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 
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. 
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). 

Region 8 

Susan Griffin 

Denver, CO 

Region 2 

Mark Maddaloni 

New York, NY 

Region 3 

Roy Smith 

Philadelphia, PA 

Region 5 

Patricia VanLeeuwen 

Chicago, IL 

Region 8 

Chris Weis 

Denver, CO 

NCEA/Washington 

Karen Hogan 

CHAIRPERSON 

MEMBERS 

NCEA/Washington 

Paul White 

NCEA/Cincinnati 

Harlal Choudhury 

NCEA/Research Triangle Park 

Robert Elias 

NCEA/Research Triangle Park 

Allan Marcus 

ORD/Washington 

Barbara Davis 

 

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
 
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. 

ii 
TABLE OF CONTENTS
 

Page 

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
 

iii 
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-1
 

APPENDIX B. DEFINITIONS AND DEFAULT VALUES FOR
 

PARAMETERS IN THE IEUBK LEAD MODEL . . B-1
 

LIST OF TABLES 

TABLE 1. INFORMATION PROVIDED IN TABLES A-1, A-2, AND A-3 . ........ 3
 

TABLE 2. INFORMATION PROVIDED IN TABLE B-1. ...................... 4
 

TABLE 3. PARTITIONING OF TOTAL GUT LEAD INTAKE BY PROCESS ...... 26
 

TABLE A.1. 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.1.	 DESCRIPTION OF THE PARAMETERS IN THE IEUBK CHILD LEAD
 

MODEL .................................................... B-2
 

iv 
TABLE OF CONTENTS 

(Continued) 

Page 

LIST OF FIGURES 

FIGURE 1. Biological structure of the IEUBK Lead Model ........................ 7
 

FIGURE 2. Mathematical structure of the IEUBK Lead Model ...................... 8
 

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 
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 

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
 

Region 3 (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 

PEER REVIEWERS
 

vi 
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 Matte3
 

Centers for Disease Control
 

Piscatawy, NJ
 

Dr. Neal Nelson
 

Office of Radiation and Indoor Air
 

US Environmental Protection Agency
 

Washington, DC
 

Dr. Ellen J. O'Flaherty
 

Department of Environmental Health
 

University of Cincinnati College of Medicine
 

Cincinnati, OH
 

vii 
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, 

1
 
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 

2
 
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-1. Table A-2 contains the 

equations relevant to the uptake component, while Table A-3 displays the biokinetic equations. 

Each of Tables A-1, A-2, and A-3 is structured as indicated in Table 1. 

TABLE 1. INFORMATION PROVIDED IN TABLES A-1, A-2, AND A-3 

Column Heading Description 

Equation Group Denotes a logical grouping of equations 

Equation Number 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. 

Equation 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-1, 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 

3
 
alphabetically. As seen in Table 2, this appendix provides comprehensive information for each 

parameter. 

TABLE 2. INFORMATION PROVIDED IN TABLE B-1. 

Column Heading Description 

Parameter Name 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. 

Description Brief description of the parameter. 

Default Values And/Or Defining Equation 

- Value and/or Equation Number 

- Age (months) 

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. 

I or E Indicates whether the parameter is an internal (I) or external (E) 

parameter. 'I' implies the user cannot change the value of the parameter, 

while 'E' implies the user can change the value of the parameter. 

Basis for Values/Equations Description of the basis for the default values the parameter assumes or 

the equation which defines the parameter. 

Units Units of the parameter. 

Parameter Use Equation 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 

4
 
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 (Fg Pb/m3, 

Fg Pb/g, Fg Pb/L), all of which are under the control of the user, to media specific lead intake 

rates (Fg 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 

5
 
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 (Fg/day) for the blood plasma. 

The total lead uptake (Fg/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. 

6
 
Air Diet Dust Paint Soil Water 

Lungs GI Tract 

Lungs GI Tract 

Exhaled 

Air 

Feces 

Plasma Extra-Cellular Fluid 

Feces 

Urine 

Skin 

Hair 

Nails 

Plasma Extra-Cellular Fluid 

Trabecular 

Bone 

Cortical 

Bone 

Red 

Blood 

Cells Kidney 

Other

Soft 

Tissues 

Liver 

- Environmental Media 

- Body Compartments 

- 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. 

7
 
Media-Specific 

Consumption Rates 

Media-Specific 

Lead Concentration 

Media-Specific 

Lead Intake Rates 

Media-Specific

Lead Intake Rates 

Total Available 

Lead Intake Rate 

Child's Body

Weight 

Saturation 

Factor 

Absorption

Coefficients 

Lead 

Rates 

Total Lead 

Uptake 

Maternal Blood 

Lead Conc 

Compartmental Lead Masses at Birth 

Compartmental Lead 

Tranfer Times 

Compartmental 

Lead Masses 

PbB 

Max Abs Coeff and 

Passive/Active Ratio 

Uptake 

- Input Only 

- Calculations and Input 

- Calculations Required in More Than One Component 

FIGURE 2. Mathematical structure of the IEUBK Model for Lead in Children. 

8
 
 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 

9
 
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
 
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. 

FIGURE 3. Iterative procedure for determining compartmental lead masses in biokinetic 

component. 

11
 
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 mediaspecific lead intake rates. The equations that govern these model calculations are listed in Table 

A-1 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 Fg 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-1 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-1 as a user-specified, constant percentage (indoorpercent) 

of the outdoor air lead concentration. A time-weighted average air lead concentration (TWA(t)) 

12
 
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 E13
 
5i, with the exception of InOtherDiet(t) , which can assume only default values. 1 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 InInfant and are not userselectable. 

14 
(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 × 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 × 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
 
! 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-11, 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 × 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, (agedependent) 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
 
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 agedependent, 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) Fg 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 Fg/m3 for 0-84 months; 

! Time weighted average air concentration (TWA(t) of 0.033, 0.036, 0.039, 

2Here 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. 

17 
0.042, 0.042, 0.042, and 0.042 Fg/m for the seven age intervals, 3 

respectively; 

! Lead intake rates from air (EXAIR(t)) of 0.07, 0.11, 0.19, 0.21, 0.21, 0.29, 

and 0.29 Fg/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 Fg/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 Fg/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 Fg/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 Fg/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 Fg/day for the seven age intervals. 

18
 
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 Fg/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 Fg/day for the seven age intervals; 

!	 Lead intake rate from alternative source dust (INDUSTA(t)) of zero 

Fg/day. 

Under the alternative dust model, default values for soil_ingest(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; 

19
 
! Indoor dust lead concentration (soil_indoor(t)) of 150 Fg/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 Fg/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 Fg/day. 

20
 
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 μg 

Pb/day is a fraction of the gut intake rate in μg 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 nonhuman 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 μg Pb/day for enough cases that the part of the relationship with lower 

absorption (usually blood lead above 25 or 30 μg/dL) can be clearly separated from the part of 

21
 
the relationship with higher absorption at gut lead intake less than about 100 to 200 μg 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. 

22
 
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-1, 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 × INDUST(t) 

+ ABSF × INDIET(t) 

+ ABSO × INOTHER(t) 

+ ABSS × INSOIL(t) 

+ABSW × INWATER(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 

3 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 
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 × 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: 

(1-PAF) × 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: 

1/(1 + [AVINTAKE(t)/SATINTAKE(t)]. 

24
 
Thus, the amount of lead that is absorbed by saturable processes is calculated as: 

(1-PAF) × AVINTAKE(t)/[1+ (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 × UPSOIL(t) 

While the saturable uptake component for soil is: 

(1-PAF) × UPSOIL(t)/[1+ (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. 

5Note that with a different choice of constant parameters, this term may be rearranged as 

(a*AVINTAKE)/(b+AVINTAKE), a form that may be more familiar to many readers. 

25 
Saturable 

Nonsaturable 

Total uptake 

SATINTAKE 

SATINTAKE * (1-PAF) 

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 PROCESS GUT INTAKE COMPONENT 

Absorbed Non-saturable PAF × AVINTAKE(t) 

Saturable absorbed (1-PAF) × AVINTAKE(t)/ 

[1+AVINTAKE(t)/SATINTAKE(t)] 

Excreted Non-available (1-ABSD) × INDUST(t) + 

(1-ABSF) × INDIET(t) + 

(1-ABSO) × INOTHER(t) + 

(1-ABSS) × INSOIL(t) + 

(1-ABSW) × INWATER(t) 

Saturable non-absorbed (1-PAF) × AVINTAKE(t)2 

/(AVINTAKE(t) + SATINTAKE(t)) 

26
 
27

Intake

INDIET

INWATER

INSOIL

INDUST

ABSW* INWATER

Total

Available

Gut Uptake

Saturable &

Nonsaturable

Fractions of

Available

Uptake

Saturable &

Nonsaturable

Component of

Gut Uptake

Total

Gut

Uptake

ABSS*

INSOIL

ABSD*

INDUST

Total

Gut

Uptake

Excretion of Unabsorbed Lead

ABSO* INOTHER

Figure 5. Conceptual model of gastrointestinal lead absorption.
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. 

28
 
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-1. 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
 
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
 
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 

31
 
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 

certainty 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 

32
 
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 

33
 
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 plasmaextracellular fluid pool, not into the red blood cells; 

(4)	 The uptake of lead from the gut into the plasma-extracellular fluid pool is ratelimited 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 

34
 
"small" but toxicologically 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 toxicologically 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), 

O'Flaherty (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 nearequilibrium 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 O'Flaherty 

(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 μg Pb in the 

plasma-diffusible compartment, about 45 μg Pb in the plasma protein-bound compartment, and 

about 1850 μg Pb in the erythrocytes in the adult subjects in the Rabinowitz et al (1976) stable 

35
 
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 Fg/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
 
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 μg/dL), and higher ( > 33 μg/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. 

37
 
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 

38
 
! 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 μg/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 

39
 
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-5l 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-5l, 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-1, 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), 

40
 
WTTRAB(t)(B-5i), WTCORT(t)(B-5h), WTOTHER(t)(B-5l), VOLBLOOD(t)(B-5a), 

CRKIDBL(t)(B-2h), CRLIVBL(t)(B-2e, B-2f), CRBONEBL(t)(B-1h), CROTHBL(t)(B-2n, B2o), and RATBLPL(B-3). 

First, the lead transfer times (Equations B-1, 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 

41
 
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 B2b). 

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), 

42
 
TBLKID(t), and TBLOTH(t) to RATBLPL, respectively. The transfer time from blood to urine 

(TBLUR, days) is estimated by the blood lead mass (μg) divided by the rate (μg/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-1). 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 CROTHBL(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 longterm 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
 
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 

44
 
value of 1,200 μg/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 (PBBLD0) 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-6.5i. 

For instance, the differential Equation B-6d 

dMRBC(t) MPLECF(t) & MRBC(t) ' 

dt TPLRBC2(t) TRBCPL 

is represented by the difference Equation B-6.5d 

MRBC(t) & MRBC(t & TimeStep) MPLECF(t) & MRBC(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
 
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(0), MRBC(0), MPLASM(0), MCORT(0), MKIDNEY(0), MLIVER(0), 

MOTHER(0), and MTRAB(0)) 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 B10a and B-10b, 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 

46
 
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 Fg/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. 

48
 
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-1 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
 
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
 
Enter Lead Model 

User-Specified Decisions and Media-Specific 

Consumption and Lead Concentration Parameters 

Air 

Media-Specific Lead Intake: 

EXAIR(t) 

INDIET(t) 

INDUST(t) 

INDUSTA(t) 

INSOIL(t) 

INWATER(t) 

Diet Dust/Soil Water 

Total Lead Uptake: 

Uptake(t) 

User-Specified Biokinetic 

Model Parameters: 

PBBLDMAT 

TimeStep 

Uptake Component 

Biokinetic Component 

Blood Lead Concentration: 

PBBLD(t) 

Exit Lead Model 

Figure 6. Structure of the IEUBK model with emphasis on the user control of input 

parameters and decisions. 

49
 
Diet: 

Alternate 

Model 

? 

Yes 

No 

UserFruitConc 

userFruitFraction 

UserFishConc 

userFishFraction 

UserVegConc 

userVegFraction 

UserGameConc 

userGameFraction 

user_diet_intake(t) 

water_consumption(t) 

Alternate 

Model 

? 

constant_water_conc 

FirstDrawFraction 

FirstDrawConc 

HomeFlushedConc 

FountainFraction 

FountainConc 

Yes 

No 

Water: 

Air: 

out_air_concentration(t) 

time_out(t) 

indoor percent 

vent_rate(t) 

Default Model Only Dust/Soil: 

soil_concentration(t) 

Calculate 

Indoor Household 

Dust Lead 

Conc.? 

Yes 

No 

ConcRatio_dust_soil 

ConcRatio_dust_air 

user_dust_conc(t) 

Alternate 

Dust Lead 

Sources 

? 

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
 
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 userprovided 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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Abstract from Ninth International Neurotoxicology Conference; Little Rock, Ark. 

Spector 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 

EQUATION 

NUMBER 

EQUATION 

Air Lead E-1 IndoorConc(t) = 0.01 * indoorpercent * air_concentration(t) 

E-2 TWA(t) ' [time_out(t) ( out_air_concentration (t)] % [(24&time_out (t)) ( IndoorConc (t)] 

24 

E-3 EXAIR(t) = TWA(t) * vent_rate(t) 

Dietary Lead E-4a 

E-4b 

INDIET(t) = diet_intake(t) 

or 

INDIET(t) = DietTotal(t) = InOtherDiet(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 

EQUATION 

NUMBER 

EQUATION 

E-5a 

E-5b 

E-5c 

E-5d 

E-5e 

E-5f 

E-5g 

E-5h 

E-5i 

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) * can_fruit(t) 

InFrFruit(t) = (1 - userFruitFraction) * f_fruit(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 

Water Lead E-6a 

E-6b 

INWATER(t) = water_consumption(t) * constant_water_conc 

or 

INWATER(t) =water_consumption(t) * (HomeFlushedConc * HomeFlushedFraction + FirstDrawConc * FirstDrawFraction + FountainConc * FountainFraction) 

E-7 HomeFlushedFraction = 1 - FirstDrawFraction - FountainFraction 

Soil Lead E-8 INSOIL(t) = constant_soil_conc * soil_ingested(t) * (0.01 * weight_soil) 

Note: Italicized variables are not parameters in the model. These variables are only intermediate variables. 

A-3 
EQUATION 

GROUP 

EQUATION 

NUMBER 

EQUATION 

Dust Lead E-9a 

E-9b 

E-9c 

E-9d 

INDUST(t) = constant_dust_conc * soil_ingested(t) * (1- 0.01 * weight_soil) 

INDUSTA(t) = 0; for all t 

INDUST(t) = DustTotal(t) * soil_indoor(t) * HouseFraction 

INDUSTA(t) = OCCUP(t) + SCHOOL(t) + DAYCARE(t) + SECHOME(t) + PAINT(t) 

E-9.5 HouseFraction = 1 - OccupFraction - SchoolFraction - DaycareFraction - SecHomeFraction - PaintFraction 

E-10 DustTotal(t) = soil_ingested(t) * (0.01 * (100 - weight_soil)) 

E-11 soil_indoor(t) = (contrib_percent * constant_soil_conc(t) + (multiply_factor * air_concentration(t))* 

E12a 

E12b 

E-12c 

E-12d 

E-12e 

OCCUP(t) = DustTotal(t) * OccupFraction * OccupConc 

SCHOOL(t) = DustTotal(t) * SchoolFraction * SchoolConc 

DAYCARE(t) = DustTotal(t) * DaycareFraction * DaycareConc 

SECHOME(t) = DustTotal(t) * SecHomeFraction * SecHomeConc 

PAINT(t) = 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 EQUATION 

NUMBER 

EQUATION 

Absorption 

Coefficients U-1a 

U-1b 

U-1c 

U-1d 

U-1e 

U-1f 

U-1g 

UPDIET(t) ' INDIET(t) ( ABSF ( AVF( PAF % 1 & PAF 

1 % AVINTAKE 

SATINTAKE(t) 

UPWATER(t) ' INWATER(t) ( ABSW ( AVW( PAF % 1 & PAF 

1 % AVINTAKE 

SATINTAKE(t) 

UPDUST(t) ' INDUST(t) ( ABSD ( AVD( PAF % 1 & PAF 

1 % AVINTAKE 

SATINTAKE(t) 

UPOTHER(t) ' INOTHER(t) ( ABSO ( AVO( PAF % 1 & PAF 

1 % AVINTAKE 

SATINTAKE(t) 

UPSOIL(t) ' INSOIL(t) ( ABSS ( AVS( PAF % 1 & PAF 

1 % AVINTAKE 

SATINTAKE(t) 

UPDUSTA(t) ' INDUSTA(t) ( ABSD ( AVD( PAF % 1 & PAF 

1 % AVINTAKE 

SATINTAKE(t) 

UPGUT(t) = UPDIET(t)+UPWATER(t)+UPDUST(t)+UPOTHER(t)+UPSOIL(t)+UPDUSTA(t) 

Absorption 

Coefficients 

U-2 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 EQUATION 

NUMBER 

EQUATION 

Absorption 

Coefficients 

U-3 SATINTAKE(t) ' SATINTAKE24( WTBODY(t) 

WTBODY(24) 

Total LeadUptake U-4 UPAIR(t) = air_absorb(t)*0.01*EXAIR(t) 

U-5 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 

Compartmental 

Lead Transfer 

Times 

B-1a 

B-1b 

B-1c 

B-1d 

B-1e 

B-1f 

B-1g 

B-1h 

TBLUR(t) ' TBLUR(24) ( WTBODY(t) 

WTBODY(24) 

0.33 

TBLOTH(t) ' TBLOTH(24) ( WTBODY(t) 

WTBODY(24) 

0.33 

TBLKID(t) ' TBLKID(24) ( WTBODY(t) 

WTBODY(24) 

0.33 

TBLBONE(t) ' TBLBONE(24) ( WTBODY(t) 

WTBODY(24) 

0.33 

TBONEBL(t) ' CRBONEBL(t)(TBLBONE(t) ( {WTTRAB(t) % WTCORT(t)} 

VOLBLOOD(t) 

10 

TBLFEC(t) = RATFECUR * TBLUR(t) 

TBLOUT(t) = RATOUTFEC * TBLFEC(t) 

Note: Italicized variables are not parameters in the model. These variables are only intermediate values. 

A-8 
EQUATION 

GROUP 

EQUATION 

NUMBER 

EQUATION 

Compartmental 

Lead Transfer 

Times (continued) 

B-2a 

B-2b 

B-2c 

B-2d 

B-2e 

TRBCPL ' TPLRBC( RATBLPL & 0.55 

(0.55%0.73) 

TPLRBC ' 0.1 

TPLUR(t) ' TBLUR(t) 

RATBLPL 

TPLLIV(t) ' TBLLIV(t) 

RATBLPL 

TLIVPL(t) ' CRLIVBL(t) ( TBLLIV(t) 

1 & TBLLIV(t) 

TBLFEC(t) 

( WTLIVER(t) 

VOLBLOOD(t) 

10 

TLIVFEC(t) ' CRLIVBL(t) ( TBLFEC(t) ( WTLIVER(t) 

VOLBLOOD(t) 

10 

Note: Italicized variables are not parameters in the model. These variables are only intermediate values. 

A-9 
EQUATION 

GROUP 

EQUATION 

NUMBER 

EQUATION 

Compartmental 

Lead Transfer 

Times 

(continued) 

B-2g 

B-2h 

B-2i 

B-2j 

B-2k 

B-2l 

B-2m 

TPLKID(t) ' TBLKID(t) 

RATBLPL 

TKIDPL(t) ' CRKIDBL(t) ( TBLKID(t) ( WTKIDNEY(t) 

VOLBLOOD(t) 

10 

TPLCORT(t) ' TBLBONE(t) 

(0.8 ( RATBLPL) 

TPLTRAB(t) ' TBLBONE(t) 

(0.2 ( RATBLPL) 

TTRABPL(t) ' TBONEBL(t) 

TPLOTH(t) ' TBLOTH(t) 

RATBLPL 

TCORTPL(t) = TBONEBL(T) 

Note: Italicized variables are not parameters in the model. These variables are only intermediate values. 

A-10 
EQUATION 

GROUP 

EQUATION 

NUMBER 

EQUATION 

Compartmental 

Lead Transfer 

Times 

(continued) 

B-2n 

B-2o 

TOTHOUT(t) ' CROTHBL(t) ( TBLOUT(t) ( WTOTHER(t) 

VOLBLOOD(t) 

10 

TOTHPL(t) ' CROTHBL(t) ( TBLOTH(t) 

1 & TBLOTH(t) 

TBLOUT(t) 

( WTOTHER(t) 

VOLBLOOD(t) 

10 

B-2.5 TPLRBC2(t) ' TPLRBC 

1 & MRBC(t) 

(VOLRBC(t&1) ( CONRBC) 

Blood to Plasma-ECF Lead 

Mass Ratio B-3 RATBLPL = 100 

Fluid Volumes 

and 

Organ Weights 

B-4a 

B-4b 

B-4c 

B-4d 

CRKIDBL(t) = 0.777 + [2.35 * {1 - exp(-0.0468*t)}] 

CRLIVBL(t) = 1.1 + [3.5 * {1 - exp(-0.0462*t)}] 

CRBONEBL(t) = 6.0 + [215.0 * {1 - exp(-0.000942*t)}] 

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 

EQUATION 

NUMBER 

EQUATION 

Fluid Volumes 

and 

Organ Weights 

(continued) 

B-5a 

B-5b 

B-5c 

B-5d 

B-5e 

B-5f 

B-5g 

VOLBLOOD(t) ' 10.67 

1 % exp & (t&6.87) 

7.09 

% 21.86 

1 % exp & (t&88.15) 

26.73 

VOLRBC(t) ' 4.31 

1 % exp & (t&6.45) 

10.0 

% 26.47 

1 % exp & (t&129.61) 

25.98 

VOLPLASM(t) ' 6.46 

1 % exp & (t&6.81) 

5.74 

% 8.83 

1 % exp & (t&65.66) 

23.62 

WTECF(t) ' 0.73 ( VOLBLOOD(t) 

10 

WTBODY(t) ' 8.375 

1 % exp & (t&3.80) 

3.60 

% 17.261 

1 % exp & (t&48.76) 

20.63 

VOLECF(t) = 0.73 * VOLBLOOD(t) 

WTBONE(t) = 0.111 * WTBODY(t) t # 12 months 

= 0.838 + 0.02 * t t > 12 months 

Note: Italicized variables are not parameters in the model. These variables are only intermediate values. 

A-12 
EQUATION 

GROUP 

EQUATION 

NUMBER 

EQUATION 

B-5h 

B-5i 

B-5j 

B-5k 

B-5l 

B-5m 

WTKIDNEY(t) ' 0.050 

1 % exp & (t&5.24) 

4.24 

% 0.106 

1 % exp & (t&65.67) 

34.11 

WTLIVER(t) ' 0.261 

1 % exp & (t&9.82) 

3.67 

% 0.584 

1 % exp & (t&55.65) 

37.64 

WTBLOOD(t) ' 1.056 ( VOLBLOOD(t) 

10 

WTCORT = 0.8*WTBONE 

WTRAB = 0.2*WTBONE 

WTOTHER(t) = WTBODY(t) - WTKIDNEY(t) - WTLIVER(t) - WTTRAB(t) - WTCORT(t) - WTBLOOD(t) - WTECF(t) 

Note: Italicized variables are not parameters in the model. These variables are only intermediate values. 

A-13 
EQUATION 

GROUP 

EQUATION 

NUMBER 

EQUATION 

Compartmental 

Lead Masses 

(Differential Equations) 

B-6a 

B-6b 

B-6c 

B-6d 

B-6e 

B-6f 

INFLOW(t) ' MLIVER(t) 

TLIVPL(t) 

% MKIDNEY(t) 

TKIDPL(t) 

% MOTHER(t) 

TOTHPL(t) 

% MTRAB(t) 

TTRABPL(t) 

% MCORT(t) 

TCORTPL(t) 

% MRBC(t) 

TRBCPL(t) 

OUTFLOW(t) ' MPLECF ( 1 

TPLUR(t) 

% 1 

TPLLIV(t) 

% 1 

TPLKID(t) 

% 1 

TPLOTH(t) 

% 1 

TPLTRAB(t) 

% 1 

TPLCORT(t) 

% 1 

TPLRBC2(t) 

dMRBC(t) 

dt 

' MPLECF(t) 

TPLRBC2(t) 

& MRBC(t) 

TRBCPL(t) 

dMLIVER(t) 

dt 

' MPLECF(t) 

TPLLIV(t) 

& MLIVER(t) ( 1 

TLIVPL(t) 

% 1 

TLIVFEC(t) 

dMKIDNEY(t) 

dt 

' MPLECF(t) 

TPLKID(t) 

& MKIDNEY 

TKIDPL 

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-6.5i, 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) 

Note: Italicized variables are not parameters in the model. These variables are only intermediate values. 

A-14 
EQUATION 

GROUP 

EQUATION 

NUMBER 

EQUATION 

Compartmental 

Lead Masses 

(Differential Equations) 

(continued) 

B-6g 

B-6h 

B-6i 

dMOTHER (t) 

dt 

' MPLECF (t) 

TPLOTH (t) 

& MOTHER (t) ( 1 

TOTHPL (t) 

% 1 

TOTHOUT (t) 

dMTRAB (t) 

dt 

' MPLECF (t) 

TPLTRAB (t) 

& MTRAB (t) 

TTRABPL (t) 

dMCORT (t) 

dt 

' MPLECF (t) 

TPLCORT (t) 

& MCORT (t) 

TCORTPL (t) 

Note: Italicized variables are not parameters in the model. These variables are only intermediate values. 

A-15 
EQUATION 

GROUP 

EQUATION 

NUMBER 

EQUATION 

Compartmental 

Lead Masses 

(Difference Equations) 

B-6.5a 

B-6.5b 

B-6.5c 

B-6.5d 

B-6.5e 

B-6.5f 

B-6.5g 

MPLECF(t) & MPLECF(t&TimeStep) 

TimeStep 

' UPTAKE(t) % INFLOW(t) & OUTFLOW(t) 

MRBC(t) & MRBC(t&TimeStep) 

TimeStep 

' MPLECF(t) 

TPLRBC2(t) 

& MRBC(t) 

TRBCPL 

MLIVER(t) & MLIVER(t&TimeStep) 

TimeStep 

' MPLECF(t) 

TPLLIV(t) 

& MLIVER(t) ( 1 

TLIVPL(t) 

% 1 

TLIVFEC(t) 

INFLOW (t) ' MLIVER (t) 

TLIVPL (t) 

% MKIDNEY (t) 

TKIDPL (t) 

% MOTHER (t) 

TOTHPL (t) 

% MTRAB (t) 

TTRABPL (t) 

% MCORT (t) 

TCORTPL (t) 

% MRBC (t) 

TRBCPL 

OUTFLOW (t) ' MPLECF ( 1 

TPLUR (t) 

% 1 

TPLLIV (t) 

% 1 

TPLKID (t) 

% 1 

TPLOTH (t) 

% 1 

TPLTRAB (t) 

% 1 

TPLCORT (t) 

% 1 

TPLRBC2 (t) 

MKIDNEY(t) & MKIDNEY(t&TimeStep) 

TimeStep 

' MPLECF(t) 

TPLKID(t) 

& MKIDNEY(t) 

TKIDPL(t) 

MOTHER(t) & MOTHER(t&TimeStep) 

TimeStep 

' MPLECF(t) 

TPLOTH(t) 

& MOTHER(t) ( 1 

TOTHPL(t) 

% 1 

TOTHOUT(t) 

Note: Italicized variables are not parameters in the model. These variables are only intermediate values. 

A-16 
EQUATION 

GROUP 

EQUATION 

NUMBER 

EQUATION 

Compartmental 

Lead Masses 

(Difference Equations) 

(continued) 

B-6.5h 

B-6.5i 

MTRAB(t) & MTRAB(t&TimeStep) 

TimeStep 

' MPLECF(t) 

TPLTRAB(t) 

& MTRAB(t) 

TTRABPL(t) 

MCORT(t) & MCORT(t&TimeStep) 

TimeStep 

' MPLECF(t) 

TPLCORT(t) 

& MCORT(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-7c 

B-7d 

MPLECF(0) ' 

PBBLD0 ( (VOLPLASM(0) % VOLRBC(0)) ( TPLRBC 

TimeStep 

( (1.7&HCT0) 

TRBCPL(0) 

TimeStep 

% TPLRBC 

TimeStep 

MRBC(0) ' 

PBBLD0 ( (VOLPLASM(0) % VOLRBC(0)) ( TRBCPL(0) 

TimeStep 

TRBCPL(0) 

TimeStep 

% TPLRBC 

TimeStep 

MPLASM(0) ' MPLECF(0) 

(1.7&HCT0) 

MPLECF(0) ' 

PBBLD0 ( (VOLPLASM(0) % VOLRBC(0)) ( TPLRBC 

TimeStep 

TRBCPL(0) 

TimeStep 

MRBC(0) ' PBBLD0 ( (VOLPLASM(0) % VOLRBC(0)) ( 1 & 0.416 TPLRBC(0) 

TRBCPL(0) 

MPLASM(0) ' MPLECF(0) 

0.416 

PBBLD0 = 0.85 * PBBLDMAT 

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. 

A-18
 
EQUATION 

GROUP 

EQUATION 

NUMBER 

EQUATION 

Tissue Lead Masses 

and Blood Lead 

Concentration at 

Birth 

B-7e 

B-7f 

B-7g 

B-7h 

B-7I 

MCORT(0) = 78.9 (* PBBLD0 * WTCORT(0) 

MKIDNEY(0) = 10.6 * PBBLD0 * WTKIDNEY(0) 

MLIVER(0) = 13.0 * PBBLD0 * WTLIVER(0) 

MOTHER(0) = 16.0 * PBBLD0 * WTOTHER(0) 

MTRAB(0) = 51.2 * PBBLD0 * WTTRAB(0) 

Note: Italicized variables are not parameters in the model. These variables are only intermediate values. 

A-19 
EQUATION 

GROUP 

EQUATION 

NUMBER 

EQUATION 

Compartmental 

Lead Masses 

(Solution 

Algorithm) 

B-8a 

B-8b 

B-8c 

B-8d 

MPLECF(t) ' 

MPLECF(t&TimeStep) % UPTAKE(t) ( TimeStep 

30 

% SUM3(t) 

[1 % {TimeStep ( SUM1 (t)} & {TimeStep ( SUM2 (t)}] 

SUM1 (t) ' 1 

TPLUR (t) 

% 1 

TPLRBC2 (t) 

% 1 

TPLLIV (t) 

% 1 

TPLKID (t) 

% 1 

TPLOTH (t) 

% 1 

TPLTRAB (t) 

% 1 

TPLCORT (t) 

SUM2 (t) ' 1 

TPLRBC2 (t) ( TRBCPL 

TimeStep 

% 1 

% 1 

TPLLIV (t) ( TLIVPL (t) 

TimeStep 

% TLIVPL (t) 

TLIVALL (t) 

% 1 

% 1 

TPLKID (t) ( TKIDPL (t) 

TimeStep 

% 1 

% 1 

TOTHPL (t) 

TimeStep 

% TOTHPL (t) 

TOTHALL (t) 

% 1 

% 1 

TPLTRAB (t) ( TTRABPL (t) 

TimeStep 

% 1 

% 1 

TPLCORT (t) ( TCORTPL (t) 

TimeStep 

% 1 

SUM3 (t) ' MRBC (t&TimeStep ) 

TRBCPL 

TimeStep 

% 1 

% MLIVER (t&TimeStep ) 

TLIVPL (t) 

TimeStep 

% TLIVPL (t) 

TLIVALL (t) 

% 1 

% MKIDNEY (t&TimeStep ) 

TKIDPL (t) 

TimeStep 

% 1 

% MOTHER (t&TimeStep ) 

TOTHPL (t) 

TimeStep 

% TOTHPL (t) 

TOTHALL (t) 

% 1 

% MTRAB (t&TimeStep ) 

TTRABPL (t) 

TimeStep 

% 1 

% MCORT (t&TimeStep ) 

TCORTPL (t) 

TimeStep 

% 1 

Note: In the solution algorithm (Equations B-8a - B-10c), 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 

B-9b 

B-9c 

B-9d 

B-9e 

MLIVER (t) ' 

MLIVER (t&TimeStep ) % MPLECF (t) ( TimeStep 

TPLLIV (t) 

1 % TimeStep 

TLIVALL (t) 

MRBC(t) ' 

MRBC(t&TimeStep) % MPLECF(t) ( TimeStep 

TPLRBC2(t) 

1 % TimeStep 

TRBCPL 

MOTHER (t) ' 

MOTHER (t&TimeStep ) % MPLECF (t) ( TimeStep 

TPLOTH (t) 

1 % TimeStep 

TOTHALL (t) 

Note: In the solution algorithm (Equations B-8a - B-10c), 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 

B-9g 

B-9h 

B-9i 

MPLASM(t) ' MPLECF(t) ( VOLPLASM(t) 

VOLECF(t) % VOLPLASM(t) 

TLIVALL (t) ' 1 

1 

TLIVPL (t) 

% 1 

TLIVFEC (t) 

TOTHALL (t) ' 1 

1 

TOTHPL (t) 

% 1 

TOTHOUT (t) 

MCORT(t) ' 

MCORT(t&TimeStep) % MPLECF(t) ( TimeStep 

TPLCORT(t) 

1 % TimeStep 

TCORTPL(t) 

Note: In the solution algorithm (Equations B-8a - B-10c), 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 

B-10a 

B-10b 

B-10c 

BLOOD (t) ' j

STEPS 

t ' 1 

MRBC (t) % MPLASM (t) 

VOLBLOOD (i&1) 

NOTE: Equation B-10a is computed by a cumulative loop 

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-10c), 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 DESCRIPTION 

DEFAUL 

T VALUE 

OR 

EQN. 

NO. 

AGE 

RANGE 

(mo) 

I 

or 

E BASIS FOR VALUES/EQUATIONS UNITS 

EQUATION 

WHERE 

USED 

ABSD 

Total absorption 

for dust at low 

saturation 

0.3 0-84 E Based on US EPA (1989a). unitless U-1c, 

U-2 

ABSF 

Total absorption 

for food at low 

saturation 

0.5 0-84 E Based on US EPA (1989a). unitless U-1a,U-2 

ABSO 

Total absorption 

for other ingested 

lead at low 

saturation 

0.0 0-84 E Based on the default condition that there is no other source of lead 

ingestion in the household. unitless U-1d,U-2 

ABSS 

Total absorption 

for soil at low 

saturation 

0.3 0-84 E Based on US EPA (1989a). unitless U-1e,U-2 

ABSW 

Total absorption 

for water at low 

saturation 

0.5 0-84 E Based on US EPA (1989a). unitless U-1b,U-2 

air_absorb(t) 

Net percentage 

absorption of air 

lead 

32 

32 

32 

32 

32 

32 

32 

0-11 

12-23 

24-35 

36-47 

48-59 

60-71 

72-84 

E 

Deposition efficiencies of airborne lead particles were estimated by U S 

EPA (1989a). 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. 

% U-4 

air_concentration(t) Outdoor air lead 

concentration 

0.1 

0.1 

0.1 

0.1 

0.1 

0.1 

0.1 

0-11 

12-23 

24-35 

36-47 

48-59 

60-71 

72-84 

E 

Based on the lower end of the range 0.1 - 0.3 μg Pb/m3 that is reported for 

outdoor air lead concentration in U.S. cities without lead point sources (US 

EPA 1989) 

μg/m3 E-1,2,11 

NOTE: I = interior parameter, E = Exterior, user selectable parameter B-2
 
PARAMETER NAME DESCRIPTION 

DEFAUL 

T VALUE 

OR 

EQN. 

NO. 

AGE 

RANGE 

(mo) 

I 

or 

E BASIS FOR VALUES/EQUATIONS UNITS 

EQUATION 

WHERE 

USED 

AVF, AVW, AVD, AVO, 

AVS Bioavailability 1 0-84 I Parameter added for later flexibility in describing the absorption process; has no effect in current algorithm. unitless U-1a-U-1e 

AVINTAKE Available intake U-2 0-84 I The amount of Pb that is available for intake μg U-1a,b,c,d,e 

can_fruit(t) 

Lead intake from 

canned fruit when 

fruit is consumed 

only in canned 

form 

1.811 

1.063 

1.058 

0.999 

0.940 

0.969 

1.027 

0-11 

12-23 

24-35 

36-47 

48-59 

60-71 

72-84 

I Pb concentration from data provided to EPA by FDA (US EPA (1986). 

Quantity consumed from Pennington (1983). μg/day E-5d 

can_veg(t) 

Lead intake from 

canned vegetables 

when vegetable is 

consumed only in 

canned form 

0.074 

0.252 

0.284 

0.295 

0.307 

0.291 

0.261 

0-11 

12-23 

24-35 

36-47 

48-59 

60-71 

72-84 

I Pb concentration from data provided to EPA by FDA (US EPA (1986). 

Quantity consumed from Pennington (1983). μg/day E-5b 

contrib_percent 

Ratio of indoor 

dust lead 

concentration to 

soil lead 

concentration 

0.70 0-84 E Analysis of soil and dust data from 1983 East Helena study (US EPA, 1989) Fg/g per 

Fg/g E-11 

CONRBC 

Maximum lead 

concentration 

capacity of red 

blood cells 

1200 0-84 I 

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). 

μg/dL B-2.5 

constant_soil_conc(t) Soil lead 

concentration 

200 

200 

200 

200 

200 

200 

200 

0-11 

12-23 

24-35 

36-47 

48-59 

60-71 

72-84 

E Air Quality Criteria Document for Lead. (US EPA, 1986) μg/g E-8 

NOTE: I = interior parameter, E = Exterior, user selectable parameter B-3 
PARAMETER NAME DESCRIPTION 

DEFAUL 

T VALUE 

OR 

EQN. 

NO. 

AGE 

RANGE 

(mo) 

I 

or 

E BASIS FOR VALUES/EQUATIONS UNITS 

EQUATION 

WHERE 

USED 

constant_water_conc Water lead 

concentration 4.0 0-84 E 

Based on analysis of data from the American Water Works Service Co. 

(Marcus, 1989) μg/L E-6a 

CRBONEBL(t) 

Ratio of lead 

concentration 

(μg/kg) in bone to 

blood lead 

concentration 

(μg/L) 

B-4c 0-84 I 

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, 0-12 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. 

L/kg B-1h 

CRKIDBL(t) 

Ratio of lead 

concentration 

(μg/kg) in kidney 

to blood lead 

concentration 

(μgL) 

B-4a 0-84 I 

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, 0-12 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. 

L/kg B-2h 

CRLIVBL(t) 

Ratio of lead 

concentration 

(μg/kg) in liver to 

blood lead 

concentration 

(μg/l) 

B-4b 0-84 I 

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, 0-12 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. 

L/kg B-2e,2f 

NOTE: I = interior parameter, E = Exterior, user selectable parameter B-4 
PARAMETER NAME DESCRIPTION 

DEFAUL 

T VALUE 

OR 

EQN. 

NO. 

AGE 

RANGE 

(mo) 

I 

or 

E BASIS FOR VALUES/EQUATIONS UNITS 

EQUATION 

WHERE 

USED 

CROTHBL(t) 

Ratio of lead 

concentration 

(μg/kg) in other 

soft tissue to blood 

lead concentration 

(μg/L) 

B-4d 0-84 I 

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%), GI 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, 0-12 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. 

L/kg B-2n,2o 

DAYCARE(t) Dust lead intake at 

daycare E-12c 0-84 I Simple combination of the total amount of dust ingested daily, fraction of total dust ingested as daycare dust, and dust lead concentration at daycare. μg/day E-9d 

DaycareConc 

Dust lead 

concentration at 

daycare 

200 0-84 E Based on the assumption that default daycare dust concentrations are the 

same as default residence dust concentrations. μg/g E-12c 

DaycareFraction 

Fraction of total 

dust ingested daily 

as daycare dust 

0 0-84 E Based on the default assumption that the child does not attend daycare. unitless E-9.5,12c 

diet_intake(t) User-specified diet 

lead intake 

5.53 

5.78 

6.49 

6.24 

6.01 

6.34 

7.00 

0-11 

12-23 

24-35 

36-47 

48-59 

60-71 

72-84 

E Pb concentration from data provided to EPA by FDA (US EPA (1986). 

Quantity consumed from Pennington (1983). μg/day E-4a 

DietTotal(t) Total Dietary 

Intake E-4b 0.84 I Summation of all dietary sources; same as INDIET(t) μg/day E-4b 

DustTotal(t) Daily amount of 

dust ingested E-10 0-84 I Simple combination of total amount soil and dust ingested daily and fraction of this combined ingestion that is dust alone. g/day E-9c,12a12e 

NOTE: I = interior parameter, E = Exterior, user selectable parameter B-5 
PARAMETER NAME DESCRIPTION 

DEFAUL 

T VALUE 

OR 

EQN. 

NO. 

AGE 

RANGE 

(mo) 

I 

or 

E BASIS FOR VALUES/EQUATIONS UNITS 

EQUATION 

WHERE 

USED 

EXAIR(t) Air lead intake E-3 0-84 I Simple combination of average air lead concentration and ventilation rate. μg/day U-4 

f_fruit(t) 

Lead intake from 

fresh fruit if no 

home-grown fruit 

is consumed 

0.039 

0.196 

0.175 

0.175 

0.179 

0.203 

0.251 

0-11 

12-23 

24-35 

36-47 

48-59 

60-71 

72-84 

I Pb concentration from data provided to EPA by FDA (US EPA (1986). 

Quantity consumed from Pennington (1983). μg/day E-5e 

f_veg(t) 

Lead intake from 

fresh vegetables if 

no home-grown 

vegetables are 

consumed 

0.148 

0.269 

0.475 

0.466 

0.456 

0.492 

0.563 

0-11 

12-23 

24-35 

36-47 

48-59 

60-71 

72-84 

I Pb concentration from data provided to EPA by FDA (US EPA (1986). 

Quantity consumed from Pennington (1983). μg/day E-5c 

FirstDrawConc First Draw water 

lead concentration 4.0 0-84 E Based on analysis of data from the American Water Works Service Co. (Marcus, 1989) μg/L E-6b 

FirstDrawFraction 

Fraction of total 

water consumed 

daily as first draw 

0.5 0-84 E 

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. 

unitless E-6b,7 

FountainConc Fountain water 

lead concentration 10 0-84 E 

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 Fg/L. 

μg/L E-6b 

FountainFraction 

Fraction of total 

water consumed 

daily from 

fountains 

0.15 0-84 E A default value was based on 4-6 trips to the water fountain at 40-50 ml per 

trip. none E-6b,7 

fruit_all(t) Daily amount of all 

frults consumed 

38.481 

169.000 

63.166 

61.672 

61.848 

67.907 

80.024 

0-11 

12-23 

24-35 

36-47 

48-59 

60-71 

72-84 

I Pb concentration from data provided to EPA by FDA (US EPA (1986). 

Quantity consumed from Pennington (1983). g/day E-5f 

NOTE: I = interior parameter, E = Exterior, user selectable parameter B-6 
PARAMETER NAME DESCRIPTION 

DEFAUL 

T VALUE 

OR 

EQN. 

NO. 

AGE 

RANGE 

(mo) 

I 

or 

E BASIS FOR VALUES/EQUATIONS UNITS 

EQUATION 

WHERE 

USED 

HomeFlushedConc 

Home flushed 

water lead 

concentration 

1.0 0-84 E Based on analysis of data from the American Water Works Service Co. 

(Marcus, 1989) μg/L E-6b 

HCT0 Hematocrit at birth 0.45 0 I Data from Silve et al. (1987); also Spector (1956) and Altman and Ditmer 

(1973) 

decimal 

percent B-7b,d 

InCanFruit(t) Lead intake from 

canned fruit E-5d 0-84 I 

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. 

μg/day E-4b 

InCanVeg(t) Lead intake from 

canned vegetables E-5b 0-84 I 

Simple combination of the fraction of vegetables consumed daily as nonhome grown, and lead intake from canned vegetables when vegetables are 

consumed only in canned form. 

μg/day E-4b 

INDIET(t) Diet lead intake 

E-4a 

or 

E-4b 

0-84 I 

Two options are provided. 

Default option - Considers composite diet lead intake. 

Alternate option - Combines lead intake from several individual components 

of diet. 

μg/day U-1a, U-2 

IndoorConc(t) Indoor air lead 

concentration E-1 0-84 I Algebraic expression of relationship μg/m3 E-2 

indoorpercent 

Ratio of indoor 

dust lead 

concentration to 

corresponding 

outdoor 

concentration 

30 0-84 E 

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). 

% E-1 

INDUST(t) Household dust 

lead intake 

E-9a 

or 

E-9c 

0-84 I 

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. 

μg/day U-1-c, U-2 

NOTE: I = interior parameter, E = Exterior, user selectable parameter B-7 
PARAMETER NAME DESCRIPTION 

DEFAUL 

T VALUE 

OR 

EQN. 

NO. 

AGE 

RANGE 

(mo) 

I 

or 

E BASIS FOR VALUES/EQUATIONS UNITS 

EQUATION 

WHERE 

USED 

INDUSTA(t) 

Lead intake from 

alternate dust 

sources 

E-9b 

or 

E-9d 

0-84 I 

Two options are provided. 

Default option - Assumes that lead intake from alternate sources is zero. 

Alternate option - Combines lead intake from several alternate sources. 

μg/day U-1.5c, U-2 

InFish(t) Lead intake from 

fish E-5h 0-84 I Simple combination of total meat consumed daily, fraction of meat consumed as fish, and lead concentration in fish. μg/day E-4b 

InFrFruit(t) 

Lead intake from 

non-home grown 

fresh fruits 

E-5e 0-84 I Simple combination of the fraction of fruits consumed daily as non-home 

grown and lead intake from fresh fruits. μg/day E-4b 

InFrVeg(t) 

Lead intake from 

non-home grown 

fresh vegetables 

E-5c 0-84 I Simple combination of the fraction of vegetables consumed daily as nonhome grown and lead intake from fresh vegetables. μg/day E-4b 

InGame(t) Lead intake from 

game animal meat E-5i 0-84 I 

Simple combination of total meat consumed daily, fraction of meat 

consumed as game animal meat, and lead concentration in game animal 

meat. 

μg/day E-4b 

InHomeFruit(t) Lead intake from 

home grown fruits E-5f 0-84 I Simple combination of total amount of fruit consumed daily, fraction of fruit consumed as home grown, and lead concentration in home grown fruit. μg/day E-4b 

InHomeVeg(t) 

Lead intake from 

home grown 

vegetables 

E-5g 0-84 I 

Simple combination of total amount of vegetable consumed daily, fraction of 

vegetables consumed as home grown, and lead concentration in home 

grown vegetables. 

μg/day E-4b 

InMeat(t) 

Lead intake from 

non-game and 

non-fish meat 

E-5a 0-84 I 

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. 

μg/day E-4b 

InOtherDiet(t) 

Combined lead 

intake from dairy 

food, juice, nuts, 

beverage, pasta, 

bread, sauce, 

candy, infant and 

formula food 

3.578 

3.506 

3.990 

3.765 

3.545 

3.784 

4.215 

0-11 

12-23 

24-35 

36-47 

48-59 

60-71 

72-84 

I 

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). 

μg/day E-4b, E-4c 

NOTE: I = interior parameter, E = Exterior, user selectable parameter B-8 
PARAMETER NAME DESCRIPTION 

DEFAUL 

T VALUE 

OR 

EQN. 

NO. 

AGE 

RANGE 

(mo) 

I 

or 

E BASIS FOR VALUES/EQUATIONS UNITS 

EQUATION 

WHERE 

USED 

INOTHER(t) 

Combined other 

sources of 

ingested lead, 

such as paint 

chips, ethnic 

medicines, etc. 

0 0-84 E Assumes no other sources of ingested lead Fg/day U-1d, U-2 

INSOIL(t) Soil lead intake E-8 0-84 I 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. μg/day U-1e,U-2 

INWATER(t) Water lead intake 

E-6a 

or 

E-6b 

0-84 I 

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. 

μg/day U-1b, U-2 

MCORT(t) Mass of lead in 

cortical bone 

B-7e 

and 

B-9f 

0 

and 

0-84 

I 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. 

μg B-6b,6i,6.5b, 

6.5i,8a,9f 

meat_all(t) 

Daily amount of 

meat (including 

fish and game) 

consumed 

29.551 

87.477 

95.700 

101.570 

107.441 

111.948 

120.961 

0-11 

12-23 

24-35 

36-47 

48-59 

60-71 

72-84 

I Pb concentration from data provided to EPA by FDA (US EPA (1986). 

Quantity consumed from Pennington (1983). g/day E-5h 

NOTE: I = interior parameter, E = Exterior, user selectable parameter B-9 
PARAMETER NAME DESCRIPTION 

DEFAUL 

T VALUE 

OR 

EQN. 

NO. 

AGE 

RANGE 

(mo) 

I 

or 

E BASIS FOR VALUES/EQUATIONS UNITS 

EQUATION 

WHERE 

USED 

meat(t) 

Lead intake from 

meat if no game 

meat or fish is 

consumed 

0.226 

0.630 

0.811 

0.871 

0.931 

1.008 

1.161 

0-11 

12-23 

24-35 

36-47 

48-59 

60-71 

72-84 

I Pb concentration from data provided to EPA by FDA (US EPA (1986). 

Quantity consumed from Pennington (1983). μg /day E-5a 

MKIDNEY(t) Mass of lead in 

kidney 

B-7f 

and 

B-9c 

0 

and 

0-84 

I 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). 

μg 

B6b,6f,6.5b,6. 

5f,8d,9c 

MLIVER(t) Mass of lead in 

liver 

B-7g 

and 

B-9b 

0 

and 

0-84 

I 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). 

μg 

B6b,6e,6.5b,6. 

5e,8d,9b 

MOTHER(t) Mass of lead in 

soft tissues 

B-7h 

and 

B-9d 

0 

and 

0-84 

I 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). 

μg 

B6b,6g,6.5b,6. 

5g,8d,9d 

MPLASM(t) Mass of lead in 

plasma pool 

B-7d 

and 

B-9g 

0 

and 

0-84 

I 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. 

μg B-10a 

NOTE: I = interior parameter, E = Exterior, user selectable parameter B-10 
PARAMETER NAME DESCRIPTION 

DEFAUL 

T VALUE 

OR 

EQN. 

NO. 

AGE 

RANGE 

(mo) 

I 

or 

E BASIS FOR VALUES/EQUATIONS UNITS 

EQUATION 

WHERE 

USED 

MPLECF(t) 

Mass of lead in 

plasma-extracellular fluid 

(plasma-ECF) 

B-7b 

and 

B-8a 

0 

and 

0-84 

I 0 months - Based on two assumptions. 

(1) masses of lead in plasma-ECF and red blood cells are in kinetic quasiequilibrium, 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). 

μg 

B-6a,6c6i,6.5a, 

6.5c6.5i,8a,9a-9g 

MRBC(t) Mass of lead in red 

blood cells 

B-7c 

and 

B-9a 

0 

and 

0-84 

I 0 months - Based on the assumption that the masses of lead in plasmaECF 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). 

μg 

B6a,6d,6.5a,6. 

5d,8d,9a,10a 

MTRAB(t) Mass of lead in 

trabecular bone 

B-7i 

and 

B-9e 

0 

and 

0-84 

I 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. 

μg 

B6b,6h,6.5b,6. 

5h,8d,9e 

multiply_factor 

Ratio of indoor 

dust lead 

concentration to 

air lead 

concentration 

100 0-84 E 

Analyses of the 1983 East Helena study in (USEPA 1989, Appendix B-8) 

suggest about 267 μg/g increment of lead in dust for each μg /m3. lead in 

air. A much smaller factor of 100 μg/g PbD per μg/m3 is assumed for nonsmelter community exposure. 

μg /g 

per 

μg/m3 

E-11 

OCCUP(t) 

Dust lead intake 

from secondary 

occupation 

E-12a 0-84 I 

Simple combination of amount of dust ingested, fraction of the total dust 

ingested as secondary occupational dust, and lead concentration in 

secondary occupational dust 

μg/day E-9d 

OccupConc 

Secondary 

occupational dust 

lead concentration 

1200 0-84 E Air Quality Criteria Document for Lead. (US EPA, 1986) μg/g E-12a 

NOTE: I = interior parameter, E = Exterior, user selectable parameter B-11 
PARAMETER NAME DESCRIPTION 

DEFAUL 

T VALUE 

OR 

EQN. 

NO. 

AGE 

RANGE 

(mo) 

I 

or 

E BASIS FOR VALUES/EQUATIONS UNITS 

EQUATION 

WHERE 

USED 

OccupFraction 

Fraction of total 

dust ingested as 

secondary 

occupation dust 

0 0-84 E The default condition is that there is no adult in the residence who works at 

a lead-related job. unitless E-9.5,12a 

PAINT(t) 

Dust lead intake 

from lead based 

home paint 

E-12e 0-84 I 

Simple combination of amount of dust ingested daily, fraction of the total 

dust ingested as lead-based home paint, and lead concentration in leadbased home paint. 

μg/day E-9d 

PaintConc 

Leadconcentration 

in housedust 

containing lead 

based paint 

1200 0-84 E Air Quality Criteria Document for Lead. (US EPA, 1986) μg/g E-12e 

PAF 

Fraction of total 

absorption as 

passive absorption 

at low dose 

0.20 0-84 E 

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) 

unitless U-1a thru U1f 

PaintFraction 

Fraction of total 

dust ingested that 

results from lead 

based home paint 

0 0-84 E The default is that there is no lead-based paint in the home. unitless E-12e 

PBBLDMAT Maternal blood 

lead concentration 2.5 adult E Based in part on Midvale 1989 study. The default value of 2.5 Fg/dL has little influence of the early post natal exposure of the child. μg/dL B-7a 

PBBLD0 Lead concentration in blood B-7a 0 I Based on 85% of maternal blood lead concentration (US EPA 1989) μg/dL B-7b, 7c, 7e7i 

PBBLOODEND(t) Lead concentration in blood B-10a 0-84 I 

Simple combination of the blood lead concentrations determined in each 

iteration in the solution algorithm between the previous month and that 

month. 

μg/dL B-10c 

RATBLPL 

Ratio of lead mass 

in blood to lead 

mass in plasmaECF 

100 0-84 I 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). unitless 

B-2b2d,2g,2i,2k,2 

m 

NOTE: I = interior parameter, E = Exterior, user selectable parameter B-12 
PARAMETER NAME DESCRIPTION 

DEFAUL 

T VALUE 

OR 

EQN. 

NO. 

AGE 

RANGE 

(mo) 

I 

or 

E BASIS FOR VALUES/EQUATIONS UNITS 

EQUATION 

WHERE 

USED 

RATFECUR 

Ratio of 

endogenous fecal 

lead elimination 

rate to urinary lead 

elimination rate 

0.75 0-84 I 

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). 

unitless B-1f 

RATOUTFEC 

Ratio of 

elimination rate via 

soft tissues to 

endogenous fecal 

lead elimination 

rate 

0.75 0-84 I Within the range of values derived from a reanalysis of data from Ziegler et 

al. (1978) and Rabinowitz and Wetherill (1973). unitless B-1g 

SATINTAKE(t) 

Half saturation 

absorbable lead 

intake 

U-3 0-84 I 

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. 

μg/day U-1a thru U1e 

SATINTAKE24 

Half saturation 

absorbable lead 

intake for a 24 

month old 

100 0-84 E Extrapolated from reanalysis of human infant data (Sherlock and Quinn, 

1986) and infant baboon data (Mallon, 1983) μg/day U-3 

SCHOOL(t) Dust lead intake 

from school E-12b 0-84 I 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 μg/day E-9d 

SchoolConc 

Dust lead 

concentration at 

school 

200 0-84 E By default, this dust lead concentration is set to the same as the residential 

dust lead concentration. μg/g E-12b 

SchoolFraction 

Fraction of total 

dust ingested daily 

as school dust 

0 0-84 E Based on the default assumption that children are not in school. unitless E-9c,E9.5,12b 

SECHOME(t) Dust lead intake at 

secondary home E-12d 0-84 I 

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. 

μg/day E-9d 

SecHomeConc 

Secondary home 

dust lead 

concentration 

200 0-84 E 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. μg/g E-12d 

NOTE: I = interior parameter, E = Exterior, user selectable parameter B-13 
PARAMETER NAME DESCRIPTION 

DEFAUL 

T VALUE 

OR 

EQN. 

NO. 

AGE 

RANGE 

(mo) 

I 

or 

E BASIS FOR VALUES/EQUATIONS UNITS 

EQUATION 

WHERE 

USED 

SecHomeFraction 

Fraction of total 

dust ingested daily 

as secondary 

home dust 

0 0-84 E Based on the default assumption that the child does not spend a significant 

amount of time in a secondary home. unitless E-9b,12d 

soil_indoor(t) 

Indoor household 

dust lead 

concentration 

E-11 

0-11 

12-23 

24-35 

36-47 

48-59 

60-71 

72-84 

I Under alternate dust sources model, based on assumption that both soil 

and outdoor air contribute to indoor dust lead. μg/g E-9c 

soil_ingested(t) 

Soil and dust 

(combined) 

consumption 

0.085 

0.135 

0.135 

0.135 

0.100 

0.090 

0.085 

0-11 

12-23 

24-35 

36-47 

48-59 

60-71 

72-84 

E 

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. 

g/day E-8-9a,10 

TBLBONE(t) Lead transfer time 

from blood to bone 

1 

and 

B-1e 

24 

and 

0-84 

I 

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). 

days B-1h,2i,2k 

TBLFEC(t) 

Lead transfer time 

from blood to 

feces 

B-1f 0-84 I 

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. 

days B-1g,2e,2f 

NOTE: I = interior parameter, E = Exterior, user selectable parameter B-14 
PARAMETER NAME DESCRIPTION 

DEFAUL 

T VALUE 

OR 

EQN. 

NO. 

AGE 

RANGE 

(mo) 

I 

or 

E BASIS FOR VALUES/EQUATIONS UNITS 

EQUATION 

WHERE 

USED 

TBLKID(t) 

Lead transfer time 

from blood to 

kidney 

10 

and 

B-1d 

24 

and 

0-84 

I 

24 months -

on information from Heard and Chamberlain, (1982) for adults, and 

O'Flaherty (1992). 

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. 

proportionality is assumed to depend on an estimate of the parameter for a 

24 month old and the corresponding body surface area. 

assumed that body surface area varies as 1/3 power of the weight of body 

based on (Mordenti, 1986). 

days B-2g,2h 

TBLLIV(t) Lead transfer time 

from blood to liver 

10 

and 

B-1b 

24 

and 

0-84 

I 

24 months -

information from Heard and Chamberlain, (1982) for adults, and O'Flaherty 

(1992). 

parameter, within a wide range of possible values, has little effect on the 

blood lead value. 

0-84 months - Assumed proportional body surface area. 

proportionality is assumed to depend on an estimate of the parameter for a 

24 month old and the corresponding body surface area. 

assumed that body surface area varies as 1/3 power of the weight of body 

based on (Mordenti, 1986). 

days B-2d,2e 

TBLOTH(t) 

Lead transfer time 

from blood to other 

soft tissue 

10 

and 

B-1c 

24 

and 

0-84 

I 

24 months -

on information from Heard and Chamberlain, (1982) for adults, and 

O'Flaherty (1992). 

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. 

proportionality is assumed to depend on an estimate of the parameter for a 

24 month old and the corresponding body surface area. 

that body surface area varies as 1/3 power of the weight of body based on 

(Mordenti, 1986). 

days B-2m,2n 

TBLOUT(t) 

Lead transfer time 

from blood to 

elimination pool 

via soft tissue 

B-1g 0-84 I 

Simple combination of an assumed ratio of 

to endogenous fecal lead elimination rate, times the lead transfer time from 

blood to feces (See RATOUTFEC). 

days B-2n,2o 

Initialization is keyed to the two year old child, based in part 

Once the concentration ratios are fixed, the exact value 

The coefficient of 

Also, it is 

Initialization is keyed to the two year old child, based in part on 

Once the concentration ratios are fixed, the exact value of this 

The coefficient of 

Also, it is 

Initialization is keyed to the two year old child, based in part 

Once the concentration ratios are fixed, the exact value 

The coefficient of 

Also, it is assumed 

elimintion rate via soft tissues 

NOTE: I = interior parameter, E = Exterior, user selectable parameter B-15 
PARAMETER NAME DESCRIPTION 

DEFAUL 

T VALUE 

OR 

EQN. 

NO. 

AGE 

RANGE 

(mo) 

I 

or 

E BASIS FOR VALUES/EQUATIONS UNITS 

EQUATION 

WHERE 

USED 

TBLUR(t) Lead transfer time 

from blood to urine 

20 

and 

B-1a 

24 

and 

0-84 

I 

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. 

days B-1f,2c 

TBONEBL(t) Lead transfer time 

from bone to blood B-1h 0-84 I Based on the assumption that masses of lead in bone and blood are in kinetic quasi-equilibrium. days B-2j,2l 

TCORTPL(t) 

Lead transfer time 

from cortical bone 

to plasma-ECF 

B-2l 0-84 I Based on the assumption that the cortical and trabecular bone pools have 

similar lead kineticsfor children younger than 84 months. days 

B-6b,6i,6.5b, 

6.5i,8d,9f 

time_out(t) Time spent 

outdoors 

1 

2 

3 

4 

4 

4 

4 

0-11 

12-23 

24-35 

36-47 

48-59 

60-71 

72-84 

E 

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). 

hrs/day E-2 

NOTE: I = interior parameter, E = Exterior, user selectable parameter B-16 
PARAMETER NAME DESCRIPTION 

DEFAUL 

T VALUE 

OR 

EQN. 

NO. 

AGE 

RANGE 

(mo) 

I 

or 

E BASIS FOR VALUES/EQUATIONS UNITS 

EQUATION 

WHERE 

USED 

TimeStep 

Length of timestep in solution 

algorithm 

1/6 0-84 E 

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. 

day 

B-6.5a,6.5d6.5i,7b,7c, 

8a,d,9a9f,10a-10b 

TKIDPL(t) 

Lead transfer time 

from kidney to 

plasma-ECF 

B-2h 0-84 I 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. days 

B6b,6f,6.5b,6. 

5f,8d,9c 

TLIVFEC(t) Lead transfer time 

from liver to feces B-2f 0-84 I Based on the assumption that the masses of lead in liver and blood are in kinetic quasi-equilibrium. days B-6e,6.5e, 8c,d,9b 

TLIVPL(t) 

Lead transfer time 

from liver to 

plasma-ECF 

B-2e 0-84 I 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. days 

B6b,6e,6.5b,6. 

5e,8c,d, 

9b 

TOTHOUT(t) 

Lead transfer time 

from soft tissues to 

elimination pool 

B-2o 0-84 I Based on the assumption that the masses of lead in soft tissues and blood 

are in kinetic quasi-equilibrium. days B-6g,6.5g, 8c,d,9h 

TOTHPL(t) 

Lead transfer time 

from soft tissues to 

plasma-ECF 

B-2n 0-84 I 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. days 

B6c,6g,6.5c,6. 

5g,8c,d, 

9h 

TPLCORT(t) 

Lead transfer time 

from plasma-ECF 

to cortical bone 

B-2k 0-84 I 

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). 

days B-6c,6i,6.5c, 

6.5i,8b,c,9f 

NOTE: I = interior parameter, E = Exterior, user selectable parameter B-17 
PARAMETER NAME DESCRIPTION 

DEFAUL 

T VALUE 

OR 

EQN. 

NO. 

AGE 

RANGE 

(mo) 

I 

or 

E BASIS FOR VALUES/EQUATIONS UNITS 

EQUATION 

WHERE 

USED 

TPLKID(t) 

Lead transfer time 

from plasma-ECF 

to kidney 

B-2g 0-84 I 

Based on the assumption that the rate at which lead leaves the plasmaECF to reach the kidney is proportional to the rate at which lead leaves the 

blood to reach the same pool. 

days 

B6c,6f,6.5c,6. 

5f,8b,c,9c 

TPLLIV(t) 

Lead transfer time 

from plasma-ECF 

to liver 

B-2d 0-84 I 

Based on the assumption that the rate at which lead leaves the plasmaECF to reach the liver is proportional to the rate at which lead leaves the 

blood to reach the same pool. 

days 

B6c,6e,6.5c,6. 

5e,8b,c, 

9b 

TPLOTH(t) 

Lead transfer time 

from plasma-ECF 

to soft tissues 

B-2m 0-84 I 

Based on the assumption that the rate at which lead leaves the plasmaECF to reach the soft tissues is proportional to the rate which lead leaves 

the blood to reach the same pool. 

days 

B6c,6g,6.5c,6. 

5g,8b,c, 

9d 

TPLRBC 

Lead transfer 

time from plasmaECF to red blood 

cells 

0.1 0-84 I 

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. 

days B-2b,2.5,7b, 

7c 

TPLRBC2(t) 

Lead transfer 

time from plasmaECF to red blood 

cells constrained 

by the maximum 

capacity of red 

blood cell lead 

concentration 

B-2.5 0-84 I 

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. 

days 

B6a,6d,6.5a,6. 

5d,8b,9a 

TPLTRAB(t) 

Lead transfer time 

from plasma-ECF 

to trabecular bone 

B-2i 0-84 I 

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). 

days 

B6c,6h,6.5c,6. 

5h,8b,c, 

9e 

TPLUR(t) 

Lead transfer time 

from plasma-ECF 

to urine 

B-2c 0-84 I 

Based on the assumption that the rate at which lead leaves the plasmaextra-cellular fluid to reach the urine pool is proportional to the rate at which 

lead leaves the blood to reach the same pool. 

days B-6c,6.5c,8a 

NOTE: I = interior parameter, E = Exterior, user selectable parameter B-18 
PARAMETER NAME DESCRIPTION 

DEFAUL 

T VALUE 

OR 

EQN. 

NO. 

AGE 

RANGE 

(mo) 

I 

or 

E BASIS FOR VALUES/EQUATIONS UNITS 

EQUATION 

WHERE 

USED 

TRBCPL 

Lead transfer time 

from red blood 

cells to plasmaECF 

B-2b 0-84 I Based on the assumption that the transfer time out of RBC is similar at all 

ages, since mean red cell value is similar. days 

B6b,6d,6.5b,6. 

5d,7b,7c, 

8c,d,9a 

TTRABPL(t) 

Lead transfer time 

from trabecular 

bone to plasmaextra-cellular fluid 

B-2j 0-84 I Based on the assumption that the cortical and trabecular bone pools have 

similar lead kinetics for children younger than 84 months. days 

B6b,6h,6.5b,6. 

5h,8c,d, 

9e 

TWA(t) 

Time weighted 

average air lead 

concentration 

E-2 0-84 I Simple combination of outdoor and indoor air lead concentrations and the 

number of hours spent outdoors. μg/m3 E-3 

UPAIR(t) Air lead uptake U-4 0-84 I Simple combination of media-specific lead intake and the corresponding net 

absorption coefficient. μg/day U-5 

UPDIET(t) Diet lead uptake U-1a 0-84 I Simple combination of media-specific lead intake and the corresponding net 

absorption coefficient. μg/day U-1f 

UPDUST(t) Dust lead uptake U-1c 0-84 I Simple combination of media-specific lead intake and the corresponding net 

absorption coefficient. μg/day U-1f 

UPDUSTA(t) 

Dust lead uptake 

rate from alternate 

sources 

U-1.5c 0-84 I Simple combination of media-specific lead intake and the corresponding net 

absorption coefficient. μg/day U-1f 

UPGUT(t) Total gut uptake U-1f 0-84 I Sum of all gastrointestinal uptake. μg/day U-5 

UPOTHER(t) Uptake of other 

ingested lead U-1d 0-84 I Assumes no other gut lead intake μg/day U-1f 

UPSOIL(t) Soil lead uptake U-1e 0-84 I Simple combination of media-specific lead intake and the corresponding net 

absorption coefficient. μg/day U-1f 

UPTAKE(t) Total lead uptake U-5 0-84 I Simple combination of the media-specific daily lead uptake rates, 

translated to a monthly rate. μg/mo B-6a,6.5a,8a 

UPWATER(t) Water lead uptake U-1b 0-84 I Simple combination of media-specific lead intake and the corresponding net 

absorption coefficient. μg/day U-1f 

NOTE: I = interior parameter, E = Exterior, user selectable parameter B-19 
PARAMETER NAME DESCRIPTION 

DEFAUL 

T VALUE 

OR 

EQN. 

NO. 

AGE 

RANGE 

(mo) 

I 

or 

E BASIS FOR VALUES/EQUATIONS UNITS 

EQUATION 

WHERE 

USED 

UserFishConc 

Lead 

concentration in 

fish 

0 0-84 E Based on the assumption that only commercially available fish are 

consumed. μg/g E-5h 

userFishFraction 

Fraction of total 

meat consumed as 

fish 

0 0-84 E Based on the assumption that only commercially available fish are 

consumed. unitless E-5a,5h 

UserFruitConc 

Lead 

concentration in 

home grown fruits 

0 0-84 E Based on the assumption that only commercially available fruits are 

consumed. μg/g E-5f 

userFruitFraction 

Fraction of total 

fruits consumed as 

home grown fruits 

0 0-84 E Based on the assumption that only commercially available fruits are 

consumed. unitless E-5d,5e,5f 

UserGameConc 

Lead 

concentration in 

game animal meat 

0 0-84 E Based on the assumption that only commercially available meat is 

consumed. μg/g E-5i 

userGameFraction 

Fraction of total 

meat consumed as 

game animal meat 

excluding fish 

0 0-84 E Based on the assumption that only commercially available meat is 

consumed. unitless E-5a,5i 

UserVegConc 

Lead 

concentration in 

home grown 

vegetables 

0 0-84 E Based on the assumption that only commercially available vegetables are 

consumed. μg/g E-5g 

userVegFraction 

Fraction of total 

vegetables 

consumed as 

home grown 

vegetables 

0 0-84 E Based on the assumption that only commercially available vegetables are 

consumed. unitless E-5b,5c,5g 

NOTE: I = interior parameter, E = Exterior, user selectable parameter B-20 
PARAMETER NAME DESCRIPTION 

DEFAUL 

T VALUE 

OR 

EQN. 

NO. 

AGE 

RANGE 

(mo) 

I 

or 

E BASIS FOR VALUES/EQUATIONS UNITS 

EQUATION 

WHERE 

USED 

veg_all(t) 

Daily amount of all 

vegetables 

consumed 

56.84 

106.50 

155.75 

157.34 

158.93 

172.50 

199.65 

0-11 

12-23 

24-35 

36-47 

48-59 

60-71 

72-84 

I Pb concentration from data provided to EPA by FDA (US EPA (1986). 

Quantity consumed from Pennington (1983). g/day E-5g 

vent_rate(t) Ventilation rate 

2 

3 

5 

5 

5 

7 

7 

0-11 

12-23 

24-35 

36-47 

48-59 

60-71 

72-84 

E 

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). 

m3/day E-3 

VOLBLOOD(t) Volume of blood B-5a 0-84 I Statistical fitting of data from Silve et al (1987); also Spector (1956) and 

Altman and Ditmer (1973) μg/dL 

B1h,2e,2f,2h,2 

n,2o,5d, 

5e,5m,10a 

VOLECF(t) Volume of extracellular fluid (ECF) B-5d 0-84 I 

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 extracellular fluid pool, which is the difference between the volume of the 

distribution and the blood volume. 

dL B-9g 

VOLPLASM(t) Volume of plasma B-5c 0-84 I Statistical fit to VOLBLOOD(t) - VOLRBC(t) dL B-7b,7c,9g 

VOLRBC(t) Volume of red 

blood cells B-5b 0-84 I Statistical fit to hematocrit × blood volume dL B-2.5 

water_consumption(t) Daily amount of 

water consumed 

0.20 

0.50 

0.52 

0.53 

0.55 

0.58 

0.59 

0-11 

12-23 

24-35 

36-47 

48-59 

60-71 

72-84 

E Exposure Factors Handbook (US EPA, 1989b) L/day E-6a,6b 

NOTE: I = interior parameter, E = Exterior, user selectable parameter B-21 
PARAMETER NAME DESCRIPTION 

DEFAUL 

T VALUE 

OR 

EQN. 

NO. 

AGE 

RANGE 

(mo) 

I 

or 

E BASIS FOR VALUES/EQUATIONS UNITS 

EQUATION 

WHERE 

USED 

weight_soil 

Percentage of total 

soil and dust 

ingestion that is 

soil 

45 0-84 E Guidance Manual, Section 2.3 (US EPA, 1994) % E-8,10 

WTBLOOD(t) Weight of blood B-5m 0-84 I Based on an blood density of 1.056 kg/l (Spector 1956). kg B-5l 

WTBODY(t) Weight of body B-5f 0-84 I 

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). 

kg B-1a1e,5f,5g,5l 

WTBONE(t) Weight of bone B-5g 0-84 I 

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 = 10 kg 

WTSKEL_ASHADULT = 2.91 kg 

0-12 months - Assumed to be 11% 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. 

kg B-5h,5i 

WTCORT(t) Weight of cortical 

bone B-5i 0-84 I Assumed to be 80% of the weight of the bone based on Leggett et al. (1982). kg B-1h,5l,7e 

WTECF(t) Weight of extracellular fluid (ECF) 

B-5e 0-84 I Based on an assumed ECF density approximately the same as water, of 

1.0 kg/L. kg B-5l 

WTKIDNEY(t) Weight of kidney B-5j 0-84 I 

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). 

kg B-5j,5l,7f 

WTLIVER(t) Weight of liver B-5k 0-84 I 

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). 

kg B-2e,2f,5l,7g 

WTOTHER(t) Weight of soft 

tissues B-5l 0-84 I Simple combination of the weight of body and the weights of kidney, liver, bone, blood and extra-cellular fluid. kg B-2n,2o,7h 

NOTE: I = interior parameter, E = Exterior, user selectable parameter B-22 
PARAMETER NAME DESCRIPTION 

DEFAUL 

T VALUE 

OR 

EQN. 

NO. 

AGE 

RANGE 

(mo) 

I 

or 

E BASIS FOR VALUES/EQUATIONS UNITS 

EQUATION 

WHERE 

USED 

WTTRAB(t) Weight of 

trabecular bone B-5h 0-84 I Assumed to be 20% of the weight of the bone based on Leggett et al. (1982). kg B-1h, 5l,7i 

NOTE: I = interior parameter, E = Exterior, user selectable parameter B-23