Physiologically-Based
Pharmacokinetic/Pharmacodynamic Modeling:
Preliminary Evaluation and Case Study
for the
N-Methyl Carbamate Pesticides
November 10, 2003
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Office of Prevention, Pesticides & Toxic Substances
U.S. Environmental Protection Agency
Washington, D C. 20460
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TABLE OF CONTENTS
EXECUTIVE SUMMARY Page 1 of 50
LIST OF ABBREVIATIONS Page 2 of 50
I. BACKGROUND AND SCOPE Page 3 of 50
II. INTRODUCTION Page 5 of 50
III. CASE STUDY: N-METHYL CARBAMATE PESTICIDES Page 7 of 50
A. Cumulative risk assessment and PBPK/PD models Page 7 of 50
B. Preliminary pharmacodynamic description of acetylcholinesterase
inhibition by N-methyl carbamate pesticides Page 8 of 50
C. Preliminary pharmacokinetic description of N-methyl carbamate pesticides
Page 11 of 50
D. Computer implementation Page 16 of 50
1. Model 1: Use of Exposure Related Dose Estimating Model
(ERDEM) Page 17 of 50
2. Model 2: PBPK development using MCSim Language
Page 19 of 50
E. Types of output from by PBPK/PD models Page 21 of 50
F. Illustrative simulations and example output Page 22 of 50
1. Simulation 1 Page 22 of 50
2. Simulation 2 Page 25 of 50
3. Simulation3 Page 27 of 50
4. Simulation 4 Page 29 of 50
5. Simulation5 Page 30 of 50
6. Simulation6 Page 32 of 50
G. Experimental data needs for a PBPK/PD model for the N-methyl
carbamates Page 34 of 50
1. Types of data needed for PBPK/PD model development
Page 35 of 50
2. Uncertainty associated with availability of appropriate data
Page 40 of 50
H. Model Evaluation and Quality Control Page 40 of 50
1. Model Purpose Page 40 of 50
2. Biological Characterization and Model Structure . . Page 41 of 50
3. Mathematical Descriptions Page 41 of 50
4. Computer Implementation Page 42 of 50
5. Parameter Analysis and Quality of Model Fit Page 43 of 50
I. Model scale-up and extrapolation from rodents to humans.
Page 44 of 50
IV. SUMMARY Page 45 of 50
V. REFERENCES
Page 47 of 50
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EXECUTIVE SUMMARY
The Food Quality Protection Act of 1996 requires EPA to consider potential human
health risks from all pathways of dietary and non-dietary exposures to more than one
pesticide acting through a common mechanism of toxicity. In 2001, EPA established
the N-methyl carbamate pesticides as a common mechanism group based on their
structural characteristics and also similarity and shared ability to inhibit
acetylcholinesterase (AChE) by carbamylation of the serine hydroxyl group located in
the active site of the enzyme. EPA has not determined what method or methods will be
used to estimate cumulative risk for this common mechanism group.
EPA is in the early stages of developing a strategy for incorporating physiologically-
based pharmacokinetic/pharmacodynamic (PBPK/PD) models into its cumulative risk
assessments. PBPK/PD models are very powerful tools that can account for anatomic
structure and physiological and biochemical processes. They can be used to estimate
internal exposure dose or concentrations of parent compounds and/or active
metabolites at the target site(s) and also toxicologically relevant effects. Typically,
inhibition of AChE is fairly rapid (within hours) for members of the N-methyl carbamate
common mechanism group. The time dependant relationship between exposure and
effect for this group make the N-methyl carbamates a good case study to aid the
Agency in developing its strategy for using PBPK/PD models in cumulative risk
assessments.
The following document provides the preliminary model structure for two separate
PBPK/PD models being developed in addition to the biological basis for their structure.
These models are being developed in separate programming languages (ACSL and
MCSim). Six simulations using are provided that show types of relevant output that can
be generated by PBPK/PD models. Theses simulations include results for in silico
experiments for a single chemical at starting values; a single chemical with adjustments
to the AChE regeneration rate and gastrointestinal parameters; two exposures to a
single chemical separated by either 1 hour or 4 hours; and one exposure each to two
different chemicals 4 hours apart. Development of PBPK/PD models are resource and
data intensive. This document details types of in vivo and in vitro data that are
desirable for development and evaluation of PBPK/PD models for individual N-methyl
carbamates and also the cumulative assessment group as a whole. The critical steps
(defining the model purpose; biological characterization; mathematical description,
computer implementation, and parameter analysis and quality of model fit) in evaluating
the quality of PBPK/PD models are also discussed.
The current document is considered a research effort that is a work-in-progress; model
development is still on-going. The level of refinement afforded during the model
development and evaluation phases will be directly related to the amount of relevant
and appropriate pharmacokinetic and pharmacodynamic data available. EPA expects
further scientific review in the future as the case study develops further and as the
strategy for incorporating PBPK/PD models in cumulative risk assessments matures.
Page 1 of 50
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LIST OF ABBREVIATIONS
AChE
Acetylcholinesterase
AUC
Area under the curve
CAG
Cumulative assessment group
FIFRA
Federal Insecticide, Fungicide, and Rodenticide Act
FQPA
Food Quality Protection Act
Gl
Gastro-intestinal
LOAEL
Lowest-Observed-Adverse-Effect Level
NHEERL
National Health and Environmental Effects Laboratory
NERL
National Exposure Research Lab
NOAEL
No-Observed-Adverse-Effect Level
OP
Organophosphate pesticide
OPP
Office of Pesticide Programs
ORD
Office of Research and Development
PBPK
Physiologically-based pharmacokinetic (typically refers to
models)
PBPK/PD
Physiologically-based pharmacokinetic/pharmacodynamic
(typically
refers to models)
PD
Pharmacodynamic
PK
Pharmacokinetic
RBC
Red blood cells
SAP
Scientific Advisory Panel
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I. BACKGROUND AND SCOPE
In 1996, passage of the Food Quality Protection Act (FQPA) imposed upon the
Office of Pesticide Programs (OPP) the requirement to consider potential human health
risks from all pathways of dietary and non-dietary exposures to more than one pesticide
acting through a common mechanism of toxicity. At each step in the development of its
cumulative risk assessment guidance and methodology, OPP has solicited scientific
peer review. Specifically, the FIFRA Scientific Advisory Panel (SAP) has reviewed
OPP's Cumulative Guidance (FIFRA SAP 1999, 2000) and the many aspects of the
cumulative risk assessment for the organophosphates pesticides (OPs; see USEPA,
2002a). The Cumulative Guidance (USEPA, 2002a) describes several methods which
could be used for performing cumulative hazard assessment. Some of these include
use of effect levels from toxicology studies [e.g., no-observed-adverse-effect (NOAELs)
and/or lowest-observed-adverse-effect levels (LOAELs)]; benchmark dose modeling
(USEPA, 2000b); and also physiologically-based pharmacokinetic/pharmacodynamic
models (PBPK/PD). Each of these methods are considered reasonable approaches to
doing cumulative hazard assessment. As discussed in the Cumulative Guidance
(USEPA, 2002a), the level of refinement for each cumulative risk assessment will be
depend on several factors, included among these is the availability of adequate and
appropriate data for the particular common mechanism group of interest. The FIFRA
SAP has previously encouraged OPP to consider using PBPK models (FIFRA SAP
2001, 2002) in developing cumulative risk assessments. EPA is currently developing a
draft strategy for utilizing pharmacokinetic data in cumulative risk assessments. As part
of this draft strategy, a collaborative research effort is underway at EPA's National
Health and Environmental Effects Laboratory (NHEERL) and National Exposure
Research Lab (NERL) along with Rory Conolly of the CUT Centers for Health Research
to develop a case study using PBPK modeling for multiple pesticides with a common
mechanism of action. This case study is being developing with the N-methyl carbamate
pesticides.
In 2001, EPA established the N-methyl carbamate pesticides as a common
mechanism group based on their structural characteristics and also similarity and
shared ability to inhibit acetylcholinesterase (AChE) by carbamylation of the serine
hydroxyl group located in the active site of the enzyme (USEPA, 2001b). The N-methyl
carbamate pesticides are, therefore, subject to cumulative risk estimation under the
FQPA (1996). OPP is in the early stages of developing its cumulative risk assessment
of this common mechanism group and expects to have a preliminary cumulative risk
assessment for the relevant AChE-inhibiting members of this class to be available to the
public by spring of 2005. The AChE inhibitory effects of N-methyl carbamates is
reversible generally within hours-although the time to recovery is chemical-dependent.
The time course of effects can be very complicated for multi chemical risk assessments
when the time to effect and/or the time to recovery varies substantially among
chemicals. OPP has not yet determined the method or methods it will use to estimate
the cumulative risk to this common mechanism group. Consistent with past practice for
single chemical assessments and the principles outlined in the Cumulative Guidance,
OPP may first perform a screening level assessment to evaluate those pesticides and
exposure scenarios which may or may not be likely to contribute to the cumulative risk
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prior to development of a more refined assessment for the contributing pesticides and/or
exposure scenarios. OPP acknowledges that consideration of the pharmacokinetics
and pharmacodynamics of AChE inhibition at the target site(s) and time to recovery are
important factors in developing the preliminary cumulative risk assessment for the N-
methyl carbamate pesticides.
As discussed below, PBPK and physiological based pharmacodynamic (PBPD)
models offer great advantages in risk assessment, such as the ability to incorporate
pharmacokinetic and mechanistic information, to consider the assumptions of dose-
additivity, and to evaluate intra- and inter-species extrapolation. There are, however,
practical implications and considerations in a regulatory setting such as the availability
of appropriate data for developing and evaluating the model and also quality
assurance/quality control. The Agency is currently drafting a strategy for utilizing
pharmacokinetic data and PBPK/PD models in cumulative risk assessments. The
purpose of the current SAP review is to consider the on-going case study for N-methyl
carbamate pesticides to aid the Agency in the development of this draft strategy.
The current evaluation considers both conceptual and technical aspects of
performing cumulative risk assessment using a PBPK/PD model. The ability to directly
consider mechanistic information, such as time to recovery data, is highlighted. The
case study includes model simulations for two theoretical chemicals with toxicological
and physical-chemical properties consistent with those for N-methyl carbamate
pesticides. The current document does not consider actual exposure scenarios or
estimate cumulative risk. The PBPK/PD models described in this document are still
under development. Parameter estimation and sensitivity analysis are not discussed
here. This document also does not consider the application of uncertainty factors or the
application of the FQPA 10X Factor for infants and children. This document does,
however, consider possible ways of incorporating exposure information and considers
types of relevant information that could be output from a PBPK/PD model.
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II. INTRODUCTION
Pharmacokinetic models range from simple empirically based models that
describe observed data to more complex PBPK models that can be used to predict
outcomes and extrapolate from one set of exposure conditions to another based upon
an understanding of the underlying biology. A PBPK model is a quantitative description
(typically with differential equations) of the biological structures and processes that
control pharmacokinetic (PK) behavior in an organism (i.e, the effect of the body on the
absorption, distribution, metabolism, and excretion of a chemical). PBPK modeling
differs from classical compartmental PK modeling in this focus on the biological
determinants of PK behavior. PBPK models simulate the events between the external
dose and the internal exposure of the chemical to a target site. PBPD models address
the events from the internal dose at the target site to the response observed (i.e., the
effects of the chemical on the body), e.g., inhibition of AChE. PBPK/PD models are
used to establish a linkage between PK behavior and the toxicological or biological
effect of a chemical on the body, such as inhibition of AChE. Thus, while classical
empirical modeling is useful for interpolation between data points, a well developed
PBPK/PD model can be used to simulate toxicological outcomes for a variety of different
exposure conditions (e.g., different test species, exposure routes, chemical
concentrations, or metabolizing capacity).
PBPK/PD models have the potential to consider internal exposure concentrations
at the site(s) of action for a single chemical and its toxicologically active metabolite(s)
and/or multiple chemicals and their respective metabolites. Dose additivity is EPA's
default assumption when evaluating the joint risk of chemicals that are toxicologically
similar and act at the same target site (USEPA, 2001a). In cases where multiple
chemical species are considered in the PBPK/PD modeling, the impact of possible
additive or non-additive interactions between the different chemical species can be
described. For example, sites of biotransformation and/or binding to enzymes can be
described. Specifically, the PBPK/PD models can provide time course quantitative
outputs of concentration, amount, or changes in endogenous enzymes and thus the
models can track the PK behavior and pharmacodynamic (PD) outcome of mixtures.
Consideration of how the biology described in the model changes with age, sex,
species and/or other factors can guide development of these models. Development and
use of these models requires knowledge of organism specific and chemical specific
biologic processes. An understanding of the parameters that govern the
pharmacokinetics is also necessary. Proper development and use of these models
often requires examination of existing data, model formulation and testing leading to
more specific data requirements, which in turn leads to model refinement. These
capabilities allow PBPK/PD models to serve two somewhat different roles. First, the
models can play key roles in the laboratory study of pharmacokinetics and mechanism
of action. This role of PBPK/PD models is particularly powerful when model
development and laboratory experiment are conducted in an iterative, mutually
supportive manner. Models help identify key data which are lacking, elucidate important
events in the chain leading to toxicity, and also identify and quantify the uncertainty. For
example, PBPK/PD models may inform us about nonlinearities in high to low dose
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extrapolation and about interspecies scaling factors that would not have been apparent
without a quantitative, mechanistic perspective.
A second role of PBPK/PD models is in the development of risk assessments.
PBPK/PD models developed from an adequate supporting database that have been
tested and evaluated, and also demonstrate reasonable ability to predict the behavior of
datasets not used during model development, can be used for partial or complete
replacement of the default assumptions used in risk assessment (e.g.,inter- and intra-
species extrapolation factors or route-to-route extrapolation). EPA has previously used
PBPK models to estimate the toxicologically relevant dose for dichloromethane
(USEPA, 1995; Anderson et al, 1987) and vinyl chloride (USEPA, 2000c; Clewell et al,
1995a, b).
The capacity of PBPK/PD models to explicitly consider mechanistic data, to
estimate exposure concentrations at the site(s) of action, and to describe the
pharmacokinetic behavior of mixtures motivate EPA's interest in this type of modeling
and specifically in the development of a case study with the N-methyl carbamate
pesticides. As stated above, the Agency is developing a draft strategy for utilizing
PBPK/PD models in cumulative risk assessments. A more detailed description of this
strategy will be provided at a later date following consideration of the comments from
the SAP and further progress has been made on the case study.
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CASE STUDY: N-METHYL CARBAMATE PESTICIDES
A. Cumulative risk assessment and PBPK/PD models
Based on the risk assessment paradigm described by the National
Research Council (1983, 1994), risk is made up of exposure and hazard
components. The discrepancy between actual and predicted risk is minimized to
the extent that these two factors are well-characterized. This minimization
serves the public health by providing the soundest possible guidance for setting
exposure standards. Society as a whole is in turn well served when the
stringency of exposure standards is aligned as closely as possible with the actual
magnitude of the health risk. This alignment helps to ensure the efficient
allocation of scarce resources. In contrast, risk assessments based largely on
default assumptions, while expected to be health-protective, provide little
assurance that exposure standard stringency and the actual magnitude of the
health risk are well aligned with each other.
In the specific case of cumulative risk assessment for the N-methyl
carbamate pesticides, AChE inhibition is considered to be the toxicologically
relevant regulatory endpoint. No PBPK or PBPD models for N-methyl
carbamates have been published to date (October, 2003). Such models have
been described for several OPs that describe the inhibition of AChE (Gearhart et
al, 1990 and 1994, Timchalk et al, 2002). The OP models describe the key
anatomical, physiological, and biochemical factors that control OP
pharmacokinetics and the transport of the AChE-inhibiting chemical to AChE.
These models thus describe the PK mechanisms of OPs as well as the inhibition
and regeneration of AChE. The existence of PBPK/PD models for OPs have
facilitated the development of the preliminary model for N-methyl carbamates.
For the on-going case study, eventually, PBPK/PD models will be prepared for
individual N-methyl carbamate pesticides and then linked together to predict
AChE inhibition following exposure to multiple N-methyl carbamate pesticides.
Both time-course and dose-response behaviors for AChE inhibition can be
tracked by PBPK/PD models with arguably greater confidence than is possible
with empirical models that do not incorporate the physiological and mechanistic
detail that characterize PBPK/PD models or with default approaches which do
not consider any chemical or exposure specific data or information. When used
for risk assessment purposes, this increased confidence in model-generated
predictions compared to empirically-based and/or default-based approaches
relates to a reduction in the overall uncertainty about risk estimates. These
models thus serve the goal of moving towards more accurate prediction of risk
without any relaxation of concern for protection of the public health.
It should be recognized that PBPK/PD modeling in support of cumulative
risk assessment for N-methyl carbamates can be expected to reduce but not to
eliminate uncertainty. PBPK/PD model structures and parameter values have
associated degrees of uncertainty some of which cannot be readily eliminated. A
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key consideration in the overall evaluation of this exercise will thus be the degree
to which PBPK/PD modeling increases confidence in the final assessment
relative to the confidence that would be obtained with a less sophisticated
approach.
The present document considers preliminary work on the methods for
estimating exposure at the site(s) of action and subsequent AChE inhibition for
the N-methyl carbamate pesticides . This document does not consider relevant
environmental exposure scenarios from food, water, and/or residential and non-
occupational settings. It should, however, be noted that a well-developed
PBPK/PD model is sufficiently flexible to consider various types and
combinations of exposure and co-exposure scenarios appropriately separated in
time. These models should also be sufficiently flexible to consider discreet
exposure scenarios for a single person or distributions of exposures for many
people. OPP is still actively considering which method or methods are most
appropriate for use in estimating the cumulative risk for these pesticides. The
degree to which OPP considers results from the PBPK/PD modeling effort will
depend, in part, on the availability of appropriate PK and PD data but also on the
resources required to perform computer simulations for specific exposure
scenarios.
B. Preliminary pharmacodynamic description of acetylcholinesterase
inhibition by N-methyl carbamate pesticides
EPA established the N-methyl carbamate pesticides as a common
mechanism group based on their structural characteristics and also similarity and
shared ability to inhibit AChE by carbamylation of the serine hydroxyl group
located in the active site of the enzyme (USEPA, 2001b). This inhibition results
in accumulation of acetylcholine at a nerve synapse or neuromuscular junction.
This inhibition can result from interaction between the parent N-methyl
carbamate pesticide or AChE-inhibiting metabolites with the enzyme, AChE.
Continued accumulation of the neurotransmitter acetylcholine may result in the
overstimulation of cholinergic pathways in the central and peripheral nervous
systems and possibly to the expression of cholinergic signs and symptoms such
as nausea, gastrointestinal distress, vomiting, tremors, paralysis and depression
of respiratory function.
Generally, AChE-inhibiting chemicals compete with the acetylcholine for
binding to the enzyme (AChE). As more AChE-inhibiting chemical binds with the
enzyme, the acetylcholine is subject to slower or less hydrolysis and its activity
is prolonged. The following outlines the basic process of AChE-inhibition for a
single N-methyl carbamate pesticide.
1. There is a certain amount of AChE in each tissue and a certain amount is
synthesized to keep this level at a near physiological steady-state (Ks).
This is a basic physiological process independent of any foreign chemicals
entering the system.
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2. A certain amount of enzyme is degraded (Kd). This also reduces the
amount of free enzyme available to perform its normal physiological
function. When no inhibitor is present this degradation process is
balanced by the synthesis described above. However in the presence of
inhibitor the formation of the complex can be thought of as another stress
that reduces the amount of enzyme available for normal physiological
function. This reduces the activity of the enzyme on its normal
physiological substrate, acetylcholine at the neurologic site.
3. Inhibitors, such as the N-methyl carbamates, enter the system and reduce
the amount of free enzyme by forming a complex with the enzyme. The
enzyme that is complexed with the AChE-inhibiting chemical is no longer
available to perform its normal physiological activity leading to the build up
of acetylcholine. (Each N-methyl carbamate pesticide has a unique rate
constant for the formation of the complex with the enzyme, K().
4. The enzyme-inhibitor complex in turn reacts to result in a break down of
the AChE-inhibiting chemical and a return or regeneration of free enzyme.
This process is also governed by a chemical specific rate constant, Kr The
period of inhibition varies for different compounds and is generally
dependent upon the rate of regeneration. Because the period of inhibition
is often brief (due to rapid regeneration) the whole process has been
dubbed as 'reversible'.
Figure 1 summarizes this process. The "released metabolite" in Figure 1
represents the N-methyl carbamate that is broken down. Note that each
carbamate has its own specific rate constants for the process. Any number of N-
methyl carbamates can interact at same time or at any time with the free AChE.
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Figure 1. Schematic diagram of N-methyl carbamates binding to AChE.
Where:
Acex is the amount of AChE (|Jmol) in compartment x
INcexj is the amount (|Jmol) complex of AChE and inhibitor j in compartment x
Ks is zero-order rate of enzyme synthesis
Kd is the first-order rate of enzyme degradation (hr1)
Kjj is the bimolecular rate of inhibition for f inhibitor
Kq is the first-order rate of regeneration for f complex
Carbamate N is AChE active chemical, parent compound or metabolite
Released metabolite is a Non-AChE active metabolite
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The following differential equations represent the mass balance for the
Figure 1.
Equationi dAce^ =
dt
/ \
^/ + lA-//xC/:v + ^KjjxINce
\ J /
Equation 2 dJNcexj = A xK C _K xINce
dt x lj JX rj J
Where:
Acex is the amount of AChE (|Jmol) in compartment x
INcexj is the amount (|Jmol) complex of AChE and inhibitor j in compartment x
Ks is zero-order rate of enzyme synthesis
Kd is the first-order rate of enzyme degradation (hr1)
K,j is the bimolecular rate of inhibition for f inhibitor
K,j is the first-order rate of regeneration for f complex
subscript x indicates tissue compartment,
subscript j indicates the identity of the inhibiting chemical
Thus, the total amount of active enzyme is equal to the amount present in
the system minus the amount degraded minus the amount forming a complex
with the inhibitor plus the amount regenerated after the enzyme breaks down or
metabolizes the inhibitor.
Cumulative risk assessments consider risk from multiple pesticides.
Therefore, the PD component of the PBPK/PD model needs to include the
capacity to consider potential mixture effects. More than one compound can act
in combination at any of the steps outlined above. The simplest interaction would
be simply adding the inhibition caused by each compound. In such cases,
depending, upon the specific rate constants, different chemical molecules would
each contribute to enzyme inhibition. It might be possible however that
interaction would involve competition between the various chemicals for binding
with the enzyme. If data suggest that interactions between the N-methyl
carbamates other than dose-additive ones are observed, these can and will be
included in the modeling efforts.
C. Preliminary pharmacokinetic description of N-methyl carbamate
pesticides
As described in previous sections, PBPK models describe the disposition
of the foreign chemical throughout the body and within the tissues. For purposes
of this assessment the N-methyl carbamates are modeled as being
predominately metabolized in the liver with secondary metabolic sites in the
kidney and brain compartments.
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Parameters for PBPK models include three distinct types of data:
physiological, chemical-specific, and parameters for determining the stochastic
behavior of model. The physiological data are independent of the chemical being
modeled and refer to such things as organ volumes and blood flows. Some
chemical-specific parameters are partition coefficients, metabolic rate constants,
and coefficients for protein binding. Parameters for determining the stochastic
behavior of model, such as inter-individual variances, are discussed below in
Sections III.G and III.H.
The specific compartments considered in the modeling are selected based
on information available for exposure, toxicology, and metabolic profile to a
particular chemical and potential active metabolites. Distribution within, between
and among organs, tissues, and fluid is modeled according to compartmental
volumes, blood flow rates, and blood tissue partitioning. The body volume is
determined for each animal species, based on sex and age. The compartment
volumes are then calculated as a percentage of the body volume. Generally,
each model has equations to explicitly describe the arterial and venous blood, the
lung, the liver, and kidney. Other organs are lumped together within two
compartments referred to as rapidly and slowly perfused tissues. Organs of
toxicological interest such as neurologic organs are also included as explicit
organs (explicit means that the organ has its own equations and is not included
in one of the lumped compartments). All of the flows of the compartments
(organs) must add up to 100% of the cardiac output. Table 1 provides selected
organs and necessary governing parameters for the N-methyl carbamate model.
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Table 1. Selected organs and parameters relevant for PBPK modeling for the N-methyl
carbamate pesticides
Organs
Parameters
Arterial and Venous Blood
cardiac output, arterial blood volume, venous
blood volume, binding constants; cholinesterase
levels, rate constants for interaction with
cholinesterase
Liver
liver volume, tissue to blood partition coefficients
for all chemicals (parents and metabolites)
metabolism rate constants; cholinesterase levels,
rate constants for interaction with cholinesterase
Stomach and intestine
absorption parameters
Kidney
kidney volume, tissue to blood partition
coefficients for all chemicals (parents and
metabolites) metabolism rate constants
Brain
brain volume, tissue to blood partition coefficients
for all chemicals (parents and metabolites)
metabolism rate constants; cholinesterase levels,
rate constants for interaction with cholinesterase
Rapidly and Slowly perfused tissues
organ volume, tissue to blood partition coefficients
for all chemicals (parents and metabolites)
Lung
respiratory rate, tissue to blood partition
coefficients for all chemicals (parents and
metabolites) and where appropriate, blood to air
partition coefficients
Appropriate tissues
Equilibrium binding constants for binding to
proteins, etc.
Absorption involves entry of a drug or chemical into the body. A chemical
may enter directly into the gastro-intestinal (Gl) tract via gastric gavage, from
ingestion of food, or from "non-dietary" ingestion. The basic Gl model has a
stomach and intestine that are simulated with rate and bolus ingestion into the
stomach, flow from the stomach to the intestine and from the intestine to
intestinal elimination. In addition there is flow from the stomach and the intestine
to the liver via portal blood. There is no bile flow from the liver to the intestine
and no lymph flow or pool. Systemic arterial blood and portal venous blood are
input into the liver. Mathematical expressions used to describe absorption into
the Gl tract are presented in Equation 3.
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The stomach has the jth chemical input by bolus ingestion (a plug of food
or drink) and rate ingestion (food or drink input over time), with chemical output to
the liver via portal blood and to the intestine. The equation for the rate of change
of the jth chemical in the stomach is:
Equation 3 dAsTj dA'BiaJ dARI°j „ A _K A
dt dt dt ABS,ST,PBj^STj ST,1Nj STj '
Where:
Ag, is the amount of chemical in the stomach
ABig is the amount of chemical resulting from a bolus ingestion
Arig is the amount of chemical resulting from a "rate" ingestion (gradual over time rather than a bolus)
Kabs st.pB's the rate constant for absorption from the stomach into the portal blood
K., in is the rate constant for transfer from stomach to intestine
The rate of change of the jth chemical in the intestine is given by the rate
of input from the stomach to the intestine and the rate of output to the liver via
portal blood, and to the feces. The equation is:
Equation 4 dAIN
- K A - K A - K A
STJNj STj ABSJN.PBj ^IN} ^IN.FECj ^IN}
Where:
Ag,, Kg, in are as previously defined
Ain is the amount of chemical in the intestine
Kabs,in pb's the rate constant for absorption from the intestine into the portal blood
Kin FEC is the rate constant for fecal elimination
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The most commonly used PBPK models assume each organ to be
homogenous and thus the fluid contained in the vascular, interstitial or
extracellular, and the intracellular regions are all combined into one. This implies
that the transfer of a chemical across the membrane, i.e., capillary wall and cell
membrane, is very rapid compared to the tissue perfusion rate. Under this
condition, the permeability across the membrane is assumed to be very large.
Therefore, the slowest or rate-limiting step in the process of drug distribution
must be its delivery by the circulatory flow. The typical mass balance differential
equation describing this is:
Equation 5
dAj j/dt = V, dCj /dt = (Q,(CJia - Cj vi) - dMj/dt)
where:
Aj | is the amount of the jth chemical in the ith organ
Cjj is the concentration of jth chemical in the ith organ
t is time
Q, is the arterial blood flow to the ith organ
Cj a is the concentration of jth chemical in the arterial blood
Cj vi is the concentration of the jth chemical in the venous blood leaving the ith organ
dMj /dt is the rate of metabolism of the jth chemical in the ith organ
V, is the volume of the ith organ
Essentially, this equation describes the transport and metabolic transformation of
the chemical into and within the tissue. Under the assumptions of a well-stirred
compartment, the instantaneous concentration of a substance in a tissue or
organ is the difference between the concentration entering the organ and that
leaving the organ adjusted by any metabolic processes also eliminating the
chemical.
Under the assumed conditions that the organ is homogenous or well-
stirred the venous blood leaving the organ is in equilibrium with the organ as
described by:
Equation 6
Cj,/Cj,vi = Rjj
Rj i is referred to as the tissue to blood partition coefficient. This value,
determined from a variety of computational and laboratory methods, is governed
by a number of thermodynamic properties of the chemical and the tissue of the
organ. In the simplest cases it represents a ratio of solubilities of the chemical in
the tissue to blood. The above equation then is transformed to:
Page 15 of 50
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Equation 7
dAjj/dt = Vj dCj /dt = (Q^C^ - q/R^) - dl\ydt)
The integral of the above equation results in the concentration at time, t.
The expression for metabolism can take any number of forms including
Michaelis-Menten, first order, or second order. For the case of the N-methyl
carbamates Michaelis-Menten and first order kinetics are employed for the
various metabolic processes. Equations such as the ones above are also written
and employed for each of the metabolites of the jth chemical. Further, in the
appropriate tissues, the equation also include the metabolic terms to account for
the transformation of the chemical caused by the cholinesterases (this has been
described in previous sections).
The liver is described with similar equations with terms that account for
absorption from the stomach and intestine as described previously. Other
organs such as the skin and lung also have input terms as appropriate.
For purposes of the N-methyl carbamate pesticides, the model must
represent multiple chemicals in some combination and even with simultaneous
exposure. The power of PBPK/PD models is in the ability to use it to represent
the biologic and physical process that go on within the body. Because the model
mathematically describes the physical, chemical, and physiological processes it
can be configured to account for the affect of multiple chemical exposure.
D. Computer implementation
The general modeling strategy described above will be implemented in
two separate modeling efforts, implemented in different languages. This activity
provides a quality control check on the modeling software and the coding of the
model, in that outputs of the two models given the same input should be similar.
Divergence of the two model outputs would indicate improper coding in at least
one of the models. Since two languages are being used that differ in syntax and
how the model code is structured, it is unlikely that a coding error would be made
similar enough in both programs that it would go undetected (i.e., both program
outputs would be the same). Moreover, the capabilities of the two modeling
languages differ, and there are features unique to each program that add to the
overall ability to develop and test the model.
The descriptions of the two models follows:
Page 16 of 50
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1. Model 1: Use of Exposure Related Dose Estimating Model
(ERDEM)
EPA's NERL has developed the Exposure Related Dose Estimating Model
(ERDEM) as a platform for the application of PBPK and PBPK/PD models.
The heart of ERDEM (USEPA, 2002c) is a PBPK model that simulates the
absorption, distribution, metabolism, and elimination of chemicals in
mammalian systems.
Simulated chemicals are introduced into the physiological system by any
of several routes including injection, ingestion, inhalation, and/or dermal
absorption. The ERDEM system is contains a large set of potential
compartments and processes, with over 30 physiological compartments
such as arterial and venous blood, brain, skin (surface and dermis), fat,
intestine, kidney, liver, rapidly and slowly perfused tissues, lung, stomach,
and intestine. Any given model is derived by selecting those
compartments and processes that are most applicable to the kinetics of
the chemical(s) and endpoint of interest. Figure 2 is a diagrammatic
depiction of the pharmacokinetic model that was developed for the N-
methyl carbamates.
ERDEM is programmed in the Advanced Continuous Simulation Language
(ACSL). Model specific parameter values are entered into ERDEM based
upon the physiological, biological, and biochemical modeling data specific
to the chemical and/or scenario of interest (USEPA, 2002c). Any PBPK
model, including ERDEM, is made up of a series of the differential
equations which describe the rates of inflow, distribution, metabolism, or
outflow of a chemical and various metabolites in each separate biological
compartment. For the application of cholinesterase inhibiting compounds
such as the N-methylcarbamates, ERDEM has been expanded to include
a PD component. This PD component is designed to describe the effect
of these compounds on the cholinesterase enzymes as described in the
previous section.
ERDEM consists of the following: An ACSL-based model engine and a
Power Builder Front End. Both of these components will be made
available to the public as executables from EPA's Office of Research and
Development (ORD)-NERL. However at present time the front end has
not been updated to include simulations for AChE-inhibiting chemicals. An
executable ACSL command file that includes the AChE inhibition
component can be provided to interested individuals or groups by EPA's
ORD-NERL. The user is advised to run the model using ACSL command
files rather than a front end. No special software is required by the user.
An ACSL software license is only needed to recompile the code and
cannot be provided by EPA. However ERDEM should require no
additional recompilation of code to run the model as described in the
document.
Page 17 of 50
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Inputs
Bolus Dose
Ingestions
Rate
Ingestions
Intraperitoneal
Injection
Intramuscular
injection
Skin Surface Water
Bolus Dose
Injections
Infusions
ST
Kst.in
Stomach
_ Liver Metabolites are modeled with binding,
elimination, and metabolism.
^¦Carcass Metabolites
¦— >Kidney Metabolites
< Kidney
Eliminatii
Elimination J
>Fat Metabolites
There are up to K metabolites
of each of the N chemicals. Each
metabolite is one of the
N chemicals. There is binding in
the Arterial Blood and Venous Blood.
Slowly
>Perfused
Tissue
Metabolites
Rapidly Perfused
Tissue Metabolites
Brain
^ Metabolites
Open Chamber
Exhalation
Open Chamber
Inhalation
>
I
CC Closed
PU Static Lung
Chamber Inhalation
QB
- AB Arterial
3
Lung Metabolites
Figure 2. Schematic diagram of PBPK model for N chemicals in ERDEM.
Page 18 of 50
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2. Model 2: PBPK development using MCSim Language
A second model is being developed in the MCSim language. Figure 3
shows a schematic of part of that model, for a single N-methyl carbamate
that has two active metabolites. MCSim is an open-source statistical
modeling package initially developed by Frederick Bois for the application
of modern Monte Carlo statistical methods in complex nonlinear models.
Since MCSim includes a sublanguage for describing dynamic models in
terms of their component differential equations and typical time-varying
inputs, it has been particularly valuable in the application of Markov chain
Monte Carlo (MCMC) methods to estimating Bayesian posterior
distributions for parameters of PBPK/PD models.
Dynamic models in MCSim are written in an algebraic language. Model
specification includes predefining all the parameters for the model,
declaring all the variables whose dynamics are governed by differential
equations, declaring all the variables whose values need to be output,
specifying input variables whose values will be determined by special
functions that provide for periodic or episodic inputs, as well as the
differential equations for the model. This model specification file is
translated by the MCSim software into the C programming language, and
then compiled and linked to libraries that provide routines for integrating
the differential equation system, carrying out the required Monte Carlo
simulations (USEPA, 1996 and 1997), and doing the input and output
functions. The resulting executable file is then run with specially formatted
input files that can change parameter values and specify the nature of the
desired simulation, whether it is a numerical integration of the differential
equation system, a Monte Carlo simulation of parameter variability or
uncertainty, or a MCMC estimate of Bayesian posterior distributions for
model parameters.
MCSim models are portable at several levels. At the lowest level, since
MCSim itself is open-source, unlike ACSL, and since open source c-
language compilers are available for almost all computing platforms (e.g.,
UNIX, Microsoft Windows, and Apple OS-X), models can be distributed as
model source, and recompiled and run with little additional cost on the part
of reviewers. Compiled models are also executable files, and can be run
without any additional software (though the executables are specific to
particular operating systems and computing hardware). Thus, the
compiled models can be distributed and their behavior evaluated without
the installation of additional software.
At the present time, the MCSim is still under development. As the case
study for the N-methyl carbamates is developed further, the computer
code will be provided to the public at a later date.
Page 19 of 50
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Hydrolysis
Hydrolysis
Hydrolysis
FAT
SLOW
RAPID
LIVER
GI2
\
Gl 1
SKIN
FAT
SLOW
RAPID
LIVER
Metabolite 1
SKIN
FAT
SLOW
RAPID
LIVER
Conjugation
Metabolite 2
Conjugation
,/
Oxidative
Clearance
Oral/
Exposure
Parent
Figure 3. Schematic diagram of PBPK model for a single N-methyl carbamate with two
active metabolites in MCSim, (Red coded compartments contain terms for AChE
inhibition.)
Page 20 of 50
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E. Types of output from by PBPK/PD models
As described above PBPK/PD models are very powerful tools that can
help account for anatomic structure and physiological and biochemical
processes. They can be used to evaluate the disposition of the chemicals and
their metabolite in the body and any relevant PD outcome(s). The types and
formats of the output from PBPK/PD models can vary and should be related and
defined by the purpose of the model. Below provides a list of possible output that
may be relevant to examining the N-methyl carbamate pesticides. Each of the
different examples provide information about single or multiple pesticide
exposure and relate to examining PD issues of AChE inhibition or the estimated
exposure dose or concentration at the target site(s). This list is not meant to be
exhaustive but rather provide examples of possible outputs.
1. Area under the curve (AUC) for AChE inhibition which equals or exceeds a
particular level. Following exposure to one or more N-methyl carbamates,
the AUC can be calculated for AChE inhibition that exceeds a pre-
determined level, 10% AChE for example.
2. Duration for AChE inhibition which equals or exceeds a particular level.
Following exposure to one or more N-methyl carbamates, the duration for
AChE inhibition that exceeds a pre-determined level, 10% AChE for
example, can be estimated.
3. AUC for AChE inhibition over a pre-determined duration of time, such as 1
hour, 4 hours, or 24 hours.
4. Peak level of AChE inhibition, particularly in red blood cell (RBC) or brain.
5. AUC for concentration(s) of active AChE-inhibiting chemicals can be
calculated.
6. Peak concentration(s) of active AChE-inhibiting chemicals can be
estimated in the target tissue(s).
7. Time to % peak concentration(s) of active AChE-inhibiting chemicals can
be estimated in the target tissue(s).
Some of these example outputs are shown in the simulations below.
Page 21 of 50
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F. Illustrative simulations and example output
Previous sections of this document have provided the biological basis and
general structure of the PBPK models under development for the N-methyl
carbamate pesticides. The following discussion describes simulations under six
different example conditions which illustrate the PBPK/PD modeling approach
and its usefulness. The first three simulations consider exposure to a single
chemical at a 'starting' set of parameters followed by changes in AChE
regeneration rate and Gl absorption. Simulations 4 and 5 consider the impact of
time to recovery and time of exposure on AChE for two exposures to a single
chemical. Simulation 6 considers single exposure to two different chemicals. All
the simulations presented here were performed using ERDEM as previously
described. The two chemicals described below have toxicological and physical-
chemical properties consistent with one or more N-methyl carbamate pesticides.
However, Chemical-1 and Chemical-2 do not represent actual pesticide
chemicals and are used here only for illustrative purposes. Similarly the
exposures simulated below do not represent actual or real exposure levels. The
exposure amounts were selected arbitrarily for purposes of illustration only.
1. Simulation 1: Single oral gavage exposure to Chemical-1 at
starting parameter values
Results from Simulation 1 are shown in Table 2 and Figures 4 and
5. In this simulation, Chemical-1 was administered in silico at 10 mg/kg
via gavage to male rats.
Table 2. Example outputs for Chemical-1 in the brain and venous blood following oral 10
mg/kg exposure by gavage*
Example Outputs
Brain
Venous Blood
Peak Inhibition (%)
36.02
32.58
AUC at 1 Hr/24 Hr (mg-Hr/L)
19.1/34.8
2.1/3.5
Duration of Inhibition above 10%
(Hours)
5.25
4.85
Peak Concentration (mg/L)
34.05
6.39
Time to 1/2 of Peak Concentration
(Hours)
0.3
0.15
*The original values are kr=0.6, Stomach to Portal Blood Rate= 13.65, Stomach to
Intestine Rate=2.18, and Intestine to Portal Blood Rate=0.044; Male Sprague-Dawley
rats, mean body weight 284g.
Page 22 of 50
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Figure 4. Comparison of simulation results for brain AChE inhibition in Chemical-1
using starting parameter values with actual experimental data for a N-methyl carbamate
pesticide.
40-,
m
0
0
E
>s
N
"O
0
0
O
0
CL
35-
30-
25-
LU 20-
15-
10-
5-
0-
- Simulated
Experimental
-5-
-r~
10
-r-
20
-r-
30
-r~
40
-r-
60
50
Time (Hours)
Page 23 of 50
-------
Figure 5. Comparison of simulation output for exposure concentrations of the
Chemical-1 with starting parameter values in the venous blood and brain.
35-
30-
O)
E,
£=
O
£=
O
£=
O
O
25-
20-
15-
10-
- Brain
Venous Blood
5-
o-
-r~
10
-r~
20
-r~
30
-r~
40
-r~
50
-r~
60
Time (Hours)
Page 24 of 50
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2. Simulation 2: Single oral gavage exposure to Chemical-1
reduction in AChE regeneration rate
The impact of reducing enzyme inhibition regeneration rate from
0.6 /hr to 0.3 /hr was tested in silico while maintaining the same Gl
absorption conditions (Table 3 and Figure 6). Compared to Table 2, the
results of Simulation 2 show that reducing the regeneration resulted in an
increase in peak inhibition and increase in duration of AChE inhibition over
10%. It should be noted, that peak exposure concentrations in brain and
venous blood remained unchanged. Relative to the starting values, peak
inhibition, although greater, is reached less rapidly and the decline in
inhibition is evidently more protracted.
Table 3. Example outputs for Chemical-1 in the brain and venous blood following oral
10mg/kg exposure by gavage with lower AChE regeneration rate*
Example Outputs
Brain
Venous Blood
Peak Inhibition (%)
43.43
39.27
AUC at 1 Hr/24 Hr (mg-Hr/L)
19.1/34.8
2.1/3.5
Duration of Inhibition above 10% (Hr)
8.65
8.15
Peak Concentration (mg/L)
34.05
6.39
Time to 1/2 of Peak Concentration (Hr)
0.3
0.15
Gl Absorption, Dose = 2.837
Amount (mg)
Time to 99.9% (Hr)
Total from Stomach to Portal Blood
2.45
0.45
Total from Intestine to Portal Blood
0.36**
>60.0
*The regeneration rate is kr=0.3. The original Gl values are St
omach to Portal Blood
Rate=13.65, Stomach to Intestine Rate=2.18, and Intestine to Portal Blood Rate=0.044;
Male Sprague-Dawley rats, mean body weight 284 g.
**0.03 mg remained unabsorbed in the intestine after 60 hours.
Page 25 of 50
-------
Figure 6. Comparison of simulation results for brain AChE inhibition in Chemical-1
using a lower AChE regeneration rate with actual experimental data.
Page 26 of 50
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3. Simulation 3: Single oral gavage exposure to Chemical-1
reduction in Gl absorption parameters
In Simulation 3, changes were made to the previously used Gl
absorption rates (Table 4 and Figure 7). These modifications included
decreases to the stomach to portal blood rate from 13.65 to 4.55 and the
stomach to intestine rate from 2.18 to 0.218, and an increase in the
intestine to portal blood rate from 0.044 to 0.10. Realistically, these
values for these parameters values will be dependent on the vehicle used
to deliver the gavage dose, the physicochemical properties of the
chemical of interest and dietary conditions during dosing.
Under these modified absorption conditions, peak inhibition in brain
(30.72%) and venous blood (27.39%) was reduced when compared with
prior absorption and AChE regeneration rate conditions (Table 2) and
under modified AChE regeneration rate conditions (Table 3).
Table 4: Example outputs for Chemical-1 in the brain and venous blood following oral
10mg/kg exposure by gavage reduced Gl values and modified
regeneration rate.*
Example Outputs
Brain
Venous Blood
Peak Inhibition (%)
30.72
27.39
AUC at 1 Hr/24 Hr (mg-Hr/L)
11.50/23.1
1.28/2.32
Duration of Inhibition above 10% (Hr)
7.65
7.05
Peak Concentration (mg/L)
18.7
2.9
Time to 1/2 of Peak Concentration (Hr)
0.45
0.2
Gl Absorption Dose=2.837 mg
Amount (mg)
Time to 99.9% (Hr)
Total from Stomach to Portal Blood
1.92
0.7
Total from Intestine to Portal Blood
0.92**
46
*The regeneration rate is kr=0.3. The modified Gl values are Stomach to Portal Blood
Rate=4.55, Stomach to Intestine Rate=0.218, and Intestine to Portal Blood Rate=0.1;
Male Sprague-Dawley rats, mean body weight 284 g.
**There was 0.023 mg still unabsorbed in the intestine after 60 hours.
Page 27 of 50
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Figure 7. Comparison of simulation results for blood AChE inhibition in Chemical-1
using a lower AChE regeneration rate and reduced Gl parameter values with actual
experimental data.
Page 28 of 50
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4. Simulation 4 : Two oral gavage exposures to Chemical-1
administered 1 hour apart
Real world exposure conditions are very complicated-from different
chemicals, routes, and media. PBPK/PD models as described here can
simulate complicated exposure profiles. For Simulation 4, two 10 mg/kg
oral gavage exposures were administered in silico one hour apart (Table
5; first value in each case is the value for only one exposure with second
value being the value resulting from two exposures):
Table 5. Example outputs for Chemical-1 in the brain and venous blood following oral
(gavage) 10 mg/kg exposures at zero hour and
one hour
Example Outputs
Brain
Venous Blood
Single/DuaMhr
Single/DuaMhr
Peak Inhibition (%)
36.02/56.26
32.58/52.74
AUC at 1 Hr/24 Hr (mg-Hr/L)
(top/bottom)
19.1/34.8
19.1/77.1
2.1/3.5
2.1/7.8
Duration of Inhibition above 10% (Hours)
5.25/7.4
4.85/7.05
Peak Concentration (mg/L)
34.05
2nd Peak 44.44
6.39
2nd Peak 7.44
Time to 1/2 of Peak Concentration (Hours)
0.3
2nd Peak 0.5
0.15
2nd Peak 0.2
The results in Table 5 show that when the second exposure is at
one hour after the first one, the peak inhibition is increased by a little over
50%, The AUC at 24 hr is more than doubled, the duration of the inhibition
is above 10% for about 40% longer and the peak concentration is
increased by 20-25 % with the second exposure.
Page 29 of 50
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5. Simulation 5 : Two oral gavage exposures to Chemical-1
administered 4 hours apart
Table 6 shows the modeled results if the dual exposures to
Chemical-1 are simulated to be within four hours of one another. For this
case the peak percent inhibition and concentrations are lower because
(and more similar to those resulting from just one exposure) the chemical
has been mostly cleared by the time the second exposure occurs. The
duration of inhibition above 10% is increased by about two hours and the
AUC at 24 hour is still close to the higher value recorded for the one hour
difference in exposures.
Table 6. Example outputs for Chemical-1 in the brain and venous blood following oral
(gavage) 10 mg/kg exposures at zero hour and four hours
Example Outputs
Brain
Venous Blood
Single/Dual-4hr
Single/Dual-4hr
Peak Inhibition (%)
36.02/43.13
32.58/39.87
AUC at 1 Hr/24 Hr (mg-Hr/L)
(top/bottom)
19.1/34.8
19.1/70.6
2.1/3.5
2.1/7.1
Duration of Inhibition above 10% (Hr)
5.25/9.55
4.85/9.15
Peak Concentration (mg/L)
34.05
2nd Peak 35.8
6.39
2nd Peak 6.58
Time to 1/2 of Peak Concentration (Hr)
0.3
2nd Peak 0.35
0.15
2nd Peak 0.15
Page 30 of 50
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Figure 8. Simulation results for brain AChE inhibition in Chemical-1 where in silico
exposures occurred at hour 0 and 4. (Points represent actual experiment data from a N-
methyl carbamate exposed only at hour 0).
50-,
>-
N
C
LD
T3
0)
C
0)
o
fc
CL
40-
30-
20-
10-
0-
Dual Exposure Simulation, 0 and 4 Hours
Experimental Data for Exposure at 0 Hours
10 20 30 40
Time (Hours)
50
60
Page 31 of 50
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6. Simulation 6 : One oral gavage exposures to Chemical-1 and
one oral gavage exposure to Chemical-2 4 hours apart
Simulation 6 illustrates the use of the model to examine the impact
of exposure to two chemicals. Here the exposure to two different N-methyl
carbamates was simulated within four hours of each other. The second
chemical was set to have slower elimination in the liver by metabolic
clearance. The maximum rate for this reaction was set to be 1/10th of the
rate for the first chemical. Table 7 shows a summary of the results:
Table 7. Example outputs for Chemical-1 and Chemical-2, exposed at time zero, and a
similar chemical, 1/10th of the Vmax, exposed at four hours, in the brain and venous
blood
Example Outputs
Brain
Venous Blood
Peak Inhibition (%)
36.02
2nd Peak 54.79
32.58
2nd Peak 50.80
AUC at 1 Hr/24 Hr (mg-Hr/L),Chem 1
AUC at 5 Hr/28 Hr (mg-Hr/L),Chem 2
19.1/34.8
27.78/223.5
2.1/3.5
3.21/22.50
Duration of Inhibition above 10% (Hr)
25.6
24.75
Peak Concentration (mg/L)
34.05
2nd Chem Peak
40.2
6.39
2nd Chem Peak 7.07
Time to 1/2 of Peak Concentration (Hr)
0.3
2nd Chem 1.25
0.15
2nd Chem 0.2
As shown in Table 7, the peak inhibition increases by 50% following
exposure to Chemical-2. The duration increases by a factor of almost
three compared to a single chemical exposure (Table 2). The AUC 24
hours after the exposure increased by more than a factor of 6 from
Chemical 1 to Chemical 2. Thus the critical factors with the chemical with
the lower Vmax is the longer duration of inhibition above 10% and the
significant increase in the AUC 24 hours after the exposure. Figure 9
shows the results on inhibition in the brain.
Page 32 of 50
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Figure 9. Simulation results for brain AChE inhibition where in silico exposure to
Chemical-1 occurred at hour 0 and in silico exposure to Chemical-2 occurred at hour 4.
(Points represent actual experiment data from a N-methyl carbamate exposed only at
hour 0).
CD
E
>*
N
C
LU
¦o
CD
CD
O
i_
CD
CL
60-,
50-
40-
30-
20-
10-
0-
hemical 2 Exposure at 4 Hours
Dual Inhibiting Chemical Exposure Simulation
Experimental Data for Exposure at 0 Hours
;hemica\1 Exposure at 1 Hour
10 20 30 40
Time (Hours)
50
60
Page 33 of 50
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The illustrations that have been shown here demonstrate how the
model can be used to estimate dose under a variety of conditions.
Different exposure scenarios and different biochemical and physiologic
conditions can all be tested. Conventional approaches do not afford the
advantages of testing these various scenarios. Further the model can be
used to test the importance of various governing factors (physiological,
biochemical, thermodynamic, exposure inputs) on the ultimate relevant
dose in the tissue. With the model the internal dose proximate to the
impacted organ can be estimated. Models based on sound and rational
science and which are well tested are very valuable and powerful tools for
elucidating the impact of many factors upon the toxicologically relevant
dose.
G. Experimental data needs for a PBPK/PD model for the N-methyl
carbamates
Typical toxicology data collected for purposes of pesticide registration
(40CFR part 158) do not include the appropriate metabolism and PK data needed
to support a PBPK/PD model. Generally, metabolism studies submitted for
pesticide registration include a metabolic pathway describing the parent chemical,
major metabolites, and excretion products. However, these studies do not
measure concentrations of parent compound and/or active metabolites in target
tissue or blood but instead generally report total radioactivity in various tissues.
Typical toxicology databases submitted for pesticide registration also do not
include PD studies such as time to peak effect or time to recovery. With the
exception of some time to recovery AChe data for a few N-methyl carbamates,
there is very little appropriate metabolism or toxicology data available from
pesticide registration databases for developing PBPK/PD models. EPA is actively
searching the scientific literature for data and information relevant to the PBPK/PD
modeling case study.
Development of PBPK/PD models is most efficient when the model
developer and laboratory scientist work collaboratively and iteratively together. By
first developing a preliminary model using the best available information, the
modeler can communicate research needs to laboratory scientists very early in
the model development process. Laboratory experiments can then be designed
to directly address to the data needs. Following consultation with EPA laboratory
scientists, consideration of available metabolism and mechanistic data, and
consideration of the existing PBPK/PD models for several AChE-inhibiting OPs
(Gearhart et al., 1990; Gearhart et al., 1994; Timchalk et al., 2002), it has been
possible to develop preliminary models before conducting laboratory studies. The
structures for the two models under development were provided in Figures 2 and
3. It is also notable that because of the data intensive nature of PBPK/PD
models, for purposes of cumulative risk assessment, it is prudent to concentrate
resources and efforts on those pesticides and exposure scenarios that are
expected to contribute to the cumulative risk for a particular common mechanism
group.
Page 34 of 50
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The types of data described below include both in vivo and in vitro
experiments. For some types of information such as partition coefficients, where
extrapolation from in vitro to the whole animal is not expected to significantly
impact model uncertainty, the use of in vitro techniques offer an opportunity to
conserve resources and to complement more resource intensive in vivo
experiments.
The law of parsimony encourages development of the simplest model that
is powerful enough to accurately predict the biological or toxicological effect of
interest. Models with structures that are more complicated than necessary are
difficult to interpret, tend to be over-parameterized which leads to problems with
parameter identifiability, and may suggest more supporting experimental work
than is really needed. The following is a discussion of what is considered to be
the minimum information necessary to develop PBPK/PD models for individual N-
methyl carbamates. In order to establish a linkage between PK with the AChE
inhibition and subsequent recovery, it is suggested that measurements of AChE in
RBC and brain are also performed with the in vivo PK studies described below.
Additional information related to interindividual variability is also discussed below.
The main focus of the following discussion, particularly the in vivo experiments, is
on development of PBPK/PD models for rodents. The issue of scale-up and
extrapolation of the rodent model to humans is considered separately (Section
III.I).
1. Types of data needed for PBPK/PD model development
~ Chemicals of interest. The PBPK/PD models for individual N-methyl
carbamates will be developed to track parent compounds and any
metabolites capable of AChE inhibition. There will be no need to
explicitly track inactive species and, in the interests of model
parsimony, it is preferable not to do so.
~ In vivo AChE inhibition. Describing the linkage between PK and
AChE inhibition, is an critical aspect of the PBPK/PD modeling
effort. Measurements of AChE inhibition, particularly RBC and
brain, during the in vivo PK studies discussed below could be used
to establish this linkage. Because of the rapid recovery of the N-
methyl carbamates, the method used to measure AChE is an
important consideration. It is suggested that in vivo measurements
of AChE are performed using a technique, such as the radiometric
method (Johnson and Russell, 1975; Hunter and Padilla, 1999;
Winteringham and Fowler, 1966), that is not impacted by the rapid
reversibility of the N-methyl carbamates.
~ In vitro kinetics of AChE binding. The reaction of an AChE-inhibiting
chemical species (whether parent compound or metabolite) with
AChE is described by a 2nd-order rate constant. The dissociation of
the inhibitor-AChE complex is described by a 1st-order rate constant.
Page 35 of 50
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These parameters can be estimated using in vitro methods and
should be obtained for blood (particularly RBC) and brain.
Estimation only of the equilibrium dissociation constant, which is the
ratio of the 2nd- and 1st-order rate constants, rather than the 2nd and
1st order constants themselves, would be acceptable for the
purposes of developing the PBPK models. These data will be
needed for all chemical species that contribute significantly to AChE
inhibition.
~ Partition coefficients. Computational algorithms are available for
prediction of partition coefficients (Poulin and Thiel, 2001; Poulin
and Krishnan, 1995; DeJongh et al., 1997). These algorithms
provide an opportunity to develop PBPK/PD models without actually
measuring partition coefficients in the laboratory. It may be prudent,
however, to obtain laboratory measurements of a subset of the
algorithmically-predicted values in order to determine the reliability
of computationally derived partition coefficients. This determination
will be particularly important if future sensitivity analyses indicate
that one or more of these coefficients are important determinants in
estimating exposure concentration at the site of action.
It is expected that blood:tissue partition coefficients will be required
for liver, kidney, fat, slowly perfused (i.e., muscle), and brain.
Blood:air partition coefficients will be needed for volatile parent
compounds or metabolites. The skin:blood partition coefficient will
be needed if dermal exposure is evaluated.
~ In vitro studies for metabolic clearance. The quantitatively most
important site of metabolism of N-methyl carbamates is expected to
be the liver. Liver homogenates or microsomes can be used to
estimate the Michaelis-Menten parameters of metabolism (Vmax:
maximum rate of metabolism, Km: concentration at which the
enzyme is half-saturated). Sufficient attention to the design of these
experiments should enable the identification of multiple metabolic
pathways characterized by different Vmax and Km values. As
mentioned previously, development of PBPK/PD models is most
efficient when model developers work collaboratively with laboratory
scientists. If a first-generation PBPK/PD model that describes only
hepatic clearance is not able to predict PK data, then screening of
other tissues such as blood and kidney as potential sites of
metabolic clearance may need to be considered.
The extrapolation from in vitro to in vivo can be a source of
uncertainty; some limited data on compound metabolism may need
to be collected in vivo to evaluate the suitability of the in vitro data.
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In vivo studies for metabolic parameters:
a. Intravenous studies: Analytical measurement of the time-
course of the amount of parent N-methyl carbamate and
AChE-active metabolites in the target tissue, site(s) of
storage (if appropriate) and metabolism are suggested in
addition to measurements of AChE inhibition. These
datasets provide an opportunity to estimate metabolic
parameters (Vmax and Km) by curve fitting without potential
confounding by incorrect specification of rates of absorption
from the Gl tract. As noted previously, even if in vitro
methods are used as the primary means of obtaining data on
Vmax and Km, some in vivo data as described here should
be obtained to evaluate the in vitro to in vivo extrapolation.
b. Oral absorption. Absorption from the Gl tract is a major route
of exposure of N-methyl carbamates into the body particularly
through the diet. However, estimation of oral absorption
parameters is best done by fitting the model to PK data where
all model parameters, except for the oral absorption
parameters, have already been set.
A blood time course dataset is a good basis for estimation of
oral absorption parameters. The specific oral absorption
parameters to be identified will depend on the types of data
available. For example, oral dosing can be administered in
various ways such as corn oil gavage, water gavage, or
feeding. Analytical measurement of the time course of the
amount of parent N-methyl carbamate and AChE-active
metabolites in blood is the minimum requirement for
estimation of the oral absorption parameters. In addition,
measurements in the target tissue, site(s) of storage (if
appropriate), and metabolism, in addition to measurements of
AChE inhibition, are suggested. (These latter measurements
would be useful when considering the reliability of model
predictions but they are not essential for estimation of oral
absorption parameters during model development.)
Interaction experiments. When exposure occurs to two or more
members of the cumulative assessment group (CAG), interactions
between compounds may occur that affect PK behaviors and the
associated degree of AChE inhibition. The expected sites of
interaction include CYP450 and carboxyl esterases that are sites of
N-methyl carbamate binding and metabolism. Development of a
single PBPK/PD model for the entire CAG will require that these
interactions be described explicitly in the equations of the model.
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The initial approach to the development of this model will be to
assume that the interactions are competitive. The mathematical
description of competitive interactions is straightforward.
Fortunately, the data obtained during development of the PBPK/PD
models for the individual members of the CAG can also be used to
parameterize competitive interaction terms for the PBPK/PD model
for the entire CAG. Similarly, the individually measured binding and
dissociation parameters for AChE (see In vitro kinetics ofAChE
binding above) should be sufficient to characterize the overall level
ofAChE inhibition for a multi-compound model. The studies
conducted in support of model development for the individual
compounds will thus provide much if not all of the data needed to
characterize these interaction terms.
An in vivo multi-chemical PK and AChE inhibition study will be
desirable to establish the reliability of the PBPK/PD model for at
least a subset of the members of the CAG (particularly for those
pesticides with the highest levels of human exposure). The
preliminary PBPK/PD model for CAG as a whole can be used to
design this study to ensure that dose sampling time points selection
is as close to optimal as is possible. Alternatively, and in lieu of this
in vivo study, it may be possible to design in vitro pharmacokinetic
and AChE inhibition time course studies that can provide useful
tests of the reliability of the CAG PBPK/PD model.
Other additional information. As noted above, development of a
PBPK/PD model is a process that iterates between model
development at the computer terminal and targeted laboratory
experiments. The data collection needs identified above should
provide robust PBPK/PD models sufficient to the task of predicting
AChE inhibition for various exposure scenarios. Some kinds of
additional data, however, may serve to increase confidence in the
model to an even greater degree and to provide additional
capabilities relevant to risk assessment.
Data on compound elimination in urine, feces, and exhaled breath
would support the model development, and test the accuracy of the
assumptions concerning mass balance. Demonstration that the
PBPK model equations accurately simulates the results of a mass
balance study increases the level of confidence in the model
structure, and in the use of its predictive capability for risk
assessment.
Data on interindividual variability in PBPK/PD model parameters, in
PK behavior and in AChE inhibition would support a "Monte Carlo"
analysis. In a Monte Carlo analysis, PBPK models parameter
values are described by statistical distributions rather than by single,
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fixed data points. At each run of the model, random samples are
taken from the distributions to create a new set of parameter values.
Each run of the model can thus be thought of as representing a
different individual in a population (USEPA 1996 and 1997). Thus, a
Monte Carlo analysis supports characterization of variability and
uncertainty in the estimates of AChE inhibition based upon the
uncertainty and variability in the parameters. A Monte Carlo
analysis would first be performed on the PBPK model for rodents.
Reparameterization of the PBPK model to humans would require
consideration of the issues addressed in the discussion on
interspecies extrapolation (see Section III.I) with additional concern
for how parameter variability scales between species. The Monte
Carlo model would provide a capability for prediction of population
variability in AChE inhibition This capability would help address the
uncertainty associated with interindividual variability.
PBPK/PD models are capable of incorporating specific information
relating to sex, age, and/or other factors that impact the manner in
which individuals are affected by chemical exposures. The datasets
used to support development of a PBPK/PD model are typically
collected in a sex-specific manner. Some sex-specific differences in
parameter values are well known, for example the differences in
hepatic CYP450 activities, the model has an associated "sex" which
is defined by the supporting datasets. Sex-specific differences in
key parameter values, such as rates of bioactivation or
detoxification, could be associated with measurable differences in
degrees of AChE inhibition for the same exposure. Once the initial
PBPK/PD model is developed for males or females, a sensitivity
analysis could be conducted to determine the degree to which
model-predicted AChE inhibition is sensitive to sex-related changes
in key parameter values. This sensitivity analysis would provide a
good indication of whether or not collection of additional data in the
other sex is necessary.
PBPK/PD models are usually developed using datasets from adult
animals. Information related to identification and description of
sensitive life stage(s), such as maturation profiles for critical
metabolic pathways, would also be helpful in developing the
PBPK/PD models. It is possible to incorporate into these models
descriptions of how parameter values change with age. This
information allows the model to describe how PK behaviors change
with age, as with the transition from childhood to adulthood. These
capabilities depend on the availability of adequate supporting
datasets, such as growth curves for the major tissue groups in the
body, and age-dependence in the activities of enzymes that activate
or clear the chemicals of interest. In the absence of such
information, the PBPK/PD model is typically developed for the adult
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and health-protective, default approaches are invoked to account for
potential age-dependent pharmacokinetic behaviors contribute to
the age-dependence of risk.
2. Uncertainty associated with availability of appropriate data
The Agency has not yet determined which method or methods that
will be used to develop the cumulative risk assessment for the N-methyl
carbamates. However, the availability of appropriate data is expected to
impact the level of refinements and type of method(s) used. At this time, it
is unknown whether or not sufficient data will be available to the Agency for
model development or for evaluating the reliability of the PBPK/PD models
for the N-methyl carbamate pesticides in a timely manner for the expected
release of the preliminary cumulative risk assessment in 2005. However,
one of the goals of the current research effort and case study is to consider
the degree to which completeness and availability of appropriate PK data
impacts model uncertainty when developing PBPK/PD models for use in
regulatory settings. As part of the case study, in the future, the Agency will
also carefully evaluate the application of uncertainty, extrapolation, and
safety factors, particularly the FQPA 10x factor for infants and children,
when using PBPK/PD models to estimate cumulative risk. The Agency
anticipates further discussion and consideration of overall uncertainty
related to data availability in the future as work on the case study
continues.
H. Model Evaluation and Quality Control.
An essential part of the modeling process is model evaluation: the process
of determining the degree to which a model satisfies the needs that led to the
model's creation. Model development is an iterative process in which model
creation (i.e., when important aspects of biology are captured in mathematical and
computer models) alternates with model evaluation (i.e., when the model is tested
and challenged with data and analysis). Any failures in the evaluation phase are
used to identify inadequate approximations and faulty biological assumptions,
which can then be corrected in a new model creation phase. When it comes time
to use the model, the process must end with an evaluation step. The following
process is a sequence of steps whose application is intended to increase
confidence that the PBPK/PD models are reliable tools for assessing risk. In
many ways, the sequence parallels the process of model creation. This approach
has been treated more generally by Clark, et al. (2003, in prep).
1. Model Purpose
The specific use for the model must be explicitly defined before an
evaluation of model suitability can be begun. The purpose of the model
constrains its structure and determines the details of the rest of its
evaluation. Some examples of questions that must be answered here are:
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Does the model need to predict AChE inhibition or parent and metabolite
concentrations? In which tissues must the model predict these values?
What metrics, such as area under the curve, peak value, or area under the
curve above a threshold value, must be computed? What sorts of
exposure inputs are required? How precisely must the model predict the
different outputs?
2. Biological Characterization and Model Structure
Although the quantitative machinery gets much of the attention, in
fact a PBPK/PD model is initially a narrative statement of biological
descriptions and hypotheses. This narrative must include the general
biological features that affect concentrations of parent chemicals and the
relevant metabolites, and also sources and the nature of intra- and inter-
individual variability. PBPK/PD models include a number of approximations
and assumptions that should be made explicit. Some aspects of model
structure, such as the treatment of tissues as well-mixed compartments,
concentrating all or most of metabolism in one or two tissues, and the
lumping of compartments with similar characteristics, are common to most
PBPK/PD models. Other aspects of model structure are specific to the
chemicals being considered, such as simplifications of metabolic pathways,
and the nature of protein binding. Still others are specific for particular
endpoints, like the description of AChE synthesis, degradation, and
inhibition.
This largely qualitative description of the biological and toxicological
profile(s) for the chemical(s) of interest should be reviewed in the context of
the relevant scientific literature. In cases where the literature is unclear
about the details needed for modeling, and/or for which the literature
supports more than one descriptions of a particular feature, it should be
possible, through modeling those alternatives, to quantify the degree to
which the ambiguity matters for the particular endpoints of concern.
3. Mathematical Descriptions
It is convenient when assessing a PBPK/PD model to abstract its
formal mathematical description from its implementation in a particular
programming language. Much of that description is well-established
(Ramsey and Andersen, 1984): the mathematical forms for perfusion-
limited and diffusion-limited compartments are well-known, for instance.
Other aspects are not so well-established, such as protein binding,
absorption from the Gl tract, dermal absorption, and submodels for AChE
inhibition and regeneration. Some mathematical descriptions of biological
features, such as receptor binding or protein binding more generally, may
carry with them assumptions about how rapidly concentrations of ligand,
receptor, and the ligand-receptor complex come to steady state relative to
the other temporal changes in the system. For completeness, it is
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desirable that the mathematical description includes the nature of inter- and
intra-individual variability, including measurement error. Details of the
probability model evaluated here, such as particular probability distributions
used will often depend upon the context within which the model is used,
such as experimental design or the risk assessment scenario, but this part
of the model description is essential for proper statistical treatment of
parameter estimation.
4. Computer Implementation
PBPK/PD models are typically written in a specialized high-level
language, which is itself a complex computer program, very often a
proprietary language whose source code is usually hidden from the
ordinary user. Thus, the reliability of the software in which the model is
written although an important concern, is one that will have been
addressed in a larger context. Thus, the primary concern in this phase of
model evaluation is that of the code for the model itself.
An advantage of analyzing PBPK/PD models first into a
mathematical description prior to a computer implementation of that
description is the opportunity to evaluate the mathematical description and
computer implementation separately. Evaluation at this step involves
checking of computer code against mathematical description and also
checking that features of the language, such as integrator options, are
used correctly (e.g., stiff methods used for systems that are likely to be
stiff, etc.)
Details of the evaluation depends upon language. For languages
such as MCSim and ACSL, which are essentially algebraic languages, the
form of the model description follows closely that of the mathematical
description. For many PBPK/PD models, like that shown in Figure 3,
details of statement syntax and the use of the proper variables in a model
that may have hundreds of similar-looking variable names becomes a
critical and difficult part of the evaluation. ERDEM, on the other hand, is
essentially a pre-coded PBPK model for a large number of potential
compartments and chemicals. The specific implementation for a particular
set of chemicals is based on limiting that general model by the use of
switches and implementation-specific parameter values. For this sort of
model, review consists of making sure the switch settings and parameter
values correspond to the intended model. Again, the large number of
parameters necessitated by a model for multiple exposures makes this a
tedious part of the model evaluation; though a good user interface can
facilitate the review significantly by making it easier to group related
variables together.
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A valuable approach for complex models is separate, independent
implementation of the same mathematical description in separate
languages. Greater confidence in the software implementation is achieved
when two independent implementations of a model give numerically similar
results to the same inputs. Two models for the N-methyl carbamates are
being developed, in ERDEM and in MCSim. This allows the software
implementations to be directly tested through comparisons of their
respective outputs given the same input. In addition, dual model
implementation provides the opportunity to take advantage of the unique
features of each language, such as the advanced statistical features of
MCSim and the ability for rapid prototyping of alternative models in
ERDEM.
5. Parameter Analysis and Quality of Model Fit
Model parameters can be grouped into several categories:
physiological parameters such as tissue volumes, blood flows, AChE
synthesis and degradation rates; chemical-specific parameters such as
partition coefficients, metabolic rate constants, coefficients for protein
binding, coefficients for AChE inhibition; and parameters for determining
the stochastic behavior of model, such as inter-individual variances of the
true parameter values. Their values are determined in different ways.
Physiological parameters are usually determined by combining body weight
with tabulated relationships between body weight and the other
physiological parameters (e.g., Brown, et al., 1997). Chemical-specific
parameters may be estimated by fitting the model to data, as is often the
case with metabolic parameters. In some cases, algorithms exist for
estimating them from other chemical-specific characteristics, such as
approaches for estimating partition coefficients from octanol:water partition
coefficients (e.g., Poulin and Krishnan, 1995; Poulin and Thiel, 2001).
Parameters for the stochastic characteristics of the model may be
estimated from experimental data by fitting the model directly. However,
especially for human stochastic parameters used for predicting human
variability, these parameters may be inferred from studies of the degree to
which people vary in, for example, relevant biochemical parameters such
as enzyme activities.
The first step in evaluating the quality of the parameters used in the
model is to affirm the correctness and relevance of particular values by
reference to literature values. Once this is completed, it is important to
determine the critical parameters important for model outputs relevant to
the risk assessment as well as for data sets used to evaluate model
reliability. This determination helps identify parameters whose values are
unreliable, because they have not been "tested" in the comparisons
between model predictions and new datasets, and identifies parameters
whose values are particularly important, and thus warrant closer
examination. Engineering tools, such as sensitivity analysis, and tools from
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statistical experimental design for non-linear model parameter estimation,
are useful for identifying the parameters that are most critical for
determining the values of model outputs.
Also important is the ability of the model to predict results in data
sets that have not been used to estimate parameters. The closer the
experimental designs of such datasets are to the regimen in which the
model will actually be used, the more reliable the results of such evaluation
will be for predicting the utility of the model. It is important to note that strict
goodness-of-fit testing is not necessarily the right approach, here. The null
hypothesis on which goodness-of-fit testing is based, that the model under
consideration is the true model that generated the particular experimental
data set, is clearly false a priori. Failure to reject a goodness-of-fit test
means no more than that the experimental design was inadequate to
detect the deviation of the PBPK/PD model from the truth, but does not
quantify how close the model is to the true model. Instead, the degree to
which the model fails to predict experimental results, in terms of readily
interpretable metrics such as percent error of prediction, with a measure of
its uncertainty, is a more useful measure. It is preferred to consider the
appropriate the level of precision at the beginning of the modeling effort,
perhaps during Stage 1 (definition of model purpose).
I. Model scale-up and extrapolation from rodents to humans.
Use of laboratory animals to study N-methyl carbamate toxicology is
justified by the assumption that the data so obtained are relevant to humans.
With respect to PBPK/PD modeling, this means that we assume that the model
structure that describes N-methyl carbamate PK and AChE inhibition in rats is
also appropriate for humans. This assumption is consistent with data on the
common role of AChE in the rodent and human nervous systems as well as with
other data on N-methyl carbamates. The problem of scale-up of the model from
rats to humans thus becomes one of identifying appropriate human values for the
model parameters. The scaling behaviors of all of the parameters of the rodent
model should be considered in this process. Identification of a full set of human
parameter values allows the model to be used for prediction of AChE inhibition in
people. In practice, most if not all of the data available to support model
development will be obtained from rodents and rodent tissues. It is a certainty
that the database of human information for PBPK/PD model development will be
minimal compared to that available for rats. Scaling and extrapolating the
PBPK/PD model from rats to people will thus involve a number of steps:
1. Use of human data when available and if appropriate. For example, data
on human physiological values such as tissue volumes and blood flows can
be used directly in the model. Chemical-specific data that can be obtained
from in vitro studies from human tissues, such as partition coefficients,
rates of metabolism, and interactions with AChE, would be valuable. The
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ability to obtain such in vitro data depends on the availability of appropriate
human tissue samples, such as hepatic microsomes and blood.
2. Identification of any relevant and appropriate non-human primate data and
evaluation of its possible use as surrogate for human data.
3. In the absence of relevant human information, allometric scaling of the
rodent parameter are values. This approach defines the parameter values
as functions of body weight. For example, the breathing rate is scaled from
rodents to humans as a fractional power (usually 0.75) of body weight
(BW). Tissue volumes, on the other hand, are usually scaled as BW1-0.
4. Use of rodent parameter values directly in the human model. In the
absence of relevant human data and a lack of information on how to
allometrically scale a parameter value, the most judicious approach may be
to use the rodent value directly, i.e., without change, in the human model.
Oral uptake absorption rate constants, for example, may be treated in this
manner. As with all approaches to scale-up, the contribution to overall
model uncertainty of this approach should be considered.
At present time, the PBPK/PD models under development for the N-methyl
carbamate pesticides have not been scaled from rodents to humans. However, it
is expected that when faced with uncertainty about the appropriate scale-up for
specific parameters, choices can often be identified that are health protective. For
example, if the appropriate scale-up of oral absorption rate constants is not clear,
then the option that maximizes the rate of absorption in the human model could
be used, since this approach is expected to maximize the inhibition of AChE
predicted by the human model. This approach will cause the human model to
over predict human health risk in the face of uncertainty about parameter scale-
up. As the case study develops further, the Agency will provide the sources of
data and relevant scaling of all parameters so as to make the PBPK/PD modeling
effort transparent and open for scientific evaluation.
The approach to scale-up described here will produce a human version of
the PBPK/PD model. Expert judgment will be required to evaluate the degree of
uncertainty associated with the scale-up with specific attention paid to the
question of how the uncertainties associated with the human PBPK/PD model
compare to the uncertainties of an empirical modeling approach.
IV. SUMMARY
The current document outlines the on-going work by EPA to develop a strategy for
performing cumulative risk using PBPK/PD modeling. A case study with AChE-inhibiting
N-methyl carbamates pesticides is under development. EPA is proposing to perform a
dual modeling effort in this case study. By developing models in two different
programming languages the advantages of each platform can be put to use. The
generation of two models is also expected to provide an additional level of quality control
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for error detection and correction. Incorporating PK and mechanistic data into risk
assessments is expected to improve the biological and scientific basis for the
assessments and is thus expected to improve regulatory decisions. Although using
PBPK/PD models is likely to reduce the overall uncertainty for a particular risk
assessment, it is not intended to remove all uncertainty and may actually highlight areas
of uncertainty that were not previously considered or evaluated. The key consideration
in evaluating the utility of PBPK/PD models is not that the model be correct in any
absolute sense but rather that it be arguably better, i.e., less uncertain, than an
alternative empirical approach or use of default assumptions. In the future, EPA will
need to critically evaluate the balance between model uncertainty particularly when
associated with incomplete PK and/or mechanistic data sets with the reduction in overall
risk assessment uncertainty associated with utilizing these types of models and
information. As appropriate PK data become available, the Agency will also address
some technical issues in the case study such as parameter estimation and sensitivity
analysis not considered in depth in the current document. Since the passage of FQPA
(1996), the Agency has taken a step-wise approach to developing its cumulative risk
assessment methodologies and risk assessments. The current document is a
continuation of this step-wise approach. Further scientific review is anticipated in the
future as the case study and PBPK/PD strategy are developed.
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