xvEPA
EPA 540/R-94/040
PB94-963505
OSWER #9285.7-22
December 1994
TECHNICAL SUPPORT DOCUMENT:
PARAMETERS AND EQUATIONS USED IN THE
INTEGRATED EXPOSURE UPTAKE BIOKINETIC
MODEL FOR
LEAD IN CHILDREN (v0.99d)
Office of Solid Waste and Emergency Response
U.S. Environmental Protection Agency
Washington, DC 20460
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NOTICE
This document provides guidance to EPA staff. It also provides guidance to the public and to the
regulated community on how EPA intends to exercise its discretion in implementing the National
Contingency Plan. The guidance is designed to implement national policy on these issues. The
document does not, however, substitute for EPA's statutes or regulations, nor is it a regulation
itself. Thus, it cannot impose legally-binding requirements on EPA, States, or the regulated
community, and may not apply to a particular situation based upon the circumstances. EPA may
change this guidance in the future, as appropriate.
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U.S. ENVIRONMENTAL PROTECTION AGENCY
TECHNICAL REVIEW WORKGROUP FOR LEAD
The Technical Review Workgroup for Lead (TRW) is an interoffice workgroup convened by the
U.S. EPA Office of Solid Waste and Emergency Response/Office of Emergency and Remedial
Response (OSWER/OERR).
CHAIRPERSON
Region 8
Susan Griffin
Denver, CO
MEMBERS
Region 2 NCEA/Washington
Mark Maddaloni Paul White
New York, NY
NCEA/Cincinnati
Region 3 Harlal Choudhury
Roy Smith
Philadelphia, PA NCEA/Research Triangle Park
Robert Elias
Region 5
Patricia VanLeeuwen NCEA/Research Triangle Park
Chicago, IL Allan Marcus
Region 8 ORD/Washington
Chris Weis Barbara Davis
Denver, CO
NCEA/Washington
Karen Hogan
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TECHNICAL SUPPORT DOCUMENT:
PARAMETERS AND EQUATIONS USED IN THE
INTEGRATED EXPOSURE UPTAKE BIOKINETIC (IEUBK)
MODEL FOR LEAD IN CHILDREN
(v 0.99d)
Prepared by
THE TECHNICAL REVIEW WORKGROUP FOR LEAD
for
THE OFFICE OF EMERGENCY AND REMEDIAL RESPONSE
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, DC 20460
with Document Production Assistance from
THE ENVIRONMENTAL CRITERIA AND ASSESSMENT OFFICE
U.S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NC 27711
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PREFACE
The Technical Support Document describes in detail the basis for the parameters and
equations that are used in the Integrated Exposure Uptake Biokinetic Model for Lead in Children,
version 0.99d. It is a supplement to the Guidance Manual that was published in February, 1994,
and is available from the National Technical Information Service as document PB93-963510. The
IEUBK Model has been recommended as a risk assessment tool to support the implementation of
the July 14, 1994 Office of Solid Waste and Emergency Response Interim Directive on Revised
Soil Lead Guidance for CERCLA Sites and RCRA Facilities.
The development of the model has included the cooperative efforts of several EPA
programs over nearly a decade. For the last four years, the development and documentation of
the model have been coordinated by the Technical Review Workgroup for Lead, whose members
are listed on page vi. This document was written by the Workgroup with extensive support from
Dr. Steven W. Rust and Prithi Kumar of Battelle Columbus and Dr. Gary Diamond of Syracuse
Research Corporation. It reflects the comments of peer reviewers from within and outside of
EPA whose names and affiliations are listed on page vii.
Although this document details the selection of parameters and equations used in the
IEUBK Model, it is not a line by line documentation of the source code. Equations and
parameters presented in this document have been simplified for clarity. Comments on the
technical content of this document or suggestions for its improvement may be brought to the
attention of the Technical Review Workgroup for Lead.
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TABLE OF CONTENTS
1.0 INTRODUCTION AND DOCUMENT OVERVIEW 1
2.0 MODEL OVERVIEW 5
3.0 EXPOSURE COMPONENT 12
3.1 Exposure Equations 12
3.1.1 Air Lead Exposure Model 12
3.1.2 Dietary Lead Exposure Model 13
3.1.3 Water Lead Exposure Model 14
3.1.4 Soil Lead Exposure Model 15
3.1.5 Dust Lead Exposure Model 15
3.2 Default Values for Exposure Parameters 17
3.2.1 Air Lead Parameter Values 17
3.2.2 Dietary Lead Parameter Values 18
3.2.3 Water Lead Parameter Values 18
3.2.4 Soil Lead Parameter Values 18
3.2.5 Dust Lead Parameter Values 19
4.0 UPTAKE COMPONENT 21
4.1 Overview 21
4.2 Parameterization of the Saturable and Non-Saturable Components of Absorption . . 23
4.3 Other Uptake Processes 28
5.0 BIOKINETIC COMPONENT 29
5.1 Basis for the Biokinetic Compartmental Structure 33
5.1.1 Postulates for Compartmental Model Structure 33
5.1.2 Division of the Whole Blood Pool 35
5.1.3 Plasma-Extracellular Fluid Compartment 38
5.2 Compartmental Specification for Model 38
in
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TABLE OF CONTENTS
(Continued)
Page
5.2.1 Fluid Volumes and Organ Weights 39
5.2.2 Compartmental Lead Transfer Times 40
5.2.3 Tissue Lead Masses at Birth 45
5.2.4 Compartmental Lead Masses and Blood Lead Concentration 45
6.0 PROBABILITY DISTRIBUTION COMPONENT 47
7.0 USER CONTROL WITHIN THE IEUBK CHILD LEAD MODEL 48
8.0 REFERENCES 53
APPENDIX A. EQUATIONS IN THE IEUBK LEAD MODEL A-l
APPENDIX B. DEFINITIONS AND DEFAULT VALUES FOR
PARAMETERS IN THE IEUBK LEAD MODEL .. B-l
LIST OF TABLES
TABLE 1. INFORMATION PROVIDED IN TABLES A-l, A-2, AND A-3 3
TABLE 2. INFORMATION PROVIDED IN TABLE B-l 4
TABLE 3. PARTITIONING OF TOTAL GUT LEAD INTAKE BY PROCESS 26
TABLE A.I. EQUATIONS OF THE EXPOSURE MODEL COMPONENT A-2
TABLE A.2. EQUATIONS OF THE UPTAKE MODEL COMPONENT A-4
TABLE A.3. EQUATIONS OF THE BIOKINETIC MODEL COMPONENT A-6
TABLE B.I. DESCRIPTION OF THE PARAMETERS IN THE IEUBK CHILD LEAD
MODEL B-2
IV
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TABLE OF CONTENTS
(Continued)
LIST OF FIGURES
FIGURE 1. Biological structure of the IEUBK Lead Model . .
FIGURE 2. Mathematical structure of the IEUBK Lead Model
Page
FIGURE 3. Iterative procedure for determining compartmental lead masses in biokinetic
component 11
FIGURE 4. Mathematical treatment of lead absorption in the IEUBK Model comprised of
saturable and non-saturable components (figure not to scale) 26
FIGURE 5. Conceptual model of gastrointestinal absorption 27
FIGURE 6. Structure of the IEUBK Lead Model with emphasis on user control of input
parameters and decisions 50
FIGURE 7. User-specified decisions and parameters used to determine the media-specific
consumption and lead concentration parameters 51
v
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TECHNICAL REVIEW WORKGROUP FOR LEAD
Harlal Choudhury
U.S. Environmental Protection Agency
Environmental Criteria and Assessment
Office
26 West Martin Luther King Dr.
Cincinnati, OH 45268
Barbara Davis
U.S. Environmental Protection Agency
(5204G)
401 M St. SW
Washington, DC 20460
Rob Elias
U.S. Environmental Protection Agency
(MD-52)
Environmental Criteria and Assessment
Office
Research Triangle Park, NC 27711
Susan Griffin (Chair)
U.S. Environmental Protection Agency
Region 8 (8 HWM-SM)
999 18th St., Suite 500
Denver, CO 80202
Karen Hogan
U.S. Environmental Protection Agency
(7403)
401 M St. SW
Washington, DC 20460
Mark Maddaloni
U.S. Environmental Protection Agency
Region 2
Emergency and Remedial Response
Division
26 Federal Plaza
New York, NY 10278
PEER REVIEWERS
Allan Marcus
U.S. Environmental Protection Agency
(MD-52)
Environmental Criteria and Assessment
Office
Research Triangle Park, NC 27711
Roy Smith
U.S. Environmental Protection Agency
Regions (3 HW15)
Hazardous Waste Management Division
841 Chestnut St.
Philadelphia, PA 19107
Pat Van Leeuwen
U.S. Environmental Protection Agency
Region 5 (HSRLT-5J)
Waste Management Division
77 West Jackson Blvd.
Chicago, IL 60604
Chris Weis
U.S. Environmental Protection Agency
Region 8 (8 HWM-SM)
999 18th St., Suite 500
Denver, CO 80202
Paul White
U.S. Environmental Protection Agency
(8603)
Office of Health and Environmental
Assessment
401 M St., SW
Washington, DC 20460
VI
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Dr. Teresa Bowers
Gradient Corporation
Cambridge, MA
Dr. Buck Grissom
Agency for Toxic Substances and Disease Registry
Atlanta, GA
Dr. Richard Leggett
Oak Ridge National Laboratory
Oak Ridge, TN
Dr. Thomas Matte"
Centers for Disease Control
Piscatawy, NJ
Dr. Neal Nelson
Office of Radiation and Indoor Air
US Environmental Protection Agency
Washington, DC
Dr. Ellen J. OTlaherty
Department of Environmental Health
University of Cincinnati College of Medicine
Cincinnati, OH
vn
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1.0 INTRODUCTION AND DOCUMENT OVERVIEW
The Integrated Exposure Uptake, and Biokinetic (IEUBK) Model for Lead in Children is a
stand-alone PC-compatible software package consisting of several related computer programs.
The IEUBK Model combines estimates of lead intake from lead in air, water, soil, dust, diet, and
other ingested media, with an absorption model for the uptake of lead from the lung or
gastrointestinal tract, and a biokinetic model of lead distribution, and elimination from a child's
body, to predict the likely distribution of blood lead for children of ages six months through 84
months exposed to lead in these environmental media. Young children are particularly sensitive
to adverse health effects from low-level lead exposures. The usual biomarker of lead exposure is
the concentration of lead in the child's blood. Blood lead concentration is not only useful as an
indicator of recent lead exposure and historical lead exposure, but is also the most widely used
index of internal lead body burdens associated with potential adverse health effects. The IEUBK
Model can be used to predict the probability that children exposed to lead in environmental media
will have blood lead concentrations exceeding a health-based level of concern. These risk
estimates can be useful in assessing the possible consequences of alternative lead exposure
scenarios, including alternative models for intervention, abatement, or other remedial actions.
Initial development of a computer simulation model containing uptake and biokinetic
components of a lead model was carried out by the U.S. Environmental Protection Agency, Office
of Air Quality Planning and Standards (OAQPS) in 1985. This model estimated the effectiveness
of alternative National Ambient Air Quality Standards for lead, particularly around point sources
of air lead emissions such as smelters. The biokinetic component of the model was based on
studies of lead metabolism in infant and juvenile baboons carried out at New York University by
N. Harley, T. Kneip, and P. Mallon in the early 1980's (Mallon 1983; Harley and Kneip 1985). In
the late 1980's, the exposure component of the IEUBK lead model was developed by the
Environmental Criteria and Assessment Office at Research Triangle Park, NC (U.S.
Environmental Protection Agency, 1989a; Cohen et al. 1990). The use of this early version of
the IEUBK lead model for setting air lead standards was documented in a staff report in 1989,
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and a subsequent staff paper in 1990 was reviewed and found acceptable by EPA's Clean Air
Science Advisory Committee of the Science Advisory Board (U.S. Environmental Protection
Agency, 1990a).
The air model was further developed to include enhancements in exposure, absorption and
biokinetics. In November, 1991, the Indoor Air Quality and Total Human Exposure Committee
of EPA's Science Advisory Board evaluated the newer version of the model for its use in
assessing total lead exposures and in aiding the development of soil cleanup levels for lead at
residential CERCLA and RCRA sites. The Committee concluded that while refinements in the
detailed specification of the model would be needed, the approach followed in the development of
the model was sound and the model could be applied effectively for many current needs even as it
continued to be refined for additional applications based upon experience gained in its use. The
Committee identified the need for guidance in some areas, such as the use of default parameters
and the use of a geometric standard deviation to characterize inter-individual variability.
Documentation for the early development stages of the IEUBK lead model exists within two
reports. Many of the initial model assumptions were documented in Appendix A of the OAQPS
staff paper on exposure assessment and methodology validation (U.S. Environmental Protection
Agency, 1989a). The 1990 Technical Support Document (U.S. Environmental Protection
Agency, 1990b) extended the documented basis for some of the model parameters.
Since 1991, development of the IEUBK lead model has been coordinated by the Technical
Review Workgroup (denoted TRW) for Lead whose members include scientists from EPA's
Office of Research and Development, the Office of Emergency and Remedial Response, the
Office of Pollution Prevention and Toxics, and from several EPA Regions. During this period,
enhancements have been made to nearly every aspect of the model. In particular, the model has
been implemented in a user-friendly software package (version 0.99d) that makes the model
accessible to the regulatory and scientific community. To assist the user in providing appropriate
input to the model, a Guidance Manual has been developed that describes the key features of the
IEUBK Model, its evolution and development, its capabilities, and its limitations. The purpose of
this report is to define the current stage of IEUBK lead model development, which was built on
previous models. The result is a single report that documents all of the parameters and equations
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employed in the IEUBK lead model, version 0.99d. Although this document describes in detail
the parameters and equations used in the IEUBK Model, it is not a line by line documentation of
the source code. Although most of the symbols and notation in this report are identical to the
source code, some notations may differ, but they are mathematically equivalent.
A major portion of the documentation in this report is embedded in Appendices A and B.
Appendix A, the equation dictionary, provides three tables that list the equations used in the
IEUBK lead model. Exposure equations are listed in Table A-l. Table A-2 contains the
equations relevant to the uptake component, while Table A-3 displays the biokinetic equations.
Each of Tables A-l, A-2, and A-3 is structured as indicated in Table 1.
TABLE 1. INFORMATION PROVIDED IN TABLES A-l, A-2, AND A-3
Column Heading
Equation Group
Equation Number
Equation
Description
Denotes a logical grouping of equations
Identifier for the individual equation. The equation number consists of:
! Component identifier
E for Exposure
U for Uptake
B for Biokinetic
! Equation numeral - unique to each equation group
! Lower case letter - uniquely identifies each equation
within an equation group. If there is only one equation in
a group, then this letter is omitted.
Actual equation
Within each table, the equation group clusters similar equations or equations that combine to
achieve a common purpose. For instance, in Table A-l, the equation groups are defined by the
different environmental media. The equation number provides a unique identifier for each
equation.
Appendix B, the parameter dictionary, lists each parameter in the IEUBK lead model
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alphabetically. As seen in Table 2, this appendix provides comprehensive information for each
parameter.
TABLE 2. INFORMATION PROVIDED IN TABLE B-l.
Column Heading
Parameter Name
Description
Default Values And/Or Defining Equation
- Value and/or Equation Number
- Age (months)
lorE
Basis for Values/Equations
Units
Parameter Use Equation
Description
Unique name used to identify parameter. Time-dependent parameters
are followed by "(t)" and may have a different value for each iteration
period. Otherwise the parameter takes on a single value.
Brief description of the parameter.
Lists the default value(s) for the parameter or the number of the
equation which defines the parameter.
Lists the age of the child for which the default value(s) or the equation
are applicable.
Indicates whether the parameter is an internal (I) or external (E)
parameter. T implies the user cannot change the value of the parameter.
while 'E' implies the user can change the value of the parameter.
Description of the basis for the default values the parameter assumes or
the equation which defines the parameter.
Units of the parameter.
List of equation numbers in Appendix A for equations that employ the
parameter.
Section 2.0 provides a brief overview of the IEUBK lead model. In particular, the
exposure, uptake, and biokinetic components of the model are described separately and
interactions between the components are defined. Following this overview, the exposure, uptake,
and biokinetic components of the model are discussed in detail in Sections 3.0, 4.0, and 5.0,
respectively, describing the scientific basis for the equation structure and default parameter values
in the IEUBK lead model.
2.0 MODEL OVERVIEW
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As indicated above, the IEUBK lead model relates lead concentrations in various
environmental media to the body burden of lead in children exposed to the environmental media.
Since a child's blood lead level is the most common biomarker of lead exposure employed in
practice, the IEUBK lead model emphasizes blood lead level in its output. Thus in simple terms,
the IEUBK lead model translates environmental lead concentrations into predicted blood lead
levels in children of different ages. In order to accomplish this, the IEUBK lead model has four
distinct functional components that work together in series. The four model components are:
! Exposure Component
! Uptake Component
! Biokinetic Component
! Probability Distribution Component
Figures 1 and 2 illustrate the biological and mathematical structures, respectively, of the
IEUBK lead model. The biological structure in Figure 1 places an emphasis on how lead can
move from the environment of a hypothetical child into the child's blood, while the mathematical
structure in Figure 2 emphasizes the parameters and calculations necessary to determine the
child's blood lead concentration. In both figures, the first three model components are clearly
delineated.
As indicated in Figure 1, the exposure component relates environmental lead concentrations
to the intake rate at which lead enters the child's body via the gastrointestinal (GI) tract and lungs.
The environmental media that act as lead sources for the child are air, which enters the body
through the lungs, and diet, dust, paint, soil, water, and other sources which enter the body
through the GI tract. As indicated in Figure 2, the exposure component converts media-specific
consumption rates (m3/day, g/day, or L/day) and media-specific lead concentrations (//g Pb/m3,
(j.g Pb/g, //g Pb/L), all of which are under the control of the user, to media specific lead intake
rates (//g Pb/day). The general equation relating the consumption rates and lead concentrations to
the lead intake rate is:
Lead Intake Rate = Media Lead Concentration * Media Intake Rate
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In this manner, the exposure component models determines how much lead enters the child's body
and captures that information in a set of media-specific lead intake rates.
As indicated in Figure 1, the uptake component relates lead intake into the lungs or GI tract
to the uptake of lead from the exposed membrane into the child's blood, for children at each age.
Lead that enters through the lungs is either absorbed into the blood plasma through the lungs,
transferred to the gastrointestinal tract through the mucociliary escalator, or eliminated from the
body via exhaled air. Very small particles (especially those 0.5 microns in diameter and smaller)
may move directly into the blood plasma or may be eliminated from the body via exhaled air.
Approximately 30-50% of particulate airborne lead is deposited in the deep parts of the adult
lung, where it is almost totally absorbed. The rate may vary, depending on factors such as particle
size and inhalation rate. The deposition rate of small particles in the child's lung may be 2-3 times
greater. The bulk of the lead in the body enters via the GI tract, either through ingestion or by
movement from the nose, throat or lung structures. Lead that enters the body via the GI tract is
either absorbed into the blood plasma or eliminated from the gut via the feces. As indicated in
Figure 2, the uptake component converts the media-specific lead intake rates produced by the
exposure component into media-specific lead uptake rates (//g/day) for the blood plasma.
The total lead uptake (//g/day) from the gastrointestinal tract is estimated as the sum of two
components, one passive (represented by a first order, linear relationship), the second active
(represented by a saturable, nonlinear relationship). These two terms are intended to represent
two different mechanisms of lead absorption, an approach that is in accord with limited available
data in humans and animals and also by analogy with what is known about calcium uptake from
the gut. First, the total lead "available" for gut uptake is defined as the sum, over all media, of the
medium intake rate times the estimated low dose fractional absorption for that medium.
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Plasma Extra-Cellular Fluid
0>
I
o
O
.o
o
in
Plasma Extra-Cellular Fluid
frabecular
Bone
g""^ - Environmental Media
l~~l - Body Compartments
Q - Elimination Pools of the Body
— - - Body Compartment or Elimination Pool Required in More Than One Component
FIGURE 1. Biological structure of the IEUBK Model for Lead in Children.
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Exposure Component
f Media-Specific j
/ Consumption Rates .f
\
1
f Media-Specific f
J Lead Concentration^r
1
< Media-Specific ^V
Lead Intake Rates^^
1
I
XMax Abs Coeff and^^
issive/Active Ratipx
Uptake Component
1
^r Media-Specific
S Lead Intake Rat
^^^^r
es/-
< Total Available ^S
Lead Intake Rate^^
/Child's Body /
Weight /
I
1
< Saturation
Factor
^
< Absorption ^^
Coefficients ^r
1
>
- Input Only
- Calculations and Input
- Calculations Required in More Than One Component
FIGURE 2. Mathematical structure of the IEUBK Model for Lead in Children.
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A passive absorption coefficient defines the dose-independent fraction of the available lead that
is absorbed by the passive absorption pathway, and allows calculation of the rate of absorption via
that pathway. The rate of absorption of the remaining available lead by the active pathway is
calculated using a non-linear relationship that allows for saturable absorption.
As indicated in Figure 1, the biokinetic component models the transfer of absorbed lead
between blood and other body tissues, or elimination of lead from the body via urine, feces, skin,
hair, and nails. The basic model that underlies the biokinetic component is a compartmental
model whose pools have physiological properties, not just kinetic properties. The compartmental
structure of the IEUBK Model was developed by identifying the anatomical components of the
body critical to lead uptake, storage, and elimination, and the routes or pathways between these
components. This compartmental scheme includes a central body compartment, six peripheral
body compartments, and three elimination pools. The blood plasma is combined with the body's
accessible extracellular fluid (ECF) to form the central plasma/ECF body compartment. Separate
body compartments are used to model the trabecular bone, cortical bone, red blood cells, kidney,
and liver. The cortical and trabecular bones can accumulate large quantities of lead, at least sixty
percent of the total body burden in children and over ninety percent of body burden in adults with
long exposure histories. Separate pools were used because of differences in cortical and
trabecular bone kinetics in adults. The kidney and liver are important target sites of toxicity and
some data are available from laboratory animal studies. Most of the lead in blood is in the red
blood cells, which is modelled as a peripheral compartment exchanging with the plasma
compartment. The remainder of the body tissues are included in the "other soft tissues" peripheral
body compartment. Three elimination pathways are included in the biokinetic model: pathways
from the central plasma/ECF compartment to the urinary pool, from the compartment for other
soft tissues to skin, hair, and nails, and from the liver to the feces. The biological basis for this
pathway is the excretion of bile by the liver into the GI tract where it is subject to the absorption
processes of the uptake component. As indicated in Figure 2, the biokinetic component converts
the total lead uptake rate produced by the uptake component into an input to the blood
plasma/ECF. Transfer coefficients are used to model movement of lead between internal
compartments and to the excretion pathway. These quantities are then combined with the total
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lead uptake rate to determine lead masses in each of the body compartments. The lead in the
plasma portion of the central plasma/ECF compartment is added to the lead in the red blood cells
to determine the blood lead concentration (PbB).
The transfer coefficients used in the IEUBK Model are based on available data, including
tissue concentrations in autopsy samples from human children (Barry, 1981); parameter estimates
from experimental studies in primates comparable in age and developmental stage to human
infants; and theoretical principles of allometric scaling that are widely applicable in biological
models (Mordenti, 1986; Chappell and Mordenti, 1991).
The transfer coefficients in the IEUBK model are not directly related to blood flows, an
approach that is used in many physiological based pharmacokinetic models. Where data to
estimate transfer coefficients was sparse, the sensitivity of model predictions to changes in
parameter values was examined. The model output was sensitive to the values of excretory
parameters, for which data in human children was very limited. Final values of these parameters
were selected with reference to comparison of model predictions to data from a community lead
study where both blood lead and environmental lead levels were measured.
The iterative nature of the calculations in the biokinetic component is illustrated in Figure 3.
The period of exposure, zero to 84 months, is divided into a number of equal time steps that are
set by the user within the range 15 minutes to one month long. During each iteration,
compartmental lead masses at the beginning of a time step are combined with the total lead
uptake, inter-compartmental transfers, and quantities of excretion during the time step to estimate
compartmental lead masses at the end of the time step. The compartmental lead transfer times
during the time step are key parameters in these calculations. The compartmental lead masses at
the end of the time step then become the compartmental lead masses at the beginning of the next
time step and the iterative process continues. As indicated in Figure 2, the iterative process is
initiated by determining the compartmental lead masses at birth from the maternal blood lead
concentration and data on the relative concentrations of lead in different tissues of stillborn
fetuses. The model calculates all of the compartmental contents from 0 to 84 months; it reports
blood lead concentrations from 6 to 84 months.
The probability distribution component of the model estimates a plausible distribution of
10
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blood lead concentrations centered on the geometric mean blood lead concentration for a
hypothetical child or population of children. This distribution can be displayed graphically, or
data can be loaded into a package for statistical analysis.
/ Total Lead Uptake \
\ During Time Step /
/Compartmental Leac
(TransferTimes During
\ Time Step
Compartmental Leak
( Masses at Beginning V
\ of Time Step Y
Compartmental Lead
Masses at End of
Time Step
FIGURE 3. Iterative procedure for determining Compartmental lead masses in biokinetic
component.
11
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3.0 EXPOSURE COMPONENT
The exposure component of the IEUBK model converts media-specific consumption rates
and media-specific lead concentrations, both of which are under the control of the user, to media-
specific lead intake rates. The equations that govern these model calculations are listed in Table
A-l of Appendix A. In these equations, the lead intake rates for air, diet, household dust,
alternate source dust, soil, water, and other ingested media are denoted by EXAIR(t),
INDIET(t), INDUST(t), INDUSTA(t), INSOIL(t), INWATER(t), and INOTHER(t),
respectively. The notation "(t)" following each variable name indicates that these lead intake rates
change with the age, t, of the child. All lead intake rates are in units of//g Pb/day. Once
calculated, the media-specific lead intake rates serve as input to the uptake component. In the
sections below, the calculations required to determine the lead intake rates are discussed by
media. All referenced equation numbers can be found in the second column of Table A-l of
Appendix A.
Note that the IEUBK lead model does not include exposure from direct ingestion of paint
chips because this exposure could not be adequately quantified, as discussed in Chapter 4 of the
Guidance Manual (U.S. Environmental Protection Agency, 1994). An indirect exposure pathway
in which lead-based paint contributes to dust lead exposure is included in the alternative dust
model discussed in Section 3.1.5. The IEUBK Model does allow users to insert their own
estimates of the daily intake rate of lead paint chips into the input parameter, INOTHER(t), which
is independent of all other inputs.
3.1 Exposure Equations
3.1.1 Air Lead Exposure Model
The air lead exposure model considers both indoor and outdoor air lead exposure for
determining the child's overall air lead exposure. The outdoor air lead concentration
(air_concentration(t)) is specified by the user. The indoor air lead concentration (IndoorConc(t))
is determined according to Equation E-l as a user-specified, constant percentage (indoorpercent)
of the outdoor air lead concentration. A time-weighted average air lead concentration (TWA(t))
12
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is determined according to Equation E-2 where the indoor and outdoor air lead concentrations are
weighted by the user-specified, age-dependent number of hours per day that a child spends
outdoors (time_out(t)). Finally, EXAIR(t) is calculated according to Equation E-3 as the product
of the time-weighted air lead concentration and a user-specified, age-dependent ventilation rate
(vent_rate(t)).
3.1.2 Dietary Lead Exposure Model
Dietary lead exposure is determined by one of two methods: (1) direct specification, or (2)
alternative diet model. Under direct specification, as indicated in Equation E-4a, INDIET(t) is set
equal to the a user-specified, age-dependent lead intake rate for diet (diet_intake(t)).
Under the alternative diet model, as indicated in Equation E-4b, INDIET(t) is calculated as
the summation of the lead intake rates for meat, vegetables, fruit and other sources. The first
three categories are sub-divided as follows.
Meat
non-game animal (InMeat(t))
game animal (InGame(t))
fish (InFish(t))
! Vegetables
canned (InCanVeg(t))
fresh (InFrVeg(t))
home-grown (InHomeVeg(t))
! Fruit
canned (InCanFruit(t))
fresh (InFrFruit(t))
home-grown (InHomeFruit(t))
These are combined in Equation E-4b. The other dietary sources included in InOtherDiet(t) are
dairy food, juice, nuts, beverages, pasta, bread, sauce, candy, and infant food and infant formula.
The terms on the right-hand side of Equation E-4b are defined in Equations E-5a through E-
13
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5i, with the exception of InOtherDiet(t)1, which can assume only default values. In these
equations:
! The model allows the user to vary local dietary factors that may influence
overall lead exposure.
! Specifically, the user may vary lead intake from home grown vegetables,
fruits, game animals and fish.
! The user specifies the fraction of total food category consumption
represented by the sources; the total quantity of food consumption from
each category (meat, vegetables, fruit) is held constant.
The approach outlined here allows the user to input the lead content of locally produced
foods, while still maintaining default assumptions about overall intake of lead from marketed
foods. When greater flexibility is needed than is afforded by this method, the user should develop
appropriate estimates for total dietary lead intake.
In Equations E-5a, through E-5e, the traditional supermarket portion of the dietary lead
intake rate is calculated as the sum of the products of each consumption fraction and the specific
lead intake for that category of food. The consumption fraction is calculated as a complement of
the user defined nonsupermarket fraction (1-user defined nonsupermarket fraction). In Equations
E-5f through E-5i, the lead intake rate is calculated as the product of the user-defined
nonsupermarket consumption fraction, and a consumption rate for that category of food.
3.1.3 Water Lead Exposure Model
Water lead exposure is determined by one of two methods: (1) direct specification, or (2) an
alternative water lead concentration model. Under direct specification, as indicated in Equation
E-6a, INWATER(t) is calculated as the product of a user-specified, age-dependent water
consumption rate (water_consumption(t)) and a user-specified, constant water lead concentration
1For the sake of simplification, the term InOtherDiet(t) is used in the text to represent components of the
diet other than meat, fruit, vegetables, fish, or game. These other dietary components are modelled as InDairy,
InJuice, InNuts, InBread, InPasta, InBeverage, InCandy, InSauce, InFormula, and Inlnfant and are not user-
selectable.
14
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(constant_water_conc).
Under the alternative water model, as indicated in Equation E-6b, INWATER(t) is
calculated as the product of the same user-specified, age-dependent water consumption rate
(water_consumption(t)) and a constant water lead concentration that is calculated as a weighted
average of user-specified, constant water lead concentrations from the first-draw on a home
faucet (FirstDrawConc), a flushed faucet at home (HomeFlushedConc), and a water fountain
outside the home (FountainConc). These concentrations are weighted by user-specified, constant
fractions of consumed water that are first-draw water (FirstDrawFraction), home flushed water
(HomeFlushFraction), and fountain water (FountainFraction). As indicated in Equation E-7,
HomeFlushedFraction is calculated by subtracting the other two fractions from one.
3.1.4 Soil Lead Exposure Model
As indicated in Equation E-8, INSOIL(t) is calculated using the user-specified soil lead
concentration (constant_soil_conc(t)), the user-accessible age-dependent soil and dust ingestion
rate (soil_ingest(t)), and a user-accessible constant fraction of soil and dust ingested that is soil
(0.01 x weight_soil). Soil lead concentration can be specified in an age-dependent manner; the
corresponding equations are not shown.
3.1.5 Dust Lead Exposure Model
Dust lead exposure is determined by one of two methods: (1) direct specification, or (2) an
alternative dust model. Under direct specification, as indicated in Equation E-9a and E-9b, the
baseline dust lead intake, INDUST(t), is calculated as the product of an age-dependent soil and
dust ingestion rate (soil_ingested(t)), the fraction of soil and dust ingestion that is in the form of
dust (1 - 0.01 x weight_soil), and a user-specified dust concentration (constant_dust_conc).
Age-dependent dust lead concentrations (user_dust_conc(t)) can be specified but are not shown
here. (When using the direct specification, the alternative source dust lead intake (INDUSTA(t),
is set to zero).
The alternative dust sources model, as indicated in Equations E-9c and E-9d, has two
alternative specifications:
15
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! The indoor dust lead concentration is calculated as a sum of contributions
from soil and air, either constant or age-dependent (not shown).
-OR-
! The indoor dust lead concentration is calculated as the sum of
contributions from several additional sources, plus the household
contribution estimated by one of the three approaches above. Only a
fraction of dust lead exposure is assumed to come from residential dust.
When data are available, the remainder is assumed to come from separately
estimated dust sources including:
Secondary exposure to leaded dust carried home from workplace
(OCCUP(t))
Leaded dust at school or pre-school (SCHOOL(t))
Leaded dust at other non-school daycare facilities (DAYCARE(t))
Leaded dust from secondary homes (e.g. grandparents)
(SECHOME(t))
Leaded dust from deteriorating interior paint (PAINT(t))
As indicated in Equation E-9c, INDUST(t) is the product of the age-dependent dust
ingestion rate (DustTotal(t)), an age-dependent indoor dust lead concentration (soil_indoor(t)),
and the fraction of dust exposure that is from residential dust (HouseFraction). As indicated in
Equation E-l 1, soil_ indoor(t) is calculated as a sum of contributions from soil and air. The
contribution from soil is the product of a user-specified, constant ratio of dust to soil lead
concentrations (0.01 x contrib_percent) and the user-specified, age-dependent soil lead
concentration (user_soil(t)). Similarly, the contribution from air is the product of a user-specified,
constant ratio of dust to air lead concentrations (multiply_factor) and the user-specified, (age-
dependent) outdoor air concentration (air_concentration(t)).
As indicated in Equation E-9.5, HouseFraction is determined by subtracting from one, the
total of the user-specified, constant fractions of dust ingested that come from the parent's
occupation (OccupFraction), school (SchoolFraction), daycare (DaycareFraction), secondary
homes (SecHomeFraction), and paint (PaintFraction). The sum of all source fractions entered
16
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cannot exceed 1.0. As indicated in Equation E-9d, INDUSTA(t) is the sum of the lead intake
rates from all five alternative sources where these individual lead intake rates are defined in
Equations E-12a through E-12e. In these equations, the lead intake rate is the product of the age-
dependent, dust ingestion rate (DustTotal(t)), the user-specified, constant fraction of dust
ingested that comes from that source (OccupFraction, SchoolFraction, DaycareFraction,
SecHomeFraction, or PaintFraction), and the user-specified, constant dust lead concentration for
dust from that source (OccupConc, SchoolConc, DaycareConc, SecHomeConc, or PaintConc).
3.2 Default Values for Exposure Parameters
For diet, water and dust exposure, the user may choose from two or more methods of
calculating exposure. Each of these exposure pathways has both concentration and intake
parameter default values built into the model that can be used to calculate default exposure levels.
Using the direct default specifications for lead exposure from diet, water, and dust, the resulting
total lead intake rate for each age interval are: 23.40 (0-11 mo), 34.89 (12-23 mo), 35.76 (24-35
mo), 35.57 (36-47 mo), 28.42 (48-59 mo), 26.95 60-71 mo), and 26.65 (72-84 mo) //g Pb/day.2
These are the total lead intake rates and are the summation of individual default rates for air, diet,
water, soil, and dust. The following sections detail default values for selected calculated
parameters associated each of these individual media. Default media concentration values,
particularly those for soil and dust, are included for purposes of illustration of model behavior;
assessment specific concentration data will be required for model applications.
3.2.1 Air Lead Parameter Values
The default values for indoorpercent, air_concentration(t), time_out(t), and vent_rate(t)
result in the following default values for calculated parameters:
! Indoor air concentration (IndoorConc(t)) of 0.03 //g/m3 for 0-84 months;
! Time weighted average air concentration (TWA(t) of 0.033, 0.036, 0.039,
Here and elsewhere it should be noted that the model calculates the uptake and biokinetic distribution of lead for
each iteration interval from 0 to 84 months. The model reports blood lead concentrations beginning with month six and accepts
user selectable options for lead exposure for 6 months to 84 months. For the period 0 to 5 months, the model does not permit
user selectable changes in exposure.
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0.042, 0.042, 0.042, and 0.042 //g/m3 for the seven age intervals,
respectively;
! Lead intake rates from air (EXAIR(t)) of 0.07, 0.11, 0.19, 0.21, 0.21, 0.29,
and 0.29 //g/day for the seven age intervals, respectively.
3.2.2 Dietary Lead Parameter Values
Under the default model specification, the lead intake rate from diet (INDIET(t)) assumes
default values of 5.53, 5.78, 6.49, 6.24, 6.01, 6.34, and 7.00 //g/day for the seven age intervals
(0-11, 12-23, 24-25, 36-47, 48-59, 60-71, and 72-84 months), respectively. Under the alternative
diet specification, the model assumes no consumption of game animal meat, fish, home-grown
vegetables, or home-grown fruit unless input by the user. Using default values for lead intake
from non-game animal meat, canned and fresh vegetables, canned and fresh fruit, and other
dietary sources, the lead intake rate from diet (INDIET(t)) assumes default values of 5.88, 5.92,
6.79, 6.57, 6.36, 6.75, and 7.48 //g/day for the seven age intervals, respectively.
3.2.3 Water Lead Parameter Values
Under the direct specification model, default values for water_consumption(t) and
constant_water_conc result in the lead intake rate from water (INWATER(t)) assuming default
values of 0.80, 2.00, 2.08, 2.12, 2.20, 2.32, and 2.36 //g/day for 0-11, 12-23, 24-25, 36-47, 48-
59, 60-71, and 72-84 months, respectively. Under the alternative water model, default values for
FirstDrawConc, HomeFlushedConc, FountainConc, FirstDrawFraction , and FountainFraction
result in a composite water lead concentration of 3.85 //g/L, which in turn with default values of
water_consumption(t) results in the lead intake rate from water (INWATER(t)) assuming default
values of 0.77, 1.92, 2.00, 2.04, 2.12, 2.23, and 2.27 //g/day for the seven age intervals.
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3.2.4 Soil Lead Parameter Values
Soil lead does not include the fraction of housedust that is derived from soil. This allows
the estimation of soil lead concentration directly from soil measurements. Default values for
constant_soil_conc(t), soil_ingest(t), and weight_soil result in the following default values for
calculated intakes:
! Soil (excluding house dust) ingestion rates of 38.25, 60.75, 60.75, 60.75,
45.00, 40.50, and 38.25 mg/day for the seven age intervals (6-11, 12-23,
24-25, 36-47, 48-59, 60-71, and 72-84 months), respectively;
! Lead intake rates from soil (INSOIL(t)) of 7.65, 12.15, 12.15, 12.15, 9.00,
8.10, and 7.65 //g/day for the seven age intervals.
3.2.5 Dust Lead Parameter Values
Under the default model specification, values for soil_ingest(t), percent_soil, and
user_dust_conc(t) result in the following default values for calculated parameters:
House dust ingestion rates (DustTotal(t)) of 46.75, 74.25, 74.25, 74.25,
55.00, 49.5, 46.75 mg/day for (6-11, 12-23, 24-25, 36-47, 48-59, 60-71,
and 72-84 months), respectively;
Lead intake rates from household dust (INDUST(t)) of 9.35, 14.85, 14.85,
14.85, 11.00, 9.90, and 9.35 //g/day for the seven age intervals;
Lead intake rate from alternative source dust (INDUSTA(t)) of zero
Mg/day.
Under the alternative dust model, default values for soiMngest(t), weight_soil,
contrib_percent, user_soil(t), multiply_factor, out_air_concentration(t), OccupFraction,
SchoolFraction, DaycareFraction, SecHomeFraction, and PaintFraction result in the following
default values for calculated parameters:
! House dust ingestion rates (dust_ingested(t)) of 46.75, 74.25, 74.25,
74.25, 55.00, 49.5, 46.75 mg/day for the seven age intervals, respectively;
these rates are the same as for the default model specification discussed
above;
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Indoor dust lead concentration (soil_indoor(t)) of 150 //g/g for all ages;
Lead intake rates from household dust (INDUST(t)) of 8.42, 13.37, 13.37,
13.37, 9.90, 8.91, and 8.42 //g/day;
Since the fraction of dust ingested that comes from each alternative dust
source has a default value of zero, the lead intake rate from alternative dust
sources (INDUSTA(t)) assumes a default value of zero //g/day.
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4.0 UPTAKE COMPONENT
4.1 Overview
The uptake component models the manner in which lead intake (lead that has entered the
child's body through ingestion or inhalation) is either transferred to the child's blood plasma or
eliminated from the body. Uptake is the quantity of lead absorbed per unit time from portals of
entry (gut, lung) into the systemic circulation of blood; that is, a rate at which lead from all media
is taken up into the blood. Since most lead is taken into a child's body through the gastrointestinal
(G.I.) tract, we will usually be discussing gut uptake. Only a fraction of the gut intake is actually
absorbed into systemic circulation during any period of time. That is, the gut uptake rate in jig
Pb/day is a fraction of the gut intake rate in jig Pb/day. This fraction is known as the absorption
fraction and usually provides the most convenient parameterization of the uptake process.
In the IEUBK model, all lead uptake from the gut is treated as the sum of saturable and
non-saturable components. This approach has been developed to address findings in studies in
humans and experimental animals as well as our current (limited) understanding of the
mechanisms of lead absorption in the gut. Human data suggest a curvilinear relationship between
lead intake and lead absorption (Sherlock and Quinn, 1986; Ryu et al., 1983). Studies in non-
human primates also suggest a nonlinear relationship between blood lead and lead intake (Mallon,
1981 and 1983). Additionally, in vivo experiments using the rat as a model show a concentration
dependence between lead intake and blood lead (Freeman et al., 1992). We have interpreted the
nonlinear relationship as representing lead absorption by at least two mechanisms (discussed
below), based on the biological plausibility of the assumption of nonlinear absorption from other
experimental studies (Aungst and Fung, 1981).
The physiological mechanisms that account for these observations of curvilinearity are not
completely established. The absorption nonlinearity, assumed in the IEUBK Model at higher
intake rates, is a plausible explanation for the nonlinear relationship observed between lead intake
and blood lead. The nonlinear relationship can be observed when the GI component of lead
intake exceeds 200 jig Pb/day for enough cases that the part of the relationship with lower
absorption (usually blood lead above 25 or 30 |ig/dL) can be clearly separated from the part of
21
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the relationship with higher absorption at gut lead intake less than about 100 to 200 jig Pb/day.
However, it should be noted that there are other nonlinear biokinetic factors that can influence the
observed relationship between lead intake and blood lead. In particular, the binding of lead in red
blood cells shows saturable behavior. The IEUBK model also incorporates a nonlinear
relationship for the binding of lead in blood. However, available data are not yet sufficient to
empirically resolve the contributions that these two nonlinear effects make to the observed
relationship between lead intake and blood lead. The mathematical approach employed here is
intended to allow plausible modeling of absorption phenomenon while important biochemical and
biophysical research into the exact mechanisms of lead absorption proceeds.
Experimental studies of soil lead absorption using appropriate animal models and feeding
patterns analogous to those of human children are being carried out by EPA. Preliminary results
(Weis et al., 1994) are consistent with the assumptions used in the IEUBK Model, but require
more complete analyses. The current parameters of the model are based on statistical analyses of
some experimentally measurable quantities in these studies and in older studies in human children
(Sherlock and Quinn, 1986).
In extending these results to a mixed multi-media gut intake scenario, we have assumed that
linear absorption at low intake rates is the best characterization for the available lead. When
doses are relatively low, human or experimental animal data may be applied to estimate the
fractional absorption of lead. A fractional absorption estimate implicitly combines the elements of
dissolution of solid particles such as particle size, chemical speciation, matrix embedding, and
stomach pH at different times after meals, for which we have no comprehensive quantitative
model at this time. While the characterization of gut uptake by a fractional absorption value is
conceptually straightforward, it may not adequately characterize the complexity of the absorption
processes. Absorption occurs in different segments of the gut, and lead concentrations in these
segments will depend on acidity, binding of lead to total gut contents, including minerals and
fibers, and other factors. We would not expect to have knowledge of all of these factors in any
real-world childhood lead exposure scenario.
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4.2 Parameterization of the Saturable and Non-Saturable Components of
Absorption
The intake rates are calculated in the exposure component of the IEUBK Model, using the
E-series equations in Table A-l, and are denoted EXAIR(t) for air lead, INDIET(t) for dietary
lead, INDUST(t) for dust lead3, INSOIL(t) for soil lead, INWATER(t) for lead in drinking water,
and INOTHER(t)4 for all other sources of ingested lead. Uptake rates are media-dependent and
age-dependent. The media specific uptake rates are designated UPAIR(t) for air lead, UPDIET(t)
for dietary lead, UPDUST(t) for dust lead, UPSOIL(t) for soil lead, UPWATER(t) for lead in
drinking water, and UPOTHER(t) for all other sources of ingested lead. The IEUBK Model is
parameterized such that, at typical blood lead levels of concern, media-specific absorption
fractions are constant. The net absorption fractions used to characterize the IEUBK Model are
denoted ABSF for dietary lead absorption, ABSD for dust lead absorption, ABSS for soil lead
absorption, ABSW for drinking water lead absorption, and ABSO for absorption of lead from
other intake sources. These parameters are accessible to the user. In the absence of saturation
effects, total lead absorption is equal to the sum of media specific absorption values where
absorption from each media is equal to the intake rate multiplied by the absorption fraction for
that media. This quantity is denoted AVINTAKE.
AVINTAKE = ABSD x INDUST(t)
+ ABSF x INDIET(t)
+ ABSO x INOTHER(t)
+ ABSS x INSOIL(t)
+ABSW x TNWATER(t)
As noted above, to more accurately model lead uptake at higher intake rates, the absorption
fractions must be modified so as to separate their non-saturable and saturable components. At
If the alternative dust intake options are used, then the alternative dust lead intake is denoted INDUST A(t) and the
uptake UPDUSTA(t), and these replace the standard INDUST(t) and UPDUST(t) values.
4 The contributors to INOTHER may include, for example, paint chips or medicines; however, the model user must
determine appropriate intake rates.
23
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doses where saturation of absorption is important, the actual uptake of lead will be less than
AVINTAKE(t). Lead uptake by the passive pathway is assumed to be linearly proportional to
intake at all dose levels. The user parameter PAF is the fraction of the total net absorption at low
intake rates that is attributable to non-saturable processes. Specifically, the lead uptake by the
passive pathway is equal to
PAF x AVINTAKE(t).
We have assumed that the fraction of absorbed lead intake that is absorbed by non-saturable
processes is the same for all media.
At low doses, the quantity of lead absorbed by the saturable pathway is:
(l-PAF) x AVINTAKE(t).
However, at higher doses, only a certain fraction of this amount will be absorbed. The equation
for a rectangular hyperbola (familiar from biochemistry as the functional form applied with
Michaelis Menton enzyme kinetics) is used to represent saturable pathway absorption. The key
parameter in this relationship is SATINTAKE(t), which represents the level of available intake
(AVINTAKE) at which the saturable pathway uptake reaches half of its maximum value. This
half-saturation parameter depends on the age t of the children. The user has access to the value of
SATINTAKE(t) at age t = 24 months, denoted SATINTAKE2, through the gut absorption
parameter menu in the Model. From SATINTAKE2, the model calculates SATINTAKE(t) for all
ages.
The fraction of potential saturable pathway uptake that is actually absorbed is given by:
11(1 + [AVINTAKE(t)/SATINTAKE(t)].
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Thus, the amount of lead that is absorbed by saturable processes is calculated as:
(l-PAF) x AVINTAKE(t)/[l+(AVINTAKE(t)/SATINTAKE(t)].5
Total lead uptake is given by the sum of the active and passive components of uptake.
Media specific uptake rates are calculated using the same proportionalities as total intake for
example, the non-saturable uptake component for soil is given by:
PAF x UPSOIL(t)
While the saturable uptake component for soil is:
(l-PAF) x UPSOIL(t)/[l+ (AVINTAKE(t)/SATINTAKE(t)].
Uptake rates for other media are calculated analogously, and the reader may verify that the sum of
media specific rates gives the values for total uptake shown above.
Figure 4 illustrates the functional relationships between intake of lead and the components
of lead uptake. The conceptual relationship between saturable and non-saturable pathways are
shown in Figure 5. The partitioning of gut lead uptake is shown in Table 3.
Note that with a different choice of constant parameters, this term may be rearranged as
(a*AVTNTAKE)/(b+AVTNTAKE), a form that may be more familiar to many readers.
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Total uptake
SATINTAKE * (1-PAF)
Nonsaturable
Saturable
Intake Available for Uptake (ug/day)
Where:
SATINTAKE=100
PAF = 20
Figure 4: The mathematical treatment of lead absorption in the IEUBK model comprised
of saturable and non-saturable components [figure not to scale].
Table 3. PARTITIONING OF TOTAL GUT LEAD INTAKE BY PROCESS.
FATE
Absorbed
Excreted
PROCESS
Non-saturable
Saturable absorbed
Non-available
Saturable non-absorbed
GUT INTAKE COMPONENT
PAF x AVINTAKE(t)
(1-PAF) x AVINTAKE(t)/
[l+AVINTAKE(t)/SATINTAKE(t)]
(1-ABSD) x INDUST(t) +
(1-ABSF) x INDIET(t) +
(1-ABSO) x INOTHER(t) +
(1-ABSS) x INSOIL(t) +
(1-ABSW) x INWATER(t)
(1-PAF) x AVINTAKE(t)2
/(AVINTAKE(t) + SATINTAKE(t))
26
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*
/
INDIET
ABSW* Ih
.'ABSS*;
•INSOIL
' ABSD* •
'INDUST-
ABSO* IN
WATER
\
•y
OTHER
Saturable'
Fraction '
Nonsaturable
Fraction
XX
Saturable
xx
**
^
Nonsaturable
Uptake
./'
Total
Gut
Uptake
Excretion of Unabsorbed Lead
INOTHE^f
Intake
Total
Available
Gut Uptake
Saturable &
Nonsaturable
Fractions of
Available
Uptake
Saturable &
Nonsaturable
Component of
Gut Uptake
Total
Gut
Uptake
Figure 5. Conceptual model of gastrointestinal lead absorption.
27
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4.3 Other Uptake Pathways
The multi-media nature of a child's lead exposure requires a detailed examination of the
mechanisms of absorption of lead through the portals of entry: skin, lungs, and GI tract. While
dermal absorption may be a significant route of entry for organolead compounds, such as
tetraethyl lead used as an additive to leaded gasoline, it is not considered a significant pathway for
inorganic lead and is not included in the IEUBK model.
The lung absorption model employed in the IEUBK Model is discussed in detail in the
OAQPS Staff Paper (U.S. Environmental Protection Agency, (1989a). This model assumes that
a fixed proportion of the lead taken into the lungs via inhaled air is transferred to the child's blood
plasma. Much of the lead that enters the lungs is probably removed by the action of the
mucociliary escalator and ultimately finds its way into the GI tract. Very small particles
(especially those 0.5 microns in diameter and smaller) may move directly into the blood plasma or
may be eliminated from the body via exhaled air. Lead that becomes entrained on the mucociliary
escalator and is subsequently swallowed is not modelled separately from the inhalation fraction.
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5.0 BIOKINETIC COMPONENT
The biokinetic component of the IEUBK model calculates age-dependent lead masses in
each of the body compartments (plasma-extra-cellular fluid, liver, kidney, trabecular bone, cortical
bone, and other soft tissue) based on the total lead uptake rate (UPTAKE(t)). The concentration
of lead in blood is then calculated by dividing mass of lead in the blood plasma and red blood cells
by the volume of blood. The equations that govern the biokinetic model calculations are listed in
Table A-3 of Appendix A. In this table there are equations for compartmental lead transfer times,
blood to plasma-ECF lead mass ratio, tissue to blood lead concentration ratios, fluid volumes and
organ weights, compartmental lead masses, blood lead concentration at birth, and blood lead
concentration. A description of the biokinetic parameters can be found in Table B-l. The
notation (t) indicates that the parameter value is adjusted for the child's age.
The calculations in the biokinetic model begin by determining the volumes and weights of
specific compartments in a child's body, as a function of age. Next, the transfer times of lead
between the compartments and through elimination pathways are estimated. Initial
compartmental lead masses and an initial blood lead level are calculated for a newborn child.
Then successive values are calculated for the compartmental lead masses and blood lead
concentration of a child at each iteration time. These calculations are performed for a child from
birth to age 84 months.
In developing estimates of parameter values, primary emphasis was placed on applying
information from studies with human children. When data for children were not available, data on
human adults were sought, with consideration for appropriate allometric scaling. Data from
primate studies were also helpful in defining plausible ranges of parameter values for human
children. However, baboon and monkey data were not used as the primary basis for any
parameters in the IEUBK Model. Where there was considerable uncertainty in parameter values
(specifically for excretory parameters), model predictions for a range of plausible parameter
values were compared to data from epidemiological studies of blood lead in children from
communities with measured environmental lead levels. The results of these comparisons were
used in the selection of specified parameter values within the varied ranges. The following steps
29
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were applied in estimation of specific parameter values:
1. Tissue/blood concentration ratios were established.
Tissue/blood concentrations were based primarily on autopsy samples from children
that were reported by Barry (1981). We assumed that near steady-state conditions
existed for most of these children corresponding to long periods of exposure to
environmental concentrations that were constant over time. For cortical bone/blood,
trabecular bone/blood, kidney/blood, liver/blood, and combined other soft
tissues/blood, tissue/blood concentrations were calculated using mean concentration
values, because individual data were not available.
2. The compartmental concentration ratio estimates were converted into the ratio of masses of
lead using compartmental size (mass or volume). These ratios were then used to relate
transfer times to and from model compartments.
A fundamental requirement for the IEUBK model is that a mass balance of lead be
maintained. When applied to the special case of near steady-state conditions, the mass
balance requirement implies that the ratio of the quantity of lead in a tissue to the
quantity of lead in the central plasma-ECF compartment equals the ratio of the transfer
time from tissue to the central compartment to the transfer time from central
compartment to tissue.
Concentration ratio data do not, by themselves, allow separate estimates of transfer
times into and out from compartments. Kinetic data to allow separate estimates of the
transfer in and out from specific compartments are scarce. Therefore, for most
compartments, the estimated ratio of transfer times is more strongly founded than the
individual transfer rates, and the exercise of judgment was necessary in assigning
specific values for transfer times from blood to the peripheral compartments.
30
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However, once the ratios of times were specified, the model predictions were found to
be quite insensitive to the specific values selected for these transfer times.
3. The relationship between blood and plasma was established, and the ratio of transfer times from
red blood cells to plasma and from plasma to red blood cells was estimated.
To estimate transfer times from red blood cells to plasma and from plasma to red
blood cells, adult data (deSilva, 1981a,b; Cavalieri et al., 1978a,b, 1981, 1984) were
applied, assuming that transfer times in adults and children are similar.
This assumption is consistent with general allometric considerations. However, there could
be biochemical differences between adults and children that could affect the partitioning of
lead between blood and urine.
To maintain mass balance in near steady-state conditions, the ratio of the quantity of
lead in the tissue to the quantity of lead in the central plasma-ECF compartment equals
the ratio of transfer time from tissue to the central compartment to transfer time from
central compartment to tissue. This relationship was inverted by fixing the ratio of
masses to correspond to the tissue/blood concentration ratios of Barry (1981), the
ratio of blood/plasma, and the weight of the tissues and volume of the plasma-ECF
pool. Data did not allow separate estimates of transfer times into and out of most
compartments. Rather, only the ratio of transfer times could be determined from data
for most compartments.
4. After these parameters were fixed, the additional modifying terms or urinary, fecal, and soft
tissue elimination times were considered.
Because of the long time needed to achieve steady-state in bone, i.e., the long transfer
time from bone to blood, the blood to bone transfer time was also considered as an
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adjusted parameter. Transfer coefficients for urinary excretion of lead by adults were
reviewed and used as a starting point for estimation of urinary excretion by children.
The ratio of endogenous fecal to urinary elimination was calculated based on statistical
reanalysis of data on children (Zeigler et al., 1978; Ryu et al., 1983), supported by information in
Alexander (1974). To determine reasonable bounds on parameters, data from adult studies
measuring relative amounts of lead eliminated by urinary, fecal, and other paths of excretion were
also examined (Rabinowitz et al., 1976). For each of the excretory terms (urinary, fecal, other
soft tissue elimination) as well as blood to bone transfer, (which, conceptually, may act similarly
to an excretory pathway in removing lead from blood), a grid of biologically plausible values was
constructed and an iterative optimization procedure established for comparing model predictions
to a data set from a field study that collected both detailed environmental data and blood data. In
this process, the model was run repeatedly in batch mode and the rate of observed to predicted
blood lead levels was examined. The bone parameters were adjusted first, followed by the urinary
elimination rate, the ratio of endogenous fecal to urinary elimination rates, and then other soft
tissue values. The elimination parameters were varied in this order because of the greater
certainly about the urinary rate and the virtual lack of information about other soft tissue routes of
elimination in children.
Using the results of these comparisons, values for the four parameters, within the varied
ranges, were established, with these parameter values, model predictions were consistent with the
geometric mean and blood lead distribution in the field study data. Test simulations were also
made with different hypothetical exposure scenarios and the bone to blood concentration ratio
from the simulation output was checked to insure that the values produced were concordant with
ratios based on data from Barry (1981).
Finally, model predictions were then compared with observed blood and environmental lead
data at a second field study. Further parameter adjustments were judged unnecessary. Other
specifications for the relative magnitudes of the three excretory pathways could produce
equivalent rates of total lead excretion and, thus, equivalent model blood lead predictions.
It is also important to note that the selected model parameters set excretory rates for the
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three pathways to levels that are at the high end of values deemed plausible. If changes were
made for the intake or absorption values used in the analysis of the community lead data, different
values for the excretory parameters may have been supported. As the excretory parameters have
substantial impact on model predictions and, as very little data for human children were available
to directly support the selection of these values, generation of better excretory data for human
children is a priority for further research.
The sections that follow provide descriptions of the calculations involved in the biokinetic
model. Since this model requires many equations, the descriptions are brief and are meant as a
general overview of the calculations. All referenced equation numbers can be found in the second
column of Table A-3 in Appendix A.
5.1 Basis for the Biokinetic Compartmental Structure
5.1.1 Postulates for the Compartmental Structure
The differential equations of the biokinetic model component are a consequence of the
Compartmental structure assumed for the model. Compartments in the model are identified as
specific physiological or anatomical compartments with the exception of a residual soft tissue
compartment designated as OTHER. The biokinetic components were chosen for several
reasons: the importance of some tissues as target sites of toxicity, such as liver or kidney; the
large potential lead burden of tissues , such as bone; the conventional definition of certain
compartments in many pharmacokinetic models; that availability of data describing the
concentrations of lead found in these tissues; and the need for a system that would require little
additional expansion for future applications. Those compartments that have not been
characterized are lumped together as other soft tissues. We chose to extend the Compartmental
structure of the biokinetic model for several purposes, looking ahead to the need for a system that
would require these additional components in future applications. The most important features
and assumptions include:
(1) Blood is divided into plasma and red blood cell compartments;
(2) The plasma compartment is extended to include the extracellular fluid that
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exchanges rapidly with plasma, but is not accessible in usual blood sampling
methods, and may account responsible for the volume of distribution of blood lead
being about 1.7 times larger than the blood volume; The larger volume of
distribution includes possible larger physical space as well as other factors such as
increases resulting from protein binding.
(3) Lead from entry portals in lung and gut is taken up directly into the plasma-
extracellular fluid pool, not into the red blood cells;
(4) The uptake of lead from the gut into the plasma-extracellular fluid pool is rate-
limited by the lead concentration in the gut, but does not depend on the plasma
lead concentration, so that uptake is independent of the internal biokinetics;
(5) The transfer of lead from plasma to red blood cells is partially limited by the finite
capacity of the red cells to bind and retain lead, so that the whole blood lead
concentration is not directly proportional to the lead uptake rate, especially at high
levels of exposure;
(6) Transfer times among compartments may be scaled for children of different ages
by means of body weight according to an allometric scaling that approximates
whole body surface area;
(7) Transfer between plasma and red cells shows little age dependence;
(8) The kidney should be used as a separate compartment because data on kidney lead
levels are available in both animal experiments and human autopsy data, because it
is an important target site of lead toxicity, and because predicted kidney lead
burdens may be of use in estimating the increased risk of hypertension or other
adverse renal effects of lead exposure;
(9) The liver should be used as a separate compartment because data on liver lead
levels are available in both animal experiments and human autopsy data, and
because the liver is a possible target site of lead toxicity at elevated exposure
levels;
(10) Separate compartments for cortical and trabecular bone were included, although
transfer times for younger children are the same in these two compartments of the
model. In older children large lead burdens in these tissues might reflect
differences in transfer times and potential ease of mobilization of lead burdens in
these tissues.
(11) Other soft tissue target sites of toxicity may be needed for future uses of the
IEUBK model, such as the bone marrow for hematopoietic toxicity, or certain
brain or central nervous system sites for neurotoxicity, these sites are biokinetically
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"small" but lexicologically significant.
5.1.2 Division of the Whole Blood Pool
It has been known for some time that red blood cells carry the majority of lead in blood.
Accordingly, a number of authors have inferred that it is necessary to subdivide the blood
compartment and model separately the lexicologically active fraction of the blood lead in the
plasma. References in Marcus (1985a,b) include McRoberts (1973), Baloh et al. (1974),
Cavalleri et al. (1978a,b), deSilva (1981a,b), Everson and Patterson (1980), and Manton and
Malloy (1983). Other studies on plasma lead include Chamberlain et al. (1978), Campbell et al.
(1984), Cavalleri et al. (1981, 1984), Cavalleri and Minola (1987), Manton and Cook (1984),
OTlaherty (1992), Ong et al. (1986), and Simons et al. (1991). An age-dependent model for lead
and other metals, using plasma as the central pool, was presented by Cristy et al. (1986), and
expanded by Leggett (1993). The use of the whole blood lead concentrations rather than the
plasma lead concentrations is traditional, based on the relative ease of accurate blood lead
measurement and the relative difficulty measuring plasma lead.
The earliest version of the IEUBK Model used the approach of Harley and Kneip (1985),
who assert that "While it is probably the plasma which provides the exchangeable fraction for the
various organs, since cells and plasma remain in a constant ratio, the blood is treated as a single
compartment since no benefit is obtained by using two compartments." However, in order to
better represent the biological system, the IEUBK Model now treats red blood cells as a
compartment separate from plasma. With the parameter values that are employed, the present
approach does imply that the plasma and red blood cell lead concentrations achieve near-
equilibrium level for most purposes.
The division of the whole blood pool into one or more plasma and erythrocyte pools in a
compartmental model is described by Cavalleri et al. (1981), Marcus (1985a,b), and OTlaherty
(1992). The plasma pool probably consists of both a filterable or diffusible component, and a
non-diffusible protein-bound component. Cavalleri et al. (1981) estimate about 4 jig Pb in the
plasma-diffusible compartment, about 45 jig Pb in the plasma protein-bound compartment, and
about 1850 jig Pb in the erythrocytes in the adult subjects in the Rabinowitz et al (1976) stable
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isotope studies. We have chosen to combine the two plasma compartments, which are probably
in a very rapid kinetic quasi-equilibrium. Attempts to model the kinetics of the plasma and
extracellular fluid pools separately (Marcus 1985a,b) were not very successful. More importantly,
we are not aware of any significant kinetic non-linearities for lead transfer between plasma
compartments or plasma-ECF fractions that would affect the interpretation of blood lead vs. lead
uptake relationships.
There is a large amount of conflicting literature on the quantitative relationship between
plasma lead concentration and either the whole blood lead concentration or the red blood cell lead
concentration. Some authors report that no predictive relationship is observed between plasma
lead concentration and blood lead concentration (Rosen et al. 1974) or a weak and statistically
non-significant relationship (Ong et al. 1986). However, most recent studies have found that
there is a statistically significant relationship, whether estimated from a linear statistical model
(Cavalleri et al. 1978a; DeSilva 1981a,b) or a non-linear statistical model (Manton and Cook
1984; Marcus 1985a). The non-linear models provide a far better fit to the data than do the linear
models.
The ratio of plasma lead concentration to blood lead concentration is roughly constant at
low concentrations (below 40-60 //g/dL) based on deSilva (1981a,b) as described and reanalyzed
in Marcus (1985c). The ratio is variously estimated as 0.014 (deSilva, 1981a,b) or 0.028
(Cavalleri et al., 1978a) in adults, compared to an estimate of 0.06 (Ong and Lee, 1980 a,b).
Concentrations are converted to mass by multiplying by compartmental volume. More recent
assessments (Diamond and O'Flaherty, 1992a,b) suggest a much lower value, in the range of 0.2
to 2 percent. However, it is likely that the regression slopes have been seriously attenuated by the
classic "error-in-variables" bias in least-squares regression models. This bias arises because the
blood lead concentration, which is the predictor variable, is measured with some analytical
uncertainty even if no systematic biases occur. It can be proven that the estimated regression
slope of plasma lead concentration vs blood lead concentration will be closer to 0 (on an average)
than the true value, and consequently the apparent value of the intercept will be higher than the
true value. We are not aware of any analyses in which the estimate has been adjusted for
measurement error bias. It is likely that the true value of the ratio of plasma lead concentration to
36
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blood lead concentration is larger than 2 percent in these studies.
The IEUBK model includes a parameter that places an upper limit on red-cell lead binding
capacity. In vivo and in vitro studies of blood lead kinetics and partitioning show evidence of
saturable binding of lead to red blood cells at relatively high lead concentrations for adults. In the
parameterization of this model, a high upper limit on binding is set, consistent with available
observations. Accordingly this phenomenon has little effect of predictions of children's blood lead
at normally anticipated levels of environmental exposure. However, as noted in the discussion of
lead uptake above, there are significant nonlinearities in the empirical relationship between lead
intake and observed blood lead. While this nonlinearity is currently attributed to saturation of
lead uptake from the gut, it is possible that nonlinear binding in red cells may also play a role in
explaining these observations.
It is known that lead is bound to two or more distinct fractions of the erythrocyte, as cited in
(Marcus 1985a): (Bruenger et al. 1973; Clarkson and Kench, 1958; Ong and Lee 1980c; Stover
1959). This is in part attributable to the presence of lead-binding proteins in different parts of the
erythrocyte (Raghavan and Gonick 1977; Raghavan et al. 1980, 1981; Gonick et al. 1981; Church
et al. 1991). While limited lead-binding capacity in the erythrocyte is known from in-vitro studies
(Barton 1989), it appears to be far more dependent on lead concentration in-vivo. The limited
lead-binding capacity of the erythrocyte appears to be highly related to the toxicity of lead
(Raghavan and Gonick 1977; Marcus and Schwartz 1987; Mushak 1991; Church et al. 1991).
Workers and children in which lead was largely bound to the erythrocytes showed less frank
toxicity and lower levels of biomarkers such as erythrocyte protoporphyrin.
An analysis by Marcus and Schwartz (1987) suggests that the blood lead concentrations at
which one could infer significant saturation of red-cell lead binding were relatively low in children
with iron deficiency (about 26 |ig/dL), and higher ( > 33 |ig/dL) in iron-replete or iron-abundant
children. It is not clear whether differences in lead-binding among erythrocyte fractions are due to
genetic polymorphism or to environmental differences such as vitamin and trace mineral
nutritional status, nor do we understand the extent to which these lead-binding proteins may be
induced by elevated lead exposure.
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5.1.3 Plasma-Extracellular Fluid Compartment
Stable lead isotope studies allow estimation of the total blood lead volume of distribution
(Rabinowitz et al. 1976). This volume is much larger than the volume of blood, averaging about
9.7 kg in a sample of five adult men whose average estimated blood volume was about 5.7 kg.
The average ratio of volume of distribution to blood lead was about 1.7. The average residence
time in blood was about 30 days. This suggests that the extra volume of distribution was due at
least in part to distribution in a larger fluid volume. It is plausible to assign this to lead in
extracellular fluids (denoted ECF) that exchange rapidly with plasma lead at the time scales of
interest, a few hours to a day, but are not accessible with ordinary blood sampling intervals of six
weeks or more. Support for the existence of an ECF pool that is kinetically indistinguishable from
plasma at intervals longer than a few minutes is provided by several authors. Chamberlain et al.
(1978), using lead radioisotopes, have argued for rapid transfer of lead into some readily
accessible ECF. The existence of an intermediate ECF pool is sketched by Cavalleri et al. (1981),
and is hinted at by Mallon (1983) and by Harley and Kneip (1985) in their discussion of a delay
compartment they call "ECS [extracellular space]- gut".
Therefore, in the IEUBK Model, we have chosen to combine the plasma pool with the
kinetically similar ECF as the central compartment.
5.2 Compartmental Specification for Model
The biokinetic component of the IEUBK model is structured as a compartmental model
with transfer times between compartments as basic model building elements. The compartments
are:
! Plasma-extracellular fluid (ECF)
! Red blood cells
! Liver
! Kidney
! Trabecular (spongy) bone
! Cortical (compact) bone
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! Other soft tissues
The whole blood consists of the plasma portion of the plasma/ECF pool along with the red
blood cells. The IEUBK model assumes that lead is transported between the central plasma-ECF
compartment and most of the other compartments by a first-order kinetic process whose rate
coefficients are independent of the compartment lead concentrations. The only rate coefficient
that is concentration-dependent is the plasma/ECF to red blood cell coefficient, which assumes
that the lead holding capacity of the red blood cells is saturable. Here, a maximum lead holding
capacity of 1200 |ig/dL is assumed for the red blood cells, based on Marcus (1993) reanalysis of
data from Mallon (1983).
The above assumptions concerning the model structure and the nature of the kinetic transfer
of lead between compartments result in the biokinetic component of the IEUBK model being
governed by Equations B-6a through B-6i. This set of first-order differential equations governs
the age-dependent accumulation of lead masses in the various body compartments. The basic
tenet underlying the formulation of the differential equations is mass-balance.
5.2.1 Fluid Volumes and Organ Weights
As mentioned earlier in this document, many of the biokinetic calculations require body fluid
volumes and organ weights as a function of the age of the child. The growth equations were
fitted using a double logistic model (El Lozy, 1978, Karlberg, 1987), where the data sets for
organ volume or weight were composites of childhood growth data from several handbooks
(Altman and Ditmer, 1973; Spector, 1956; Silve et al., 1987). The fluid volumes calculated in
Equations B-5a through B-5d are for blood (VOLBLOOD(t)), red blood cells (VOLRBC(t)),
plasma (VOLPLASM(t)), and ECF (VOLECF(t)). All fluid volumes are in deciliters (dL). The
weights calculated in Equations B-5e through B-5m are of the child's extra-cellular fluid
(WTECF(t)), body (WTBODY(t)), bone (WTBONE(t)), trabecular bone (WTTRAB(t)), cortical
bone (WTCORT(t)), kidney (WTKIDNEY(t)), liver (WTLIVER(t)), other soft tissue
(WTOTHER(t)), and blood (WTBLOOD(t)). All weights are in kilograms (kg).
As indicated in Equation B-5d, the ECF volume is assumed to be 73% of the blood volume
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based on Rabinowitz et al. (1976). This is the difference between the volume of distribution and
the blood volume, which is assumed to be an actual physical volume. Other interpretations are
possible. Rabinowitz measured the volumes in adults. These were proportionally adjusted on an
age-relative basis for use in the model. Equations B-5e through B-51 are for organ weights and
body weight. The divisor of 10 in Equation B-5e and B-5m converts deciliters of blood to liters
of blood. The density of the ECF is assumed to be similar to water, one kg/L.
As indicated in Equation B-5g, for a child older than 12 months, WTBONE(t) is assumed to
be a linear function of age. The slope and intercept parameters were estimated by fitting a simple
linear regression model to data from Harley and Kneip (1985). Since little bone information was
available for children less than one year of age, the weight of the bone is assumed to be a constant
percentage of the weight of the body up to one year of age. As indicated in Equations B-5h and
B-5i, trabecular and cortical bone are assumed to account for 20% and 80%, respectively, of the
total bone weight (Leggett et al., 1982). As indicated in Equation B-5m, the density of blood is
assumed to be 1.056 kg/L. Finally, as indicated in Equation B-51, the weight of the other soft
tissues is determined by subtracting the weight of all other body compartments from the weight of
the body.
5.2.2 Compartmental Lead Transfer Times
The biokinetic model determines the compartmental lead transfer times as a function of
tissue to blood lead concentration ratios. The ratios of lead concentration in the kidney
(CRKIDBL(t)), liver (CRLIVBL(t)), bone (CRBONEBL(t)), and other soft tissue
(CROTHBL(t)) (equations B-4a to 4d) to blood concentration are calculated based solely on the
age of the child. The ratio of the lead mass in blood to the lead mass in plasma-ECF (RATBLPL)
is assigned a value of 100 (equation B-3).
The compartmental lead transfer time equations (Equations B-l, B-2) model the movement
of lead between the plasma-ECF and the red blood cells, the liver, the kidney, bone (trabecular
and cortical), and other soft tissue, and the elimination pathways of skin, hair, and feces (See
Figure 1). The rates at which the lead moves between the compartments are based on
WTBODY(t) (equation B-5f), WTKIDNEY(t) (B-5j), WTLIVER(t)(B-5k), WTBONE(t)(B-5g),
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WTTRAB(t)(B-5i), WTCORT(t)(B-5h), WTOTHER(t)(B-51), VOLBLOOD(t)(B-5a),
CRKIDBL(t)(B-2h), CRLIVBL(t)(B-2e, B-2f), CRBONEBL(t)(B-lh), CROTHBL(t)(B-2n, B-
2o), and RATBLPL(B-3).
First, the lead transfer times (Equations B-l, B-2) from blood to urine (TBLUR(t))(B-5c),
the liver (TBLLIV(t))(B-5b), the kidney (TBLKID(t))(B-5d), bone (TBLBONE(t))(B-5e), and
other soft tissues (TBLOTH(t))(B-5c) are estimated. The transfer times are allometrically scaled
by the ratio of WTBODY(t)(B-5f) to the weight of a child at 24 months (12.3 kg) raised to the
1/3 power. That is, multiplying the transfer times TBLUR(24), TBLLIV(24), TBLKID(24),
TBLBONE(24), and TBLOTH(24) by the 1/3 power of the ratio of WTBODY(t) to
WTBODY(24),
WTBODY(t)
0.33
, yields TBLUR(t), TBLLIV(t), TBLKID(t), TBLBONE(t),
WTBODY(24)
and TBLOTH(t), respectively. The 1/3 power scaling exponent for transfer times (-1/3 power for
transfer rates) corresponds to surface area scaling for growing children. That is, the surface area
of the organ increased in proportion to the 2/3 power of child's increase in weight, and this
increase in weight is a function of the child's age. For some applications, the empirical value of
0.26 fits better than 0.33 (Mordenti, 1986), but the difference is numerically unimportant in this
application because the child grows only from 3.4 kg to 20 kg in this age range. In earlier
versions of the model, scaling was based on organ weight or volume of fluid pool. For this
version, all scaling is based on body weight to the 1/3 power, which is roughly the equivalent of
body surface area scaling rather than organ surface area scaling. This simpler approach was
adopted because of the uncertainties about other developmental changes in tissues that might
affect age-dependent biokinetics, so that the more complicated earlier scaling approximation was
not justified at this time.
Next, the lead transfer time from blood through the bile duct to feces (TBLFEC(t)) is the
product of TBLUR(t) and the ratio of the urinary lead elimination rate to the endogenous fecal
lead elimination rate (i.e., the ratio of endogenous fecal lead transfer time to urinary transfer time,
denoted RATFECUR). TBLOUT(t), the lead transfer time from blood to the elimination pool via
the soft tissue is TBLFEC(t) times the ratio of the endogenous fecal lead elimination rate to the
elimination rate via soft tissue (RATOUTFEC). The lead transfer time from bone to blood
(TBONEBL(t)) is the product of CRBONEBL(t), TBLBONE(t), and the ratio of the weight of
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the bone (WTTRAB(t) plus WTCORT(t)) to VOLBLOOD(t) divided by 10.
At low concentrations when the red blood cell is nearly unsaturated, the ratio of lead mass in
blood to lead mass in plasma-ECF (RATBLPL) is set to 100 (Equation B-3). The plasma-ECF to
red blood cell lead transfer time (TPLRBC) is directly assigned a nominal value of 0.1 days. This
value was chosen from a plausible range of values (0.02 to 0.25) based on several studies that
examined the fate of injected, ingested, or inhaled lead over very short time intervals (Hursh and
Suomela, 1968, Chamberlain et al., 1978, deSilva, 1981a,b, Campbell et al., 1984). The selection
of 0.1 days represents our best judgment on the appropriate time scales for the composite process
of the transfer of lead through the red blood cell membrane to the various lead-binding
components of the red blood cell. An adjustment to the transfer time from plasma to red blood
cells must then be made in the general case where the red blood cell is partially saturated
(TBLRBC2). Our model assumption is that the transfer time from plasma to red blood cells
increases with increasing saturation (Equation B-2.5). Transfer between plasma and red blood
cells is assumed to show little age dependence apart from dependence on concentration.
Fixing the value of RATBLPL also affects the relationship of TBLUR to TPLUR and that of
TBLBONE to TPLBONE. TRBCPL, the red blood cell to plasma-ECF lead transfer time, is the
product of TPLRBC and RATBLPL minus a constant. The transfer of lead from plasma to red
blood cells is partially limited by the finite capacity of the red cells to bind and retain lead. The
whole blood lead concentration is therefore not directly proportional to lead uptake rates,
especially at high levels of exposure. At high levels of exposure, the plasma lead concentration
will increase in proportion to the uptake rate, but red blood cells that are partially saturated will
increase with increasing uptake much more slowly, eventually approaching a maximum
concentration, CONRBC. Therefore, the whole blood (weighted sum of lead concentration in
plasma and lead concentration in red blood cells) will contain an increasingly larger fraction of the
lead in plasma as uptake rates increase. The calculated blood lead concentration shows little
dependence on TPLRBC for a wide range of values, once RATBLPL is specified (Equation B-
2b).
The lead transfer times from plasma to urine (TPLUR(t)), the liver (TPLLIV(t)), the kidney
(TPLKID(t)), and other soft tissue (TPLOTH(t)) are the ratios of TBLUR(t), TBLLIV(t),
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TBLKID(t), and TBLOTH(t) to RATBLPL, respectively. The transfer time from blood to urine
(TBLUR, days) is estimated by the blood lead mass (jig) divided by the rate (jig/day) at which
lead is eliminated from the blood through the urine. A literature review revealed 17 adult studies
for evaluating TBLUR (See Table B-l). The adult value of TBLUR was allometrically scaled to
the range 0 to 84 months based on the proportionality between the blood volume (VOLBLOOD,
dL) and the glomerular filtration rate (GFR, dL/day) for that age group. No direct data on the
ratio VOLBLOOD/GFR was available; therefore, since GFR is proportional to body surface area
for infants (10-20 weeks) and toddlers (24 months) (West, 1948) and for ages > 24 months (Weil,
1955), scaling by surface area is equivalent to scaling by GFR.
TLIVFEC(t), TKIDPL(t), and TOTHOUT(t), the lead transfer times from the liver to the
feces, the kidney to the plasma-ECF, and the other soft tissue to the elimination pool are the
products of the concentration ratios of lead in the tissues to blood (CRLIVBL(t), CRKIDBL(t),
and CROTFffiL(t)), the transfer times from blood to the tissue of elimination pool (TBLFEC(t),
TBLKID(t), and TBLOUT(t)), and a ratio of the weight of the tissue (WTLIVER(t),
WTKIDNEY(t), and WTOTHER(t)) to VOLBLOOD(t). The lead transfer times from the liver
to the plasma-ECF (TLIVPL(t)) and the other soft tissue to the plasma-ECF (TOTHPL(t)) are
similarly calculated. The distinction is the transfer time term. TLIVPL(t) replaces TBLFEC(t) by
a term involving TBLLIV(t) and TBLFEC(t), while TOTHPL(t) replaces TBLOUT(t) with a term
involving TBLOTH(t) and TBLOUT(t).
While we recognize the complexity of bone kinetics, the Technical Review Workgroup for
Lead concluded that a simplified approximation of bone lead kinetics would be adequate for
modeling the relationship between bone and blood in young children. The primary purpose of the
cortical and trabecular compartments in the IEUBK model is to provide the potential for long-
term retention and storage of lead as an endogenous or internal source. Several more
complicated models for bone lead kinetics have been developed (Marcus, 1985c,d; O'Flaherty,
1992; Leggett, 1993).
The kinetics of lead in bone can be extremely complicated. Bone is conventionally divided into two ty
cortical (compact or dense bone material) and trabecular (cancellous or spongy bone, often plate-like structur
Andriot and O'Flaherty (1993) have shown that bulk physical properties of cortical and trabecular bone in yo
43
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mammals may be very similar. In view of the similar concentration ratios between lead in different bones an
blood lead that may be calculated for children based on autopsy data (Barry 1981), we concluded that the bio
properties of cortical and trabecular bone may also be rather similar for children less than 84 months.
In a detailed examination, skeletal tissue cannot be regarded as a single well-mixed fluid-like compartm
Various models for lead transport in bone have been proposed, including non-first-order spatial diffusion mo
(Marcus 1983, 1985c), first-order models with a series of radial concentric rings (O'Flaherty 1992) based on
models for other bone-seeking elements (Marshall and Onckelinx 1968; Marshall 1969), and as a series of bo
compartments that may be characterized as surface, shallow, or deep slow-turnover pools (Cristy 1986; Legg
1993). Marcus (1985c,d) showed that a compartmental approximation to bone lead diffusion was possible, w
time scale for the longest-term retention depended on diffusion parameters. The most appropriate compartm
model depends on the intended purpose of the model. The IEUBK model uses a single compartment for eac
cortical and trabecular bone tissue, with a long retention time.
Isotopic tracer studies in adults do not usually allow detection of longer-lived plasma lead kinetic comp
For example, in a three compartment first-order pharmacokinetic system, the elimination of lead from a sing
intravenous injection can be described as the sum of three exponential terms (Gibaldi, 1982). In the central
compartment (either plasma or whole blood, depending on the model) the lead concentration can be written a
of three exponentially decreasing functions of time. The "fast" component goes to zero very quickly with in
time from injection, and the "slow" component goes to zero only over a relatively long period of time. The I
Model was designed for application to exposure scenarios in which there are long periods of relatively steady
exposure, not to acute or relatively rapid sub-chronic exposure scenarios, so that only the slowest transfer com
affect kinetics on the time scales of interest. In essence, the equivalent model is plasma exchange with the lo
lead-binding constituents of the skeleton.
Both the lead transfer times from the trabecular bone and cortical bone to the plasma-ECF
(TTRABPL(t), TCORTPL(t)), are assigned TBONEBL(t). TPLTRAB(t) and TPLCORT(t), the
lead transfer times from the plasma-ECF to the trabecular and cortical bones are calculated as the
ratio of TBLBONE(t) to a percentage of RATBLPL. TPLTRAB(t) uses 20% of RATBLPL in
the denominator, while TPLCORT(t) uses 80% of RATBLPL.
Finally, TPLRBC2(t), the scaled lead transfer time from the plasma-ECF to the red blood
cells, is calculated as the ratio of TPLRBC to a term involving MRBC, VOLRBC, and the
maximum lead concentration capacity of red blood cells (CONRBC). CONRBC is assigned a
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value of 1,200 |ig/dL, based on estimates for adults (Marcus, 1985a), and infant baboons using
data in Mallon (1983).
5.2.3 Tissue Lead Masses at Birth
The iterative nature of the biokinetic solution algorithm requires that compartmental lead
masses be determined for a newborn child to begin the solution process. As indicated in Equation
B-7a, the blood lead concentration of a newborn child (PBBLDO) is assumed to be 85% of the
user-specified mother's blood lead concentration (PBBLDMAT). This relationship is discussed in
U.S. Environmental Protection Agency, (1989a, pp.C-15 to C-18) and is based on data from the
sources referred to in that document. Bioconcentration ratios in newborn children, using data in
Barry (1981) were used to calculate tissue lead burdens at birth.
5.2.4 Compartmental Lead Masses and Blood Lead Concentration
The differential equations corresponding to the compartmental structure discussed in
Section 5.1.1 represent the continuous lead kinetics in a child's body. From a computational
viewpoint, however, the change in time does not occur continuously, but in discrete timesteps.
Therefore, for the purpose of calculations, the differential equations labeled Equations B-6a
through B-6i are represented by difference equations labeled Equations B-6.5a through B-6.5L
For instance, the differential Equation B-6d
dMRBC(t) g MPLECF(t) gMRBC(t)
dt TPLRBC2(t) TRBCPL
is represented by the difference Equation B-6.5d
MRBC(t) -QV[RBC(t -DrimeStep) _g MPLECF(t) gMRBC(t)
TimeStep TPLRBC2(t) TRBCPL'
The backward Euler solution algorithm solves the difference equations for the compartmental lead
masses at the end of the iteration time "t". These compartmental lead masses are then used to
determine the child's blood lead concentration at time "t". Details of the difference equations and
45
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the solution algorithm are provided below.
The difference equations are structured to represent the lead masses, transfer rates, and
elimination rates at the beginning and end of a time interval. The argument "t-TimeStep" denotes
lead masses and transfer rates at the beginning of the time interval, while the argument "t"
represents these quantities at the end of the interval. The length of the interval is denoted by the
user-specified variable, TimeStep. The backward Euler solution algorithm solves these difference
equations so that the child's compartmental lead masses and blood lead concentration at the end of
the iteration may be determined.
The backward Euler solution algorithm is a stable, time-efficient numerical algorithm. The
stability of the algorithm allows larger timesteps to be employed, thus reducing the required
computational time. The basic premise of the solution algorithm is that the increase in a
compartmental lead mass over an interval divided by the length of the interval is equal to the total
lead inflow rate minus the total lead outflow rate at the end of the interval. The solution to the
difference equations over a specified interval gives the compartmental lead masses at the end of
the interval as a function of the inflow and outflow rates at the end of the interval. Equating the
unknown changes in the compartmental lead mass over the interval to the difference between the
unknown lead inflow and outflow rates at the end of the interval yields a solution. That is, the
equation for the compartmental lead masses at the end of the interval can be solved in terms of
the compartmental lead masses at the beginning of the interval. The equations employed by the
backward Euler solution algorithm are presented as Equations B-9a through B-9i.
The compartmental lead masses for a newborn child discussed in Section 5.2.3
(MPLECF(O), MRBC(O), MPLASM(O), MCORT(O), MKIDNEY(O), MLIVER(O),
MOTHER(O), and MTRAB(O)) are used as initial values to begin the iterative biokinetic solution
algorithm. Given these parameters, the lead masses for the red blood cells (MRBC(t)), liver
(MLIVER(t)), kidney (MKIDNEY(t)), trabecular and cortical bone (MTRAB(t), MCORT(t)),
plasma-ECF (MPLASM(t)), and other soft tissue (MOTHER(t)) are calculated. Each of these
parameters are calculated at each iteration through age 84 months. As indicated in Equations B-
lOa and B-lOb, the child's blood lead concentration (PBBLD(t)) is calculated as an average
monthly value over the number of time intervals in the month.
6.0 PROBABILITY DISTRIBUTION COMPONENT
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The fourth component of the IEUBK model estimates, for a hypothetical child or population
of children, a plausible distribution of blood lead concentrations centered on the geometric mean
blood lead concentration predicted by the model from available information about children's
exposure to lead. From this distribution, the model calculates the probability that children's blood
lead concentrations will exceed the user-selected level of concern.
Risk estimation and plotting of probability distributions requires the selection of two
parameters, the blood lead level of concern or cutoff level and the Geometric Standard Deviation
(GSD). A value of 10 //g/dL is generally used as the blood lead level of concern, but other values
can be selected by the user.
The GSD is a measure of the relative variability in the blood lead of a child of a specified
age, or of children from a hypothetical population, whose lead exposures in a specified dwelling
are known. Many factors can cause children in environments with similar environmental lead
concentrations to have different blood lead concentrations. These include biological and
behavioral variability, measurement variability from repeat sampling, sample location variability,
and analytical error. In the model, the GSD is intended to reflect only individual blood lead
variability, not variability in blood lead concentrations where different individuals are exposed to
substantially different media concentrations of lead.
The determination of the GSD and its use in risk estimation are discussed in detail in the
Guidance Manual. The Guidance Manual describes the selection of the GSD value of 1.6, based
on calculations of GSDs from a number of specific sites. The manual emphasizes that the GSD
values should be similar at all sites and site-specific values should not be needed unless there are
great differences in child behavior and lead biokinetics among different sites. It also describes
how to estimate a site-specific, inter-individual GSD when necessary.
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7.0 USER CONTROL WITHIN THE IEUBK MODEL
The purpose of this section is to explicitly outline the choices a user of the IEUBK lead
model may make in estimating a child's blood lead concentration. Throughout Sections 3 through
5, references have been made to "user- specified" parameters or decisions. Two flow-charts are
provided to illustrate where the user-specified parameters or decisions occur and exactly which
parameters are affected. Parameter names are listed in each flow-chart. Table B-l provides an
index of all the parameters a user may access.
Figure 6 describes the overall structure of the IEUBK lead model emphasizing the decisions
and input parameters a user may control. From the Main Menu and the Parameter Entry
Submenu, the user may make several decisions on the sources of lead intake. These decisions and
the associated user specified parameters are shown in Figure 6. Turning to Figure 7, the user may
provide the outdoor air lead concentration (out_air_concentration), the percentage of outdoor air
lead that becomes indoor air lead (indoorpercent), the time a child spends outdoors (time_out(t)),
and the ventilation rate for a child (vent_rate(t)).
The diet model component requires the user to decide if the dietary lead intake should be
calculated from individual dietary sources. The user may choose to enter the dietary lead intake
directly (user_diet_intake(t)). Otherwise, individual sources of dietary lead are considered. The
user may enter the lead concentration for fish (UserFishConc), game animal meat
(UserGameConc), home grown fruits (UserFruitConc), and home grown vegetables
(UserVegConc) and the fraction of meat consumed as fish or game animal meat
(userFishFraction, userGameFraction), fruit consumed as home grown fruit (userFruitFraction),
and vegetables consumed as home grown vegetables (userVegFraction).
For the water lead model, the user may first enter the child's water consumption
(water_consumption(t)). Next, the user decides which of the two model options to use to
determine the water lead intake. Either the user can assume a constant water lead concentration,
by entering values for constant_water_conc, or the user may calculate the water lead
concentration by considering several sources of water. If several sources of water are to be
considered, the user would enter the fraction of total water consumed as first draw water
(FirstDrawFraction) and fountain water (FountainFraction) with the remainder being the amount
47
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of water consumed as HomeFlushed. The lead concentration in first draw water
(FirstDrawConc), fountain water (FountainConc), and a flushed faucet at home
(HomeFlushedConc) are also entered.
In the soil and dust lead model option, the user may first enter the lead concentration in soil
(soil_concentration(t)). The user may then decide if the household dust lead concentration is to
be calculated. The user may enter the indoor household dust lead concentration
(user_dust_conc(t)) directly. This choice is used when household dust is a measured source of
dust exposure for the child.
If the user chooses to calculate the dust lead concentration, then the user may enter the
percentage of soil lead concentration that characterizes the soil contribution to indoor household
48
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I
User-Specified Decisions and Media-Specific
Consumption and Lead Concentration Parameters
1 [ Diet ] [ Dust/Soil ] [ Water ]
ExposureComponent
'Media-Specific Lead Intake:^
EXAIR(t)
INDIET(t)
INDUST(t)
INDUSTA(t)
INSOIL(t)
INWATER(t)
I
User-Specified Media-Specific
Lead Absorption Parameters/
AIR: air_absorb((t)
DIET: ABSF
DUST: ABSD
SOIL: ABSS
WATER: ABSW
OTHER: flBSO
Uptake Component
Total Lead Uptake:
Uptake(t)
User-Specified Biokinetic
Model Parameters:
PBBLDMAT
TimeStep
Biokinetic Component
Blood Lead Concentration:
PBBLD(t)
ion: y^
Figure 6. Structure of the IEUBK model with emphasis on the user control of input
parameters and decisions.
49
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Air: Default Model Only
out_air_concentration(t)
time_out(t)
indoor percent
vent_rate(t)
Diet:
>^lter
\ Mo
X^ '
1
nate>
del y
? /
No
t
w Yes
^~l
UserFruitConc
userFruitFraction
UserFishConc
userFishFraction
UserVegConc
userVegFraction
UserGameConc
userGameFraction
user_diet_intake(t) 1
Water:
|water_consumption(t) |
Yes
No
FirstDrawFraction
FirstDrawConc
HomeFlushedConc
FountainFraction
FountainConc
Dust/Soil:
constant_water_conc|
soil_concentration(t)
Calculate
Indoor Househol
Dust Lead
one.
ConcRatio_dust_soil
ConcRatio dust air
user_dust_conc(t)
Alternate
Dust Lead
Source
OccupConc
OccupFraction
SchoolConc
SchoolFraction
DayCareConc
DayCareFraction
SecHomeConc
SecHomeFraction
PaintConc
PaintFraction
percent_soil
soil&dust_ingested(t)
Figure 7. User specified decisions and parameters that determine the media-specific
consumption and lead concentration parameters.
50
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dust lead (contrib_percent); the user may also enter a factor that relates the air lead contribution
to house dust lead concentration (multiply_factor). Once these have been entered, the user may
decide that alternate sources of dust lead should be considered. The user may enter values for the
fraction of total dust ingested as dust from any of the following: the parents occupation
(OccupFraction), school (SchoolFraction), daycare (DaycareFraction), secondary home
(SecHomeFraction), and paint (PaintFraction), and the corresponding dust lead concentration
from the parents occupation (OccupConc), school (SchoolConc), daycare (DaycareConc),
secondary home (SecHomeConc), or paint (PaintConc).
Finally, for all dust model options, the user may enter the values for the percentage of dust
and soil ingested as soil (weight_soil) and the amount of soil and dust ingested (soil_ingested).
Returning to Figure 6, once the decisions have been made and the parameter values entered
for the media-specific consumption and lead concentrations, the calculations for the exposure
component are performed. The output from this component are the media-specific lead intakes,
EXAIR(t), INDIET(t), INDUST(t), INDUSTA(t), INSOIL(t), INWATER(t), and INOTHER(t).
These values are used as input into the uptake component.
The user may then enter the media-specific lead absorption parameters. These parameters
are the passive absorption fraction at low doses (PAF), the net absorption coefficient for air lead
(air_absorb(t)), and the total absorption coefficient for dietary lead at low doses (ABSF), dust
lead (ABSD), soil lead (ABSS), and water lead (ABSW), and other ingested lead sources
(ABSO). UPTAKE(t), the child's total lead uptake, is calculated by combining all of the user-
provided default parameters in the exposure and uptake components of the model.
The final set of parameters the user may specify are the maternal blood lead concentration
(PBBLDMAT) and the length of the time-step to be used in the solution algorithm (TimeStep).
PBBLDMAT and TimeStep serve as input to the biokinetic component, where the child's blood
lead concentration (PBBLOODEND(t), averaged across each month, is calculated.
51
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infants: The Glasgow Duplicate Diet Study 1979-1980. Food Additives and Contaminants 3:167-176.
57
-------
Silve, H.K.; Kempe, C.H.; Bruyn, H.B.; et al.; (1987) Handbook of Pediatrics, Los Altos CA; Appleton and Lange.
Simons, T.J.B.; al-Modhefer, A.; Bradbury, M.W.B.; (1991) The lead-binding characteristics of human serum;
Abstract from Ninth International Neurotoxicology Conference: Little Rock, Ark.
Specter W; (1956) Handbook of Biological Data.
Stover, B.J.; (1959) 212Pb (ThB) Tracer studies in adult beagle dogs; Proc Soc Exp Biol Med 100:269-272.
U.S. Environmental Protection Agency; (1986) Air Quality Criteria for Lead. Vol I-IV. EPA 600/8-83-028a-d.
Environmental Criteria and Assessment Office, Research Triangle Park, NC.
U.S. Environmental Protection Agency; (1989a) Review of the National Ambient Air Quality Standards for Lead:
Exposure Analysis Methodology and Validation; Report No. EPA-450/2-89/011; U.S. Environmental
Protection Agency, Office of Air Quality Planning and Standards, Research Triangle Park, NC.
U.S. Environmental Protection Agency (1989b). Exposure Factors Handbook. U.S. EPA Office of Health and
Environmental Assessment, Washington, DC. EPA/600/8-89/043.
U.S. Environmental Protection Agency; (1990a) Report of the Clean Air Scientific Advisory Committee on Its
Review of the OAQPS Lead Staff Paper. EPA-SAB-CASAC-90-002. January 1990.
U.S. Environmental Protection Agency; (1990b); Technical Support Document; U.S. Environmental Protection
Agency, Environmental Criteria and Assessment Office; Report No. ECAO-CIN -757; Cincinnati, OH.
U.S. Environmental Protection Agency; (1994) Guidance Manual for the Integrated Exposure Uptake Biokinetic
Model for Lead in Children. Office of Emergancy and Remedial Response. Washington DC. NTIS PB 93-
963510.
Weil, W.B., Jr. (1955) Evaluation of renal function in infancy and childhood. Amer. J. Med Soc. 229:678.
Weis, C.P.; Poppenga, R.L.; Thacker, B.J. et al; (1994) Pharmacokinetics of soil-lead absorption into immature
swine following subchronic oral and iv exposure. Toxicologist 14:119 (Abstract 395).
West, J. R.; Smith, H. W.; Chasis, H. (1948). Glomerular filtration rate, effective renal blood flow, and maximal
tubular excretory capacity in infancy. J. Pediatr. 32: 10-18.
Yokoyama, K.; Araki, S.; Yamamoto, R.; (1985) Renal Handling of Filterable Plasma Metals and Organic
Substances in Man; J App Toxicology 5:2; pp 94-96.
Zeigler, E.E.; Edwards, B.B.; Jensen, R.L. et al.; (1978) Absorption and retention of lead by infants. Pediatr. Res.
12-29-34.
58
-------
APPENDIX A: EQUATIONS AND PARAMETERS
IN THE IEUBK LEAD MODEL
-------
TABLE A-1. EQUATIONS OF THE EXPOSURE MODEL COMPONENT
EQUATION
GROUP
Air Lead
Dietary Lead
EQUATION
NUMBER
E-1
E-2
E-3
E-4a
E-4b
EQUATION
lndoorConc(t) = 0.01 * indoorpercent * air_concentration(t)
TWAftl n[time-outW *Q)ut_air_concentration (t)] +D[(24-time_out (t)) *DlndoorConc (t)]
24
EXAIR(t) = TWA(t) * vent_rate(t)
INDIET(t) = diet_intake(t)
or
INDIET(t) = DietTotal(t) = lnOtherDiet(t)+ InMeat(t) + InGame(t) + InFish(t) + InCanVeg(t) + InFrVeg(t) + InHomeVeg(t) +
InCanFruit(t) + InFrFruit(t) + InHomeFruit(t)
Note: Italicized variables are not parameters in the model. These variables are only intermediate variables.
A-2
-------
EQUATION
GROUP
Water Lead
Soil Lead
EQUATION
NUMBER
E-5a
E-5b
E-5c
E-5d
E-5e
E-5f
E-5g
E-5h
E-5i
E-6a
E-6b
E-7
E-8
EQUATION
InMeat(t) = (1 - userFishFraction - userGameFraction) * meat(t)
InCanVeg(t) = (1 - userVegFraction) * can_veg(t)
InFrVeg(t) = (1 - userVegFraction) * f_veg(t)
InCanFruit(t) = (1 - userFruitFraction) * canjruit(t)
InFrFruit(t) = (1 - userFruitFraction) * fjruit(t)
InHomeFruit(t) = userFruitFraction * fruit_all(t) * UserFruitConc
InHomeVeg(t) = userVegFraction * veg_all(t) * UserVegConc
InFish(t) = userFishFraction * fish(t) * UserFishConc
InGame(t) = userGameFraction * game(t) * UserGameConc
INWATER(t) = water_consumption(t) * constant_water_conc
or
INWATER(t) =water_consumption(t) * (HomeFlushedConc * HomeFlushedFraction + FirstDrawConc * FirstDrawFraction + FountainConc * FountainFraction)
HomeFlushedFraction = 1 - FirstDrarf faction - FountainFraction
INSOIL(t) = constantjoiLconc * soiljngested(t) * (0.01 * weightjoil)
Note: Italicized variables are not parameters in the model. These variables are only intermediate variables.
A-3
-------
EQUATION
GROUP
Dust Lead
EQUATION
NUMBER
E-9a
E-9b
E-9c
E-9d
E-9.5
E-10
E-11
E12a
E12b
E-12C
E-12d
E-12e
EQUATION
INDUST(t) =
INDUSTA(t)
INDUST(t) =
INDUSTA(t)
constantJusLconc * soiljngested(t) * (1- 0.01 * weighLsoil)
= 0; for all t
DustTotal(t) * soiljndoor(t) * HouseFraction
= OCCUP(t) + SCHOOL(t) + DAVCARE(t) + SECHOME(t) + PAINT(t)
HouseFraction = 1 - OccupFraction - SchoolFraction - DaycareFraction - SecHomeFraction - PaintFraction
DustTotal(t) = soiljngested(t) * (0.01 * (100 - weight_soil))
soiljndoor
OCCUP(t) =
SCHOOL(t)
DAVCARE(t)
SECHOME(t)
PAINT(t) =
t) = (contribjercent * constanLsoiLconc(t) + (multiplyjactor * airjoncentration(t))*
DustTotal(t) * OccupFraction * OccupConc
= DustTotal(t) * SchoolFraction * SchoolConc
= DustTotal(t) * DaycareFraction * DaycareConc
= DustTotal(t) * SecHomeFraction * SecHomeConc
DustTotal(t) * PaintFraction * PaintConc
" Age dependent
Note: Italicized variables are not parameters in the model. These variables are only intermediate variables.
A-4
-------
TABLE A-2. EQUATIONS OF THE UPTAKE MODEL COMPONENT
EQUATION GROUP
Absorption
Coefficients
Absorption
Coefficients
EQUATION
NUMBER
U-la
U-lb
U-lc
U-ld
U-lf
U-lg
U-2
EQUATION
I 1 HPAF
UPDIETft) DINDIETft) -i-QMBSF -i-OWF-i-H PAF iD urnr
1 1 |Q AVINTAKE
[ SATINTAKEffl
1 |Q AVINTAKE
SATINTAKEffl
_[ 1 HP A P
1 1 |fj AVINTAKE
[ SATINTAKE(t) J
[ * rip A p
1 1 |fj AVINTAKE
[ SATINTAKE(t)
I * riPAF
UPSniLft) DINSniLft) -i-DABSS -i-DAVS-i-d PAF iD urnr
1 1 |Q AVINTAKE
[ SATINTAKE(t)
[ -i np A P
1 1 |Q AVINTAKE
[ SATINTAKEffl
UPGm(t) = UPDIET(t)+UPWATER(t)+UPDUST(t)+UPOTHER(t)+UPSOIL(t)+UPDUSTA(t)
AVINTAKE = ABSD ' INDUST(t) + ABSD ' INDUSTA(t) + ABSS ' INSOIL(t) + ABSF ' INDIET(t) + ABSO ' INOTHER(t) + ABSW ' INWATER(t)
Note: Italicized variables are not parameters in the model. These variables are only intermediate variables.
A-5
-------
EQUATION GROUP
Absorption
Coefficients
Total LeadUptake
EQUATION
NUMBER
U-3
U-4
U-5
EQUATION
SATINTAKEft) -QATINTAKE'Mi-II WTBODY(t)
" ^' "' ^[WTBODY(24)
UPAIR(t) = air_absorb(t)*0.01*EXAIR(t)
UPTAKE(t) = 30*{(UPDIET(t) + UPWATER(t) + UPDUST(t) + UPSOIL(t) + UPDUSTA(t) + UPOTHER(t) + UPAIR(t)}
Note: Italicized variables are not parameters in the model. These variables are only intermediate variables.
A-6
-------
TABLE A-3. EQUATIONS OF THE BIOKINETIC MODEL COMPONENT
Note: Italicized variables are not parameters in the model. These variables are only intermediate values.
A-7
-------
EQUATION
GROUP
EQUATION
NUMBER
EQUATION
Lead Transfer
Times
B-1a
B-1b
B-1c
B-1d
B-1e
B-1f
B-1h
TBLUR(t) =Q[BLUR(24)
TBLOTH(t) =D[BLOTH(24)
TBLKID(t) =Q[BLKID(24)
TBLBONE(t) =D[BLBONE(24)
TBLFEC(t) = RATFECUR * TBLUR(t)
= RATOUTFEC * TBLFEC(t)
(WTTRAB(t) +QA/TCORT(t)}
10
Note: Italicized variables are not parameters in the model. These variables are only intermediate values.
A-8
-------
EQUATION
GROUP
Compartmental
Lead Transfer
Times (continued)
EQUATION
NUMBER
B-2a
B-2b
B-2c
B-2d
B-2e
EQUATION
TPLRBC =D0.1
TPLUpm -nTBilURW n nw
1 JurtV "HR p w#; t Cm w ,p n
^H (0.55+0.73)
~rpi i iw/t\ n ' tjLLIV^lJ
RATBLPL
TLI»PL(t) -D-PLI-BL(t) 4 TBLLIV(t) 1 J WTLIVER(t) 1
L D TBLLIV(t) ^ ( VOLBLOOD(t)'|
[ TBLFEC(t)J J [ 10 J J
TLIVFEC(t) DCRLIVBL(t) t^TBLFEC(t) t[ WTLIVER(t)
u w u w ^ / VOLBLOOD(t)\
1 10 J J
Note: Italicized variables are not parameters in the model. These variables are only intermediate values.
A-9
-------
EQUATION
GROUP
Compartmental
Lead Transfer
Times
(continued)
EQUATION
NUMBER
B-2g
B-2h
B-2i
B-2J
B-2k
B-21
B-2m
EQUATION
TPLKID(t) =DTBLKID(t)
RATBLPL
TKIDPL(t) DCRKIDBL(t) tDTBLKID(t) t[ WTKIDNEY(t)
( VOLBLOOD(t)1
I 10 j J
TPLTP-B(t) -D TBLBONE(t)
" " ~w "(0.2 *DRATBLPL)
TTRABPL(t) =ffTBONEBL(t)
TPL— PT(t) -D TBLBONE(()
" w "(0.8 *DRATBLPL)
TCORTPL(t) = TBONEBL(T)
TPLOTH(t) =DTBLOTH(t)
RATBLPL
Note: Italicized variables are not parameters in the model. These variables are only intermediate values.
A-10
-------
EQUATION
GROUP
Compartmental
Lead Transfer
Times
(continued)
Blood to Plasma-ECF Lead
Mass Ratio
Fluid Volumes
and
Organ Weights
EQUATION
NUMBER
B-2n
B-2o
B-3
B-4a
B-4b
B-4c
B-4d
EQUATION
T-THPL(t) -D-P-THBL(t) trf TBLOTH(t) 1 J WTOTHER(t) 1
(. nTBLOTH(t)^ ( VOLBLOOD(t)'!
( TBLOUT(t)jJ ( 10 JJ
TOTHOUT(t) DCROTHBL(t) tLTTBLOUT(t) t[ WTOTHER(t)
C VOLBLOOD(t)1
I 10 j J
TPLPBC'ft) -D TPLRBC
L D MRBC(t)
[ (VOLRBC(t-1) *DCONRBC)
RATBLPL = 100
CRKIDBL(t) = 0.777 + [2.35 * {1 - exp(-0.0468*t)J]
CRLIVBL(t) = 1.1 + [3.5 * {1 - exp(-0.0462*t)}]
CRBONEBLft) = 6.0 + [215.0 * {1 - exp(-0.000942*t)J]
CROTHBL(t) = 0.931 + [0.437 * {1 - exp(-0.00749*t)}]
Note: Italicized variables are not parameters in the model. These variables are only intermediate values.
A-11
-------
EQUATION
GROUP
Fluid Volumes
and
Organ Weights
(continued)
EQUATION
NUMBER
B-5a
B-5b
B-5c
B-5d
B-5e
B-5f
B-5g
EQUATION
VOLBLOOD(t) \\ 10'67 I +[f 21'86 ]
XP 1 7.09 J + 6> 12 months
Note: Italicized variables are not parameters in the model. These variables are only intermediate values.
A-12
-------
EQUATION
GROUP
EQUATION
NUMBER
B-5h
B-5i
B-5J
B-5k
B-51
B-5m
EQUATION
WTCORT = 0.8*WTBONE
WTRAB = 0.2*WTBONE
WTKIDNEY(t) -d °-050 i[f °'106 ]
1 +Dexp l-pft-5-24) 1 1 +Dexp I-D^65-67)
1 4.24 |[ 1 34.11 JJ
WTLIVEP(t) -[f °'261 I i[f °'584 |
1+DexpfDfil§^l 1 +DexpfD
-------
EQUATION
GROUP
EQUATION
NUMBER
EQUATION
Lead Masses
(Differential Equations)
B-6a
B-6b
NOTE: The following equations (B-6a to B-6i) represent the correct mathematical specification. These differential equations are translated
into difference equations employing the forward Euler solution in the series B-6.5a to B-6.5J, then to the solution algorithm for differential
equations using the backward Euler method, or alternate difference equation scheme.
dMPLECF(t)/dt = UPTAKE(t) + INFLOW(t) - OUTFLOW(t)
INFLOW(t) -pMLIVER(t) |DMKIDNEY(t) |DMOTHER(t) |D MTRAB(t) |D MCORT(t) |D MRBC(t)
TLIVPL(t) TKIDPL(t) TOTHPL(t) TTRABPL(t) TCORTPL(t) TRBCPL(t)
OUTFLOW(t) =DMPLECF
1
1
1
1
1
1
1
TPLUR(t) TPLLIV(t) TPLKID(t) TPLOTH(t) TPLTRAB(t) TPLCORT(t) TPLRBC2(t)
B-6d
dMRBC(t) D MPLECF(t) D MRBC(t)
dt TPLRBC2(t) TRBCPL(t)
=DMPLECF(t) _DML|VER(t) J_| +D 1
dt TPLLIV(t) iTLIVPL(t) TLIVFEC(t)
dMKIDNEY(t) DMPLECF(t) gMKIDNEY
dt TPLKID(t) TKIDPL
Note: Italicized variables are not parameters in the model. These variables are only intermediate values.
A-14
-------
EQUATION
GROUP
EQUATION
NUMBER
EQUATION
Lead Masses
(Differential Equations)
B-6g
B-6h
dMOTHER (*) =DMPLECF (*) -DMOTHER (t)
dt TPLOTH (t)
dMTRAB (t) _D MPLECF (t) D MTRAB (t)
dt ~ TPLTRAB (t) TTRABPL (t)
dMCORT (t) _D MPLECF (t) D MCORT (t)
dt ~ TPLCORT (t) TCORTPL (t)
+D
TOTHPL (t) TOTHOUT (t)
Note: Italicized variables are not parameters in the model. These variables are only intermediate values.
A-15
-------
EQUATION
GROUP
Compartmental
Lead Masses
(Difference Equations)
EQUATION
NUMBER
B-6.5a
B-6.5b
D K Cr
B-6.5d
B-6.5e
B-6.5f
B-6.5g
EQUATION
MPLECF(t) -OVIPLECF(t-TimeStep) =DupTAKE(t) +D|NFLOW(t) -DOUTFLOW(t)
TimeStep
INFLOW m -DMLIVER (t) ,DMKIDNEY(t) |QMOTHER (t) |Q MTRAB (t) |Q MCORT (t) |QMRBC (t)
TLIVPL (t) TKIDPL (t) TOTHPL (t) TTRABPL (t) TCORTPL (t) TRBCPL
OUTFLOW (t) CMPLECF tH ^ iD ^ iD ^ iD ^ iD ^ iD ^ iD ^
ITPLUR (t) TPLLIV (t) TPLKID (t) TPLOTH (t) TPLTRAB (t) TPLCORT (t) TPLRBC2 (t)
MRBC(t) -QVIRBC(t-TimeStep) Q MPLECF(t) QMRBC(t)
TimeStep TPLRBC2(t) TRBCPL
MLIVER(t) -OVILIVER(t-TimeStep) QMPLECF(t) Q^i^pm J 1 ,D 1
TimeStep TPLLIV(t) ^TLIVPL(t) TLIVFEC(t)
MKIDNEY(t) -OVIKIDNEY(t-TimeStep) QMPLECF(t) QMKIDNEY(t)
TimeStep TPLKID(t) TKIDPL(t)
MOTHER(t) -OVIOTHER(t-TimeStep) QMPLECF(t) QyioyHEp/n [I 1 D 1
TimeStep TPLOTH(t) lTOTHPL(t) TOTHOUT(t)
Note: Italicized variables are not parameters in the model. These variables are only intermediate values.
A-16
-------
EQUATION
GROUP
EQUATION
NUMBER
EQUATION
Lead Masses
MTRAB(t) -DMTRAB(t-TimeStep) _D MPLECF(t) D MTRAB(t)
TimeStep ~ TPLTRAB(t) TTRABPL(t)
B-6.51
MCORT(t) -DMCORT(t-TimeStep) D MPLECF(t) D MCORT(t)
TimeStep TPLCORT(t) TCORTPL(t)
Note: Italicized variables are not parameters in the model. These variables are only intermediate values.
A-17
-------
EQUATION
GROUP
EQUATION
NUMBER
EQUATION
Tissue Lead Masses and
Blood Lead Concentration at
Birth
B-7a
B-7b
B-7d
PBBLDO = 0.85 * PBBLDMAT
PBBLDO *D(VOLPLASM(0) +DVOLRBC(0)) *[( TPLRBC | *D(1.7-
MPLECF(O) =0-
\ TimeStepJ
TRBCPL(O)
{ TimeStep TimeStep
PBBLDO *D(VOLPLASM(0) +DVOLRBC(0)) *[( TRBCPL(°)|
MRBC(O) =0-
TimeStep }
( TRBCPL(O)
{ TimeStep TimeStep
MPLASM(O) =DMPLECF(0)
(1.7-HCTO)
NOTE: Equations B-7b, B-7c, and B-7d represent the distribuition of fetal blood lead, derived from the mother's blood lead, at birth. In this simplified form, these equations are numerically equivalent
to the following equations that more precisely represent the distribution of lead at birth. The difference in these two sets of equations is insignificant after 2-3 iteration steps.
PBBLDO *D(VOLPLASM(0) +DVOLRBC(0)) *[( TPLRBC [
MPLECF(O) =0-
\ TimeStepJ
TRBCPL(0)'|
\ TimeStep J
MRBC(O) =DPBBLDO *D(VOLPLASM(0) +DVOLRBC(0)) *ni -DO,
TPLRBC(O)]
TRBCPL(0)J
MPLASM(O) =
0.416
A-18
-------
EQUATION
GROUP
Tissue Lead Masses
and Blood Lead
Concentration at
Birth
EQUATION
NUMBER
B-7e
B-7f
B-7g
B-7h
B-71
EQUATION
MCORT(O) = 78.9 ** PBBLDO * WTCORT(O)
MKIDNEY(O) = 10.6 * PBBLDO * WTKIDNEY(O)
MLIVER(O) = 13.0 * PBBLDO * WTLIVER(O)
MOTHER(O) = 16.0 * PBBLDO * WTOTHER(O)
MTRAB(O) = 51.2 * PBBLDO * WTTRAB(O)
Note: Italicized variables are not parameters in the model. These variables are only intermediate values.
A-19
-------
EQUATION
GROUP
Compartmental
Lead Masses
(Solution
Algorithm)
EQUATION
NUMBER
B-8a
B-8b
B-8c
B-8d
EQUATION
MPLECF(t-TimeStep) +q UPTAKE(t) *DTlmeStep| +D SUM3(t)
MPLECF(t) -D • ^ 30 j
"" w " [1 +D{TimeStep *DSUM1 (t)} -D{TimeStep *DSUM2 (t)}]
SUM1 (t) D ^ +D ^ +D ^ +D ^ +D ^ +D ^ +D ^
w "TPLUR (t) "TPLRBC2 (t) "TPLLIV (t) "TPLKID (t) "TPLOTH (t) "TPLTRAB (t) "TPLCORT (t)
TPLPE^ (t) -i-d TRBCPL iDll TPLLI" (0 -i-d TLIVPL (t) ,DTLIVPL (t) D1 1
w "\TimeStep "'/ " """ w "\TimeStep "TLIVALL (t) ~')
iD 1 iD 1
TPLKID (t) 4 TKIDPL (t) :0\\ fTOTHPL ffl ,DTOTHPL (t) |ffl]
w 1 TimeStep / ( TimeStep TOTHALL (t) )
iD 1 iD 1
TPLTP-E (t) -,-[(TTRABPL ('' ,Dll TPL^PT (t) -,-[( TCORTPL « ,Dll
w ~\ TimeStep 1 w T, TimeStep )
SUM3 (t) D MRBC (t-TimeStep ) Q MLIVER (t-TimeStep )
[TRBCPL |Q1] TLIVPL (t) Q TLIVPL (t) m \
( TimeStep J TimeStep TLIVALL (t) /
QMKIDNEY (t-TimeStep ) |Q MOTHER (t-TimeStep )
f TKIDPL (t) :m\ ("TOTHPL (t) |QTOTHPL (t) m \
( TimeStep J [ TimeStep TOTHALL (t) j
QMTRAB (t-TimeStep ) |QMCORT (t-TimeStep )
CTTRABPL (t) |Q1| f TCORTPL (t) |Q1^
[ TimeStep } { TimeStep J
Note: In the solution algorithm (Equations B-8a - B-1 Oc), we have chosen for clarity to distinguish the subscript (i) as denoting parameter values that change each month, whereas the
subscript (t) indicates values that change with each iteration interval. The source code uses a different notation.
A-20
-------
EQUATION
GROUP
EQUATION
NUMBER
EQUATION
Compartmental
Lead Masss
(Solution
Algorithm)
(continued)
B-9a
MRBC(t) =0
MRBC(t-TimeStep) +qMPLECF(t) *q TlmeSteP
__ T 1. TPLRBC2Q
TRBCPL
B-9b
MLIVER (t) =D.
MLIVER (t-TimeStep ) +nMPLECF (t) *q TlmeSteP |
^_^_ T 1.TPLLIV (f) j
n TimeStep
+ TLIVALL (f)
B-9c
B-9d
MOTHER (t) =D-
MOTHER
3P)
1 +D
+CJMPLECF
TimeStep
TOTHALL (
ffl
t>
rl TimeStep \
\ TPLOTH (t) /
B-9e
Note: In the solution algorithm (Equations B-8a - B-1 Oc), we have chosen for clarity to distinguish the subscript (i) as denoting parameter values that change each month, whereas the
subscript (t) indicates values that change with each iteration interval. The source code uses a different notation.
A-21
-------
EQUATION
GROUP
EQUATION
NUMBER
EQUATION
Compartmental
Lead Masses
(Solution
Algorithm)
(continued)
B-9f
MCORT(t-TimeStep) +nMPLECF(t)
MCORT(t) =D-
*[( TlmeSteP |
^TPLCORT(t)j
1 +[
TimeStep
~TCORTPL(t)J
B-9
MPLASM(t) =DMPLECF(t) .WOLPLASM(t)
VOLECF(t) +DVOLPLASM(t)
TOTHALL (t) =D
B-9h
B-9i
1
1
TOTHPL (t) TOTHOUT (t)
TLIVALL (t) =[
1
TLIVPL (t)
1
TLIVFEC (t)
Note: In the solution algorithm (Equations B-8a - B-1 Oc), we have chosen for clarity to distinguish the subscript (i) as denoting parameter values that change each month, whereas the
subscript (t) indicates values that change with each iteration interval. The source code uses a different notation.
A-22
-------
EQUATION
GROUP
EQUATION
NUMBER
EQUATION
Blood Lead
Concentration
NOTE: Equation B-10a is computed by a cumulative loop
B-10a
BLOOD (t) -
MRBC (t) +DMPLASM
VOLBLOOD (i-1)
B-10b
B-10c
TimeStep = 1/iterations per day
STEPS = 30 / TimeStep = iterations per month
PBBLOODEND(i) = BLOOD(t)/STEPS
Note: In the solution algorithm (Equations B-8a - B-1 Oc), we have chosen for clarity to distinguish the subscript (i) as denoting parameter values that change each month, whereas the
subscript (t) indicates values that change with each iteration interval. The source code uses a different notation.
A-23
-------
APPENDIX B: DESCRIPTION OF PARAMETERS
IN THE IEUBK LEAD MODEL
-------
TABLE B-1. DESCRIPTION OF PARAMETERS IN THE IEUBK LEAD MODEL
PARAMETER NAME
ABSD
ABSF
ABSO
ABSS
ABSW
air_absorb(t)
air_concentration(t)
DESCRIPTION
Total absorption
for dust at low
saturation
Total absorption
for food at low
saturation
Total absorption
for other ingested
lead at low
saturation
Total absorption
for soil at low
saturation
Total absorption
for water at low
saturation
Net percentage
absorption of air
lead
Outdoor air lead
concentration
DEFAUL
T VALUE
OR
EON.
NO.
0.3
0.5
0.0
0.3
0.5
32
32
32
32
32
32
32
0.1
0.1
0.1
0.1
0.1
0.1
0.1
AGE
RANGE
(mo)
0-84
0-84
0-84
0-84
0-84
0-11
12-23
24-35
36-47
48-59
60-71
72-84
0-11
12-23
24-35
36-47
48-59
60-71
72-84
I
or
E
b
E
E
E
E
E
E
BASIS FOR VALUES/EQUATIONS
BasedonUSEPA(1989a).
BasedonUSEPA(1989a).
Based on the default condition that there is no other source of lead
ingestion in the household.
BasedonUSEPA(1989a).
BasedonUSEPA(1989a).
Deposition efficiencies of airborne lead particles were estimated by U S
EPA (1 989a). A respiratory deposition/absorption rate of 25% to 45% is
reported for young children living in non-point source areas while a rate of
42% is calculated for those living near point sources. An intermediate value
of 32% was chosen.
Based on the lower end of the range 0.1 - 0.3 |jg Pb/m3 that is reported for
outdoor air lead concentration in U.S. cities without lead point sources (US
EPA 1989)
UNITS
unitless
unitless
unitless
unitless
unitless
%
|jg/m3
EQUATION
WHERE
USED
U-1c
U-2
U-1a,U-2
U-1d,U-2
U-1e,U-2
U-1b,U-2
U-4
E-1,2,11
NOTE: I = interior parameter, E = Exterior, user selectable parameter
B-2
-------
PARAMETER NAME
AVF, AVW, AVD, AVO,
AVS
AVINTAKE
can_fruit(t)
can_veg(t)
contrib_percent
CONRBC
constant_soil_conc(t)
DESCRIPTION
Bioavailability
Available intake
Lead intake from
canned fruit when
fruit is consumed
only in canned
form
Lead intake from
canned vegetables
when vegetable is
consumed only in
canned form
Ratio of indoor
dust lead
concentration to
soil lead
concentration
Maximum lead
concentration
capacity of red
blood cells
Soil lead
concentration
DEFAUL
T VALUE
OR
EON.
NO.
1
U-2
1.811
1.063
1.058
0.999
0.940
0.969
1.027
0.074
0.252
0.284
0.295
0.307
0.291
0.261
0.70
1200
200
200
200
200
200
200
200
AGE
RANGE
(mo)
0-84
0-84
0-11
12-23
24-35
36-47
48-59
60-71
72-84
0-11
12-23
24-35
36-47
48-59
60-71
72-84
0-84
0-84
0-11
12-23
24-35
36-47
48-59
60-71
72-84
I
or
E
I
I
I
I
E
I
E
BASIS FOR VALUES/EQUATIONS
Parameter added for later flexibility in describing the absorption process;
has no effect in current algorithm.
The amount of Pb that is available for intake
Pb concentration from data provided to EPA by FDA (US EPA (1986).
Quantity consumed from Pennington (1983).
Pb concentration from data provided to EPA by FDA (US EPA (1986).
Quantity consumed from Pennington (1983).
Analysis of soil and dust data from 1983 East Helena study (US EPA, 1989)
Based on Marcus (1983) reanalysis of infant baboon data from Mallon
(1983). See Marcus (1985a) for assessment of form of relationship and
estimates from data on human adults [data from deSilva (1981a,b), Manton
and Malloy (1983), and Manton and Cook (1984)] and infant and juvenile
baboons (Mallon, 1983).
Air Quality Criteria Document for Lead. (US EPA, 1986)
UNITS
unitless
M9
|jg/day
|jg/day
ngig per
ng/g
|jg/dL
|jg/g
EQUATION
WHERE
USED
U-1a-U-1e
U-1a,b,c,d,e
E-5d
E-5b
E-11
B-2.5
E-8
NOTE: I = interior parameter, E = Exterior, user selectable parameter
B-3
-------
PARAMETER NAME
constant_water_conc
CRBONEBL(t)
CRKIDBL(t)
CRLIVBL(t)
DESCRIPTION
Water lead
concentration
Rstio of l&cid
concsntrstion
(|jg/kg) in bone to
blood l&cid
concsntrstion
(MS )
Ratio of lead
concentration
(|jg/kg) in kidney
to blood lead
concentration
(|jgL)
Rstio of l&cid
concentration
(|jg/kg) in liver to
blood lead
concentration
fnn/h
IMa'U
DEFAUL
T VALUE
OR
EON.
NO.
4.0
B-4c
B-4a
B-4b
AGE
RANGE
(mo)
0-84
0-84
0-84
0-84
1
or
E
E
1
1
1
BASIS FOR VALUES/EQUATIONS
Based on analysis of data from the American Waterworks Service Co.
(Marcus, 1989)
Data in Barry (1981) were used.
Bone lead concentration was calculated as an arithmetic average of the
concentrations in the rib, tibia, and calvaria. The blood lead concentrations
were taken directly from the study.
Concentrations in each of the following eight age groups were considered:
stillbirths, 0-1 2 days, 1-11 mos, 1-5 yrs, 6-9 yrs, 11 -16 yrs, adult (men), and
adult (women). Ages 0 and 40 yrs were assumed for stillbirths and adults,
respectively.
Data in Barry (1981) were used.
Lead concentrations in kidney (combined values for cortex and medulla)
and blood were taken directly from the study.
Concentrations in each of the following eight age groups were considered:
stillbirths, 0-1 2 days, 1-11 mos, 1-5 yrs, 6-9 yrs, 11 -16 yrs, adult (men), and
adult (women). Ages 0 and 40 yrs were assumed for stillbirths and adults,
respectively.
Data in Barry (1981) were used.
Lead concentrations in liver and blood were taken directly from the study.
Concentrations in each of the following eight age groups were considered:
stillbirths, 0-1 2 days, 1-11 mos, 1-5 yrs, 6-9 yrs, 11 -16 yrs, adult (men), and
adult (women). Ages 0 and 40 yrs were assumed for stillbirths and adults,
respectively.
UNITS
ug/L
L/kg
L/kg
L/kg
EQUATION
WHERE
USED
E-6a
B-1h
B-2h
B-2e,2f
NOTE: I = interior parameter, E = Exterior, user selectable parameter
B-4
-------
PARAMETER NAME
CROTHBL(t)
DAYCARE(t)
DaycareConc
DaycareFraction
dietjntake(t)
DietTotal(t)
DustTotal(t)
DESCRIPTION
Ratio of lead
concentration
(|jg/kg) in other
soft tissue to blood
lead concentration
(M9/L)
Dust lead intake at
daycare
Dust lead
concentration at
daycare
Fraction of total
dust ingested daily
as daycare dust
User-specified diet
lead intake
Total Dietary
Intake
Daily amount of
dust ingested
DEFAUL
T VALUE
OR
EON.
NO.
B-4d
E-12c
200
0
5.53
5.78
6.49
6.24
6.01
6.34
7.00
E-4b
E-10
AGE
RANGE
(mo)
0-84
0-84
0-84
0-84
0-11
12-23
24-35
36-47
48-59
60-71
72-84
0.84
0-84
I
or
E
I
I
E
E
E
I
I
BASIS FOR VALUES/EQUATIONS
Data in Barry (1981) were used.
Lead concentration ratio for soft tissues was calculated as a weighted
arithmetic average of concentration ratios for muscle (53.8%), fat (24.0%),
skin (9.4%), dense connective tissue (4.4%), brain (2.7%), Gl tract (2.3%),
lung (1 .9%), heart (0.7%), spleen (0.3%), pancreas (0.2%), and aorta
(0.2%), where the weights applied are given in parentheses. The weight
associated with each soft tissue component was equal to the weight of the
component (kg) divided by weight of all soft tissues (kg). These weights
were estimated from Schroeder and Tipton (1968) and are assumed to
apply in the range 0-84 months of age.
Concentrations in each of the following eight age groups were considered:
stillbirths, 0-1 2 days, 1-11 mos, 1-5yrs, 6-9 yrs, 11-16yrs, adult (men), and
adult (women). Ages 0 and 40 yrs were assumed for stillbirths and adults,
respectively.
Simple combination of the total amount of dust ingested daily, fraction of
total dust ingested as daycare dust, and dust lead concentration at daycare.
Based on the assumption that default daycare dust concentrations are the
same as default residence dust concentrations.
Based on the default assumption that the child does not attend daycare.
Pb concentration from data provided to EPA by FDA (US EPA (1986).
Quantity consumed from Pennington (1983).
Summation of all dietary sources; same as INDIET(t)
Simple combination of total amount soil and dust ingested daily and fraction
of this combined ingestion that is dust alone.
UNITS
L/kg
|jg/day
^g/g
unitless
|jg/day
|jg/day
g/day
EQUATION
WHERE
USED
B-2n,2o
E-9d
E-12c
E-9.5,12c
E-4a
E-4b
E-9c,12a-
12e
NOTE: I = interior parameter, E = Exterior, user selectable parameter
B-5
-------
PARAMETER NAME
EXAIR(t)
f_fruit(t)
f_veg(t)
FirstDrawConc
FirstDrawFraction
FountainConc
FountainFraction
fruit_all(t)
DESCRIPTION
Air lead intake
Lead intake from
fresh fruit if no
home-grown fruit
is consumed
Lead intake from
fresh vegetables if
no home-grown
vegetables are
consumed
First Draw water
lead concentration
Fraction of total
water consumed
daily as first draw
Fountain water
lead concentration
Fraction of total
water consumed
daily from
fountains
Daily amount of all
fruits consumed
DEFAUL
T VALUE
OR
EON.
NO.
E-3
0.039
0 196
0.175
0 179
0.203
0.251
0.148
0.269
0.475
0.466
0.456
0.492
0.563
4.0
0.5
10
0.15
38.481
169.000
63 166
61 .672
61 .848
67.907
80.024
AGE
RANGE
(mo)
0-84
0-11
12-23
36-47
48-59
60-71
72-84
0-11
12-23
24-35
36-47
48-59
60-71
72-84
0-84
0-84
0-84
0-84
0-11
12-23
24-35
36-47
48-59
60-71
72-84
I
or
E
I
I
I
E
E
E
E
I
BASIS FOR VALUES/EQUATIONS
Simple combination of average air lead concentration and ventilation rate.
Pb concentration from data provided to EPA by FDA (US EPA (1986).
Quantity consumed from Pennington (1983).
Pb concentration from data provided to EPA by FDA (US EPA (1986).
Quantity consumed from Pennington (1983).
Based on analysis of data from the American Waterworks Service Co.
(Marcus, 1989)
In the absence of appropriate data, a conservative value corresponding to
consumption largely after four fours stagnation time was used, e.g. early
morning or late afternoon.
Default assumption is that the drinking fountain has a lead-lined reservoir,
but that consumption is not always first draw. Therefore, a value was
selected from the range of 5-25 ^g/L.
A default value was based on 4-6 trips to the water fountain at 40-50 ml per
trip.
Pb concentration from data provided to EPA by FDA (US EPA (1986).
Quantity consumed from Pennington (1983).
UNITS
|jg/day
|jg/day
|jg/day
m/L
unitless
|jg/L
none
g/day
EQUATION
WHERE
USED
U-4
E-5e
E-5c
E-6b
E-6b,7
E-6b
E-6b,7
E-5f
NOTE: I = interior parameter, E = Exterior, user selectable parameter
B-6
-------
PARAMETER NAME
HomeFlushedConc
HCTO
InCanFruit(t)
InCanVeg(t)
INDIET(t)
IndoorConc(t)
indoorpercent
INDUST(t)
DESCRIPTION
Home flushed
water lead
concentration
Hematocrit at birth
Lead intake from
canned fruit
Lead intake from
canned vegetables
Diet lead intake
Indoor air lead
concentration
Ratio of indoor
dust lead
concentration to
corresponding
outdoor
concentration
Household dust
lead intake
DEFAUL
T VALUE
OR
EON.
NO.
1.0
0.45
E-5d
E-5b
E-4a
or
E-4b
E-1
30
E-9a
or
E-9c
AGE
RANGE
(mo)
0-84
0
0-84
0-84
0-84
0-84
0-84
0-84
I
or
E
E
I
I
I
I
I
E
I
BASIS FOR VALUES/EQUATIONS
Based on analysis of data from the American Waterworks Service Co.
(Marcus, 1989)
Data from Silve et al. (1987); also Spector (1956) and Altman and Ditmer
(1973)
Simple combination of the fraction of non-home grown fruits consumed
daily, and lead intake from canned fruits when fruits are consumed only in
canned form.
Simple combination of the fraction of vegetables consumed daily as non-
home grown, and lead intake from canned vegetables when vegetables are
consumed only in canned form.
Two options are provided.
Default option - Considers composite diet lead intake.
Alternate option - Combines lead intake from several individual components
of diet.
Algebraic expression of relationship
Based on homes near lead point sources. The default value is reported in
OAQPS (USEPA 1989, pp A-1) and is estimated by Cohen and Cohen
(1980).
Two options are provided.
Default option - Assumes that all dust lead exposure is from the household.
Alternate option - Considers dust lead exposure from several alternative
sources as well.
UNITS
m/L
decimal
percent
|jg/day
|jg/day
|jg/day
|jg/m3
%
|jg/day
EQUATION
WHERE
USED
E-6b
B-7b,d
E-4b
E-4b
U-1a, U-2
E-2
E-1
U-1-c, U-2
NOTE: I = interior parameter, E = Exterior, user selectable parameter
B-7
-------
PARAMETER NAME
INDUSTA(t)
InFish(t)
InFrFruit(t)
InFrVeg(t)
InGame(t)
InHomeFruit(t)
InHomeVeg(t)
InMeat(t)
InOtherDiet(t)
DESCRIPTION
Lead intake from
alternate dust
sources
Lead intake from
fish
non-home grown
fresh fruits
non-home grown
fresh vegetables
game animal meat
Lead intake from
home grown fruits
Lead intake from
home grown
vegetables
Lead intake from
non-game and
non-fish meat
Combined lead
intake from dairy
food, juice, nuts,
beverage, pasta,
bread, sauce,
candy, infant and
formula food
DEFAUL
T VALUE
OR
EON.
NO.
E-9b
or
E-9d
E-5h
E-5e
E-5c
E-5i
E-5f
E-5g
E-5a
3.578
3.506
3.990
3.765
3.545
3.784
4.215
AGE
RANGE
(mo)
0-84
0-84
0-84
0-84
0-84
0-84
0-84
0-84
0-11
12-23
24-35
36-47
48-59
60-71
72-84
I
or
E
I
I
I
I
I
I
I
I
I
BASIS FOR VALUES/EQUATIONS
Two options are provided.
Default option - Assumes that lead intake from alternate sources is zero.
Alternate option - Combines lead intake from several alternate sources.
Simple combination of total meat consumed daily, fraction of meat
consumed as fish, and lead concentration in fish.
Simple combination of the fraction of fruits consumed daily as non-home
grown and lead intake from fresh fruits.
Simple combination of the fraction of vegetables consumed daily as non-
home grown and lead intake from fresh vegetables.
Simple combination of total meat consumed daily, fraction of meat
consumed as game animal meat, and lead concentration in game animal
meat.
Simple combination of total amount of fruit consumed daily, fraction of fruit
consumed as home grown, and lead concentration in home grown fruit.
Simple combination of total amount of vegetable consumed daily, fraction of
vegetables consumed as home grown, and lead concentration in home
grown vegetables.
Simple combination of total amount of meat consumed daily, fraction of
meat consumed as non-game and non-fish meat, and lead concentration in
non-game and non-fish meat.
Sum of the amounts of lead ingested in food items not substituted by the
calculation of exposure to lead in home grown fruits and vegetables, wild
game or fish. Pb concentration from data provided to EPA by FDA (US EPA
(1986). Quantity consumed from Pennington (1983).
UNITS
|jg/day
|jg/day
|jg/day
|jg/day
|jg/day
|jg/day
|jg/day
|jg/day
|jg/day
EQUATION
WHERE
USED
U-1 .5c, U-2
E-4b
E-4b
E-4b
E-4b
E-4b
E-4b
E-4b
E-4b, E-4c
NOTE: I = interior parameter, E = Exterior, user selectable parameter
B-8
-------
PARAMETER NAME
INOTHER(t)
INSOIL(t)
INWATER(t)
MCORT(t)
meat_all(t)
DESCRIPTION
Combined other
sources of
ingested lead,
such as paint
chips, ethnic
medicines, etc.
Soil lead intake
Water lead intake
Mass of lead in
cortical bone
Daily amount of
meat (including
fish and game)
consumed
DEFAUL
T VALUE
OR
EON.
NO.
0
E-8
E-6a
or
E-6b
B-7e
and
B-9f
29.551
87.477
95.700
101.570
107.441
1 1 1 .948
120.961
AGE
RANGE
(mo)
0-84
0-84
0-84
0
and
0-84
0-11
12-23
24-35
36-47
48-59
60-71
72-84
I
or
E
E
I
I
I
I
BASIS FOR VALUES/EQUATIONS
Assumes no other sources of ingested lead
Simple combination of total amount of soil and dust ingested daily, fraction
of this combined ingestion that is soil alone, and lead concentration in soil.
Two options are provided.
Default option - Simple combination of water consumed daily and a
constant water lead concentration.
Alternate option - Water lead concentration depends on contribution from
several individual sources of water.
0 months - Simple combination of an assumed bone to blood lead
concentration ratio, blood lead concentration, and weight of cortical bone.
Basis for value of bone to blood lead concentration ratio was human
autopsy data (Barry, 1981).
0-84 months - Application of the Backward Euler solution algorithm to the
system of differential equations (B-6a-B-6i in Table A-3).
Both cases above assume that the cortical bone to blood lead concentration
ratio is equal to the bone (composite) to blood lead concentration ratio.
Pb concentration from data provided to EPA by FDA (US EPA (1986).
Quantity consumed from Pennington (1983).
UNITS
i/g/day
|jg/day
|jg/day
M9
g/day
EQUATION
WHERE
USED
U-1d, U-2
U-1e,U-2
U-1b, U-2
B-6b,6i,6.5b,
6.5i,8a,9f
E-5h
NOTE: I = interior parameter, E = Exterior, user selectable parameter
B-9
-------
PARAMETER NAME
meat(t)
MKIDNEY(t)
MLIVER(t)
MOTHER(t)
MPLASM(t)
DESCRIPTION
Lead intake from
meat if no game
meat or fish is
consumed
Mciss of l&cid in
Kidnsy
Mciss of l&cid in
hvsr
Mass of lead in
soft tissues
Mciss of l&cid in
plasma pool
DEFAUL
T VALUE
OR
EON.
NO.
0.226
0630
0 81 1
0.871
0.931
1.008
1.161
B-7f
and
B-9c
B-7g
and
B-9b
B-7h
and
B-9d
B-7d
and
B-9g
AGE
RANGE
(mo)
0-11
12-23
24-35
36-47
48-59
60-71
72-84
0
and
0-84
0
and
0-84
Q
and
0-84
o
and
0-84
I
or
E
I
I
I
I
I
BASIS FOR VALUES/EQUATIONS
Pb concentration from data provided to EPA by FDA (US EPA (1986).
Quantity consumed from Pennington (1983).
0 months - Simple combination of an assumed kidney to blood lead
concentration ratio, blood lead concentration, and weight of kidney. Basis
for the value of the kidney to blood lead concentration ratio was human
autopsy data (Barry, 1981).
0-84 months - Application of the Backward Euler solution algorithm to the
system of differential equations (B-6a-B-6i in Table A-3).
0 months - Simple combination of an assumed liver to blood lead
concentration ratio, blood lead concentration, and weight of the liver. Basis
for the value of the liver to blood lead concentration ratio was human
autopsy data (Barry, 1981).
0-84 months - Application of the Backward Euler solution algorithm to the
system of differential equations (B-6a-B-6i in Table A-3).
0 months - Simple combination of an assumed soft tissue to blood lead
concentration ratio, blood lead concentration, and weight of the soft tissues
at birth. Basis for the value of soft tissue to blood lead concentration ratio
was human autopsy data (Barry et al., 1981), using total lead and total
weight of other tissue.
0-84 months - Application of the Backward Euler solution algorithm to the
system of differential equations (B-6a-B-6i in Table A-3).
0 months - Simple combination of the mass of lead in blood and red blood
cells
0-84 months - Based on the assumption that the lead concentration in
plasma-ECF is equal to the lead concentration in the plasma.
UNITS
|jg /day
M9
M9
M9
M9
EQUATION
WHERE
USED
E-5a
B-
6b,6f,6.5b,6.
5f,8d,9c
B-
6b,6e,6.5b,6.
5e,8d,9b
B-
6b,6g,6.5b,6.
5g,8d,9d
B-10a
NOTE: I = interior parameter, E = Exterior, user selectable parameter
B-10
-------
PARAMETER NAME
MPLECF(t)
MRBC(t)
MTRAB(t)
multiply_factor
OCCUP(t)
OccupConc
DESCRIPTION
Mass of lead in
plasma-extra-
cellular fluid
(plasma-ECF)
Mass of lead in red
blood cells
Mass of lead in
trabecular bone
Ratio of indoor
dust lead
concentration to
air lead
concentration
Dust lead intake
from secondary
occupation
Secondary
occupational dust
lead concentration
DEFAUL
T VALUE
OR
EON.
NO.
B-7b
and
B-8a
B-7c
and
B-9a
B-7i
and
B-9e
100
E-12a
1200
AGE
RANGE
(mo)
0
and
0-84
0
and
0-84
0
and
0-84
0-84
0-84
0-84
I
or
E
I
I
I
E
I
E
BASIS FOR VALUES/EQUATIONS
0 months - Based on two assumptions.
(1) masses of lead in plasma-ECF and red blood cells are in kinetic quasi-
equilibrium, and
(2) lead concentration in the plasma-ECF is equal to lead concentration in
the plasma.
0-84 months - Application of the Backward Euler solution algorithm to the
system of differential equations (B-6a-B-6i in Table A-3).
0 months - Based on the assumption that the masses of lead in plasma-
ECF and red blood cells are in kinetic quasi-equilibrium.
0-84 months - Application of the Backward Euler solution algorithm to the
system of differential equations (B-6a-B-6i in Table A-3).
0 months - Simple combination of an assumed bone to blood lead
concentration ratio, blood lead concentration, and weight of trabecular
bone. Basis for the value of bone to blood lead concentration ratio was
human autopsy data (Barry, 1981).
0-84 months - Application of the Backward Euler solution algorithm to the
system of differential equations (B-6a-B-6i in Table A-3).
Both cases above assume that trabecular bone to blood lead concentration
ratio is equal to bone (composite) to blood lead concentration ratio.
Analyses of the 1983 East Helena study in (USEPA 1989, Appendix B-8)
suggest about 267 |jg/g increment of lead in dust for each |jg /m3. lead in
air. A much smaller factor of 100 |jg/g PbD per |jg/m3 is assumed for non-
smelter community exposure.
Simple combination of amount of dust ingested, fraction of the total dust
ingested as secondary occupational dust, and lead concentration in
secondary occupational dust
Air Quality Criteria Document for Lead. (US EPA, 1986)
UNITS
UCI
UQ
UQ
UQ /Q
per
|jg/m3
|jg/day
*
EQUATION
WHERE
USED
B-6a,6c-
6i,6.5a,
6.5c-
6.5i,8a,9a-9g
B-
6a,6d,6.5a,6.
5d,8d,9a,10a
B-
6b,6h,6.5b,6.
5h,8d,9e
E-11
E-9d
E-12a
NOTE: I = interior parameter, E = Exterior, user selectable parameter
B-11
-------
PARAMETER NAME
OccupFraction
PAINT(t)
PaintConc
PAF
PaintFraction
PBBLDMAT
PBBLDO
PBBLOODEND(t)
RATBLPL
DESCRIPTION
Fraction of total
dust ingested as
secondary
occupation dust
Dust lead intake
from lead based
home paint
Leadconcentration
in housedust
containing lead
based paint
Fraction of total
absorption as
passive absorption
at low dose
Fraction of total
dust ingested that
results from lead
based home paint
Maternal blood
lead concentration
Lead concen-
tration in blood
Lead concen-
tration in blood
Ratio of lead mass
in blood to lead
mass in plasma-
ECF
DEFAUL
T VALUE
OR
EON.
NO.
0
E-12e
1200
0.20
0
2.5
B-7a
B-10a
100
AGE
RANGE
(mo)
0-84
0-84
0-84
0-84
0-84
adult
0
0-84
0-84
I
or
E
E
I
E
E
E
E
I
I
I
BASIS FOR VALUES/EQUATIONS
The default condition is that there is no adult in the residence who works at
a lead-related job.
Simple combination of amount of dust ingested daily, fraction of the total
dust ingested as lead-based home paint, and lead concentration in lead-
based home paint.
Air Quality Criteria Document for Lead. (US EPA, 1986)
Based on in vitro everted rat intestine data (Aungst and Fung, 1981),
reanalyses (Marcus, 1994) of infant baboon data (Mallon, 1983) and infant
duplicate diet study (Sherlock and Quinn, 1986)
The default is that there is no lead-based paint in the home.
Based in part on Midvale 1 989 study. The default value of 2.5 t^gldL has
little influence of the early post natal exposure of the child.
Based on 85% of maternal blood lead concentration (US EPA 1989)
Simple combination of the blood lead concentrations determined in each
iteration in the solution algorithm between the previous month and that
month.
Based on the lower end of the 50-500 range for the red cell/plasma lead
concentration ratio recommended in Diamond and O'Flaherty (1992a).
UNITS
unitless
|jg/day
^g/g
unitless
unitless
|jg/dL
|jg/dL
|jg/dL
unitless
EQUATION
WHERE
USED
E-9.5,12a
E-9d
E-12e
U-1athru U-
1f
E-12e
B-7a
B-7b, 7c, 7e-
7i
B-10c
B-2b-
2d,2g,2i,2k,2
m
NOTE: I = interior parameter, E = Exterior, user selectable parameter
B-12
-------
PARAMETER NAME
RATFECUR
RATOUTFEC
SATINTAKE(t)
SATINTAKE24
SCHOOL(t)
SchoolConc
SchoolFraction
SECHOME(t)
SecHomeConc
DESCRIPTION
Ratio of
endogenous fecal
lead elimination
rate to urinary lead
elimination rate
Ratio of
elimination rate via
soft tissues to
endogenous fecal
lead elimination
rate
Half saturation
absorbable lead
intake
Half saturation
absorbable lead
intake for a 24
month old
Dust lead intake
from school
Dust lead
concentration at
school
Fraction of total
dust ingested daily
as school dust
Dust lead intake at
secondary home
Secondary home
dust lead
concentration
DEFAUL
T VALUE
OR
EON.
NO.
0.75
0.75
U-3
100
E-12b
200
0
E-12d
200
AGE
RANGE
(mo)
0-84
0-84
0-84
0-84
0-84
0-84
0-84
0-84
0-84
I
or
E
I
I
I
E
I
E
E
I
E
BASIS FOR VALUES/EQUATIONS
Assume child ratio is larger than the adult ratio; values derived from a
reanalysis of data from Ziegler et al. (1978) and Rabinowitz and Wetherill
(1973).
Within the range of values derived from a reanalysis of data from Ziegler et
al. (1978) and Rabinowitz and Wetherill (1973).
Assumed proportional to the weight of body . The coefficient of
proportionality is assumed to depend on the estimate of the parameter for a
24 month old and the corresponding body weight.
Extrapolated from reanalysis of human infant data (Sherlock and Quinn,
1986) and infant baboon data (Mallon, 1983)
Simple combination of amount of dust ingested daily, the fraction of total
dust ingested daily as school dust, and lead concentration in dust at school
By default, this dust lead concentration is set to the same as the residential
dust lead concentration.
Based on the default assumption that children are not in school.
Simple combination of amount of dust ingested daily, fraction of dust
ingested daily as secondary home dust, and lead concentration in dust at
the secondary home.
Based on the assumption that dust lead concentration in a secondary home
is the same as the default dust lead concentration in the primary home.
UNITS
unitless
unitless
|jg/day
|jg/day
|jg/day
|jg/g
unitless
|jg/day
^g/g
EQUATION
WHERE
USED
B-1f
B-1g
U-1athru U-
1e
U-3
E-9d
E-12b
E-9c,E-
9.5, 12b
E-9d
E-12d
NOTE: I = interior parameter, E = Exterior, user selectable parameter
B-13
-------
PARAMETER NAME
SecHomeFraction
soiljndoor(t)
soiljngested(t)
TBLBONE(t)
TBLFEC(t)
DESCRIPTION
Fraction of total
dust ingested daily
as secondary
home dust
Indoor household
dust lead
concentration
Soil and dust
(combined)
consumption
Lead transfer time
from blood to bone
Lead transfer time
from blood to
feces
DEFAUL
T VALUE
OR
EON.
NO.
0
E-11
0.085
0 135
0.135
0.135
0.100
0.090
0.085
1
and
B-1e
B-1f
AGE
RANGE
(mo)
0-84
0-11
12-23
24-35
36-47
48-59
60-71
72-84
0-11
12-23
24-35
36-47
48-59
60-71
72-84
24
and
0-84
0-84
I
or
E
E
I
E
I
I
BASIS FOR VALUES/EQUATIONS
Based on the default assumption that the child does not spend a significant
amount of time in a secondary home.
Under alternate dust sources model, based on assumption that both soil
and outdoor air contribute to indoor dust lead.
Based on values reported in OAQPS report (USEPA 1989, pp. A-16). The
values reported were estimated for children, ages 12-48 mos, by several
authors such as Binder et al. (1986) and Clausing et al. (1987). Sedman
(1987) extrapolated these estimates to those for children, ages 0-84 mos.
24 months - Initialization is keyed to the two year old child, based in part on
information from Heard and Chamberlain, (1982) for adults, and O'Flaherty
(1992). Once the concentration ratios are fixed, the exact value of this
parameter, within a wide range of possible values, has little effect on the
blood lead value.
0-84 months - Assumed proportional body surface area. The coefficient of
proportionality is assumed to depend on an estimate of the parameter for a
24 month old and the corresponding body surface area. Also, it is
assumed that body surface area varies as 1/3 power of the weight of body
based on Mordent! (1986).
Simple combination of an assumed ratio of urinary lead elimination rate to
endogenous fecal lead elimination rate, and lead transfer time from blood to
urine (See RATFECUR).
The ratio of of elimination rates was estimated for adults using Chamberlain
et al. (1978), and Chamberlain (1985) and is assumed to apply to ages 0-84
months.
UNITS
unitless
^g/g
g/day
days
days
EQUATION
WHERE
USED
E-9b,12d
E-9c
E-8-9a,10
B-1h,2i,2k
B-1g,2e,2f
NOTE: I = interior parameter, E = Exterior, user selectable parameter
B-14
-------
PARAMETER NAME
TBLKID(t)
TBLLIV(t)
TBLOTH(t)
TBLOUT(t)
DESCRIPTION
Lead transfer time
from blood to
kidney
L&cid trsnsfsr tims
from blood to hvsr
Lead transfer time
from blood to other
soft tissue
L&cid trsnsfsr tims
from blood to
shminstion oool
via soft tissue
DEFAUL
T VALUE
OR
EON.
NO.
10
and
B-1d
10
and
B-1b
10
and
B-1c
B-1g
AGE
RANGE
(mo)
24
and
0-84
24
and
0-84
24
and
0-84
0-84
I
or
E
I
I
I
I
BASIS FOR VALUES/EQUATIONS
24 months - Initialization is keyed to the two year old child, based in part
on information from Heard and Chamberlain, (1982) for adults, and
O'Flaherty (1992). Once the concentration ratios are fixed, the exact value
of this parameter, within a wide range of possible values, has little effect on
the blood lead value.
0-84 months - Assumed proportional body surface area. The coefficient of
proportionality is assumed to depend on an estimate of the parameter for a
24 month old and the corresponding body surface area. Also, it is
assumed that body surface area varies as 1/3 power of the weight of body
based on (Mordenti, 1986).
24 months - Initialization is keyed to the two year old child, based in part on
information from Heard and Chamberlain, (1982) for adults, and O'Flaherty
(1992). Once the concentration ratios are fixed, the exact value of this
parameter, within a wide range of possible values, has little effect on the
blood lead value.
0-84 months - Assumed proportional body surface area. The coefficient of
proportionality is assumed to depend on an estimate of the parameter for a
24 month old and the corresponding body surface area. Also, it is
assumed that body surface area varies as 1/3 power of the weight of body
based on (Mordenti, 1986).
24 months - Initialization is keyed to the two year old child, based in part
on information from Heard and Chamberlain, (1982) for adults, and
O'Flaherty (1992). Once the concentration ratios are fixed, the exact value
of this parameter, within a wide range of possible values, has little effect on
the blood lead value.
0-84 months - Assumed proportional body surface area. The coefficient of
proportionality is assumed to depend on an estimate of the parameter for a
24 month old and the corresponding body surface area. Also, it is assumed
that body surface area varies as 1/3 power of the weight of body based on
(Mordenti, 1986).
Simple combination of an assumed ratio of elimintion rate via soft tissues
to endogenous fecal lead elimination rate, times the lead transfer time from
blood to feces (See RATOUTFEC).
UNITS
days
days
days
days
EQUATION
WHERE
USED
B-2g,2h
B-2d,2e
B-2m,2n
B-2n,2o
NOTE: I = interior parameter, E = Exterior, user selectable parameter
B-15
-------
PARAMETER NAME
TBLUR(t)
TBONEBL(t)
TCORTPL(t)
time_out(t)
DESCRIPTION
Lead transfer time
from blood to urine
Lead transfer time
from bone to blood
Lead transfer time
from cortical bone
to plasma-ECF
Tims SDsnt
outdoors
DEFAUL
T VALUE
OR
EON.
NO.
20
and
B-1a
B-1h
B-2I
1
2
3
4
4
4
4
AGE
RANGE
(mo)
24
and
0-84
0-84
0-84
0-11
12-23
24-35
36-47
48-59
60-71
72-84
I
or
E
I
I
I
E
BASIS FOR VALUES/EQUATIONS
24 months - Assumed proportional to body surface area. The coefficient of
proportionality is assumed to depend on an adult estimate for the parameter
and the corresponding body surface area. The adult estimate of 39 days
was obtained using Araki et al (1986a, 1986b, 1987), Assenato et al
(1986), Campbell et al (1981), Carton et al (1987), Chamberlain et al.
(1978), Folashade et al (1991), Heard and Chamberlain (1981), He et al
(1988), Kawaii et al (1983), Kehoe (1961), Koster et al (1989), Manton and
Malloy (1983), Rabinowitz and Wetherill (1973), Rabinowitz et al (1976),
and Yokoyama et al (1985).
0-84 months - Assumed proportional body surface area. The coefficient of
proportionality is assumed to depend on an estimate of the parameter for a
24 month old and the corresponding body surface area.
Both cases above assume that (a) body surface area varies as 1/3 power of
weight of body based on (Mordenti, 1986) and (b) respectively, 70 kg and
12.3 kg are standard adult and 2 year old body weights based on Spector
(1956).
Since glomerular filtration rate (GFR) is proportional to body surface area
for ages > 24 months based on (Weil, 1955), surface area scaling is
equivalent to scaling by GFR for ages > 24 months.
Based on the assumption that masses of lead in bone and blood are in
kinetic quasi-equilibrium.
Based on the assumption that the cortical and trabecular bone pools have
similar lead kineticsfor children younger than 84 months.
Values are reported in the OAQPS staff report (USEPA 1989, pp. A-2) and
the TSD (USEPA 1990a). The values have been derived from a literature
review (Pope, 1985).
UNITS
days
days
days
hrs/day
EQUATION
WHERE
USED
B-1f,2c
B-2J.2I
B-6b,6i,6.5b,
6.5i,8d,9f
E-2
NOTE: I = interior parameter, E = Exterior, user selectable parameter
B-16
-------
PARAMETER NAME
TimeStep
TKIDPL(t)
TLIVFEC(t)
TLIVPL(t)
TOTHOUT(t)
TOTHPL(t)
TPLCORT(t)
DESCRIPTION
Length of time-
step in solution
algorithm
Lead transfer time
from kidney to
plasma-ECF
Lead transfer time
from liver to feces
from liver to
plasma-ECF
from soft tissues to
elimination pool
from soft tissues to
plasma-ECF
Lead transfer time
from plasma-ECF
DEFAUL
T VALUE
OR
EON.
NO.
1/6
B-2h
B-2f
B-2e
B-2o
B-2n
B-2k
AGE
RANGE
(mo)
0-84
0-84
0-84
0-84
0-84
0-84
0-84
I
or
E
E
I
I
I
I
I
I
BASIS FOR VALUES/EQUATIONS
This user-selectable parameter is available mainly for adjusting the model
run time to the speed of the computer. Newer, faster computers can run
the model at the shortest TimeStep (15 min) in less than one minute. The
default value, 4 hours, is based on a tradeoff between numerical accuracy
of results and computer run-time. Except in the case of extreme exposure
scenarios, there is no difference in the numerical accuracy at any user
selectable value for TimeStep.
Based on the assumption that the lead transfer time from kidney to blood is
equal to the lead transfer time from kidney to plasma-ECF.
Based on the assumption that the masses of lead in liver and blood are in
kinetic quasi-equilibrium.
Based on the assumption that the lead transfer time from liver to blood is
equal to the lead transfer time from liver to plasma-ECF.
Based on the assumption that the masses of lead in soft tissues and blood
are in kinetic quasi-equilibrium.
Based on the assumption that the lead transfer time from soft tissues to
blood is equal to the lead transfer time from soft tissues to plasma-ECF.
Based on the following assumptions:
The rate at which lead leaves the plasma-ECF to reach the bone is
proportional to the rate which lead leaves the blood to reach the same pool.
The cortical and trabecular bone pools have similar lead kinetics for
children younger than 84 months.
The cortical bone is 80% of the weight of bone based on Leggett et al.
(1982).
UNITS
day
days
days
days
days
days
days
EQUATION
WHERE
USED
B-6.5a,6.5d-
6.5i,7b,7c,
8a,d,9a-
9f,10a-10b
B-
6b,6f,6.5b,6.
5f,8d,9c
B-6e,6.5e,
8c,d,9b
B-
6b,6e,6.5b,6.
5e,8c,d,
9b
B-6g,6.5g,
8c,d,9h
B-
6c,6g,6.5c,6.
5g,8c,d,
9h
6.5i,8b,c,9f
NOTE: I = interior parameter, E = Exterior, user selectable parameter
B-17
-------
PARAMETER NAME
TPLKID(t)
TPLLIV(t)
TPLOTH(t)
TPLRBC
TPLRBC2(t)
TPLTRAB(t)
TPLUR(t)
DESCRIPTION
Lead transfer time
from plasma-ECF
to kidney
Lead transfer time
from plasma-ECF
to liver
Lead transfer time
from plasma-ECF
to soft tissues
Lead transfer
time from plasma-
ECF to red blood
cells
Lead transfer
time from plasma-
ECF to red blood
cells constrained
by the maximum
capacity of red
blood cell lead
concentration
Lead transfer time
from plasma-ECF
to trabecular bone
Lead transfer time
from plasma-ECF
to urine
DEFAUL
T VALUE
OR
EON.
NO.
B-2g
B-2d
B-2m
0.1
B-2.5
B-2i
B-2c
AGE
RANGE
(mo)
0-84
0-84
0-84
0-84
0-84
0-84
0-84
I
or
E
I
I
I
I
I
I
I
BASIS FOR VALUES/EQUATIONS
Based on the assumption that the rate at which lead leaves the plasma-
ECF to reach the kidney is proportional to the rate at which lead leaves the
blood to reach the same pool.
Based on the assumption that the rate at which lead leaves the plasma-
ECF to reach the liver is proportional to the rate at which lead leaves the
blood to reach the same pool.
Based on the assumption that the rate at which lead leaves the plasma-
ECF to reach the soft tissues is proportional to the rate which lead leaves
the blood to reach the same pool.
Initialization value of 0.1 was assigned as plausible nominal value reflecting
best professional judgement on appropriate time scale for composite
process of transfer of lead through the red blood cell membrane to lead
binding components.
Simple combination of the lead transfer time from plasma-ECF to red blood
cells, and the ratio of red blood cell lead concentration to the corresponding
maximum concentration. Based on Marcus (1985a) and reanalysis of infant
baboon data.
Based on the following assumptions:
The rate at which lead leaves the plasma-ECF to reach the bone is
proportional to the rate which lead leaves the blood to reach the same pool.
The cortical and trabecular bone pools have similar lead kinetics.
The trabecular bone is 20% of the weight of bone based on Leggett et al.
(1982).
Based on the assumption that the rate at which lead leaves the plasma-
extra-cellular fluid to reach the urine pool is proportional to the rate at which
lead leaves the blood to reach the same pool.
UNITS
days
days
days
days
days
days
days
EQUATION
WHERE
USED
B-
6c,6f,6.5c,6.
5f,8b,c,9c
B-
6c,6e,6.5c,6.
5e,8b,c,
9b
B-
6c,6g,6.5c,6.
5g,8b,c,
9d
B-2b,2.5,7b,
7c
B-
6a,6d,6.5a,6.
5d,8b,9a
B-
6c,6h,6.5c,6.
5h,8b,c,
9e
B-6c,6.5c,8a
NOTE: I = interior parameter, E = Exterior, user selectable parameter
B-18
-------
PARAMETER NAME
TRBCPL
TTRABPL(t)
TWA(t)
UPAIR(t)
UPDIET(t)
UPDUST(t)
UPDUSTA(t)
UPGUT(t)
UPOTHER(t)
UPSOIL(t)
UPTAKE(t)
UPWATER(t)
DESCRIPTION
Lead transfer time
from red blood
cells to plasma-
ECF
Lead transfer time
from trabecular
bone to plasma-
extra-cellular fluid
Time weighted
average air lead
concentration
Air lead uptake
Diet lead uptake
Dust lead uptake
Dust lead uptake
rate from alternate
sources
Total gut uptake
Uptake of other
ingested lead
Soil lead uptake
Total lead uptake
Water lead uptake
DEFAUL
T VALUE
OR
EON.
NO.
B-2b
B-2J
E-2
U-4
U-1a
U-1c
U-1 .5c
U-1f
U-1d
U-1e
U-5
U-1b
AGE
RANGE
(mo)
0-84
0-84
0-84
0-84
0-84
0-84
0-84
0-84
0-84
0-84
0-84
0-84
I
or
E
I
I
I
I
I
I
I
I
I
I
I
I
BASIS FOR VALUES/EQUATIONS
Based on the assumption that the transfer time out of RBC is similar at all
ages, since mean red cell value is similar.
Based on the assumption that the cortical and trabecular bone pools have
similar lead kinetics for children younger than 84 months.
Simple combination of outdoor and indoor air lead concentrations and the
number of hours spent outdoors.
Simple combination of media-specific lead intake and the corresponding net
absorption coefficient.
Simple combination of media-specific lead intake and the corresponding net
absorption coefficient.
Simple combination of media-specific lead intake and the corresponding net
absorption coefficient.
Simple combination of media-specific lead intake and the corresponding net
absorption coefficient.
Sum of all gastrointestinal uptake.
Assumes no other gut lead intake
Simple combination of media-specific lead intake and the corresponding net
absorption coefficient.
Simple combination of the media-specific daily lead uptake rates,
translated to a monthly rate.
Simple combination of media-specific lead intake and the corresponding net
absorption coefficient.
UNITS
days
days
|jg/m3
|jg/day
|jg/day
|jg/day
|jg/day
|jg/day
|jg/day
|jg/day
|jg/mo
|jg/day
EQUATION
WHERE
USED
B-
6b,6d,6.5b,6.
5d,7b,7c,
8c,d,9a
B-
6b,6h,6.5b,6.
5h,8c,d,
9e
E-3
U-5
U-1f
U-1f
U-1f
U-5
U-1f
U-1f
B-6a,6.5a,8a
U-1f
NOTE: I = interior parameter, E = Exterior, user selectable parameter
B-19
-------
PARAMETER NAME
UserFishConc
userFishFraction
UserFruitConc
userFruitFraction
UserGameConc
userGameFraction
UserVegConc
userVeg Fraction
DESCRIPTION
Lead
concentration in
fish
Fraction of total
meat consumed as
fish
Lead
concentration in
home grown fruits
Fraction of total
fruits consumed as
home grown fruits
Lead
concentration in
game animal meat
Fraction of total
meat consumed as
game animal meat
excluding fish
Lead
concentration in
home grown
vegetables
Fraction of total
vegetables
consumed as
home grown
vegetables
DEFAUL
T VALUE
OR
EON.
NO.
0
0
0
0
0
0
0
0
AGE
RANGE
(mo)
0-84
0-84
0-84
0-84
0-84
0-84
0-84
0-84
1
or
E
E
E
E
E
E
E
E
E
BASIS FOR VALUES/EQUATIONS
Based on the assumption that only commercially available fish are
consumed.
Based on the assumption that only commercially available fish are
consumed.
Based on the assumption that only commercially available fruits are
consumed.
Based on the assumption that only commercially available fruits are
consumed.
Based on the assumption that only commercially available meat is
consumed.
Based on the assumption that only commercially available meat is
consumed.
Based on the assumption that only commercially available vegetables are
consumed.
Based on the assumption that only commercially available vegetables are
consumed.
UNITS
M9/g
unitless
M9/g
unitless
M9/9
unitless
M9/9
unitless
EQUATION
WHERE
USED
E-5h
E-5a,5h
E-5f
E-5d,5e,5f
E-5i
E-5a,5i
E-5g
E-5b,5c,5g
NOTE: I = interior parameter, E = Exterior, user selectable parameter
B-20
-------
PARAMETER NAME
veg_all(t)
vent_rate(t)
VOLBLOOD(t)
VOLECF(t)
VOLPLASM(t)
VOLRBC(t)
water_consumption(t)
DESCRIPTION
Daily amount of all
vegetables
consumed
Ventilation rate
Volume of blood
Volume of extra-
cellular fluid (EOF)
Volume of plasma
Volume of red
blood cells
Daily amount of
water consumed
DEFAUL
T VALUE
OR
EON.
NO.
56.84
106.50
155.75
157.34
158.93
172.50
199.65
2
3
5
5
5
7
7
B-5a
B-5d
B-5c
B-5b
0.20
0.50
0.52
0.53
0.55
0.58
0.59
AGE
RANGE
(mo)
0-11
12-23
24-35
36-47
48-59
60-71
72-84
0-11
12-23
24-35
36-47
48-59
60-71
72-84
0-84
0-84
0-84
0-84
0-11
12-23
24-35
36-47
48-59
60-71
72-84
I
or
E
I
E
I
I
I
I
E
BASIS FOR VALUES/EQUATIONS
Pb concentration from data provided to EPA by FDA (US EPA (1986).
Quantity consumed from Pennington (1983).
Values are reported in the OAQPS report (USEPA 1989, pp. A-3) and the
TSD (USEPA 1990a). These estimates are based on body size in
combination with smoothed data from Phalen et al., (1985).
Statistical fitting of data from Silve et al (1987); also Spector (1956) and
Altman and Ditmer (1973)
The volume of extracellular fluid that exchanges rapidly with plasma is
estimated 73% of the blood volume based on Rabinowitz (1976). This
additional volume of distribution is assumed to be the volume the extra-
cellular fluid pool, which is the difference between the volume of the
distribution and the blood volume.
Statistical fit to VOLBLOOD(t) - VOLRBC(t)
Statistical fit to hematocrit x blood volume
Exposure Factors Handbook (US EPA, 1989b)
UNITS
g/day
m3/day
|jg/dL
dL
dL
dL
L/day
EQUATION
WHERE
USED
E-5g
E-3
B-
1h,2e,2f,2h,2
n,2o,5d,
5e,5m,10a
B-9g
B-7b,7c,9g
B-2.5
E-6a,6b
NOTE: I = interior parameter, E = Exterior, user selectable parameter
B-21
-------
PARAMETER NAME
weight_soil
WTBLOOD(t)
WTBODY(t)
WTBONE(t)
WTCORT(t)
WTECF(t)
WTKIDNEY(t)
WTLIVER(t)
WTOTHER(t)
DESCRIPTION
Percentage of total
soil and dust
ingestion that is
soil
Weight of blood
Weight of body
Weight of bone
Weight of cortical
bone
Weight of extra-
cellular fluid (EOF)
Weight of kidney
Weight of liver
Weight of soft
tissues
DEFAUL
T VALUE
OR
EON.
NO.
45
B-5m
B-5f
B-5g
B-5i
B-5e
B-5J
B-5k
B-51
AGE
RANGE
(mo)
0-84
0-84
0-84
0-84
0-84
0-84
0-84
0-84
0-84
1
or
E
E
1
1
1
1
1
1
1
1
BASIS FOR VALUES/EQUATIONS
Guidance Manual, Section 2.3 (US EPA, 1994)
Based on an blood density of 1 .056 kg/I (Spector 1956).
Statistical fitting of data from Silve et al. (1987); also Spector (1956) and
Altman and Ditmer (1973). Also, body weight of 24 month old is assumed
to be 12.3 kg (Spector 1956).
12-84 months - Based on child skeletal ash data in Harley and Kneip
(1984) and the following assumptions.
WTBONE = (WTBONEADULT / WTSKEL_ASHADULT) * WTSKEL_ASH
where
WTBONEADULT = 10kg
WTSKEL_ASHADULT = 2.91 kg
0-12 months - Assumed to be 1 1% of the weight of the body. The ratio of
weight of bone to weight of body (11%) is based on the 12-month estimate
for WTBONE from the above equation, and an estimate for WTBODY at the
same age.
Assumed to be 80% of the weight of the bone based on Leggett et al.
(1982).
Based on an assumed ECF density approximately the same as water, of
1 .0 kg/L.
Statistical fitting of data from Silve et al. (1987); also Spector (1956) and
Altman and Ditmer (1973). Also, body weight of 24 month old is assumed
to be 12.3 kg (Spector 1956).
Statistical fitting of data from Silve et al. (1987); also Spector (1956) and
Altman and Ditmer (1973). Also, body weight of 24 month old is assumed
to be 12.3 kg (Spector 1956).
Simple combination of the weight of body and the weights of kidney, liver,
bone, blood and extra-cellular fluid.
UNITS
%
kg
kg
kg
kg
kg
kg
kg
kg
EQUATION
WHERE
USED
E-8,10
B-5I
B-1a-
1e,5f,5g,5l
B-5h,5i
B-1h,5l,7e
B-5I
B-5j,5l,7f
B-2e,2f,5l,7g
B-2n,2o,7h
NOTE: I = interior parameter, E = Exterior, user selectable parameter
B-22
-------
PARAMETER NAME
WTTRAB(t)
DESCRIPTION
Weight of
trabecular bone
DEFAUL
T VALUE
OR
EON.
NO.
B-5h
AGE
RANGE
(mo)
0-84
1
or
E
1
BASIS FOR VALUES/EQUATIONS
Assumed to be 20% of the weight of the bone based on Leggett et al.
(1982).
UNITS
kg
EQUATION
WHERE
USED
B-1h, 5l,7i
NOTE: I = interior parameter, E = Exterior, user selectable parameter
B-23
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