacokinetic processes occurring at high doses. In other words, the target tissue dose of the
5 toxic moiety is often disproportional to the administered doses used in animal bioassays (Figure
6 2-1). Therefore, dose-response analysis based on the appropriate dose metric often results in the
7 linearization of the relationship (Andersen et al., 1987; Clewell et al., 1995, 2002). The slope
8 factor derived using the dose metric versus the response curve will have units of (dose metric)"1;
9 similarly, NOAELs are converted using PBPK models to the dose metric at which no significant
10 incidence of cancer is expected on the basis of MO A of the chemical and dose-response data.
11 Linkage of PBPK models with BBDR models (e.g., clonal expansion and progression
12 models as well as two-stage models) would represent the ideal framework for characterizing the
13 health risk associated with human exposure to chemical carcinogens. However, such models still
14 continue to be developed and improved upon, and currently there is not a standard model that is
15 used or recommended (U.S. EPA, 2005a).
16
17 2.7.2. Interspecies Extrapolation
18 The default procedure for conducting interspecies extrapolation (e.g., rat to humans) of
19 the oral dose of carcinogens involves scaling in proportion to body weight to the 0.75 power
20 (U.S. EPA, 2005a). This scaling approach is based on the observation that several physiological,
21 anatomical, and biochemical processes in mammalian species are closely related to body surface
22 area (Voisin et al., 1990; U.S. EPA, 2002). In other words, this default approach implies that the
23 delivered doses (following oral exposure) are related to applied dose by 0.75 power of body
24 weight, independent of the species. For gases and particulates, however, the default procedure
25 for interspecies extrapolation would involve the derivation of a HEC, as described in Section
26 2.4.4 (U.S. EPA, 1994; Jarabek, 1995a, b).
27 The nature and slope of the dose-response relationship for carcinogens may not be
28 identical in test species and humans due to pharmacokinetic and pharmacodynamic differences
29 (Monro, 1994). Interspecies extrapolations of an equivalent dose of carcinogens can be
30 conducted if appropriate data (tissue or blood concentrations of potential toxic moiety or
31 promutagenic adducts) are available in both the test species and humans. In the absence of such
32 data, PBPK models can be used to characterize the relationship between applied dose and
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1 delivered dose of carcinogens in the species of interest for subsequent extrapolation to humans
2 (Andersen et al., 1987).
3
4 2.7.3. Route-to-Route Extrapolation
5 Route-to-route extrapolation is necessary if the cancer dose-response data were obtained
6 in test species exposed by a route different from the anticipated human exposure and the effect is
7 considered pertinent to the human exposure route. Route-to-route extrapolation is considered
8 appropriate for a chemical that induces tumors at a site different from the portal of entry and if
9 the chemical is absorbed to give an internal dose. Simplistic route-to-route extrapolations are
10 performed by assuming that the relationship between applied dose and tissue dose of toxic
11 moiety (dose metric) is the same, regardless of the exposure route. The uncertainty associated
12 with this approach is that the first-pass effect as well as the rates and extent of absorption and
13 metabolism may vary from one route to another (Pauluhn, 2003). The data on route-specific
14 fraction absorbed are now used to improve the scientific basis of the route-to-route extrapolation
15 process (e.g., U.S. EPA, 1999a).
16 PBPK models, by accounting for the route-specific rate and magnitude of absorption,
17 first-pass effect, and metabolism, facilitate the conduct of route-to-route extrapolation (Clewell
18 and Andersen, 1994). The slope factor or the NOAEL associated with an exposure route can be
19 translated into applied dose by another route on the basis of equal delivered doses. Basically, by
20 simulating the tissue dose of toxic moiety associated with the applied doses given by different
21 routes, PBPK models facilitate conducting route-to-route extrapolation of the NOAEL or slope
22 factor of chemical carcinogens (Gerrity et al., 1990; U.S. EPA, 2000b).
23
24 2.7.4. Intraspecies Variability
25 Intraspecies variability in pharmacokinetics or pharmacodynamics has not usually been
26 considered in the context of cancer risk assessment. In characterizing risk, the CSF has been
27 used without adjustment for susceptible populations. The newer supplemental guidance suggests
28 the use of an adjustment factor to the cancer slope or unit risk value to account for enhanced
29 susceptibility related to early -life exposures of neonates and young children, particularly for
30 carcinogens exhibiting a mutagenic MOA (U.S. EPA, 2005b). Further, when assessing the less-
31 than-lifetime exposures occurring in childhood, the guidelines stipulate adjustments for adult-
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1 children differences in exposure factors (e.g., skin surface area, drinking water ingestion rate)
2 (U.S. EPA, 2005b).
3 PBPK models are potentially of use in evaluating the pharmacokinetic basis of the adult-
4 children differences in tissue dose of carcinogens (Price et al., 2003b; Gentry et al., 2003;
5 Ginsberg et al., 2004). However, the quantitation of the tissue dose differences between adults
6 and children would not be sufficient to account for pharmacodynamic differences related to
7 early-life exposures of neonates and children. PBPK models can still be of use in determining
8 the adjustment factor for early-life exposures of neonates and young children on the basis of
9 equivalent internal doses.
10
11 2.7.5. Summary
12 PBPK models, by facilitating the
10 .,. _. , f. • • 4, f * Route-to-route extrapolation
13 simulation of tissue dose of toxic moiety of T . * . „ , ,- • „
•» Interspecies extrapolations of pharmacokinetically
14 chemical carcinogens, play an important
15 role in reducing the uncertainties associated
Box 2-4. Role of PBPK models in cancer risk
assessment
• High-dose to low-dose extrapolation
equivalent doses
16 with some of the extrapolations used in the cancer risk assessment process (Box 2-4).
17
18 2.8. USE OF PHARMACOKINETIC DATA AND MODELS IN EXPOSURE
19 ASSESSMENT
20 2.8.1. Conventional Approaches
21 The conventional approach to exposure assessment involves the calculation of potential
22 dose for each route of exposure, with knowledge of concentration of the chemical in the medium,
23 frequency and duration of exposure, rate of contact with the medium, and body weight of the
24 individual (Paustenbach, 2000). With increased data availability, however, absorbed dose can be
25 calculated (U.S. EPA, 1992). For calculating absorbed dose, pharmacokinetic data such as time-
26 course data on concentration or total quantity in alveolar air, urine, or blood would be required
27 (Paustenbach, 2000). The conversion of biomarker data, absorbed dose, or potential dose into
28 delivered dose is not straightforward and requires the use of appropriate modeling techniques.
29 The need for the use of pharmacokinetic models is further emphasized by the fact that the tissue
30 dose is not always directly proportional to the exposure concentration or potential dose.
31
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1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
2.8.2. Role of PBPK Models
PBPK models allow the conversion of potential dose or exposure concentration to tissue
dose, which can then be used for risk characterization purposes. As the dose-response
relationships are being increasingly established on the basis of tissue dose, it is also essential that
the potential doses calculated during exposure assessments be translated into tissue doses to
facilitate risk characterization. PBPK models are additionally useful in investigating and
establishing the relationship between biomonitoring or biomarker data and potential dose as well
as the relationship between biomarker levels and tissue dose of chemicals by iterative simulation
(e.g., Fennell et al., 1992; Krishnan et al., 1992; Csanady et al., 1996; Timchalk et al., 2001).
This ability of PBPK models has been explored for establishing biological exposure
indices (e.g., breath, blood, or breath concentrations) associated with worker exposure to
threshold limit values of solvents (Perbellini et al., 1990; Leung, 1992; Kumagai and Matsunaga,
1995; Thomas et al., 1996b; Droz et al., 1999). PBPK models also offer a framework for
reconstructing human exposure over a period of time (Vinegar et al., 1990; Roy and
Georgopoulos, 1998; Canuel et al., 2000). Further, such dose reconstructions and tissue dose
resulting from multiroute (oral, inhalation, dermal) and multimedia (air, water, food, soil)
exposures can be computed with the use of PBPK models (e.g., Georgopoulos et al., 1994; Roy
et al., 1996; Rao and Ginsberg, 1997; Corley et al., 2000; Levesque et al., 2002). The net tissue
dose associated with a particular exposure situation (multiroute and multisource) can then be
obtained with PBPK models and used for risk characterization purposes.
2.8.3. Summary
The potential roles of PBPK
models in exposure assessment are
summarized in Box 2-5.
Box 2-5. Role of PBPK models in exposure assessment
• Conversion of potential dose into tissue dose
• Tissue dose estimation for aggregate exposures
• Dose reconstruction based on exposure biomarkers
2.9. PHARMACOKINETIC DATA NEEDS IN RISK ASSESSMENT: SUMMARY
Adverse tissue responses are more directly and closely related to tissue dose of the toxic
moiety than is the concentration of the parent chemical in the environment. Therefore, there is
no question that the scientific basis of, and confidence in, risk assessments are enhanced by the
use of tissue dose information. Because the tissue dose is not directly and simply related to
exposure concentration or potential dose at all tunes, there is some uncertainty regarding the use
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1 of potential dose in risk assessment. If the relationship between potential dose and tissue dose of
2 the toxic moiety of chemicals is linear and proportional at all dose levels used in animals and
3 humans, then there is no need for PBPK models. However, this is not usually the case.
4 Therefore, the PBPK models are used for addressing specific areas of uncertainty in dose-
5 response assessment and exposure assessment on the basis of the simulation of tissue dose of
6 potential toxic moiety.
7
8 In the context of dose-response assessment, PBPK models are needed for conducting
9
10 1. Route-to-route extrapolation of the POD (RfC, RfD, and unit risk estimates),
11 2. Duration adjustment of the POD (RfC derivation),
12 3. High-dose to low-dose extrapolation (unit risk estimates),
13 4. Interspecies extrapolation of pharmacokinetically equivalent doses (RfD, RfC, and unit
14 risk estimates), and
15 5. Estimation of the pharmacokinetic component of the IVF (RfC and RfD derivation).
16
17 In the context of exposure assessment, PBPK models are needed for
18
19 1. Converting potential dose into tissue dose,
20 2. Calculating tissue dose associated with multiroute and multimedia exposures, and
21 3. Relating biomarker data to tissue dose and potential dose by exposure reconstruction.
22
23 The PBPK models intended for use in dose-response and exposure assessments should be
24 evaluated for their adequacy. The next chapter presents the process and criteria for evaluating
25 PBPK models intended for use in risk assessment.
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1 3. EVALUATION OF PBPK MODELS INTENDED FOR USE IN
2 RISK ASSESSMENT
3
4 PBPK models intended for risk assessment applications should be evaluated for their
5 adequacy. There are no published documents that specify either model validation standards or
6 criteria of adequate PBPK models. However, several publications have dealt with good
7 modeling practices as well as approaches for evaluating and documenting biological models
8 intended for risk or safety assessments (Yates, 1978; Andersen et al., 1995; Clark et al., 2004).
9 Evaluation of PBPK models intended for risk assessment applications should be undertaken
10 along the lines of model purpose, model structure, mathematical representation, parameter
11 estimation (calibration), and computer implementation aspects, as detailed in the following
12 sections.
13
14 3.1. MODEL PURPOSE
15 The purpose for which a PBPK model is developed basically determines its structure and
16 level of detail. Not all PBPK models are developed for the purpose of supporting risk
17 assessments. Some are actually used as a tool for hypothesis testing for particular modes of
18 action and for guiding improved experimental design. The structure of a PBPK model used
19 strictly for responding to the needs of a curiosity-driven researcher may not serve the intent and
20 purposes of a risk assessor. PBPK models, therefore, are of varying complexities and
21 capabilities, according to the intended purpose. PBPK models, in general, are developed for one
22 of the following three purposes:
23 1. Integrate diverse sets of pharmacokinetic data on a particular chemical,
24 2. Investigate the pharmacokinetic basis of toxicity of a chemical that appears complex
25 at the administered dose level, and
26 3. Predict tissue dosimetry for situations other than what has been or could be tested
27 experimentally (see Section 3.6).
28
29 Models that permit the integration of diverse sets of data are useful in uncovering
30 mechanistic determinants of pharmacokinetics of specific chemicals (e.g., Clewell and Andersen,
31 1997; Haddad et al., 1998). However, PBPK models resulting from such efforts are not routinely
32 evaluated for their predictive value but still are useful for the purpose of uncovering unusual
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1 determinants of pharmacokinetics (e.g., suicide inhibition, diffusion-limited uptake). On the
2 other hand, PBPK models developed to improve the understanding of toxicological behavior of
3 chemicals that appears complex at the administered dose level (e.g., species, sex, or route
4 differences in response) may be either predictive or integrative. Typically, the PBPK models of
5 use to the risk assessor are those that have predictive value at the quantitative level with respect
6 to the production or pharmacokinetics of potential toxic moieties (parent chemical or
7 metabolite).
8
9 A PBPK model capable of predicting the pharmacokinetics and tissue dose of the
10 potential toxic moiety of a chemical is the preferred one for risk assessment applications.
11
12 3.2. MODEL STRUCTURE
13 The structure of a PBPK model in large part depends upon the purpose for which the
14 model is developed and the philosophy of the modeler. There is virtually no limit to the number
15 and size of compartments in a model intended to describe molecular/cellular events. Parsimony
16 in selecting model structures, however, is an important and guiding principle in developing
17 models for use in risk assessments. The complexity of PBPK models used in risk assessment is
18 often constrained by limited data available to calibrate and test the model, and the need for risk
19 assessors to defend the model assumptions and the values derived from model simulations.
20 The simplest conceptual model represents the organism as a one-compartment system.
21 PBPK models differ from single-compartment models by representing many more physiological
22 and biochemical processes that are relevant to the toxicokinetics of the chemical in question.
23 This complexity is represented by differentiating or lumping tissues into specific compartments
24 each with a unique set of physiological (i.e., blood flows) and biochemical parameters (i.e.,
25 partition coefficients). A PBPK model intended for risk assessment applications should,
26 preferably, include the target organ as one of the compartments. Minimally, it should facilitate
27 the calculation of blood concentration, which is often used as a surrogate for tissue
28 concentrations. Major portals of entry (e.g., lung, gastrointestinal tract), storage organs (e.g.,
29 adipose tissue), metabolism/transformation sites (e.g., liver, kidney) as well as elimination routes
30 (e.g., renal, pulmonary, fecal) should be included. It is often acceptable to mathematically
31 describe absorption, distribution, metabolism and excretion (ADME) of chemicals in PBPK
32 models without physically representing the tissues where these processes occur (Krishnan and
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1 Andersen 2001), provided that this lack of physical representation does not interfere with a
2 model's use as an extrapolation tool. In some cases, a compartment is subdivided into several
3 sub-compartments based on mechanistic and biological considerations. For example, the liver
4 can be divided into separate compartments depending on the localization of enzymatic activity.
5 Figure 3-1 represents examples of PBPK model structures that have been commonly used to
6 simulate the kinetics of volatile and nonvolatile substances. Note that all these models facilitate
7 the simulation of the concentration of chemicals or their metabolites in the target organ or a
8 surrogate tissue (usually blood).
9 It is important to realize that compartments in PBPK models are usually assumed to be
10 homogenously and completely mixed reactors. This means that the concentration of the chemical
11 anywhere in the tissue is the same and equal to the concentration of the chemical as it leaves the
12 tissue in venous blood. This assumption is necessary to simplify the differential equations
13 representing the mass balance of the chemical in the tissue. The numerical solution of the final
14 set of equations representing the PBPK model is further simplified because of the complete-
15 mixing assumption.
16 The structure of a PBPK model intended for risk assessment applications should contain
17 the target organ (or a surrogate tissue) as well as compartments representing tissues of unique
18 physiological and biochemical relevance to the pharmacokinetics of the chemical in question.
19
20 3.3. MATHEMATICAL REPRESENTATION
21 In PBPK modeling, each tissue compartment is generally described with a mass balance
22 differential equation (MBDE) that consists of a series of clearance terms with units of volume
23 per time, i.e., liters per hour or milliliters per minute. The clearance terms, in most cases, relate
24 to tissue uptake, tissue-to-blood transfer, metabolism, or excretion of chemicals. The uptake of a
25 chemical in systemic circulation by a tissue is described according to Pick's law of simple
26 diffusion, which states that the flux of a chemical is proportional to its concentration gradient.
27 Descriptions of passive and blood flow-limited uptake have been used successfully in many of
28 the past efforts in PBPK modeling that dealt with small-molecular-weight organics. For high-
29 molecular-weight compounds, however, membrane diffusion is often the rate-limiting process,
30 and in such cases chemical uptake is described with differential equations for the tissue blood
31 and cellular matrix subcompartments (Rowland, 1985; Leung, 1991; Andersen, 1995; Krishnan
32 and Andersen, 2001) (Tables 3-1 and 3-2).
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B
Inhaled air
Expired air
Inhaled air
Expired air
2
3
4
5
6
7
8
9
10
^
r
'
A
LUNG
RICHLY
TISSUES
POORLY
TISSUES
1 I\/CD
fc
*
^
'
Motahnlici
LUNGS
0u tichangt
•-Jfc
LUNGS
IMOIXXC
D
Metabolism
Figure 3-1. Conceptual representations of PBPK models for (A) toluene, (B)
ethylene oxide, (C) 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD), and (D)
vinyl acetate. The input and output arrows associated with individual
compartments represent arterial and venous blood flows. Note that model D
contains 5 compartments for the nasal cavity alone (the site of toxicity). From
Bogdanffy et al. (1999), Krishnan et al. (1992), and Andersen et al. (1993).
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1
2
Table 3-1. Equations of a four-compartment PBPK model to simulate the
inhalation exposure of volatile organic compounds
Tissue compartments
Equations8
Arterial blood
Ca ^
Pi,
Liver
dt
l -
'"-1' Km + Cv. .
* n— i
dA,
Fat
dA,
dt
Af =
J n
Cv, =•
dA,
Richly perfused tissues
dt
r -
^ ~
y
Cv =
^-V
= r"
Poorly perfused tissues
dASn
~dt
A, =
sn
-Cv
M Sft-
dA,
2*
?-> _ Sn
~
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1
2
3
4
5
6
7
8
9
10
11
12
13
14
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
Equations8
^ QlxCvln+QfxCvfn+QrxCvrn+QSxCv,n
" Qc
Calv - Ca"
" P»
1 Equations are from Ramsey and Andersen (1984).
bThe 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 = bloodiair
C = concentration (mg/L or mmol/L)
c = cardiac output
f=fat
inh = inhaled air
Km = Michaelis Menten affinity constant (mg/L)
1 = liver
n = current time
n-1 = previous simulation time
P = partition coefficient
p = pulmonary ventilation
Q = How 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
Vraax = 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
f\ ' ~ JZrt ^ \ m ~~ nut ) ~ I-* VT- 1 ^ \1 "7 /
M/
^^• = Mx(c,-c2)
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)
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1 The rate of the amount of chemical consumed by macromolecular binding process is
2 described in PBPK models as a second-order reaction or by using equations based on reversible
3 equilibrium relationship. The rate of metabolism in PBPK models has been described as a first-
4 order, second-order, or saturable process. Conjugation reactions, on the other hand, are
5 traditionally described as a second-order process with respect to the concentrations of the
6 cofactor and the chemical. Alternatively, descriptions based on ping-pong mechanism have also
7 been used successfully. In each case, the reason for using a particular description should be
8 clearly provided. PBPK models using particular mathematical descriptions of tissue uptake,
9 metabolism, and binding without any justification cannot be used confidently for risk assessment
10 applications. For example, if enzyme-mediated metabolism is described as a first-order process
11 in a PBPK model, the scientific rationale for employing such a description is needed before the
12 model can be used for purposes of extrapolation and prediction. Because PBPK models are
13 simplified representations of the real systems, the actual details and complexity of the
14 physiological and biochemical processes are not reflected by the equations used. Depending on
15 the level of detail required and the objective of the modeling effort, appropriate descriptions of
16 the biochemical processes can be included in these models.
17 - The MBDEs in PBPK models should have units of mass per time (e.g., mg/hr) or
18 concentration per time (mg/L-hr'1), and the type of equations chosen to describe tissue uptake,
19 binding, and metabolism should be justified.
20
21 3.4. PARAMETER ESTIMATION
22 Knowledge of chemical-specific and species-specific parameters would be required to
23 solve the equations constituting PBPK models. For a model to be used for estimating
24 interindividual differences in tissue dosimetry, knowledge of the distributions of input
25 parameters is essential. However, for all other purposes, the knowledge of the average value or
26 the range of plausible values of model parameters is sufficient. Typically, PBPK models require
27 the numerical values of physiological parameters, such as alveolar ventilation rate, cardiac
28 output, tissue blood flow rates and tissue volumes, and clearance parameters related to renal,
29 hepatic, and biliary excretion pathways, as well as certain partition coefficients (blood:air,
30 skin:water, skin:air, and tissue:blood). Additional parameters (e.g., tissue DNA levels,
31 hematocrit, number and concentration of binding proteins) may be required in some cases.
32
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1 3.4.1. Physiological Parameters
2 The physiological parameters used in PBPK models should either correspond to those
3 obtained in the experimental pharmacokinetic study or be within the range of plausible values for
4 the species and life stage. Even though peer-reviewed compilations of ranges and reference
5 values of physiological parameters for adult animals and humans are available (Arms and Travis,
6 1988; Leggett and Williams, 1991; Fiserova-Bergerova, 1995; Brown et al., 1997; Davies and
7 Morris, 1997) (Tables 3-3 through 3-6), this is not the case with respect to physiological
8 parameters for specific subgroups of populations (e.g., developing and lactating animals,
9 pregnant women, children). There are some reports on physiological parameters for specific
10 subgroups but no compilations as yet of definitive ranges or reference values (Luecke et al.,
11 1994; Schoeffner et al., 1999; Haddad et al., 2001a; Hattis et al., 2003; Price et al., 2003a, b;
12 Pelekisetal., 2003).
13 In PBPK models for organic chemicals, the sum total of the volumes of compartments
14 corresponding to soft tissues should be smaller than the body weight, usually about 91% of the
15 body weight (100% [body weight] - 9% [weight of skeletal/structural components as percent
16 body weight]). Even though the tissue volumes (L) are needed for PBPK modeling, tissue
17 weights (kg) are usually used with the assumption of unit density (L = Kg). This assumption,
18 which may seem questionable, is inconsequential for practical reasons, particularly with respect
19 to the application of PBPK models in risk assessment.
20 The tissue flow rates in the model should add up to cardiac output. Fundamentally,
21 maintaining the mass balance in PBPK models requires that the sum of the flows to the
22 compartments be equal to the cardiac output. The ratio of cardiac output to alveolar ventilation
23 rate is around 1 in a resting individual (e.g., Andersen et al., 1987). The specification of cardiac
24 output independent of the value of ventilation rate is unacceptable, particularly if the their ratio
25 (ventilation:perfusion ratio) is not in the normal physiological range. Frequently in PBPK
26 models, ventilation rate, cardiac output, and tissue perfusion rates and tissue volumes are
27 specified for an individual animal or human being simulated. For predicting kinetics in another
28 animal or human with a different body weight, the physiological parameters are calculated anew.
29 To simplify this process, all tissue volumes are expressed as fractions of body weight such that
30 for any given body weight, the volumes in liters can be readily calculated by multiplying the
31 body weight by the corresponding fractional value. Similarly, because the cardiac output and
32 alveolar ventilation rate are related to body surface rather than body weight, the PBPK models
33
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Table 3-3. Reference physiological parameters for mice, rats, and humans
Physiological parameters
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
Humans
70
0.026
0.19
0.05
0.62
6.2
0.26
0.05
0.44
0.25
7.5
5
2
3
4
Source: Travis and Hattemer-Frey (1991).
6
7
8
9
10
11
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)
5-1 4a
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
* Varies proportionately with body weight.
Source: Brown et al. (1997).
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1
2
Table 3-5. Range of values of the volume and perfusion of select tissues in
the rat
Tissue
Adipose
Brain
Heart
Kidneys
Liver
Lungs
Muscle
Skin
Volume (% body weight)
4.6-1 2a
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
3
4
5
6
a Varies proportionately with body weight.
Source: Brown et al. (1997).
Table 3-6. Range of values of perfusion of select tissues in humans
9
10
11
12
13
14
15
16
17
Tissue
Adipose
Brain
Heart
Kidneys
Liver
Muscle
Skin
Regional blood flow
(% cardiac output)
3.7-11.8"
8.6-20.4
3.8-8
12.2-22.9
11-34.2
5.7^t2.2
3.3-8.6
a Varies proportionately with body weight.
Source: Brown et al. (1997).
specify these parameters as a power function of body weight, with the exponent varying from
0.67 to 0.75 (e.g., Andersen et al., 1987; Tardif et al., 1997).
An acceptable PBPK model should contain tissue volumes, flow rates, and
ventilation:perfusion ratios that are within physiological limits. Particularly, the sum total of
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1 the tissue volumes should not exceed the body weight, and the sum total of tissue blood flow rates
2 should equal cardiac output.
3
4 3.4.2. Partition Coefficients
5 The calibration of PBPK models for partition coefficients has sometimes been done using
6 in vivo data. In such cases, pharmacokinetic data collected following a single bolus dose or
7 repeated doses leading to steady state are analyzed to determine the tissue:blood partition
8 coefficients (Chen and Gross, 1979; Lam et al., 1982; Gabrielsson and Bondesson, 1987; Gallo
9 et al., 1987). The steady-state data provide the most straight forward data for model calibration;
10 however, they are valid only for tissues in which there are no significant binding or metabolic
11 processes. In case of significant level of metabolism or binding, the calculation of tissue:blood
12 partition coefficients should account for the amount of chemical consumed by such processes
13 (Chen and Gross, 1979). The estimation of partition coefficients for PBPK models from in vivo
14 data is acceptable as long as the same data set is not used for external evaluation later on.
15 The tissue:air, skin:water, skin:air, and blood:air partition coefficients required for PBPK
16 modeling of volatile organic chemicals are conveniently determined in vitro using vial
17 equilibration method (Sato and Nakajima, 1979; Gargas et al., 1989; Johanson and Dynesius,
18 1988; Fiserova-Bergerova and Diaz, 1986; Kaneko et al., 1994; Perbellini et al., 1995; Beliveau
19 and Krishnan, 2000). Tissue:blood partition coefficients for nonvolatile chemicals can be
20 determined in vitro using radioactive chemicals in ultrafiltration, equilibrium dialysis, or vial
21 equilibration procedure (Lin et al., 1982; Igari et al., 1983; Sultatos et al., 1990; Jepson et al.,
22 1994; Murphy et al., 1995). The partition coefficients estimated by these in vitro methods are
23 acceptable, provided equilibrium is attained during the experimental conditions. The
24 experimenter/modeler should have conducted a time-course analysis to choose an appropriate
25 time point (at which equilibrium is attained) for determining partition coefficients in vitro.
26 Algorithms based on the consideration of solubility and binding of chemicals in
27 biological matrices have been developed and applied for predicting tissue:blood, tissue:air, and
28 blood: air partition coefficients of volatile organic chemicals. This approach requires knowledge
29 of tissue and blood composition in terms of lipid and water contents, and octanol: water or
30 oil:water partition coefficients of the chemical as well as the binding association constants, if
31 applicable (e.g., Poulin and Krishnan, 1995,1996a,b; Poulin and Thiel, 2000). At the present
32 time, there is no validated animal-replacement approach for predicting association constants for
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1 blood or tissue protein binding of organic chemicals (Poulin and Krishnan, 1996b). The
2 biologically based algorithms as such are useful in providing initial estimates of tissue:blood
3 partition coefficients solely based on the consideration of solubility in water and lipid contents of
4 tissues and blood. A number of other empirical or semiempirical methods relating molecular
5 structure or physicochemical characteristics to tissue:blood and blood:air partition coefficients of
6 chemicals are also available (Payne and Kenney, 2002; Beliveau and Krishnan, 2003) (Appendix
7 1). Their use is acceptable, as long as the qualitative and quantitative aspects of structural
8 features and physicochemical characteristics of the new chemical are within those used in
9 calibrating the algorithm.
10 Partition coefficients required for PBPK models should be obtained using in vitro
11 methods, in vivo data obtained at steady-state, or theoretical algorithms within the boundary of
12 valid application.
13
14 3.4.3. Biochemical Parameters
15 Absorption rates, metabolic parameters (e.g., first-order or second-order rate constants,
16 maximal velocity, and Michaelis affinity constant) and tissue diffusion constants (for describing
17 diffusion-limited uptake) required for PBPK modeling can confidently be determined using in
18 vivo studies. For estimating these parameters, pharmacokinetic data (e.g., time course of tissue
19 or blood concentration of parent chemicals, urinary metabolite levels) obtained following a
20 single bolus dose or infusion may be used. For volatile organic chemicals, the use of exhaled
21 breath and gas uptake studies has frequently been adopted with success (Filser and Bolt, 1979,
22 1981; Andersen et al., 1980; Gargas et al., 1986). The rate constants of chemical reaction with
23 hemoglobin and tissue proteins determined in vitro or in vivo have been incorporated into the
24 PBPK model to make predictions of these phenomena in vivo (e.g., Krishnan et al., 1992). The
25 use of in vivo data for parameter estimation is acceptable, as long as the same data set is not used
26 for model evaluation purposes as well. The use of Bayesian approach is likely to enhance the
27 precision of parameter estimations from in vivo data (e.g., Vicini et al., 1999).
28 Receptor binding and DNA-binding properties of chemicals have been successfully
29 described with PBPK models on the basis of in vitro-derived data (Terasaki et al., 1984; Farris et
30 al., 1988). The appropriateness of the usefulness of in vitro systems (e.g., freshly isolated
31 hepatocytes, microsomes, post-mitochondrial fractions, cytosols) to provide metabolic constants
32 for incorporation into PBPK models continues to be an active area of investigation. These data
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1 may be applicable to modeling using the parallelogram approach. For example, chemical-
2 specific in vitro metabolic data from cultured hepatocytes can be scaled to represent in vivo liver
3 clearance using in vitro data such as estimates of the number of hepatocytes present per one gram
4 of liver tissue and the average liver weight (in grams) of the species and age group of interest.
5 In vitro data for humans is then extrapolated to in vivo by assuming that the same relationship
6 that successfully describes the in vitro to in vivo relationship in animals effectively converts the
7 human in vitro data to the in vivo situation. Even though there are several examples of
8 successful application based on appropriate in vitro-in vivo scaring methods (Reitz et al., 1989,
9 1996a; Gearhart et al., 1990; Hwang et al., 1996; De Jongh and Blaauboer, 1996,1997; Iwatsubo
10 et al., 1996; Kedderis and Held, 1996; Mortensen et al., 1997; Mortensen and Nilsen, 1998; Cole
11 et al., 2001; Hissink et al., 2002; Lipscomb et al., 1998, 2003), the extrapolation of in vitro data
12 to intact animal is not clear in all cases (e.g., Haddad et al., 1997,1998). But the in vitro studies
13 are particularly useful for evaluating the extent of metabolism in target tissues, characterizing
14 interindividual differences in metabolism, and conducting animal-human extrapolation of
15 metabolism constants based on a parallelogram approach (Andersen et al., 1991; Reitz et al.,
16 1996b; Ploeman et al., 1997; Thrall et al., 2000; Kedderis and Lipscomb, 2001).
17
18 Biochemical parameters for PBPK models can be estimated using in vivo data or on the
19 basis of adequate scaling of in vitro data.
20
21 3.5. COMPUTER IMPLEMENTATION
22 Most of the PBPK models require the use of numerical simulation methods because they
23 contain differential equations and descriptions of nonlinear processes. Therefore, the PBPK
24 model equations are written along with the integration algorithms and solved using programming
25 languages, simulation software, or spreadsheets. Simulation languages and commercially
26 available packages (Table 3-7) routinely make use of integration algorithms to obtain numerical
27 solution to differential equations (Menzel et al., 1987; Burmaster and Murray, 1997; Easterling et
28 al., 2000, Reddy et al., 2003) such that there is no need either for the modeler or the risk assessor
29 to evaluate this aspect. However, if a programming language (FORTRAN, BASIC) or
30 spreadsheet (Lotus 1-2-3, QuattroPro, Microsoft Excel) is used for modeling, then the modeler
31 should write the codes for an appropriate numerical integration algorithm (e.g., Euler, Gear,
32 Runge-Kutta routines; predictor-corrector methods). In such cases, the integration algorithm as
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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 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.)
f
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 integration algorithm and
interval should be specified
by the user.
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 (1 995); Karba et al.
(1990)
Ramsey and Andersen
(1984); Thomas etal.
(1996); Dong (1994)
Rey and Havranek (1996)
Easterling et al. (2000)
Johanson and Naslund
(1 988); Haddad et al. (1 996)
Menzel etal. (1987)
Hoang (1995)
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1
2
Table 3-7. Examples of simulation software used for PBPK modeling
(continued)
Software
Mathematica
Berkely Madonna
SONCHES (Simulation
of Nonlinear Complex
Hierarchical Ecological
Systems)
CMATRIX
BASICA
AVS
(Application
Visualization System)
MCSim
Developer/vendor
Wolfram Research, Inc.,
Champaign, IL
Robert Macey and George
Oster, University of
California at Berkeley, CA
Central institute of
Cybernetics and Information
Processes, Academy of
Sciences of GDR, Berlin
Robert Ball and Sorell L.
Schwartz, Georgetown
University, Washington, DC
California Department of
Pesticide Regulation,
Sacramento, CA
Advanced Visual Systems,
Inc., Waltham, MA
Drs. Bois and Maszle
Salient features
Mathematical software with
matrix-related computations;
numerical integration
algorithms capable of
solving systems of ordinary
differential equations
This program is a general-
purpose differential equation
solver. Developed on the
Berkeley campus under the
sponsorship of National
Science Foundation and the
National Institutes of Health.
It is currently used by
academic and commercial
institutions for constructing
mathematical models for
research and teaching.
A computer system where
connections between various
data libraries in the
preparation and post-
processing of simulation are
executed by macro
commands
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
Numerical integration
algorithms developed by the
Department for PBPK
modeling
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
This software, facilitates the
conduct of Bayesian analysis
with PBPK models but has
no graphical interphase.
Examples of application
Burmaster and Murray
(1997)
Reddy et al. (2003)
Wunscheretal. (1991)
Ball and Schwartz (1994)
Dong (1994)
Nichols etal. (1994)
Jonsson and Johanson
(2003)
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1 well as the integration interval used should be specified (e.g., Blancato and Saleh, 1994; Haddad
2 et al., 1996).
3 The modeler should also be aware of the optimization routine offered by software
4 packages, particularly if parameters are to be estimated from experimental data by statistical
5 optimization (Holmes et al., 2000). The personal and portable computers marketed today
6 possess the acceptable speed, disk space, and run time memory required for PBPK modeling and
7 parameter optimization; therefore, this aspect needs no formal evaluation.
8 The accuracy of computational representation of PBPK models is evaluated by
9 "debugging," which refers to the process of error detection in computer programs. The "bugs" in
10 PBPK models written as a program may result either from typing errors or from illogical
11 mathematical statements. To eliminate these errors, it is essential to carefully verify the model
12 codes after entry into the computer. Commercially available simulation software, while
13 converting the model codes written in a source language to machine language, can detect
14 syntax/language errors related to incorrect writing of model codes. However, such error
15 diagnostic features cannot detect errors associated with incorrect mathematical representation of
16 a process written in correct programming language without any typing mistakes. The onus is on
17 the modeler to ensure that the equations are entered correctly using the programming/simulation
18 software, and risk assessors cannot be expected to go through the PBPK model codes to perform
19 a routine error diagnostic check. Such verification should be done by the developer initially and
20 then by individuals not involved in model development, such as peer-reviewers and co-workers
21 (Clark et al., 2004).
22 The computer implementation of PBPK model need not be evaluated by risk assessors if a
23 highly reputable commercial or open source simulation software has been used. The onus is on
24 the model developer to ensure that the computer implementation of the PBPK model is free from
25 errors. When the modeler writes his/her own program, the appropriateness of the integration
26 algorithm and integration intervals should be justified; similar concerns would exist initially for
27 newly developed commercial or open source software.
28
29 3.6. MODEL EVALUATION
30 The purpose of model evaluation is to assess the adequacy of the model and its
31 parameters to consistently describe the available data sets representing the pharmacokinetics of a
32 chemical. A model that has been adequately evaluated would not only capture the critical
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1 determinants of the pharmacokinetics of a chemical but also characterize the elements of
2 uncertainty associated with the parameters.
3 The first step to ensure validity of the PBPK model is to check on the mass balance of the
4 chemical in the whole body. The model should not create or destroy matter. Basically, when all
5 the tissue levels, blood levels, and any excretion or metabolic transformation levels are added
6 they should sum up to the same exposure dose level used in the model. Although trivial, this
7 check is important in understanding the sources in the model that would falsely increase or
8 decrease the level of the chemical in tissues. Another initial evaluation step is to check the model
9 behavior when exposure is set to zero. The zero check is necessary to make sure that the model
10 can represent steady-state levels of the chemical and to make sure that this level does not change
11 with time in the absence of exposure.
12 The PBPK model evaluation to date has not been done rigorously from a statistical
13 perspective. The most common approach to model evaluation has involved visual inspection of
14 the plots of model predictions (usually continuous and represented by solid lines) with
15 experimental values (usually discrete and represented by symbols) against a common
16 independent variable (usually time). The rationale underlying this qualitative approach to model
17 evaluation is that the greater the commonality between the predicted and experimental data, the
18 greater the confidence in the model structure and parameters. The correspondence between
19 predictions and experimental data should be not only at the level of numbers (e.g., blood
20 concentration values) but also at the level of the profile (i.e., bumps and valleys in the
21 pharmacokinetic curve). Because PBPK modeling is not a fitting exercise, model simulations
22 are not expected to touch upon each experimental data point. Rather, the shape of the simulated
23 curve should correspond to that of the experimental data, and the simulated data should
24 preferably be within two standard deviations of the mean of experimental values, even though
25 this is not a rule of thumb used by the modeling community.
26 Figure 3-2 shows several examples of visual evaluation of the adequacy of PBPK models.
27 The models used in cases A and C would be considered adequate because they simulate the
28 behavior of the experimental data even though they do not accurately simulate every single
29 experimental data. On the other hand, models used in cases B and D would not be considered
30 adequate, and further work would be required to refine the models, either because they do not
31 simulate the profile appropriately (B) or the model simulations are outside two standard
32 deviations of the experimental data(D).
33
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1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
A
_ I — I—. c
I ^ — V, i 1 -
1 °-1-f \ *
1 \^ 5 ai~
Om . , n m
Time
B
Time
C D
1 1 1 "
. r T-\
•I /"^~^ V I
2 / ^v £5
1 ° 1 \ 1 °-1 '
0 ' * \»_ o
O \v^ O
OrH — i n 0*1 -
I 5
, f
\^
Time Time
Figure 3-2. Comparison of PBPK model simulations (solid lines) with
experimental data (symbols).
The above 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 behaviour. 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. Figure 3-2 (B) depicts a model whose
structure is inadequate because the simulated profile is not consistent with the experimental data
for the chemical. As a caveat, it is possible that the lack of fit in Figure 3-2 (B) is due to a
problem with the model parameters, not the structure. If the model cannot fit the
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1 pharmacokinetic profiles for any realistic parameter values, or only using values that are
2 inconsistent with other data, then one can reasonably conclude that the structure is inadequate.
3 This evaluation of model structure provides the developer an opportunity to think about
4 the need for additional compartments, critical determinants of disposition, or different
5 quantitative descriptions of the phenomena, and to improve the capability of the model,
6 accordingly. A useful way of comparing the experimental and simulated data is to plot the
7 residuals (i.e., difference between experimental and simulated data) as a function of time or as a
8 function of various controllable variables. If more than one model fits the experimental data
9 equally well, new experiments may be designed to identify the model that more accurately
10 predicts the other attributes of the biological system (Kohn, 1995).
11 Prior to the discussion about evaluating model parameters, it is important to correct a
12 common misunderstanding about what a "validated model" means. A model that has been
13 calibrated against one dataset, and that adequately simulates a different data set, can be said to be
14 "validated," but it is only validated to the extent to which those two dataset accurately represent
15 the larger population, not in any global sense independent from the data used to develop the
16 model. PBPK models are used to extrapolate to other exposure conditions or dosing regimens,
17 but here again, only to the extent that the data used to calibrate and test the model are of
18 sufficient quality to support the extrapolations. To avoid giving the impression that a model is
19 "validated" to predict outcomes for which it has not been adequately tested, many PBPK
20 modelers today prefer to use the terms "calibrated" model (accompanied by a description of the
21 data used to calibrate the model) and the "predictive capability" or utility of the model, again
22 specifying the data that the model was adequately able to simulate. In this sense, the more quality
23 data available to calibrate and test the model, the more confidence one can place in the model's
24 predictive capability. PBPK modelers are in the process of developing better qualitative and
25 quantitative descriptors for both models and the data used to develop models, to assist risk
26 assessors in their evaluation and application of PBPK models.
27 The adequacy of model parameter values may be evaluated in different ways; no single
28 method has been accepted or endorsed by the modeling or regulatory community as yet.
29 Statistical methods required for evaluating the adequacy of model parameters are based on
30 comparison of simulations with experimental data, and depend on whether the objective is to
31 perform internal evaluation (in which all model parameters are estimated from the same data
32 set), external evaluation (in which different datasets are used for model calibration and testing
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1 the predictive capability of the model) or serai-external evaluation (in which some of the model
2 parameters are based on the data set). Although no systematic research effort or guidance is
3 available in this regard, there is much interest in developing consistent and acceptable evaluation
4 methods, and progress is being made.
5 For external evaluations, none of the classical tests (t, Mann-Whitney, two-sample x2,
6 two-sample Kolmogrov, etc.) that determine whether the underlying distributions of the two
7 datasets are similar is applicable, since the output processes of almost all real world systems and
8 simulations are non-stationary and autocorrelated. Furthermore, there is a question of whether
9 the use of statistical hypothesis tests is even appropriate. Since the model is only an
10 approximation of the actual system, a null hypothesis that the system and model are the same is
11 clearly false. The more appropriate question is to ask whether or not the differences between the
12 system and the model are significant enough to affect conclusions derived from the model. In
13 this regard, Haddad et al. (1995) screened various statistical procedures (correlation, regression,
14 confidence interval approach, lack fit F test, univariate analysis of variance, and multivariate
15 analysis of variance) for their potential usefulness in evaluating the degree of agreement between
16 PBPK model simulations and experimental data According to these authors, the multivariate
17 analysis of variance represents the most appropriate statistical test for the purpose of comparing
18 . PBPK model predictions with experimental data. For now, however, the visual inspection is the
19 most frequently used approach, if not the best approach, to the external evaluation of the
20 performance of PBPK models.
21 One approach for determining if the level of complexity (number of parameters) in a
22 model is justified by the data is to use a nested modeling approach, where the model is reduced
23 to a simpler (nested) model when one or more parameters are set to zero. The increase in
24 goodness-of-fit obtained by allowing those parameters to be non-zero can then be evaluated
25 statistically using a x2 statistic, to determine if the additional degrees of freedom afforded by
26 those parameters are justified (Collins et al., 1999).
27 There is increasing concern about the relevance and usefulness of external evaluation in
28 PBPK modeling, particularly as it relates to humans. External evaluation requires that some of
29 the available pharmacokinetic data not be used during model calibration phase, but kept for
30 evaluating the performance of the model. Not everyone is in agreement with such an approach.
31 Some people believe that all the data used for model evaluation should be used to improve the
32 parameter estimates, so that no data are "wasted" towards that end. Such an iterative approach to
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1 model evaluation and calibration maximizes the use of the available data. This is particularly an
2 issue of relevance to human data since the actual parameters for each individual in a population
3 might be different such that a model with a single set of parameters may not be reasonably
4 expected to simulate the observed kinetics in all individuals. Therefore, the process of modeling
5 should not only take into account the existing information on parameters, but also be able to
6 accommodate the new information based on fits to additional datasets. In this context, Bayesian
7 analysis is being increasingly explored for use in PBPK modeling (Bois et al., ZOOOa, b; Jonsson
8 and Johanson 2001, 2002). In the Bayesian approach, the prior information on parameters is
9 updated with new pharmacokinetic data such that the resulting posterior estimates consistently
10 describe all data, and support better characterization of the uncertainty and distribution in the
11 parameter values. Cross validation is another potentially useful approach in this regard (Keys et
12 al., 2003). As used in structure-activity relationship modeling arena (Beliveau et al., 2003), cross
13 validation involves using all the available data sets by repeated sub-sampling. This type of a
14 leave-one-out cross validation allows the use of available data both for estimation and evaluation
15 of model parameters. It is likely that no single approach will be sufficient or applicable in all
16 contexts. Each of these approaches has its merits and limitations, and their applicability for
17 PBPK model evaluation depends upon the purpose of the model and data availability.
18 PBPK models intended for use in risk assessment should be evaluated to ensure that they
19 provide simulations of pharmacokinetic profile consistent with the experimental data and that
20 the parameters (point estimates, range of values, or distributions) are appropriate for the
21 intended application.
22
23 3.7. SENSITIVITY, UNCERTAINTY, AND VARIABILITY ANALYSES
24 The variability, uncertainty, and sensitivity of parameters constituting the PBPK models
25 may need to be evaluated, depending on the intended application(s) of the model.
26
27 3.7.1. Sensitivity Analysis
28 Sensitivity analysis deals with the quantitative evaluation of how parameters or input
29 functions influence the outcome. Such an analysis conducted in the context of risk assessment
30 would identify how each parameter influences the risk estimate and which specific one(s)
31 drive(s) the risk estimate (U.S. EPA, 2001). By identifying the most sensitive parameters,
32 sensitivity analysis facilitates focused use of resources for uncertainty and variability analyses.
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1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Sensitivity analysis in the context of PBPK modeling involves determining the magnitude
of change in pharmacokinetic simulations for a defined change in the input parameters. The
results of sensitivity analysis are the 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 the
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 PBPK model parameter with respect to the dose metric (i.e., parent chemical AUC
in target tissue). In this case, a sensitivity ratio of 2 associated with the breathing rate signifies
that 1% change in the numerical value of this parameter will lead to a 2% change in the dose
metric (Figure 3-3).
3 -
2 -
o
•S3
(D
(2
2? .
;5 1 -
0)
W
-1 -
'
:jjjlj!|:;:;:|:|S
:W:$:*x:x:::
0 0) .t 0) X
ra ^ c ro c ra
if I 12 |i >
o 2
0) m CD
Figure 3-3. Sensitivity ratios associated with certain input parameters of a
PBPK model.
Sensitivity analysis is informative for identifying the key parameters that are likely to
affect the performance of the model and output such that efficient resource allocation for further
research to enhance confidence in the parameter estimates can be done (e.g., Bois et al., 1991;
Hetrick et al., 1991; Clewell et al., 1994). A sensitivity analysis is not obligatory for a PBPK
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1 model to be acceptable for risk assessment applications, but it greatly strengthens the credibility
2 of the model and guides resource allocation for risk assessment-oriented research.
3 One caveat when conducting individual parameter sensitivity analyses (such as described
4 above) is that they only show the sensitivity of the model predictions to a change in the single
5 parameter when all other parameters are held constant. For example, consider the sensitivity to
6 breathing rate depicted in Figure 3-3. What would have happened if one had known, before
7 starting the modeling process, that the breathing rate was 20% higher than the default value
8 actually used? Would the predicted dose metric have then turned out to be 40% higher? Only if
9 none of the other parameters were calibrated to the model data during the modeling process. If
10 in each case (default breathing rate vs. 40% higher) one had started with that value of the
11 breathing rate, and then calibrated the Vmax and other parameters to the data, the result would be
12 different values of Vmax, etc., that would compensate to some extent for the change in Vmax. As a
13 simple analogy, consider the fit of a straight line to some data, where the intercept is a "known"
14 parameter and the slope is fitted. After fitting the line one might determine that the "fit" is very
15 sensitive to the intercept by showing that if the intercept is changed while holding the slope
16 constant (i.e., standard sensitivity analysis), the value of the line equation changes a lot. But if
17 one had started with a larger value of the intercept at the beginning of the "modeling" process,
18 fitting the line to the data would have resulted in a lower value for the slope, such that the value
19 of the line equation would not change as much as when only the intercept is increased. In short,
20 the parameter estimation process leads to certain correlations between the values of parameters
21 that are fixed as inputs and those that are fitted. Thus, standard sensitivity analysis, while very
22 informative about the importance of individual parameters, over-estimates the actual impact of
23 changes in individual parameters because it does not account for correlations. In the case of
24 Figure 3-3, it might be that starting with a different breathing rate and then calibrating Vmax, etc.,
25 would have yielded almost identical values for the dose metric, and that the overall modeling
26 process is insensitive to breathing rate, even though the model predictions are sensitive to
27 changes in breathing rate when none of the other parameters are changed.
28
29 3.7.2. Variability Analysis
30 The focus of a variability analysis is to evaluate the range of values for a parameter
31 expected to be present in individuals of a population and its impact on tissue dose simulations.
32 PBPK models accounting for individual-specific parameters (e.g., enzyme levels, tissue volumes,
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1 body weights, workload) may be constructed to simulate tissue dose variability in populations
2 (e.g., Sato et al., 1991; Dankovic and Bailer, 1994). Alternatively, PBPK models for an average
3 individual representing specific subgroups of populations (e.g., adult women, pregnant women,
4 lactating women, children) may be constructed by accounting for subgroup-specific
5 physiological, biochemical, and physicochemical parameters (e.g., Fisher et al., 1997; Krishnan
6 and Andersen, 1998; Corley et al., 2003; Price et al., 2003b). These analyses, however, would
7 not provide the probability or likelihood of a particular output for a population.
8 With information such as the tissue dose corresponding to the 95th percentile and 50th
9 percentile, the magnitude of the interindividual variability factor can be computed. For this
10 purpose, Monte Carlo simulation approaches based on prior distributions of input parameters
11 (physiological parameters, enzyme content/activity with or without the consideration of
12 polymorphism) have frequently been used (Thomas et al., 1996; El-Masri et al., 1999; Bogaards
13 et al., 2001; Haber et al., 2002; Lipscomb and Kedderis, 2002; Timchalk et al., 2002; Lipscomb
14 et al., 2003). This method involves repeated computations using inputs selected at random from
15 statistical distributions for each parameter in order to provide a statistical distribution of the
16 output, i.e., dose metric (Figure 3-4). The Monte Carlo approach to variability analysis has also
17 helped in evaluating the net impact of the variability of critical biochemical and physiological
18 parameters (e.g., Portier and Kaplan, 1989).
19 When conducting variability analysis, it is important that correlations in model
20 parameters be included in the evaluation. For example, cardiac output (Qc) and breathing rate
21 (QA) are expected to vary in proportion to each other, so using independent distributions that
22 might give a very high value of Qc with a very low value of QA would be unrealistic. On the
23 other hand, one could consider the distributions of Qc and the distribution of the fAc = QA/Q, and
24 multiply the value selected from the fAc distribution by the value selected from the Qc
25 distribution to obtain the value of QA to be used.
26 More recent research has indicated the potential usefulness of Bayesian framework based
27 on Markov Chain Monte Carlo simulation (Jonsson and Johanson, 2001, 2002). This method
28 combines prior knowledge about parameters and data from new experimental studies to generate
29 posterior parameter distributions, which in turn are used in Monte Carlo simulations for
30 conducting variability and uncertainty analyses (Bois, 1999; Johanson et al., 1999; Bernillon and
31 Bois, 2000).
32
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1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Metab $jbj|fi zy m es
" " " f
ff f
Partition fcospcients
Monte
Carlo
Simulation
Time
INPUT
DISTRIBUTIONS
COMPUTER
PROGRAM
SIMULATIONS
Figure 3-4. Illustration of the use of the Monte Carlo approach for
simulating the distribution of internal concentration versus time on the basis
of population distributions of PBPK model parameters.
Conducting a variability analysis with 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 factor (pharmacokinetic component).
3.7.3. Uncertainty Analysis
Uncertainty analysis in the context of PBPK modeling refers to the evaluation of the
impact of the lack of precise knowledge about the numerical value of a parameter or model
structure itself on dose metric simulations. The uncertainty regarding model structure and
parameter values may contribute to uncertain predictions of dose metrics, particularly for low-
dose exposure situations (Hattis et al., 1990). The 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 inadequacy of the model
structure chosen for the study. In these cases, either a quantitative uncertainty analysis or model-
directed mechanistic studies should help improve the predictive ability and robustness of the
PBPK model (Clewell and Andersen, 1997; Haddad et al., 1998).
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1 Quantitative uncertainty analyses of PBPK model have frequently been conducted using
2 either a Monte Carlo approach or Bayesian framework based on Markov Chain Monte Carlo
3 simulations with respect to specific endpoints (e.g., amount metabolized, tissue concentration of
4 parent chemical at a specific time, cancer estimates) (e.g., Farrar et al., 1989; Krewski et al.,
5 1995; Gelman et al., 1996; Elder, 1999). Alternatively, a stochastic response surface method or a
6 fuzzy simulation approach may be used for uncertainty analysis with PBPK models (Isukapalli et
7 al., 1998; Nesterov, 2001). The latter method is particularly useful when statistical distributions
8 of parameters cannot be defined reliably and only semi quantitative, qualitative, and vague
9 information is available.
10 If there is a lack of confidence regarding the numerical value of a parameter (e.g.,
11 imprecision due to the method used for parameter estimation), a quantitative analysis of the
12 uncertainty associated with parameter(s) of the PBPK model should be conducted. Such analysis
13 will provide an indication of the impact on tissue dose simulations of the imprecision or lack of
14 accurate knowledge of a parameter value. However, if a PBPK model has been evaluated using
15 various sets of data (e.g., species, dose levels, routes), then the benefits of uncertainty analysis
16 are limited. Particularly, if the model with its set of parameters has been shown to predict
17 adequately the kinetics of a chemical following various dose levels administered by more than
18 one route in more than one species, conducting a quantitative uncertainty analysis cannot help
19 improve any further the closeness of model predictions to experimental data. In other words, the
20 improvement of the precision of parameter estimates, after a certain level, may not help improve
21 the predictive ability of the model. Models that have been adequately evaluated may therefore
22 be used for risk assessment applications without detailed uncertainty analysis. Where possible
23 and relevant, uncertainty analysis should be performed to strengthen the credibility of the PBPK
24 model and guide resource allocation to risk assessment-oriented research.
25 The conduct of sensitivity, uncertainty, and variability analyses should be based on
26 acceptable statistical methods. EPA has published guiding principles for Monte Carlo analysis
27 (U.S. EPA, 1997), but there is no such guidance for Bayesian and Markov Chain Monte Carlo
28 methods. When using these methods, care should be taken to ensure that the resulting PBPK
29 model simulations respect the following basic conditions:
30 • The numerical values of physiological parameters (representing prior or posterior
31 distributions) are within known, plausible limits;
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1 • The sum of tissue volumes is lower than the body weight;
2 • The sum of tissue blood flows is equal to cardiac output;
3 • The mass balance is respected (chemical absorbed = chemical in body + chemical
4 eliminated); and
5 • The covariant nature of the parameters is appropriately respected (e.g., the person
6 with lowest breathing rate should not be the one receiving the highest cardiac output)
7
8 While taking advantage of the sophisticated statistical approaches, it is important to
9 ensure that the resulting model and parameters are within plausible range or representative of the
10 reality.
11 Sensitivity, uncertainty, and variability analyses can help improve the credibility of
12 PBPK models as well as prioritize research needs to improve the model for risk assessment
13 applications. However, such analyses may not be required for all PBPK models intended for
14 risk assessment applications.
15
16 3.8. DEVELOPING PBPK MODELS FOR USE IN RISK ASSESSMENT:
17 STRATEGIES FOR DEALING WITH DATA-POOR SITUATIONS
18 3.8.1. Minimal Data Needs for Constructing PBPK Models
19 When an adequately evaluated PBPK model is not available for the species, life stage,
20 and route relevant to a risk assessment application, significant resources may be needed to
21 develop such a model, depending on the chemical, the availability of prior information, and the
22 complexity of disposition mechanisms being modeled. The minimal data required for
23 developing such models for a chemical in any given species are:
24 • Partition coefficients,
25 • Biochemical constants,
26 • Route-specific absorption parameters, and
27 • In vivo pharmacokinetic data for model evaluation.
28
29 As outlined in this chapter, the partition coefficients required for PBPK modeling may be
30 estimated using the theoretical algorithms found in the literature (Appendix 1). Their use,
31 however, should be limited to the domain of validity and the families of chemicals for which
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1 such algorithms have been developed and validated. Biochemical constants such as metabolism
2 rates may be obtained using in vitro systems. Other biochemical parameters, such as binding
3 association constants and renal clearance, may be required, depending on the chemical.
4 Additionally, route-specific absorption parameters such as the rate of oral absorption and the skin
5 permeability constant are required for describing oral absorption and dermal absorption,
6 respectively. Of these, the skin permeability coefficient can be obtained using available
7 quantitative structure-activity relationships (QSARs) (Appendix 1). However, such absorption
8 parameters are not required for simulating intravenous administration and inhalation exposures.
9 Finally, some in vivo pharmacokinetic data (at a minimum blood concentration time-course data
10 at two dose levels) are required for evaluating the PBPK model for a particular route of
11 exposure.
12 The minimal data set identified above should be available for the species used in the
13 critical study. Human models, however, may be constructed with knowledge of species-specific
14 blood solubility/binding characteristics. Other model parameters, including metabolism rates,
15 may be either scaled or kept species-invariant according to the current state of knowledge
16 (Section 4.5). The availability of the data set for external evaluation in humans, of course, may
17 be a limiting factor. In such cases surrogate data sets may be used for model evaluation
18 purposes.
19
20 3.8.2. Surrogate Data for Interspecies and Interchemical Extrapolations
21 In the absence of human data for model evaluation purposes, a parallelogram approach
22 based on surrogate data has been used successfully. This approach uses two data sets (e.g. one
23 demonstrating the relationship between in vitro and in vivo findings in a test species and the
24 other demonstrating the relationship between in vitro human and in vitro test species findings) in
25 order to predict the in vivo effects in humans. Accordingly, if human data either cannot be
26 collected or is not available for a chemical of interest, it suffices to evaluate a related chemical
27 for which such data are available. Jarabek et al. (1994) used this parallelogram approach for
28 model development and interspecies extrapolation of the pharmacokinetics of HCFC-123 (2,2-
29 dichloro-l,l,l-trifluoroethane). In this case, the authors developed rat PBPK models for HCFC-
30 123 as well as a structural analog (halothane) by estimating partition coefficients and metabolic
31 constants. Following the evaluation of the rat PBPK model for each of these chemicals, human
32 models were constructed. The adequacy of the human model for halothane was evaluated using
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1 available pharmacokinetic data and by structural and metabolic analogy. HCFC-123 was
2 assumed to be able to reasonably simulate the in vivo pharmacokinetics in humans, even though
3 human data were not available for this chemical for model evaluation purposes (Jarabek et al.,
4 1994; Williams et al., 1996). This is one practical way of getting around the lack of human data
5 for model evaluation, particularly when external evaluation is intended.
6 To deal with situations of lack of data on PODs for closely related chemicals, a family
7 approach has been suggested. This approach, proposed by Barton et al. (2000), is based on the
8 principle that the acceptable concentrations for related chemicals, particularly metabolites, can
9 be derived using data on the parent chemical. Thus, if the NOAEL for the parent chemical is
10 established, there would also have been internal systemic exposures to its metabolites. By
11 determining the external exposure levels for these compounds that result in the same systemic
12 exposure, the NOAELs for these compounds can be established. The determination of the
13 internal dose and systemic exposures for the parent chemical and metabolites is accomplished
14 using PBPK models, thus facilitating the derivation and establishment of the RfD/RfC with a
15 poor database.
16 QSAR approaches are also available for constructing inhalation PBPK models for
17 volatile organic chemicals in the rat (Beliveau et al., 2003). Accordingly, the contributions of
18 various molecular fragments (CH3, CH2, CH, C, C=C, H, Cl, Br, F, benzene ring, and H in
19 benzene ring) toward the parameters of PBPK models have been determined. With the
20 knowledge of the number of the fragments occurring in a given molecule, the partition
21 coefficients and metabolic constants required for constructing a first-generation PBPK model can
22 be obtained. This QSAR approach is useful to initially develop PBPK models for other
23 chemicals, as long as the number and nature of fragments do not exceed the ones in the
24 calibration set used in the study (Beliveau et al., 2003).
25 Finally, in dealing with data-poor situations, the parameters, algorithms, and references
26 provided in the appendices provide a good starting point. Useful data and equations for PBPK
27 modeling may also be found in reliable electronic resources. For example, Nestorov (1998)
28 outlines a web-based resource for PBPK modeling (http://www.capkr.man.ac.uk). The site
29 provides instant access to resources such as data, methodology, and tools necessary to start a
30 PBPK modeling effort. Another site pioneered by Dr. Loizou (England) will become available
31 in the near future.
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1
2 3.9. EVALUATION OF PBPK MODELS: SUMMARY
3 The basic criteria for evaluation of PBPK models, as outlined in Sections 3.1 through 3.7,
4 are summarized below.
5 • The structure of a PBPK model intended for risk assessment applications should
6 contain the target organ (or a surrogate tissue).
7 • The MBDEs in PBPK models should have units of quantity per time (e.g., mg/hr) or
8 concentration per time (mg/L-hr"1), and the type of equations chosen to describe
9 ADME should be justified on the basis of hypothetical or known mechanisms of such
10 processes.
11 • The tissue volumes, flow rates, and ventilation:perfusion ratios specified in the model
12 should be within physiological limits. Particularly, the sum total of the tissue
13 volumes should be within the body weight, and the sum total of tissue blood flow
14 rates should equal cardiac output.
15
16 • The power function used for scaling of physiological flows on the basis of body
17 weight should be within 0.67 and 0.75, unless species- or individual-specific data are
18 available.
19 • The power function used for scaling physiological flows and maximal velocity of
20 metabolism on the basis of body weight should be within 0.67 and 0.75.
21 • Maximal velocities of metabolism may also be scaled on the basis of body weight, but
22 measured values for specific enzymes in humans do not generally correlate with body
23 weight, so the choice of whether and how to scale metabolism is at the discretion of
24 the modeler.
25 • Partition coefficients required for PBPK models should be obtained from in vivo data,
26 in vitro data, or theoretical algorithms in the application domain.
27 • Biochemical parameters for PBPK models should be estimated using in vivo data or
28 valid in vitro methods.
29 • The PBPK model should be implemented using commercially available software. If
30 the modeler chooses to write his/her own program, then the appropriateness of the
31 integration algorithm and integration interval should be justified.
32
33 • It is suggested that the PBPK model code be checked for accuracy of units, mass
34 balance, blood flow balance, and behavior at zero dose. A model used in a risk
35 assessment should be accompanied by sufficient documentation to support an
36 independent evaluation and reconstruction of the model and simulation results. A
37 more rigorous verification that may be considered by the risk assessor is to
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1 independently re-code the model to assure that the documentation is thorough and that
2 there are no "bugs" in the code.
3 • Evaluation of the PBPK model structure and parameters should be conducted to
4 ensure that the model adequately predicts the pharmacokinetic behavior (i.e., bumps
5 and valleys in the concentration vs. time plot) of the chemical and that the parameters
6 (point estimates, range of values or distributions) consistently describe available data.
7
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1 4. APPLICATION OF PBPK MODELS IN RISK ASSESSMENT
2
3 4.1. CHOOSING PBPK MODELS APPROPRIATE FOR USE IN RISK ASSESSMENT
4 Whether or not a PBPK model was initially intended for risk assessment purposes, it can
5 be useful for risk assessment if it permits simulations of the tissue and blood concentrations of
6 the toxic moiety (parent chemical or metabolite) associated with the animal toxicity or human
7 epidemiological study serving as the basis for the derivation of health protective values (e.g.,
8 RfC, RfD, cancer slope factors). Specifically, the model should be able to simulate the dose
9 metrics in the test species as well as in humans for the exposure route and exposure scenario of
10 relevance. For use in risk assessment, a PBPK model:
11 • Should have been developed or calibrated for species and life stage of relevance to the
12 risk assessment,
13 • Must have been peer-reviewed and evaluated for its structure and parameters,
14 • Should consist of parameters essential for simulating uptake via routes associated
15 with human exposures as well as the critical study chosen for the assessment, and
16 • Should be able to provide predictions of the time-course of concentration of toxic
17 moiety (parent chemical or metabolite) in the target organ or a surrogate
18 compartment.
19
20 Figure 4-1 depicts how the above criteria can be applied for selecting appropriate PBPK models.
21 Basically, a peer-reviewed PBPK model for the relevant species and life stage consisting of
22 parameters for simulating relevant routes of exposure and potentially relevant dose metrics is
23 appropriate for use in risk assessment.
24 The first criterion, though appearing self-evident, is quite fundamental, because the
25 models available in the literature sometimes may not have been developed for the specific life
26 stage and species used in the critical lexicological study forming the basis of a risk assessment.
27 For example, PBPK models for methanol have been developed in rats, monkeys, and humans
28 (Horton et al., 1992; Rogers et al., 1993; Bouchard et al., 2001), yet the critical study appears to
29 be a developmental toxicity study in mice, although a newer two-generation study in rats may
30 also be important (Clark et al., 2004). When the PBPK model has not been developed for the life
31 stage or species used in the study forming the basis of the POD for an assessment, additional
32
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Is the PBPK model
available for the test
species and humans?
Model
development
Are the parameters
for simulating
relevant routes
available?
Has the model been
evaluated and
eer-reviewed?
Does the model
simulate dose metrics
of relevance to risk
assessment?
Undertake evaluation
and peer review
Use in risk
assessment
Use for mechanistic
studies & investigation
of mode of action
2
3
4
Figure 4-1. Decision tree for selecting PBPK models appropriate for use in
risk assessment.
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1 work may have to be undertaken to
2 resolve the situation before the PBPK
3 model can be used for that particular
4 assessment.
5 The PBPK model for the
6 relevant species and life stage should
7 have been peer-reviewed to determine
8 the adequacy of the structure,
9 parameter estimation methods, and
10 the evaluation efforts. If the PBPK
11 model for a chemical is available in
12 the species and life stage
13 corresponding to the study forming
14 the basis of an assessment but it has
15 not been peer-reviewed, then efforts
16 may be directed towards such a
17 review. Box 4-1 enlists the
18 fundamental questions and issues to
19 be considered while conducting a
20 peer-review evaluation of the
21 adequacy of PBPK models intended
22 for risk assessment applications.
23 Finally, the peer-reviewed model(s)
24 chosen for risk assessment
25 applications should be able to provide
26 simulations of the tissue dose of the
27 toxic moiety or an appropriate dose
28 metric for exposure scenarios and
29 routes associated with the critical
30 study as well as human exposures.
31 Peer-reviewed PBPK models
32 that facilitate the prediction of dose
Box 4-1. Questions and issues to be considered while
evaluating the adequacy of a PBPK model
• Is an appropriate target organ or a surrogate tissue
identified as one of the model compartments?
• Are the known major sites of storage,
transformation, and clearance included in the
model structure?
• Is the form of equation used to describe chemical
uptake justified on the basis of hypothesis of tissue
uptake of the chemical?
• Have enzymatic processes been described
appropriately? (If simulated exposure levels are
well below saturation, use of first-order kinetics is
acceptable.)
• Are the units throughout differential equations
consistent (e.g., concentration should not be in
mg/ml in one place and \iM in another)?
* Are the input parameters related to the
characteristics of the host, chemical, or
environment?
• Is the sum total of compartment volumes within
100% of the body weight?
• Do the tissue blood flow rates add up to the cardiac
output?
• Is the ventilationiperfusion ratio specified in the
model within physiological limits?
• Is the volume of each tissue compartment within
known physiological limits?
• Is the approach used to establish partition
coefficients valid?
• Is the method used for estimating biochemical
parameters adequate?
• Is the allometric scaling done appropriately?
• Is the integration algorithm used in the study
known for solving differential equations and
dealing with stiff and nonstiff conditions?
• Does the shape of the pharmacokinetic curve
generated by the model match that obtained
experimentally?
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1 metrics of chemicals for relevant exposure route and life stage of species used in the critical
2 study as well as humans are a prerequisite for their use in risk assessments.
3
4 4.2. EVALUATION OF DOSE METRICS FOR PBPK MODEL-BASED ASSESSMENTS
5 When using PBPK models in risk assessment (RfD, RfC, and unit risk estimates), the
6 basic data needed are:
7 1. POD and critical effect from one or more key studies,
8 2. Peer-reviewed PBPK model for the relevant test species and humans, and
9 3. Dose metric appropriate for the risk assessment.
10
11 The methods and challenges associated with the identification of critical effects and
12 PODs for an assessment remain the same regardless of whether one uses PBPK models or not.
13 The approaches for identifying PODs can be found elsewhere (U.S. EPA, 1994, 2005a). The
14 criteria and issues associated with the selection of PBPK models useful for risk assessment were
15 considered in the previous section. The third data need noted above, i.e., the identification of the
16 appropriate dose metric, is a key aspect determining the use of PBPK models in risk assessment.
17 The dose metric, or the appropriate form of chemical closely associated with the toxicity,
18 varies from chemical to chemical, depending on the MOA and critical effect. The dose metric
19 for PBPK-based risk assessment is chosen following the identification of the potential toxic
20 moiety and evaluation of the relationship with the end point of concern. Analysis of available
21 information on MOA of a chemical along with descriptive toxicity data from various studies,
22 including those using inhibitors or inducers of hepatic metabolism, should be useful in
23 identifying the potential toxic moiety (parent chemical or metabolite). Further, the available data
24 on closely related chemicals may be used to infer the likely toxic moiety. If the induction of
25 toxic effects by a chemical is not altered following treatment with a specific inhibitor of hepatic
26 metabolism, then it would implicate the parent chemical as the toxic moiety. Alternatively, if the
27 induction of the rate of metabolism enhances the extent of toxic effects produced, it would
28 indicate the metabolite as the toxic moiety. Similarly, the toxicity data for various exposure
29 routes and modes of administration may be compared to infer the potential toxic moiety (IPCS,
30 2001).
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1 After the potential toxic moiety has been identified, the appropriate measure of tissue
2 exposure to the toxic moiety should be chosen (Figure 4-2). For example, the peak concentration
3 has been related to neurotoxic effects of solvents (e.g., Bushnell, 1997; Benignus et al., 1998;
4 Pierce et al., 1998; MacDonald et al., 2002), and concentration of trichloroethylene at the time of
5 testing correlated with effects on behavioural and visual functions (Boyes et al., 2000). Tissue
6 concentrations of TCDD measured during a critical period of gestation have been reported to
7 predict the intensity of developmental responses (Hurst et al., 2000). Gender-specific genotoxic
8 effects of benzene in mice are related to differences in the rate of oxidative metabolism (Kenyon
9 etal., 1996).
10 For chronic effects of chemicals, the integrated concentration of the toxic form of
11 chemical in target tissue over time (i.e., AUC) is often considered a reasonable dose metric
12 (Andersen et al., 1987; Collins, 1987; Voisin et al., 1990; Clewell et al., 2002). For carcinogens
13 producing reactive intermediates, the amount of metabolite produced per unit time and the
14 amount of metabolite in target tissue over a period of time (e.g., mg metabolite/L tissue during
15 24 hours) have been used as dose metrics (Andersen and Dennison, 2001). For developmental
16 effects, the dose surrogate is defined in the context of window of susceptibility for a particular
17 gestational event (e.g., Welsch et al., 1985). Although the AUC and rate of metabolite formation
18 figure among the most commonly investigated dose metrics, other surrogates of tissue exposure
19 may also be appropriate for risk assessment purposes, depending on the chemical and its MOA
20 (e.g., maximal concentration of the toxic moiety, duration and extent of receptor occupancy,
21 macromolecular adduct formation, or depletion of glutathione) (Clewell et al., 2002). Table 4-1
22 lists the dose metrics used successfully in a number of PBPK-based cancer and noncancer risk
23 assessments.
24 When the appropriate dose metric cannot be identified readily, the evaluation of the
25 relationship with the end point of concern should be undertaken with each of the dose metrics in
26 order to identify the one that exhibits the closest or the best association (e.g., Andersen et al.,
27 1987; Kirman et al., 2000). This becomes particularly important when there are little or
28 confusing data on the plausible MOA of the chemical. At a minimum, the appropriate dose
29 metric can be identified as the one that demonstrates a consistent relationship with positive and
30 negative responses observed at various dose levels, routes, and scenarios in a given species. In
31
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Potential
Toxic Moiety
Unknown
AUC
mg/L tissue x time
(Parent chemical or metabolite)
Concentration
Amount
Concentration
Amount
Rate of production
Quantity in tissue
\
Quantity
in tissue
Integrated
/
Average
Cmax
(mg/L. Tissue)
AUC
(mg/L tissue
xtime)
Cmax
(mg/L. Tissue)
AUC
(mg/L tissue
xtime)
mg formed
per unit time
(e.g. mg/hr)
mg formed
over time specified
(e.g. mg/day)
Figure 4-2. Examples of measure of tissue exposure to toxic moiety for risk assessment applications.
-------
1
2
Table 4-1. Dose metrics used in PBPK model-based cancer and noncancer
risk assessments
Chemical
Acrylonitrile
Bromotrifluoromethane
Butoxyethanol (2-)
Chloroform
Chloropentafluorobenzene
Dichlorofluoroethane
1 ,4-Dioxane
Ethyl acrylate
Ethylene glycol ethers
Formaldehye
Heptafluoropropane
Isopropanol
Methoxyacetic acid
Methyl chloroform
Methyl mercury
Methyl methacrylate
Endpoint
Brain tumors
Cardiac sensitization
Forestomach lesions and
tumors
Liver cancer
Hepatic effects and kidney
tumor
Liver toxicity
Cardiac sensitization
Liver tumors
Forestomach tumors
Developmental toxicity
Cancer
Cardiac sensitization
Neurobehavioral effects
Developmental/
reproductive effects
Developmental effects
Hepatic effects
Neurological effects
Nasal lesions
Dose metric
Peak metabolite
concentration in target
tissue
Concentration of parent
chemical at the end of
exposure
Levels of butoxyethanol/
butoxy acetic acid in
forestomach
Amount of metabolites
covalently bound to
biological macromolecules
per L liver per day; % cell
kill/day
Maximal rate of
metabolism per unit kidney
cortex volume
AUC of parent chemical in
liver
Concentration of parent
chemical at the end of
exposure
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 (g, day 8)
Area under the liver
concentration vs. time
curve
Fetal brain concentrations
Amount metabolized/time
Reference
Kirman et al. (2000)
Vinegar and Jepson (1996)
Poet et al. (2003)
Reitzetal. (1990)
Meek et al. (2002)
Clewell and Jarnot (1994)
Vinegar and Jepson (1996)
Leung and Paustenbach
(1990)
Reitzetal. (1990b)
Frederick etal. (1992)
Sweeney etal. (2001)
Casanova et al. (1996);
Schlosser et al. (2003)
Vinegar and Jepson (1 996)
Gentry et al. (2002)
Gentry et al. (2002)
Clarke etal. (1992, 1993)
Welsch etal. (1995)
Reitzetal. (1988a)
Gearhart etal. (1995)
Andersen etal. (1999,
2002)
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1
2
Table 4-1. Dose metrics used in PBPK model-based cancer and noncancer
risk assessments (continued)
Chemical
Methylene chloride
Pentafluoroethane
Styrene
TCDD
Toluene
Trichloroethylene
Trifluoroiodomethane
Vinyl acetate
Vinyl chloride
Endpoint
Cancer
Cardiac sensitization
Lung tumors (mouse)
Biochemical responses
Cancer risk
Behavioral effects
Renal toxicity
Neurotoxicity
Cancer (liver lung and
kidney)
Cardiac sensitization
Olfactory, degeneration
and tumor development
Angio sarcoma
Dose metric
Rate of glutathione
metabolites produced/L
liver/time
Concentration of parent
chemical at the end of
exposure
Steady state concentration
of ring oxidation
metabolite mediated by
CYP2F
Body burden
Time- weighted receptor
occupancy
Up/down regulation of
receptor occupancy
Number 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 in
plasma; production of
thioacetylating
intermediate from
dichlorovinylcysteine in
kidney
Concentration of parent
chemical at the end of
exposure
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. (1987)
Vinegar and Jepson (1 996)
Cruzen et al. (2002)
Kim et al. (2002)
Andersen etal. (1993);
Portieretal. (1993);
Conolly and Andersen
(1997)
van Asperen et al. (2003)
Barton and Clewell (2000)
Barton & Clewell (2000)
Fisher and Allen (1993);
Clewell et al. (2000)
Vinegar and Jepson (1 996)
Bogdanffy etal. (1999,
2001)
Clewell etal. (2001);
Reitzetal. (1996b)
3
4
AUC = area under the curve
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1 other words, the level of the dose metric should be lower for exposure conditions with no effect
2 and higher for toxic exposures, regardless of the route and exposure scenario (Clewell et al.,
3 2002).
4 Where there is inadequate basis for giving priority to one dose metric over another, the
5 most conservative one (the dose metric producing the highest risk or lowest acceptable exposure
6 level) should be used in order to be health protective (Clewell et al., 2002). The use of
7 appropriate dose metric helps to reconcile route and species differences in cancer responses,
8 provided there are no pharmacodynamic differences. There has been at least one instance in
9 which PBPK model-derived dose measures could not reconcile rat and mouse kidney tumor data
10 (Smith et al., 1995), indicating the significant role of factors other than the target tissue exposure
11 to toxic moiety.
12 The following section describes the various plausible applications of PBPK models in
13 risk assessment. These applications relate to high-dose to low-dose extrapolation, interspecies
14 extrapolation, intraspecies extrapolation, route-to-route extrapolation, and duration extrapolation
15 as required for RfD derivation, RfC derivation, and cancer risk assessment.
16
17 4.3. EXAMPLES OF THE USE OF PBPK MODELS IN RISK ASSESSMENT
18 4.3.1. High-Dose to Low-Dose Extrapolation
19 PBPK models facilitate high-dose to low-dose extrapolation of tissue dosimetry by
20 accounting for the dose-dependency of relevant processes (e.g., saturable metabolism, enzyme
21 induction, enzyme inactivation, protein binding, and depletion of glutathione reserves) (Clewell
22 and Andersen, 1997). The description of metabolism in PBPK models has frequently included a
23 capacity-limited metabolic process that becomes saturated at high doses. Nonlinearity arising
24 from mechanisms other than saturable metabolism, such as enzyme induction, enzyme
25 inactivation, depletion of glutathione reserves, and binding to macromolecules, have also been
26 described with PBPK models (e.g., Clewell and Andersen, 1997; Krishnan et al., 1992). A
27 PBPK model intended for use in high-dose to low-dose extrapolation should have the equations
28 and parameters describing dose-dependent phenomena if dose-dependence occurs in the range of
29 interest or assessment. Because the determinants of nonlinear behavior may not be identical
30 across species and age groups (e.g., maximal velocity for metabolism, glutathione
31 concentrations), these parameters are required for each species/age group. During the conduct of
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1 high-dose to low-dose extrapolation, no change in the parameters of PBPK model is required
2 except for the administered dose or exposure concentration.
3 An example of high-dose to low-dose extrapolation is presented in Figure 4-3. In this
4 figure, both the blood AUC and the amount metabolized over a period of time (12 hr) are plotted
5 as a function of exposure concentrations of toluene. For conducting high-dose to low-dose
6 simulation in this particular example, only the numerical value of the exposure concentration
7 (which is an input parameter for the PBPK model) was changed during every model run. All
8 other model parameters remained the same. The model simulations shown in Figure 4-3 indicate
9 the nonlinear nature of blood AUC as well as the amount of toluene metabolized per unit time in
10 the exposure concentration range simulated. In such cases, the high-dose to low-dose
11 extrapolation of tissue dosimetry should not be conducted assuming linearity; rather it should be
12 performed using tools such as the PBPK models.
13
14 4.3.2. Interspecies Extrapolation
15 The application of PBPK models for interspecies extrapolation of tissue dosimetry is
16 performed in several steps. First, a rodent model is developed to describe the uptake and
17 disposition of the chemical in question by integrating information on the physiological,
18 biochemical, and physicochemical parameters. Then, a priori predictions of the PBPK model
19 are compared with experimental observations to evaluate the adequacy of the structure and the
20 parameter estimates of the rodent model. The next step involves using species-specific or
21 allometrically scaled physiological parameters in the model and replacement of the chemical-
22 specific parameters with appropriate estimates for the species of interest (e.g., humans). Thus, in
23 this approach, the qualitative determinants of pharmacokinetics are considered to be invariant
24 among the various mammalian species. Qualitative differences between species, if any, can also
25 be factored into the existing structure of PBPK models (e.g., if different metabolic pathways
26 existed among species).
27 For conducting interspecies extrapolation of pharmacokinetic behavior of a chemical,
28 quantitative estimates of model parameter values (i.e., partition coefficients, physiological
29 parameters, and metabolic rate constants) in the second species are required. The tissue:air
30 partition coefficients of chemicals appear to be relatively constant across species, whereas
31 blood:air partition coefficients show some species-dependent variability. Therefore, the
32 tissue:blood partition coefficients for human PBPK models have been calculated by dividing the
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2
3
4
5
6
7
8
9
10
11
12
13
14
15
: i Exposure; ;eonre;ntratrans((;ipm
illl-Hlpiltigiljg:;;:.
s;;:Exposure j Goncienrt Hatipri ilpgrnji i
Figure 4-3. High-dose to low-dose extrapolation of dose metrics using PBPK
model for toluene. Inhalation exposures were for 4 hr and AUCs and amount
metabolized were calculated for 12 hr. Based on Tardif et al. (1997).
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 should be obtained in the species of interest. In vivo
approaches for determining metabolic rate constants are not always feasible for application in
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1 humans. The alternative is to obtain such data under in vitro conditions (e.g., Lipscomb et al.,
2 1998, 2003). A parallelogram approach may also be used to predict values for the human PBPK
3 model on the basis of metabolic rate constants obtained in vivo in rodents as well as in vitro
4 using rodent and human tissue fractions (Reitz et al., 1988b; Lipscomb et al., 1998). Alternately,
5 for chemicals exhibiting high affinity (low Km) for metabolizing enzymes, Vmax has been scaled
6 to the 0.75 power of body weight, keeping the Km species invariant. This approach may be
7 useful as a crude approximation, but it should be used only when other direct measurements of
8 metabolic parameters are not available or feasible.
9 An example of rat-human extrapolation of the kinetics of toluene using a PBPK model is
10 presented in Figure 2-2. Here the structure of the PBPK model developed in rats was kept
11 unchanged, but the species-specific parameters were determined either by scaling or
12 experimentally, as described above (Tardif et al., 1997). The model was then able to predict
13 accurately the kinetics of toluene in humans (Figure 2-2). Whenever the human data for a
14 particular chemical are not available for evaluation purposes, a corollary approach permitting the
15 use of human data on similar chemicals may be attempted (Jarabek et al., 1994).
16
17 4.3.3. Route-to-Route Extrapolation
18 There are two different approaches to route extrapolation involving PBPK models. The
19 first one is to use an animal model to extrapolate a POD for one route to POD by another route
20 on the basis of equivalent dose metric. The second approach would involve the estimation of the
21 human POD for one route from the available animal POD for another route on the basis of
22 equivalent dose metric.
23 The extrapolation of the kinetic behavior of a chemical from one exposure route to
24 another is performed by adding appropriate equations to represent each exposure pathway. For
25 simulating the intravenous administration of a chemical, a single input representing the dose
26 administered to the animal is included in the equation for mixed venous concentration. Oral
27 gavage of a chemical dissolved in a carrier solvent may be modeled by introducing a first-order
28 or a zero-order uptake rate constant, and dermal absorption has been modeled by including a
29 diffusion-limited compartment to represent skin as a portal of entry (Krishnan and Andersen,
30 2001). After the equations describing the route-specific entry of chemicals into systemic
31 circulation are included in the model, it is possible to conduct extrapolations of pharmacokinetics
32 and dose metrics. This approach is illustrated in Figure 4-4 for inhalation -» oral extrapolation
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Oral
c
.2
•o
2
JO
§
g
ID
>
100 -i
10
1 •
0.1 •
0.01 -
0.001
2345
Time (hours)
Inhalation
3
4
5
6
7
8
9
10
11
12
13
i:::::::::;:;;; VeRbus:blftOd:iiS)nc:entfati(jihi:
::;:;;:;::;:;;;::;;:;;;;::;;::::;::(mgA:J ;;
100 -
10 •
1 -
0.1 •
r V^
01234567
Time (hours)
Figure 4-4. Oral-to-inhalation extrapolation of the pharmacokinetics of
chloroform on the basis of same AUC in blood (7.06 mg/L-hr). The oral dose
was 1 mg/kg and the inhaled concentration was 83.4 ppm (4 hr). Based on Corley
etal. (1990).
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).
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1
2
3
4
5
6
7
8
9
10
11
43.4. Duration Adjustment
On the basis of equivalent dose metric, the duration-adjusted exposure values can be
obtained with PBPK models (Andersen et al., 1987; Brodeur et al., 1990). Accordingly, the
AUC of a chemical for the exposure duration of the critical study is determined initially 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.
O _l
0 "Si
E E
100-
10-
0.1 -
0.01 -
0.001 -
0.0001
RAT
8 12 16
Time (hours)
20
24
HUMAN
12
13
14
15
c
o
•»=
1
8^!
•o g>
o E
.2
%
8
(U
^>
10 -
1 -
0.1 -
0.01 -
0.001 -
n nnm -
^
0 4 8 12 16 20 2'
Time (hours)
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. Based on Tardif et al. (1997).
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1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
4.3.5. Intraspecies Extrapolation
Intraspecies extrapolation of the dose metric is conducted using PBPK models with the
sole intent of estimating the magnitude of the interindividual variability factor (pharmacokinetic
component) for RfC and RfD derivations. In this regard, the population distributions of
parameters, particularly those relating to physiology and metabolizing enzymes, 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 (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 the 95th percentile and 50th percentile for
unimodel, normal distribution (Naumann et al., 2001), the magnitude of the inter-individual
variability factor can be computed for risk assessment purposes (Figure 4-6).
.a
OJ
.0
o
50th percentile
Interindividual
variability factor
111 i ' *°
Illlli
95th percentile
Concentration
Figure 4-6. Estimation of the interindividual factor from the 50th (median)
and 95th percentile values of a dose metric simulated with a probabilistic
PBPK model.
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1 Even though several past efforts have characterized the impact of the distributions of
2 parameters in adult population, such variability analyses should also account for the life stage-
3 specific changes in physiology, tissue composition, and metabolic activity (reviewed in
4 O'Flaherty, 1994, Corley et al, 2003).
5
6 4.3.6. RfD Derivation
7 When a PBPK model is available for the oral route in test species and adult humans, RfD
8 derivation has been accomplished as follows (e.g., U.S. EPA, 1999b):
9 1. The PBPK model with the parameters of the test species is exercised to determine the
10 dose metric associated with the POD (NOAEL, LOAEL, or BMD),
11 2. The human PBPK model is exercised to determine the oral dose that is associated
12 with the dose metric established in step (1) above, and
13 3. The resulting oral dose is divided by the appropriate uncertainty factors to establish
14 the RfD.
15
16 A variant of the above approach involved dividing the dose metric associated with the
17 POD by the uncertainty factors before exercising the human model to determine equivalent doses
18 (e.g-, Gentry et al., 2002). The outcome is essentially the same if the uncertainty factors are
19 being applied to doses (internal or external) in the linear range of pharmacokinetic processes in
20 the species of interest. Clewell et al., (2002) suggest that the uncertainty factors are more
21 appropriately applied to the dose metric rather than to the external dose. The difference in
22 outcome between the two approaches is likely to exist if the POD is in the partially or completely
23 saturating range. Because the Agency has traditionally applied the uncertainty factors to the
24 external dose and not to the internal dose, it may be useful to undertake a systematic evaluation
25 of the outcome of applying the uncertainty factors to the external and internal doses for various
26 chemicals and situations.
27 In the PBPK model-based approach to RfD derivation, the magnitude of uncertainty
28 factors used is identical to that of the conventional approach except that the animal-to-human
29 uncertainty factor is reduced to three to account for the pharmacodynamic aspect (e.g., Clewell et
30 al., 1997; Gentry et al., 2002).
31 The RfD derivation for ethylene glycol monobutyl ether exemplifies the current approach
32 of PBPK model application (U.S. EPA, 1999b). hi this case, the LOAEL identified in an animal
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1 study (59 mg/kg-d) was provided as input to the PBPK model to determine the maximal
2 concentration of the metabolite, butoxy acetic acid in blood (BAAmax) (Corley et al., 1997). The
3 dose metric (BAAmax) associated with LOAEL was established in the test species (103 yuM). The
4 human PBPK model was then run to determine the exposure dose that would give the target dose
5 metric (103 |JM) (Corley et al., 1997). The resulting human-equivalent dose of 7.6 mg/kg-d was
6 divided by the appropriate uncertainty factors (30; 10 for interindividual differences and 3 for
7 LOAEL-to-NOAEL extrapolation) to establish the RfD (0.3 mg/kg-d). In this particular case,
8 the interspecies pharmacodynamic factor was set to 1 because in vitro studies suggested that
9 humans are less sensitive than rats to the hematologic effects of ethylene glycol monobutyl ether
10 (U.S. EPA, 1999b).
11 When the BMD is available, a similar approach is used to establish the RfD. In the case
12 of ethylene glycol monobutyl ether, initially the dose metric associated with the BMD was
13 established (BAAmax = 64 /uM) and then the human PBPK model was used to back-calculate the
14 equivalent dose (5.1 mg/kg-d). Using the appropriate uncertainty factor (10 for interindividual
15 variability), the RfD was derived (0.5 mg/kg-d) (U.S. EPA, 1999b). If the human PBPK model
16 was probabilistic in nature, accounting for the population distribution of parameters
17 (biochemical, physiological, and physicochemical), the pharmacokinetic component of the
18 interindividual variability factor could be addressed. Such a PBPK model-based assessment of
19 interindividual variability factor in the derivation of the RfD has been shown with methyl
20 mercury (Clewell et al., 1999).
21
22 4.3.7. RfC Derivation
23 When an inhalation PBPK model is available for the test species and humans, the HEC is
24 derived as follows:
25 1. The PBPK model with the parameters of the test species is run to determine the dose
26 metric associated with the POD (unadjusted or duration-adjusted NOAEL, LOAEL,
27 BMC), and
28 2. The PBPK model with the parameters for an average individual is run to determine
29 the continuous exposure concentration that is associated with the dose metric
30 established in step (1) above.
31
32 Subsequently, appropriate uncertainty factors are used the same way as in the conventional
33 approach (e.g., Clewell et al., 1997; Gentry et al., 2002; also see Section 4.3.6).
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1 The RfC derivations for m-xylene and vinyl chloride exemplify the application of PBPK
2 models. In the case of m-xylene, using the adjusted NOAEL of 39 mg/m3 as input to the rat
3 PBPK model, the steady-state blood concentration was established (0.144 mg/L) (Tardif et al.,
4 1997). The human model was then run to determine the exposure concentration yielding that
5 same dose metric (HEC = 41 mg/m3) (U.S. EPA, 2003). In an alternative approach, the dose
6 metric associated with the unadjusted NOAEL (217 mg/m3, 6 hr/d, 5 d/wk, 13 wks) in the rat
7 was determined using the PBPK model (time-weighted average blood concentration = 0.198
8 mg/L). Then, the human PBPK model was used to determine the 24-hr exposure concentration
9 that would produce this target dose metric (39 mg/m3). Dividing this value by the appropriate
10 uncertainty factors (3 for interspecies pharmacodynamic differences, 10 for interindividual
11 variability, 3 for subchronic to chronic extrapolation, and 3 for database deficiency), the RfC was
12 determined (0.1 mg/m3).
13 In the case of vinyl chloride, the RfC was derived from the NOAEL for the oral route
14 (U.S. EPA, 2000b). The PBPK model was initially used to derive the dose metric associated
15 with the rat NOAEL (0.13 mg/kg-d). Then, the human PBPK model was exercised to determine
16 the continuous exposure concentration associated with the same dose metric (2.5 mg/m3)
17 (Clewell et al., 1995). Using a total uncertainty factor of 30 (3 for toxicodynamic component of
18 IUF, 10 for interindividual variability factor), the RfC was established (0.1 mg/m3).
19 If the available human PBPK model is probabilistic in nature, accounting for the
20 population distribution of parameters (biochemical, physiological, and physicochemical), the
21 magnitude of the interindividual variability factor can be estimated (Delic et al., 2000). In that
22 case, the interindividual variability factor will be set to 3 (to account only for pharmacodynamic
23 differences).
24
25 4.3.8. Cancer Risk Assessment (unit risk estimates, RfC, and RfD)
26 When data for the MOA in a cancer risk assessment suggest a threshold (curvilinear)
27 dose-response relationship, the applications of PBPK models are similar to those in the
28 reference dose process (i.e., RfD and RfC derivation). If a linear dose-response model is
29 more applicable, or the MOA is unknown, then the following steps describe uses for a PBPK
30 model (e.g., Andersen et al., 1987):
31
32
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2 1. The relationship between administered dose or exposure concentration and dose
3 metric is established for the test species using PBPK model,
4 2. The quantitative relationship between dose metric and the cancer incidence observed
5 in the bioassay(s) is characterized to estimate the dose metric-based slope factor, and
6 3. The potential doses or exposure concentrations yielding the dose metric associated
7 with various levels of risk (e.g., 1 x 10~6) are back-calculated using the human PBPK
8 model.
9
10 For assessing the cancer risk associated with human exposures, the exposure
11 concentration is provided as input to human PBPK model to simulate the dose metric, which is
12 then multiplied with the dose metric-based slope factor. In the cancer risk assessments using
13 PBPK models, it is assumed that the tissue response associated with a given level of dose metric
14 in the target tissue is the same in test animals and in humans (e.g., Andersen et al., 1987). It is a
15 reasonable assumption that can be revised as a function of species-specific mechanistic
16 information available for a given chemical.
17 The demonstration of the applicability of PBPK models in cancer risk assessment was
18 first accomplished with dichloromethane, which caused liver and lung tumors in mice exposed to
19 2,000 or 4,000 ppm 6 hr/d, 5 d/wk for lifetime (Andersen et al., 1987). In this case, the mouse
20 PBPK model was used to calculate the tissue dose of metabolites and parent chemical arising
21 from exposure scenarios comparable to those of the cancer bioassay study, and their relationship
22 to the observed tumor incidence was then examined. Because the parent chemical is nonreactive,
23 Andersen et al. (1987) considered it an unlikely candidate responsible for the tumorigenicity.
24 Hence the relationship between the tissue exposure to its metabolites and tumor incidence was
25 examined (Table 4-2). Whereas the dose metric based on oxidative pathway varied little
26 between 2,000 and 4,000 ppm, the flux through the glutathione pathway increased with
27 increasing dose of dichloromethane and corresponded well with the degree of dichloromethane-
28 induced tumors at these exposure concentrations.
29 The model prediction of the target tissue dose of the glutathione conjugate resulting from
30 6-hour inhalation exposures to 1-4,000 ppm dichloromethane is presented in Figure 4-7
31 (Andersen etal., 1987). The estimation of target tissue dose of dichloromethane-glutathione
32 conjugate by linear back-extrapolation gives rise to a 21-fold higher estimate than that obtained
33 by the PBPK modeling approach. This discrepancy arises from the nonlinear behavior of
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1
2
3
Table 4-2. Relationship between tumor prevalence and dichloromethane
metabolites produced by microsomal and glutathione pathway for the
bioassay conditions (methylene chloride-dose response in female mice)
Exposure
(ppm)
0
2,000
4,000
Microsomal pathway
dose8
Liver
—
3,575
3,701
(Lung)
—
(1,531)
(1,583)
Gluthathione pathway
dose8
Liver
—
851
1,811
(Lung)
—
(123)
(256)
Tumor prevalence
Liver
6
33
83
(Lung)
(60)
(63)
(85)
4
5
6
7
a Tissue dose is cumulative daily exposure (mg metabolized/volume tissue/day).
Source: Adapted from Andersen et al. (1987).
8
9
10
11
12
13
14
15
16
17
innn -
to -inn .
H Pathway (mg/L/d
0 I
0.1 •
0.01 •
/X
X
X
/..-'•-
/
X
XX
**
Y
/>'
^ •
•*
X
S
10 100 1000 10C
PPM in air
Figure 4-7. PBPK model predictions of glutathione-pathway metabolites in
liver in mice. 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). Similar curves were
published in Andersen et al. (1987). The curvature occurs because oxidation
reactions that are favored at low inhaled concentrations become saturated as
inhaled concentration increases above several hundred ppm.
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1 dichloromethane metabolism at high-exposure concentrations. At exposure concentrations
2 exceeding 300 ppm, the cytochrome P-450-mediated oxidation pathway is saturated, giving rise
3 to a corresponding disproportionate increase in the flux through glutathione conjugation
4 pathway. By accounting for the species-specific differences in metabolism rates and physiology
5 in the PBPK model, the target tissue dose for humans was estimated to be some 2.7 times lower
6 than that for the mouse. The target tissue dose-based slope factor has subsequently been used for
7 characterizing the cancer risk associated with human exposures (Andersen et al., 1987; Reitz et
8 al., 1989; Haddad et al., 2001). The case of dichloromethane exemplifies how PBPK models can
9 be used for improving the dose-response relationship on the basis of appropriate dose metrics,
0 thus leading to scientifically sound conduct of interspecies and high-dose to low-dose
11 extrapolations essential for cancer risk assessments.
12
13 4.3.9. Mixture Risk Assessment
14 PBPK. models permit the risk assessment of chemical mixtures by facilitating the
15 simulation of change in dose metrics due to muitichemical interactions (Haddad et al., 2001).
16 For conducting tissue dosimetry-based assessments for mixtures, adequately evaluated PBPK
17 models for the mixture in the test species and in humans are required. Further, the health-
18 protective values for the individual chemicals (e.g., slope factor, RfD, RfC) should be known.
19 The approach for using PBPK models in risk assessment of mixtures of systemic toxicants or
20 carcinogens exhibiting threshold mechanism of action, would consist of (Haddad et al., 2001):
21 1. Characterizing the dose metrics associated with the RfC or RfD of mixture
22 components,
23 2. Obtaining predictions of dose metrics of each mixture component in humans, based
24 on information on exposure levels provided as input to the mixture PBPK model; and
25 3. Determining the sum total of the ratios of the results of steps (1) and (2) for each
26 component during mixed exposures.
27
28 Notationally, for chemicals in mixture acting on the same target organ:
" C
TJJ ^~* tissue,exp,i.
fll — /
• C
'=1 tissue, ref ,i.
29
30
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1
2 where HI is the hazard index, CtisSUe;eXp,i refers to the tissue concentration of the dose metric of
3 component / predicted in the experimental animal at the POD using PBPK model that accounts
4 for multiple interactions occurring in the mixture, and Ctissue,ref,/ is the dose metric associated with
5 human exposure to the RfD or RfC of component /'.
6
7 Similarly, for carcinogens with slope factor (Haddad et al., 2001):
8 1. The dose metric-based slope factor should be established for each component using
9 the animal PBPK model,
10 2. The dose metric associated with human exposure concentrations should be
11 established using mixture PBPK models, and
12 3. The results of steps (1) and (2) should be combined to determine the potentially
13 altered cancer response during mixed exposures.
14
15 Notationally,
16
17
18
19 where P(d) is the probability of excess cancer incidence in an exposed population, q*i,tissme = dose
20 metric-based cancer slope factor for each of the mixture components (i = 1,2, ..., n), and d^ssue
21 refers to the dose metric for each mixture component simulated using PBPK models that account
22 for multi-chemical interactions.
23 Risk assessments based on the use of PBPK models for single chemicals and mixtures, as
24 detailed in Section 4.3, account for only the pharmacokinetic aspect or, more specifically, target
25 tissue exposure to toxic moiety. If these tissue exposure simulations are combined with
26 pharmacodynamic models, then better characterization of dose-response relationships and
27 prediction of PODs (NOAEL, BMD, BMC) may become possible.
28
29 4.4. LINKAGE TO PHARMACODYNAMIC MODELS
30 The identification of PODs by simulation may become possible with the use of BBDR
31 models. These models would require the linkage of quantitative descriptions of
32 pharmacokinetics and pharmacodynamics via mechanism of action. Accordingly, the output of
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1 PBPK models is linked to the pharmacodynamic model using an equation that reflects the
2 researchers' hypothesis of how the toxic chemical participates in the initiation of cellular
3 changes leading to measurable toxic responses. For example, certain DNA adducts cause
4 mutations, cytotoxic metabolites kill individual cells, and expression of growth factors can act as
5 a direct proliferation stimulus. In each of these cases, the temporal change in the dose metric
6 simulated by the PBPK model is linked with mathematical descriptions of the process of adduct
7 formation, cytotoxicity, or proliferation in the BBDR models to simulate the quantitative
8 influence of these processes on tumor outcome.
9 Figure 4-8 presents an example of the relationship between dose metric (simulated by the
10 PBPK model) and fraction of liver cells killed (simulated by pharmacodynamic model) for
11 chloroform. In this case, the pharmacodynamic model consisted of difference equations to
12 simulate time-dependent changes in the number of hepatocytes in the liver as a function of basal
13
14
15
16
17
18
0.90
0.00 1.09 2.00 3,0Q 4,60 5,00 9.90
Liver dose surrogate (|X«K>| metabolized/g liver/60 tniii)
Figure 4-8. Relationship between the dose metric (pmol metabolized/g
liver/hr) simulated by PBPK model and the cell killing inferred from
pharmacodynamic model for chloroform.
Source: Page et al. (1997).
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1 rates of cell division and death, chloroform-induced cytolethality, and regenerative replications
2 (Conolly and Butterworth, 1995; Page et al., 1997).
3 Table 4-3 presents a list of pharmacodynamic models for cancer and noncancer
4 endpoints. A characteristic of several of these pharmacodynamic models is that they are able to
5 simulate the normal physiological processes (e.g., cell proliferation rates, hormonal cycle) and
6 additionally account for the ways in which chemicals perturbate such phenomena, leading to the
7 onset and progression of injury. The pharmacodynamic models, for linkage with PBPK models,
8 are not available for a number of toxic effects and modes of action. This situation is a result, in
9 part, of the complex nature of these models and the extensive data requirements for development
10 and evaluation of these models for various exposure and physiological conditions.
11 With the availability of integrated pharmacokinetic-pharmacodynamic models, the
12 scientific basis of the process of estimating PODs and characterizing the dose-response curve
13 will be significantly enhanced. Additionally, such a modeling framework will facilitate a
14 quantitative analysis of the impact of pharmacodynamic determinants on the toxicity outcome,
15 such that the magnitude of the pharmacodynamic component of the interspecies and intraspecies
16 factors can be characterized more confidently. Even though some PBPK models have been used
17 in RfD, RfC, and unit risk estimate derivation for a number of substances (Table 4-1), the need
18 for applying such models (where possible) should be continuously explored.
19
20
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1
2
Table 4-3. Examples of biologically based models of endpoints and processes
of toxicological relevance
Toxicity end
point or process
Cancer
Cholinesterase
inhibition
Developmental
toxicity
Estrus cycle
Gene expression
Granulopoiesis
Nephrotoxicity
Teratogenic effect
Features
Simulation of relative roles of
initiation, promotion,
cyclothality, 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
CYP1 Al/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
PCBs
Pentachlorobenzene
Saccharin
Organophophates
Methyl mercury
Endocrine-modulating
substances
TCDD
Cyclophosphamide
2,2,4-trimethyl-2-phenol
Hydroxyurea
References
Armitage and Doll (1957);
Moolgavkar and Venzon
(1 979); Moolgavkar and
Knudson (1981); Cohen and
Ellwein (1990); Moolgavkar
& Luebeck (1 990); Luebeck et
al. (1991); Chen (1993);
Conolly and Andersen (1997);
Conolly and Kimbell (1994);
Thomas et al. (2000); Conolly
et al. (2003); Tan et al. (2003)
Gearhart et al. (1990, 1994);
Timchalk et al. (2002)
Leroux et al. (1996); Faustman
etal. (1999)
Andersen et al. (1997)
Santostefano et al. (1998)
Steinbach et al. (1980)
Kohn and Melnick (1 999)
Luecke etal. (1997)
3
4
5
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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: 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 model: A predictive model that describes biological
processes at the cellular and molecular level linking the target organ dose to the adverse effect.
Cancer scope factor: 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 interactions with biologically
significant receptors in the target organ.
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
subjects (or populations), or the probability of occurrence or change in level of response within a
population.
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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.
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.
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 (i) sample each model's parameters from their prior
distributions, (ii) fit the model with the sampled parameters to several additional experimental
data sets, and (iii) 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. Pharmacokinetic
models take into account absorption, distribution, metabolism, and elimination of the
administered chemical and its metabolites.
Pharmacodynamic models: Mathematical descriptions simulating the relationship between a
biologically effective dose and the occurrence of a tissue response.
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: 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 NOAEL or LOAEL 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
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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.
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.
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/variability factors: Generally 10-fold, default factors used in operationally
deriving the RfD and RfC from experimental data. The factors are intended to account for (i)
variation in sensitivity among the members of the human population (i.e., interindividual
variability), (ii) uncertainty in extrapolating animal data to humans (i.e., interspecies
uncertainty), (iii) uncertainty in extrapolating from data obtained in a study with less-than-
lifetime exposure to lifetime exposure (i.e., extrapolating from subchronic to chronic exposure),
(iv) uncertainty in extrapolating from a LOAEL rather than from a NOAEL, and (v) 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.
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