United States
Environmental Protection
Agency
Office of Health and
Environmental Assessment
Washington, DC 20460
Research and Development
EPA/600/S6-88/004 July 1988
v°/EPA Project Summary
Reference Physiological
Parameters in Pharmacokinetic
Modeling
Angela 0. Arms and Curtis C. Travis
This document presents a
compilation of measured values for
physiological parameters used in
Pharmacokinetic modeling. The
physiological parameters Include
body weight, tissue volumes, cardiac
output distribution, and respiration
parameters. Reference values for use
in risk assessment are given for each
of the physiological parameters
based on analyses of valid
measurements obtained from the
literature and other reliable sources.
The proposed reference values are
for generic mice and rats without
regard to sex or strain. Reference
values for humans are without regard
to age or sex. Differences between
the sexes in mice, rats, and humans
are accounted for by scaling the
reference parameters within species
on the basis of body weight.
Reference physiological parameters
are for a 0.025 kg mouse, 0.25 kg rat,
and a 70 kg man.
The Project Summary presents an
introduction to pharmacoklnetics,
discusses Pharmacokinetic
modeling, and diagrams a typical
Pharmacokinetic model with an
accompanying table defining the
nomenclature used.
The Project Summary concludes
with a brief overview of animal
scale-up (body weight scaling).
Scaling is discussed in detail in the
final report.
This Project Summary was
developed by EPA's Office of Health
and Environmental Assessment,
Washington, DC to announce key
findings of the research project that is
fully documented In a separate report
of the same title (see Project Report
ordering information at back).
Introduction
Pharmacokinetics is the science of
quantitatively predicting the fate of an
exogenous substance in an organism
Utilizing computational techniques,
Pharmacokinetics provides the means of
studying the uptake, distribution.
metabolism, and excretion of chemicals
by the body. This is accomplished by
dividing the body into various anatomical
compartments The mathematical
representation of these compartments
provides a description of the time course
of drug disposition throughout the body.
Pharmacokinetics eliminates some of the
ambiguities in determining the risk of
human exposure to environmental
chemicals and provides a basis for
evaluating the scientific assumptions
upon which the risk assessment process
is based.
A recent development in the area of
Pharmacokinetics is the advent of
physiologically-based-pharmacokinetic
(PBPK) models. Relying on actual
physiological parameters such as body
weight, breathing rates, cardiac output,
blood flow rates, tissues volumes, etc., to
describe the metabolic process, the
PBPK models can relate exposure
concentrations to organ concentrations
over a range of exposure conditions. The
final report provides a literature review of
the physiological parameters used in
PBPK models, and recommends
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reference physiological parameters for
use in risk assessment.
Pharmacokinetic Modeling
A pharmacokinetic model is a set of
equations used to describe the time
course of a parent chemical or
metabolite in an animal system. There
are two types of pharmacokinetic
models: data-based and physio-
logically-based. A data-based model
divides the animal system into a series of
compartments which, in general, do not
represent real, identifiable anatomic
regions of the body. In applying these
models, time-course concentration
curves are first determined from in vivo
animal experiments. Then, model
compartment volumes and rate constants
are determined by trial and error so that
the model predictions fit the empirical
data. These models are useful for
interpolation and limited extrapolation
within the same species. However, since
the parameters in these data-based
models generally correspond to
physiologically-identifiable entities, they
do not allow for extrapolation across
animal species.
A physiologically-based-pharma-
cokinetic model is comprised of a series
of compartments representing organs or
tissue groups with realistic weights and
blood flows. These models require a
variety of physiological information:
tissue volumes, blood flow rates to
tissues, cardiac output, alveolar
ventilation rates (for volatile compounds)
and, possibly, membrane permeabilities.
The models also utilize biochemical
information such as air/blood partition
coefficients, and metabolic parameters.
The uniqueness of the physiological-
based approach rests on this reliance on
measured physiological and biochemical
parameters. An appealing aspect of
these physiological models is that they
allow ready extrapolation of observed
experimental results from a test species
to an untested species simply by placing
the appropriate physiological and
biochemical parameters in the model.
Similarly, the effect of route of
administration can be investigated by
allowing different administration
pathways.
The authors emphasize that no one
pharmacokinetic model can be used to
determine the distribution of all
chemicals, The number of compartments
and the way they are connected will vary
from chemical to chemical depending
upon the chemical's metabolic behavior
and the nature of the questions being
asked concerning dose to target tissues.
Despite this fact, most physio-
logically-based-pharmacokinetic
models in current use divide the body
into four physiological groups, all
connected by the arterial and venous
blood flow pathways (see Figure 1 and
Table 1). The first group is the vessel-
Qa/V ^
cinh ^
ob ^
Cven
Cvf
Cvm
Cvr
Cvt
Alveolar
Space
Lung
Blood
Fat
Tissue
Group
Muscle
Group
Vessel
Rich
Group
Liver
Metabolizing
Tissue
Group
Qalv ^
calv ^
ob
Cart
4 °(
Cart
^ Qm
Cart
4 Qf
Cart
< °'
cart
Metabolites
(Linear Pathway)
Metabolites
(Michaelis-Menten)
Figure 1. Diagram of a typical pharma-
cokinetic model used to simulate
the behavior of inhaled volatile
organics. The model divides the
body into four physiological
groups, all connected by Wood
flow pathways. The symbols are
defined in Table 1.
rich group (VRG) and is made up of
those tissues most profusely supplied
with blood vessels. These include the
brain, heart, kidney and viscera. The
second group is composed of muscle
and skin and is called the muscle group,
(MG). The third group is composed
adipose (fat) tissue. The fourth groi
contains organs with a high capacity
metabolize (principally liver). Each tissi
group is described mathematically by
set of differential equations whii
calculate the rate of change of tl
amount of chemical in ea(
compartment. Metabolism, occurrii
chiefly in the liver, is described by
combination of a linear metabol
component and a Michaelis-Menti
component accounting for saturab
metabolism. Again, we stress that oth
model descriptions are possible, but thi
will, in general, have the san
physiological parameters.
Physiological Parameters
The physiological parameters typica
used in pharmacokinetic modeling a
listed in Table 2. Measured values
these parameters in mice and rats a
age, sex, and strain-dependent. F
example, female rats tend to have high
mass-specific ventilation rates thi
males, and young rats have values high
than mature rats. In addition, the status
the animals during measurement (boi
position, conditioning, etc.,) and tl
measurement technique can ha'
substantial influences. Lack of data 1
many physiological parameters, howevi
limits attempts to account for the
factors. The reference parameters are I
a generic mouse or rat, without regard
sex or strain. Differences between sex
are accounted for by scaling tl
reference parameters within species
the basis of body weight. Referen
physiological values for humans are foi
resting 70 kg man. For rodents, t
reference physiological parameters a
for a 0.025 kg mouse and a 0.25 kg rat
rest.
Scope of the Final Report
The final report summarized here
reviews the measured values
physiological parameters found in t
literature. The specific paramete
detailed in the final report ar
respectively, body weights, tiss
volumes, cardiac output distribution a
respiration parameters. The concludi
chapter in the final report discuss
scaling which is defined as the orde
variation of anatomic and physioloc
properties with body weights. Scaling
possible because both large and srr
animals are physiologically similar in
species of animals, including humans.
Many of the physiological parametc
used in pharmacokinetic modeling i
directly correlated to the body weight
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the particular organism. These
physiological parameters generally vary
with the body weight according to a
power function expressed as:
y = aBWb
where y is a physiological parameter of
interest, and a and b are constants. If the
constant b equals one, the physiological
parameter y correlates directly with body
weight. If the constant b equals two-
thirds, the parameter y correlates with
surface area. This formula was taken
from the 1949 classical paper by E. F.
Adolph* which is generally recognized as
the definitive source on the quantitative
relationship between body weight and
the physiological parameters.
The most desirable method of
obtaining the physiological parameters
used in a pharmacokinetic model is
direct measurement. When such values
are not available, necessary biological
parameters for an untested species can
be obtained through scaling.
Each section of the final report is
organized as follows. A summary table of
the recommended reference values is
presented; a literature review supports
the recommended values, and the actual
parameter values used in the various
pharmacokinetic models are
summarized. (Table 3 summarizes the
reference physiological parameters
which are fully discussed in the final
report).
The full report also presents a
complete list of references and an
appendix consisting of a table of partition
coefficients. Finally, the text of the full
report is augmented by 45 tables.
Table 1. Nomenclature Used In Describing a Physiologically-Based-
Pharmacokinetic Model
Qalv Alveolar ventilation rate (liters air/hr)
C,nh Concentration in inhaled air (mg/liter air)
Ca|V Concentration in alveolar air (mg/liter air)
Ab Blood/air partition coefficient (liters air/liters blood)
Ob Cardiac output (liters blood/hr)
Cart Concentrtion in arterial blood (mg/liter blood)
Cven Concentration in mixed venous blood (mg/liter blood)
Vmax Michaelis-Menten metabolism rate (mg/hr)
Km Michaelis constant (mg/liter blood)
Kf Linear metabolism rate (hr1)
Am Amount metabolized in the liver (mg)
Qi Blood flow rate to tissue group i (liters blood/hr)"
Vj Volume of tissue group i (liters)
C; Concentration in tissue group i (mg/liter)
A, Amound in tissue group i (mg)
CVj Concentration in venous blood leaving tissue group i (mg/liter blood)
H, Tissue/blood partition coefficient for tissue i (liters blood/liter i)
\.jla Tissue/air partition coefficient for tissue i (liters air/liter i)
k Gavage or oral rate constant (hr'1)
D0 Total quantify of PCE absorbed via gavage route (mg)
"Subscripts (i) for tissue groups or compartments:
I Liver (metabolizing tissue group)
f Fat tissue group
r Vessel-rich tissue group
m Muscle tissue group
Table 2. Physiological Parameters Used for Modeling
Parameters
Body weight (kg)
Cardiac output (l/min)
Minute volume (llmin)
Alveolar ventilation (I/mm)
Physiological dead space ("/»)
Frequency (breaths/min)
Organs
(Volumes and Blood Flows)
Liver
Fat
Vessel-Rich Group
Muscle Group
"Quantitative relations in the physiological
constituents of mammals. Science 109' 579-
585
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Table 3. Reference Physiological Parameters
Mouse Rat Human
Body weights (kg) 0.025 0.25 70.0
Tissue volumes
(fractions)
Liver 0.055 0.04 0.026
Fat 0.10 0.07 0.19
VRG 0.05 0.05 0.05
MG 0.70 0.75 0.62
Cardiac output 0.017 0.083 6.2
(l/min)
Tissue perfusion
(fractions)
Liver 0.25 0.25 0.26
Fat 0.09 0.09 0.05
VRG 0.51 0.51 0.44
MG 0.15 0.15 0.25
Minute volume 0.037 0.174 7.5
(l/min)
Alveolar ventilation 0.025 0.117 5.0
(l/min)
Angela D. Arms and Curtis C. Travis are with Oak Ridge National Laboratory,
Oak Ridge, TN 37831-6109.
Richard Walentowlcz is the EPA Project Officer (see below).
The complete report, entitled "Reference Physiological Parameters in
Pharmacokinetic Modeling," (Order No. PB 88-196 019/AS; Cost: $19.95,
subject to change) will be available only from:
National Technical Information Service
5285 Port Royal Road *&
Springfield, VA22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Office of Health and Environmental Assessment
U.S. Environmental Protection Agency
Washington, DC 20460
United States
Environmental Protection
Agency
Center for Environmental Research
Information
Cincinnati OH 45268
Official Business
Penalty for Private Use $300
EPA/600/S6-88/004
°GQ0329 »,
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