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£% |-r%|| United States
^NMil Environmental Protection
LbI M * Agency
Technical Support Document for the All Ages Lead
Model (AALM) - Parameters, Equations, and
Evaluations
Office of Research and Development
U.S. Environmental Protection Agency
Washington, DC 20460
EPA600/R-19/011
May 2019
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Disclaimer
This document is an external review draft. This document does not represent and should not be construed
to represent any Agency determination or policy. Mention of trade names or commercial products does
not constitute endorsement or recommendation for use. This document and the work described in it was
conducted under contracts EP-W-17-008, EP-W-09-031, EP-BPA-1 l-C-018, EP-13-H-000037, EP-08-H-
000055, and EP-C-14-001.
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CONTENTS
Acronyms and Abbreviations vi
Chapter 1. Introduction and History of All Ages Lead Model 1
1.1. Introduction 1
1.2. History of the AALM 2
1.2.1. AALM.C 2
1.2.2. AALM.CSL 4
1.2.3. AALM.FOR 4
Chapter 2. Theoretical Framework, Parameters, and Equations 6
2.1. Overview of AALM.FOR Structure 6
2.2. Exposure Model 7
2.2.1. General Structure of the Exposure Model 7
2.2.2. Parameters That Define a Hypothetical Individual 9
2.2.3. Exposure Media Intakes and Lead Concentrations 9
2.2.3.1. Air Pb Exposure 9
2.2.3.2. Indoor Dust Pb Exposure 10
2.2.3.3. Soil Pb Exposure 11
2.2.3.4. Water Pb Exposure 13
2.2.3.5. Food Pb Exposure 14
2.2.3.6. Other Exposure Media 15
2.3. Biokinetics 16
2.3.1. Computational Structure of the Aalm.For Biokinetics Model 16
2.3.2. Compartment Structure of the AALM.FOR Biokinetics Model 18
2.3.2.1. Rate Equations for Pb Transfers 18
2.3.2.2. Deposition Fractions 19
2.3.2.3. Scaling of Rate Coefficients and Deposition Fractions 20
2.3.2.4. Growth of Blood and Tissues for Calculation of Pb Concentrations 21
2.3.2.5. Age Dependencies of Parameter Values 22
2.3.3. Absorption 22
2.3.3.1. Absorption from the Respiratory Tract 23
2.3.3.2. Absorption from the Gastrointestinal Tract 24
2.3.4. Vascular and Extravascular Fluid 26
2.3.4.1. Diffusible Plasma 26
2.3.4.2. Bound Pb in Plasma 26
2.3.4.3. Red Blood Cells 26
2.3.4.4. Extravascular Fluid 27
2.3.5. Skeleton 27
2.3.5.1. General Structure of Bone Model 27
2.3.5.2. Cortical and Trabecular Bone Surface 28
2.3.5.3. Cortical and Trabecular Bone Volume 28
2.3.6. Liver 29
2.3.7. Kidney 30
2.3.8. Brain 31
2.3.9. Other Soft Tissues 31
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2.3.10. Excretion 32
2.3.11. Fetus 32
2.3.12. Chelation 33
Chapter 3. Evaluation and Development of AALM.FOR 53
3.1. Introduction and Ojbectives ofThis Analysis 53
3.2. Model Predictions of Blood and Bone Pb 54
3.2.1. Constant Pb Intake 54
3.2.2. Dose-Response for Blood and Bone Pb 55
3.3. Comparisons of Model Predictions to Observations 55
3.3.1. Pb Elimination Kinetics in Workers with Dose Reconstruction (Hattis Data) 56
3.3.2. Pb Elimination Kinetics in Workers with Dose Reconstruction (Nilsson et al., 1991).... 57
3.3.3. Blood Pb Accrual and Elimination Kinetics in Adults with Known Pb Doses
(Rabinowittiz et al. 1976) 58
3.3.4. Post-mortem Soft Tissue-to-Bone Pb Ratio (Barry, 1975) 58
3.3.5. Plasma-to-Bone Pb Ratio in Workers (Cake et al., 1996; Hernandez-Avila et al., 1998)59
3.3.6. Plasma Pb - Blood Pb Relationship (Meta-data) 59
3.3.7. Blood Pb Elimination Kinetics in Infants with Known Doses (Ryu et al., 1983; Sherlock
and Quinn, 1986) 59
3.3.8. Blood Pb Elimination Kinetics in Infants with Dose Reconstruction (ATSDR) 60
3.3.9. Comparison to IEUBK Model for Pb in Children 61
3.3.10. Comparison to Adult Lead Methodology 61
3.4. Data Needs for Further Refinement of the AALM 62
3.5. Conclusions and Implications for Modeling Lead Body Burdens 63
3.5.1. Evaluation of AALM.FOR Performance 63
3.5.2. Response to Peer Review of ICRPv005.FOR 64
3.5.3. Summary 66
Chapter 4. Evaluation and Development of AALM.CLS 95
4.1. Introduction 95
4.2. Overview of AALM.CLS Structure 95
4.3. Comparison of Structures of AALM-LG and AALM-OF Biokinetics Models 96
4.4. Comparison of AALM-LG and AALM-of Predictions of Blood and Tissue Pb 97
4.4.1. Comparison of Model Predictions for Constant Pb Intake 98
4.4.2. Comparison of Predicted Dose-Response for Blood and Tissue Pb 99
4.5. Sensitivity Analysis of AALM-LG and AALM-OF 100
4.5.1. Sensitivity Analysis of AALM-LG 101
4.5.1.1. Influential Parameters Common to All Tissues 101
4.5.1.2. Sensitivity Analysis of AALM-LG Blood Pb Predictions 103
4.5.1.3. Sensitivity Analysis of AALM-LG Bone Pb Predictions 103
4.5.1.4. Sensitivity Analysis of AALM-LG Liver Pb Predictions 103
4.5.1.5. Sensitivity Analysis of AALM-LG Kidney Pb Predictions 103
4.5.1.6. Sensitivity Analysis of AALM-LG Other Soft Tissue Pb Predictions 103
4.5.2. Sensitivity Analysis of AALM-OF 104
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4.5.2.1. Influential Parameters Common to All Tissues 104
4.5.2.2. Sensitivity Analysis of AALM-OF Blood Pb Predictions 104
4.5.2.3. Sensitivity Analysis of AALM-OF Bone Pb Predictions 104
4.5.2.4. Sensitivity Analysis of AALM-OF Liver Pb Predictions 104
4.5.2.5. Sensitivity Analysis of AALM-OF Kidney Pb Predictions 105
4.5.2.6. Sensitivity Analysis of AALM-OF Poorly Perfused Tissue Pb Predictions .. 105
4.5.2.7. Sensitivity Analysis of AALM-OF Well-Perfused Tissue Pb Predictions 105
4.6. Conclusions from Model Comparisons and Sensitivity Analyses 105
4.7. Evaluation and Optimization of the AALM 106
4.7.1. Unification of Simulation of GI Absorption and Growth 106
4.7.2. Optimization of Plasma Pb - Blood Pb Relationship 107
4.7.3. Optimization of Plasma-to-Urine Pb Clearance 108
4.7.4. Optimization of Soft Tissue-to-Bone Pb Ratio 108
4.7.5. Optimization of Soft Blood-to-Bone Pb Ratio 109
4.7.6. Optimization of Bone Pb Elimination Kinetics 109
4.7.7. Evaluation of Blood Pb Elimination Kinetics in Adults 110
4.7.8. Evaluation of Blood Pb Elimination Kinetics in Infants Ill
4.8. Conclusions and Implications of Performance of Optimized Models 112
4.9. Calibrating the AALM to the IEUBK Model 114
4.10. Data Needs and Further Evaluation of the AALM 115
5. References 188
Appendix A - Equations in AALM.FOR 194
Appendix B - All Ages Lead Model (AALM.FOR) Parameters 257
Table B-l. All Ages Lead Model Parameter Descriptions 257
Appendix C - All Ages Lead Model (AALM.FOR) Exposure Parameter Values 274
Air Concentration 274
Indoor Dust Lead Concentration 275
Soil Lead Concentration 276
Water Concentration 277
Food Lead Intake 278
Dust and Soil Ingestion Rates 280
Water Intake Rate 281
Ventilation Rate 282
Table C-l. List of Parameters that Are Assigned Constants or Are Represented by Age Arrays 286
Appendix C References - Exposure Variables (Primary Only) 293
Appendix D - All Ages Lead Model (AALM.FOR) Biokinetics Parameter Values 296
Table D-l. AALM biokinetics parameters and values 306
Appendix D References 319
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LIST ;s
Table 2-1. Exposure Equations of AALM.FOR 34
Table 2-2. Biokinetics Equations of AALM.FOR 36
Table 2-3. Rate Coefficients for Pb Transfers in AALM 47
Table 3-1. Changes Made to ICRPv004.FORto Create ICRPv005.FOR 67
Table 3-2. Differences in ICRPv005.FOR and AALM.CLS Biokinetics 69
Table 3-3. Differences Between AALM.FOR and AALM.CSL 72
Table 3-4. Blood Lead Predictions from the AALM for 57 Subjects in the Hattis Dataset 73
Table 3-5. Comparison of Predicted and Observed Plasma Pb/Bone Pb Slopes 74
Table 3-6. Comparison of ALM and AALM Predictions of Blood Pb Concentrations in Adults 74
Table 4-1. Summary of Major Differences Between Structures of AALM-LG and AALM-OF 118
Table 4-2. AALM-LG Input Parameters Controlling Post-absorption Pb Kinetics 119
Table 4-3. AALM-OF Input Parameters Controlling Post-absorption Pb Kinetics 121
Table 4-4. AALM-LG Standardized Sensitivity Coefficients for Blood Pb in Children (5 Years) and
Adults (30 Years) 123
Table 4-5. AALM-LG Standardized Sensitivity Coefficients for Bone Pb in Children (5 Years) and
Adults (30 Years) 126
Table 4-6. AALM-LG Standardized Sensitivity Coefficients for Liver Pb in Children (5 Years) and
Adults (30 Years) 129
Table 4-7. AALM-LG Standardized Sensitivity Coefficients for Kidney Pb in Children (5 Years) and
Adults (30 Years) 132
Table 4-8. AALM-LG Standardized Sensitivity Coefficients for Other Soft Tissue Pb in Children (5
Years) and Adults (30 Years) 135
Table 4-9. AALM-OF Standardized Sensitivity Coefficients for Blood Pb in Children (5 Years) and
Adults (30 Years) 138
Table 4-10. AALM-OF Standardized Sensitivity Coefficients for Bone Pb in Children (5 Years) and
Adults (30 Years) 140
Table 4-11. AALM-OF Standardized Sensitivity Coefficients for Liver Pb in Children (5 Years) and
Adults (30 Years) 142
Table 4-12. AALM-OF Standardized Sensitivity Coefficients for Kidney Pb in Children (5 Years) and
Adults (30 Years) 144
Table 4-13. AALM-OF Standardized Sensitivity Coefficients for Poorly perfused Tissues Pb in Children
(5 Years) and Adults (30 Years) 146
Table 4-14. AALM-OF Standardized Sensitivity Coefficients for Well-perfused Tissues Pb in Children (5
Years) and Adults (30 Years) 148
Table 4-15. Dominant Parameters Influencing Major Differences in Predictions from AALM-LG and
AALM-OF 150
Table 4-16. Strategy Used for Sequential Optimization of AALM Biokinetics Model 151
Table 4-17. Comparison of Predicted and Observed Plasma Pb/Bone Pb Slopes 152
Table 4-18. Changes to O'Flaherty (1993, 1995) and Leggett (1993) Models Incorporated into AALM 153
Table 4-19. Comparison of AALM-LG and AALM-OF Predictions of Blood and Tissue Pb
Concentrations 154
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Table 4-20. Comparison of Adult Lead Methodology, AALM-LG and AALM-OF Predictions of Blood
Pb Concentrations in Adults 155
Table 4-21. Comparison of AALM-LG and AALM-OF Predictions of Blood and Tissue Pb
Concentrations After Calibrating RBC Parameter Values to the IEUBK Model Output 156
Table 4-22. Changes Made to THE LEGGETT (1993) MODEL to Create aalm-lg.csl 157
Table A-l. Equations of the All Ages Lead Model (AALM.FOR) 194
Table B-l. All Ages Lead Model Parameter Descriptions 257
Table C-l. List of Parameters that Are Assigned Constants or Are Represented by Age Arrays 286
Table D-l. AALM Biokinetics Parameters and Values 306
LIST
Figure 2-1. Structure of AALM.FOR biokinetics model 49
Figure 2-2. Body and tissue growth in the AALM.FOR 50
Figure 2-3. Gastrointestinal absorption of Pb as optimized in AALM.FOR 51
Figure 2-4. Structure of AALM.FOR bone model 52
Figure 3-1. Gastrointestinal absorption of Pb in the Leggett (1993) model and AALM, optimized to Ryu
etal. (1983) 75
Figure 3-2. Comparison of accrual and elimination kinetics of blood Pb in children (A) and adults (B)
predicted from AALM.CSL, AALM.FOR and ICRPv005.FOR 76
Figure 3-3. Comparison of accrual and elimination kinetics of cortical bone (A, B) and trabecular bone
(C, D) Pb in children (A, C) and adults (B, D) predicted from AALM.CSL, AALM.FOR and
ICRPv005.FOR 77
Figure 3-4. Comparison of relationships between Pb intake (g/day) and blood Pb in children (A) and
adults (B) predicted from AALM.CSL, AALM.FOR and ICRPv005.FOR 78
Figure 3-5. Comparison of relationships between Pb intake (g/day) and cortical (A, B) and trabecular (C,
D) bone Pb in children (A, C) and adults (B, D) predicted from AALM.CSL, AALM.FOR and
ICRPv005.FOR 79
Figure 3-6. AALM.CLS simulation of observations for Hattis cohort Subject 5 80
Figure 3-7. Comparison of AALM.CSL (A) and ICRPv005.FOR (B) predictions and observed blood Pb
concentrations after the strike for 57 subjects in the Hattis cohort 81
Figure 3-8. AALM.CSL, AALM.FOR and ICRPv005.FOR simulations of blood Pb elimination half-time
for 57 subjects in the Hattis cohort 82
Figure 3-9. AALM.CSL and AALM.FOR simulations of elimination kinetics of Pb from blood (A) and
bone (B) 83
Figure 3-10. AALM.CSL and AALM.FOR simulations of blood Pb concentrations in individuals who
received ingestion doses of [202Pb]-nitrate (Rabinowitz et al. 1976) 84
Figure 3-11. AALM and LFM simulations of post-mortem soft tissue/tibia Pb ratios 85
Figure 3-12. AALM.CSL and AALM.FOR simulations of plasma Pb/bone Pb ratio in adults 86
Figure 3-13. Simulation of whole blood and plasma Pb in adults 87
Figure 3-14. AALM.CSL (A) and AALM.FOR (B) simulations of formula-fed infants from Ryu et al.
(1983) 88
Figure 3-15. AALM.CSL and AALM.FOR simulations of formula-fed infants 89
Figure 3-16. AALM simulation of subject 48490 (female) 90
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Figure 3-17. AALM simulation of subject 3030 (male) 91
Figure 3-18. AALM simulation of subject 87350 (female) 92
Figure 3-19. Comparison of blood Pb predictions of AALM and IEUBK model 93
Figure 3-20. Comparison of blood Pb predictions of AALM and ALM 94
Figure 4-1. Data flow diagram for AALM 160
Figure 4-2. Structure of AALM-LG model 161
Figure 4-3. Structure of AALM-OF model 162
Figure 4-4. Structure of AALM-LG bone model 163
Figure 4-5. Structure of AALM-OF bone model 164
Figure 4-6. Comparison of Pb (|_ig) levels predicted from AALM-OF and AALM-LG for a constant
ingestion of 5 (ig Pb/day for ages 0 to 30 years 165
Figure 4-7. Differences in Pb levels predicted from AALM-LG and AALM-OF 166
Figure 4-8. Comparison of cumulative urinary and fecal Pb excretion (fig) levels predicted from AALM-
OF and AALM-LG for a constant ingestion of 5 (ig Pb/day for ages 0 to 30 years 167
Figure 4-9. Decline in Pb levels following cessation of exposure predicted from AALM-LG and AALM-
OF for ages 5 and 30 years 168
Figure 4-10. Comparison of Pb concentrations predicted from AALM-LG and AALM-OF for a constant
ingestion of 5 (ig Pb/day for ages 0 to 30 years 169
Figure 4-11. Dose-response relationship for Pb levels at age 5 years predicted from AALM-LG and
AALM-OF 170
Figure 4-12. Dose-response relationship for Pb levels at age 30 years predicted from AALM-LG and
AALM-OF 171
Figure 4-13. Gastrointestinal absorption of Pb in the O'Flaherty (1993, 1995; OF) model, Leggett (1993,
LG) model and AALM, optimized to Ryu et al. (1983) 172
Figure 4-14. Body and tissue growth in AALM 173
Figure 4-15. Simulation of whole blood and plasma Pb in adults (Bergdahl et al. 1997, 1998, 1999;
Hernandez-Avila et al. 1998; Schiitz et al. 1996; Smith et al. 2002) 174
Figure 4-16. Simulation of plasma-to-urine clearance 175
Figure 4-17. Simulation of post-mortem soft tissue/tibia Pb ratios 176
Figure 4-18. Simulation of plasma Pb/bone Pb ratio in adults 177
Figure 4-19. Simulation of elimination kinetics of Pb from blood (left panel) and bone (right panel).... 178
Figure 4-20. Comparison of observed and predicted blood Pb concentrations in individuals who received
ingestion doses of [202Pb]-nitrate (Rabinowitz et al. 1976) 179
Figure 4-21. Simulation of formula-fed infants from Ryu et al. (1983) 180
Figure 4-22. Simulation of formula-fed infants (n = 131, age 91 days) from Sherlock and Quinn (1986).
181
Figure 4-23. Comparison of previous and optimized AALM-LG and AALM-OF models for continuous
Pb intake of 5 (ig/day 182
Figure 4-24. Comparison of previous and optimized AALM-LG and AALM-OF models for continuous
Pb intake of 5 (ig/day 183
Figure 4-25. Comparison of blood Pb predictions of AALM and IEUBK model 184
Figure 4-26. Comparison of blood Pb predictions of AALM and IEUBK model after adjustment of red
blood cell parameters (RRBC in AALM-LG, KBIND in AALM-OF) 185
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Figure 4-27. Simulation of formula-fed infants from Ryu et al. (1983) after adjustment of red blood cell
(RRBC in AALM-LG, KBIND in AAI.M-OI ) 186
Figure 4-28. Simulation of formula-fed infants (n = 131, age 91 days) from Sherlock and Quinn (1986)
after adjustment of red blood cell (RRBC in AALM-LG, KBIND in AALM-OF) 187
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ACRONYMS AND ABBREVIATIONS
AALM All Ages Lead Model
AALM-LE ACSL implementation of Leggett model
AALM-OF ACSL implementation of O'Flaherty model
ABLOOD amount of Pb in blood
ABONE amount of Pb in bone
ACSL Advanced Continuous Simulation Language
AF absorption fraction
AKIDNEY amount of Pb in kidney
ALIVER amount of Pb in liver
ALM Adult Lead Methodology
ASOFT amount of Pb in soft tissue
ATSDR Agency for Toxic Substances and Disease Registry
AMTBLD Leggett model blood volume
BLDHCT age-dependent hematocrit
BLL blood lead level
CB O'Flaherty model blood Pb concentration
CF AALM adjustment factor for Pb deposition into RBCs
CIIIAR AALM fraction of inhaled Pb trasnfered to stomach
CSFII continuing survey of food intakes
CSV comma-delimited text file
DF deposition fractions
EFH Exposure Factors Handbook
EPA Environmental Protection Agency
EVF extravascular fluid
FRX O'Flaherty model Pb excretory clearance
GI gastrointestinal
GIT gastrointestinal tract
GFR glomerular filtration rate
GM geometric mean
GSD geometric standard deviation
HCTA adult hematocrit
HRTM Human Respiratory Tract Model
ICR Information Collection Request
ICRP International Commission on Radiological Protection
IEUBK Integrated Exposure Uptake Biokinetics
IVBA validated in vitro bioaccessibility
LFM Leggett Fortran Model
LLIC lower large intestine contents
NCEA National Center for Environmental Assessment
NHANES National Health and Nutrition Examination Survey
NHEXAS National Human Exposure Assessment Survey
NSLAH National Survey of Lead and Allergens
NTIS National Technical Information Service
OCSPP Office of Chemical Safety and Pollution Prevention
OEHHA Office of Environmental Health Hazard Assessment
OLEM Office of Land and Emergency Management
OPPT Office of Pollution Prevention and Toxics
ORD Office of Research and Development
OSWER Office of Solid Waste and Emergency Response
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Pb lead
PK O'Flaherty model plasma-kidney partition coefficient
PL O' Flaherty model plasma-liver partition coefficient
PP O'Flaherty model plasma-poorly perfused tissue partition coefficient
PW O'Flaherty model plasma-well perfused tissue partition coefficient
RBA relative bioavailability
RBC red blood cell
RBCONC red blood cell Pb concentration
RRBC rate transfer of Pb from red blood cells to diffusible plasma
RT respiratory tract
SAB Science Advisory Board
SOF Other Soft Tissues
SSC standardized sensitivity coefficient
ST soft tissue
ULIC upper large intestine contents
VBLC blood volume fraction of body weight
VBONE bone volume
VK kidney volume
VL liver volume
VR ventilation rate
XRF X-ray fluorescence
WBODY body weight
WBONE bone weight
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CHAPTER 1. INTRODUCTION AND HISTORY OF ALL AGES LEAD MODEL
1.1. INTRODUCTION
The All Ages Lead Model (AALM) is a tool for quantitatively relating lead (Pb) exposures from
environmental media that occur over the life time to Pb levels and concentrations in blood, other body
tissues, and excreta. The primary intended use of the model is for computational Pb toxicology and risk
assessment. The AALM represents an extension of research and regulatory models previously developed
by EPA such as the Integrated Exposure Uptake Biokinetics (IEUBK) Model for Pb in Children which
simulates exposure-blood Pb concentration relationships occurring from birth to age 7 years (Hogan et al..
1998; White et al.. 1998; Zaragoza and Hogan. 1998). The AALM also incorporates Pb modeling
concepts explored in models developed in other research efforts, including those of Leggett (Pounds and
Leggett. 1998; Leggett. 1993; Leggett et al.. 1993). O'Flaherty (O'Flahertv et al.. 1998; O'Flahertv. 1998.
1995. 1993. 1991a. b, c) and others (U.S. EPA. 2006; Maddaloni et al.. 2005).
As discussed in Section 1.2, the AALM has been implemented in several platforms over the course of its
development. The AALM was first developed and implemented in Visual C+ (AALM.C) by U.S. EPA's
Office of Research and Development (ORD). Subsequently, ORD implemented the AALM in Advance
Continuous Simulation Language, ACSL®, a.k.a. acslX, (AALM.CLS) to further develop and evaluate the
model. In a parallel effort, EPA's Office of Chemical Safety and Pollution Prevention (OCSPP) was
developing a biokinetic Fortran model (ICRPv005.FOR) with similar capabilities to the AALM.CLS
being developed by ORD. Since 2015, EPA's ORD and OCSPP have coordinated efforts to advance Pb
biokinetic modeling and produced the current version of the AALM software implemented in Fortran
(AALM.FOR) with a Microsoft Excel user interface.
This document, in Chapter 2, describes in detail the conceptual and computational structure of the current
Fortran version of the AALM (AALM.FOR), including an inventory and explanation of all parameters,
variables, and expressions used in the model to calculate Pb intakes and Pb tissue and excreta levels
and/or concentrations. Chapter 2 has two primary subsections. The initial primary section (exposure
model) describes components of the AALM.FOR that relate environmental and diet Pb exposures to rates
of Pb intake. This is followed by a section that provides a detailed description of model components that
relate Pb intakes to Pb levels and concentrations in body tissues and excreta. Appendices A and B
provide a complete listing of equations and parameters used in the model, respectively, that are directly
pertinent to calculations of Pb intakes and Pb levels and concentrations in body tissues and excreta.
Appendices C and D provide a complete list of parameter names and default values used in the model.
Chapter 3 describes the development and evaluation of AALM.FOR. This chapter describes the process
of harmonizing two model versions [AALM.CLS and OCSPP's biokinetic model in Fortran
(ICRPv005.FOR)], evaluating the differing biokinetics for the two versions against available human data,
and selection of final model parameters for use in AALM.FOR. The side-by-side comparisons of
AALM.CLS and AALM.FOR provided a quality assurance opportunity to ensure code was implemented
and operating as expected, i.e., the mathematical relationships posited by the model were correctly
translated into computer code and its operation was free of numerical errors. Model parameter
optimization and sensitivity analyses discussed in Chapter 4 provides the basis for parameters in
AALM.CLS that were ultimately used in AALM.FOR. These analyses were not repeated using
AALM.FOR since it provides identical predictions to AALM.CLS. Model evaluations in Chapter 3
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compare AALM.CLS and AALM.FOR against the same datasets used in Chapter 4 as well as some
additional datasets for striking workers and children.
Chapter 4 describes the ORD development and evaluation of AALM.CLS. The AALM.CLS version
implemented both the Leggett model (Leggett. 1993) and O'Flaherty model (O'Flahertv. 1995. 1993).
The chapter begins with a comparison of the Leggett and O'Flaherty model structures and then provides a
comparison of predicted blood and bone concentrations of Pb between the models. Sensitivity analyses
are subsequently provided that were utilized to determine the most influential biokinetic parameters in the
models. An evaluation and optimization biokinetics models against observations is provided. A
biokinetic parameter controlling Pb binding to red blood cells Pb concentrations was adjusted to align the
AALM.CLS results more closely with the IEUBK model for children without adversely affecting the
good model agreement and predictive capability for infants or adults.
1.1.1. Quality Assurance and Peer Review
The use of quality assurance (QA) and peer review helps ensure that EPA conducts high-quality science
that can be used to inform policymakers, industry, and the public. Quality assurance activities performed
by EPA ensure that the Agency's environmental data are of sufficient quantity and quality to support the
Agency's intended use. Detailed QA Project Plans (QAPPs) have been developed as a requirement for
contracted technical support during the development of the AALM. The AALM is classified as providing
Influential Scientific Information (ISI), which is defined by the Office of Management and Budget
(OMB) as scientific information the agency reasonably can determine will have or does have a clear and
substantial impact on important public policies or private sector decisions (OMB. 2004). OMB requires
the Agency to subject ISI to be peer review prior to dissemination. To meet this requirement, EPA often
engages the Scientific Advisory Board (SAB) as an independent federal advisory committee to conduct
peer reviews. The SAB released a call for peer review panel nominations on November 1, 2018
(83FR54923). Panel members were chosen to create a balanced review panel based on factors such as
technical expertise, knowledge, experience, and absence of any real or perceived conflicts of interest.
Both peer review comments provided by the SAB panel and public comments submitted to the panel
during their deliberations about the external review draft will be considered in the development of a final
version of the AALM.
1.2. HISTORY OF THE AALM
The AALM was developed as a computational tool for predicting blood Pb concentrations associated with
multimedia exposures to Pb that occur from birth through adulthood. The model is a substantial
conceptual extension of an earlier IEUBK model developed by EPA to predict blood Pb concentrations in
children, the IEUBK model (Hogan et al.. 1998; White et al.. 1998; Zaragoza and Hogan. 1998; U.S.
EPA. 1994a. c, 1989). The IEUBK model has been widely used at Superfund sites to develop remedial
objectives.
1.2.1. AALM.C
Development of the AALM implemented in Visual C (AALM.C) by the EPA National Center for
Environmental Assessment (NCEA) began in 1999 to extend Pb exposure and biokinetics modeling
capability of the IEUBK model to address a wider range of model applications in computational Pb
toxicology and risk assessment; these include:
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• Simulation of Pb biokinetics associated with multimedia exposures occurring within any age
range from birth through adulthood (the IEUBK model is limited to birth to age 84 months);
• Simulation of Pb biokinetics in blood, bone, soft tissues, and excreta (in the IEUBK model,
Pb levels in tissues and excreta are intermediary variables used to support the blood Pb
simulation, and are not output variables);
• Simulation of Pb biokinetics in response to changes in Pb exposure that occur over periods of
days (the IEUBK model exposure averaging time is typically > 1 year and predicts quasi-
steady state blood Pb concentrations); and
• Expansion of the exposure model to include multiple sources of exposure from air, drinking
water, food, and indoor dust and soil.
Over the intervening years between initiation of the development of the IEUBK model in 1989 and its
release for regulatory (U.S. EPA. 1994b). several modeling approaches were reported for simulating Pb
biokinetics of ages extending beyond early childhood. Two models in particular were influential in
developing the structure of the AALM. The first was the Leggett model (Pounds and Leggett. 1998:
Leggett. 1993). based on a biokinetic model originally developed for the International Commission on
Radiological Protection (ICRP) that calculated radiation doses from environmentally important bone-
seeking radionuclides, including radioisotopes of Pb (Leggett. 1992a. b, 1985). The original model was
used to develop cancer risk coefficients for internal radiation exposures to Pb and other alkaline earth
elements that have biokinetics similar to those of calcium (U.S. EPA. 1998; ICRP. 1993). The
compartment structure, Pb transfer coefficients, and numerical integration method of the Leggett model
were adopted in the early versions of the AALM. The second model was the O'Flaherty model that
simulates Pb exposure, uptake, and disposition in humans, from birth through adulthood (O'Flaherty.
2000; O'Flaherty et al.. 1998; O'Flaherty. 1998. 1995. 1993. 1991a. b, c). Important features that
distinguish the O'Flaherty model from the Leggett model are simulation of growth (the Leggett model
simulates growth of blood volume only), bone formation, and resorption (the Leggett model simulates the
"effects" of bone growth and resorption on Pb kinetics, but does not simulate bone growth and resorption
explicitly). Uptake and release of Pb from trabecular bone and metabolically active cortical bone are
functions of bone formation and resorption rates, respectively, and are simulated in the O'Flaherty model;
this establishes a relationship between the age-dependence and the Pb kinetics in and out of bone, and
allows for explicit simulation of the effects of bone formation (e.g., growth and loss, changes in bone
volume, and bone maturation) on Pb uptake and release from bone. In contrast, the Leggett model
represents age-dependence of bone Pb kinetics as age-dependent rate coefficients for transfer of Pb into
and out of bone. Although the O'Flaherty model had a more physiologically accurate representation of
bone growth and resorption, the Leggett model configuration for growth of the blood volume and bone Pb
kinetics was used for early versions of the AALM.
In October of 2005, the EPA Science Advisory Board (SAB) reviewed a Visual C implementation of the
AALM (AALMvl.05.C) and highlighted the need for expanded documentation and further evaluation of
the model (U.S. EPA. 2007). The SAB also identified a number of deficiencies, and suggested potential
improvements. EPA expanded the documentation and evaluation of the AALM to include the following:
(1) a Guidance Manual for the AALM that describes the conceptual basis and structure of the model
(including all equations, parameters, and parameter values) (SRC. 2008); (2) review and evaluation of
evidence supporting further extension and/or refinement of the model (SRC. 2009a); and (3) a
comparative review of alternative modeling approaches (SRC. 2009b).
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1.2.2. AALM.CSL
Research initiated by EPA NCEA in early 2013 expanded the AALM further to address deficiencies
identified by the SAB and re-evaluated performance of the model. The AALM was migrated to acslX
which removed the need to develop and maintain computer code for the numerical integration solution of
the AALM biokinetics model, and made use of existing acslX code to implement the Leggett and
O'Flaherty models (Lorenzana et al.. 2005). An exposure model was developed in Excel which removed
the need to develop de novo computer code for the exposure model, and allowed development of
exposure scenarios in Excel without the requirement for a license or knowledge of acslX. Development
of the acslX version of the AALM is described in Chapter 4. The latest version of the model is
AALMv4.2.CSL (July 2015).
AALM.CSL included the user option to link the exposure model to either the Leggett or O'Flaherty
biokinetics models. It also introduced several changes to both the Leggett and O'Flaherty biokinetics
models including some new parameters and as well as revised parameter values. Some of these data used
in the optimization were not available at the time the original models were developed. Optimization
against a common set of data resulted in general convergence of AALM-LG.CSL and AALM-OF.CSL
predictions for blood, bone, and soft tissue, and agreement with blood Pb predictions for children from
the IEUBK model (Chapter 4).
1.2.3. AALM.FOR
In 2014, the EPA Office of Pollution Prevention and Toxics (OPPT) developed an implementation of the
Leggett model (Pounds and Leggett. 1998; Leggett. 1993) biokinetics model to support the Agency's
Approach for Estimating Exposures and Incremental Health Effects from Lead Due to Renovation,
Repair, and Painting Activities in Public and Commercial Buildings (U.S. EPA. 2014b). The latest
released version of the model, ICRPv005.FOR, has the capability of simulating Pb levels in body tissues
(e.g., blood, bone, brain) and excreta at resulting from acute or chronic exposures to inorganic Pb that
occur from birth through adulthood.
In developing ICRPv005.FOR, several changes were made to Leggett biokinetics model (see Table 3-1 in
Chapter 3); however, up to ICRPv004.FOR, the biokinetics model was unchanged from Leggett (1993).
The major changes included (1) age-dependent blood and tissue masses, adjustments to RBC uptake
parameters, and adjustment of bone-to-plasma transfer rates. Collectively, updates made to
ICRPv004.FORto create ICRPv005.FOR resulted in lower predicted blood Pb concentrations for a given
Pb intake in children, that more closely agreed with predictions from the IEUBK model (see Figure M-4
in. U.S. EPA. 2014a); and lower blood and bone Pb concentrations in adults (see Figure M-6 in. U.S.
EPA. 2014a). ICRPv005.FOR was evaluated against data on blood and bone Pb levels in occupationally
exposed adults reported in Nie et al. (2005). although some of these data have not been published. The
conclusion from these evaluations was that the model tended to predict lower cortical bone Pb
concentrations than observed and higher blood Pb concentrations (see Figures M-5 and M-6 in. U.S. EPA.
2014a).
External peer review of the Approach for Estimating Exposures and Incremental Health Effects from
Lead Due to Renovation, Repair, and Painting Activities in Public and Commercial Buildings (U.S. EPA.
2014b) resulted in several recommendations (Post-Meeting Peer Review Summary Report. Versar. 2015).
including the need for further evaluation of ICRPv005.FOR. Based on these evaluations, ICRPv005.FOR
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1 was revised and parameter values updated to create AALM.FOR (Chapter 3). In the development of
2 AALM.FOR, the model was evaluated with a larger set of observations in children and adults, including
3 some data that had not been used in previous evaluations of ICRPv005 .FOR, including all datasets used
4 in the evaluation and development of the AALM.CSL (Chapter 4). AALM.FOR utilizes the same
5 exposure and biokinetic parameter values as the AALM.CSL and, as a result, both models predict the
6 same blood and tissue Pb levels when the same exposure inputs are used in both models. Similar to the
7 AALM.CSL, AALM.FOR utilizes a spreadsheet graphical user interface for setting exposure and
8 biokinetics parameter model inputs and processing output. The major difference between the general
9 architecture of the two models is that the biokinetics model of the AALM.FOR is implemented in Fortran,
10 whereas, the biokinetics model of the AALM.CSL is implemented in acslX.
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CHAPTER 2. THEORETICAL FRAMEWORK, PARAMETERS, AND EQUATIONS
2.1. OVERVIEW OF AALM.FOR STRUCTURE
The AALM.FOR consists of two major submodels that simulate Pb exposure and Pb biokinetics,
respectively. The exposure model described in Section 2.2 calculates rates of Pb intake (|_ig Pb/day) from
ingestion or inhalation based on inputs for exposure concentrations in air, indoor dust, soil and water; and
Pb intakes ((ig/day) from food or other sources. The exposure model simulates a hypothetical individual
(subject), defined in terms of age, sex and rates of contact with environmental media (e.g., drinking water
or indoor dust or soil ingestion rates).
The AALM.FOR biokinetics model described in Section 2.3 simulates kinetics of absorption of Pb into a
central (diffusible blood plasma) compartment, transfers of Pb between the central compartment and
various tissues, and transfers of Pb to excreta. Absorption of Pb from the respiratory tract is simulated as
a first-order process governed by rate coefficients (d1) for absorption from each of four respiratory tract
compartments. Absorption from the gastrointestinal tract is simulated as a first-order process governed
by age-dependent absorption fractions and first-order rate coefficients for transfers of Pb within the
gastrointestinal tract. Rates of absorption from inhaled and ingested Pb are summed to yield a total rate
of transfer (|_ig Pb/day) to the central plasma compartment; these rates include Pb absorbed from intakes
from exposures as well as Pb transferred to the gastrointestinal tract from the respiratory tract (i.e.,
mucocilliary clearance), and from the liver (i.e., biliary secretion). Biokinetics model output variables are
tissue Pb masses and concentrations, and Pb masses in excreta corresponding to the exposure and
absorption scenarios constructed in the exposure and absorption models. Tissues represented in the
model include red blood cells and blood plasma (including a pool of Pb in plasma that is bound to
proteins), brain, cortical and trabecular bone, kidney, liver, and other soft tissues. Distinct excretory
pathways represented in the model include feces, urine, sweat, and other routes (e.g., hair and nails,
exfoliated skin). Transfers of Pb between compartments are simulated as first-order processes governed
by first-order rate coefficients (d1) that are scaled for age.
The AALM.FOR architecture consists of two components: (1) a macro-enabled Excel workbook (AALM
Fortan.xlsm) that implements the exposure model and provides user access to all exposure and biokinetics
parameters in the AALM.FOR; (2) a Fortran program that implements the biokinetics model. Input
parameter values are selected by the user in AALMFortran.xlsm. Macros in the AALMFortran.xlsm file
pass the input parameter values to a comma-delimited (CSV) text file (AALM LG INPUTDATA.DAT)
which are imported into the AALM Fortran program. Output variables from the simulation are passed to
a CSV file (AALM LG OUTPUTDATA.DAT) and are read into the AALM.Fortran.xlsm file with Excel
macros.
AALM.FOR inputs and outputs are controlled and recorded in AALM Fortan.xlsm workbook. This
workbook has several functions: (1) allows setting of input parameter values for AALM.FOR
simulations; (2) macros in this workbook are used to pass data to and from Fortran; (3) allows plotting of
AALM.FOR output data; and (4) provides a complete record of input values and results of each
AALM.FOR simulation. Worksheets in AALM Fortran.xlsm allow the user to set exposure scenarios for
Pb in air (Air), food (Food), indoor dust, (Dust), soil (Soil), drinking water (Water), and/or other ingestion
intakes (other). Exposures can be discrete (i.e., a series of exposures at selected ages), and/or pulsed in a
repeating frequency (e.g., 2 days/week for 3 months/year, for a selected age range). The AALM.FOR
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uses inputs from all exposure media when it creates biokinetics simulations. This allows construction of
complex multi-pathway exposure scenarios having varying temporal patterns. Worksheets in AALM
Fortran.xlsm also allow the user to set values for parameters that control Pb absorption and relative
bioavailability in individual exposure media (RBA), and biokinetics (Lung, Systemic, Sex). All settings
are recorded in the AALM Fortran.xlsm workbook and can be recalled to re-run the simulation.
2.2. EXPOSURE MODEL
2.2.1. General Structure of the Exposure Model
The exposure model of the AALM.FOR calculates rates of Pb intake from ingestion and inhalation
pathways, for a hypothetical individual (subject) based on inputs for exposure to Pb in air, food, indoor
dust, soil, water, and from miscellaneous ingestion intakes (designated in the model as other). Intakes
(|_ig Pb/day) derived from the exposure model are passed to the biokinetics model and provide the bases
for calculating Pb masses in tissues and excreta for each age day simulated. Calculations of Pb intakes
are controlled by model parameters that can specify two major categories of exposure parameters:
(1) parameters that define the individual (e.g., age, sex); and (2) parameters that define Pb intake rates. A
list of all equations used in the AALM.FORto calculate Pb intakes as they appear in the AALM.FOR
code is provided in Appendix A of this chapter, and parameters used in these equations are defined in
Appendix C.
An AALM.FOR simulation progresses through a series of exposure time steps representing age-days. A
simulation begins at birth and progresses to a terminal age for the simulation (e.g., 32,850 days for a
simulation of approximately 90 years). As a simulation progresses, Pb intakes (|_ig Pb/day) are calculated
for each day based on values specified for Pb concentrations in exposure media (e.g., |_ig Pb/g dust) and
rates of media intakes (e.g., |_ig dust ingested/day); or based on inputted Pb intake rates (|_ig Pb/day) for
ingestion of Pb in food or in other media. The exposure time step of one day is independent of the
numerical integration time step described in Section 2.3.1 (setting one has no effect on the other). Lead
intakes passed to the biokinetics model are in units of (ig/day and are adjusted (along with other time-
dependent parameters and variables) in biokinetics differential equations to agree with the integration
time step used at every point in the simulation. Lead intakes calculated from the exposure model are
accessible as output to the AALM Fortran.xlsm file.
Lead intakes resulting from exposures to Pb in air, indoor dust, soil, or water are calculated from inputs of
Pb concentrations. The general form of the equations for calculating Pb intakes from Pb concentrations is
given in Equation 2.2-1:
INmedium = Y1i=i(Pbmedium.i ¦ fmediumi) ¦ IRmedium ¦ RBAmedium Eq. (2.2-1)
where INmedium is the Pb intake rate (|_ig Pb/day) for a specific environmental medium (e.g.,
water), Pbmediumi is the exposure concentration (e.g., |_ig Pb/L water) in that medium for a given
exposure setting i, fmediumi is the fraction of total intake of the medium that occurs in setting IRmedium
is the intake rate of the medium (e.g., L water/day), and RBAmedium is the relative bioavailability of Pb
in the exposure medium (relative to completely water-soluble Pb). Parameter values in Equation 2.2-1
representing exposure concentrations, media intakes, and fractional media intakes for each setting can be
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assigned age-dependent values; whereas, the value assigned to RBA represents the entire age range
simulated. The application of RBA as an adjustment to Pb intake rather than an adjustment to the
gastrointestinal absorption fraction is a simplification that results in an underprediction of fecal excretion
of unabsorbed Pb and negative mass balance (intake>body burden + excreted) when RBA <1.
Lead intakes resulting from exposures to Pb in food and other media are calculated from inputs of Pb
intake rate (e.g. |ag Pb/day) using equations of the following general form (Equation 2.2-2):
INmedium = £f=1(Pbintakei) ¦ RBAmedium Eq. (2.2-2)
where Pbintaket is the rate of Pb intake ((ig/day) entered for the medium for exposure setting
Lead exposure concentrations (air, indoor dust, soil, water) or intakes (food, other) can be entered into the
AALM.FOR as discrete values representing specific ages, or as pulse trains in which the exposure Pb
concentration or Pb intake is turned on or off at specific ages. The AALM User Guide should be
consulted for specific examples of how this functionality is implemented in the Excel User Interface.
Pulse train intakes or exposure concentrations are fixed as constant over periods specified by users. Users
can select whether discrete exposure concentrations or intakes are constant (stepwise) or interpolated
between ages specified in the discrete time series. Selection of stepwise or interpolation will be applied to
all discrete media concentrations or intakes. In the discrete mode, exposure settings for each exposure
medium are simulated as a time (age-day) series of exposure concentrations (air, indoor dust, soil, water)
or Pb intakes (food, other) and weighting factors for exposure concentrations that represent the
percentage of exposure contributed by each setting, each day, at each age. The exposure setting functions
allow the user to simulate exposure scenarios in which exposure to a Pb in a specific medium may occur
from different sources, or at different locations (e.g., home, school, work) within a day. Concentrations
of Pb in air, water, indoor dust or soil, at each specified age, are calculated as the weighted average of
contributions from all exposure settings represented in the simulation that contribute to that particular
exposure medium (Equation 2.2-3).
Pbmediumweighted = Y1i=i(Pbmedium.i ¦ fmediumi) Eq. (2.2-3)
where fmediumi is the fraction contributed by exposure setting Intakes of Pb in food and other
at each specified age are calculated as the sum intakes for exposure settings represented in the simulation
that contribute to that particular exposure medium (Equation 2.2-4).
lNmediumsurn = (JNmedium^) Eq. (2.2-4)
The exposure model allows inputs of up to three different exposure settings for each medium (n = 3 in
Equations 2.2-3 and 2.2-4) and setting discrete exposures for up to 50 ages.
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1 The pulse train functions can be used to represent episodic exposures or intakes that occur at fixed
2 frequency (pulse period) and duration (pulse width) schedule (e.g., 2 days per 7 days), over a given age
3 range (pulse start, pulse stop) above a user-inputted baseline Pb concentration or intake. The exposure
4 model allows the user to specify up to two overlapping pulse trains, which can be used to simulate more
5 complex intermittent exposure patterns (e.g., 2 days per 7 days; 3 months per 12 months). A combination
6 of discrete and pulsed exposures can be simulated by assigning a value of <1 to the parameter fpuise. This
7 parameter apportions the relative contributions of the discrete and pulsed Pb intakes according to the
8 fraction of total assigned to the pulse (Equation 2.2-5)
9
10 IN7n6diu7nf0f-ai IN7n6diu7ncnscref-e ¦ (1 fpuise) I NTn,6diuTn,pUise ¦ fpUise Eq. (2.2-5)
11
12 Equations used in the AALM.FOR to calculate Pb inhalation and ingestion intakes concentrations in
13 tissues are presented in Tables 2-1 and 2-2 and in Appendix A of this chapter and parameters are defined
14 in Appendix B. The main differences between these two presentations of the equations are that: (1)
15 equations in Appendix A use the exact nomenclature for parameters as they appear in the AALM.FOR
16 code (Appendix B), whereas, nomenclature in Table 2-1 has been modified for simplicity; and (2) the
17 equations in Appendix A are presented in their integrated forms as used in the AALM.FOR numerical
18 integration routine, whereas, the differential equations are shown in Table 2-1. For readability, tables and
19 appendices are provide at the end of this chapter.
20 2.2.2. Parameters That Define a Hypothetical Individual
21 Age: Each step in the simulation represents a day of age, beginning at birth (age = 0).
22 Sex: The sex specification links the subject to an appropriate sex-specific growth algorithm (O'Flahertv.
23 1995. 1993) described in Section 3.5.2.
24 Fetal Exposure: The AALM.FOR simulation begins at birth with the neonatal tissue Pb masses assigned
25 values based on the user-designated maternal blood Pb, described in Section 2.3.11.
26 2.2.3. Exposure Media Intakes and Lead Concentrations
27 It should be noted that for ingested Pb, the adjustment for RBA is applied to Pb intake rather than an
28 adjustment to the gastrointestinal absorption fraction (Section 2.3.3.2) is a simplification that results in an
29 underprediction of fecal excretion of unabsorbed Pb and negative mass balance (intake > body burden +
30 excreted) when RBA < 1.
31 2.2.3.1. Air Pb Exposure
32 Air Pb intakes (|_ig Pb/day) are calculated as the product of air Pb concentration (|_ig Pb/m3) and
33 ventilation rates (m3 air/day) that are specified for a given age range (Equation 2.2-6).
34
35 INair = Pbair ¦ VR Eq. (2.2-6)
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where VR is the ventilation rate (m3/day). The values assigned to ventilation rates represent the
average daily values for specific age ranges. These values can be modified to represent specific activity
levels (e.g., ventilation during periods of rest, moderate activity, strenuous activity, etc.). Values for VR
are interpolated between inputted ages. Air Pb intakes (|_ig Pb/day) are passed to the biokinetics model
where they represent values for rates of deposition of Pb in the respiratory tract (see BRETH in Section
2.3.3.1).
The discrete mode allows the user to specify exposures to multiple (i.e., n = 3) sources; for example,
indoor air, outdoor air, or air at different locations (e.g., home, school, work). In the discrete mode, the
PbAir term in Equation 2.2-6 is the weighted average from all exposure settings (Equation 2.2-7):
Pbairdiscrete weighted ~ ^i=\{Pb(MTi ' fa^i) Eq. (2.2-7)
where Pbairt is the air concentration for exposure setting /' at a given age and fairt is the fraction
of total daily exposure assigned to setting
The pulse mode allows the user to represent episodic exposures to air Pb that occur at fixed frequency
(pulse period) and duration (pulse width) schedule. In the pulse mode, air Pb concentration is specified
with values for a baseline concentration (jig Pb/m3), a pulsed concentration, the start and ending ages of
the pulse train (day), the width of each pulse (days) and the period of each pulse (the number of days
between pulses). During each pulse, air Pb concentration is calculated as the sum of the baseline and
pulsed concentrations (Equation 2.2-8):
Pbairpuise sum PbaiT^aseiine Pb&iVpuise Eq. (2.2-8)
Air Pb intakes calculated for discrete and pulse train inputs are summed to calculate total Pb intake
associated with exposures to Pb in air (Equation 2.2-9):
INairTotai INctiVcnscrete ¦ (1 Fpuise) IN aiYpuise ' Ppuise Eq. (2.2-9)
2.2.3.2. Indoor Dust Pb Exposure
Ingestion intakes resulting from contact with Pb in indoor dusts (e.g., adherence on hand-to-mouth) from
all sources are simulated by specifying values for dust exposure parameters. Dust Pb intakes (|_ig Pb/day)
are calculated as the product of Pb concentration (|_ig Pb/g) and ingestion rate (g dust/day, Equation 2.2-
10):
INdust = Pbdust ¦ IRdust ¦ RBAdust Eq. (2.2-10)
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where INdust is the intake of dust Pb (|ag Pb/day), Pbdust is the Pb concentration in dust (|_ig
Pb/g), IRdust is the intake rate of dust from all sources (g dust/day) and RBAdust is the relative
bioavailability of Pb in dust, relative to water-soluble Pb. Values for IRdust are interpolated between
inputted ages. The model accepts a single inputted value for RBA which represents dust from all sources,
in all exposure settings. Dust Pb intakes (|_ig Pb/day) are summed with other ingestion intakes (i.e., soil,
food, water, other) and passed to the biokinetics model as rates of intake Pb to the stomach compartment
of the gastrointestinal tract (see Section 2.3.3.2).
The discrete mode allows the user to specify exposures to multiple (i.e., n = 3) sources; for example,
indoor dusts at different locations (e.g., home, school, playground). In the discreet mode, the Pbdust term
in Equation 2.2-10 is the weighted concentration for all exposure settings (Equation 2.2-11):
where Pbdusti is the soil or dust Pb concentration for exposure setting i at a given age and fdusti is
the fraction of total daily exposure assigned to setting
The pulse mode allows the user to simulate episodic exposures to dust Pb that occur at fixed frequency
(pulse period) and duration (pulse width) schedule. In the pulse mode, dust Pb concentration is specified
with values for a baseline concentration (jig Pb/g), a pulsed concentration, the start and ending ages of the
pulse train (day), the width of each pulse (days) and the period of each pulse (the number of days between
pulses). During each pulse, dust Pb concentration is calculated as the sum of the baseline and pulsed
concentrations (Equation 2.2-12):
PbdustpUisg sum Pbdustbaseune + PbdustpUise Eq. (2.2-12)
Dust Pb intakes calculated for discrete and pulse train inputs are summed to calculate total Pb intake
associated with exposures to Pb in dust (Equation 2.2-13):
2.2.3.3. Soil Pb Exposure
Ingestion intakes resulting from contact with Pb in soil (e.g., adherence on hand-to-mouth) from all
sources are simulated by specifying values for soil exposure parameters. Exposure to soil could include
hand-to-mouth contact with soil transported from surficial soil to other surfaces (e.g., indoor), or direct
hand-to-mouth contact with surficial soil. Ingestion of bulk soil (e.g. pica) can also be simulated as a
pathway separate from dust (i.e., other). The main consideration for including exposures to soil in the
soil pathway rather than simulating the soil exposures in the other pathway is the determination of
Pbdustdiscrete weighted 2i=±(.Pbdusti ¦ fdustf)
Eq. (2.2-11)
INdustf0fai INdust(iiscrefe ' (1 fpulse) "I" INdllStpUise ¦ fpulse
Eq. (2.2-13)
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whether or not parameter values for soil ingestion rate (IRsoil, Equation 2.2-14) apply to the soil
exposure.
Soil Pb intakes (|_ig Pb/day) are calculated as the product of Pb concentration (jig Pb/g) and ingestion rate
(g dust/day, Equation 2.2-14):
where INsoil is the intake of soil Pb (|_ig Pb/day), Pbsoil is the Pb concentration in soil (|_ig Pb/g),
IRsoil is the intake rate of soil from all sources (g soil/day) and RBAsoil is the relative bioavailability of
Pb in soil, relative to water-soluble Pb. Values for IRsoil are interpolated between inputted ages. The
model accepts a single inputted value for RBA which represents soil from all sources, in all exposure
settings. Soil Pb intakes (|_ig Pb/day) are summed with other ingestion intakes (i.e., dust, food, water,
other) and passed to the biokinetics model as rates of intake Pb to the stomach compartment of the
gastrointestinal tract (see Section 2.3.3.2).
The discrete mode allows the user to specify exposures to multiple (i.e., n = 3) sources; for example, soils
at different locations (e.g., home, school, playground). In the discreet mode, the Pbsoil term in Equation
2.2-14 is the weighted concentration for all exposure settings (Equation 2.2-15):
where Pbsoil, is the soil or soil Pb concentration for exposure setting i at a given age and fsoil, is
the fraction of total daily exposure assigned to setting
The pulse mode allows the user to simulate episodic exposures to soil Pb that occur at fixed frequency
(pulse period) and duration (pulse width) schedule. In the pulse mode, soil Pb concentration is specified
with values for a baseline concentration (|_ig Pb/g), a pulsed concentration, the start and ending ages of the
pulse train (day), the width of each pulse (days) and the period of each pulse (the number of days between
pulses). During each pulse, soil Pb concentration is calculated as the sum of the baseline and pulsed
concentrations (Equation 2.2-16):
PbsoilpUisg sum Pbsoilfraseiine PbsoilpUise Eq. (2.2-16)
Soil Pb intakes calculated for discrete and pulse train inputs are summed to calculate total Pb intake
associated with exposures to Pb in soil (Equation 2.2-17):
INsoil = Pbsoil ¦ IRsoil ¦ RBAsoil
Eq. (2.2-14)
PbS0ildiscrete weighted Yii=i(Pbsoi-h ' fso^i)
Eq. (2.2-15)
INSOilTotai — INsoildiscrete ¦ (1 fpulse) INsoilpuise ' fpulse
Eq. (2.2-17)
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2.2.3.4. Water Pb Exposure
Lead intakes from ingestion of water (jig Pb/day) are calculated as the product of Pb concentration (jig
Pb/L) and ingestion rate (L/day, Equation 2.2-18):
where INwater is the intake of Pb in water (fig Pb/day), Pbwater is the Pb concentration in water
(|LLg Pb/L), IRwater is the rate ingestion of water (L/day) and RBAwater is the relative bioavailability of
Pb in water and dust, relative to water-soluble Pb. Values for IRwater are interpolated between inputted
ages. The model accepts a single inputted value for RBA which represents both water, in all exposure
settings. Lead dissolved in water would, by definition, have RBA = 1; however, the RBA parameter
could be used in scenarios in which ingestion exposures include Pb-bearing particulates suspended in
water for which the RBA may be <1. Water Pb intakes (|ag Pb/day) are summed with other ingestion
intakes (i.e., food, dust, soil, other) and passed to the biokinetics model as rates of intake Pb to the
stomach compartment of the gastrointestinal tract (see Section 2.3.3.2).
The discrete mode allows the user to specify exposures to multiple (i.e., n = 3) sources of water Pb; for
example, first-draw, flushed, bottled; or water consumed different locations (e.g., home, school, work).
In the discreet mode, the Pbwater term in Equation 2.2-18 is the weighted concentration for all exposure
settings (Equation 2.2-19):
Pbwaterweighted = YH=1(Pbwateri ¦ fwater{) Eq. (2.2-19)
where Pbwaler, is the water Pb concentration for exposure setting /' at a given age and fwater, is
the fraction of total daily exposure assigned to setting
The pulse mode allows the user to simulate episodic exposure to water Pb that occur at fixed frequency
(pulse period) and duration (pulse width) schedule. In the pulse mode, water Pb concentration is specified
with values for a baseline concentration (jig Pb/L), a pulsed concentration, the start and ending ages of the
pulse train (day), the width of each pulse (days) and the period of each pulse (the number of days between
pulses). During each pulse, dust Pb concentration is calculated as the sum of the baseline and pulsed
concentrations (Equation 2.2-20):
Pbwaterpuise sum = PbwaterbaseUne + Pbwaterpuise Eq. (2.2-20)
Intakes assigned to discrete and pulse train inputs are summed to calculate total Pb intake associated with
exposures to Pb in water (Equation 2.2-21):
INwater = Pbwater ¦ IRwater ¦ RBAwater
Eq. (2.2-18)
INwaterTotai I Nwater^^^g^g ¦ (1 fpulse} INwaterpUise ' fpuise
Eq. (2.2-21)
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2.2.3.5. Food Pb Exposure
Food Pb exposures are inputted as Pb intakes from ingestion of food (|_ig Pb/day) and are adjusted by
RBA (Equation 2.2-22):
IN food = IN food input ¦ RBAfood Eq. (2.2-22)
Inputted food Pb intakes represent the total Pb intakes from all foods consumed and included in the
simulation. The model does not calculate food Pb intakes from inputted data on Pb concentrations in
foods and food consumption rates. Lead intakes from food are summed with other ingestion intakes (i.e.,
water, dust, soil, other) and passed to the biokinetics model as rates of Pb transferred to the stomach
compartment of the gastrointestinal tract (see Section 2.3.3.2).
The discrete mode allows the user to specify exposures to multiple (i.e., n = 3) sources of food Pb (e.g.
market basket, home grown produce, local fish or game). In the discrete mode, the Pbfoodinput term in
Equation 2.2-22 is the sum of Pb intakes from all exposure settings (Equation 2.2-23):
IN f ooddiscete sum = Y'i=\ (IN f oodi) - RBAfood Eq. (2.2-23)
where INfoodi is the food Pb intake for exposure setting /' at a given age, and RBAfood is the
relative bioavailability of Pb in food, relative to water-soluble Pb. The model accepts a single inputted
value for RBA which represents food in all exposure settings.
The pulse mode allows the user to simulate episodic food Pb intakes that occur at fixed frequency (pulse
period) and duration (pulse width) schedule. In the pulse mode, food intake is specified with values for a
baseline Pb intake (|_ig/day). a pulsed Pb intake (|_ig/day ). the start and ending ages of the pulse train (day),
the width of each pulse (days) and the period of each pulse (the number of days between pulses). During
each pulse, Pb intake is calculated as the sum of the baseline and pulsed intakes (Equation 2.2-24):
INfoodpUise sum INfoodfoaseiine //Vfood^jS(l Eq. (2.2-24)
Intakes assigned to discrete and pulse train inputs are summed to calculate total Pb intake from ingestion
of food (Equation 2.2-25):
INfoodj0fai INfood^iscrefe ¦ (1 fpulse) INfoodpUise ¦ fpuise Eq. (2.2-25)
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1 2.2.3.6. Other Exposure Media
2 The other ingestion category is a placeholder for miscellaneous exposures that are not accounted for by
3 other media (e.g., paint, pica). The other ingestion category may also be used to establish a baseline
4 blood Pb concentration such as based on National Health and Nutrition Examination Survey (NHANES)
5 above which the contribution from soil or other media may be determined. Other Pb exposures are
6 inputted as Pb intakes (|_ig Pb/day) and are adjusted by RBA (Equation 2.2-26):
7
8 INother = INotherinput ¦ RBAother Eq. (2.2-26)
9
10 Other Pb intakes are summed with other ingestion intakes (i.e., water, dust, soil, water) and passed to the
11 biokinetics model as rates of Pb transferred to the stomach compartment of the gastrointestinal tract (see
12 Section 2.3.3.2).
13 The discrete mode allows the user to specify exposures to multiple (i.e., n = 3) sources of other Pb (e.g.
14 home, school, work). In the discrete mode, the INotherinput term in Equation 2.2-26 is the sum of Pb
15 intakes from all exposure settings (Equation 2.2-27):
16
17 INothersum = YH=1(JN other{) ¦ RBAother Eq. (2.2-27)
18
19 where INother * is the Pb intake for exposure setting i at a given age, Fi is the fraction of total
20 daily other Pb intake assigned to setting and RBAother is the relative bioavailability of Pb in the other
21 medium, relative to water-soluble Pb. The model accepts a single inputted value for RBAother which
22 represents Pb in all other exposure settings.
23 The pulse mode allows the user to simulate episodic other Pb intakes that occur at fixed frequency (pulse
24 period) and duration (pulse width) schedule. In the pulse mode, other intake is specified with values for a
25 baseline Pb intake ((.ig/day). a pulsed Pb intake ((.ig/day). the start and ending ages of the pulse train (day),
26 the width of each pulse (days) and the period of each pulse (the number of days between pulses). During
27 each pulse, Pb intake is calculated as the sum of the baseline and pulsed intakes (Equation 2.2-28):
28
29 INotherpUise sum INotherfoasenne + INotherpUise Eq. (2.2-28)
30
31 Intakes assigned to discrete and pulse train inputs are summed to calculate total Pb intake (Equation 2.2-
32 29):
33
34 INotherf0fai INother^iscref-e ¦ (1 fpuise) INotherpUise ' fpuise Eq. (2.2-29)
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1 2.3. BIOKINETICS
2 2.3.1. Computational Structure of the Aalm.For Biokinetics Model
3 The AALM.FOR computes Pb masses (|_ig) in tissues and excreta for each age day simulated (e.g.,
4 assuming 365 days/year, a simulation extending to age 90 years would include 32,850 days). These
5 masses are used to calculate secondary variables such as blood Pb concentration. Lead masses calculated
6 for each age day are based on Pb intake rates (|_ig Pb/day) calculated in the exposure model and passed to
7 the biokinetics model. Lead intakes contribute to rates of entry of Pb into the central plasma compartment
8 (i.e., Pb absorption, (.ig Pb/day), along with transfers to the central compartment resulting from Pb
9 exchanges with other tissues. Lead masses in each biokinetics compartment are computed by numerical
10 integration applied to a series of differential equations that represent the rate of change in Pb mass in each
11 compartment. The general form of the differential equations used in the biokinetics model is as follows
12 (Equation 2.3-1):
13
14 ^ = -Rj ¦ Yj + Pj Eq. (2.3-1)
15
16 where dY/dt is the change in Pb mass (|_ig) in compartment j over time t, Rj is the rate coefficient
17 for transfer of Pb out of compartment j over time i (r1), and Pj is the rate of transfer of Pb into
18 compartment j (|_ig Pb/t). Starting values for compartment Pb masses are inputs to the model, allowing
19 the user to start simulations with pre-existing Pb masses {starting values for compartment Pb masses are
20 set to zero in the current version of AALM.FOR and can be modified in the Fortran input file,
21 POUNDS GUI.DAT). The fundamental unit of time in the biokinetics model is day (i.e., rates used in
22 differential equations are in units of |_ig Pb/day or d"1). Equation 2.3-2 is solved for each state variable
23 (e.g., compartment) using the following numerical approximation for small time steps, At (Lcggctt. 1993;
24 Leggett et al.. 1993) as follows (Equations 2.3-2 to 2.3-4):
25
26 Yt+At = (Yt -1) ¦ e~R
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pj =
Ri^j ¦ YINTj
At
Eq. (2.3-4)
where, Pj is the inflow rate of Pb into compartment /. R, is the rate coefficient for transfer of Pb from
compartment /' to /, and YIN'I', is the time-integrated Pb mass in compartment The above numerical
integration approach can be expected to achieve numerical integration errors that do not exceed a 0.5% if
the integration step size (10~N) is selected such that (Equation 2.3-5):
10-(w+i) <
in(2)
Eq. (2.3-5)
where Rmax is largest rate coefficient in the model, and TV is an integer value (Leggett et al.. 1993).
In the AALM.FOR, the largest rate coefficient is 1000 d1, for transfer of Pb from the plasma to the
extravascular compartment and the corresponding integration step size (10"N) that satisfies Equation 2.3-5
is 0.001 day (i.e., N = 3). At a fixed time step, integration error will be more pronounced in the early
parts of a simulation, when Pb masses are changing in compartments with fast turnover rates (high R
values), and will decrease as the simulation progresses and steady states are achieved in these
compartments. In the AALM.FOR, the integration time step can be varied during the simulation by
assigning values to the step length at different points in the simulation. This allows for relatively short
time steps in the early phases of the simulation to minimize error in integration of fast compartments, and
use of longer steps (requiring less computation time) in later phases of the simulation. An integration
scheme recommended by Leggett et al. (1993) to minimize error in the early phases of the simulation and
achieve computational speed in the later phases is as follows:
Step Length (day)
Integration Cycles
Simulation Day
0.001
1-1000
0-1
0.01
1000-1900
1-10
0.1
1900-2800
10-100
1
>2800
>100
In this scheme, the first 1000 integration cycles (an integration cycle is completed when all state variables
have been integrated over a given time step) are computed using a step length of 0.001 day, at the
conclusion of which the first age day of the simulation is concluded. The next 900 cycles are computed
using a step length of 0.01 days, concluding at age day 10. The next 900 cycles are computed using a step
length of 0.1 day, and the remaining cycles are computed with a step length of 1 day. While step length is
a user-defined model input, the recommended step length for AALM.FOR is a constant step length of 0.1
to 1 days, which should result in acceptable integration error for anticipated applications of the model,
including intermittent exposures. Adequacy of the step length can be determined by evaluating the
sensitivity of the output to changes in step length. When using the pulse train function for a brief exposure
(e.g., 1-2 days), it is recommended that a step length of <0.01 day be used. Varying the step within a
simulation (i.e., using different lengths at different times) is not recommended.
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2.3.2. Compartment Structure of the AALM.FOR Biokinetics Model
The structure of the AALM.FOR biokinetics model is based on the Leggett (1993) model. The model
includes a central exchange compartment, 15 peripheral body compartments, and 3 elimination pools
(Figure 2-1). The central exchange compartment is the diffusible Pb in plasma distinguished from a
bound pool in plasma representing Pb bound to plasma proteins. Lead is absorbed from the
gastrointestinal tract, respiratory tract into the diffusible plasma compartment. Lead in diffusible plasma
exchanges with Pb in bone, brain, kidney, liver, red blood cells (RBC), and other soft tissues. Absorbed
Pb is excreted in urine, sweat, and in a combined pathway representing hair, nails, and exfoliated skin.
Unabsorbed ingested Pb is excreted in feces along with a fraction of absorbed Pb transferred to the
gastrointestinal tract from diffusible plasma and liver (i.e., bile pathway). The application of RBA as an
adjustment to Pb intake rather than an adjustment to the gastrointestinal absorption fraction is a
simplification that results in an underprediction of fecal excretion of unabsorbed Pb and negative mass
balance (intake>body burden + excreted) when RBA <1.
Transfers of Pb between compartments are assumed to follow first-order kinetics governed by rate
coefficients (d1), where each rate coefficient represents a fraction of Pb mass (|_ig) in the compartment
that is transferred per day. Lead masses (|ag) in compartments are computed by numerical integration of
linear differential equations representing the rates of change of Pb mass in each compartment (see section
2.3.1). The computed Pb masses in tissues and tissue masses (g) and/or volumes (dL) are used to
calculate Pb concentrations in tissues. A conceptual representation of equations used in the AALM.FOR
to calculate Pb masses and concentrations in tissues are presented in Table 2-2. A more comprehensive
and accurate presentation of the equations as they appear in the AALM.FOR code is presented in
Appendix A of this chapter and parameters are defined in Appendix B. The main differences between
these two presentations of the equations are that: (1) equations in Appendix A use the exact nomenclature
for parameters as they appear in the AALM.FOR code (Appendix B), whereas, nomenclature in Table 2-2
has been modified for simplicity; and (2) the equations in Appendix A are presented in their integrated
forms as used in the AALM.FOR numerical integration routine, whereas, the differential equations are
shown in Table 2-2. General concepts that underlie equations used in the AALM.FOR for calculating Pb
masses and concentrations are presented in the sections that follow. For readability, tables and
appendixes are provide at the end of this chapter.
2.3.2.1. Rate Equations for Pb Transfers
Transfers of Pb between compartments are assumed to follow first-order kinetics governed by rate
coefficients (d1) and described by first-order rate equations having the following general form (Equations
2.3-6 to 2.3-8):
= INFLOW) - OUTFLOW,-
dt J J
Eq. (2.3-6)
INFLOWj = Yf=](R^j ¦ Yt)
Eq. (2.3-7)
OUTFLOWj = Y£=1(-RHi ¦ Yj)
Eq. (2.3-8)
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where dY/dt is the change in Pb mass in compartment j over time t, INFLOWi is the sum of all
transfers into compartment j (Equation 2.3-7), OUTFLOWj is the sum of all transfers out of compartment
j (Equation 2.3-8), Rj „ is the rate coefficient for transfer of Pb out of compartment j to compartment /'
over time t (t1), Yj is the Pb mass in compartment j (|ig), Rt is the rate coefficient for transfer of Pb from
compartment /' to compartment j, and Yt is the Pb mass in compartment The current version of the
AALM.FOR uses values for rate coefficients that are based on Leggett (1993) and updated based on more
recent evaluations of the model (Chapter 3); these values are presented in Table 2-3 located at the end of
this chapter.
The AALM.FOR uses two approaches to assigning values to INFLOW and OUTFLOW rate coefficients:
(1) rate coefficients representing transfers of Pb out of individual compartments are assigned values for
specific, user-designated, age ranges in the simulation and are designated in rate equations with the prefix
R (e.g., RLV1 for the rate coefficient for transfer of Pb from liver compartment 1 to diffusible plasma);
(2) rate coefficients representing transfers of Pb from the diffusible plasma compartment to tissues are
variables computed from expressions relating deposition fractions to each tissue and a rate coefficient for
transfer of Pb from the diffusible plasma compartment to all receiving compartments. Deposition
fractions are designated with the prefix T (e.g., TLVR1 for the deposition fraction from diffusible plasma
to liver compartment 1). Deposition fractions represent the instantaneous fractional outflow of Pb from
diffusible plasma and are used in the AALM.FOR to establish corresponding rate coefficients.
2.3.2.2. Deposition Fractions
As a means to ensure mass balance of transfers between tissues and the diffusible plasma compartment,
transfer rates from the central compartment are expressed as fractions of the combined rate of transfer
from the central compartment to all compartments (Equation 2.3-9):
where Rplas^j is the rate coefficient for transfer of Pb from diffusible plasma to compartment j (d~
' ). Tplas—>j is the deposition fraction for transfer of Pb from diffusible plasma to compartment /, and
RPLAS is the rate coefficient for transfer of Pb from diffusible plasma to all receiving compartments
(2000 d"1). The sum of all deposition fractions from diffusible plasma must equal one to ensure mass
balance. The product of the sum of all age-adjusted deposition fractions and the Pb mass in the diffusible
plasma compartment is the rate of Pb transfer out of the diffusible plasma to all receiving compartments,
and is designated in the AALM.FOR as BTEMP (Equations 2.3-10 and 2.3-11):
RpLAS^j — Tplas^)
¦ RPLAS
Eq. (2.3-9)
RPLS = TpLAS_>j
¦RPLAS
Eq. (2.3-10)
BTEMP = RPLS ¦ YPLS
Eq. (2.3-11)
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where RPLS is the age-adjusted rate coefficient for or transfer of Pb from the diffusible plasma to
all receiving compartments (d1), and YPLS is the mass of Pb (|_ig) in the diffusible plasma compartment.
2.3.2.3. Scaling of Rate Coefficients and Deposition Fractions
Values for deposition fractions and rate coefficients are age-dependent and are assigned values for
specific ages. Values between ages are interpolated. The input values for deposition fractions from
diffusible plasma (designated with the prefix TO; e.g., TOBONE) are scaled in the biokinetics model to
account for two factors: (1) growth of bone surface area and resulting age-dependence of deposition of Pb
to bone surface, which changes the deposition fractions to other tissues; and (2) non-linear uptake of Pb
from diffusible plasma to RBCs, which changes the RBC deposition fraction as the RBC Pb concentration
increases. Scaled deposition fractions designated with the prefix T (e.g., TBONE). The scaling
adjustment for bone surface takes the form (Equations 2.3-12 and 2.3-13):
AGESCL = 1 TEVF TB0NE Eq (2.3-12)
1-TEVF-TBONEL 1 v '
TpLAS^>j AGESCL • TOPLAS^,j Eq. (2.3-13)
where TEVF is the deposition fraction to the extravascular fluid (see description of central
compartment and bone Pb kinetics), TBONE is the deposition fraction to bone surface, TBONEL is the
limiting adult value for the bone deposition fraction, and TOplas^j is the input value for the deposition
fraction from diffusible plasma to compartment /. before adjustment for bone surface area.
Uptake of Pb into RBCs is simulated as a capacity-limited process, in which the deposition fraction to
RBCs (TRBC) decreases with increasing RBC Pb concentration above a limiting threshold (see
description of RBC compartment in Section 2.3.4.3). The decrease in RBC deposition fraction as the
RBC concentration approaches the limiting value results in greater Pb available for deposition to other
tissues. This change is accounted for in the model by adjusting the deposition fractions to other tissues by
the factor CF (Equation 2.3-14):
cp = i toorbc (2.3-14)
1-TRBC M v '
where TRBC is the deposition fraction to RBCs below the limiting RBC Pb concentration, and
TOORBC is the deposition fraction to RBCs above the limiting RBC Pb concentration. The adjustment
factor, CF, increases as the RBC Pb concentration approaches saturation, and deposition fractions to other
tissues (TOPLAS^j) are proportionately increased.
Equations 2.3-9 to 2.3-14 yield rate equations for the change in Pb mass with time (i.e., integration time
step) of the following typical form, for example for liver compartment 1 (Equation 2.3-15):
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= TLVR1 ¦ CF ¦ BTEMP - RLVR1 ¦ YLVR1 Eq. (2.3-15)
2.3.2.4. Growth of Blood and Tissues for Calculation of Pb Concentrations
The AALM.FOR biokinetics equations are used to compute Pb masses in each tissue compartment.
Concentrations of Pb in selected tissues are calculated as the quotient of Pb mass and tissue volumes (e.g.,
dL blood) or masses (e.g., g kidney, cortical bone, trabecular bone, skeleton). Tissue volumes and masses
are calculated based on growth equations and parameters from O'Flaherty's studies (O'Flahcrtv. 1995.
1993) (see Table 2-2 Equations Nl-N 17). Tissue volumes and masses are functions of body weight
(Equation 2.3-16):
unjru,v un>,,yru WCHILD-AGEYEAR WADULT „ - ...
WBODY = WBIRTH H 1 r WAmnr ArwrwAT, Ecl- (2-3-16)
HALF + AGEYEAR 1 + KAPPA ¦ e-lambda-wadult-aoeyear
In the AALM.FOR code, the variable AGEYEAR in Equation 2.3-16 is replaced with the variable
HOWOLD. Equation 2.3-16 calculates body weight as the sum of three growth phases: (1) pre-natal
which achieves birth weight; (2) rapid (hyperbolic) post-natal growth that occurs before age 10 years; and
(3) logistic growth beginning at puberty and continuing into early adulthood. WBODY is the body weight
at any given age (AGEYEAR), WBIRTH is the body weight at birth, WCHILD is the maximum body
weight achieved during early hyperbolic growth phase, HALF is the age at which body weight is one half
of WCHILD, WADULT is the maximum adult body weight, and KAPPA and LAMBDA are empirically
derived logistic parameters. The body weight parameters enable simulation of different growth patterns,
including distinct patterns for males and females. The current default growth simulations are show in in
Figure 2-2.
Volume growth of blood (AMTBLD) is a linear function of body weight (Equation 2.3-17):
AMTBLD = VBLC ¦ WBODY • 10 Eq. (2.3-17)
where VBLC is the blood volume expressed as a fraction of body weight (WBODY). Plasma and
RBC volumes are functions of blood volume and age-dependent hematocrit (BLDHCT), which increases
during the first 4 days post-natal from approximately 0.52 to 0.66 (default value), and then decreases to
0.46 (default value) by age 1 year (Equations 2.3-18 and 2.3-19):
BLDHCTAGEYEARi001 = 0.52 + AGEYEAR ¦ 14 Eq. (2.3-18)
BLDHCT4GErEAR>om = HCTA ¦ (1 + (0.66 - HCTA) ¦ e-^GEYEAR-o.om^ Eq (2.3-19)
where HCTA is the adult hematocrit (default = 0.46).
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Volume growth of kidney (VK) and liver (VL) are power functions of body weight (Equations 2.3-20 and
2.3-21).
WBODY
VK = 1000 • VKC • (WBIRTH + WADULT + WCHILD) •1
WBIRTH + WADULT + WCHILD
Eq. (2.3-20)
WBODY
VL = 1000 • VIX' • (iWBIRTH + WADULT + WCHILD) ¦
WBIRTH + WADULT + WCHILD
Eq. (2.3-21)
where VKC and VLC are fractions of body weight (WBODY). Kidney and liver are weights
(KIDWT, LIVWT) are calculated form tissue density (Equations 2.3-22 and 2.3-23):
KIDWT = VK ¦ 1.05 Eq. (2.3-22)
LIVWT = VL -1.05 Eq. (2.3-23)
The growth of bone volume (VBONE) and weight (WBONE) are calculated as a power functions of body
weight, with cortical bone volume (CVBONE) assigned 0.8 of total bone volume (VBONE, Equations
2.3-24 to 2.3-26):
WBONE = 1000 • 0.0290 • WBODY121 Eq. (2.3-24)
VBONE = 1000 • 0.0168 • WBODY1188 Eq. (2.3-25)
CVBONE = 0.8 • VBOONE Eq. (2.3-26)
2.3.2.5. Age Dependencies of Parameter Values
Biokinetics parameters that are assumed to change with age are assigned values for specific ages. These
assignments are made as arrays of parameter values and corresponding ages (year), beginning with birth
(age = 0 years). Parameter values between age designations are calculated by linear interpolation.
2.3.3. Absorption
The AALM.FOR model simulates Pb absorption from inhalation, ingestion, or dermal contact with
surface dust. In the AALM.FOR, absorption represents the transfer of Pb intake (|_ig Pb intake/day),
computed in the exposure model, to a rate of entry of Pb into the diffusible plasma compartment of the
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biokinetics model (|_ig Pb absorbed/day). Absorption from each exposure pathway is simulated as a first-
order processes governed by absorption fractions and/or first-order rate coefficients (d1).
2.3.3.1. Absorption from the Respiratory Tract
In the AALM.FOR, the respiratory tract is simulated as four compartments into which inhaled Pb (INair,
(.ig Pb/day) is deposited and from which Pb is absorbed into the diffusible plasma compartment. Division
of the respiratory tract into four compartments provides a means for simulating multi-phase absorption
kinetics of inhaled Pb observed in studies of human exposures to Pb particulates (Lcggctt. 1993). The
four compartments are intended to represent the intrathoracic, bronchiolar, bronchiole, and alveolar
regions of the respiratory tract. In the current version of the AALM.FOR, Pb deposition and absorption
are assigned the following values (half-times, tin, are estimated as ln(2)/BR):
Compartment
1
2
3
4
Deposition Fraction (R)
0.08
0.14
0.14
0.04
Rate Coefficient (BR, day1)
16.6
5.4
1.66
0.347
ti/2 (hour)
1
3
10
40
The above deposition fractions correspond to the regional distribution of deposited Pb from the Lcggctt
(1993) model partitioned to have 40% total deposition of inhaled Pb in the respiratory tract. Of the total
amount of Pb initially deposited, 4% (0.016 of deposited Pb, i.e., 0.04x0.4) is transferred to the stomach
(i.e., mucociliary clearance). The above parameter values reflect the data on which the model was based,
which were derived from studies in which human subjects inhaled submicron Pb-bearing particles
(Morrow et al.. 1980; Chamberlain et al.. 1978; Wells et al.. 1977; Hursh and Mercer. 1970; Hursh et al..
1969). These assumptions would not necessarily apply for exposures to larger or less soluble airborne
particles.
Rate equations describing the rates of change of Pb mass (|_ig) in the respiratory tract are presented in
Table 2-2 (Equations C1-C10). In these equations, the parameter BRETH (Equation G1 in Table 2-1)
represents the total intake of Pb from exposure to Pb in air (|_ig Pb/day, equivalent to INAIRtotal from
Equation A4 in Table 2-1). The mucociliary clearance fraction, designated CIILAR, appears in the rate
equations for diffusible plasma (Table 2-2, Equation E2), in which the rates for transfer of Pb from all
respiratory tract compartments to diffusible plasma are factored by the value l-CILIAR (e.g., Equation
2.3-27):
UPTAKERT = (1 - C1L1AR) ¦ ¦ YRt) Eq. (2.3-27)
where UPTAKERT is the rate of absorptive transfer of Pb from the respiratory tract to diffusible
plasma, CILIAR is the fraction of inhaled Pb transferred to the stomach, BRt is the fraction of inhaled Pb
deposited in respiratory tract compartment /, and YRi is the Pb mass (|_ig) in respiratory tract compartment
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2.3.3.2. Absorption from the Gastrointestinal Tract
In the AALM.FOR, the gastrointestinal tract contents (i.e., Pb masses in the lumen of the gastrointestinal
tract) is simulated as four compartments representing: (1) stomach contents (STMC); (2) small intestine
contents (SIC); (3) upper large intestine contents (ULIC); and (4) lower large intestine contents (LLIC).
Total intake of Pb from ingestion (see Equation G2 in Table 2-1) enters the stomach and is passed, in
series, to the small intestine, upper large intestine, lower large intestine, and feces at rates represented by
first-order rate coefficients. Absorption of Pb from the gastrointestinal tract is assumed to occur in the
small intestine, and is represented by an absorption fraction (AF1), representing the fraction of Pb mass in
the small intestine that is transferred to the diffusible plasma compartment. The absorption fraction given
by Equation 2.3-28 is age-dependent, and calculated based on an expression from O'Flaherty's studies
(O'Flahertv. 1995. 1993):
afageyear = AFC1 - 1+30ate-ageyear EcL- (2.3-28)
Values for AFci and AFc2 were assigned values of 0.4 and 0.28, respectively based on fitting simulations
to data on blood Pb concentration in children (Sherlock and Ouinn. 1986; Ryu et al.. 1983) and adults
(Rabinowitz et al.. 1976) who ingested Pb in formula or food, respectively, as described in Chapter 4.
These parameter values produce a decrease in the absorption fraction from a value of 0.39 at birth to a
value of 0.12 at age 8 years (Figure 2-3), which aligns with the fractional gastrointestinal tract absorption
for adults in the Adult Lead Methodology (U.S. EPA. 2003). This age pattern of higher absorption
fraction in infants and children is generally consistent with observations made in mass balance studies in
infants and children (Ziegler et al.. 1978: Alexander et al.. 1974) and in isotope studies of Pb absorption
in adults (Watson et al.. 1986: James et al.. 1985; Heard and Chamberlain. 1982; Rabinowitz et al.. 1980).
Rate equations describing the rates of change of Pb mass (|_ig) in gastrointestinal tract contents are
presented in Table 2-2 (Equations D1-D10). Values of rate coefficients for movement of Pb through the
gastrointestinal tract are derived from Leggett (1993); the approximate half-times in adults are assumed to
be 0.69, 2.8, 9.0, and 17 hours, respectively. These rate coefficients are scaled for age (GSCAL), relative
to adult values:
AGE
0
100 d
1 yr
5 yr
10 yr
15
>25
GSCAL
1.67
1.67
1.67
1.67
1.33
1.33
1.00
In addition to intake of Pb from ingestion of environmental media, the stomach also receives Pb from the
respiratory tract (i.e., mucociliary clearance). The rate equation describing stomach inflow of Pb to
stomach contents (Table 2-2 Equation Dl) includes this mucociliary contribution (Equation 2.3-29):
INstmc = EATCRN + CILIAR ¦ ¦ YRt) Eq. (2.3-29)
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where EATCRN is the sum of Pb intakes from all ingestion pathways (fig/day). CILIAR is the
fraction of inhaled Pb transferred to the stomach, BRt is the fraction of inhaled Pb deposited in respiratory
tract compartment /, and YRt is the Pb mass (|_ig) in respiratory tract compartment i.
The small intestine receives Pb from the stomach as well as from liver (i.e., biliary secretion) and
diffusible plasma (Table 2-2 Equation D3). Transfer from the liver to the small intestine is represented in
Equation D3 as (Equation 2.3-30):
INLVR1^sic = H1TOSI ¦ RLVR1 ¦ YLVR1 Eq. (2.3-30)
where H1TOSI is the fraction of Pb in liver compartment 1 (LVR1) that goes to the small
intestine, RLVR1 is the rate coefficient for transfer of Pb out of liver compartment 1 (d1), and YLVR1 is
the Pb mass in the fast liver compartment (|_ig).
Transfer of Pb from the diffusible plasma to the small intestine is represented as (Equation 2.3-31):
INPLAS->sic = TFECE ¦ CF ¦ BTEMP Eq. (2.3-31)
where TFECE is the scaled deposition fraction from plasma to small intestine; CP' is an
adjustment factor for deposition fractions from diffusible plasma to account for non-linear uptake of Pb
into RBCs (Equation 2.3-14) and BTEMP is the rate transfer of Pb from plasma to all receiving
compartments (|_ig Pb/day, Equation 2.3-11).
Although absorption occurs from the small intestine, it is accounted for in the equations for inflow of Pb
to the upper large intestine (Table 2-2 Equation D6) and into diffusible plasma (Table 2-2, Equation El
and E2). All inflows of Pb to the small intestine, including from liver and diffusible plasma, are subject
to absorption; as a result, inflow of Pb to the upper large intestine is equivalent to the 1 -API fraction
(where API is the absorption fraction) of the total rate of transfer from the small intestine (Equation 2.3-
32), and inflow from the small intestine to the diffusible plasma includes the corresponding AP I fraction
(Equation 2.3-33):
INsic^>ulic = (1 - AF1) ¦ GSCAL ¦ RSIC ¦ YSIC Eq. (2.3-32)
INSic^plas = AF1 ¦ GSCAL ¦ RSIC ¦ YSIC Eq. (2.3-33)
where INsic^plas is the absorption rate (ABSORBG1), AP I is the absorption fraction, GSCAL is
the age adjustment factor for movement of Pb through the gastrointestinal tract, RSIC is the rate
coefficient for transfer of Pb from small intestine contents to upper large intestine contents (d1), and YSIC
is the Pb mass in the small intestine contents ((.ig). Relative bioavailability (RBA) of ingested Pb (e.g., in
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dust) is considered in the exposure model (see Sections 2.2.1 and 2.2.3). The application of RBA as an
adjustment to Pb intake rather than an adjustment to the gastrointestinal absorption fraction is a
simplification that results in an underprediction of fecal excretion of unabsorbed Pb and negative mass
balance (intake>body burden + excreted) when RBA <1.
2.3.4. Vascular and Extravascular Fluid
2.3.4.1. Diffusible Plasma
The AALM.FOR represents Pb in the vasculature as three compartments: (1) diffusible plasma; (2) bound
plasma; and (3) RBCs. The diffusible plasma compartment receives Pb from all absorption pathways and
exchanges with Pb bound to plasma protein, Pb in RBCs, Pb in an extravascular fluid compartment, and
Pb in extravascular tissues (bone, brain, kidney, liver, and other soft tissues). Lead is also transferred
from diffusible plasma to the small intestine, where it can contribute to fecal elimination of absorbed Pb.
The rate coefficient for transfer of Pb from diffusible plasma to all receiving compartments (RPLS) is
2000 day"1 (ti 2~0.5 min; ln(2)/rate constant). This rate constant is subdivided into deposition fractions
that represent the fractions of the total transfer assigned to each receiving compartment. Deposition
fractions appear in all rate equations that include inflows of Pb from diffusible plasma to any
compartment, and appear as the product of the deposition fraction ( 7an adjustment factor for variable
deposition fraction to RBCs (CF, from Equation 2.3-14), and the rate of total outflow of Pb from
diffusible plasma (BTEMP, from Equations 2.3-10 and 2.3-11) (Equation 2.3-34):
INplas^c = TCi ¦ CFt ¦ BTEMP Eq. (2.3-34)
Values of corresponding rate coefficients for transfers from diffusible plasma to receiving compartments
(i.e., TCi * RPLS), based on Leggett (1993). are presented in Table 2-2. The highest rates are for transfers
to the extravascular fluid compartment, RBCs, and bone surface.
2.3.4.2. Bound Pb in Plasma
Lead in the bound plasma compartment represents Pb reversibly bound to plasma proteins. Bound Pb in
plasma is confined to the vascular fluid. Reversible binding is simulated as first-order transfers between
compartments, with no maximum capacity for binding (Table 2-2, Equation E8). The transfer rate ratio
establishes the equilibrium for binding. Based on Leggett (1993). these values for adults are 0.8 day-1
(ti/2 = 0.9 day) for transfer to the bound compartment and 0.139 day"1 (ti/2 = 5.0 day) for transfer from the
bound compartment, providing an equilibrium ratio (bound/free) of approximately 6. Values for children
are similar, but transfer to the bound compartment is slightly slower.
2.3.4.3. Red Blood Cells
Lead in diffusible plasma exchanges with Pb in RBCs (Table 2-2, Equation El3) and is governed by a
deposition fraction and corresponding rate coefficient for uptake (TOORBC) and return from the RBC
(RRBC). Uptake of Pb in RBCs is assumed to be limited by a maximum capacity, represented in the
AALM.FOR by a maximum Pb concentration in RBCs (SATRAT, (.ig Pb/dL RBC volume). Above a
threshold concentration in red blood cells (RBCNL, (.ig Pb/dL RBC volume), the deposition fraction (and
corresponding rate coefficient) for transfer from diffusible plasma to RBCs (TOORBC) declines
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(Equation 2.3-35) and deposition fractions to all other tissues increase proportionally by the factor CF
(from Equation 2.3-14).
Values for rate coefficients for transfer in and out of the RBC, SATRAT (350 (.ig Pb/dL RBC) and RBCNL
(20 (.ig Pb/dL RBC) result in rapid uptake of Pb into RBCs (adult ti 2~2 min in adults, 2-3 min in children)
and replicate the non-linear relationship between plasma and red blood observed in adults (Smith et al..
2002; Manton et al.. 2001; Bergdahl etal.. 1999; Bergdahl et al.. 1998; Bergdahl et al.. 1997). The values
for RBCNL and RRBC in Equations D-12 and 13 of Table 2-2 were adjusted upward from the values
assigned in Leggett (1993) to provide improved fit to plasma-whole blood Pb relationships in adults and
to harmonize blood Pb predictions in young children with the IEUBK model at the ages of 1, 5, and 10
years (see Chapter 4).
2.3.4.4. Extravascular Fluid
Lead in diffusible plasma exchanges with Pb in an extravascular fluid (EVF) compartment (Table 2-2
Equation Fl). The conceptual basis for including the EVF compartment is to allow simulation of the
dynamics of Pb in plasma of efflux of Pb from plasma and return to the plasma during the first minutes
following intravenous injection of Pb that has been observed following intravenous injection of Pb, as
summarized in Leggett (1993) based on various experimental studies (Heard and Chamberlain. 1984;
Booker etal.. 1969; Hursh and Suomela. 1968; Stover. 1959). Efflux of Pb from the plasma is assumed
to occur immediately after its entrance into plasma and prior to binding of binding of Pb to plasma
proteins (ti 2~1 day, adults) and uptake into RBCs (adult ti 2~2 min, adults). Uptake of Pb into RBCs
subsequently provides a driving force for return of Pb to the plasma. These dynamics are simulated as
rapid exchanges of Pb between the diffusible plasma and EVF compartments. For all ages, rate
coefficients for transfers to and from the EVF, based on Leggett (1993). are 1000 day"1 (ti 2~1 min) and
333 day"1 (11,2~3 min). These values produce a rapid efflux of Pb to the EVF compartment and return to
diffusible plasma, with an equilibrium ratio for EVF/diffusible plasma Pb mass of approximately 3. The
corresponding volume of distribution for the rapidly exchanging EVF compartment of three times
diffusible plasma is consistent with observations made for the distribution of calcium, summarized in
Leggett (1993) based on Harrison et al. (1967) and (Hart and Spencer. 1976).
2.3.5. Skeleton
2.3.5.1. General Structure of Bone Model
A major concept underlying the AALM.FOR simulation of bone Pb kinetics is that Pb kinetics behavior
in bone is similar to that of calcium and other bone accumulating elements that mimic calcium (e.g.,
strontium). Observations that formed the bases for the Leggett (1993) bone Pb model included
experimental studies of the kinetics of Pb, calcium, and strontium in humans, non-human primates, and
dogs (e.g., Heard and Chamberlain. 1984; Llovd et al.. 1975; Cohen et al.. 1970). The AALM.FOR
simulates Pb biokinetics in bone as a combination of three processes: (1) relatively rapid exchange of Pb
between diffusible plasma and surfaces of cortical and trabecular bone; (2) slower exchange of Pb at bone
surfaces with an exchangeable Pb pool in bone volume; and (3) slow transfer of a portion of Pb in bone
/
TOORBC = 1- [¦
RBCONC-RBCNLA1'5
;)
Eq. (2.3-35)
SATRAT-RBCNL
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volume to a non-exchangeable pool that is released from bone to diffusible plasma only when bone is
resorbed (Figure 2-4). These features are represented in the AALM.FOR as six bone subcompartments;
three separate compartments for cortical and trabecular bone, each, representing bone surface,
exchangeable Pb in bone volume, and non-exchangeable Pb in bone volume. Cortical and trabecular
bone volume are assumed to account for 80% and 20% of total bone volume, respectively (Leggett.
1993). Transfers of Pb in and out of the bone surface compartment are assumed to be relatively rapid:
values forti/2 are approximately 0.01 day for transfer from plasma-to-bone surface; and 1.4 days for
return from bone surface to plasma and transfer from bone surface to exchangeable bone volume
(Leggett. 1993). Transfer from bone surface is faster in children (ti/2 ~ 1.1 days). Return of Pb from the
exchangeable bone volume to bone surface is slower (ti :~37 days); however, the dominant transfer
processes determining long-term accrual of bone Pb burden («90% of body burden) are the slower rate
coefficients for transfer of Pb from the non-exchangeable compartments of trabecular and cortical bone to
diffusible plasma (adult ti/2«l .9 and 12 years, respectively). Bone transfer coefficients vary with age
(faster in children) to reflect age-dependence of bone turnover. The slow, non-exchangeable, bone
volume compartment is assumed to be much more labile in infants and children than in adults (e.g.,
cortical 11,2~42 days at birth, 677 days at 15 years, and 4220 days at >25 years; trabecular ti :~42 days at
birth, 363 days at 15 years, and 703 days at >25 years). Other physiological states that affect bone
turnover and, therefore, bone Pb kinetics, such as pregnancy and menopause, could be accommodated
with adjustments to tissue (e.g., bone) transfer coefficients.
2.3.5.2. Cortical and Trabecular Bone Surface
Cortical and trabecular bone surfaces exchange Pb with diffusible plasma and the exchangeable
compartment of bone volume (Table 2-2, Equations G5 and G11). Bone surfaces, in this context,
represent surfaces of bone in contact with the plasma (e.g., Haversian and Volkmann canals) and/or
involved in bone production and resorption (e.g., endosteal and periosteal surfaces for cortical bone,
resorption cavities, surfaces of trabecular bone). Deposition of Pb in bone surface is considered to reflect
(and be in proportion to) rates of incorporation of calcium in bone that occur during growth, modeling,
and remodeling of bone. Rates change with age, reflecting periods of more intense growth (e.g., infancy,
pre-adolescence). In the AALM.FOR, bone Pb kinetics have the following three general characteristics.
First, transfers are relatively rapid: adult ti 2~0.01 day for plasma-to-bone surface, adult ti 1.4 days for
bone surface to plasma. Second, rates of transfer are age-dependent with highest rates during infancy (0-
1 years) and adolescence (10-15 years), during periods of rapid bone growth. In infancy, transfer of Pb to
bone surface accounts for approximately 24% of total flow of Pb out of the diffusible plasma (8% in
adults). And third, relative fractions of transfer from diffusible plasma to cortical and trabecular bone is
also age-dependent, decreasing from 80% of total transfer going to cortical bone during infancy, to
approximately 44% in adults.
2.3.5.3. Cortical and Trabecular Bone Volume
Bone volume compartments are subdivided into cortical (80%) and trabecular bone (20%), with each
further subdivided into exchangeable and non-exchangeable subcompartments (Table 2-2, Equations G7,
G9, G13, and G15). Exchangeable and non-exchangeable compartments represent Pb pools in bone
volume having different rates and mechanisms of turnover. Lead in the exchangeable compartment is
assumed to be subject to heteroionic exchange with other bone minerals (e.g., calcium) and/or diffusion of
Pb into osteons (Leggett. 1993). Lead that enters the non-exchangeable compartment remains there,
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unless subject to bone resorption. Turnover of Pb in the non-exchangeable compartment reflects bone
turnover rates.
Lead enters bone volume from bone surface. In the AALM.FOR, exchanges of Pb between bone surface
and bone volume have the following three characteristics. First, the transfer to bone volume is faster
(adult ti 2~1.4 days) compared to return to bone surface (adult 112~3 7 days), resulting in accumulation of
Pb in bone volume, relative to bone surface. Second, transfer rates from bone surface to bone volume are
constant (ti/2«2 days) up through adolescence, and slower than in adults (ti 2~l .4 days). And third,
transfer rates between bone volume and bone surface are assumed to be similar for cortical and trabecular
bone.
A portion of the Pb that enters bone from bone surface becomes associated with deep bone mineral
deposits that can be mobilized during periods of bone resorption (including that which occurs during bone
modeling associated with growth). In the AALM.FOR, kinetics of Pb in this non-exchangeable pool have
the following six characteristics. First, transfer of Pb from the exchangeable compartment to the non-
exchangeable compartment is relatively faster (ti 2~30 days) than transfer to surface bone (ti 2~37 days).
Second, the transfer rate to the non-exchangeable compartment is independent of age. Third, transfer to
the non-exchangeable compartments of cortical and trabecular bone occur at the same rates. Fourth,
transfer of Pb out of the non-exchangeable compartment returns Pb directly to the diffusible plasma.
Fifth, rates of transfer from the non-exchangeable compartment reflect bone turnover rate and are
relatively slow (adult 112~ 12 years for cortical bone, adult ti 2~1.9 years for trabecular bone) compared to
rates of removal of Pb from the exchangeable compartment. And sixth, age-dependent changes in bone
turnover rates give rise to movement of Pb out of the non-exchangeable compartments that declines with
increasing age:
AGE
100 d
1 yr
5 yr
10 yr
15 yr
>25
Cortical tin (yr)
0.12
0.33
0.62
1.1
1.9
12
Trabecular tin (yr)
0.12
0.33
0.52
0.72
1.0
1.9
Discussed in Chapter 4, values for RCORT and RTRAB in Equations G9 and G15 of Table 2-2, and
FLONG (Equation G1-G4) were adjusted to improve agreement between predicted and observed
elimination kinetics of Pb from bone in adults (Nilsson et al.. 1991).
2.3.6. Liver
The AALM.FOR simulates Pb kinetics in liver as the combination of three properties. First, there is
relatively rapid exchange between Pb in diffusible plasma and a fast compartment in liver (LVR1).
Second, slower transfer of Pb from the fast liver compartment to a slow compartment in liver (LVR2),
which can release Pb to the diffusible plasma. And third, there is transfer of Pb from the fast liver
compartment to the small intestine (i.e., biliary secretion). This configuration gives rise to Pb kinetics
following a single absorbed dose that result in a relatively rapid initial uptake of Pb in liver, followed by a
slow decline in liver Pb burden, consistent with experimental studies conducted in humans, non-human
primate, and dogs (Lcggctt. 1993). based on several studies (Heard and Chamberlain. 1984; Llovd et al..
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1 1975; Cohen et al.. 1970V With chronic dosing, liver Pb levels increase to approximately 10% of total
2 body burden in early childhood and decline to 2% by age 40 years.
3 Rate equations for transfers of Pb in and out of liver are presented in Table 2-2 (Equations J1 and J3). In
4 the AALM.FOR, kinetics of Pb in liver have the following four general characteristics. First, transfer to
5 the fast liver compartment (LRV1) from diffusible plasma is relatively rapid (adult ti 2~0.01 day) and
6 accounts for approximately 4% of total transfer of Pb from diffusible plasma. Second, transfers from the
7 LVR1 to diffusible plasma and to the small intestine are assumed to occur at approximately the same rate
8 (ti 2~22 days) and is slower than uptake from diffusible plasma, resulting in Pb accumulates in the fast
9 pool. Third, Pb in the fast liver compartment is slowly transferred to the slow liver pool (LVR2, ti/2«100
10 day). Fourth, rates of return of Pb from the slow compartment to diffusible plasma are age-dependent,
11 with half-times decreasing from ti 1000 days at birth to 500 days at age 5 years, increasing to
12 approximately 1200 days at age >10 years. This results in increasing rate of accumulation of Pb in the
13 slow compartment with age, with chronic dosing. As discussed in Chapter 4, the value for RLIV2 in
14 Equation J3 of Table 2-2 was adjusted from the value reported in Leggett (1993) to improve agreement
15 between predicted and observed soft tissue-bone Pb ratios (Barry. 1975).
16 Biliary secretion of Pb is simulated as transfer of Pb from the fast liver compartment (LVR1) to the small
17 intestine (Table 2-2, Equation D3). The biliary contribution to the small intestine Pb contents is given by
18 Equation 2.3-36:
19
20 INLVR1^SIC = H1TOSI ¦ RLVR1 ¦ YLVR1 Eq. (2.3-36)
21
22 where H1TOSI is the fraction of Pb in LVR1 that goes to the small intestine, RLVR1 is the rate
23 coefficient for transfer of Pb out of LVR1 (day1), and YLVR1 is the Pb mass in LVR1 ((.ig). A value of
24 0.45 is assumed for H1TOSI. This value is the rate constant from LVR1 to the small intestine divided by
25 the sum of rate constants for movement from LVR1 to the small intestine, plasma, and LVR2 (Leggett.
26 1993).
27 2.3.7. Kidney
28 Similar to liver, kidney Pb kinetics exhibit multiple components that include an initial phase of rapid
29 uptake of Pb following a single dose of Pb, followed by a slow decline in kidney Pb burden, with long-
30 term retention of <1% of the body burden during chronic dosing. The AALM.FOR simulates Pb kinetics
31 in kidney as the combination of two parallel processes: (1) relatively rapid transfer between Pb from
32 diffusible plasma to a fast compartment in kidney (KDN1), a portion of which is excreted in urine
33 (urinary path)-, and (2) slower exchange Pb between diffusible plasma and a slow compartment in kidney
34 (KDN2). This configuration gives rise to Pb kinetics following a single absorbed dose that result in a
35 relatively rapid initial uptake of Pb in kidney, followed by a slow decline in kidney Pb burden. With
36 chronic dosing, kidney Pb levels increase to approximately 2% of total body burden in early childhood
37 and decline progressively 0.2-0.3% after age 40 years.
38 Rate equations for transfers of Pb in and out of kidney are presented in Table 2-2 (Equations II and 13).
39 In the AALM.FOR, kinetics of Pb in kidney have the following four general characteristics. First,
40 transfer from the diffusible plasma to the fast (urinary path) kidney compartment (KDN1) is relatively
30
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rapid (ti 2~0.02 day) and accounts for approximately 2.5% of total transfer of Pb from diffusible plasma.
Second, transfer from the fast compartment of kidney (KDN1) to bladder urine is slower than uptake from
diffusible plasma (ti 2~5 days). As a result, Pb accumulates in the fast compartment. Third, transfer of Pb
from diffusible plasma to the slow kidney compartment (KDN2) is approximately 100 times slower than
that to the fast compartment (adult ti 2~2 days), receiving approximately 0.04% of the total transfer out of
the diffusible plasma), and fourth, rates of return of Pb from the slow compartment (KDN2) to diffusible
plasma are age-dependent, with half-times increasing from ti 2~ 1000 days until age 5 years and to 3648
days at age >10 years. This results in increasing rate of accumulation of Pb in the slow compartment with
age, with chronic dosing.
The value for TKDN1 in Equation II of Table 2-2 was adjusted (see Chapter 4) from the value reported in
Leggett (1993) to improve agreement between predicted and observed plasma-to-urine clearance in adults
(Araki et al.. 1986; Manton and Cook. 1984; Manton and Mallov. 1983; Chamberlain et al.. 1978). The
value for RKDN2 in Equation 13 of Table 2-2 was adjusted (see Chapter 4) from the value reported in
Leggett (1993) to improve agreement between predicted and observed soft tissue-bone Pb ratios reported
by Barry (1975).
2.3.8. Brain
In the AALM.FOR, the brain is treated as a homogenous compartment (Table 2-2, Equations HI, H2).
This assumption is a gross simplification of more complex, non-uniform distribution of Pb in brain
tissues. Nevertheless, the simplification has little consequence of overall kinetics of Pb, since brain
constitutes a relatively small site of deposition. In the AALM.FOR, the brain is assumed to receive
approximately 0.05% total outflow of Pb from the diffusible plasma up to age 1 year and 0.015% at ages
>5 years. Transfer rates into brain (adult ti 2~2.3 day) and from brain to diffusible plasma (ti 2~730 day)
result in brain Pb burdens that are 0.1-0.2% of body burden, with chronic dosing. Transfer rates into
brain are age-dependent, and are highest during the first year (ti/2~ 1 day) and decrease (ti 2~2—3 days) at
ages >5 years. The age-dependence in transfer rates contribute to a peak in the Pb mass in brain («0.8%
of body burden) between ages 3-4 years, with chronic exposure.
2.3.9. Other Soft Tissues
In the AALM.FOR, soft tissues not explicitly simulated as distinct compartments (e.g., muscle, skin, etc.)
are lumped into a single compartment (Other Soft Tissue, SOF). This compartment is assumed to
comprise three subcompartments that are characterized with relatively fast, intermediate, or slow
exchange kinetics with diffusible plasma (Table 2-2, Equations Kl, K3, and K5), and no exchanges
between subcompartments. The fast compartment (SOFO) receives approximately 8-9% of the outflow of
Pb from diffusible plasma (adult ti/2«0.004 day, child ti/2 0.5-1 day), with slower return of Pb to the
diffusible plasma (ti/2«0.33 day). The intermediate compartment (SOF1) receives approximately 0.5-1%
of the outflow form diffusible plasma (adult ti/2«0.07 day, child ti/2 0.04-0.06 day), with slower return
kinetics (adult ti 167 day). The slow compartment (SOF2) receives approximately 0.1% of the total
outflow of Pb from diffusible plasma (adult ti/2«0.35 day, child ti/2 0.400.6 day), with slower return
(ti2~l 800 day). This configuration results in approximately 9% of the Pb body burden residing in the
combined subcompartments that comprise the other soft tissue compartment during early childhood
followed by a decrease to approximately 3% by age 40 years. A pathway for elimination of Pb to hair,
31
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
nails, and exfoliated skin is assigned to the intermediate soft tissue compartment (Table 2-2, Equation
L9).
2.3.10. Excretion
The AALM.FOR simulates excretion of absorbed Pb as five separate pathways representing urine,
secretion from liver to small intestine (e.g., biliary), secretion from diffusible plasma to small intestine,
sweat, and other routes (e.g., hair, nails, exfoliated skin as described in Section 2.3.9). The urinary
pathway includes excretion of Pb deposited from the diffusible plasma into the fast kidney compartment
(KDN1, Table 2-2, Equation LI). This pathway contributes approximately 2.5% of total outflow of Pb
from the diffusible plasma. The corresponding plasma clearance (L plasma/day) is approximately 2.4
L/day at age 1 year and 20 L/day at age >25 years, and blood clearance (L blood/day) is approximately
0.05 L/day at age 1 year and 0.07 L/day at age >25 years. The urinary pathway contributes approximately
45% of total excretion of absorbed Pb in adults and approximately 80% up at ages < 12 years. The
AALM.FOR also includes rate coefficient for direct transfer of Pb from plasma to urine (TURIN in
Equation LI of Table 2-2). Improved agreement between predicted and observed plasma-to-urine
clearance in adults was achieved with adjustments to the parameter TKDN1 (Equation II of Table 2-2).
Because values assigned to TURIN did not improve the fit to observations, the direct excretion pathway
was nulled by setting TURIN to zero.
The fecal excretion pathway in the AALM.FOR includes the unabsorbed fraction of Pb that enters the
small intestine from three sources (Table 2-2 Equation L5): (1) ingestion; (2) transfer from the liver
(biliary secretion, Table 2-2 Equation D3); and (3) transfer from diffusible plasma. Biliary secretion
contributes approximately 32% of total excretion of absorbed Pb in adults (55% up to age 12 years) and
transfer from plasma contributes approximately 11% (18% at age <12 years).
Sweat is simulated as a direct transfer out of diffusible plasma and accounts for approximately 6% in of
total excretion of absorbed Pb in adults and approximately 11% at ages <12 years (Table 2-2, Equation
L7). All other pathways of Pb excretion, not simulated with specific pathways, are accounted for in
transfer of Pb from the intermediate soft tissue compartment (SOF1; Table 2-2 Equation L9). These
pathways include losses to hair, nails, and exfoliated skin and, combined, account for approximately 6%
of total excretion of absorbed Pb in adults and 12% at ages <12 years.
2.3.11. Fetus
Lead masses in all compartments at birth are assigned values based on a value for maternal blood Pb
concentration (Table 2-2, Equations A1-A7). The general equation for the fetal distribution of Pb masses
is in the form (Equation 2.3-37):
= IF
YFrBC
where Yi is the Pb mass (|ag) in tissue i at birth, YFi is the fraction of total body burden in tissue /'
at birth, PbBu is the maternal blood Pb concentration ((.ig/dL). PbhiM is the fetal/maternal blood Pb
concentration ratio, YFrbc is the fraction of body burden in RBCs at birth and Ybiood is the blood volume at
birth (assumed to be 3 liters). The value 3 in the numerator represents the assumed blood volume(dL) at
32
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
birth. Tissue compartments assigned values at birth include: brain, kidney (KDN2), liver (LVR2), RBC,
soft tissue (SOFO), and non-exchangeable bone volume (80% cortical, 20% trabecular).
2.3.12. Chelation
The AALM.FOR includes parameters to simulate of the effect of chelation therapy on internal Pb
kinetics. The chelation simulation decreases transfer of Pb from diffusible plasma and increases transfer
from diffusible plasm to urine. Chelation parameters include the beginning and end age (days) of
chelation (CHEL1, CHEL2) and a parameter that adjusts the deposition fractions of Pb transfer from
diffusible plasma to tissues (CHLEFE). The adjustment of the deposition fraction takes the following
general form (Equation 2.3-38):
where TBONE is the deposition fraction for transfer from diffusible plasma to bone. The same
adjustment is made to the deposition fractions for all tissue and excretory compartments, except urine
(TURIN). During the chelation period, the deposition fraction from diffusible plasma to urine is
calculated as follows (Equation 2.3-39):
TBONE = (1 - CHLEFE) ¦ TBONE
Eq. (2.3-38)
TURIN = ZILiCl - Tt)
where /', represents the deposition fraction for a given tissue.
Eq. (2.3-39)
33
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 TABLE 2-1. EXPOSURE EQUATIONS OF AALM.FOR
No.
Equation
A
Pb Intakes from Inhaled Air
A
1
INair = PbAir ¦ VR
A
2
PbAirdiScrete weighted ~ ^ii=i(PbAiri ¦ f{)
A
3
PbAirpulse sum — PbAirbaseline + PbAiVpUiSe
A
4
INairTotal — IN airdiscref-e ¦ (1 — fpUise) + INcLiVpUise ¦ fpUise
B
Pb Intakes from Ingested Indoor Dust
B
1
INdust = PbDust ¦ IRdust ¦ RBA
B
2
IRdust = IRsd ¦ fiRsoil
B
3
PbDustdiscrete weighted ~ Yii = i(PbDusti ¦ /)
B
4
PbDustpUise sum PbDust baseline PbDustpUise
B
5
IN dustf0fai IN dust discrete ' (1 fpulse) IN dustpUise ' fpulse
C
Pb Intakes from Ingested Soil
c
1
INsoil = PbSoil ¦ IRsoil ¦ RBA
c
2
IRsoil = IRsd ¦ (1 — fmsoil)
c
3
PbSoil discrete weighted ~ ^ii = i(Pbsoili ¦ /)
c
4
PbSoil\puise sum PbSoilfoaseiing + PbSoilpUise
c
5
INsoilTotai — INsoil(nscref-e ¦ (1 — fpuise) Is°Hpulse ' fpulse
D
Pb Intakes from Ingested Water
D
1
INwater = PbWater ¦ IRwater ¦ RBA
D
2
PbWaterdiscrete weighted ~ Yii = i(PbWdteYi ¦ f)
D
3
PbWaterpuise sum PbWCLt6rfoasenne "1" PbW(xt6TpUise
D
4
INwaterTotai IN\V&t6Ydiscrete ' (1 fpulse) "1" INwatSVpuise ' fpulse
E
Pb Intakes from Ingested Food
E
1
IN food = IN food input ¦ RBA
E
2
INfooddiScrete sum 21 i=i(/ocij) ¦RBA
E
3
INfoodpuise sum IN foodfoaSeline IN foodpUise
E
4
INf OOdTotai — INf OOddiscrete ' (1 — fpulse) INfoodpUise ' fpulse
F
Pb Intakes from Ingested Other Media
34
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
No.
Equation
F
1
IN other = INotherinput ¦ RBA
F
2
IN oth6T^iscref-e sum Yji=1i.lN otheri) RBA
F
3
INotherpuise sum INotheVfoasenne + INotheVpUise
F
4
INotheTj0fai INotheT^iscref-e ¦ (1 fpuise) INotheVpUise ¦ fpuise
G
Pb Intakes from All Exposure Pathways
G
1
BRETH = lNairtotai
G
2
INingestiontotai ~ ^water ^dust ^'food INother
G
3
PAT — JM.
nsii l ivingestiontotai
See text (Section 2.2.1) for explanation of parameter names. The prefix IN refers to Pb intake
((ig/day) and the prefix Pb refers to Pb concentration (e.g. (.ig/L. jj.g/g).
1
35
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 TABLE 2-2. BIOKINETICS EQUATIONS OF AALM.FOR
No.
Equation
A
Pb Masses at Birth
A
1
BRANIN ¦ BLDMOT ¦ BRATIO • 3
YBRAN =
RBCIN
A
2
0.8 • BONIN ¦ BLDMOT ¦ BRATIO ¦ 3
i U V L/L —
RBCIN
A
3
RENIN ¦ BLDMOT ¦ BRA TIO • 3
YKDN2 =
RBCIN
A
4
„TTr^ HEPIN -BLDMOT -BRATIO -3
YLVR2 =
RBCIN
A
5
V1) I RBCIN ¦ BLDMOT ¦ BRA TIO ¦ 3
YixijC —
RBCIN
A
6
,, SOFIN ¦ BLDMOT ¦ BRA TIO ¦ 3
YSOF =
RBCIN
A
7
i, _ 0.2- BONIN ¦ BLDMOT ¦ BRA TIO ¦ 3
1 J V L/L —
RBCIN
B
Age-scaling of Diffusible Plasma-to-tissue Deposition Fractions
B
1
AGSCL= 1 -TEVF-TBONE
1 - TEVF - TBONEL
B
2
TBRAN = AGESCL ¦ TOBRAN
B
3
TFECE = AGESCL ¦ TOFECE
B
4
TKDNl = AGESCL ¦ TOKDNl
B
5
TKDN2 = AGESCL ¦ TOKDNl
B
6
TLVRl = AGESCL ¦ TOLVRl
B
7
TPROT = AGESCL ¦ TOPROT
B
8
TRBC = AGESCL ¦ TORBC
B
9
TSOFO = AGESCL ¦ TOSOFO
B
10
TSOFl = AGESCL ¦ TOSOFl
B
12
TSOF2 = AGESCL ¦ TOSOFl
B
13
TSWET = AGESCL ¦ TOSWET
B
14
TURIN = AGESCL ¦ TOURIN
36
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
No.
Equation
C
Respiratory Tract (RT)
c
1
/7/?1
= R1 ¦ BRTCRN BRl ¦ YR\
dt
c
2
YR\ = f ———dt
o dt
c
3
JDO
= R2 ¦ INHALE BR2 ¦ YR2
dt
c
4
YR2= \^dt
o dt
c
5
= R3 ¦ INHALE BR3 ¦ YR3
dt
c
6
CO
II
CO
£
c
7
dR4 = R4 ¦ INHALE BRA ¦ YR4
dt
c
8
%
S ^
ll
^r
c
9
YLUNG = YR\ + YR2 + YR3 + YR4
c
Rate of Pb Absorption from RI
c
10
TTnrr. (1 - CILIAR) • (BRl ¦ YRl ¦ BR2 ¦ YR2 ¦ BR2 ¦ YR3 ¦ BRA ¦ YR4)
Ur !A Kr.Ri —
dt
D
Gastrointestinal Tract (GIT) - Stomach (STMC)
D
1
7nmi yv~1
= EATCRN ¦ CILIAR ¦ (BRl-YRl + BR2 ¦ YR2 + BR3-YR3 + BR4 ¦ YR4)
dt
GSCAL ¦ RSTMC ¦ YSTMC
D
2
YSTMC = \ dS™Cdt
o dt
D
Gastrointestinal Tract (GIT) - Small Intestine (SI)
D
3
= GSCAL ¦ RSTMC ¦ YSTMC + HITOSI -RLVRl- YLVRl + TFECE ¦ CF ¦ BTEMP
dt
GSCAL ¦ RSIC ¦ YSIC
37
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
No.
Equation
D
4
II
£
D
Gastrointestinal Tract (GIT) - Upper Large Intestine (ULI)
D
5
AFc2
T? A 17 ^
rl nrC 1 1 + 30 * g-AGEYEAR
D
6
dULIC =(| F1^ GSCAL. RSIC. YSIC GSCAL ¦ RULI ¦ YULIC
dt
D
7
YULIC = \dULICdt
o dl
D
Gastrointestinal Tract (GIT) - Lower Large Intestine (LLI)
D
8
dLLIC = GSCAL -RULI- YULIC GSCAL ¦ RLLI ¦ YLLIC
dt
D
9
VTTT^ r dl.I.IC' ,
YLLIC = dt
o dt
D
Rate of Absorption from Gastrointestinal Tract (GI)
D
10
UPTAKEGI = F]-GSCALE-RS'C-rSIC
dt
E
Blood - Plasma (Diffusible)
E
1
PPl = RPROT ¦ YPROT + RRBC ¦ YRBC + •REVF ¦ YEVF + RSOFO ¦ YSOFO +
(1 - S2HAIR) ¦ RSOFl ¦ YSOFl + RSOF2 ¦ YSOF2 + HITOBL -RLVRl- YLVRl +
RLVR2 ¦ YLVRl + RKDN2 ¦ YKDN2 + RCS2B ¦ YCSUR + RTS2B ¦ YTSUR +
RCORT ¦ YCVOL + RTRAB ¦ YTVOL + RBRAN ¦ YBRAN + Fl ¦ GSCAL ¦ RSIC ¦ YSIC
E
2
dPLS = PPl + (1 CILIAR) • (BRl ¦ YR\ + BR2 ¦ YR2 + BR3 ¦ YR3 + BR4 ¦ YR4)
dt
RPLS¦YPLS
E
3
YPLS = \^-^-dt
o dt
E
4
RPLS = TSUM ¦ RPLAS
E
5
TSUM = TOORBC + TEVF + TPROT + TBONE + TURIN + TFECE + TSWET +
TLIVR1 + TKDNI+ TKDN2 + TSOFO + TSOFI+ TSOF2 + TBRAN
E
6
BTEMP = RPLS -YPLS
38
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
No.
Equation
E
7
^ 1 -TOORBC
CF =
l-TRBC
E
Blood - Plasma - Protein Bound
E
8
dP ROT
= TPROT ¦ CF ¦ BTEMP RPROT ¦ YPROT
dt
E
9
nam-]!*™!*
o dt
E
Blood - Total Pb in Plasma (Diffusible, Protein Bound)
E
10
YPLAS = YPLS + YPROT
E
Blood - Red Blood Cell (RBC)
E
11
RBCONC < RBCNL:
TOORBC = TRBC
E
12
RBCONC > RBCNL:
TOORBC - TRBC • fl - RBCONC ~ T
{ SATRAT- RBCNL )
E
13
dRBC = TOQRBC. BTEMP RRBC. yrbC
dt
E
14
t zr>r,^ \dRBC
YRBC = dt
o dt
E
Blood - Total Pb in Blood
E
15
YBLUD = YPLAS + YRBC
E
Blood - Concentrations and Clearance
E
16
BLCONC= YBLUD
AMTBLD
E
17
YPFtC1
RBCONC =
BLDHCT ¦ AMTBLD
E
18
pcent=10°-yplas
YBLUD
E
19
CLEAR — l°°-UR1N
DELT ¦ YPLAS
E
20
BCLEAR - ]°°-URIN
DELT ¦ YBLUD
39
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
No.
Equation
F
Extravascular Fluid
F
1
= TEVF ¦ CF ¦ BTEMP REVF ¦ YEVF
dt
F
2
REVF = TEVF ¦ R''LS
SIZEVF
F
3
YEVF-]™**
o dt
G
Bone - Transfer Rates within Bone
G
1
RDF2CS = (1 - FLONG) • RDIFF
G
2
RDF2TS = (1 - FLONG) • RDIFF
G
3
RDF2DC = CFLONG) • RDIFF
G
4
RDF2DT = {FLONG) ¦ RDIFF
G
Bone - Cortical Bone Surface
G
5
J/tOT TIT)
= TBONE ¦ (1 TFRA C)-CF¦ BTEMP + RDF2CS ¦ YCDIF
(.RCS2B + RCS2DF) ¦ YCSUR
G
6
yCSUR = ]****
0 dt
G
Bone - Exchangeable Cortical Bone
G
7
dCDIF = RCS2DF. YCSUR (RDF2CS + RDF2DC) • YCDIF
dt
G
8
WI,W,, r dCDII-'
YCDIF = dt
o dt
G
Bone - Non-Exchangeable Cortical Bone Volume
G
9
dCVOL = RDF2DC. YCDIF RCORT ¦ YCVOL
dt
G
10
YCVOL = \dCV°Ldt
o dt
G
Bone - Trabecular Bone Surface
G
11
7'T,rTT" Tn
= TBONE ¦ TFRAC ¦ CF ¦ BTEMP + RDF2TS ¦ YTDIF
dt
(RTS2B + RTS2DF) • YTSUR
40
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
No.
Equation
G
12
nsm=\*™**
t *
G
Bone - Exchangeable Trabecular Bone
G
13
dTDIF = RTS2DF. YTSUR (RDF2TS + RDF2DT) • YTDIF
dt
G
14
YTDIF = \dTDIF dt
o dt
G
Bone - Non-Exchangeable Trabecular Bone
G
15
dTVOL = RDF2DT. jtDIF RTRAB ¦ YTVOI
dt
G
16
rnvL-]™™*
0 *
G
Total Pb in Cortical, Trabecular, and Total Bone
G
17
YCORT = YCVOL + YCDIF + YCSUR
G
18
YTRAB = YTVOL + YTDIF + YTSUR
G
19
YSKEL = YCVOL + YTVOL + YCDIF + YTDIF + YCSUR + YTSUR
G
Bone - Pb Concentration
G
20
CRTCON = YCORT
CORTWT
G
21
CRTCONBM = CRTCON
0.55
G
22
TRBCON = YTRAB
TRBWT
G
23
TRBCONBM = TRABCON
0.50
G
24
ASHCON= YSKEL
TSKELWT
H
Brain
H
1
dBRAN = TBRAN CF BTEMp RBRAN. YBRAN
dt
41
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
No.
Equation
H
2
tzr, r> A TV T f dBRAN
YBRAN = dt
o dt
I
Kidney - Compartments 1 (fast, urinary path) and 2 (slow)
I
1
dKDNl = TKDm cp BTEMP RKi)N\. YKDNl
dt
I
2
o dl
I
3
dKDN2 = TKDN2 CF BTEMP RKDN2 ¦ YKDNl
dt
I
4
YKDN2=Y-^!,
I
Kidney - Total Pb in Kidney
I
5
YKDNE = YKDNl + YKDNl
I
Kidney - Pb Concentration in Kidney
I
6
RENCON-YKDNE
KIDWT
J
Liver - Fast Compartment 1
J
1
dL VRl = TL VRl ¦ CF ¦ BTEMP RL VRl ¦ YL VRl
dt
J
2
wt.™ f dLVR \ ,
YLVRl = dt
o dt
J
Liver - Slow Compartment 2
J
3
dL VR2 = HITOH2 -RLVRl- YL VRl RL VRl ¦ YL VRl
dt
J
4
wt™ \dLVR2.
YLVRl = dt
o dt
J
Liver - Total Pb in Liver
J
5
YLIVR = YLVRl + YLVER2
J
Liver - Pb Concentration in Liver
J
6
LWCON- YLIVR
LLVWT
42
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
No.
Equation
K
Soft Tissue - Compartments 0 (fast), 1 (intermediate), and 2 (slow)
K
1
dSOF0 = TSQF0 CF BTEMp RSOF0 ¦ YSOFO
dt
K
2
YSOFO = f dS°F°dt
o dt
K
3
dSOF 1 = TSQFl CF BTEMP RSOFl ¦ YSOFl
dt
K
4
'cdSOI'l .
YSOFl = dt
o dt
K
5
rrr/^j T—¦
= TSOF2 ¦ CF ¦ BTEMP RSOF2 ¦ YSOFl
dt
K
6
YSOFl = \dS°F2dt
o dl
K
Soft Tissue - Total Pb in Soft Tissue
K
7
YSOFT = YSOFO + YSOFl + YSOFl
L
Excretion - Urinary Bladder
L
1
dBLAD = TJJRIN CF BTEMP + RKi)N\. YKDNl RBLAD ¦ YBLAD
dt
L
2
YBLAD = \dBLADdt
o dt
L
Excretion - Urine
L
3
dURIN = RBLAD. jBLAD
dt
L
4
TURIN
i *
L
Excretion - Feces
L
5
= GSCAL ¦ RLLI ¦ YLLIC
dT
L
6
YFECE = \dFECEdt
o dt
L
Excretion - Sweat
43
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
No.
Equation
L
7
dSWET = TSWET CF BTEMP
dt
L
8
yswet- I™™*
o dt
L
Excretion - Other (e.g., hair, nails, desquamated skin)
L
9
{jTT A TD
= S2HAIR ¦ RSOFl ¦ YSOFl
dt
L
10
YHAIR = \dHAIRdt
o dt
M
Lead Body Burden and Distribution
M
1
SIGMA = YPLAS + YRBC + YEVF + YSOFO + YSOFl + YSOFl + YBRAN +
YCVOL + YTVOL + YCSUR + YTSUR + YCDIF + YTDIF + YKDNl + YKDN2 + YBLAD+
YLVRI+ YL VR2 + YRI+YR2 + YR3 + YR4 + YSTMC + YSIC + YULIC + YLLIC
+ YURIN + YFECE + YSWET + YHAIR
M
2
TBODYl = YPLAS + YRBC + YEVF + YSOFO + YSOFl + YSOFl + YBRAN +
YCVOL + YTVOL + YCSUR + YTSUR + YCDIF + YTDIF + YKDNl + YKDNl
+ YLVRI + YLVR1
M
3
TBODYl = YPLAS + YRBC + YEVF + YSOFO + YSOFI+ YSOFl + YBRAN + YCVOL +
YTVOL + YCSUR + YTSUR + YCDIF + YTDIF + YKDNl + YKDNl + YBLAD+ YLVRI+
YLVR1+ YRI+YR1 + YR3 + YR4 + YSTMC + YSIC + YULIC + YLLIC
M
4
TSOFTALL = YSOFT + YKDNE + YLIVR + YBRAN + YBL UD + YEVF
M
5
BLDFRC - WLUD
TBODYl
M
6
BONFRC - YSKEL
TBODYl
M
7
BRNFRC - YBRAN
TBODYl
M
8
HEPFRC - YLIVR
TBODYl
M
9
RENFRC - YKDNE
TBODYl
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No.
Equation
M
10
OTHFRC= YSOFT
TBODYl
N
Growth and Tissue Volumes and Masses
N
1
u/uru ,v u/u,u rLJ WCHILD ¦ AGEYEAR WADULT
WBODY — WBIRTH + 1 . ..... UfAmn T d CT7YT7A 7?
HALF + AGEYEAR 1 + KAPPA ¦ e-^MBDA-WADULT-AGEYEAR
N
2
AMTBLD = VBLC ¦ WBODY • 10
N
3
PLSVOL = AMTBLD ¦ (1 - BLDHCT)
N
4
RBCVOL = AMTBLD ¦ {BLDHCT)
N
5
BLDHCT4GEYEARom = HCTA ¦ (1 + (0.66 - HCTA) ¦ )
N
6
VK = 1000 • VKC ¦ (WBIRTH + WADULT + WCHILD) •
f WBODY Y'84
t WBIRTH + WADULT + WCHILD J
N
7
KIDWT = VK -1.05
N
8
VI, = 1000 • VLC ¦ (WBIRTH + WADULT + WCHILD) ¦
f WBODY Y'85
t WBIRTH + WADULT + WCHILD J
N
9
LIVWT = VL-1.05
N
10
VK = 1000 • VKC ¦ (WBIRTH + WADULT + WCHILD) ¦
f WBODY y84
t WBIRTH + WADULT + WCHILD J
N
11
TSKELWT = 1000 • 0.058 • WBODY121
N
12
WBONE = 1000 • 0.0290 • WBODY121
N
13
VBONE = 1000 • 0.0168 • WBODY1188
N
14
CVBONE = 0.8 • VBONE
N
15
TVBONE = VBONE - CVBONE
N
16
cortwt-wbone-cvbone
VBONE
N
17
TRABWT=WBONE-n'BONE
VBONE
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No. Equation
See Appendix B for parameter name definitions and descriptions. Generally, prefix R indicates a rate
constant from a compartment, prefix T indicates deposition fractions from plasma into a
compartment, and prefix Y indicates mass in a compartment. Also see text (Section 2.3) for
discussion of equations.
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1 TABLE 2-3. RATE COEFFICIENTS FOR PB TRANSFERS IN AALM
Pathway
100 days
1 year
5 years
10 years
15 years
>25 years
Plasma-D to EVF
1000
1000
1000
1000
1000
1000
Plasma-D to RBCs
297.1
406.9
425.1
366.9
300.6
480.0
Plasma-D to Plasma-B
0.495
0.678
0.709
0.611
0.501
0.800
Plasma-D to Urinary
Bladder
0
0
0
0
0
0
Plasma-D to Small
Intestine
7.429
10.171
10.629
9.171
7.514
12.000
Plasma-D to Trab Surf
96.00
57.60
56.83
89.50
132.25
88.96
Plasma-D to Cort Surf
384.0
230.4
199.2
268.5
341.8
71.0
Plasma-D to Liver 1
49.52
67.81
70.86
61.14
50.10
80.00
Plasma-D to Kidney 1
31.0
42.4
44.3
38.2
31.3
50.0
Plasma-D to Kidney 2
0.496
0.678
0.708
0.612
0.500
0.800
Plasma-D to STO
103.3
141.5
148.4
128.0
104.9
177.5
Plasma-D to ST1
12.38
16.95
17.71
15.29
12.52
10.00
Plasma-D to ST2
1.238
1.695
1.771
1.529
1.252
2.000
Plasma-D to Brain
0.557
0.763
0.266
0.229
0.188
0.300
Plasma-D to Sweat
4.333
5.933
6.200
5.350
4.383
7.000
RBCs to Plasma-D
0.4620
0.7854
0.4986
0.1946
0.1390
0.1390
EVF to Plasma-D
333.3
333.3
333.3
333.3
333.3
333.3
Plasma-B to Plasma-D
0.139
0.139
0.139
0.139
0.139
0.139
Cort Surf to Plasma-D
0.65
0.65
0.65
0.65
0.65
0.50
Trab Surf to Plasma-D
0.65
0.65
0.65
0.65
0.65
0.50
Cort Surf to Exch Vol
0.35
0.35
0.35
0.35
0.35
0.50
Trab Surf to Exch Vol
0.35
0.35
0.35
0.35
0.35
0.50
Cort Exch Vol to Surf
0.0185
0.0185
0.0185
0.0185
0.0185
0.0185
Trab Exch Vol to Surf
0.0185
0.0185
0.0185
0.0185
0.0185
0.0185
Cort Exch Vol to
Nonexch Vol
0.02311
0.02311
0.02311
0.02311
0.02311
0.02311
Trab Exch Vol to
Nonexch Vol
0.02311
0.02311
0.02311
0.02311
0.02311
0.02311
Cort Nonexch Vol to
Plasma-D
0.01644
0.00576
0.00308
0.00178
0.00102
0.00016
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Pathway
100 days
1 year
5 years
10 years
15 years
>25 years
Trab Nonexch Vol to
Plasma-D
0.01644
0.00576
0.00362
0.00264
0.00191
0.00099
Liver 1 to Plasma-D
0.0312
0.0312
0.0312
0.0312
0.0312
0.0312
Liver 1 to Small
Intestine
0.0312
0.0312
0.0312
0.0312
0.0312
0.0312
Liver 1 to Liver 2
0.00693
0.00693
0.00693
0.00693
0.00693
0.00693
Liver 2 to Plasma-D
0.000693
0.000693
0.001386
0.000570
0.000570
0.000570
Kidney 1 to Urinary
Bladder
0.139
0.139
0.139
0.139
0.139
0.139
Kidney 2 to Plasma-D
0.000693
0.000693
0.000693
0.000190
0.000190
0.000190
STO to Plasma-D
2.079
2.079
2.079
2.079
2.079
2.079
ST1 to Plasma-D
0.00416
0.00416
0.00416
0.00416
0.00416
0.00416
ST1 to Excreta
0.00277
0.00277
0.00277
0.00277
0.00277
0.00277
ST2 to Plasma-D
0.00038
0.00038
0.00038
0.00038
0.00038
0.00038
Brain to Plasma-D
0.00095
0.00095
0.00095
0.00095
0.00095
0.00095
Coefficients are in units of d"1. Coefficients from diffusible plasma (Plasma-D) are derived from the
product of scaled deposition fractions and the rate coefficient for transfer from the diffusible plasma to
all receiving compartments (RPLS, 2000 d1), from Equation 2.3-9.
Cort, cortical bone; Exch, exchangeable; EVF, extravascular fluid; Nonexch, nonexchangeable; Plasma-
D, diffusible plasma; Plasma-B, Pb-bound plasma RBC, red blood cell; Surf, surface; STO, ST1, and
ST2, soft tissues with fast, moderate, and slow exchange rates, respectively, Trab, trabecular bone; vol,
volume.
1
2
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1 FIGURE 2-1. STRUCTURE OF AALM.FOR BIOKINETICS MODEL.
Other Soft Tissues
>'
Skeleton
Diffusible
Plasma
Extra-
Vascular
Liver
> <
RBC
Kidneys
Bound
Plasma
Feces
Sweat
Brain
Liver 1
Liver 2
Urine
RT Tract
Gl Tract
Other
Kidney
Tissue
Urinary
Path
Bladder
Contents
Tenacious
Turnover
Rapid
Turnover
Intermediate
Turnover
Trabecular
Surface
Cortical
Surface
Losses in
Hair, Nails,
Skin
Non-
Exchange
Trabecular Volume
Exchange
Non-
Exchange
Cortical Volume
Exchange
3 Based on Leggett (1993). Lines with arrows represent Pb transfers.
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FIGURE 2-2. BODY AND TISSUE GROWTH IN THE AALM.FOR.
Female
Female
Female
Female
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1 FIGURE 2-3. GASTROINTESTINAL ABSORPTION OF PB AS OPTIMIZED IN AALM.FOR.
0.5
0.4
AALM
£
O
U
2 0.3
U_
£
O
E- 0.2
o
-Q
<
0.1
0.0
0
10
20
30
40
50
2 Age (year)
3 Optimization based on Ryu et al. (1983). Sherlock and Ouinn (1986). Rabinowitz et al. (1976) and
4 Maddaloni et al. (2005).
5
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1 FIGURE 2-4. STRUCTURE OF AALM.FOR BONE MODEL.
2
Central
Blood
Plasma
Cortical
Bone
Surface
Trabecular
Bone
Surface
Exchangeable
Cortical
Bone
Volume
Exchangeable
Trabecular
Bone
Volume
Nonexchangeable
Cortical
Bone
Volume
Nonexchangeable
Trabecular
Bone
Volume
4
5 This figure is based on Leggett (1993).
6
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CHAPTER 3. EVALUATION AND DEVELOPMENT OF AALM.FOR
3.1. INTRODUCTION AND OJBECTIVES OF THIS ANALYSIS
In 2014, EPA released the report Framework for Identifying and Evaluating Lead-Based Paint Hazards
from Renovation, Repair, and Painting Activities in Public and Commercial Buildings (U.S. EPA. 2014c')
which described how EPA could identify and evaluate hazards in public and commercial buildings. The
framework report was followed by a more detailed Approach for Estimating Exposures and Incremental
Health Effects due to Lead During Renovation, Repair and Painting Activities in Public and Commercial
Buildings (U.S. EPA. 2014b) and appendices (U.S. EPA. 2014a). The latter report describes in greater
detail an approach to estimating potential environmental concentrations, Pb body burdens, and
incremental health effects related to exposure to Pb from renovations of public and commercial buildings.
A key element in the approach was a Monte Carlo Analysis of Pb exposure scenarios and predicted blood
and bone Pb concentrations in children and adults. Blood and bone Pb were predicted using an
implementation of the Leggett (Pounds and Lcggctt. 1998; Lcggctt. 1993) biokinetics model (Leggett
Fortran Model, LFM). Several modifications were made to the LFM to improve its performance and
facilitate the Monte Carlo Analysis. The results of these modifications produced ICRPv005.FOR, also
referred to as Leggett Model Version 5 (https://www.epa.gov/lead/approach-estimating-exposures-and-
incremental-health-effects-lead-due-renovation-repair-and). In developing ICRPv005.FOR, several
changes were made to the Leggett biokinetics model (Table 3-1). ICRPv005.FOR performed well when
evaluated using the NHANES data for children and occupational Pb smelter data for adults, indicating
good agreement with both these measured data sources and IEUBK model estimates. As part of the
response to peer review comments on the approach, EPA undertook the analyses described in another
report (Post-Meeting Peer Review Summary Report. Versar. 2015).
In the months following EPA OPPT's release of the Approach for Estimating Exposures and Incremental
Health Effects due to Lead During Renovation, Repair and Painting Activities in Public and Commercial
Buildings document, EPA ORD NCEA completed a beta test version of the All Ages Lead Model
(AALM.CLS; v. 4.2, July 2015) which also implemented an updated and expanded version of the Leggett
model (Pounds and Leggett. 1998; Leggett. 1993) in Advanced Continuous Simulation Language (ACSL;
a.k.a. acslX). The development of AALM.CSL included calibration and evaluation of model performance
that are described in Chapter 4 using several data sets that were of potential value for further evaluations
of the ICRPv005.FOR model. EPA was also interested in exploring differences in the structures and
predictions of blood and bone Pb from the two models. In part, to determine if one or the other model
might offer advantages for applications in predicting Pb body burdens related to public and commercial
building renovations as well as other potential research and regulatory applications of the models for
predicting exposure-body burden relationships.
This chapter summarizes results of analyses undertaken by EPA to explore differences in the structures
and predictions of blood and bone Pb between AALM.CSL and ICRPv005.FOR. The specific objectives
of these analyses were as follows:
• Conduct further evaluations of ICRPv005.FOR and AALM.CSL;
• Modify the models as needed, based on the outcome of these evaluations; and
• Harmonize the two models so that the models predict similar blood and bone Pb levels for similar
exposure inputs.
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A detailed description of the structure of the AALM.FOR is provided in Chapter 2.
Within this chapter, Section 3.2 compares predictions of blood and bone Pb concentrations obtained from
the models. Section 3.3 describes the outcomes of comparisons of model predictions to observations.
Section 3.4 discusses data needs for potential further refinement and evaluation of the models. Section 3.5
summarizes conclusions from the model comparisons, model harmonization and responses to peer review
comments on approaches to blood and bone Pb modeling.
3.2. MODEL PREDICTIONS OF BLOOD AND BONE PB
Differences in the parameter values used in ICRPv005.FOR and AALM.CSL biokinetics models (Table
3-2) resulted in different predictions of blood and tissue Pb levels for similar Pb exposure assumptions.
Ultimately it was decided to harmonize the two models and a Fortran version (AALM.FOR) of
AALM.CSL was created. Thus, Table 3-2 essentially provides the changes in ICRPv005 FOR that were
required to create AALM.FOR. The AALM.FOR and AALM.CSL implementations are structurally
identical and have only few differences in parameter values and computational schemes that do not affect
simulations of blood and bone Pb concentrations (Table 3-3). The most important changes made to
ICRPv005.FORto create AALM.FOR include the following: (1) Growth parameters from O'Flahertv
(1995. 1993) were adopted in AALM.FOR, this results in identical age profiles for blood volumes and
tissue masses between the models (see Chapter 2, Figure 2-2); and (2) GI absorption parameters from
AALM.CSL were adopted in AALM.FOR (see Section 4.7.1 and Figure 4-13). The GI absorption
fraction is 0.39 at birth and decreases to 0.12 at age 8 years (Figure 3-1). All other parameter values (e.g.
transfer rates and deposition fractions) from AALM.CSL were adopted in AALM.FOR.
Two types of comparisons were made of ICRPv005.FOR and AALM: (1) age profiles for blood and
tissue Pb levels following an exposure to a constant Pb intake (fig/day) were simulated and compared;
and (2) dose-response relationships between ingested dose and Pb levels were compared by simulating a
series of increasing Pb intakes. In either type of simulation, parameters that control Pb absorption and
growth were set to the same values, so that differences in blood and tissue Pb levels could be attributed
entirely to differences in the simulation of systemic (post-absorption) biokinetics.
3.2.1. Constant Pb Intake
Figures 3-2 and 3-3 show simulations of the accrual and elimination of Pb in blood and bone,
respectively, in children and adults. Exposures were simulated as a constant baseline Pb intake (5
(ig/day) with a period of elevated intake (40 (ig/day in children and 105 (ig/day in adults). This exposure
results in predicted blood Pb concentrations <5 (ig/dL, which is well below the concentration at which
saturation of uptake into RBCs significantly affects blood Pb levels. Several differences are evident from
these comparisons:
• The harmonized AALM.FOR and AALM.CSL produce identical predictions of blood and bone
Pb concentrations.
• The AALM predicts higher blood and bone Pb concentrations than ICRPv005.FOR. The
difference is more pronounced in the adult simulation (Figure 3-2).
• The AALM predicts a slower approach to a quasi-state state blood Pb concentration than
ICRPv005.FOR and slower elimination and return to baseline (Figure 3-2). The difference is
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more pronounced in the adult simulation. The AALM predicts a return to baseline over a period
of decades in adults; whereas, ICRPv005.FOR predicts a return to baseline within one year.
• The pattern of decline in blood Pb concentration following an abrupt decrease in Pb intake is also
different in the AALM and ICRPv005 .FOR. Both models predict multi-phasic elimination of Pb
from blood in children (Figure 3-2A); however, the AALM predicts an early rapid phase,
followed by a slower phase; whereas, ICRPv005.FOR predicts a slower early phase, followed by
more rapid phase.
• The AALM predicts similar cortical and trabecular bone Pb concentrations in children; whereas,
ICRPv005.FOR predicts trabecular bone Pb concentrations that are approximately 25% of
cortical bone (Figure 3-3A, 8C).
• The AALM and ICRPv005 .FOR predict higher Pb concentrations in adult trabecular bone,
compared to cortical bone, and slower accrual and elimination kinetics in cortical bone (Figure 3-
3 B, D).
• The AALM predicts faster elimination of Pb from adult cortical bone compared to
ICRPv005.FOR (Figure 3-3B).
3.2.2. Dose-Response for Blood and Bone Pb
Although both the AALM and ICRPv005.FOR model are mathematically linear models (i.e., all
compartment Pb masses are defined with linear differential equations), they predict curvilinear dose-
response relationships for blood Pb resulting from a saturable capacity of RBCs to take up Pb. Dose-
response relationships predicted from AALM.CSL, AALM.FOR and ICRPv005.FOR are shown in
Figures 3-4 for blood and 3-5 for bone, in children (age 2 years) and adults (age 30 years). In the AALM,
curvature in the intake-blood Pb relationship is negligible at blood Pb concentrations <10 (ig/dL. Both
models predict linear dose-response relationships for bone Pb.
3.3. COMPARISONS OF MODEL PREDICTIONS TO OBSERVATIONS
Peer reviewers of Approach for Estimating Exposures and Incremental Health Effects due to Lead During
Renovation, Repair and Painting Activities in Public and Commercial Buildings (U.S. EPA. 2014b)
suggested that data be used to evaluate blood and bone Pb predictions in adults from Hattis (1981) and
Nie et al. (2005). including additional unpublished Nie et al. data.
Data that were available from the Nie study consisted of three longitudinal blood and bone XRF
measurements for 209 adult Pb workers. The measurements were made in 1991, 1999 and 2008. This
period included a nine-month strike (July 1990 to May 1991), during which exposures at the plant were
interrupted. The available data also included birth dates and dates of hire. There were no data on actual
exposures at the plant. Although attempts were made to reconstruct exposures so that blood and bone Pb
concentrations could be predicted and compared to observations, ultimately, it was concluded that the
data were not suitable for model evaluations because of the uncertainty in the exposures that preceded the
blood and bone Pb measurements and that occurred during the measurement period. Exposures prior to
1991, including the period of the strike, had to be reconstructed with no basis for verification other than
the observed blood and bone Pb measurements. In one reconstruction attempted, each subject was
assumed to have an age-intake profile that predicted an age-blood Pb profile that was similar to the
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central estimates from the NHANES survey that corresponded to the subject's age date. Added to this
background intake was a constant occupational intake (except during the strike) that was calibrated to
achieve a good fit to the weighted MSE for observed bone Pb (tibia and calcaneus) and blood Pb (relative
weights: cortical bone 3, trabecular bone 2, blood 1). This fitting procedure resulted in good agreement
between cortical and trabecular bone Pb predicted from ICRPv005.FOR and corresponding observations
(r2 > 0.8). However, a good fit to the observations could be expected for a wide range biokinetics
parameter settings; therefore, these data would not allow a determination of whether ICRPv005.FOR or
the AALM would perform better at predicting the observations.
Data that were available from the Hattis study were much more suitable for model evaluation. These data
included blood Pb concentrations in 57 workers at hire and prior to and following a nine-month strike.
Although pre-hire exposures were unknown, it was possible to calibrate the post-hire and pre-strike
exposures to achieve agreement with blood Pb concentrations at the time of hire and just prior to the
strike, and then predict without further calibration the post-strike blood Pb. Agreement between post-
strike observations and predictions would be sensitive to biokinetics parameter settings that control blood
Pb elimination rates. Therefore, these data were used to compare performance of ICRPv005.FOR and
AALM. The outcome of this comparison indicated that the AALM performed better at predicting the
Hattis observations than ICRPv005.FOR (described in detail in Section 3.3.1). Based on these
evaluations, a Fortran version of the AALM (AALM.FOR) was developed and additional evaluations of
AALM.FOR and AALM.CSL were conducted. These evaluations are described in Sections 3.3.2 to 3.3-
10.
Goodness of fit of model predictions to observations were evaluated three approaches: (1) visual
inspection of observed and predicted values; (2) inspection of standardized residuals (Equation 3-1); and
(3) r2 for the least-squares linear regression of observed and predicted values.
„ -i i Predicted-Observed. „ 1S
Standardized Residual = Eq. (3-1)
Standard Deviation of Observed Mean
Standardized residuals < ±2 and r2 > 0.70 were considered acceptable fit to the observations.
3.3.1. Pb Elimination Kinetics in Workers with Dose Reconstruction (Hattis Data)
The Hattis data set used in this analysis included the following data on 57 adult Pb workers: (1) duration
of employment prior to strike (Days_prestrike); (2) blood Pb concentration prior to start of employment
(BLLstart); (3) blood Pb just prior to a nine-month strike (BLL_prestrike); and (4) blood Pb on return to
work, following strike (BLL_poststrike). The 57 subjects comprised a subset of the 66 subjects in the
dataset described in Hattis (1981). Subjects were excluded from the analysis if pre-strike blood Pb was
>75 (ig/dL, post-strike blood Pb was < blood Pb at date of hire, or post-strike blood Pb was > pre-strike
blood Pb. In the absence of information on pre-employment Pb exposures, pre-hire Pb intake was
simulated as a constant ingestion intake ((.ig/day/kg body weight) that would result in a predicted blood
Pb concentration at age 20 years that was similar to BLL start (±1 (ig/dL). Pre-strike occupational
exposure was simulated as a constant ingestion intake (fig/day) that would result in a predicted blood Pb
concentration at age = (20 years + duration of strike) that was similar to BLL_start (±1 j^ig/dL). During
the strike (assumed to be 270 days in duration), ingestion intake reverted to the pre-hire Pb intake.
An example of a simulation for a single subject from the Hattis data is shown in Figure 3-6 for
AALM.CSL. In this simulation, the pre-hire Pb intake and pre-strike exposure intake were calibrated to
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predict blood Pb concentrations similar to the observations made at the time of hire and at the start of the
strike. In this case, the predicted post-strike blood Pb concentration (18.5 (ig/dL) was within 10% of the
observed (17.0 /dL). A pseudo first-order elimination rate (d1) and tm were estimated from the observed
blood Pb concentrations at the beginning and end of the strike as follows (Equations 3-2 and 3-3):
k = In (BLLpre-strike\
\BLL post-strike J
ti/2 = ^ Eq. (3-3)
The ti/2 calculated from the blood Pb concentrations predicted from the model and observations were 371
days and 320 days, respectively. The calculated values forti/2 do not reflect the actual elimination kinetics
of Pb from blood in this subject, or predicted from the AALM, because both would be expected to be
multi-phasic over the 270-day interval. However, it serves as a convenient metric for comparing model
performance when applied to the entire set of 57 subjects.
Both ICRPv005.FOR and AALM.CSL were successfully calibrated to the blood Pb
concentrations measured at time of hire and just prior to the strike (r2 = 1.0). Predicted and observed
post-strike blood Pb concentrations were also correlated, but showed substantially more variability that
could not be accounted for by the models, as expected for model predictions (r2 = 0.47; Figure 3-7).
Figure 3-8 shows the distribution of calculated tin values for the Hattis subjects. Summary
statistics for the evaluation are presented in Table 3-4. The median ti/2 predicted from the observations
was 633 days (GSD 2.4). The median from AALM.CSL was 483 days (GSD 1.6) and the median from
ICRPv005.FOR was 274 days (GSD 1.6). The average difference between the individual observed and
predicted tin values was -5% for AALM.CSL and -37% for ICRPv005.FOR. AALM.FOR predicted tin
(median 465 days, GSD 1.6; percent difference -8%) that were similar to AALM.CSL prediction.
3.3.2. Pb Elimination Kinetics in Workers with Dose Reconstruction (Nilsson et al., 1991)
Nilsson et al. (1991) reported longitudinal data on blood and finger bone Pb concentrations in 14 Pb
workers for period ranging from 8-18 years following cessation of their occupational exposures. The
median blood Pb concentration at the end of exposure was approximately 45 (ig/dL. The decline in bone
Pb concentration was described by a first-order model with a single rate constant. Estimates of
elimination half-times for each individual were reported. The group median was 16 years (95% CI: 12,
23). The decline in blood Pb was described by a tri-exponential model with the following parameters.
CI C2 C3
Parameter Unit (95% CI) (95% CI) (95% CI)
tin year 34 day 1.2 year 13 year
(29,41) (0.85,1.8) (10,18)
C (ig/dL 10.2 12.6 22.8
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AALM simulations were run for a constant Pb intake from birth to age 60 years, to achieve a terminal
blood Pb concentration of approximately 45 (ig/dL (2000 (ig/day), followed by 20 years without
exposure. A first-order exponential rate was estimated for the decline in cortical bone Pb concentrations
predicted for 20 years following cessation of exposure. Figure 3-9 compares rates of elimination of Pb
from bone and blood with the corresponding empirical models derived for the Pb workers (Nilsson et al..
1991). Elimination rates of Pb from bone predicted from the optimized models are within the 95% CI of
the empirical model and yield standardized residuals that range within the -2, 2, criteria (r2 = 0.99).
Elimination half-times predicted for bone Pb (16 years) were identical to estimates from Nilsson et al.
(1991). Although elimination rates from blood predicted by the optimized models are approximately at
the confidence limits of the empirical model, the initial model divergence is due largely to the slower
elimination kinetics observed during the first 5 years following cessation of exposure; after which the
models converge on the empirical model (r2 = 0.96). Half-times predicted for the period 5 to 20 years
after exposure were 1.25 years, similar to values predicted for C2 (1.2 year) from Nilsson et al. (1991).
3.3.3. Blood Pb Accrual and Elimination Kinetics in Adults with Known Pb Doses
(Rabinowitz et al., 1976)
Rabinowitz et al. (1976) conducted a pharmacokinetics study in which four adults ingested daily doses of
[207Pb] nitrate for periods up to 124 days. Concentrations of 207Pb in blood, urine, and feces were then
monitored during and following cessation of exposure, and data on daily intakes and blood concentrations
for each subject were reported. Absorption fractions for Pb were estimated for each individual based on
mass balance in feces.
Figure 3-10 compares observed and predicted blood 207Pb concentrations from AALM.FOR and
AALM.CSL. Gastrointestinal absorption fractions were set in both models to the estimates for each
individual reported in Rabinowitz et al. (1976). No other changes were made to parameter values. Both
models predicted the rise and decline in blood Pb concentrations in temporal patterns that agreed with
observations. Values for r2 for AALM predictions are 0.99, 0.98, 0.92, and 0.97 for Subjects A, B, D, and
E, respectively.
3.3.4. Post-mortem Soft Tissue-to-Bone Pb Ratio (Barry, 1975)
Four studies provide data for measurements of post-mortem soft tissue and bone Pb concentrations
(Gerhardsson et al.. 1995; Barry. 1981. 1975; Gross et al.. 1975). Gerhardsson et al. (1995) reported only
soft tissue Pb concentrations; whereas, the other three studies reported soft tissue and bone Pb
concentrations that can be used to estimate the ratios. Barry (1981. 1975) reported data for children and
adults in age brackets, so the data from Barry (1975) was used as the primary source to optimize
parameters for kidney/bone and liver/bone Pb ratios as a function of age. Barry (1975) reported data on
tibia Pb concentrations that are simulated as cortical bone concentrations in the AALM models. Since
Barry (1975) reported group mean tissue concentrations (not ratios in autopsy cases), the mean tissue-to-
bone ratios were approximated from the group means. Figure 3-11 compares predicted and observed
kidney/bone and liver/bone Pb ratios in adults. Values for r2 for kidney/bone predictions (of average of
male and female ratios) were 0.95. Values for r2 for liver/bone predictions were 0.96 and 0.93 for AALM,
respectively.
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3.3.5. Plasma-to-Bone Pb Ratio in Workers (Hernandez-Avila et al., 1998; Cake et al.,
1996)
Two studies provide data to evaluate the relationship between plasma or serum blood Pb and bone Pb
concentrations (Hernandez-Avila et al.. 1998; Cake et al.. 1996). Cake et al. (1996) measured paired
serum, tibia, and calcaneus Pb concentrations in 49 adult male Pb workers, and reported corresponding
linear regression parameters. Hernandez-Avila et al. (1998) measured paired plasma, tibia and patella Pb
concentrations in 26 adults (20 female) who had no known occupational exposures to Pb. These data can
be used to derive corresponding linear regression parameters for the log-transformed plasma Pb.
Individual subject data were digitized from Figure 1 of Hernandez-Avila et al. (1998). and linear
regression parameters derived for the untransformed plasma Pb concentrations, in order to compare these
with the linear regression parameters from Cake et al. (1996).
Bone Pb/plasma Pb slopes at age 50 years were predicted from the AALM for a series of simulations in
which Pb intake was varied from 1 to 1000 (ig/day. Table 3-5 and Figure 3-12 compare predicted and
observed slopes based on data from Cake et al. (1996) and Hernandez-Avila et al. (1998). The
bone/plasma ratios predicted from the AALM were within the 95% CI of the Cake et al. (1996) estimates
and were also within the 95% CI of the Hernandez-Avila et al. (1998) for tibia.
3.3.6. Plasma Pb - Blood Pb Relationship (Meta-data)
Six studies provided data on individual human subjects that can be used to evaluate the relationship
between plasma Pb and blood Pb concentrations. Measurements of plasma Pb were made using either
inductively coupled plasma mass spectrometry (Smith et al.. 2002; Bergdahl et al.. 1999; Bergdahl et al..
1998; Hernandez-Avila et al.. 1998; Bergdahl etal.. 1997; Schutz et al.. 1996) or stable isotope dilution
with thermal ionization mass spectrometry (Manton et al.. 2001). In all of these studies, methods were
employed to control for sample contamination, which is of particular importance in measurements of the
low Pb levels found in plasma. Taken together, the observations from these reports varied over a wide
range of blood Pb (approximately 0.34-94.8 (ig/dL) and plasma Pb (approximately 0.0014-1.92 (ig/dL)
levels. These studies provided 406 individual measurements of plasma Pb and blood Pb, in adult workers
as well as individuals with no known history of occupational exposure to Pb (SRC. 2003). Only one
study provides similar data in children (Bergdahl et al.. 1999). The observations in children do not appear
to differ substantially from those for adults.
A best fit (least-squares) model for combined data from the above six studies was identified, and is
presented in Equation 3-4:
Blood Pb = 87.0 ¦ Plasma Pb0 5 - 3.89 (r2=0.90) Eq. (3-4)
Figures 3-13 compares the observed and predicted plasma-whole blood Pb relationship in adults.
Standardized residuals for the optimized models are within acceptable limits (-2, 2). The r2 values for
predictions are 0.99 and 0.98.
3.3.7. Blood Pb Elimination Kinetics in Infants with Known Doses (Sherlock and Quinn,
1986: Ryu et al.. 1983)
Only two studies provide data on the relationships between Pb dose and blood Pb concentration in infants
(Sherlock and Quinn. 1986; Ryu et al.. 1983). In the Rvu et al. (1983) study, blood Pb concentrations
were monitored in 25 formula-fed infants. From birth to age 111 days, infants were fed formula
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(packaged in cartons) that had a Pb concentration of approximately 20 (ig/L. From age 112 to 195 days, a
subset of the infants (n = 7) were switched to formula (packaged in cans) that had a Pb concentration of
approximately 57 (ig/L. Formula intakes were measured, and provided estimates of Pb intakes in each
subject. Rvu et al. (1983) reported a table of individual Pb intakes, and presented a figure illustrating
group mean blood Pb concentrations at various ages (these data were digitized for use in this analysis).
Standard errors (or deviations) of mean blood Pb concentrations were not reported; however, as discussed
below, based on Sherlock and Ouinn (1986). standard errors may have been approximately 10% of the
means. The parameter for maternal blood Pb concentration was set at 10 (ig/dL, the reported maternal
mean for the study. Lead absorption was not quantified in Rvu etal. (1983); therefore, the
gastrointestinal absorption fraction during infancy was set to 40%, based on estimates from mass balance
studies (Ziegleretal.. 1978). No other changes were made to parameter values. Figure 3-14 compares
predicted and observed blood Pb concentrations for the two exposure regimens (carton formula or carton
followed by canned formula). Simulations are shown for the mean intake (12-20 (ig/day) and ± 1 SD
(10-18 (ig/day, 15-22 (ig/day). AALM.CSL and AALM.FOR simulations encompass most of the
observations within ±1 SD of the mean intakes. If standard errors of mean blood Pb concentrations were
10% of the mean, standardized residuals for AALM predictions ranged from -3.7 to 0.15 for carton
exposures (mean -1.2). The AALM captures the increase in blood Pb concentration associated with the
switch the higher Pb intakes for canned formula and the overall temporal trends in the observations; r2 for
predictions were 0.85.
Sherlock and Ouinn (1986) measured blood Pb concentration in 131 infants at age 13 weeks and
estimated dietary intake of Pb for each infant based on Pb measurements made in duplicate diet samples
collected daily during week 13. Sherlock and Ouinn (1986) provided a plot of blood Pb means and
standard errors for group mean dietary Pb intakes (these data were digitized for use in this analysis). The
parameter for maternal blood Pb concentration was set at 18 (ig/dL, the reported maternal geometric
mean. The gastrointestinal absorption fraction was set at 40% for infants; the same value used in
simulations of Rvu et al. (1983). Figure 3-15 compares predicted and observed blood Pb concentrations
for the range of Pb intakes in the study. AALM.CSL and AALM.FOR models reproduce the general
shape of the observed curvilinear dose-blood Pb relationship; the apparent plateau observed at the higher
end of the dose range, however, it is achieved at higher doses in the models (>800 (ig/day). Although the
model results for the plateau contributed to high residuals at the highest Pb intake (>200 (ig/day),
standardized residuals for lower Pb doses ranged from -4.8 to 1.5 (mean -2.3). The overall dynamics of
increasing blood Pb with increasing Pb dose was predicted with r2 = 0.95. One possible explanation for
the higher plateaus in the dose-blood Pb relationship predicted from both models is that the models may
estimate higher saturation levels of Pb in RBCs than actually occurred in the infants in the Sherlock and
Ouinn (1986) study. Parameter values for RBC uptake are based on data collected on adults, and have not
been optimized for infants due to an absence of good supporting data (see Section 3.3.6).
3.3.8. Blood Pb Elimination Kinetics in Infants with Dose Reconstruction (ATSDR)
Agency for Toxic Substances and Disease Registry (ATSDR) made available for this analysis
longitudinal blood Pb data in children following intervention in response to measurement of an elevated
blood Pb concentration. The data included dates of birth and dates and results of repeated Pb
measurements in 12 females and 12 males. Interventions included interruption of the exposure which
allows an evaluation of elimination kinetics of blood Pb. However, other interventions may have also
been conducted but were not documented in the data made available for this analysis. Intervention is
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likely to have included chelation therapy in children whose blood Pb concentration exceeded 45 (ig/dL.
Chelation would be expected to have affected rates of decline in blood Pb concentration during the first 1-
3 weeks following the diagnosis of elevated blood Pb. The longitudinal blood Pb data available for
longer periods would reflect post-chelation kinetics and are suitable for evaluating model predictions of
blood Pb elimination kinetics.
Since actual exposures to Pb were unknown for each child, the exposures leading up to the first blood Pb
measurements were reconstructed as a constant baseline Pb intake (fig/day) that resulted in a blood Pb
concentration of 5 (ig/dL at age 6 months. Selection of 5 (ig/dL as the target for the baseline simulation is
supported by the observations that that average terminal blood Pb concentration was 5.5 (ig/dL (±2.4 SD,
n = 24). Some children had blood Pb concentrations reported prior to an episode of elevated blood Pb
concentrations; the mean was 5.3 (ig/dL (±2.4 SD, n = 4). Another uncertainty is the reconstruction of the
level and duration of the elevated exposure that occurred prior to the detection of the elevated blood Pb.
Since there was no information about the exposure level or duration, these were parameters were
calibrated to the blood Pb observations to achieve optimal residuals and r2 for the predictions. Examples
of successful exposure constructions are shown in Figures 3-16 to 3-18. Although, there is considerable
uncertainty about the reconstructed exposures, in each case, the AALM simulated the blood Pb
elimination kinetics from observations well beyond the expected period of chelation. Figure 3-18 shows
one of the few cases in which a baseline blood Pb measurement was available prior to the elevated
exposure. The timing of this baseline measurement considerably decreases the uncertainty about the
duration of the elevated exposure. Since the baseline measurement was made at age 450 days and first
elevated blood Pb was measured at age 810 days, the duration was likely to have been no more than 360
days. The optimized duration (age day 600 - 800) and exposure level (13,000 ppm Pb in dust) provided a
good fit to the observed elimination kinetics (r2 0.81). The simulations shown in Figures 3-16 to 3-18 are
examples of one approach to reconstructing the Pb exposures that occurred prior to the blood Pb
observations.
3.3.9. Comparison to IEUBK Model for Pb in Children
Figure 3-19 compares predictions of the AALM and the IEUBK model for a continuous dust Pb intake of
10 |_ig/day . In both models, the relative bioavailability (RBA) for Pb in dust was assumed to be 60%.
This corresponds to an absolute bioavailability of approximately 20% at age 2 years in the AALM and
30% in the IEUBK model. At age 2 years the IEUBK model predicts a blood Pb concentration of 1.18
(ig/dL; the AALM predicts 1.25 (ig/dL.
3.3.10. Comparison to Adult Lead Methodology
Figure 3-20 and Table 3-6 compare predictions of adult blood Pb concentrations from the Adult Lead
Methodology and AALM, for an exposure to 1000 ppm. In both models, the RBA for Pb in dust was
assumed to be 60%. This corresponds to an absolute bioavailability of approximately 4.8% in the AALM
and 12% in the Adult Lead Methodology. The Adult Lead Methodology predicts a blood Pb
concentration of 2.9 (ig/dL; the AALM predicts 3.1 (ig/dL at age 30 years (mid-point for age range in the
Adult Lead Methodology, 17-45 years).
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3.4. DATA NEEDS FOR FURTHER REFINEMENT OF THE AALM
The AALM.FOR model discussed in this report demonstrates the considerable advancements that have
been made since a development of ICRPv005.FOR in terms of its capability and evaluation predictions of
Pb body burdens, including blood Pb concentrations in children and blood and bone Pb concentrations in
adults. Blood Pb concentrations in adults predicted from the AALM are very similar to predictions from
the EPA Adult Lead Methodology (ALM) for the same soil Pb concentrations. Predictions for infants are
similar between the AALM and the IEUBK. Work done to date has been responsive to comments
received on both models from peer reviews conducted in 2005 and 2014 (see Section 3.5).
Recommendations for data to reduce uncertainty in the predictions obtained from AALM.FOR and
AALM.CSL, and improve the consistency among all model predictions include the following:
• Further verify A ATM predictions. Additional observations in humans should be identified that
can serve to evaluate the performance of the optimized AALM (and that were not used in the
optimization). Ideally, these would be blood and/or bone Pb measurements in people for whom
Pb intakes are known with reasonable certainty. Ethical concerns typically preclude Pb dosing
experiments; therefore, Pb doses must be estimated with accurate tools such as duplicate diet
surveys or dietary recalls and information on Pb levels in diet and other relevant exposure media.
Types of data that would be valuable for model validation include: (1) blood soft tissue or bone
Pb levels in children or adults for whom Pb dosage is known or can be reliable estimated from
exposure data; (2) changes in blood, soft tissue or bone Pb levels in children or adults following
and abrupt change (increase or decrease) in Pb exposure; (3) steady state (or quasi-steady state)
blood/soft tissue blood/bone Pb ratios in children or adults; (4) urinary Pb clearance from blood
or plasma in children or adults; and (5) plasma/whole blood concentration ratios in children.
• Evaluate and document the empirical basis for exposure model parameters. Most of the
exposure parameter values currently in the AALM serve as placeholders and should, in the future,
be replaced with default values for specific receptor populations for which an empirical basis can
be provided.
• Further refine the gastrointestinal tract model. AALM.FOR allows the user to input values for
RBA of Pb in exposure media. This is important for risk assessment applications because the
absorption fraction Pb is known to vary with the environmental medium in which it is contained
(e.g. Pb in soil can have a lower absorption fraction than Pb dissolved in water). However, in the
current version of AALM.FOR, the RBA adjustment is applied to the media-specific Pb intake
rather than to the absorption fraction (/
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particle size and minute (day) and volume day volume (m3/day). A model that would use inputs
of air Pb concentration, particle size and Pb species would be more useful for applications to
simulating air Pb exposures. This could be similar to the simplified version of the ICRP (1994)
model that was implemented in the beta test version of AALM.CSL (v. 4.2, July 2015).
• Refinement of the bone mineral model. The AALM includes calculations for converting
concentrations of Pb in bone wet weight to concentration per g bone mineral by dividing the wet
weight concentration by the ash fraction of bone. This conversion is important for comparing
model predictions of bone Pb concentrations with bone X-ray fluorescence (XRF) data, which is
typically reported in units of Pb per g bone mineral. In AALM.CSL, bone ash fractions were
assumed to be 0.55 and 0.50 for cortical and trabecular bone, respectively (ICRP. 1981). In
ICRPv005.FOR, the bone ash fractions were assumed to be 0.55 for cortical bone and 0.18 for
trabecular bone. AALM.CSL values have been adopted for AALM.FOR and the different values
for trabecular bone have not been reconciled. Further research that could provide a stronger
empirical basis for these values would improve confidence in simulations of XRF observations.
3.5. CONCLUSIONS AND IMPLICATIONS FOR MODELING LEAD BODY BURDENS
The current version of AALM.FOR represents a substantial update to ICRPv005.FOR used in the
Approach for Estimating Exposures and Incremental Health Effects due to Lead During Renovation,
Repair and Painting Activities in Public and Commercial Buildings (U.S. EPA. 2014b) and appendices
(U.S. EPA. 2014a) . The updates include new parameters for simulating physiological growth and
gastrointestinal absorption, as well as updated parameters that govern rates of exchange of Pb between
plasma, RBCs, bone, kidney and liver (Table 3-2). AALM.FOR predicts blood, bone and soft tissue Pb
levels that are identical AALM.CSL and provides an alternative Fortran platform to acslX, which is no
longer commercially supported, for implementing the AALM.
3.5.1. Evaluation of AALM.FOR Performance
AALM.FOR was evaluated with a larger set of observations in children and adults, including some data
that had not been used in previous evaluations of ICRPv005 .FOR. Data on Pb dose-blood Pb
relationships is limited to a three studies; one of adults in which five male subjects were administered
known doses of a stable Pb isotope for periods of 2 to 6 months (Rabinowitz et al.. 1976) and two studies
of infants in which Pb ingestion doses were estimated from dietary (formula) Pb measurements and
exposures were for approximately 3 months (Rvu et al.. 1983. n = 25); (Sherlock and Ouinn. 1986. n =
131). No data were available on dose-blood Pb concentration relationships in older children or
adolescents for whom Pb ingestion doses were known with certainty. Several studies have reconstructed
Pb intakes in children from exposure models supported by measurements of environmental exposure
concentrations (Dixon et al.. 2009; TerraGraphics Environmental Engineering. 2004; Malcoe et al.. 2002;
Hogan et al.. 1998; Lanphear et al.. 1998; Bornschein et al.. 1985). However, these studies were not
considered in the current evaluations of AALM.FOR and may be useful for future efforts to validate a
version of the AALM that combines the biokinetics model (AALM.FOR) with a multimedia exposure
model.
Although limited in size, these evaluations suggest that AALM.FOR can provide an accurate prediction of
dose-blood Pb relationships when actual doses are known or can be calculated with certainty. In general,
AALM.FOR predicted the observed blood Pb concentrations and dynamics in infants and adults in
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response to changing Pb dosing (see Figures 3-10, 3-14). AALM.FOR also predicted quasi-steady state
blood Pb concentrations in infants across a range of ingestion doses of Pb (Figures 3-15). The model
predicted a higher plateau for the dose-blood Pb relationship than was observed in infants (Figure 3-15),
however, this difference would be of quantitative significance only at intakes resulting in blood Pb
concentrations >30 (ig/dL. These evaluations show that the model reliably predicts both quasi-steady
state blood Pb concentrations as well the rates of change Pb that occur with a change in exposure.
AALM.FOR also predicted the observed relationships between plasma and whole blood Pb
concentrations in adults (Figure 3-13). Transfer out of RBCs in AALM.FOR is age-dependent and faster
in children than in adults. The validity of the age-dependence was not rigorously explored in this
analysis. What little data there are on plasma-blood Pb relationships in children does not suggest an
appreciable difference in the relationship for children and adults (Bcrgdahl et al.. 1999). Since the age-
dependence could not be rigorously evaluated it is retained in AALM.FOR. AALM.FOR also predicted
the observed relationships between plasma and bone Pb concentrations in adults (Figure 3-12) and
between kidney, liver and bone Pb concentrations in children and adults based on post-mortem data
(Figure 3-11). This suggests that the model accurately predicts the ratios of the exchange kinetics (rates
into tissue and out to plasma) that give rise to the age-dependent distribution of Pb between bone and soft
tissue.
AALM.FOR predicted the observed changes in blood Pb concentrations in children and adults for
reconstructed exposures estimated based on observed blood Pb measurements (Figures 3-8, 3-9, 3-16 to
3-18). These evaluations indicate that the model accurately predicts observed elimination kinetics of Pb
from blood in children and adults, and bone in adults. AALM.FOR predicts more rapid elimination of Pb
from bone in children compared to adults (Figure 3-3). This is consistent with more active bone growth
and turnover of bone mineral during childhood which should contribute to more volatile bone Pb stores
(O'Flahcrtv. 1995; Leggett. 1993). However, the kinetics of bone Pb in children predicted by the model
have not been quantitatively verified as no data were available on kinetics of elimination of Pb from bone
in children.
Collectively, the above observations provide added confidence for applications of AALM.FOR for
predicting Pb body burdens associated with long-term steady state exposures or short-term intermittent
exposures, such as those associated with public and commercial building renovations.
3.5.2. Response to Peer Review of ICRPv005.FOR
The updates made to ICRPv005 .FOR and further evaluations of ICRPv005 .FOR and AALM.FOR address
several comments made by peer reviewers of the Approach for Estimating Exposures and Incremental
Health Effects due to Lead During Renovation, Repair and Painting Activities in Public and Commercial
Buildings (Vcrsar. 2015; U.S. EPA. 2014b). These are summarized below.
Rationale for selecting the Leggett model over the O 'Flaherty model. Peer reviewers suggested that
performance of the Leggett and O'Flaherty models be evaluated and that a stronger rationale be provided
for selecting the Leggett model for applications to public and commercial renovation assessments. This
report does not specifically address performance of the O'Flaherty model; however, the model was
extensively evaluated Chapter 4. The latter report described the development and evaluation of
AALM.CSL which includes modules that implement biokinetics models based on either the Leggett
model (AALM-LG.CSL) or O'Flaherty model (AALM-OF.CSL). A conclusion of the latter report was
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that AALM-LG.CSL provided superior agreement to the Rabinowitz et al. (1976) observations compared
to AALM-OF.CSL. This conclusion supports selection of the Leggett model as the basis for AALM.FOR
and for applications of AALM.FOR, rather than the O'Flaherty model, to assessments of public and
commercial building renovations. Additional considerations that support use of AALM.FOR were: (1)
the need for Monte Carlo applications of the model which require sufficient computational speed afforded
by the Fortran code; and (2) limited future availability of an acslX program to run AALM.CSL, because
acslX is no longer being commercially supported.
Accounting for sex differences in biokinetics. The peer reviewers suggested that the model should
simulate sex differences in Pb biokinetics. The analyses described in this report could not evaluate sex
differences in biokinetics because there are no data on dose-body burden relationships in humans that
would allow such evaluations. ICRPv005 .FOR was updated in creating AALM.FOR to include
algorithms that control growth of the body, volumes of plasma and blood and masses of bone and soft
tissues AALM.FOR includes parameters to simulate male or female growth. AALM.FOR was shown to
predict elimination kinetics of Pb from blood in male and female children when exposures were
reconstructed (Figure 3-16 to 3-17), and soft tissue-bone Pb relationships in males and females (Figure 3-
11).
Evaluation of relationship between plasma-whole blood Pb concentrations. The peer reviewers
suggested that the model should be evaluated for accurately predicting the plasma-blood Pb concentration
ratio. A meta-dataset of observations of plasma-blood Pb concentrations in children and adults was
assembled for evaluation of model performance. In all of these studies, methods were employed to
control for sample contamination, which is of particular importance in measurements of the low Pb levels
found in plasma. The dataset used in the evaluation included paired observations of plasma and whole
blood Pb concentration for 409 adults (Smith et al.. 2002; Bcrgdahl etal.. 1999; Bergdahl et al.. 1998;
Hernandez-Avila et al.. 1998; Bergdahl et al.. 1997; Schutzetal.. 1996). The relationship between
plasma and whole blood Pb concentrations predicted from AALM.FOR agreed with observations (Figure
3-13). Only one study provides similar data in children (Bergdahl et al.. 1999). Based on these data, the
plasma-blood relationships in children and adults do not appear to differ substantially.
Accounting for relative bioavailability (RBA) of ingested Pb. The peer reviewers suggested that RBA of
Pb in dust/soil needs to be included as part of the ingestion calculations. This has been included in
AALM.FOR. However, by making RBA an adjustment on the ingested dose, rather than the
gastrointestinal absorption fraction, the RBA adjustment will result in an underestimation of fecal Pb
excretion and a negative mass balance (excretion < intake) if RBA is <1 (see Sections 2.2.3). An error in
the Pb intake-excretion mass balance will not affect the simulation internal kinetics of Pb or body burdens
(e.g., blood or bone concentrations), although, it may be noteworthy for some research applications.
Further refinement of the model at some point in the future to make the RBA an adjustment to the
absorption fraction in the small intestine is discussed in Section 3.4.
Revaluation of model predictions of blood Pb kinetics in the Rabinowitz et al. (1976) study. The peer
reviewers suggested that the model should be revaluated with the Rabinowitz et al. (1976) data to ensure
that changes made to the model in creating ICRPv005.FOR did not degrade performance of the model to
accurately simulate these observations. AALM.FOR predicted blood Pb concentrations and the temporal
pattern of the rise and decline in blood Pb concentrations observed in the Rabinowitz et al. (1976)
subjects (Figure 3-10).
65
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1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Evaluation of model performance for Hattis data. The peer reviewers suggested that the model be
evaluated for predicting blood Pb concentrations in a cohort of workers described in Hattis (1981). These
data included blood Pb concentrations in workers measured at the date of hire and prior to and following a
nine-month strike. Although pre-hire exposures were unknown, it was possible to calibrate the post-hire
and pre-strike exposures to achieve agreement with blood Pb concentrations at the time of hire and just
prior to the strike, and then predict without further calibration the post-strike blood Pb. After calibration
to the blood Pb concentrations measured at time of hire and just prior to the strike (r2 = 1.0), AALM.FOR
predicted rates of decline in blood Pb concentration (pseudo first-order ti/2) for individual subjects and for
the group median that agreed with the observations (Table 3-4).
Evaluation of model performance for the Nie et al. data. The peer reviewers suggested that the model be
evaluated for predicting blood and bone Pb concentrations in a cohort of workers described in Nie et al.
(2005) including use of some unpublished Nie et al. data. These data were used in an analyses of an
implementation of the Leggett model developed by California EPA (CalEPA. 2013). There were no data
on actual exposures experienced by the workers in this cohort. As described in Section 3.3, the Nie et al.
data were reviewed and evaluated. Although attempts were made to reconstruct exposures so that blood
and bone Pb concentrations could be predicted and compared to observations, ultimately, it was
concluded that the data were not suitable for model evaluations because of the uncertainty in the
exposures that preceded the blood and bone Pb measurements and that occurred during the measurement
period.
Evaluation of model performance for intermittent exposures. Renovations of public and commercial
building renovations can result in elevated Pb exposures that may persist for several days to several
months. Therefore, assessment methods applied to renovation-related exposure scenarios must be able to
predict blood and bone Pb levels that might occur as a result of short-term or intermittent exposures to
children or adults. Several evaluations described in this report suggest that AALM.FOR can be expected
to reliably predict blood Pb kinetics associated with short-term or intermittent exposures. (1)
AALM.FOR predicted the rate of accrual and elimination of Pb from blood in adult subjects who were
exposed to Pb over periods of 2-6 months (Figure 3-10). (2) The model predicted the increase in blood
Pb that was observed in infants who were abruptly switched to a higher Pb level diet following
approximately 100 days of ingesting a lower Pb level diet (Figure 3-14). (3) The model predicted the rate
of decline in blood Pb that was observed following interventions to decrease elevated exposures that
occurred over periods of 200 - 400 days (Figures 3-16 to 3-18). (4) The model predicted the decrease in
blood Pb concentrations that occurred in Pb workers following a nine-month strike (Table 3-4).
3.5.3. Summary
Collectively, the updates made to ICRPv005.FORto create AALM.FOR and evaluations of AALM.FOR
provide increased confidence in applying a biokinetics modeling approach to support estimations of Pb
body burdens following a variety of potential Pb exposure scenarios. AALM.FOR offers an improved
modeling tool for predicting exposure-body burden relationships for intermittent as well as chronic Pb
exposures.
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1 TABLE 3-1. CHANGES MADE TO ICRPV004.FOR TO CREATE ICRPV005.FOR
ICRPv004.FORa
ICRPv005.FOR
Output/Functionality Affected
Adult kidney mass
Age-dependent kidney mass
based on ICRP (2002)
Age-dependent kidney Pb
concentrations
Adult bone mass
Age-dependent bone mass based
on ICRP (2002)
Age-dependent bone Pb
concentrations
Constant hematocrit
Age-dependent hematocrit based
on ICRP (2002)
Age-dependent RBC and plasma
volumes
Constant trabecular bone
fraction (20%)
Age-dependent trabecular bone
fraction from Table M-l of U.S.
EPA (2014a)
Age-dependent cortical and
trabecular bone Pb
concentrations
RBC Pb saturation threshold (25
(ig/dL blood) and maximum
(350 (ig/dL RBC)
RBC Pb saturation threshold (0
(ig/dL blood) and maximum
(270 (ig/dL RBC)
Pb uptake- blood Pb
relationship
Transfer rate from (d1) plasma
to RBC birth-10 years:
• birth: 0.462
• 0.27 y: 0.462
• 1 y: 0.462
• 5 y: 0.277
• lOy: 0.139
Transfer rate from (d1) plasma
to RBC birth-10 years:
• birth: 0.562
• 0.27 y: 0.562
• 1 y: 0.562
• 5 y: 0.277
• 10 y: 0.277
Plasma- RBC Pb relationship in
children
Depostion fraction from RBC to
diffusible plasma (0.24)
Deposition fraction from RBC
to diffusible plasma:
• birth: 0.20
• 0.27 y: 0.20
• 1 y: 0.20
• 5 y: 0.21
• 10 y: 0.22
• >15 y: 0.22
Plasma- RBC Pb relationship in
children
Transfer rate (d1) from non-
exchangeable cortical bone to
diffusible plasma:
• birth: 0.00822
• 0.27 y: 0.00822
• 1 y: 0.00288
• 5 y: 0.00154
• 10 y: 0.00089
• 15 y: 0.000512
• >25 y: 0.000082
Transfer rate (d1) from non-
exchangeable cortical bone to
diffusible plasma:
• birth: 0.0102
• 0.27 y: 0.00822
• 1 y: 0.00288
• 5 y: 0.00154
• 10 y: 0.00089
• 15 y: 0.000512
• 18 y: 0.000370
• 24 y: 0.000082
• >30 y: 0.000041
Bone to plasma Pb kinetics, in
late adolescence (age 15-19
years) and adults (>30 years)
67
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
ICRPv004.FORa
ICRPv005.FOR
Output/Functionality Affected
Transfer rate (d1) from non-
Transfer rate (d1) from non-
Bone-to-plasma Pb transfer
exchangeable trabecular bone to
exchangeable trabecular bone to
kinetics (age 15-18 years),
diffusible plasma:
diffusible plasma:
adults (>25 years)
• birth: 0.00822
• birth
: 0.0102
• 0.27 y: 0.00822
• 0.27
y: 0.00822
• 1 y: 0.00288
• ly:
0.00288
• 5 y: 0.00181
• 5 y:
0.00181
• 10 y: 0.00132
• lOy
0.00132
• 15 y: 0.000956
• 15 y
0.000956
• >25 y: 0.000493
• 18 y
0.000781
• 24 y
0.000493
• 30 y
0.000247
• 40 y
0.000247
• 45 y
0.000274
• 55 y
0.000301
• 65 y
0.000329
• 75 y
0.000356
Based on (U.S. EPA. 2014a. b).
aICRPv004.FOR is an implementation of the Leggett (1993) model.
1
2
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1 TABLE 3-2. DIFFERENCES IN ICRPV005.FOR AND AALM.CLS BIOKINETICS
ICRPv005.FOR
AALM.FOR
Output/Functionality
Affected
Age-dependent blood and plasma
volumes based on ICRP (2002)
Age-dependent blood and plasma volumes
based on O'Flahertv (1995. 1993)
Age-dependent blood Pb
concentration
Age-dependent bone mass based
on ICRP (2002)
Age-dependent bone mass based on
O'Flahertv (1995. 1993)
Age-dependent cortical
and trabecular bone Pb
concentration
Age-dependent trabecular bone
fraction based from Table M-l of
U.S. EPA (2014a)
Age-dependent cortical and trabecular bone
masses based on O'Flahertv (1995. 1993)
Age-dependent cortical
and trabecular bone Pb
concentration
Age-dependent kidney mass
based on ICRP (2002)
Age-dependent kidney mass based on
O'Flahertv (1995. 1993)
Age-dependent kidney Pb
concentration
Adult liver mass
Age-dependent liver mass based on
O'Flahertv (1995. 1993)
Age-dependent liver Pb
concentration
Age-dependent absorption
fraction (/' /):
• birth: 0.45
• 0.27 y: 0.45
• 1 y: 0.30
• 5 y: 0.30
• 10 y: 0.30
• 15 y: 0.30
• >25 y: 0.15
Age-dependent absorption fraction (/'/):
• birth: 0.39
• 0.27 y: 0.39
• 1 y: 0.38
• 5 y: 0.17
• >10 y: 0.12
Absorption fraction for
ingested Pb
Absorption fraction for ingested
Pb not adjusted for RBA
Media-specific ingestion intakes adjusted
for RBA
Intake-fecal mass balance
RBC Pb saturation threshold: 0
(ig/dL blood)
Maximum: 270 (ig/dL RBC
RBC Pb saturation threshold: 20 (ig/dL
blood)
Maximum: 350 (ig/dL RBC)
Pb uptake-blood Pb
relationship
Transfer rate (d1) from non-
exchangeable cortical bone to
diffusible plasma (RCORT):
• birth: 0.0102
• 0.27 y: 0.00822
• 1 y: 0.00288
• 5 y: 0.00154
• 10 y: 0.00089
• 15 y: 0.00512
• >25 y: 0.0000822
Transfer rate (d1) from non-exchangeable
cortical bone to diffusible plasma (RCORT):
• birth: 0.0204
• 0.27 y: 0.01644
• 1 y: 0.00576
• 5 y: 0.00308
• 10 y: 0.00178
• 15 y: 0.00124
• >25 y: 0.0001644
Shorter retention of Pb in
cortical bone
Transfer rate (d1) from non-
exchangeable trabecular bone to
diffusible plasma (RTRAB):
• birth: 0.0102
Transfer rate (d1) from non-exchangeable
trabecular bone to diffusible plasma
(RTRAB):
• birth: 0.0204
Shorter retention of Pb on
trabecular bone
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ICRPv005.FOR
AALM.FOR
Output/Functionality
Affected
• 0.27 y: 0.00822
• 0.27
y: 0.01644
• 1 y: 0.00288
• ly:
0.00576
• 5 y: 0.00181
• 5 y:
0.00362
• 10 y: 0.00132
• lOy
0.00264
• 15 y: 0.000956
• 15 y
0.001912
• >25 y: 0.000493
• >25 y: 0.000986
Fraction of total transfer from the
Fraction of total transfer from the
Longer retention of Pb in
exchangeable bone directed to
exchangeable bone directed to non-
cortical and trabecular
non-exchangeable bone
exchangeable bone (FLONG): 0.6
bone
(FLONG): 0.2
Transfer rate (d1) from liver
Transfer rate (d1) from liver compartment 2
Longer retention of Pb in
compartment 2 to diffusible
to diffusible plasma (RLVR2):
liver
plasma (RLVR2):
• birth
: 0.000693
• birth: 0.00693
• 0.27
y: 0.000693
• 0.27 y: 0.00693
• ly:
0.000693
• 1 y: 0.00693
• 5 y:
0.001386
• 5 y: 0.00693
• lOy
0.000570
• 10 y: 0.00190
• 15 y
0.000570
• 15 y: 0.00190
• 25 y
0.000570
• >25 y: 0.00190
• 30 y
0.001425
• 40 y
0.003040
• 60 y
0.003420
• 90 y
0.00380
Transfer rate (d1) from kidney
Transfer rate (d1) from kidney compartment
Longer retention of Pb in
compartment 2 to diffusible
2 to diffusible plasma (RKDN2):
kidney
plasma (RKDN2):
• birth
: 0.000693
• birth: 0.00693
• 0.27
y: 0.000693
• 0.27 y: 0.00693
• ly:
0.000693
• 1 y: 0.00693
• 5 y:
0.000693
• 5 y: 0.00693
• lOy
0.000190
• 10 y: 0.00190
• 15 y
0.000190
• 15 y: 0.00190
• 25 y
0.000190
• >25 y: 0.00190
• 30 y
0.000950
• >40
y: 0.00190
Deposition fraction from
Transfer rate (d1) from kidney compartment
Faster transfer from
diffusible plasma to kidney
2 to diffusible plasma (TKDN2): 0.0004
diffusible plasma to
compartment 2 (TKDN2): 0.0002
kidney at all ages
Deposition fraction from
Deposition fraction from diffusible plasma
Faster transfer from
diffusible plasma to kidney
to kidney compartment 1 (TKDN1): 0.025
diffusible plasma to
compartment 1 (TKDN1): 0.02
kidney at all ages
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
ICRPv005.FOR
AALM.FOR
Output/Functionality
Affected
Deposition fraction from
diffusible plasma to urine
(TOURIN): 0.015
Deposition fraction from diffusible plasma
to urine (TOURIN): 0
All urinary excretion
occurs from kidney
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1 TABLE 3-3. DIFFERENCES BETWEEN AALM.FOR AND AALM.CSL
AALM.FOR
AALM.CSL
Output/Functionality Affected
Numerical integration time steps
controlled by user input
Numerical integration time steps
controlled bv user Gear (1971)
algorithm
Numerical integration error
Media-specific ingestion intakes
adjusted for RBA
GI tract absorption fraction
adjusted for media-specific RBA
Fecal Pb mass balance
4-compartment RT model that
requires user inputs for
deposition rate ((ig/day)
12-compartment model that
accepts user inputs for air
concentration, particle size and
absorption class
Simulations of Pb deposition
and absorption of inhaled Pb
2
3
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1 TABLE 3-4. BLOOD LEAD PREDICTIONS FROM THE AALM FOR 57 SUBJECTS IN THE
2 HATTIS DATASET
Hattis
ICRPv005
AALM.CSL
AALM.FOR
Mean
SD
Mean
SD
Mean
SD
Mean
SD
BLL at hire
1-ig/dL
20
7
20
7
20
7
20
7
BLL at strike
1-ig/dL
48
11
49
13
48
11
48
11
BLL after strike
1-ig/dL
33
9
23
7
31
7
31
7
BLL half-time
days
1027
1433
312
184
553
370
523
314
BLL half-time delta
-0.37
0.59
-0.05
0.54
-0.08
0.52
Hattis
ICRPv005
AALM.CSL
AALM.FOR
GM
GSD
GM
GSD
GM
GSD
GM
GSD
BLL half-time
days
633
2.4
274
1.6
483
1.6
465
1.6
3
4
5
Hattis ICRPv005.FOR AALM.CSL AALM.FOR
Mea SD Mean SD Mean SD Mean SD
n
BLL at hire (j^ig/dL)
20
7
20
7
20
7
20
7
BLL at strike (|ig/dL)
48
11
49
13
48
11
48
11
BLL after strike (|ig/dL)
33
9
23
7
31
7
31
7
BLL half-time (d)
1027
1433
312
184
553
370
523
314
BLL half-time delta (d)
-0.37
0.59
-0.05
0.54
-0.08
0.52
Hattis
ICRPv005.FOR
AALM.CSL
AALM.FOR
GM
GSD
GM
GSD
GM
GSD
GM
GSD
BLL half-time (d)
633
2.4
274
1.6
483
1.6
465
1.6
6
7
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1 TABLE 3-5. COMPARISON OF PREDICTED AND OBSERVED PLASMA PB/BONE PB
2 SLOPES
Predicted Observed
Model
Study
Bone
Slope
Slope
SE
95%CL
Residual
AALM
CA96
Cortical
0.037
0.052
0.013
0.027, 0.077
-1.16
AALM
CA96
Trabecular
0.040
0.041
0.007
0.027, 0.054
-0.16
AALM
HE98
Cortical
0.037
0.036
0.011
0.014, 0.058
0.12
AALM
HE98
Trabecular
0.040
0.025
0.004
0.017, 0.033
3.67
CA96, Cake et al. (1996); HE98, Hernandez-Avila et al. (1998)
3
4 TABLE 3-6. COMPARISON OF ALM AND AALM PREDICTIONS OF BLOOD PB
5 CONCENTRATIONS IN ADULTS
Parameter
Description
Units
ALM
AALM
PbS
Soil lead concentration
f-ig/g or ppm
1000
1000
BKSF
Biokinetic Slope Factor
(ig/dL per (ig/day
0.4
NA
PbBo
Baseline Blood Pb
1-ig/dL
1.5
1.5
IRs
Soil Ingestion Rate
g/day
0.050
0.05
AFs, d
Absorption Fraction
--
0.12
0.072
EFs, d
Exposure Frequency
days/yr
219
219
ATs, d
Averaging Time
days/yr
365
365
PbBadult
Blood Pb Concentration
1-ig/dL
2.9
2.9
ALM, Adult Lead Methodology. See Figure 3-20 for AALM input parameter values.
6
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1 FIGURE 3-1. GASTROINTESTINAL ABSORPTION OF PB IN THE (LEGGETT, 1993)
2 MODEL AND AALM, OPTIMIZED TO (RYU ET AL., 1983).
0.6
0.5
- • - Leggett AALM
0.4
0.3
0.2
0.1
0.0
0
10
20
30
40
50
3 Age (year)
4
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 3-2. COMPARISON OF ACCRUAL AND ELIMINATION KINETICS OF BLOOD PB
2 IN CHILDREN (A) AND ADULTS (B) PREDICTED FROM AALM.CSL, AALM.FOR AND
3 ICRPV005.FOR.
6.0
6.0
AALM.CSL
AALM.CSL
5.0
- -AALM.FOR
5.0
- -AALM.FOR
• - ICRPvOOS.FOR
ICRPvOOS.FOR
-4.0
4.0
J3 3.0
3.0
10 2.0
2.0
1.0
1.0
0.0
0.0
0
1000
2000
3000
4000
^ Age (day) Age (year)
5 The simulated Pb exposure was a constant baseline intake (5 (ig/day) beginning at birth. In the child
6 simulation, a period of elevated intake of (40 (ig/day) began on day 720 and ended on day 1300. In the
7 adult simulation, a period of elevated intake of (105 (ig/day) began at age 25 years and ended at age 40
8 years.
9
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 3-3. COMPARISON OF ACCRUAL AND ELIMINATION KINETICS OF CORTICAL
2 BONE (A, B) AND TRABECULAR BONE (C, D) PB IN CHILDREN (A, C) AND ADULTS (B, D)
3 PREDICTED FROM AALM.CSL, AALM.FOR AND ICRPV005.FOR.
ICRPV005.FOR
ICRPV005.FOR
ICRPV005.FOR
ICRPV005.FOR
5 The simulated Pb exposure was a constant baseline intake (5 (ig/day) beginning at birth. In the child
6 simulation, a period of elevated intake of (40 (ig/day) began on day 720 and ended on day 1300. In the
7 adult simulation, a period of elevated intake of (105 (ig/day) began at age 25 years and ended at age 40
8 years.
9
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1 FIGURE 3-4. COMPARISON OF RELATIONSHIPS BETWEEN PB INTAKE (G/DAY) AND
2 BLOOD PB IN CHILDREN (A) AND ADULTS (B) PREDICTED FROM AALM.CSL,
3 AALM.FOR AND ICRPV005.FOR.
50
50
Age 2 years
Age 30 years
AALM.CSL
AALM.CSL
40
40
- -AALM.FOR
- -AALM.FOR
¦ - ICRPV005.FOR
• - ICRPV005.FOR
30
-Q
CI-
TS
| 20
CO
o 20
10
0
50
100
150
200
0
200
400
600
800
1000
Pb Intake (ng/day) Pb Intake (jig/day)
78
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 3-5. COMPARISON OF RELATIONSHIPS BETWEEN PB INTAKE (G/DAY) AND
2 CORTICAL (A, B) AND TRABECULAR (C, D) BONE PB IN CHILDREN (A, C) AND ADULTS
3 (B, D) PREDICTED FROM AALM.CSL, AALM.FOR AND ICRPV005.FOR.
50
40
Age 2 years
AALM.CSL
Age 30 years
AALM.CSL
— — AALM.FOR
- = AALM.FOR
30
¦ - ICRPv005.FOR
• - ICRPV005.FOR
.~ 30
5 20
50
100
Pb Intake (|ig/day)
150
200
0
200
400
600
Pb Intake (ng/day)
800
1000
50
30
Age 2 years
AALM.CSL
- - -AALM.FOR
Age 30 years
AALM.CSL
- - - AALM.FOR
40
• - ICRPV005.FOR
• - ICRPv005.FOR
2 20
a- 30
50
100
Pb Intake (ng/day)
150
200
0
200
400
600
Pb Intake (ng/day)
800
1000
4
5
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1 FIGURE 3-6. AALM.CLS SIMULATION OF OBSERVATIONS FOR HATTIS COHORT
2 SUBJECT 5.
35
• Subject 5
Work
30
25
Baseline
2P 20
15
10
5
0
0
5000
10000
15000
20000
Age (day)
3
Age
AALM
BLL
(ug/dL)
Observed
BLL
(Ug/dL)
Ratio
(Pred./Obs.)
7300
days
10.6
11.0
0.96
10384
days
30.6
30.5
1.00
10654
days
18.5
17.0
1.09
k
day-1
0.00187
0.00216
0.86
tl/2
day
372
320
1.16
4
5 The subject (unknown age and sex) experience an occupational exposure that was interrupted by 9-month
6 strike. Pre-strike exposures were reconstructed as a constant Pb ingestion ((.ig/kg/day) that resulted in a
7 pre-hire blood Pb that was within 1 (ig/dL of the reported pre-hire blood Pb (11 (ig/dL) for the subject.
8 Pre-strike exposures were reconstructed as a constant Pb ingestion ((.ig/day). for the reported pre-strike
9 employment durations (3084 days), that resulted in a pre-strike blood Pb that was within 1 (ig/dL of the
10 reported pre-strike blood Pb (30.5 (ig/dL) for the subject. During the 9-month strike (assumed to be 270
11 days), exposure reverted to the per/kg baseline level. The elimination half-time from blood was
12 calculated from pre-strike and post-strike blood Pb concentrations, assuming a first-order elimination.
13 The elimination half-time predicted from the observed blood Pb data is 320 days. The half-time predicted
14 from the AALM.CLS is 372 days.
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1 FIGURE 3-7. COMPARISON OF ICRPV005.FOR (TOP) AND AALM.FOR (BOTTOM)
2 PREDICTIONS AND OBSERVED BLOOD PB CONCENTRATIONS AFTER THE STRIKE
3 FOR 57 SUBJECTS IN THE HATTIS COHORT.
4
70
60
50
.2 40
+¦»
¦M
05
1 30
20
10
0
0 10 20 30 40 50 60 70
ICRP V005.FOR
Post-strike BLL
•
y = 0.46x +22.17
R2 = 0.11
• •• #
•
•
70
60
50
.2 40
4-»
¦M
05
1 30
20
10
0
0 10 20 30 40 50 60 70
AALM.FOR
5
Post-strike BLL
y = 0.91x + 4.56
R2 = 0.47
••• •
• A** %
*
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 3-8. AALM.CSL, AALM.FOR AND ICRPV005.FOR SIMULATIONS OF BLOOD PB
2 ELIMINATION HALF-TIME FOR 57 SUBJECTS IN THE HATTIS COHORT.
l.E+04
3
4
5
6
7
l.E+02
1.0
0.8
= 06
c
01
I 0.4
Hattis
• Hattis median
•AALM.CSL
•ICRPV005.FOR
o Hattis
• AALM.CSL
~ ICRPv005.FOR
l.E+04 q
O
g O Hattis
O Hattis median
| —•—AALM.CSL
^ —A—AALM.FOR
l.E+03 :
l.E+02 -
3
1.0
0.8
0.6
o. 0.4
0.E+00 2.E+03 4.E+03 6.E+03 8.E+03 l.E+04
Blood half-time (days)
o Hattis
• AALM,CSL
A AALM.FOR
0.E+00 2.E+03 4.E+03 6.E+03 8.E+03 l.E+04
Blood half-time (days)
Panel A compares the half-times predicted for the observations with medians predicted from the
AALM.CSL and ICRPv005.FOR. Panel C displays the same data as percentiles of the half-times
predicted from the observations for AALM.CSL and ICRPv005.FOR. Panels B and D display the
corresponding plots comparing AALM.CSL and AALM.FOR. Half-times were calculated as follows:
half-time = ln(2)/[ln(pre-strike/post-strike)/270].
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 3-9. AALM.CSL AND AALM.FOR SIMULATIONS OF ELIMINATION KINETICS OF
2 PB FROM BLOOD (A) AND BONE (B).
NI91
AALM.CSL
AALM.FOR
q 0.6
o 0.4
5 10 15 20
Years from End of Exposure
1.2
1.0
o 0.8
0.6
c
o
CO
(5 0.4
o
u 0.2
0.0
B
Model T1/2 = 15.5 yr
NI91
AALM.CSL
- - AALM.FOR
10 15 20
Years from End of Exposure
25
4 Dotted lines show the elimination from based on the median and upper and lower 95% confidence limits
5 of the tri-exponential model retired Pb workers (n = 14, median age 60 years at time of retirement)
6 reported in Nilsson et al. (1991).
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1 FIGURE 3-10. AALM.CSL AND AALM.FOR SIMULATIONS OF BLOOD PB
2 CONCENTRATIONS IN INDIVIDUALS WHO RECEIVED INGESTION DOSES OF [202PB]-
3 NITRATE (RABINOWITZ ET AL.. 1976).
10.0
• Subject A
AALM.CSL
AALM.FOR
_i
¦o
J2
Q_
¦a
o
o
CQ
•m
o.o
0
48 96 144 192 240 288 336 384 432
6.0
• Subject B
AALM.CSL
AALM.FOR
••
IT 4.0
0.0
0 24 48 72 96 120 144 168 192 216 240
Time (day) Time (day)
1.2
6.0
• Subject E
AALM.CSL
AALM.FOR
• Subject D
AALM.CSL
AALM.FOR
j 0.8
••
¦a 0.6
¦Q 3.0
0.0
0.0
24
48
Time (day)
72
96
120
0 24 48 72 96 120 144 168 192 216 240
Time (day)
4
5 Subject A received 204 (ig/day for 104 days, Subject B received 185 (ig/day for 124 days, Subject D
6 received 105 (ig/day for 83 days, and Subject E received 99 (ig/day for on days 1-8 and days 42-51.
7 Estimated absorption fractions were 8.5% for Subject A, 6.5% for Subject B, 10.9% for Subject D and
8 9.1% for Subject E.
9
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FIGURE 3-11. AALM AND LFM SIMULATIONS OF POST-MORTEM SOFT TISSUE/TIBIA
PB RATIOS.
0.30
• Male
¦ Female
0.25
AALM.FOR Male
0.20
AALM.FOR Female
0.15
0.10
0.05
0.00
0
20
40
60
80
100
0.30
• Male
¦ Female
0.25
AALM.CSL Male
AALM.CSL Female
^ 0.20
P3
£
re
2 0.15
f/m
<5
~ 0.10
0.05
0.00
0
20
40
60
80
100
0.16
• Male
¦ Female
0.14
•—AALM.CSL Female
0.12
AALM.CSL Male
0.10
0.08
c 0.06
0.04
0.02
0.00
0.16
• Male
0.14
¦ Female
¦/
—AALM.FOR Female
0.12
AALM.FOR Male
0.10
0.08
0.06
0.04
0.02
0.00
0
20
40
60
80
100
Shown are means for 9 (liver, A and B) and 8 (kidney, C and D) individual predicted from the
AALM.CSL (A, C) or AALM.FOR (B, D), based on Barry (1975).
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1 FIGURE 3-12. AALM.CSL AND AALM.FOR SIMULATIONS OF PLASMA PB/BONE PB
2 RATIO IN ADULTS.
3
4
5
01 2
Q- a;
_o c
2 E
Pi CD
£ §
o
CD
Q_ -1-
™
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 3-13. SIMULATION OF WHOLE BLOOD AND PLASMA PB IN ADULTS.
70
60
50
co
• Observations - Adults
O Observations - Children
AALM.CSL
AALM.FOR
20
10
0
0.00
0.10
0.20 0.30
Plasma Pb (|-ig/dl)
0.40
0.50
3 Combined data for adult individuals (N = 406) from all studies were quantized into ranges of plasma Pb;
4 shown are mean and standard deviations for ranges (Smith et al.. 2002; Bergdahl et al.. 1999; Bergdahl et
5 al.. 1998; Hernandez-Avila et al.. 1998; Bergdahl et al.. 1997; Schutzetal.. 1996). The r2 for predictions
6 and observatiosn was 0.99. Data for children (n = 29) are are overlayed on the adult data (Bergdahl et al..
7 1999).
8
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1 FIGURE 3-14. AALM.CSL (A) AND AALM.FOR (B) SIMULATIONS OF FORMULA-FED
2 INFANTS FROM (RYU ET AL., 1983).
A
20
• RY83
AALM.CSL
16
5 12
3.
.Q
0.
¦c
o
o
m
0
50
100
150
200
20
• RY83
AALM.FOR
16
12
8
4
0
0
50
100
150
200
Age (day) Age (day)
3
4
5 Data (RY83) are from infants fed formula from cartons (12-20 (ig/day) from age 8-196 days (closed
6 circles, n=25) and then a subset (closed squares, n = 7) that were switched to formula from cans at age
7 112 days (60-63 (ig/day). Solid lines show simulations of the mean Pb intakes; dotted lines show
8 simulations of ±1 SD of mean intakes.
9
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1 FIGURE 3-15. AALM.CSL AND AALM.FOR SIMULATIONS OF FORMULA-FED INFANTS.
60
30
20
• SH86
AALM.CSL
AALM.FOR
0
100
200
300
400
Pb Intake (|jg/day)
2
3 Data are for 131 infants, age 91 days from Sherlock and Ouinn (1986).
4
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FIGURE 3-16. AALM SIMULATION OF SUBJECT 48490 (FEMALE).
70
70
60
_ 50
T3
40
1
1
%
•
m
• 48490
•
•
48490
AALM exposure
AALM baseline
T3
1
-Q
a.
60
50
40
•
-Q
a.
-a 30
<
*•>
o
o
CO
30
•
•
•
o
CO
20
10
0
•
*
0)
>
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1 FIGURE 3-17. AALM SIMULATION OF SUBJECT 3030 (MALE).
45
40
35
ZJ 30
T3
j£ 25
-Q
S 20
o
o
co 15
10
5
0
g* • 3030
j ^ -—AALM exposure
|| AALM baseline
U
\-
a
2000 3000 4000
Age (day)
40
35
^ 30
jT 25
a.
T3
"S 15
>
3030
•
y'mm
y = 0.89x + 2.30
R2 = 0.90
10 20 30 40
Predicted Blood Pb (ng/dL)
3 Baseline (15 (ig/day) was set to achieve a 6-month BLL of approximately 5 (ig/dL, consistent with data
4 for other subjects. Exposure to 11,000 ppm dust Pb (RBA = 0.6) began on age day 1000 and continued to
5 age day 1400. Data provided by ATSDR.
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1 FIGURE 3-18. AALM SIMULATION OF SUBJECT 87350 (FEMALE).
2
3
4
5
50
45
if
40
»'j
_ 35
1
l
T3
"S3 30
>
.~ 25
Q.
V
o 20
o
£•
QQ
15
•
10
5
0
• 87350
--—AALM exposure
AALM baseline
v?
1000
*
2000 3000 4000
Age (day)
5000
6000
50
45
IT 40
T3
"eS 35
3
£ 30
¦C
§ 25
CO
-O 20
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 3-19. COMPARISON OF BLOOD PB PREDICTIONS OF AALM AND IEUBK
2 MODEL.
2.0
AALM
• IEUBK Model
1.5
_i
-a
60
3
X! 1.0
Q.
-a
o
_o
CO
0.5
0.0
0
2
4
6
8
10
Age (year)
4 Maternal blood Pb was assumed to be 1 (ig/dL. Exposure was to Pb in soil (RBA = 0.6) at a constant
5 intake (10 (ig/day). Absorption parameters were: AF1 Cl=0.40 (AF1=0.39 at birth), AF1 C2=0.28
6 (AF1=0.12 at age >10 years). The average AF1 for age 0-7 years was 0.26.
7
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FIGURE 3-20. COMPARISON OF BLOOD PB PREDICTIONS OF AALM AND ALM.
4.0
3.0
_i
-a
60
3
ji 2.0
Q.
-a
o
_o
CO
— AALM Baseline
AALM Soil
— ALM Baseline
— ALM Soil
1.0
0.0
0
20
40
60
80
Age (year)
AALM input parameters:
OTHER Baseline Pb=6 (ig/day
OTHER Pulse Pb=12 (ig/day
OTHER Pulse start= 6205 day (17 years)
OTHER RBA = 1
SOIL baseline Pn = 0 (ig/day
SOIL Pulse Pb=600 jig/g (1000*219/365)
SOIL IRs = 0.05 at age >15 years
SOIL RBA = 0.6
AF1 Cl=0.40 (AF1=0.39 at birth), AF1 C2=0.28 (AF1=0.12 at age >10 years)
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CHAPTER 4. EVALUATION AND DEVELOPMENT OF AALM.CLS
4.1. INTRODUCTION
This chapter summarizes developments in the AALM that were initiated in early 2013 by EPA's Office of
Research and Development (ORD)/National Center for Environmental Assessment (NCEA). Six major
objectives have been realized in this most recent effort, and are described in this report including: (1)
recoding of the AALM biokinetics models from Visual C to the more robust kinetic model development
software, Advance Continuous Simulation Language, ACSL® (acslX); (2) addition of a user friendly,
flexible, and transparent exposure model interface implemented in Microsoft Excel®(Excel); (3)
capability to run either the Leggett (AALM-LG) or O'Flaherty (AALM-OF) biokinetics models from the
same exposure model interface, and with the same exposure and absorption conditions; (4) a more
realistic RT model representation in both the Leggett and O'Flaherty biokinetics models compared with
earlier versions; (5) accessible and transparent output for easy comparison of the predictions from the
Leggett and O'Flaherty biokinetics models; and (6) an evaluation and optimization of the Leggett and
O'Flaherty biokinetics models against a common set of observations that lead to the version of the
AALM in acslX (AALM.CLS v.4.2, July 2015).
Section 4.2 provides a brief overview the functional structure of AALM.CLS. Section 4.3 compares the
structures of the two biokinetics models contained in the AALM.CLS (AALM-LG, AALM-OF). Section
4.4 describes the outcomes of model runs that compare predictions of blood and tissue Pb levels obtained
from the AALM-LG and AALM-OF. Section 4.5 presents the results of sensitivity analyses coefficients
(SSCs) conducted from the AALM.CLS biokinetics models. Section 4.6 presents the conclusions from
the model comparison. Section 4.7 presents results of an empirical evaluation and optimization of the
AALM-LG and AALM-OF. Section 4.8 provides conclusions and discusses implications of performance
of the optimized models for model applications. Section 4.9 discusses differences between the
AALM.CLS model output and the IEUBK model for similar exposures, identifies AALM model
parameter changes that resolve the differences, and provides a rationale for changes in the parameter
values. Section 4.10 outlines the next steps to be taken, and the data needed to further develop and
evaluate the AALM.CLS.
4.2. OVERVIEW OF AALM.CLS STRUCTURE
The AALM predicts blood and tissue Pb masses (|_ig) and concentrations (jj.g/g) resulting from exposures
to Pb in air, drinking water, surface dust, food, or miscellaneous Pb ingestion pathways. The AALM
exposure module allows the user to simulate multi-pathway exposures that are constant or that vary in
time increments as small as one day; and that occur at any age from birth to 90 years. The user can select
to run a Pb biokinetics simulation based on either the Leggett (AALM-LG) or O'Flaherty (AALM-OF)
biokinetics models. The ICRP Human Respiratory Tract Model (HRTM: ICRP. 1994) deposition and
absorption parameters are used in both the AALM-LG and AALM-OF. The user can select
gastrointestinal absorption fractions for any age values as well as values for relative bioavailability (RBA)
of Pb from all ingestion pathways.
The AALM software architecture consists of three components: (1) a macro-enabled Excel workbook
(INPUT&OUTPUT.xlsm) that implements the exposure model and provides user access to all exposure
and biokinetics parameters in the AALM; (2) an acslX program that implements a Leggett-based
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
biokinetics model (AALM-LG.csl); and (3) an acslX program that implements an O'Flaherty-based
biokinetics model (AALM-OF.csl).
The data flow for AALM simulations is shown in Figure 4-1. The AALM simulation is implemented in
acslX with AALM_LG.csl (or AALM_OF.csl). Input parameter values are selected by the user in a
macro-enabled INPUT&OUTPUT Excel file (.xlsm). Macros in the INPUT&OUTPUT Excel file pass the
input parameter values to a comma-delimited (CSV) text file (INPUT.DAT). Data in INPUT.DAT are
imported into the AALM acslX program with acslX m-file scripts. Output variables from the simulation
are passed from acslX to a CSV file (OUTPUT.DAT) and are read into the INPUT&OUTPUT Excel file
with Excel macros.
AALM inputs and outputs are controlled and recorded in the INPUT&OUTPUT.xlsm workbook. This
workbook has several functions: (1) allows setting of input parameter values for AALM simulations; (2)
macros in this workbook are used to pass data to and from acslX; (3) allows plotting of AALM output
data; and (4) provides a complete record of input values and results of each AALM simulation.
Worksheets in INPUT&OUTPUT.xlsm allow the user to set exposure scenarios for Pb in air (Air), surface
dust, (Dust), drinking water (Water), food (Food) and/or other ingestion intakes (Other). Exposures can
be discrete (i.e., a series of exposures at selected ages), and/or pulsed in a repeating frequency (e.g., 2
days/week for 3 months/year, for a selected age range). The AALM uses inputs from all exposure media
when it creates biokinetics simulations. This allows construction of complex multi-pathway exposure
scenarios having varying temporal patterns. Worksheets inlNPUT&OUTPUT.xlsm also allow the userto
set values for parameters that control Pb absorption and relative bioavailability in each medium (RBA),
and biokinetics (Lung, Systemic, Sex). All settings are recorded in the INPUT&OUTPUT.xlsm workbook
and can be recalled to re-run the simulation.
The two biokinetics models in the AALM have been modified from the originally reported Leggett (1993)
and O'Flahertv (1995. 1993) models. The important modifications include: (1) removal of all exposure
components (moved to the Excel implementation); (2) implementation of a simplified version of the
ICRP HRTM (ICRP. 1994) in both biokinetics models; (3) implementation of the O'Flaherty model
growth algorithms in both biokinetics models to enable output of Pb concentrations in tissues in both
models, and to unify blood and tissue volumes; and (4) implementation of relative bioavailability factors
for ingested Pb from each exposure medium.
4.3. COMPARISON OF STRUCTURES OF AALM-LG AND AALM-OF BIOKINETICS
MODELS
The AALM has two systemic biokinetics modules, one that is based on the Leggett (1993) model
(AALM-LG) and the other based on the O'Flahertv (1995. 1993) model (AALM-OF). Figures 4-2 and 4-3
show the structures of both models. Table 4-1 summarizes some of the major differences between the two
modules. The most important difference is the way each model simulates Pb kinetics in bone. Both
models represent kinetics of Pb in bone that are influenced by changes in the rates of bone turnover (bone
formation and resorption). In general, the major features of bone Pb kinetics in both models are as
follows: (1) relatively rapid transfers of Pb between plasma and bone forming surfaces; (2) increased
bone Pb uptake during periods of bone growth; (3) incorporation of Pb into bone matrix and release of Pb
from bone matrix during bone resorption; (4) maturation of bone associated with lower rates of bone
turnover and related decreased mobility of Pb in bone matrix; and (5) more rapid turnover of trabecular
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bone Pb, relative to mature cortical bone. However, these processes are parameterized very differently in
the two models.
AALM-LG simulates bone as a multi (6)-compartment system (see Figure 4-4) consisting of 3 cortical
and 3 trabecular compartments that are distinguished by different Pb transfer rates: (1) relatively rapid
exchange of Pb between diffusible plasma and surfaces of cortical and trabecular bone; (2) slower
exchange of Pb at bone surfaces with an exchangeable Pb pool in bone volume; and (3) slow transfer of a
portion of Pb in bone volume to a non-exchangeable pool that is released from bone to diffusible plasma
only when bone is resorbed. Bone growth and maturation are simulated by age-dependent adjustments in
rate coefficients for Pb transfers from plasma-to-bone surfaces, and from bone matrix to plasma. This
approach simulates outcomes of the bone formation and resorption with bone Pb kinetics parameters,
rather than simulating the underlying physiology of bone formation and resorption directly with
parameters that govern formation and resorption.
AALM-OF simulates bone formation, resorption, and maturation of bone explicitly, and links these
processes to uptake and release of Pb from bone (see Figure 4-5). In AALM-OF, bone turnover in cortical
and trabecular bone is simulated with parameters that govern age-dependent bone formation and
resorption of bone. Two phases of bone turnover are simulated. In juvenile bone, formation and resorption
rates in cortical and trabecular bone are relatively high (high bone turnover) and formation dominates,
resulting in bone growth, which ceases at age 25 years. In mature bone, formation and resorption rates are
slower and bone formation rate equals resorption rate, resulting in remodeling, but no net growth of bone.
Transfers of Pb into and out of trabecular bone are governed by age-dependent rates of bone formation
and resorption, respectively. Cortical bone is assumed to consist of two regions: (1) metabolically active
cortical bone in which Pb transfers are governed solely by rates of bone formation and resorption; and
(2) mature cortical bone in which Pb undergoes exchange with bone calcium. The later process is
simulated as bidirectional radial diffusion of Pb in between eight concentric shells of cortical bone.
The approach to modeling bone in AALM-OF (i.e., bone Pb kinetics as a function of bone physiological
parameters) offers two major advantages: (1) inclusion of parameters that control bone physiology (e.g.,
growth, volume, maturation) supports simulation of changes to bone mineral metabolism that might affect
bone production, growth, or maturation (e.g., disease, nutrition, menopause, weightlessness), and
predictions of the effects that these changes might have on bone Pb kinetics. An analogous simulation in
the AALM-LG requires direct knowledge (or assumptions) of the effects of these changes on bone Pb
transfer coefficients; and (2) advances in the knowledge of bone physiology (e.g., metabolism, growth,
resorption, disease) and of bone kinetics for other elements (e.g., calcium, strontium) can be incorporated
into the model to improve the parameterization and parameter values of the model, and its capability to
simulate and predict bone growth, volume, and maturation. In contrast, specialized studies for all the
different age related scenarios would be needed to improve values for the less physiologically
representation of bone Pb kinetics in the AALM-LG model based on compartment transfer rates that
change with age.
4.4. COMPARISON OF AALM-LG AND AALM-OF PREDICTIONS OF BLOOD AND
TISSUE PB
Differences in the structures of the Leggett and O'Flaherty biokinetics models would be expected to result
in different predictions of blood and tissue Pb levels for similar Pb exposure assumptions (Maddaloni et
al.. 2005). The revised AALM provides a convenient platform for comparing the models, because it
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allows both to be run using the same exposure and absorption settings. Two types of comparisons were
made of AALM-LG and AALM-OF: (1) age profiles for blood and tissue Pb levels following an exposure
to a constant Pb intake ((ig/day) were simulated and compared; and (2) dose-response relationships
between ingested dose and Pb levels were compared by simulating a series of increasing Pb intakes. In
either type of simulation, parameters that control Pb absorption and growth were set to the same values
(defaults for AALM-OF), so that differences in blood and tissue Pb levels could be attributed entirely to
differences in the simulation of systemic (post-absorption) biokinetics.
4.4.1. Comparison of Model Predictions for Constant Pb Intake
Figures 4-6 thru 4-9 show results of the simulations for a constant ingestion of 5 (.ig Pb/day beginning at
birth and extending to age 30 years. This exposure results in predicted blood Pb concentrations less than 5
(ig/dL, which is well below the concentration at which saturation of uptake into RBCs significantly
affects blood Pb levels. Figure 4-6 shows the age profiles for selected output variables (|_ig Pb in blood,
bone, soft tissue and total body). Figure 4-7 shows the differences expressed relative to the AALM-LG
(arbitrarily selected as the reference for presentation of the results). A negative value in Figure 4-7
indicates that the prediction from AALM-OF is less than that from AALM-LG. For example, -0.65 in
Figure 4-7 indicates that the AALM-OF blood Pb prediction is less than the AALM-LG prediction, and
the magnitude of the difference is 65% relative to the AALM-LG value. Figure 4-8 compares predicted
cumulative urinary and fecal Pb excretion. Figure 4-9 compares elimination rates following cessation of
exposure.
Several differences between the models are evident from these comparisons.
• AALM-OF predicts lower blood Pb levels prior to age 10 years (64-65%), after which, the
models begin to converge on similar blood Pb levels, with adult predictions from the AALM-OF
exceeding AALM-LG by approximately 20%.
• AALM-OF predicts lower bone Pb levels in children prior to age 10 years (63-68%), after which,
the models begin to converge on similar bone Pb levels, with adult predictions from the AALM-
OF exceeding AALM-LG by approximately 18%.
• AALM-OF predicts lower soft tissue Pb levels (all tissues combined, excluding bone) at all ages
(59-92%).
• Both models predict similar accumulation of Pb over the lifetime, reflected in similar total body
burdens (agreement is within 10%).
• With cessation of exposure, both models predict rapid declines of Pb in blood (tin = 30-50 days)
and soft tissue, with a slower decline in bone Pb (ti/2 10-20 years).
• Both models predict multiple rates of decline in blood Pb. In adults, the half-time for the first
50 days following cessation of exposure is approximately 36 days in AALM-LG and 46 days in
AALM-OF. The half-time for the period 5-20 years following cessation of exposure is 12.7 years
in AALM-LG, and 10.9 years in AALM-OF. The slow phase results from transfer of bone Pb to
blood.
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• Both models predict a more rapid decline in bone Pb in children compared to adults following
cessation of exposure. The two models predicted similar half-times for bone Pb elimination in
children (ti/2 = 3.00 [AALM-LG], 2.24 years [AALM-OF]).
• Although both models predict slower elimination of Pb from bone in adults, AALM-OF predicts
a more rapid decline (ti/2 = 12.6 year) than AALM-LG (ti/2 = 19.7 year).
• AALM-OF predicts a higher rate of urinary excretion of Pb compared to AALM-LG. Fecal
excretion is identical in both models because it is dominated by unabsorbed Pb and
gastrointestinal absorption parameters were set to the same values in both models for the
comparison simulations.
Amounts of Pb in tissues are converted to Pb concentrations in both models by dividing Pb masses by
age-dependent values for tissue weights. The latter are predicted in both models from the body growth
and tissue growth models developed by O'Flahertv (1995). The blood and bone Pb concentrations
predicted for an exposure to 5 (.ig Pb/day are shown in Figure 4-10. Differences in the model predictions
of tissue Pb masses are reflected in the tissue Pb concentrations. The magnitudes of the differences
between models (i.e., ratio AALM-LG/AALM-OF) are the same for Pb masses and concentrations,
because both models use the same tissue growth algorithms, which predict the same tissue volumes and
weights.
4.4.2. Comparison of Predicted Dose-Response for Blood and Tissue Pb
Although both AALM-LG and AALM-OF are mathematically linear models (i.e., all state variables are
defined with linear differential equations), they predict curvilinear dose-response relationships for blood
Pb resulting from a saturable capacity of red blood cells (RBC) to take up Pb. Dose-response relationships
predicted from AALM-LG and AALM-OF are shown in Figures 4-11 and 4-12, for children (age 5 years)
and adults (age 30 years), respectively. Although curvature of the dose-response relationship for blood
derives from saturation of uptake of Pb in RBCs, the two models use different computational approaches
to model the saturable uptake. AALM-LG simulates binding of Pb in red blood cells with rate coefficients
for transfer of Pb from plasma to RBCs (child and adult, ti/2 = 0.0014 days), and from RBCs to plasma
(child ti/2 = 2.5 days, adult ti/2 = 5 days). This results in a rapid uptake, slower release, and accumulation
of RBC Pb. The plasma-blood concentration ratio is governed, in part, by the ratio of these transfer
coefficients (plasma to RBC/RBC to plasma). The higher ratio in children (i.e., exit rate is faster) results
in higher plasma-RBC concentration ratios in children. Above a non-linear, threshold Pb concentration in
red blood cells (60 (.ig/L). the rate constant for transfer into RBCs declines with increasing intracellular
concentration, approaching zero (no uptake) at a saturating concentration of 350 (ig/dL RBC (see
Equation 4-1).
TOORBC = TORBC ¦ [1 - fRBCC0NC~RBCNL\is E (4-1)
L V SATRAT-RBCNL )J
where TOORBC is the deposition fraction from diffusible plasma to red blood cells; TORBC the age-
scaled deposition fraction from diffusible plasma to red blood cells below non-linear threshold;
RBCCONC the red blood cell Pb concentration ((.ig/dL RBC volume); RBCNL the non-linear uptake
kinetics threshold concentration ((.ig Pb/dL RBC volume); and SATRAT the maximum capacity of the red
blood cell compartment (|_ig Pb/dL RBC volume).
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AALM-OF simulates a binding equilibrium (rather than kinetics) in which Pb in plasma achieves
instantaneous equilibrium with unbound Pb in RBCs, which is in equilibrium with bound Pb. Binding
parameters include a maximum capacity (270 (.ig Pb/dL RBC) and half-saturation concentration (0.75
(ig/dL RBC), with the relationship represented as follows (see Equation 4-2):
CB = (1 — HCT) ¦ CP + HCT ¦CP-\g+ B'ND } Eq. (4-2)
v J I KBIND+CP) M v '
where CB is the blood Pb concentration ((ig/dL), CP the plasma Pb concentration ((ig/dL); HCT is the
hematocrit; G the ratio of unbound RBC Pb to plasma Pb; BIND the maximum capacity of RBC binding
(|_ig/dL): and KBIND the half-saturation coefficient (|_ig/dL). One advantage of this approach is that the
parameters BIND and KBIND have a direct empirical basis, as they have been estimated from data on Pb
concentrations in plasma and RBCs (e.g., Bergdahl et al.. 1998; O'Flahertv. 1993). However, a
disadvantage is that it represents plasma-RBC kinetics as essentially being instantaneous; whereas,
observations made following injection of radiolead suggest that kinetics may be slower and more complex
[see Leggett (1993) for discussion of these observations].
The different parameterizations of RBC saturation are evident in the relationships between plasma and
blood Pb predicted from the two models. In both models, the plasma-blood concentration ratio increases
with increasing blood Pb concentration, as the RBC approaches saturation. In AALM-OF, the plasma-
blood Pb ratio below saturation remains nearly constant with age (0.007); whereas, in AALM-LG, the
plasma:blood ratios are higher in children compared to adults. AALM-LG predicts a plasma-blood ratio
that declines from 0.01 at age 1 year to 0.003 at ages beyond 10 years (below saturation).
Both models predict linear dose-response relationships for bone Pb, and for all other tissue Pb. The
predicted dose-response relationships for bone are more similar in adults, whereas, AALM-LG predicts a
steeper dose-response relationship for bone in children. The steeper dose-response relationship for bone
Pb in children occurs in AALM-LG even though the elimination rates from bone are similar in both
models. This suggests that the differences between model results for bone Pb is related to the rates of
deposition of Pb in bone, rather than to differences in rates of bone Pb elimination.
4.5. SENSITIVITY ANALYSIS OF AALM-LG AND AALM-OF
Relative to the AALM-LG, AALM-OF predicts lower amounts and concentrations of Pb in blood in
children, higher amounts and concentrations of Pb in blood in adults, and lower amounts and
concentrations of Pb in soft tissues in at all ages. Numerous individual parameters or combinations of
parameters could contribute to these differences. AALM-LG has 39 parameters and AALM-OF has
35 parameters that collectively determine the biokinetics of absorbed Pb in each model to varying
degrees. These parameters and their nominal values are presented in Tables 4-2 (AALM-LG) and 4-3
(AALM-OF). A univariate sensitivity analysis was conducted to determine the effect of each parameter
on predictions of Pb in blood, bone, and soft tissues.1 The sensitivity analysis consisted of running each
model before and after perturbing values for single parameters by a factor of 0.01, in the up and down
1 This approach to sensitivity analysis does not consider potential interactions between
parameters. Sensitivity coefficients measured in univariate analyses may be larger or smaller
than SSCs measured in multivariate analyses (i.e., when multiple parameters are varied
simultaneously).
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directions. Parameter sensitivities were assessed by comparing standardized sensitivity coefficients (see
Equation 4-3):
SSC = /' (*) = ABS [/(* +^ - fiX - A)]. Eq (4-3)
2Ax f(x)
where SSC is the standardized sensitivity coefficient;/fx) the output variable (e.g., blood Pb) at parameter
value x; and A the perturbation of x (e.g., 0.0lx). Values for SSC were determined for blood, bone, and
soft tissue Pb at ages selected to represent children (5 years) or adults (30 years).
4.5.1. Sensitivity Analysis of AALM-LG
SSCs were derived for all input parameters to AALM-LG other than those that control Pb absorption or
growth. Separate sensitivity analyses were run to determine parameter sensitivity of the total amount of
Pb in blood, bone, liver, kidney, or other soft tissues, in children (age 5 years) and adults (age 30 years).
SSCs are displayed in order of highest to smallest value for adults in Tables 4-4 thru 4-8. Larger values of
SSC indicate larger effects of the parameter on blood Pb. For example, blood Pb is most sensitive to the
value of the parameter TEVF, the deposition fraction for Pb transfer from diffusible plasma to the
extravascular fluid (see Table 4-4). The value 8.38 indicates that a 1% change in TEVF results in an
8.38% change in blood Pb. Influential parameters have SSCs that exceed 0.1 (>0.1% change in tissue Pb
per 1% change in the input parameter).
In the discussion that follows, input parameter values are expressed as their equivalent first-order transfer
rates (day1) shown in Table 4-2 and their corresponding approximate first-order half-times (ti/2, day). In
AALM-LG, the central distribution compartment is diffusible plasma, which exchanges Pb with other
tissue compartments. Input parameters that control transfers of Pb from tissues to diffusible plasma are
expressed as first-order rates. Input parameters that control transfers from diffusible plasma to tissues are
expressed as deposition fractions. Deposition fractions represent the fractional apportionment of the total
outflow of Pb from diffusible plasma (Leggett. 1993). First-order rates are derived in the AALM-LG as
the product of deposition fraction and total outflow of Pb from the diffusible plasma compartment
(RPLAS, see Equation 4-4).
REFV = TEFV ¦ RPLAS Eq. (4-4)
where REFV is the transfer rate from diffusible plasma to the extravascular fluid (day1); TEFV the
deposition fraction for transfer to the extravascular fluid; and RPLAS the total rate of transfer of Pb to all
tissues (day1). The nominal value for RPLAS is 2000 day"1. If the deposition fraction for TEFV is 0.5, the
corresponding transfer rate for TEFV is 1000 day"1 (0.5x2000 day"1). Values for transfer rates
corresponding to deposition fractions are presented in Table 4-2, so that they can be directly compared to
the return transfer rates from tissue to diffusible plasma. The values for the corresponding depositions
fractions can be calculated from Equation 4-4.
4.5.1.1. Influential Parameters Common to All Tissues
Several parameters had relatively large influences (SSC > 0.1) across all or most of the tissues that were
included in the sensitivity analysis and dominate Pb biokinetics in the AALM-LG. These parameters are
TEVF, TORBC, TOSOFO, TOLVR1, H1TOBL, and TBONE.
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The parameter TEVF controls the rate of transfer of Pb from diffusible (non-bound) plasma to the
extravascular space. The nominal value for the rate is 1000 day"1 (ti/2 =1.0 min) or approximately one
half of the total transfer rate out of diffusible plasma to all tissues (2000 day"1). The return rate to
diffusible plasma is 333 day"1 (tin = 3.0 min). This results in a rapid exchange of Pb in diffusible plasma
with the extravascular fluid, with an equilibrium ratio in which the extravascular fluid contains
approximately 3 times the amount of Pb in diffusible plasma. The extravascular fluid serves as a rapid
exchange reservoir that contributes to plasma Pb. Increasing or decreasing the value of TEVF increases or
decreases, respectively, the amount of Pb in plasma and, thereby, blood Pb and the amount of Pb
available for distribution to other tissues. The prominence of TEVF in the SSCs for all tissues may also
result from its use in age-scaling of deposition fractions in the model. Deposition fractions for all tissues
other than bone are scaled as function of TEVF and TBONE (the deposition fraction to bone surfaces) (see
Equation 4-5).
AGESCL = i-w-tbonev
1—TEVF—TBONEL M v '
where TBONEL is the terminal value for TBONE on the last day of the simulation. The AGESCL variable
adjusts the deposition fractions (and total outflow) from diffusible plasma to soft tissues so that their sum
does not exceed total outflow (TEFV), while outflow to bone (TBONE) varies with age. As a result of its
use to age scale deposition fractions, changes to TEVF affects Pb kinetics of RBC, kidney, liver, and other
soft tissues.
The parameters TORBC and RRBC control the transfer rates of Pb into and out of RBCs, respectively.
The nominal values in adults are 480 day"1 (ti/2 = 2.1 min) and 0.139 day"1 (ti/2 = 5.0 day). The equilibrium
ratio (TORBC/RRBC) is approximately 3450, which results in accumulation of Pb in the RBC, relative to
plasma, and Pb in red blood cells being the dominant contributor to blood Pb. Increasing the transfer rate
into red blood cells (TORBC), without a change in the return rate (RRBC) increases blood Pb, whereas,
increasing the transfer rate out of red blood cells (RRBC), makes more Pb available to the diffusible
plasma compartment for distribution to other tissues, and decreases blood Pb.
AALM-LG has three soft tissue compartments, representing fast (SOFO), moderate (SOF1), and slow
(SOF2) kinetic pools of Pb in soft tissues other than blood, kidney, or liver. The parameter TOSOFO
controls the rate of transfer from diffusible plasma to the fast compartment. The nominal value in adults is
178 day"1 (ti/2 =5.6 min) and the return rate is 2.08 day"1 (ti/2 = 8.0 hours). Similar to the extravascular
fluid, this soft tissue compartment provides an exchange reservoir to support plasma and blood Pb, as
well as Pb available for distribution to other tissues.
The parameters TOLVR1 and H1TOBL control the transfer of Pb from diffusible plasma to liver and the
return to plasma, respectively. Nominal values are 80 day"1 (ti/2 =12.5 min) for transfer to liver and 0.03
day"1 (ti/2 = 23.1 day) for return. Similar to the rapid exchange soft tissue compartment, this liver
compartment provides a reservoir to support plasma and blood Pb.
The parameter TBONE controls the transfer rate from diffusible plasma to surface bone, the only pathway
for entrance of Pb into bone where it can be sequestered into slower kinetic pools of bone volume. The
nominal values are 89 day"1 and 71 day"1 (ti/2 = 11.2 min, 14.1 min) for trabecular and cortical bone,
respectively. The return value from both types of bone is 0.5 day"1 (14 day). More than 90% of the Pb
body burden resides in bone, as a result, the transfer to bone affects Pb levels in all other tissues. The
terminal value of TBONE (TBONEL) is also used in the age-scaling of deposition fractions to all tissues
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other than bone (see Equation 4-5). This is reason why it shows up as an influential parameter across all
tissues.
4.5.1.2. Sensitivity Analysis of AALM-LG Blood Pb Predictions
AALM-LG SSCs for blood Pb (ABLOOD) are shown in Table 4-4. The most influential parameters on
blood Pb (SSCs > 0.1) are TEFV, TORBC, TOSOFO, RRBC, TOLVR1, H1TOBL, and TBONE. These
parameters have SSCs >0.1 across all tissues (see Section 4.5.1.1).
4.5.1.3. Sensitivity Analysis of AALM-LG Bone Pb Predictions
AALM-LG SSCs for bone Pb (ABONE) are shown in Table 4-5. The most influential parameters on bone
Pb (SSCs > 0.1) are TEFV, TORBC, TBONE, TOSOFO, FLONG, RCS2DF, TOLVR1, H1TOBL, and
RTS2DF. The bone model in AALM-LG includes three sub-compartments for cortical and trabecular
bone that represent fast (surface bone), moderate (exchangeable), and slow (non-exchangeable) Pb pools
(see Figure 4-4). The slow compartment contains most (>90%) of the Pb in bone and, therefore, is the
major determinant of the amount of Pb in bone. The parameter FLONG controls the rate of transfer of Pb
from the moderate to the slow compartment. Lead enters the moderate and slow bone compartments from
surface bone, which is in direct exchange with plasma. The parameter TBONE controls the rate of transfer
of Pb to bone surfaces; nominal values are 89 day"1 and 71 day"1 (ti/2 = 11.2 min, 14.1 min) for trabecular
and cortical bone, respectively. The parameters RCS2DF and RTS2DF control the rate of return of Pb
from bone surface to plasma (0.5 day"1, tin =1.4 day).
4.5.1.4. Sensitivity Analysis of AALM-LG Liver Pb Predictions
The most influential parameters on liver Pb (SSCs > 0.1) are TEFV, TORBC, TOSOFO, TOLVR1,
H1TOH2, RLVR2, H1TOBL, and RLVR1 (see Table 4-6). The liver model in AALM-LG includes two
sub-compartments representing fast (HI) and slow (H2) pools. Lead in the fast compartment exchanges
with plasma and delivers Pb into the slow compartment and to bile. Transfer of Pb into the fast
compartments controlled by the parameter TOLVR1 (80 day"1, tin = 11.2 min) and return to plasma is
controlled by RLVR1 (0.0312 day"1, tin = 22.2 day). Transfer of Pb from the fast to the slow compartment
is controlled by H1TOH2 (0.00693 day"1, tin =100 day) and transfer to bile is controlled by H1TOBL
(0.0312day_1, 22.2 day). Return of Pb to plasma is controlled by RLVR2 (0.0019 day"1, tin = 365 day).
4.5.1.5. Sensitivity Analysis of AALM-LG Kidney Pb Predictions
The most influential parameters on kidney Pb (SSCs > 0.1) are TEFV, TORBC, TOSOFO, RKDN2,
TOKDN1, TOKDN2, RKDN2, TOLV1, and H1TOBL (see Table 4-7). The kidney model in AALM-LG
includes two sub-compartments representing urinary route through the kidney (RK1) and a storage
compartment that exchanges with plasma (RK2) pools. Transfer of Pb into kidney is controlled by the
parameters TOKDN1 (40 day"1, tin = 25 min) and TOKDN2 (0.4 day"1, tin =1.7 day). Return of Pb to
plasma is controlled by the parameter RKDN2 (0.0019 day"1, tin = 365 day).
4.5.1.6. Sensitivity Analysis of AALM-LG Other Soft Tissue Pb Predictions
The most influential parameters on other soft tissue Pb (SSCs > 0.1) are TEFV, TORBC, TOSOFO,
RSOF2, TOSOF2, TOLVR1, H1TOBL, TOSOF1, and RSOF1 (see Table 4-8). AALM-LG has three soft
tissue compartments, representing fast (SOFO), moderate (SOF1), and slow (SOF2) kinetic pools of Pb in
soft tissues other than blood, kidney, or liver. Transfer into each compartment is controlled by parameters
TOSOFO (178 day"1, tin = 5.6 min), TOSOF1 (10 day"1, 1.7 hours), and TOSOF2 (2 day"1, tin = 8.3
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1 hours). Return of Pb to plasma is controlled by parameters RSOFO (2.08 day"1, Xm = 8.0 hours), RSOF1
2 (0.00416 day1, Xm = 167 day), and RSOF2 (0.00038 day1, 1824 day).
3 4.5.2. Sensitivity Analysis of AALM-OF
4 SSCs were derived for all input parameters to AALM-OF other than those that control Pb absorption or
5 growth. Separate sensitivity analyses were run to determine parameter sensitivity of the total amount of
6 Pb in blood, bone, liver, kidney, or poorly perfused and well-perfused tissues, in children (age 5 years)
7 and adults (age 30 years). Input parameter values for AALM-OF are presented in Table 4-3. This is a mix
8 of parameters for Pb, and parameters that control bone formation and resorption rates that determine
9 transfer of Pb in and out of deep bone. SSCs for each tissue are displayed in order from highest to
10 smallest value for adults in Tables 4-9 thru 4-14.
11 4.5.2.1. Influential Parameters Common to All Tissues
12 Three parameters had large influences (SSC >0.1) across all, or most, of the tissues that were included in
13 the sensitivity analysis, and dominate Pb kinetics in the AALM-OF. These parameters are CI, C2, and
14 C3. Urinary excretory clearance of Pb from plasma is simulated in AALM-OF as a function of glomerular
15 filtration rate (GFR). The parameters CI, C2, and C3 are unitless parameters in the function that simulates
16 GFR as a function of age. Changes to these parameters alter the rate of removal of Pb from plasma to
17 urine and, thereby, the amount of Pb in blood and available for distribution to other tissues.
18 4.5.2.2. Sensitivity Analysis of AALM-OF Blood Pb Predictions
19 The most influential parameters on blood Pb (SSCs > 0.1) are CI, C2, BIND, KB1ND, and C3 (see Table
20 4-9). Uptake of Pb into RBCs is simulated in AALM-OF as a binding equilibrium between plasma Pb and
21 RBC Pb (see Section 2.2). The parameters BIND (2.7 mg/L) and KBIND (0.0075 mg/L) are the
22 maximum binding capacity of the RBCs, and the half-saturation concentration of Pb for binding,
23 respectively. Changing BIND or KBIND affects the amount of Pb sequestered in RBCs, and the amount
24 of Pb available to the plasma compartment for distribution to other tissues. Increasing BIND increases
25 RBC binding, and increases blood Pb. Increasing KBIND increases the plasma Pb concentration needed
26 to achieve a given RBC Pb concentration, and decreases blood Pb.
27 4.5.2.3. Sensitivity Analysis of AALM-OF Bone Pb Predictions
28 The most influential parameters on bone Pb (SSCs > 0.1) are CI, C2, R0, RAD8, EXPO, and C3 (see
29 Table 4-10). The parameter R0 controls the clearance of Pb from bone into the vascular sites in bone
30 (canaliculi) where exchange with plasma occurs. The nominal value is 5E-7 cm3/day. Increasing R0
31 decreases bone Pb. The parameter RAD8 is the radius of the deepest (eight of 8) diffusion shells in
32 mature cortical bone. This parameter determines the diffusion volume (2.14E-3 cm) and, thereby, the
33 clearance of Pb from the deepest bone compartment. Increasing RAD8 decreases bone Pb. The parameter
34 EXPO is a unitless exponent constant in the function that simulates the age-dependency of the bone
35 volume participating in adult remodeling. During adult remodeling, bone formation and resorption rates
36 are slower than during child and adolescent growth periods. As a result, exchange of Pb between deep
37 bone deposits and plasma is slower in mature bone than during growth.
38 4.5.2.4. Sensitivity Analysis of AALM-OF Liver Pb Predictions
39 The most influential parameters on liver Pb (SSCs > 0.1) are CI, C2, PL, and C3 (see Table 4-11).
40 Exchange of Pb between plasma and liver is simulated in AALM-OF as a flow-limited process
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1 determined by the liver/plasma partition coefficient and blood flow to the liver. The parameter PL is the
2 liver/plasma partition coefficient (PL = 50). The nominal value is 50. Increasing PL increases liver Pb.
3 4.5.2.5. Sensitivity Analysis of AALM-OF Kidney Pb Predictions
4 The most influential parameters on kidney Pb (SSCs > 0.1) are CI, C2, PK, and C3 (see Table 4-12).
5 Similar to liver, exchange of Pb between plasma and kidney is simulated in AALM-OF as a flow-limited
6 process determined by the kidney/plasma partition coefficient (PK =50) and blood flow to the kidney.
7 Increasing .PAT increases kidney Pb.
8 4.5.2.6. Sensitivity Analysis of AALM-OF Poorly Perfused Tissue Pb Predictions
9 The most influential parameters on poorly perfused tissue Pb (SSCs > 0.1) are CI, C2, PP, and C3 (see
10 Table 4-13). Exchange of Pb between plasma and poorly perfused tissue is simulated in AALM-OF as a
11 flow-limited process determined by the tissue/plasma partition coefficient (PP = 2.0) and blood flow to
12 the tissue. Increasing PP increases poorly perfused tissue Pb.
13 4.5.2.7. Sensitivity Analysis of AALM-OF Well-Perfused Tissue Pb Predictions
14 The most influential parameters on well-perfused tissue Pb (SSCs > 0.1) are CI, C2, PW, and C3 (see
15 Table 4-14). Exchange of Pb between plasma and well-perfused tissue is simulated in AALM-OF as a
16 flow-limited process determined by the tissue/plasma partition coefficient (PW= 50) and blood flow to
17 the tissue. Increasing PW increases well-perfused tissue Pb.
18 4.6. CONCLUSIONS FROM MODEL COMPARISONS AND SENSITIVITY ANALYSES
19 Table 4-15 lists the dominate parameters causing major differences between predictions from AALM-LG
20 and AALM-OF and corresponding parameter values that had the highest SSCs for each prediction. Data
21 may exist for some of the significant parameters that would allow evaluation and/or optimization of
22 parameter values. AALM-OF parameters CI and C2 control GFR, and thereby, urinary clearance of Pb
23 from plasma. Abundant data exist on rates and age (i.e., body size) dependence of glomerular filtration in
24 humans (e.g., Peters. 2004; Peters et al.. 2000). Data on urinary clearance of Pb in humans also exist that
25 may be useful for evaluating model predictions (e.g.. Diamond. 1992).
26 AALM-OF parameters BIND and KBIND and AALM-LG parameters TORBC and RRBC control uptake
27 of Pb into RBCs and, thereby, influence plasma Pb and its distribution to tissues. These parameters can
28 be evaluated against data from studies in which levels of Pb in plasma and whole blood (and/or RBCs)
29 have been measured in humans with methods that ensure sampling of plasma Pb without contamination
30 with Pb from lysed red cells (e.g.. SRC. 2003).
31 Direct empirical evaluation of AALM-OF and AALM-LG parameters that control bone Pb may not be
32 feasible because of lack of data to directly estimate parameter values. However, optimization of
33 influential parameters that control bone Pb levels and relationships between blood and bone Pb may be
34 feasible with data from long-term monitoring studies of blood and bone, where exposure to Pb was
35 abruptly changed (e.g.. retired Pb workers; see U.S. EPA. 2013).
36 Similarly, direct empirical evaluation of AALM-OF tissue-plasma partition coefficients, and AALM-LG
37 transfer rates and deposition fractions that control Pb levels in liver, kidney, and other soft tissues may not
38 be feasible because of lack of data to directly estimate parameter values. However, it may be possible to
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optimize these parameters against data from cadaver studies in which the distribution of Pb body burden
in bone and soft tissue has been measured.
4.7. EVALUATION AND OPTIMIZATION OF THE AALM
Although the sensitivity analyses described in Section 5.0 provide some insight regarding the parameters
that contribute to differences in predictions from the two models; a more important objective is to
determine what set of parameters provides the most accurate representation of observations of Pb kinetics
in humans. Extensive documentation of the development and calibration of the Leggett and O'Flaherty
models has been reported (O'Flaherty. 2000; O'Flaherty et al.. 1998; O'Flaherty. 1998. 1995; Leggett.
1993; O'Flaherty. 1993). New data have become available since the development of the models (U.S.
EPA. 2013). Important objectives for further development of the AALM are: (1) collect and re-examine
all available data for utility in model evaluation, optimization, and validation; (2) conduct a
comprehensive evaluation of the models against a common set of data; (3) optimize influential parameters
identified in Section 5 that can be informed by the observation data sets; and (4) validate the model
against a set of observations not utilized in optimization of the models.
Searches for studies of the toxicokinetics of Pb in humans that provide data that might be useful for
estimated model parameter values were conducted. Three types of data were of particular interest:
(1) blood, tissue, or excreted Pb paired with measured Pb intakes and/or exposures; (2) temporal patterns
of blood, tissue, or excreted Pb following an abrupt change in Pb intake or exposure; and (3) paired data
for blood and tissues or excreted Pb (e.g., urine/blood or tissue/blood ratios). Based on the available data
retrieved and processed from the searches as well as considerations of the results of comparisons of the
two models, a stepwise optimization approach was developed, in which specific outputs of the models
were evaluated against observations in humans, and key parameters were optimized to achieve agreement
with the observations (see Table 4-16).
Optimization was achieved using maximum likelihood (MLE) algorithms available in acslX (e.g., Nelder
Mead) or if this was not possible, by visual inspection. Optimizations were evaluated by inspection of
residuals (Equation 4-6) and the r2 for the least-squares linear regression of observed and predicted
values.
, , Predicted-Observed. „ , . ^s
Residual = :—: Eq. (4-6)
Standard Deviation of Mean
The optimization objectives were residuals < ±2 and r2 > 0.70.
Most pertinent to the AALM.FOR model are the changes made to the Leggett (1993) model to create the
AALM-LG model, based on the evaluations described below. These changes are summarized in Table 4-
22.
4.7.1. Unification of Simulation of GI Absorption and Growth
A goal of the optimization was to determine if AALM-LG and AALM-OF would converge on similar
predictions for post-absorption kinetics of blood and tissue Pb concentrations. To remove effects of
differences in absorption and growth parameters in the two biokinetics modules, the GI absorption and
growth parameters from the O'Flaherty (1995. 1993) model were adopted for both AALM sub-models.
The resulting AALM GI absorption model is a continuous function (Equation 4-7) that simulates an age-
dependent decline in the absorption fraction (AFAge), from the value in infancy to the value in adults.
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1+30-e~A9e
Eq. (4-7)
2 The settings (AFci = 0.60, AFc2 = 0.52) result in AF = 0.58 at birth and AF = 0.08 in adults (see Figure 4-
3 13, OF default). As discussed in Section 4.7.8, AFci was set to 0.40 for infants based on Ryu et al. (1983).
4 An AFc2 of 0.28 keeps the AF for adults at 0.12 (see Figure 4-13, AALM), which aligns with the Adult
5 Lead Methodology (U.S. EPA. 2003).
6 Tissue growth in the AALM is simulated as a function of body weight, which is age-dependent (see
7 Figure 4-14). Tissue Pb concentrations are calculated as the Pb mass (|_ig) divided by the tissue weight (g).
8 Concentrations of Pb in bone wet weight are converted to concentration per gram bone mineral by
9 dividing the wet weight concentration by the ash fraction of bone. This conversion was used to compare
10 model predictions with bone X-ray fluorescence (XRF) data, which is typically reported in units of Pb per
11 g bone mineral. Bone ash fractions were assumed to be 0.55 and 0.50 for cortical and trabecular bone,
12 respectively (ICRP. 1981).
13 4.7.2. Optimization of Plasma Pb - Blood Pb Relationship
14 Six studies provided data on individual human subjects that can be used to evaluate the relationship
15 between plasma Pb and blood Pb concentrations. Measurements of plasma Pb were made using either
16 inductively coupled plasma mass spectrometry (Smith et al.. 2002; Bergdahl et al.. 1999; Bergdahl et al..
17 1998; Hernandez-Avila et al.. 1998; Bergdahl etal.. 1997; Schutz et al.. 1996) or stable isotope dilution
18 with thermal ionization mass spectrometry (Manton et al.. 2001). In all of these studies, methods were
19 employed to control for sample contamination, which is of particular importance in measurements of the
20 low Pb levels found in plasma. Taken together, the observations from these reports varied over a wide
21 range of blood Pb (approximately 0.34-94.8 (ig/dL) and plasma Pb (approximately 0.0014-1.92 (ig/dL)
22 levels. These studies provided 406 individual measurements of plasma Pb and blood Pb, in adult workers
23 as well as individuals with no known history of occupational exposure to Pb (SRC. 2003). Only one study
24 provides similar data in children (Bergdahl etal.. 1999). The observations in children do not appear to
25 differ substantially from those for adults.
26 A best fit (least-squares) model for combined data from the above six studies was identified, and is
27 presented in Equation 4-8:
28 Blood Pb = 87.0 ¦ Plasma Pb0 5 - 3.89 (r2 = 0.90) Eq. (4-8)
29 AALM-OF parameters KBIND and BIND were optimized (Nelder Mead) against this data set in the
30 AALM-OF function relating plasma Pb and blood Pb (Equation 4-9):
32 AALM-LG parameter RBCNL was optimized by visual inspection (it was not possible to derive an
33 independent expression for the plasma Pb and blood Pb relationship because relevant parameters control
34 rate constants for transfer of Pb between plasma and RBC compartments).
35 Figures 4-15 compares the observed and predicted whole blood and plasma Pb in adults relationship.
36 Residuals for the optimized models are within acceptable limits (-2, 2). The r2 values for predictions are
31
CB = (1 — HCT) ¦ CP + HCT ¦ CP ¦ ( G+B1ND) )
v y \KBIND+CPJ
Eq. (4-9)
37 0.99 and 0.98.
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4.7.3. Optimization of Plasma-to-Urine Pb Clearance
Four studies provide data to derive estimates of the Pb plasma-to-urine clearance rate (L/day) (Araki et
al.. 1986; Manton and Cook. 1984; Manton and Mallov. 1983; Chamberlain et al.. 1978). Clearance
estimates from these studies are reported in Diamond (1992). These estimated clearance rates are based
on measurements made in a total of 32 ("normal" subjects). The mean of the estimates from the four
studies is 18 L/day ± 4 (SD).
Rentschler et al. (2012) reported individual subject data on urinary excretion of Pb (jj.g/g creatinine) and
plasma Pb concentration in in five cases of Pb poisoning (blood Pb>80 (ig/dL). The cases were followed
for periods up to 800 days. If assumptions are made about body weight (not reported) and established
associations between creatinine excretion and lead body mass, clearance rates can be estimated from these
data. The estimated mean plasma clearance was 43 L/day ±13 (SD) (range: 32-64 L/day). Lead poisoning
may have been a contributing factor to the relatively high clearances based on Rentschler et al. (2012).
Therefore, for the purpose of model optimization, 18 L/day was selected as the representative value for
plasma-to-urine clearance.
In AALM-OF, urinary excretion of Pb is an age-dependent fraction of GFR. Parameters for the GFR
function were modified to achieve an adult GFR of approximately 170 L/day/1.73m2 (120 mL/min/1.73
m2 body surface area (ICRP. 1981). with infant (<1 year) values 30% of the adult value (Dewoskin and
Thompson. 2008). AALM-OF parameters C2 and C3 were optimized in a function relating age and total
Pb excretory clearance (FRX) as shown in Equation 4-10.
FRX = CI - C2/(l + C3 ¦ e~AGE) Eq. (4-10)
AALM-LG parameters TKDN1 and TOURIN were optimized by visual inspection.
Figure 4-16 compares predicted and observed urinary clearance in adults. No data are available to
evaluate the different age patterns for urinary clearance predicted by AALM-LG and AALM-OF.
4.7.4. Optimization of Soft Tissue-to-Bone Pb Ratio
Four studies provide data for measurements of post-mortem soft tissue and bone Pb concentrations
(Gerhardsson et al.. 1995; Barry. 1981. 1975; Gross et al.. 1975). Gerhardsson et al. (1995) reported only
soft tissue Pb concentrations; whereas, the other three studies reported soft tissue and bone Pb
concentrations that can be used to estimate the ratios. Barry (1981. 1975) reported data for children and
adults in age brackets, so the data from Barry (1975) was used as the primary source to optimize
parameters for kidney/bone and liver/bone Pb ratios as a function of age.
Barry (1975) reported data on tibia Pb concentrations that are simulated as cortical bone concentrations in
the AALM models. Since Barry (1975) reported group mean tissue concentrations (not ratios in autopsy
cases), the mean tissue-to-bone ratios were approximated from the group means.
In AALM-OF, uptake of Pb into kidney, liver, and other well-perfused tissue is assumed to be flow-
limited and governed by blood flow and the tissue/plasma partition coefficients, PK, PL, and PW.
Attempts to optimize these three parameters failed to accurately simulate the decline in the tissue/bone
ratios predicted from the Barry (1975) observations. An improved fit was achieved when the constants
PK, PL, and PW were allowed to vary with age according to the function shown in Equation 4-11.
PK = PKC ¦ (1 + e-PK*AGE)-) Eq (4_ii)
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The parameters PKC and PKA (for kidney), PLC and PLA (for liver), and PWC and PWA (for other
well-perfused) were optimized (Nelder Mead) against the tissue/cortical bone ratios derived from the data
reported in Barry (1975).
AALM-LG parameters TOKDN2 and RKDN2 (for kidney) and RLVR2 (for liver) were optimized by
visual inspection. It was not possible to use acslX parameter estimation functions because RKDN2 and
RLVR2 are array variables.
Figure 4-17 compares predicted and observed kidney/bone and liver/bone Pb ratios in adults. Standard
deviations of observed means were not available for calculating residuals because they were calculated
from group mean tissue concentration reported in Barry (1975). Values for r2 for kidney/bone predictions
(of average of male and female ratios) were 0.95 and 0.77 for AALM-LG and AALM-OF, respectively.
Values for r2 for liver/bone predictions were 0.96 and 0.93 for AALM-LG and AALM-OF, respectively.
4.7.5. Optimization of Blood-to-Bone Pb Ratio
Two studies provide data to evaluate the relationship between plasma or serum blood Pb and bone Pb
concentrations (Hernandez-Avila et al.. 1998; Cake et al.. 1996). Cake et al. (1996) measured paired
serum, tibia, and calcaneus Pb concentrations in 49 adult male Pb workers, and reported corresponding
linear regression parameters. Hernandez-Avila et al. (1998) measured paired plasma, tibia and patella Pb
concentrations in 26 adults (20 female) who had no known occupational exposures to Pb. These data can
be used to derive corresponding linear regression parameters for the log-transformed plasma Pb.
Individual subject data were digitized from Figure 1 of Hernandez-Avila et al. (1998). and linear
regression parameters derived for the untransformed plasma Pb concentrations, in order to compare these
with the linear regression parameters from Cake et al. (1996).
Bone Pb/Plasma Pb slopes at age 50 years were predicted from AALM-LG and AALM-OF from a series
of simulations in which Pb intake was varied from 1 to 1000 (ig/day. Table 4-17 and Figure 4-18 compare
predicted and observed slopes based on data from Cake et al. (1996) and Hernandez-Avila et al. (1998).
Given the relatively low residuals for cortical bone, which were within the range -2 to 2, no further
optimization for either model was needed for the respective parameters.
4.7.6. Optimization of Bone Pb Elimination Kinetics
Nilsson et al. (1991) reported longitudinal data on blood and finger bone Pb concentrations in 14 Pb
workers for period ranging from 8-18 years following cessation of their occupational exposures. The
median blood Pb concentration at the end of exposure was approximately 45 (ig/dL. The decline in bone
Pb concentration was described by a first-order model with a single rate constant. Estimates of
elimination half-times for each individual were reported. The group median was 16 years (95% CI: 12,
23). The decline in blood Pb was described by a tri-exponential model with the following parameters.
CI
C2
C3
Parameter
Unit
(95% CI)
(95% CI)
(95% CI)
tl/2
year
34 day
1.2 year
13 year
(29,41)
(0.85, 1.8)
(10, 18)
c
Hg/dL
10.2
12.6
22.8
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AALM-OF simulations were run for a constant Pb intake from birth to age 60 years, to achieve a terminal
blood Pb concentration of approximately 45 (ig/dL (1000 (ig/day), followed by 20 years without
exposure. A first-order exponential rate was estimated for the decline in cortical bone Pb concentrations
predicted for 20 years following cessation of exposure. The AALM-OF parameter R0 (coefficient for Pb
diffusion out of bone mineral into canalicules) was optimized (visual inspection) to achieve an
elimination half-time from cortical cone of 16 years, the median value based on the Nilsson et al. (1991)
results.
AALM-LG simulations were run for a constant Pb intake from birth to age 60 years, to achieve a terminal
blood Pb concentration of approximately 45 (ig/dL (2000 (ig/day), followed by 20 years without
exposure. A first-order exponential rate was estimated for the decline in cortical bone Pb concentrations
predicted for 20 years following cessation of exposure. The AALM-LG parameters FLONG (fraction of
total transfer from the exchangeable bone directed to non-exchangeable bone) and RCORT (transfer rate
from non-exchangeable cortical bone to diffusible plasma) were optimized (visual inspection) to achieve
an elimination half-time from cortical bone of 16 years, the median value based on the Nilsson et al.
(1991) results. FLONG and RCORT are age-dependent arrays and were varied in the optimization by
applying a constant (proportional) adjustment to all elements in the age array. The same adjustment factor
was therefore applied to child and adult values, even though the optimization was made against data only
for adults. The same adjustment factor was also applied to RTRAB (transfer rate from non-exchangeable
cortical bone to diffusible plasma).
Figure 4-19 compares rates of elimination of Pb from bone and blood with the corresponding empirical
models derived for Pb workers (Nilsson et al.. 1991). Elimination rates of Pb from bone predicted from
the optimized models are within the 95% CI of the empirical model and yield residuals that range within
the -2, 2, criteria (r2 = 0.99). Elimination half-times predicted for bone Pb (16 years) were identical to
estimates from Nilsson et al. (1991). Although elimination rates from blood predicted by the optimized
models are approximately at the confidence limits of the empirical model, the initial model divergence is
due largely to the slower (AALM-LG) or faster (AALM-OF) elimination kinetics during the first 5 years
following cessation of exposure; after which the models converge on the empirical model (r2 = 0.96
AALM-LG; r2 = 0.99 AALM-OF). Half-times predicted for the period 5 to 20 years after exposure were
1.25 years from AALM-LG and 1.06 years from AALM-OF, similar to values predicted for C2 (1.2 year)
from Nilsson etal. (1991).
4.7.7. Evaluation of Blood Pb Elimination Kinetics in Adults
Rabinowitz et al. (1976) conducted a pharmacokinetics study in which four adults ingested daily doses of
[207Pb] nitrate for periods up to 124 days. Concentrations of 207Pb in blood, urine, and feces were then
monitored during and following cessation of exposure, and data on daily intakes and blood concentrations
for each subject were reported. Absorption fractions for Pb were estimated for each individual based on
mass balance in feces.
Figure 4-20 compares observed and predicted blood 207Pb concentrations for the optimized AALM-LG
and AALM-OF. Gastrointestinal absorption fractions were set in both models to the estimates for each
individual reported in Rabinowitz et al. (1976). No other changes were made to parameter values.
Although both models AALM-LG predict a rise and decline in blood Pb concentrations, AALM-LG
predictions are closer to the observations. Values for r2 for AALM-LG predictions are 0.99, 0.98, 0.92,
and 0.97 for Subjects A, B, D, and E, respectively. Values for r2 for AALM-OF predictions range from
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0.08 (Subject E) to 0.24 (Subjects A, B, and D). AALM-OF predicts slower accrual and decline of blood
Pb, and lower peak blood Pb concentrations.
4.7.8. Evaluation of Blood Pb Elimination Kinetics in Infants
Only two studies provide data on the relationships between Pb dose and blood Pb concentration in infants
(Sherlock and Ouinn. 1986; Ryu et al.. 1983). In the Rvu et al. (1983) study, blood Pb concentrations
were monitored in 25 formula-fed infants. From birth to age 111 days, infants were fed formula
(packaged in cartons) that had a Pb concentration of approximately 20 |_ig/L. From age 112 to 195 days, a
subset of the infants (n = 7) were switched to formula (packaged in cans) that had a Pb concentration of
approximately 57 (ig/L. Formula intakes were measured, and provided estimates of Pb intakes in each
subject. Rvu et al. (1983) reported a table of individual Pb intakes, and presented a figure illustrating
group mean blood Pb concentrations at various ages (these data were digitized for use in this analysis).
Standard errors (or deviations) of mean blood Pb concentrations were not reported; however, as discussed
below, based on Sherlock and Ouinn (1986). standard errors may have been approximately 10% of the
means. The parameter for maternal blood Pb concentration was set at 10 (ig/dL, the reported maternal
mean for the study. Lead absorption was not quantified in Ryu et al. (1983); therefore, the gastrointestinal
absorption fraction during infancy was set to 40%, based on estimates from mass balance studies (Ziegler
et al.. 1978). No other changes were made to parameter values. Figure 4-21 compares predicted and
observed blood Pb concentrations for the two exposure regimens (carton formula or carton followed by
canned formula). Simulations are shown for the mean intake (12-20 (ig/day) and ± 1 SD (10-18 (ig/day,
15-22 (ig/day). AALM-LG encompasses most of the observations within ±1 SD of the mean intakes.
AALM-OF predictions are higher than observations. If standard errors of mean blood Pb concentrations
were 10% of the mean, residuals for AALM-LG predictions ranged from -3.7 to 0.15 for carton exposures
(mean -1.2). Residuals for AALM-OF predictions ranged from -3.0 to 4.4 (mean 2.0). Both models
capture the increase in blood Pb concentration associated with the switch the higher Pb intakes for canned
formula and the overall temporal trends in the observations; r2 for predictions were 0.85 and 0.76 for
AALM-LG and AALM-OF, respectively.
Sherlock and Ouinn (1986) measured blood Pb concentration in 131 infants at age 13 weeks and
estimated dietary intake of Pb for each infant based on Pb measurements made in duplicate diet samples
collected daily during week 13. Sherlock and Ouinn (1986) reported a plot of blood Pb means and
standard errors for group mean dietary Pb intakes (these data were digitized for use in this analysis). The
parameter for maternal blood Pb concentration was set at 18 (ig/dL, the reported maternal geometric
mean. The gastrointestinal absorption fraction was set at 40% for infants; the same value used in
simulations of Rvu et al. (1983). Figure 4-22 compares predicted and observed blood Pb concentrations
for the range of Pb intakes in the study. Both models reproduce the general shape of the observed
curvilinear dose-blood Pb relationship; the apparent plateau observed at the higher end of the dose range,
however, is achieved at higher doses in the models (>800 (ig/day AALM-LG, >600 AALM-OF).
Although the model results for the plateau contributed to high residuals at the highest Pb intake (>200
(ig/day), residuals for lower Pb doses ranged from -4.8 to 1.5 (mean -2.3) for AALM-LG and -4.3 to 2.2
(mean - 1.0) for AALM-OF. The overall dynamics of increasing blood Pb with increasing Pb dose was
predicted with r2 = 0.95 for AALM-LG and 0.98 for AALM-OF. One possible explanation for the higher
plateaus in the dose-blood Pb relationship predicted from both models is that the models may estimate
higher saturation levels of Pb in RBCs than actually occurred in the infants in the Sherlock and Ouinn
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(1986) study. Parameter values for RBC uptake are based on data collected on adults, and have not been
optimized for infants due to an absence of good supporting data (see Section 4.7.2).
4.8. CONCLUSIONS AND IMPLICATIONS OF PERFORMANCE OF OPTIMIZED
MODELS
The initial configuration of the AALM biokinetics model was an acslX implementation of the Lcggctt
(1993) and O'Flahertv (1995. 1993) models. The AALM.CLS (v. 4.2, July 2015) introduced several
changes to both models, including new parameters (see Table 4-18), and has optimized parameter values
against the same data sets. Some of the data used in the optimization were not available at the time the
original models were developed. Optimization against a common set of data resulted in convergence of
model predictions for blood, bone, and soft tissue (see Figures 4-23 and 4-24). The optimized AALM-LG
and AALM-OF predict similar blood, bone, and soft tissue Pb concentration (see Table 4-19). Evaluation
of model predictions of blood Pb relationships at known ingestion doses of Pb was limited to data in a
few adult subjects (Rabinowitz et al.. 1976). and only two studies in infants (where Pb ingestion doses
were estimated from dietary [formula] Pb measurements) (Sherlock and Ouinn. 1986; Ryu et al.. 1983).
No data were available on blood Pb concentrations in children or adolescents, for whom Pb ingestion
doses were known with certainty. Several studies have reconstructed Pb intakes in children from exposure
models supported by measurements of environmental exposure concentrations (Dixon et al.. 2009;
TerraGraphics Environmental Engineering. 2004; Malcoe et al.. 2002; Hogan et al.. 1998; Lanphear et al..
1998; Lanphear and Roghmann. 1997; Bornschein et al.. 1985). However, these studies were not
considered for evaluation of the AALM biokinetics models since they would introduce exposure
uncertainty into the evaluation.
Although limited in scope, these evaluations provide several insights into model performance. In general,
the AALM, in both AALM-LG and AALM-OF configurations, predicted-observed blood Pb dynamics in
infants and adults, in response to changing Pb dosing (see Figures 4-20 thru 4-22). In infants, observed
blood Pb concentrations were on average within ±2 SE of the observed mean (mean residual range -2, 2).
AALM-LG and AALM-OF predict similar quasi-steady state blood Pb concentrations in infants
(Figures 4-21 and 4-22). Both models predict a higher plateau for the dose-blood Pb relationship than was
observed in infants, however, this difference would be of quantitative significance only at intakes
resulting in blood Pb concentrations >30 (ig/dL.
AALM-OF predicts slower than observed blood Pb kinetics in adults compared to AALM-LG. This
resulted in larger differences between predicted and observed blood Pb concentrations in controlled,
short-term, exposure studies. More rapid blood Pb kinetics predicted by AALM-LG provided a closer
agreement to observations (see Figure 4-20). Although short-term exposure studies revealed important
differences in blood Pb kinetics predicted by AALM-LG and AALM-OF, both models predict well the
long-term elimination rates of Pb from bone following decades of exposure, and its effect on long-term
elimination of Pb from blood, that have been observed in worker populations following cessation of
exposure (see Figure 4-19).
Optimization exercises also revealed differences in model structure that are relevant to model
applications. Attempts to optimize AALM soft tissue/bone lead ratios solely by adjusting tissue/plasma
partition coefficients were unsuccessful. Improved performance was achieved by introducing age-
dependence and larger values for partition coefficients. O'Flahertv (1995. 1993) assigned values of 50 to
the kidney/plasma and liver/plasma partition coefficients. The optimized values are substantially higher;
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approximately 1350 for plasma/kidney, and 1600 for plasma/liver, in infants that progressively decrease
with age to adult values of approximately 700 and 800 respectively. It is possible, and likely, that these
large adjustments were necessary because the assumption of flow-limited transfer of Pb into and out of
soft tissue Pb does not accurately reflect the complexities of age-dependent transport and retention of Pb
in soft tissues. In support of this hypothesis, optimization of the bidirectional transfer coefficients that
govern uptake and retention of Pb in kidney and liver successfully predicted observations made in infants,
children and adults (see Figure 4-17).
AALM-LG and AALM-OF were also successfully optimized to predict observed relationships between
plasma and whole blood Pb concentrations in adults even though the two models use very different
mathematical approaches to simulating uptake and retention of Pb in RBCs. AALM-OF simulates binding
of Pb with RBCs as a saturable instantaneous equilibrium. AALM-LG simulates bidirectional transfer
between plasma and RBCs, with saturable transfer into RBCs. Transfer out of RBCs in AALM-LG is
age-dependent and faster in children than in adults. The validity of the age-dependence was not rigorously
explored in this analysis. What little data there are on plasma-RBC relationships in children does not
suggest an appreciable difference in the relationship for children and adults (Bcrgdahl et al.. 1999). Since
the age-dependence assumption could not be rigorously evaluated it is retained in AALM-LG.
The most substantial differences in the structures of AALM-LG and AALM-OF are in the simulation of
bone Pb kinetics. In AALM-LG, bone Pb kinetics are represented as age-dependent rate coefficients for
transfer of Pb into and out of bone. In AALM-OF, bone Pb kinetics are simulated as outcomes of a
physiological model of bone formation and resorption. The physiological approach to bone metabolism
implemented in AALM-OF allows the model to be used to explore relationships between bone
metabolism and Pb kinetics. This is potentially useful for simulating Pb kinetics in various bone
metabolism contexts associated with life stages [e.g., pregnancy and menopause, O'Flahertv (2000);
diseases (e.g., bone wasting diseases); and environments (e.g., weightlessness)].
Although, at this time, the AALM remains a research model, it possesses several attributes (discussed in
the following bullets) that make it attractive in human health risk assessment when estimating Pb internal
dosimetry following real or hypothetical environmental exposures.
• Currently, human health risk assessment of Pb is conducted using two separate regulatory
models, the IEUBK model for Lead in Children and Adult Lead Methodology. The IEUBK
model has a terminal age of 7 years. The Adult Lead Methodology is limited to adults. The
AALM provides a single physiological/compartmental model capable of predicting blood Pb
concentrations at all ages from birth through adulthood. The AALM would replace or supplement
the results of the two separate models, and would provide additional assessment capability for
older children and adolescent subpopulations.
• The current regulatory model, the Adult Lead Methodology is a slope factor model in which
biokinetics are represented as a single variable relating the linear slope of the change in blood Pb
concentration per unit change of absorbed Pb (fig/day). The AALM offers a more mechanistic
approach to simulating Pb kinetics that can incorporate information on age, growth, life stage,
and other physiological variables that may affect Pb kinetics.
• The AALM can simulate exposures in time steps as small as a single day. This allows predictions
of blood Pb concentrations associated with acute or highly intermittent exposures. The IEUBK
model and Adult Lead Methodology simulate quasi-steady state blood Pb concentration
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associated with exposures that have durations of >3 months. Shorter-term dynamics of blood Pb
concentrations expected to occur with exposures that vary over days or weeks cannot be
simulated with the IEUBK model or the ALM.
• The AALM can predict concentrations of Pb in bone. This offers the potential for using estimates
of bone Pb as an internal dosimeter in assessing health risk from exposure to environmental Pb.
Bone Pb may be more suitable than blood Pb when predicting risk for certain effects of Pb such
as hypertension (U.S. EPA. 2013).
• The RT model in the AALM provides a more realistic simulation of inhaled aerosols of Pb that
incorporates information on air Pb concentrations, air Pb particle size, solubility, receptor activity
levels (which determine inhalation volumes), and age. This capability of the AALM is a major
improvement over the RT representation in the IEUBK model, which consists only of parameters
for inhalation volumes, and a single parameter for the absorption fraction of inhaled Pb (from the
lung and GI tract). The Adult Lead Methodology does not represent the RT.
4.9. CALIBRATING THE AALM TO THE IEUBK MODEL
Figure 4-25 compares predictions of the AALM and the IEUBK model for a continuous dust Pb intake of
10 (ig/day. In both models, the relative bioavailability (RBA) for Pb in dust was assumed to be 60%. This
corresponds to an absolute bioavailability of approximately 20% at age 2 years in the AALM and 30% in
the IEUBK model. At age 2-3 years the IEUBK model predicts a blood Pb concentration of 1.1 (ig/dL;
AALM-LG and AALM-OF predict 2.1 and 2.8 (ig/dL, respectively.
Table 4-20 compares predictions of adult blood Pb concentrations from the Adult Lead Methodology and
AALM.CLS, for an exposure to 1000 ppm. In both models, the RBA for Pb in dust was assumed to be
60%. This corresponds to an absolute bioavailability of approximately 4.8% in the AALM and 12% in the
Adult Lead Methodology. The Adult Lead Methodology predicts a blood Pb concentration of 2.9 (ig/dL;
AALM-LG and AALM-OF predict 3.1 and 4.6 (ig/dL at age 30 years (mid-point for age range in the
Adult Lead Methodology, 17-45 years), respectively.
The optimized AALM discussed in Section 4.7 thus predicts blood Pb concentrations in children that are
approximately 2-fold higher than the currently established regulatory IEUBK model based on the same Pb
intakes. Data available for optimizing and evaluating performance of the Pb biokinetics models are
largely limited to data for Pb kinetics in adults. Only two studies have reported data on intake-blood Pb
relationships in infants (Sherlock and Ouinn. 1986; Ryu et al.. 1983). and no data of this type are
available for children in the age range 1-7 years, the age range simulated in the IEUBK model. Given the
large uncertainties in the available data on intake-blood Pb relationships in children, the model
differences in absolute terms are relatively small in the context of model capabilities (e.g., approximately
1-2 (ig/dL in children for a dust Pb ingestion rate of 10 (ig/day). These small differences in model
estimates, however, could have implications to consider in making risk management decisions at
contaminated sites, which are typically based on a "not-to-exceed" blood Pb concentration (U.S. EPA.
1994a).
The IEUBK model has a long, established history of use in risk assessment and support for soil clean-up
goals at hazardous waste sites. Thus, it was deemed worthwhile to further evaluate the most sensitive
AALM parameter values to determine which parameters values could be calibrated against the IEUBK
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model output for child blood Pb concentrations relative to Pb intake without altering the AALM model
performance in simulating the infant and adult data.
This additional evaluation identified value changes for a single biokinetic parameter, RRBC, that were
sufficient to align the AALM-LG results more closely with the IEUBK model results. The RRBC
parameter controls the rate of return of Pb from RBCs to plasma. Support for adjusting this parameter is
based on the following three arguments: (1) sensitivity analyses of the AALM-LG revealed that blood Pb
predictions were highly sensitive to parameters controlling plasma-RBC Pb exchange rates (Section 4.5,
Table 4-4), (2) the parameter RRBC value is derived from an age-dependent array that allows adjustment
of the parameter value for children without altering values for infants or adults, precluding degradation of
model performance in estimating Pb kinetics for infant and adult subpopulations; and (3) the RRBC
parameter value for children remains uncertain and has no data support, however the upward adjustment
needed for this parameter (i.e., faster outflow from RBCs) is consistent with assumptions that were made
in the early development of the Leggett model, namely that removal half-times of Pb from RBCs are
expected to be shorter in young children than in adults (Leggett. 1993). The RRBC parameter was
adjusted upward until close agreement was achieved between blood Pb predicted by AALM-LG and the
IEUBK model for a constant ingestion intake of 10 (ig/day Pb in surface dust, and an RBA relative to
soluble Pb = 0.60 (compare Figure 4-25 with 4-26).
Using the same rationale, red cell parameters in AALM-OF were adjusted to align the AALM-OF blood
Pb predictions in children more closely with the IEUBK model results. Unlike the AALM-LG, which
represents Pb exchanges between plasma and RBC with first-order rate coefficients, the AALM-OF
represents binding of Pb in RBCs as an instantaneous binding equilibrium with plasma Pb controlled by
two parameters, a half-saturation parameter (KBIND) and maximum binding capacity (BIND), both of
which are constants and independent of age. Although, either of the two parameters could be adjusted, the
half-saturation parameter (KBIND) was selected in order to keep the binding capacity unchanged, which
is similar to the strategy used in resolving differences with AALM-LG.
As illustrated in Figure 4-26, adjustments to the RBC parameters in the AALM-LG and AALM-OF
resulted in close agreement with child blood Pb profiles in children predicted by the IEUBK model. At
age 2-3 years the IEUBK model predicts a blood Pb concentration of 1.1 (ig/dL; AALM-LG and AALM-
OF predict 1.3 and 1.5 (ig/dL, respectively, for a dust Pb intake of 10 (ig/dL. Because the parameter
adjustments were age-dependent and were restricted to children, the adjustments had no effect on
predictions of Pb kinetics in adults, and the revised AALM models performed similarly to the optimized
version in predicting observed Pb kinetics in adults. Similarly, the adjustments made to the AALM RBC
parameter values for the children subpopulation had minimal effect on the model predictions of blood Pb
levels or kinetics in infants (see Figures 4-27 and 4-28). Blood and tissue Pb concentrations predicted by
the revised AALM are presented in Table 4-21.
4.10. DATA NEEDS AND FURTHER EVALUATION OF THE AALM
The improvements in the AALM discussed in this report demonstrate the considerable advancements
made in the AALM model capability and exposure interface, as well as the optimized parameters that
control important model predictions (e.g., plasma/RBC ratios, soft tissue/bone ratios, plasma-to-urine
clearance), and that have been optimized against the available data in infants and adults.
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Of particular interest to risk assessment applications are predictions of blood and bone Pb, as these two
biomarkers have been used extensively to establish dose-response relationships for health effects of Pb in
humans (U.S. EPA. 2013). The two models predict long-term accrual of Pb in blood and bone Pb levels in
adults (ages >16 years), that differ by less than 20%. This agreement is remarkable, given the very
different approaches used to simulate bone Pb, which is the major depot for Pb in the body. This
magnitude of difference is less than observed inter-individual variability in blood and bone Pb
measurements in humans (CDC. 2013; U.S. EPA. 2013; Hu et al.. 2007). The two models also predict
similar blood Pb concentrations in children. At an earlier age of 2 years, however, blood Pb
concentrations predicted from AALM-LG are approximately 25% lower than predictions from AALM-
OF, however, data are limited, and additional data are likely to result in improvements in model
performance.
Blood Pb concentrations in adults predicted from the AALM are very similar to predictions from the
Adult Lead Methodology for the same soil Pb concentrations. Predictions for infants are similar between
the AALM and the IEUBK. With the adjusted RBC parameter value, the AALM and IEUBK model
predict similar blood Pb concentrations in children for the same dust Pb intakes and RBA assumptions.
Subject to further external peer review and verification of the AALM results, the agreement between the
AALM, the IEUBK model, and the ALM supports the potential future use of the AALM in risk
assessment applications to supplement or replace the IEUBK model and the ALM in supporting
regulatory decisions. At present, however, the IEUBK model and the ALM remain the established
methods that will be used for regulatory decisions.
Recommendations for data to reduce uncertainty in the AALM model results, and improve the
consistency among all model predictions include the following:
• Resolve differences between the AALM-LG and AALM-OF predictions of blood Pb kinetics.
AALM-OF predicts slower accrual and elimination of Pb from blood compared to AALM-LG,
while AALM-LG more close reproduced blood Pb kinetics observed in the short-term Pb dosing
studies of Rabinowitz et al. (1976). Additional data on blood Pb kinetics may serve to improve
the optimization of both models, and resolve these differences. This will be important for
application of either model to simulating blood Pb dynamics associated with short-term or highly
variable exposures.
• Evaluate and optimize AALM-OF bone metabolism parameters. A literature search and review of
newer data on rates of bone production and resorption may provide a basis for re-optimization of
AALM-OF or its extension to include simulations of specific bone metabolism scenarios of
interest to toxicology or risk assessment (e.g., pregnancy, osteomalacia).
• Further verify AALM-LG and AALM-OF predictions. Additional observations in humans should
be identified that can serve to evaluate the performance of the optimized AALM (and that were
not used in the optimization). Ideally, these would be blood and/or bone Pb measurements in
people for whom Pb intakes are known with reasonable certainty. Ethical concerns typically
preclude Pb dosing experiments; therefore, Pb doses must be estimated with accurate tools such
as duplicate diet surveys or dietary recalls and information on Pb levels in diet and other relevant
exposure media. Types of data that would be valuable for model validation include: (1) blood soft
tissue or bone Pb levels in children or adults for whom Pb dosage is known or can be reliable
estimated from exposure data; (2) changes in blood, soft tissue or bone Pb levels in children or
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adults following and abrupt change (increase or decrease) in Pb exposure; (3) steady state (or
quasi-steady state) blood/soft tissue blood/bone Pb ratios in children or adults; (4) urinary Pb
clearance from blood or plasma in children or adults; and (5) plasma/whole blood concentration
ratios in children.
• Evaluate and document the empirical basis for exposure model parameters. Most of the exposure
parameter values in the AALM.CLS serve as placeholders and should, in the future, be replaced
with default values for specific receptor populations for which an empirical basis can be
provided.
• Further refine the RT model. The AALM.CLS includes values for inhalation rates and deposition
fractions for the general public, as defined by ICRP (1994). These values do not adequately
represent many receptor populations of interest who have activity levels that differ from general
population assumptions (e.g., workers). Additional parameter value matrices should be developed
to represent selected receptor populations of interest.
Finally, the AALM has been developed with a relatively easy to use and versatile exposure interface,
access to model parameters and values, and transparency of model code to support stakeholder use and
evaluation internally and external to the Agency. It is recommendation of this report that the AALM be
made available to the Agency and the research community as a beta test version to facilitate additional
case studies, parameter refinements and external evaluation; and to advance the model towards regulatory
use and exposure assessment.
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1 TABLE 4-1. SUMMARY OF MAJOR DIFFERENCES BETWEEN STRUCTURES OF AALM-
2 LG AND AALM-OF
Model Component
AALM-LG
AALM-OF
GI tract
Absorption from GI
tract
Plasma
RBC
Kidney
Liver
Other soft tissue
Well-perfused tissue
Brain
Bone
Four compartments representing
stomach, small intestine, upper and
lower large intestine
First-order transfer from small
intestine to blood
Two compartments representing
diffusible (transferable to other
tissues) and bound
Binding represented with first-order
rate transfer rates adjusted for
saturating concentration
Two compartments, first-order
transfer rates
Two compartments, first-order
transfer rates
Three compartments, first-order
transfer rates
Poorly perfused tissue None
Sweat
Miscellaneous excretory
routes (e.g., hair)
None
One compartment, first-order
transfer rates
Six compartments representing
surface, exchangeable and non-
exchangeable cortical and trabecular
bone. Pb transfers governed by age-
dependent first-order transfer rates
First-order transfer from plasma to
sweat
First-order transfer from other soft
tissues to other excretory routes
No GI tract compartment
First-order transfer of ingested Pb to
liver (portal blood)
One compartment in equilibrium
with bound Pb in RBC
Binding represented with non-linear
binding function (i.e., maximum and
half-saturating concentration)
One compartment with flow-limited
transfer
One compartment with flow-limited
transfer
None
One compartment with flow-limited
transfer
One compartment with flow-limit
transfer
None
Transfer to and from metabolically
active trabecular and cortical bone
governed by age-dependent bone
formation and resorption rates,
respectively; transfer to and from
mature cortical bone governed by
radial diffusion
None
None
3
4
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1 TABLE 4-2. AALM-LG INPUT PARAMETERS CONTROLLING POST-ABSORPTION PB
2 KINETICS
Rate at Specified Age (day1)
No.
Transfer
Pathway
Controlling
Parameter(s)
0-100
days
1 year
5 years
10 years
15 years
>25 years
1
Plasma-D to
EVF
TEVF
1.00E+03
1.00E+03
1.00E+03
1.00E+03
1.00E+03
1.00E+03
2
Plasma-D to
RBCs
TORBC
2.97E+02
4.07E+02
4.25E+02
3.67E+02
3.01E+02
4.80E+02
3
Plasma-D to
Plasma-B
TOPROT
4.95E-01
6.78E-01
7.09E-01
6.11E-01
5.01E-01
8.00E-01
4
Plasma-D to
Urinary
bladder
TOURIN
1.86E+01
2.54E+01
2.66E+01
2.29E+01
1.88E+01
3.00E+01
5
Plasma-D to
Small intestine
TOFECE
7.43E+00
1.02E+01
1.06E+01
9.17E+00
7.51E+00
1.20E+01
6
Plasma-D to
Trab surf
TOBONE
(TFRAC)
9.60E+01
5.76E+01
5.68E+01
8.95E+01
1.32E+02
8.90E+01
7
Plasma-D to
Cort surf
TBONE (1-
TFRAC)
3.84E+02
2.30E+02
1.99E+02
2.69E+02
3.42E+02
7.10E+01
8
Plasma-D to
Liver 1
TOLVR1
4.95E+01
6.78E+01
7.09E+01
6.11E+01
5.01E+01
8.00E+01
9
Plasma-D to
Urinary path
TOKDN1
2.48E+01
3.39E+01
3.54E+01
3.06E+01
2.51E+01
4.00E+01
10
Plasma-D to
Other kidney
TOKDN2
2.48E-01
3.39E-01
3.54E-01
3.06E-01
2.50E-01
4.00E-01
11
Plasma-D to
STO
TOSOFO
1.03E+02
1.42E+02
1.48E+02
1.28E+02
1.05E+02
1.78E+02
12
Plasma-D to
ST1
TOSOF1
1.24E+01
1.70E+01
1.77E+01
1.53E+01
1.25E+01
1.00E+01
13
Plasma-D to
ST2
TOSOF2
1.24E+00
1.70E+00
1.77E+00
1.53E+00
1.25E+00
2.00E+00
14
Plasma-D to
Brain
TOBRAN
5.57E-01
7.63E-01
2.66E-01
2.29E-01
1.88E-01
3.00E-01
15
Plasma-D to
Sweat
TOWET
4.33E+00
5.93E+00
6.20E+00
5.35E+00
4.38E+00
7.00E+00
16
RBCs to
Plasma-D
RRBC
4.62E-01
4.62E-01
2.77E-01
1.39E-01
1.39E-01
1.39E-01
17
EVF to
Plasma-D
RPLAS
3.33E+02
3.33E+02
3.33E+02
3.33E+02
3.33E+02
3.33E+02
18
Plasma-B to
Plasma-D
RPROT
1.39E-01
1.39E-01
1.39E-01
1.39E-01
1.39E-01
1.39E-01
19
Cort surf to
Plasma-D
RCS2DF
6.50E-01
6.50E-01
6.50E-01
6.50E-01
6.50E-01
5.00E-01
20
Trab surf to
Plasma-D
RTS2DF
6.50E-01
6.50E-01
6.50E-01
6.50E-01
6.50E-01
5.00E-01
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Rate at Specified Age (day1)
No.
Transfer
Pathway
Controlling
Parameter(s)
0-100
days
1 year
5 years
10 years
15 years
>25 years
21
Cort surf to
Exch vol
RCS2B
3.50E-01
3.50E-01
3.50E-01
3.50E-01
3.50E-01
5.00E-01
22
Trab surf to
Exch vol
RTS2B
3.50E-01
3.50E-01
3.50E-01
3.50E-01
3.50E-01
5.00E-01
23
Cort exch vol
to Surl
RDIFF*(1-
FLONG)
1.85E-02
1.85E-02
1.85E-02
1.85E-02
1.85E-02
1.85E-02
24
Trab exch vol
to Surf
RDIFF*(1-
FLONG)
1.85E-02
1.85E-02
1.85E-02
1.85E-02
1.85E-02
1.85E-02
25
Cort exch vol
to Nonexch vol
RDIFF*FLO
NG
4.62E-03
4.62E-03
4.62E-03
4.62E-03
4.62E-03
4.62E-03
26
Trab exch vol
to Nonexcn vol
RDIFF*FLO
NG
4.62E-03
4.62E-03
4.62E-03
4.62E-03
4.62E-03
4.62E-03
27
Cort nonexch
vol to Plasma-
D
RCORT
8.22E-03
2.88E-03
1.54E-03
8.90E-04
5.12E-04
8.22E-05
28
Trab nonexch
vol to Plasma-
D
RCORT
8.22E-03
2.88E-03
1.81E-03
1.32E-03
9.56E-04
4.93E-04
29
Liver 1 to
Plasma-D
RLVR1
3.12E-02
3.12E-02
3.12E-02
3.12E-02
3.12E-02
3.12E-02
30
Liver 1 to
Small intestine
H1TOSI
3.12E-02
3.12E-02
3.12E-02
3.12E-02
3.12E-02
3.12E-02
31
Liver 1 to
Liver 2
H1TOH2
6.93E-03
6.93E-03
6.93E-03
6.93E-03
6.93E-03
6.93E-03
32
Liver 2 to
Plasma-D
RLVR2
6.93E-03
6.93E-03
6.93E-03
1.90E-03
1.90E-03
1.90E-03
33
Urinary path to
Urinary
bladder
RBLAD
1.39E-01
1.39E-01
1.39E-01
1.39E-01
1.39E-01
1.39E-01
34
Other kidney to
Plasma-D
RKDN2
6.93E-03
6.93E-03
6.93E-03
1.90E-03
1.90E-03
1.90E-03
35
STOto
Plasma-D
RSOFO
2.08E+00
2.08E+00
2.08E+00
2.08E+00
2.08E+00
2.08E+00
36
STlto
Plasma-D
RSOF1
4.16E-03
4.16E-03
4.16E-03
4.16E-03
4.16E-03
4.16E-03
37
ST1 to Excreta
S2HAIR
2.77E-03
2.77E-03
2.77E-03
2.77E-03
2.77E-03
2.77E-03
38
ST2 to
Plasma-D
RSOF2
3.80E-04
3.80E-04
3.80E-04
3.80E-04
3.80E-04
3.80E-04
39
Brain to
Plasma-D
RBRAN
9.50E-04
9.50E-04
9.50E-04
9.50E-04
9.50E-04
9.50E-04
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1 TABLE 4-3. AALM-OF INPUT PARAMETERS CONTROLLING POST-ABSORPTION PB
2 KINETICS
No. Parameter Unit Value Parameter Description
1 A1 - 4.0 Constant 1 for bone formation rate algorithm
2 A2 - 0.4 Constant 2 for bone formation rate algorithm
3 A3 - 4.0 Constant 3 for bone formation rate algorithm
4 A5 - 0.6 Constant 5 for bone formation rate algorithm
5 AGEO year 0 Age at which simulation begins
6 BASE - 0.1 Base bone formation rate in bone growth algorithm
7 BIND mg/L 2.7 Maximum capacity of sites in red cells to bind Pb
8 CI - 1.0 Constant 1 for urinary clearance of Pb as a fraction
of GFR
9 C2 - 0.9 Constant 2 for urinary clearance of Pb as a fraction
of GFR
10 C3 - 50 Constant 3 for urinary clearance of Pb as a fraction
of GFR
11 CON f 0.65 Fraction of bone blood flow to trabecular bone
12 DO cm3/day 0.0000005 Diffusion constant
13 EXPO - 0.6 Exponent constant for bone volume participating in
adult-type bone remodeling
14 G NA 1.2 Linear parameter for unbound lead in red cells
15 KBIND mg/L 0.0075 Half-saturation concentration of Pb for binding by
sites in red cells
16 P0 cm3/day 0.02 Permeability constant for diffusion from canaliculi
to bone
17 PK f 50 Kidney/plasma partition coefficient
18 PL f 50 Liver/plasma partition coefficient
19 PP f 2.0 Poorly perfused/plasma partition coefficient
20 PW f 50 Well-perfused/plasma partition coefficient
21 QBONEC f 0.05 Fraction cardiac output going to bone
22 QCC L/day/kg 340 Cardiac output in the adult
23 QKC f 0.17 Fraction cardiac output going to kidney
24 QLC f 0.25 Fraction cardiac output going to liver
25 QWC f 0.44 Fraction cardiac output going to other well-perfused
tissues
26 R0 cm3/day 0.0000005 Permeability constant for diffusion from bone to
canaliculi
27 RAD1 cm 0.000027 Radius of shell 1 of bone in the canalicular diffusion
region of deeper bone
28 RAD2 cm 0.000052 Radius of shell 2 of bone in the canalicular diffusion
region of deeper bone
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No.
Parameter
Unit
Value
Parameter Description
29
RAD3
cm
0.000079
Radius of shell 3 of bone in the canalicular diffusion
region of deeper bone
30
RAD4
cm
0.000106
Radius of shell 4 of bone in the canalicular diffusion
region of deeper bone
31
RAD5
cm
0.000133
Radius of shell 5 of bone in the canalicular diffusion
region of deeper bone
32
RAD6
cm
0.000160
Radius of shell 6 of bone in the canalicular diffusion
region of deeper bone
33
RAD7
cm
0.000187
Radius of shell 7 of bone in the canalicular diffusion
region of deeper bone
34
RAD 8
cm
0.000214
Radius of shell 8 of bone in the canalicular diffusion
region of deeper bone
35
S
cm2/cm
0.000126
Surface area of canaliculi
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1 TABLE 4-4. AALM-LG STANDARDIZED SENSITIVITY COEFFICIENTS FOR BLOOD PB IN
2 CHILDREN (5 YEARS) AND ADULTS (30 YEARS)
Variable Parameter Child
Adult
Parameter Description
ABLOOD TEVF 9.16E+00
ABLOOD TORBC 5.30E+00
ABLOOD TOSOFO 1.50E+00
ABLOOD TBONEL 1.42E+00
ABLOOD RRBC
ABLOOD TFRAC
ABLOOD RDIFF
1.00E+00
ABLOOD TOLVR1 4.90E-01
ABLOOD H1TOBL 3.25E-01
ABLOOD TBONE 1.05E-01
8.33E-03
ABLOOD H1TOH2 7.70E-02
ABLOOD TOSOF1 1.16E-01
ABLOOD S2HAIR 7.63E-02
ABLOOD H1TOSI 8.91E-02
ABLOOD TOSOF2 9.31E-03
ABLOOD RCORT 9.00E-02
ABLOOD RTS2B 8.11E-03
ABLOOD RTS2DF 7.59E-03
ABLOOD RTRAB 2.12E-02
6.04E-02
8.38E+00 Deposition fraction from diffusible plasma to
extravascular fluid
4.93E+00 Deposition fraction from diffusible plasma to RBCs,
below non-linear threshold
1.44E+00 Age-scaled deposition fraction from diffusible
plasma to soft tissue compartment 0
1.30E+00 Terminal value of age-scaled deposition fraction
from diffusible plasma to surface bone
9.98E-01 Age-scaled transfer rate from RBC to diffusible
plasma
3.85E-01 Deposition fraction from diffusible plasma to liver
compartment 2
2.94E-01 Fraction of transfer out of liver compartment 1 to
diffusible plasma
7.16E-02 Age-scaled deposition fraction from diffusible
plasma to surface bone
7.10E-02 Bone deposition-scaled fraction of diffusible
plasma-to-bone deposition that goes to trabecular
surface bone; 1-TFRAC is the fraction that goes to
cortical surface bone
6.58E-02 Fraction of transfer out of liver compartment 1 to
liver compartment 2
5.52E-02 Age-scaled deposition fraction from diffusible
plasma to soft tissue compartment 1
3.63E-02 Deposition fraction from soft tissue compartment 1
to other excreta
2.49E-02 Fraction of transfer out of liver compartment 1 to
the small intestine
1.76E-02 Age-scaled deposition fraction from diffusible
plasma to soft tissue compartment 2
1.27E-02 Age-scaled transfer rate from non-exchangeable
cortical bone to diffusible plasma
1.17E-02 Age-scaled transfer rate from surface trabecular
bone to exchangeable trabecular bone
1.17E-02 Age-scaled transfer rate from trabecular bone
surface to diffusible plasma
1.06E-02 Age-scaled transfer rate from non-exchangeable
trabecular bone to diffusible plasma
1.04E-02 Age-scaled transfer rate from the exchangeable
bone, including transfer to surface and non-
exchangeable bone
123
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable Parameter Child
Adult
Parameter Description
ABLOOD TOFECE 3.23E-02 9.00E-03
ABLOOD TOPROT 1.06E-02
ABLOOD TOKDN2 3.81E-03
ABLOOD TOBRAN 5.10E-03
ABLOOD RSOF2 8.49E-03
ABLOOD RPROT 3.38E-03
ABLOOD RCS2DF 2.21E-02
ABLOOD RCS2B
2.42E-02
ABLOOD FLONG 4.12E-02
ABLOOD RSOF1 5.63E-03
ABLOOD RPLAS 6.95E-04
ABLOOD RLVR2 3.70E-03
ABLOOD RBRAN 1.66E-03
ABLOOD RLVR1 3.03E-03
ABLOOD RSOFO 3.74E-04
ABLOOD RKDN2 1.93E-04
ABLOOD TOKDN1 1.18E-05
ABLOOD TOURIN 8.88E-06
ABLOOD RSTMC 1.42E-05
ABLOOD SIZEVF 6.52E-06
ABLOOD GSCAL 2.30E-05
ABLOOD RULI 4.98E-05
8.24E-03
3.28E-03
2.62E-03
2.40E-03
1.66E-03
1.57E-03
1.34E-03
1.25E-03
4.37E-04
2.94E-04
2.20E-04
1.76E-04
1.00E-04
1.09E-05
1.09E-05
5.81E-06
4.35E-06
3.62E-06
3.27E-06
2.63E-06
1.07E-06
Deposition fraction from diffusible plasma directly
to the small intestine (not including the transfer
from biliary secretion, specified by RLVR1)
Deposition fraction from diffusible plasma to
protein-bound plasma
Deposition fraction from diffusible plasma to
kidney compartment 2
Age-scaled deposition fraction from diffusible
plasma to brain
Transfer rate from soft tissue compartment 2 to
diffusible plasma
Transfer rate from bound plasma to diffusible
plasma
Age-scaled transfer rate from cortical bone surface
to diffusible plasma
Age-scaled transfer rate from cortical bone surface
to exchangeable cortical bone
Age-scaled fraction of total transfer from the
exchangeable bone directed to non-exchangeable
bone
Transfer rate from soft tissue compartment 1 to
diffusible plasma
Total transfer rate from diffusible plasma to all
compartments
Age-scaled transfer rate from the slow liver
compartment 2 to diffusible plasma
Age-scaled transfer rate from brain to diffusible
plasma
Transfer rate out of the liver compartment 1,
including to small intestine and diffusible plasma
Transfer rate from soft tissue compartment 0 to
diffusible plasma
Age-scaled transfer rate from kidney compartment 2
to diffusible plasma
Deposition fraction from diffusible plasma to
kidney compartment 1
Deposition fraction from diffusible plasma to urine
Transfer rate from stomach to small intestine
Relative volume of the EVF compartment compared
to plasma (EVF/Plasma)
Age-scaling factor for GIT transfer
Transfer rate from upper large intestine to lower
large intestine
124
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable
Parameter
Child
Adult
Parameter Description
ABLOOD
TOSWET
2.18E-06
1.06E-06
Deposition fraction from diffusible plasma to sweat
ABLOOD
RSIC
5.92E-05
7.18E-07
Transfer rate from small intestine to upper large
intestine
ABLOOD
RLLI
5.28E-06
1.16E-07
Transfer rate from lower large intestine to feces
ABLOOD
RKDN1
5.83E-10
1.31E-08
Transfer rate from kidney compartment 1 to urinary
pathway
ABLOOD
POWER
0.00E+00
0.00E+00
Exponent for RBC deposition
ABLOOD
RBCNL
0.00E+00
0.00E+00
Threshold concentration in RBC for non-linear
deposition from diffusible plasma to RBC
ABLOOD
SATRAT
0.00E+00
0.00E+00
Maximum (saturating) concentration of lead in RBC
ABLOOD
RBLAD
0.00E+00
0.00E+00
Age-scaled transfer rate from urinary bladder to
urine
1
2
125
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 TABLE 4-5. AALM-LG STANDARDIZED SENSITIVITY COEFFICIENTS FOR BONE PB IN
2 CHILDREN (5 YEARS) AND ADULTS (30 YEARS)
Variable Parameter Child
Adult
Parameter Description
ABONE TEVF
ABONE TORBC 3.75E+00
ABONE TBONE 1.27E+00
ABONE TOSOFO 1.31E+00
ABONE TBONEL 1.07E+00
ABONE FLONG 3.93E-01
ABONE RCS2DF 5.33E-01
ABONE TOLVR1 4.44E-01
ABONE H1TOBL 2.81E-01
ABONE RTS2DF 1.36E-01
ABONE TOSOF1 9.53E-02
ABONE H1TOH2 6.29E-02
ABONE H1TOSI 9.98E-02
ABONE TOSOF2 5.70E-03
ABONE TOFECE 3.60E-02
ABONE TOPROT 6.28E-03
ABONE TOBRAN 3.68E-03
ABONE TOKDN2 3.13E-03
ABONE RLVR2
8.11E+00 8.12E+00 Deposition fraction from diffusible plasma to
extravascular fluid
3.71E+00 Deposition fraction from diffusible plasma to RBCs,
below non-linear threshold
1.42E+00 Age-scaled deposition fraction from diffusible
plasma to surface bone
1.32E+00 Age-scaled deposition fraction from diffusible
plasma to soft tissue compartment 0
1.05E+00 Terminal value of age-scaled deposition fraction
from diffusible plasma to surface bone
6.80E-01 Age-scaled fraction of total transfer from the
exchangeable bone directed to non-exchangeable
bone
6.02E-01 Age-scaled transfer rate from cortical bone surface
to diffusible plasma
3.70E-01 Deposition fraction from diffusible plasma to liver
compartment 2
2.78E-01 Fraction of transfer out of liver compartment 1 to
diffusible plasma
1.48E-01 Age-scaled transfer rate from trabecular bone
surface to diffusible plasma
7.79E-02 Age-scaled deposition fraction from diffusible
plasma to soft tissue compartment 1
6.13E-02 Fraction of transfer out of liver compartment 1 to
liver compartment 2
3.06E-02 Fraction of transfer out of liver compartment 1 to
the small intestine
1.94E-02 Age-scaled deposition fraction from diffusible
plasma to soft tissue compartment 2
1.11E-02 Deposition fraction from diffusible plasma directly
to the small intestine (not including the transfer
from biliary secretion, specified by RLVR1)
6.20E-03 Deposition fraction from diffusible plasma to
protein-bound plasma
3.25E-03 Age-scaled deposition fraction from diffusible
plasma to brain
3.05E-03 Deposition fraction from diffusible plasma to
kidney compartment 2
8.15E-04 6.26E-04 Age-scaled transfer rate from the slow liver
compartment 2 to diffusible plasma
126
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable Parameter Child
Adult
Parameter Description
ABONE RKDN2
ABONE GSCAL
ABONE RULI
ABONE RLLI
ABONE RKDN1
3.09E-05 3.22E-05
ABONE RSOFO
ABONE RRBC
ABONE RSOF2
ABONE RSOF1
4.15E-05
8.28E-05
8.76E-06
9.84E-10
ABONE POWER 0.00E+00
ABONE RBCNL 0.00E+00
ABONE SATRAT 0.00E+00
ABONE RBLAD 0.00E+00
ABONE TOSWET 1.38E-08
ABONE TOURIN 5.72E-08
ABONE TOKDN1 7.63E-08
ABONE RPROT 5.69E-06
ABONE RSIC 1.12E-04
ABONE SIZEVF 4.23E-06
ABONE RSTMC 1.52E-05
ABONE RPLAS 3.87E-05
7.55E-05
1.06E-03
ABONE RLVR1 1.51E-04
ABONE RBRAN 1.82E-03
6.31E-03
1.16E-03
ABONE S2HAIR 6.27E-02
1.35E-05
6.79E-06
7.29E-07
8.50E-08
0.00E+00
0.00E+00
0.00E+00
0.00E+00
9.86E-09
4.07E-08
1.38E-07
3.42E-06
8.33E-06
2.34E-05
2.48E-05
3.19E-05
4.18E-05
6.84E-05
4.01E-04
1.03E-03
1.26E-03
2.10E-03
5.13E-02
Age-scaled transfer rate from kidney compartment 2
to diffusible plasma
Age-scaling factor for GIT transfer
Transfer rate from upper large intestine to lower
large intestine
Transfer rate from lower large intestine to feces
Transfer rate from kidney compartment 1 to urinary
pathway
Exponent for RBC deposition
Threshold concentration in RBC for non-linear
deposition from diffusible plasma to RBC
Maximum (saturating) concentration of lead in RBC
Age-scaled transfer rate from urinary bladder to
urine
Deposition fraction from diffusible plasma to sweat
Deposition fraction from diffusible plasma to urine
Deposition fraction from diffusible plasma to
kidney compartment 1
Transfer rate from bound plasma to diffusible
plasma
Transfer rate from small intestine to upper large
intestine
Relative volume of the EVF compartment compared
to plasma (EVF/Plasma)
Transfer rate from stomach to small intestine
Total transfer rate from diffusible plasma to all
compartments
Transfer rate from soft tissue compartment 0 to
diffusible plasma
Age-scaled transfer rate from RBC to diffusible
plasma
Transfer rate out of the liver compartment 1,
including to small intestine and diffusible plasma
Age-scaled transfer rate from brain to diffusible
plasma
Transfer rate from soft tissue compartment 2 to
diffusible plasma
Transfer rate from soft tissue compartment 1 to
diffusible plasma
Deposition fraction from soft tissue compartment 1
to other excreta
127
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable
Parameter
Child
Adult
Parameter Description
ABONE
RDIFF
2.93E-01
8.41E-02
Age-scaled transfer rate from the exchangeable
bone, including transfer to surface and non-
exchangeable bone
ABONE
RTS2B
1.38E-01
1.48E-01
Age-scaled transfer rate from surface trabecular
bone to exchangeable trabecular bone
ABONE
RTRAB
1.17E-01
1.83E-01
Age-scaled transfer rate from non-exchangeable
trabecular bone to diffusible plasma
ABONE
TFRAC
1.03E-02
3.00E-01
Bone deposition-scaled fraction of diffusible
plasma-to-bone deposition that goes to trabecular
surface bone; 1-TFRAC is the fraction that goes to
cortical surface bone
ABONE
RCS2B
5.41E-01
6.03E-01
Age-scaled transfer rate from cortical bone surface
to exchangeable cortical bone
ABONE
RCORT
4.61E-01
7.07E-01
Age-scaled transfer rate from non-exchangeable
cortical bone to diffusible plasma
128
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 TABLE 4-6. AALM-LG STANDARDIZED SENSITIVITY COEFFICIENTS FOR LIVER PB IN
2 CHILDREN (5 YEARS) AND ADULTS (30 YEARS)
Variable Parameter Child Adult
Parameter Description
ALIVER TEVF
8.91E+00 8.41E+00
ALIVER TORBC 4.19E+00 3.94E+00
ALIVER TOSOFO 1.46E+00 1.45E+00
ALIVER TOLVR1 1.48E+00 1.39E+00
ALIVER TBONEL 1.39E+00 1.31E+00
ALIVER H1TOH2 6.09E-01 8.54E-01
ALIVER RLVR2 5.99E-01 7.92E-01
ALIVER H1TOBL 3.16E-01 2.95E-01
ALIVER RLVR1 4.83E-01 2.14E-01
ALIVER TBONE 6.32E-02 7.96E-02
ALIVER TFRAC 7.36E-03 7.60E-02
ALIVER TOSOF1 1.12E-01 5.62E-02
ALIVER S2HAIR 7.35E-02 3.69E-02
ALIVER H1TOSI 9.28E-02 2.54E-02
ALIVER TOSOF2 8.37E-03 1.77E-02
ALIVER RCORT 9.61E-02 1.41E-02
ALIVER RTS2B 3.07E-03 1.36E-02
ALIVER RTS2DF 2.66E-03 1.35E-02
ALIVER RDIFF
4.72E-02 1.26E-02
Deposition fraction from diffusible plasma to
extravascular fluid
Deposition fraction from diffusible plasma to
RBCs, below non-linear threshold
Age-scaled deposition fraction from diffusible
plasma to soft tissue compartment 0
Deposition fraction from diffusible plasma to liver
compartment 2
Terminal value of age-scaled deposition fraction
from diffusible plasma to surface bone
Fraction of transfer out of liver compartment 1 to
liver compartment 2
Age-scaled transfer rate from the slow liver
compartment 2 to diffusible plasma
Fraction of transfer out of liver compartment 1 to
diffusible plasma
Transfer rate out of the liver compartment 1,
including to small intestine and diffusible plasma
Age-scaled deposition fraction from diffusible
plasma to surface bone
Bone deposition-scaled fraction of diffusible
plasma-to-bone deposition that goes to trabecular
surface bone; 1-TFRAC is the fraction that goes to
cortical surface bone
Age-scaled deposition fraction from diffusible
plasma to soft tissue compartment 1
Deposition fraction from soft tissue compartment 1
to other excreta
Fraction of transfer out of liver compartment 1 to
the small intestine
Age-scaled deposition fraction from diffusible
plasma to soft tissue compartment 2
Age-scaled transfer rate from non-exchangeable
cortical bone to diffusible plasma
Age-scaled transfer rate from surface trabecular
bone to exchangeable trabecular bone
Age-scaled transfer rate from trabecular bone
surface to diffusible plasma
Age-scaled transfer rate from the exchangeable
bone, including transfer to surface and non-
exchangeable bone
129
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable Parameter Child
Adult
Parameter Description
ALIVER TOFECE 3.34E-02 9.08E-03
ALIVER RTRAB 2.34E-02 8.01E-03
ALIVER TOPROT 7.10E-03 6.65E-03
ALIVER TOKDN2 3.67E-03 3.29E-03
ALIVER TOBRAN 4.79E-03 2.64E-03
ALIVER RSOF2 7.94E-03 2.61E-03
ALIVER RCS2DF 5.38E-03 1.75E-03
ALIVER RCS2B 7.19E-03 1.48E-03
ALIVER FLONG 4.94E-02 7.59E-04
ALIVER RSOF1
ALIVER RRBC
4.17E-03 5.79E-04
2.10E-03 2.48E-04
ALIVER RBRAN 1.76E-03 1.89E-04
ALIVER RSOFO
3.13E-04 1.22E-05
ALIVER RPLAS 5.46E-05 5.13E-06
ALIVER GSCAL 2.56E-05 3.35E-06
ALIVER RSTMC 2.51E-05 3.23E-06
ALIVER SIZEVF 6.72E-06 2.84E-06
ALIVER RKDN2 1.45E-04 2.69E-06
ALIVER RULI
5.24E-05 1.17E-06
ALIVER RPROT 2.25E-05 9.68E-07
ALIVER RSIC
ALIVER RLLI
5.27E-05 2.33E-07
5.56E-06 1.27E-07
Deposition fraction from diffusible plasma directly
to the small intestine (not including the transfer
from biliary secretion, specified by RLVR1)
Age-scaled transfer rate from non-exchangeable
trabecular bone to diffusible plasma
Deposition fraction from diffusible plasma to
protein-bound plasma
Deposition fraction from diffusible plasma to
kidney compartment 2
Age-scaled deposition fraction from diffusible
plasma to brain
Transfer rate from soft tissue compartment 2 to
diffusible plasma
Age-scaled transfer rate from cortical bone surface
to diffusible plasma
Age-scaled transfer rate from cortical bone surface
to exchangeable cortical bone
Age-scaled fraction of total transfer from the
exchangeable bone directed to non-exchangeable
bone
Transfer rate from soft tissue compartment 1 to
diffusible plasma
Age-scaled transfer rate from RBC to diffusible
plasma
Age-scaled transfer rate from brain to diffusible
plasma
Transfer rate from soft tissue compartment 0 to
diffusible plasma
Total transfer rate from diffusible plasma to all
compartments
Age-scaling factor for GIT transfer
Transfer rate from stomach to small intestine
Relative volume of the EVF compartment
compared to plasma (EVF/Plasma)
Age-scaled transfer rate from kidney compartment
2 to diffusible plasma
Transfer rate from upper large intestine to lower
large intestine
Transfer rate from bound plasma to diffusible
plasma
Transfer rate from small intestine to upper large
intestine
Transfer rate from lower large intestine to feces
130
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable
Parameter
Child
Adult
Parameter Description
ALIVER
TOKDN1
3.12E-07
3.12E-08
Deposition fraction from diffusible plasma to
kidney compartment 1
ALIVER
RKDN1
6.21E-10
1.44E-08
Transfer rate from kidney compartment 1 to
urinary pathway
ALIVER
TOURIN
2.34E-07
1.28E-08
Deposition fraction from diffusible plasma to urine
ALIVER
TOSWET
5.69E-08
3.10E-09
Deposition fraction from diffusible plasma to sweat
ALIVER
POWER
0.00E+00
0.00E+00
Exponent for RBC deposition
ALIVER
RBCNL
0.00E+00
0.00E+00
Threshold concentration in RBC for non-linear
deposition from diffusible plasma to RBC
ALIVER
SATRAT
0.00E+00
0.00E+00
Maximum (saturating) concentration of lead in
RBC
ALIVER
RBLAD
0.00E+00
0.00E+00
Age-scaled transfer rate from urinary bladder to
urine
131
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 TABLE 4-7. AALM-LG STANDARDIZED SENSITIVITY COEFFICIENTS FOR KIDNEY PB IN
2 CHILDREN (5 YEARS) AND ADULTS (30 YEARS)
Variable Parameter Child
Adult
Parameter Description
AKIDNEY TEVF
AKIDNEY TORBC 4.27E+00
AKIDNEY TOSOFO 1.48E+00
AKIDNEY TBONEL 1.41E+00
AKIDNEY RKDN1 8.20E-01
AKIDNEY TOKDN1 8.15E-01
AKIDNEY TOKDN2 1.91E-01
AKIDNEY RKDN2 2.08E-01
AKIDNEY TOLVR1 4.88E-01
AKIDNEY H1TOBL 3.22E-01
AKIDNEY TBONE 9.11E-02
AKIDNEY TFRAC
AKIDNEY H1TOH2 7.60E-02
AKIDNEY TOSOF1 1.15E-01
AKIDNEY S2HAIR 7.53E-02
AKIDNEY H1TOSI 9.02E-02
AKIDNEY TOSOF2 8.99E-03
AKIDNEY RCORT 9.20E-02
AKIDNEY RTS2B
9.08E+00 8.40E+00 Deposition fraction from diffusible plasma to
extravascular fluid
3.94E+00 Deposition fraction from diffusible plasma to
RBCs, below non-linear threshold
1.44E+00 Age-scaled deposition fraction from diffusible
plasma to soft tissue compartment 0
1.31E+00 Terminal value of age-scaled deposition fraction
from diffusible plasma to surface bone
5.76E-01 Transfer rate from kidney compartment 1 to
urinary pathway
5.76E-01 Deposition fraction from diffusible plasma to
kidney compartment 1
4.30E-01 Deposition fraction from diffusible plasma to
kidney compartment 2
4.27E-01 Age-scaled transfer rate from kidney
compartment 2 to diffusible plasma
3.87E-01 Deposition fraction from diffusible plasma to
liver compartment 2
2.95E-01 Fraction of transfer out of liver compartment 1 to
diffusible plasma
7.58E-02 Age-scaled deposition fraction from diffusible
plasma to surface bone
8.00E-03 7.36E-02 Bone deposition-scaled fraction of diffusible
plasma-to-bone deposition that goes to trabecular
surface bone; 1-TFRAC is the fraction that goes
to cortical surface bone
6.59E-02 Fraction of transfer out of liver compartment 1 to
liver compartment 2
5.57E-02 Age-scaled deposition fraction from diffusible
plasma to soft tissue compartment 1
3.66E-02 Deposition fraction from soft tissue compartment
1 to other excreta
2.51E-02 Fraction of transfer out of liver compartment 1 to
the small intestine
1.76E-02 Age-scaled deposition fraction from diffusible
plasma to soft tissue compartment 2
1.34E-02 Age-scaled transfer rate from non-exchangeable
cortical bone to diffusible plasma
6.42E-03 1.27E-02 Age-scaled transfer rate from surface trabecular
bone to exchangeable trabecular bone
132
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable Parameter Child
Adult
Parameter Description
AKIDNEY RTS2DF 5.94E-03
AKIDNEY RDIFF
AKIDNEY RSOF2
AKIDNEY RCS2B
AKIDNEY RSOF1
AKIDNEY RRBC
5.60E-02
AKIDNEY RTRAB 2.21E-02
AKIDNEY TOFECE 3.27E-02
AKIDNEY TOPROT 7.16E-03
AKIDNEY TOBRAN 4.99E-03
8.31E-03
AKIDNEY RCS2DF 1.65E-02
1.85E-02
AKIDNEY FLONG 4.39E-02
5.14E-03
2.76E-03
AKIDNEY RBRAN 1.69E-03
AKIDNEY RLVR2 3.37E-03
AKIDNEY RLVR1 2.85E-03
AKIDNEY RSOFO 3.53E-04
AKIDNEY RPLAS 4.93E-05
AKIDNEY RSTMC 1.74E-05
AKIDNEY SIZEVF 2.54E-06
1.26E-02
1.16E-02
9.30E-03
9.04E-03
6.58E-03
2.63E-03
2.51E-03
1.67E-03
1.41E-03
9.93E-04
5.12E-04
2.28E-04
1.83E-04
1.32E-04
1.07E-04
1.16E-05
5.15E-06
3.41E-06
3.05E-06
AKIDNEY GSCAL 2.37E-05 3.01E-06
Age-scaled transfer rate from trabecular bone
surface to diffusible plasma
Age-scaled transfer rate from the exchangeable
bone, including transfer to surface and non-
exchangeable bone
Age-scaled transfer rate from non-exchangeable
trabecular bone to diffusible plasma
Deposition fraction from diffusible plasma
directly to the small intestine (not including the
transfer from biliary secretion, specified by
RLVR1)
Deposition fraction from diffusible plasma to
protein-bound plasma
Age-scaled deposition fraction from diffusible
plasma to brain
Transfer rate from soft tissue compartment 2 to
diffusible plasma
Age-scaled transfer rate from cortical bone
surface to diffusible plasma
Age-scaled transfer rate from cortical bone
surface to exchangeable cortical bone
Age-scaled fraction of total transfer from the
exchangeable bone directed to non-exchangeable
bone
Transfer rate from soft tissue compartment 1 to
diffusible plasma
Age-scaled transfer rate from RBC to diffusible
plasma
Age-scaled transfer rate from brain to diffusible
plasma
Age-scaled transfer rate from the slow liver
compartment 2 to diffusible plasma
Transfer rate out of the liver compartment 1,
including to small intestine and diffusible plasma
Transfer rate from soft tissue compartment 0 to
diffusible plasma
Total transfer rate from diffusible plasma to all
compartments
Transfer rate from stomach to small intestine
Relative volume of the EVF compartment
compared to plasma (EVF/Plasma)
Age-scaling factor for GIT transfer
133
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable Parameter Child
Adult
Parameter Description
AKIDNEY RULI 5.06E-05
AKIDNEY RPROT 2.54E-05
AKIDNEY RSIC 5.75E-05
AKIDNEY RLLI 5.33E-06
AKIDNEY TOURIN 2.64E-07
AKIDNEY TOSWET 6.43E-08 2.93E-09
AKIDNEY POWER 0.00E+00
AKIDNEY RBCNL 0.00E+00
AKIDNEY SATRAT 0.00E+00
AKIDNEY RBLAD
0.00E+00
1.12E-06 Transfer rate from upper large intestine to lower
large intestine
9.09E-07 Transfer rate from bound plasma to diffusible
plasma
2.19E-07 Transfer rate from small intestine to upper large
intestine
1.21E-07 Transfer rate from lower large intestine to feces
1.21E-08 Deposition fraction from diffusible plasma to
urine
Deposition fraction from diffusible plasma to
sweat
0.00E+00 Exponent for RBC deposition
0.00E+00 Threshold concentration in RBC for non-linear
deposition from diffusible plasma to RBC
0.00E+00 Maximum (saturating) concentration of lead in
RBC
0.00E+00 Age-scaled transfer rate from urinary bladder to
urine
134
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 TABLE 4-8. AALM-LG STANDARDIZED SENSITIVITY COEFFICIENTS FOR OTHER SOFT
2 TISSUE PB IN CHILDREN (5 YEARS) AND ADULTS (30 YEARS)
Variable Parameter Child
Adult
Parameter Description
ASOFT TEVF 6.63E+00
ASOFT TORBC 3.14E+00
ASOFT TOSOFO 1.10E+00
ASOFT TBONEL 1.06E+00
ASOFT RSOF2
ASOFT RCORT
ASOFT RDIFF
2.36E-01
ASOFT TOSOF2 4.68E-01
ASOFT TOLVR1 3.71E-01
ASOFT H1TOBL 2.35E-01
ASOFT TOSOF1 4.74E-01
ASOFT RSOF1 4.36E-01
ASOFT TFRAC 3.97E-03
ASOFT H1TOH2 5.20E-02
ASOFT S2HAIR 5.19E-02
ASOFT TBONE 1.17E-01
ASOFT H1TOSI 8.38E-02
9.33E-02
ASOFT FLONG 6.62E-02
8.12E+00
3.81E+00
1.39E+00
1.27E+00
8.95E-01
7.90E-01
3.80E-01
2.86E-01
2.71E-01
2.04E-01
6.66E-02
6.32E-02
4.28E-02
3.82E-02
3.11E-02
2.72E-02
2.38E-02
1.38E-02 1.85E-02
Deposition fraction from diffusible plasma to
extravascular fluid
Deposition fraction from diffusible plasma to
RBCs, below non-linear threshold
Age-scaled deposition fraction from diffusible
plasma to soft tissue compartment 0
Terminal value of age-scaled deposition fraction
from diffusible plasma to surface bone
Transfer rate from soft tissue compartment 2 to
diffusible plasma
Age-scaled deposition fraction from diffusible
plasma to soft tissue compartment 2
Deposition fraction from diffusible plasma to liver
compartment 2
Fraction of transfer out of liver compartment 1 to
diffusible plasma
Age-scaled deposition fraction from diffusible
plasma to soft tissue compartment 1
Transfer rate from soft tissue compartment 1 to
diffusible plasma
Bone deposition-scaled fraction of diffusible
plasma-to-bone deposition that goes to trabecular
surface bone; 1-TFRAC is the fraction that goes to
cortical surface bone
Fraction of transfer out of liver compartment 1 to
liver compartment 2
Deposition fraction from soft tissue compartment
1 to other excreta
Age-scaled deposition fraction from diffusible
plasma to surface bone
Fraction of transfer out of liver compartment 1 to
the small intestine
Age-scaled transfer rate from non-exchangeable
cortical bone to diffusible plasma
Age-scaled fraction of total transfer from the
exchangeable bone directed to non-exchangeable
bone
Age-scaled transfer rate from the exchangeable
bone, including transfer to surface and non-
exchangeable bone
135
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable Parameter Child
Adult
Parameter Description
ASOFT RSOFO
ASOFT TOFECE 2.99E-02
ASOFT
ASOFT
ASOFT
ASOFT
ASOFT
ASOFT
ASOFT
ASOFT
ASOFT
ASOFT
ASOFT
ASOFT
ASOFT
ASOFT
ASOFT
ASOFT
ASOFT
ASOFT
ASOFT
RCS2DF 5.93E-02
RTS2DF 1.48E-02
RTRAB 2.34E-02
TOKDN2 2.59E-03
TOBRAN 3.04E-03
9.54E-03 1.20E-02 Transfer rate from soft tissue compartment 0 to
diffusible plasma
1.12E-02 Deposition fraction from diffusible plasma
directly to the small intestine (not including the
transfer from biliary secretion, specified by
RLVR1)
1.07E-02 Age-scaled transfer rate from cortical bone
surface to diffusible plasma
RCS2B 5.94E-02 1.02E-02 Age-scaled transfer rate from cortical bone
surface to exchangeable cortical bone
TOPROT 5.25E-03 6.37E-03 Deposition fraction from diffusible plasma to
protein-bound plasma
RTS2B 1.48E-02 5.37E-03 Age-scaled transfer rate from surface trabecular
bone to exchangeable trabecular bone
5.23E-03 Age-scaled transfer rate from trabecular bone
surface to diffusible plasma
3.25E-03 Age-scaled transfer rate from non-exchangeable
trabecular bone to diffusible plasma
3.15E-03 Deposition fraction from diffusible plasma to
kidney compartment 2
2.83E-03 Age-scaled deposition fraction from diffusible
plasma to brain
RLVR2 1.04E-03 6.65E-04 Age-scaled transfer rate from the slow liver
compartment 2 to diffusible plasma
RBRAN 1.49E-03 3.24E-04 Age-scaled transfer rate from brain to diffusible
plasma
RLVR1 4.97E-04 8.64E-05 Transfer rate out of the liver compartment 1,
including to small intestine and diffusible plasma
RRBC 1.51E-03 6.63E-05 Age-scaled transfer rate from RBC to diffusible
plasma
3.31E-05 Age-scaled transfer rate from kidney compartment
2 to diffusible plasma
7.97E-05 1.29E-05 Transfer rate from small intestine to upper large
intestine
1.26E-05 Age-scaling factor for GIT transfer
4.38E-06 Total transfer rate from diffusible plasma to all
compartments
3.04E-05 4.28E-06 Transfer rate from upper large intestine to lower
large intestine
1.18E-06 Transfer rate from bound plasma to diffusible
plasma
3.76E-06 5.16E-07 Transfer rate from lower large intestine to feces
RKDN2 4.71E-05
RSIC
GSCAL 5.87E-05
RPLAS 4.96E-06
RULI
RPROT 4.81E-07
RLLI
136
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable Parameter Child
Adult
Parameter Description
ASOFT SIZEVF 5.87E-07 5.06E-07
ASOFT RSTMC 5.46E-06
ASOFT TOKDN1 8.53E-09
ASOFT RKDN1
ASOFT RBLAD
3.29E-11
ASOFT TOURIN 6.40E-09
ASOFT TOSWET 1.54E-09
ASOFT POWER 0.00E+00
ASOFT RBCNL 0.00E+00
ASOFT SATRAT 0.00E+00
0.00E+00
1.73E-07
4.76E-08
3.21E-08
1.19E-08
2.88E-09
0.00E+00
0.00E+00
0.00E+00
0.00E+00
Relative volume of the EVF compartment
compared to plasma (EVF/Plasma)
Transfer rate from stomach to small intestine
Deposition fraction from diffusible plasma to
kidney compartment 1
Transfer rate from kidney compartment 1 to
urinary pathway
Deposition fraction from diffusible plasma to
urine
Deposition fraction from diffusible plasma to
sweat
Exponent for RBC deposition
Threshold concentration in RBC for non-linear
deposition from diffusible plasma to RBC
Maximum (saturating) concentration of lead in
RBC
Age-scaled transfer rate from urinary bladder to
urine
137
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 TABLE 4-9. AALM-OF STANDARDIZED SENSITIVITY COEFFICIENTS FOR BLOOD PB IN
2 CHILDREN (5 YEARS) AND ADULTS (30 YEARS)
Variable Parameter Child
Adult
Parameter Description
ABLOOD CI 2.41E+00 9.34E+00 Constant 1 for urinary clearance of Pb as a fraction
of GFR
ABLOOD C2 1.38E+00 7.54E+00 Constant 2 for urinary clearance of Pb as a fraction
of GFR
ABLOOD BIND 9.92E-01 9.92E-01 Maximum capacity of sites in red cells to bind Pb
ABLOOD KBIND 9.88E-01 9.89E-01 Half-saturation concentration of Pb for binding by
sites in red cells
ABLOOD P0 5.73E-03 6.19E-02 Permeability constant for diffusion from canaliculi
to bone
ABLOOD R0 4.96E-03 5.58E-02 Permeability constant for diffusion from bone to
canaliculi
ABLOOD RAD8 4.27E-03 3.97E-02 Radius of shell 8 of bone in the canalicular
diffusion region of deeper bone
ABLOOD CON 7.51E-04 2.50E-02 Fraction of bone blood flow to trabecular bone
ABLOOD DO 9.99E-04 1.07E-02 Diffusion constant
ABLOOD BASE 1.72E-04 9.01E-03 Base bone formation rate in bone growth algorithm
ABLOOD C3 4.46E-01 7.10E-03 Constant 3 for urinary clearance of Pb as a fraction
of GFR
ABLOOD S 8.26E-04 6.67E-03 Surface area of canaliculi
ABLOOD RAD1 6.66E-04 5.09E-03 Radius of shell 1 of bone in the canalicular
diffusion region of deeper bone
ABLOOD G 1.13E-02 3.48E-03 Linear parameter for unbound lead in red cells
ABLOOD RAD2 3.67E-04 2.85E-03 Radius of shell 2 of bone in the canalicular
diffusion region of deeper bone
ABLOOD RAD3 2.27E-04 2.16E-03 Radius of shell 3 of bone in the canalicular
diffusion region of deeper bone
ABLOOD PL 1.12E-02 2.08E-03 Liver/plasma partition coefficient
ABLOOD RAD4 1.51E-04 1.88E-03 Radius of shell 4 of bone in the canalicular
diffusion region of deeper bone
ABLOOD RAD5 1.04E-04 1.64E-03 Radius of shell 5 of bone in the canalicular
diffusion region of deeper bone
ABLOOD RAD6 6.93E-05 1.29E-03 Radius of shell 6 of bone in the canalicular
diffusion region of deeper bone
ABLOOD EXPO 7.16E-03 1.12E-03 Exponent constant for bone volume participating in
adult-type bone remodeling
ABLOOD QKC 1.52E-03 1.11E-03 Fraction cardiac output going to kidney
ABLOOD A1 9.16E-03 1.01E-03 Constant 1 for bone formation rate algorithm
ABLOOD A3 4.20E-03 9.44E-04 Constant 3 for bone formation rate algorithm
138
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable
Parameter
Child
Adult
Parameter Description
ABLOOD
QWC
1.33E-02
9.31E-04
Fraction cardiac output going to other well-
perfused tissues
ABLOOD
QLC
1.32E-02
9.16E-04
Fraction cardiac output going to liver
ABLOOD
RAD7
3.62E-05
7.55E-04
Radius of shell 7 of bone in the canalicular
diffusion region of deeper bone
ABLOOD
A5
0.00E+00
6.65E-04
Constant 5 for bone formation rate algorithm
ABLOOD
PW
2.64E-03
6.07E-04
Well-perfused/plasma partition coefficient
ABLOOD
A2
3.06E-03
1.98E-04
Constant 2 for bone formation rate algorithm
ABLOOD
QBONEC
7.94E-03
1.62E-04
Fraction cardiac output going to bone
ABLOOD
PP
8.01E-05
1.12E-04
Poorly perfused/plasma partition coefficient
ABLOOD
PK
3.60E-05
2.25E-05
Kidney/plasma partition coefficient
ABLOOD
QCC
0.00E+00
0.00E+00
Cardiac output in the adult
1
2
3
139
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 TABLE 4-10. AALM-OF STANDARDIZED SENSITIVITY COEFFICIENTS FOR BONE PB IN
2 CHILDREN (5 YEARS) AND ADULTS (30 YEARS)
Variable
Parameter
Child
Adult
Parameter Description
ABONE
CI
1.99E+00
8.70E+00
Constant 1 for urinary clearance of Pb as a fraction
of GFR
ABONE
C2
9.73E-01
7.12E+00
Constant 2 for urinary clearance of Pb as a fraction
of GFR
ABONE
R0
2.79E-02
2.14E-01
Permeability constant for diffusion from bone to
canaliculi
ABONE
RAD 8
2.63E-02
1.64E-01
Radius of shell 8 of bone in the canalicular
diffusion region of deeper bone
ABONE
P0
5.73E-03
6.19E-02
Permeability constant for diffusion from canaliculi
to bone
ABONE
DO
5.61E-03
4.12E-02
Diffusion constant
ABONE
CON
8.59E-02
3.71E-02
Fraction of bone blood flow to trabecular bone
ABONE
EXPO
2.16E-01
3.07E-02
Exponent constant for bone volume participating in
adult-type bone remodeling
ABONE
S
5.50E-03
2.97E-02
Surface area of canaliculi
ABONE
C3
3.78E-01
2.47E-02
Constant 3 for urinary clearance of Pb as a fraction
of GFR
ABONE
RAD1
4.42E-03
2.35E-02
Radius of shell 1 of bone in the canalicular
diffusion region of deeper bone
ABONE
RAD2
2.28E-03
1.29E-02
Radius of shell 2 of bone in the canalicular
diffusion region of deeper bone
ABONE
BASE
4.36E-05
1.08E-02
Base bone formation rate in bone growth algorithm
ABONE
RAD3
1.35E-03
9.01E-03
Radius of shell 3 of bone in the canalicular
diffusion region of deeper bone
ABONE
RAD4
8.09E-04
6.94E-03
Radius of shell 4 of bone in the canalicular
diffusion region of deeper bone
ABONE
RAD5
4.66E-04
5.34E-03
Radius of shell 5 of bone in the canalicular
diffusion region of deeper bone
ABONE
RAD6
2.46E-04
3.78E-03
Radius of shell 6 of bone in the canalicular
diffusion region of deeper bone
ABONE
RAD7
1.06E-04
2.07E-03
Radius of shell 7 of bone in the canalicular
diffusion region of deeper bone
ABONE
A3
6.95E-03
1.18E-03
Constant 3 for bone formation rate algorithm
ABONE
PL
3.82E-03
1.10E-03
Liver/plasma partition coefficient
ABONE
QKC
4.17E-03
9.41E-04
Fraction cardiac output going to kidney
ABONE
PW
6.23E-03
9.31E-04
Well-perfused/plasma partition coefficient
ABONE
BIND
1.37E-03
8.40E-04
Maximum capacity of sites in red cells to bind Pb
ABONE
KBIND
1.12E-03
8.30E-04
Half-saturation concentration of Pb for binding by
140
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable
Parameter
Child
Adult
Parameter Description
ABONE
G
2.96E-03
5.62E-04
Linear parameter for unbound lead in red cells
ABONE
QBONEC
2.66E-03
5.61E-04
Fraction cardiac output going to bone
ABONE
A2
3.42E-03
4.88E-04
Constant 2 for bone formation rate algorithm
ABONE
A5
0.00E+00
2.72E-04
Constant 5 for bone formation rate algorithm
ABONE
QLC
9.11E-03
2.41E-04
Fraction cardiac output going to liver
ABONE
QWC
9.22E-03
2.24E-04
Fraction cardiac output going to other well-
perfused tissues
ABONE
PP
1.43E-04
1.36E-04
Poorly perfused/plasma partition coefficient
ABONE
A1
1.50E-02
3.05E-05
Constant 1 for bone formation rate algorithm
ABONE
PK
1.73E-04
1.20E-05
Kidney/plasma partition coefficient
ABONE
QCC
0.00E+00
0.00E+00
Cardiac output in the adult
1
2
141
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 TABLE 4-11. AALM-OF STANDARDIZED SENSITIVITY COEFFICIENTS FOR LIVER PB IN
2 CHILDREN (5 YEARS) AND ADULTS (30 YEARS)
Variable
Parameter
Child
Adult
Parameter Description
ALIVER
CI
2.39E+00
9.28E+00
Constant 1 for urinary clearance of Pb as a fraction
of GFR
ALIVER
C2
1.38E+00
7.56E+00
Constant 2 for urinary clearance of Pb as a fraction
of GFR
ALIVER
PL
1.01E+00
9.98E-01
Liver/plasma partition coefficient
ALIVER
P0
5.73E-03
6.19E-02
Permeability constant for diffusion from canaliculi
to bone
ALIVER
R0
4.98E-03
5.60E-02
Permeability constant for diffusion from bone to
canaliculi
ALIVER
RAD 8
4.29E-03
3.98E-02
Radius of shell 8 of bone in the canalicular
diffusion region of deeper bone
ALIVER
CON
7.53E-04
2.51E-02
Fraction of bone blood flow to trabecular bone
ALIVER
DO
1.00E-03
1.07E-02
Diffusion constant
ALIVER
BASE
1.73E-04
9.04E-03
Base bone formation rate in bone growth algorithm
ALIVER
C3
4.48E-01
7.12E-03
Constant 3 for urinary clearance of Pb as a fraction
of GFR
ALIVER
S
8.29E-04
6.69E-03
Surface area of canaliculi
ALIVER
RAD1
6.69E-04
5.11E-03
Radius of shell 1 of bone in the canalicular
diffusion region of deeper bone
ALIVER
RAD2
3.68E-04
2.85E-03
Radius of shell 2 of bone in the canalicular
diffusion region of deeper bone
ALIVER
RAD3
2.28E-04
2.16E-03
Radius of shell 3 of bone in the canalicular
diffusion region of deeper bone
ALIVER
RAD4
1.51E-04
1.89E-03
Radius of shell 4 of bone in the canalicular
diffusion region of deeper bone
ALIVER
RAD5
1.05E-04
1.65E-03
Radius of shell 5 of bone in the canalicular
diffusion region of deeper bone
ALIVER
RAD6
6.96E-05
1.29E-03
Radius of shell 6 of bone in the canalicular
diffusion region of deeper bone
ALIVER
EXPO
7.19E-03
1.12E-03
Exponent constant for bone volume participating in
adult-type bone remodeling
ALIVER
QKC
1.24E-03
1.12E-03
Fraction cardiac output going to kidney
ALIVER
A1
9.35E-03
1.01E-03
Constant 1 for bone formation rate algorithm
ALIVER
QLC
1.34E-02
9.67E-04
Fraction cardiac output going to liver
ALIVER
A3
4.21E-03
9.38E-04
Constant 3 for bone formation rate algorithm
ALIVER
QWC
1.33E-02
9.34E-04
Fraction cardiac output going to other well-
ALIVER BIND
8.28E-04 7.63E-04
perfused tissues
Maximum capacity of sites in red cells to bind Pb
142
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable
Parameter
Child
Adult
Parameter Description
ALIVER
KBIND
8.44E-04
7.58E-04
Half-saturation concentration of Pb for binding by
sites in red cells
ALIVER
RAD7
3.63E-05
7.57E-04
Radius of shell 7 of bone in the canalicular
diffusion region of deeper bone
ALIVER
A5
0.00E+00
6.67E-04
Constant 5 for bone formation rate algorithm
ALIVER
PW
2.11E-03
6.09E-04
Well-perfused/plasma partition coefficient
ALIVER
A2
3.08E-03
1.98E-04
Constant 2 for bone formation rate algorithm
ALIVER
QBONEC
8.66E-03
1.62E-04
Fraction cardiac output going to bone
ALIVER
G
8.74E-03
1.60E-04
Linear parameter for unbound lead in red cells
ALIVER
PP
8.13E-05
1.14E-04
Poorly perfused/plasma partition coefficient
ALIVER
PK
3.61E-05
2.25E-05
Kidney/plasma partition coefficient
ALIVER
QCC
0.00E+00
0.00E+00
Cardiac output in the adult
143
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 TABLE 4-12. AALM-OF STANDARDIZED SENSITIVITY COEFFICIENTS FOR KIDNEY PB
2 IN CHILDREN (5 YEARS) AND ADULTS (30 YEARS)
Variable Parameter Child
Adult
Parameter Description
AKIDNEY CI
AKIDNEY C2
AKIDNEY PK
AKIDNEY P0
AKIDNEY R0
AKIDNEY RAD8
AKIDNEY CON
AKIDNEY DO
AKIDNEY BASE
AKIDNEY C3
AKIDNEY S
AKIDNEY RAD1
AKIDNEY RAD2
AKIDNEY RAD3
AKIDNEY PL
AKIDNEY RAD4
AKIDNEY RAD5
AKIDNEY RAD6
AKIDNEY EXPO
AKIDNEY QKC
AKIDNEY A1
AKIDNEY A3
AKIDNEY QWC
AKIDNEY QLC
2.39E+00
1.38E+00
1.00E+00
5.73E-03
4.99E-03
4.29E-03
7.53E-04
1.00E-03
1.73E-04
8.29E-04
6.69E-04
3.68E-04
2.28E-04
1.13E-02
1.51E-04
1.05E-04
6.96E-05
7.19E-03
1.47E-03
9.32E-03
4.22E-03
1.33E-02
9.28E+00
7.56E+00
9.99E-01
6.19E-02
5.60E-02
3.98E-02
2.51E-02
1.07E-02
9.04E-03
4.48E-01 7.12E-03
6.69E-03
5.11E-03
2.85E-03
2.16E-03
2.10E-03
1.89E-03
1.65E-03
1.29E-03
1.12E-03
1.05E-03
1.01E-03
9.37E-04
9.34E-04
1.32E-02 9.19E-04
Constant 1 for urinary clearance of Pb as a
fraction of GFR
Constant 2 for urinary clearance of Pb as a
fraction of GFR
Kidney/plasma partition coefficient
Permeability constant for diffusion from
canaliculi to bone
Permeability constant for diffusion from bone to
canaliculi
Radius of shell 8 of bone in the canalicular
diffusion region of deeper bone
Fraction of bone blood flow to trabecular bone
Diffusion constant
Base bone formation rate in bone growth
algorithm
Constant 3 for urinary clearance of Pb as a
fraction of GFR
Surface area of canaliculi
Radius of shell 1 of bone in the canalicular
diffusion region of deeper bone
Radius of shell 2 of bone in the canalicular
diffusion region of deeper bone
Radius of shell 3 of bone in the canalicular
diffusion region of deeper bone
Liver/plasma partition coefficient
Radius of shell 4 of bone in the canalicular
diffusion region of deeper bone
Radius of shell 5 of bone in the canalicular
diffusion region of deeper bone
Radius of shell 6 of bone in the canalicular
diffusion region of deeper bone
Exponent constant for bone volume participating
in adult-type bone remodeling
Fraction cardiac output going to kidney
Constant 1 for bone formation rate algorithm
Constant 3 for bone formation rate algorithm
Fraction cardiac output going to other well-
perfused tissues
Fraction cardiac output going to liver
144
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable
Parameter
Child
Adult
Parameter Description
AKIDNEY
RAD7
3.63E-05
7.57E-04
Radius of shell 7 of bone in the canalicular
diffusion region of deeper bone
AKIDNEY
A5
0.00E+00
6.67E-04
Constant 5 for bone formation rate algorithm
AKIDNEY
BIND
3.64E-04
6.52E-04
Maximum capacity of sites in red cells to bind Pb
AKIDNEY
KBIND
3.85E-04
6.47E-04
Half-saturation concentration of Pb for binding
by sites in red cells
AKIDNEY
PW
2.05E-03
6.09E-04
Well-perfused/plasma partition coefficient
AKIDNEY
A2
3.08E-03
1.98E-04
Constant 2 for bone formation rate algorithm
AKIDNEY
QBONEC
8.68E-03
1.62E-04
Fraction cardiac output going to bone
AKIDNEY
G
8.77E-03
1.60E-04
Linear parameter for unbound lead in red cells
AKIDNEY
PP
8.05E-05
1.13E-04
Poorly perfused/plasma partition coefficient
AKIDNEY
QCC
0.00E+00
0.00E+00
Cardiac output in the adult
145
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 TABLE 4-13. AALM-OF STANDARDIZED SENSITIVITY COEFFICIENTS FOR POORLY
2 PERFUSED TISSUES PB IN CHILDREN (5 YEARS) AND ADULTS (30 YEARS)
Variable Parameter Child
Adult
Parameter Description
APOOR
APOOR
APOOR
APOOR
APOOR
APOOR
APOOR
APOOR
APOOR
APOOR
APOOR
APOOR
APOOR
APOOR
APOOR
APOOR
APOOR
APOOR
APOOR
APOOR
APOOR
APOOR
APOOR
CI
C2
PP
P0
R0
RAD 8
CON
DO
BASE
C3
S
RAD1
RAD2
RAD3
PL
RAD4
RAD5
RAD6
EXPO
QKC
A1
A3
QWC
2.39E+00
1.38E+00
1.00E+00
5.73E-03
4.99E-03
4.29E-03
7.54E-04
1.00E-03
1.73E-04
4.48E-01
8.29E-04
6.69E-04
3.68E-04
2.28E-04
1.13E-02
1.51E-04
1.05E-04
6.96E-05
7.19E-03
1.55E-03
9.13E-03
4.22E-03
1.34E-02
9.28E+00
7.56E+00
1.00E+00
6.19E-02
5.60E-02
3.98E-02
2.51E-02
1.07E-02
9.03E-03
7.12E-03
6.69E-03
5.11E-03
2.85E-03
2.16E-03
2.08E-03
1.89E-03
1.65E-03
1.29E-03
1.12E-03
1.12E-03
1.01E-03
9.48E-04
9.34E-04
APOOR QLC
1.33E-02 9.19E-04
Constant 1 for urinary clearance of Pb as a fraction
of GFR
Constant 2 for urinary clearance of Pb as a fraction
of GFR
Poorly perfused/plasma partition coefficient
Permeability constant for diffusion from canaliculi
to bone
Permeability constant for diffusion from bone to
canaliculi
Radius of shell 8 of bone in the canalicular
diffusion region of deeper bone
Fraction of bone blood flow to trabecular bone
Diffusion constant
Base bone formation rate in bone growth algorithm
Constant 3 for urinary clearance of Pb as a fraction
of GFR
Surface area of canaliculi
Radius of shell 1 of bone in the canalicular
diffusion region of deeper bone
Radius of shell 2 of bone in the canalicular
diffusion region of deeper bone
Radius of shell 3 of bone in the canalicular
diffusion region of deeper bone
Liver/plasma partition coefficient
Radius of shell 4 of bone in the canalicular
diffusion region of deeper bone
Radius of shell 5 of bone in the canalicular
diffusion region of deeper bone
Radius of shell 6 of bone in the canalicular
diffusion region of deeper bone
Exponent constant for bone volume participating in
adult-type bone remodeling
Fraction cardiac output going to kidney
Constant 1 for bone formation rate algorithm
Constant 3 for bone formation rate algorithm
Fraction cardiac output going to other well-
perfused tissues
Fraction cardiac output going to liver
146
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable
Parameter
Child
Adult
Parameter Description
APOOR
RAD7
3.63E-05
7.57E-04
Radius of shell 7 of bone in the canalicular
diffusion region of deeper bone
APOOR
BIND
6.34E-04
7.16E-04
Maximum capacity of sites in red cells to bind Pb
APOOR
KBIND
6.52E-04
7.11E-04
Half-saturation concentration of Pb for binding by
sites in red cells
APOOR
A5
0.00E+00
6.67E-04
Constant 5 for bone formation rate algorithm
APOOR
PW
2.74E-03
6.15E-04
Well-perfused/plasma partition coefficient
APOOR
A2
3.08E-03
1.98E-04
Constant 2 for bone formation rate algorithm
APOOR
QBONEC
7.84E-03
1.62E-04
Fraction cardiac output going to bone
APOOR
G
7.92E-03
1.60E-04
Linear parameter for unbound lead in red cells
APOOR
PK
3.62E-05
2.25E-05
Kidney/plasma partition coefficient
APOOR
QCC
0.00E+00
0.00E+00
Cardiac output in the adult
147
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 TABLE 4-14. AALM-OF STANDARDIZED SENSITIVITY COEFFICIENTS FOR WELL-
2 PERFUSED TISSUES PB IN CHILDREN (5 YEARS) AND ADULTS (30 YEARS)
Variable Parameter Child
Adult
Parameter Description
AWELL CI 2.39E+00 9.28E+00 Constant 1 for urinary clearance of Pb as a fraction
of GFR
AWELL C2 1.38E+00 7.56E+00 Constant 2 for urinary clearance of Pb as a fraction
of GFR
AWELL PW 1.00E+00 1.00E+00 Well-perfused/plasma partition coefficient
AWELL P0 5.73E-03 6.19E-02 Permeability constant for diffusion from canaliculi
to bone
AWELL R0 4.99E-03 5.60E-02 Permeability constant for diffusion from bone to
canaliculi
AWELL RAD8 4.29E-03 3.98E-02 Radius of shell 8 of bone in the canalicular
diffusion region of deeper bone
AWELL CON 7.53E-04 2.51E-02 Fraction of bone blood flow to trabecular bone
AWELL DO 1.00E-03 1.07E-02 Diffusion constant
AWELL BASE 1.73E-04 9.05E-03 Base bone formation rate in bone growth algorithm
AWELL C3 4.48E-01 7.12E-03 Constant 3 for urinary clearance of Pb as a fraction
of GFR
AWELL S 8.29E-04 6.69E-03 Surface area of canaliculi
AWELL RAD1 6.69E-04 5.11E-03 Radius of shell 1 of bone in the canalicular
diffusion region of deeper bone
AWELL RAD2 3.68E-04 2.85E-03 Radius of shell 2 of bone in the canalicular
diffusion region of deeper bone
AWELL RAD3 2.28E-04 2.16E-03 Radius of shell 3 of bone in the canalicular
diffusion region of deeper bone
AWELL PL 1.11E-02 2.08E-03 Liver/plasma partition coefficient
AWELL RAD4 1.51E-04 1.89E-03 Radius of shell 4 of bone in the canalicular
diffusion region of deeper bone
AWELL RAD5 1.05E-04 1.65E-03 Radius of shell 5 of bone in the canalicular
diffusion region of deeper bone
AWELL RAD6 6.96E-05 1.29E-03 Radius of shell 6 of bone in the canalicular
diffusion region of deeper bone
AWELL EXPO 7.19E-03 1.12E-03 Exponent constant for bone volume participating in
adult-type bone remodeling
AWELL QKC 1.09E-03 1.12E-03 Fraction cardiac output going to kidney
AWELL A1 9.45E-03 1.01E-03 Constant 1 for bone formation rate algorithm
AWELL QWC 1.32E-02 9.34E-04 Fraction cardiac output going to other well-
perfused tissues
AWELL A3 4.21E-03 9.30E-04 Constant 3 for bone formation rate algorithm
AWELL QLC 1.31E-02 9.19E-04 Fraction cardiac output going to liver
148
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable
Parameter
Child
Adult
Parameter Description
AWELL
RAD7
3.63E-05
7.57E-04
Radius of shell 7 of bone in the canalicular
diffusion region of deeper bone
AWELL
BIND
6.34E-04
7.16E-04
Maximum capacity of sites in red cells to bind Pb
AWELL
KBIND
6.52E-04
7.11E-04
Half-saturation concentration of Pb for binding by
sites in red cells
AWELL
A5
0.00E+00
6.67E-04
Constant 5 for bone formation rate algorithm
AWELL
A2
3.08E-03
1.98E-04
Constant 2 for bone formation rate algorithm
AWELL
QBONEC
9.15E-03
1.64E-04
Fraction cardiac output going to bone
AWELL
G
9.14E-03
1.60E-04
Linear parameter for unbound lead in red cells
AWELL
PP
8.05E-05
1.13E-04
Poorly perfused/plasma partition coefficient
AWELL
PK
3.61E-05
2.25E-05
Kidney/plasma partition coefficient
AWELL
QCC
0.00E+00
0.00E+00
Cardiac output in the adult
149
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 TABLE 4-15. DOMINANT PARAMETERS INFLUENCING MAJOR DIFFERENCES IN
2 PREDICTIONS FROM AALM-LG AND AALM-OF
Predicted Variable
Model Difference
Dominant Parameters
AALM-LG
AALM-OF
Child blood Pb
AALM-OF < AALM-LG
TEVF
CI
TORBC
C2
TOSOFO
BIND
RRBC
KBIND
TOLVR1
H1TOBL
TBONE
Child bone Pb
AALM-OF < AALM-LG
TEVF
CI
TORBC
C2
TBONE
R0
TOSOFO
RAD 8
FLONG
RCS2DF
TOLVR1
H1TOBL
RTS2DF
Liver Pb
AALM-OF < AALM-LG
TEVF
CI
TORBC
C2
TOSOFO
PL
TOLVR1
H1TOH2
RLVR2
H1TOBL
RLVR1
Kidney Pb
AALM-OF < AALM-LG
TEVF
CI
TORBC
C2
TOSOFO
PK
RKDN1
TOKDN1
TOKDN2
RKDN2
Other soft tissues
AALM-OF < AALM-LG
TEVF
CI
TORBC
C2
TOSOFO
PP
RSOF2
PW
TOSOF2
TOLVR1
H1TOBL
TOSOF1
RSOF1
3
150
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 TABLE 4-16. STRATEGY USED FOR SEQUENTIAL OPTIMIZATION OF AALM
2 BIOKINETICS MODEL
Step
Objective
Observation Data Sources
1
Unify parameter values for GI absorption and growth
(O'Flahertv. 1995. 1993)
2
Optimize plasma/RBC ratio
(Smith et al.. 2002; Bcredahl et
al.. 1999; Bersdahl etal.. 1998;
Hernandez-Avila et al.. 1998;
Beradahl et al.. 1997; Schutz et
al.. 1996)
3
Optimize plasma(blood)-to-urine clearance
(Rentschler et al.. 2012;
Dewoskin and Thompson. 2008;
Manton and Cook. 1984;
Manton and Mallov. 1983;
Chamberlain et al.. 1978)
4
Optimize soft tissue (kidney, liver, muscle)/bone ratios
(Gerhardsson et al.. 1995; Barrv.
1981. 1975; Gross etal.. 1975)
5
Optimize plasma(blood)/bone ratios
(Hernandez-Avila et al.. 1998;
Cake et al.. 1996)
6
Optimize bone Pb elimination kinetics
(Nilsson et al.. 1991)
7
Evaluate blood Pb elimination kinetics - adults
(Rabinowitz et al.. 1976)
8
Evaluate blood Pb elimination kinetics - infants
(Sherlock and Ouinn. 1986; Rvu
etal.. 1983)
3
4
151
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 TABLE 4-17. COMPARISON OF PREDICTED AND OBSERVED PLASMA PB/BONE PB
2 SLOPES
Predicted Observed
Model
Study
Bone
Slope
Slope
SE
95%CL
Residual
AALM-LG
CA96
Cortical
0.037
0.052
0.013
0.027, 0.077
-1.16
AALM-LG
CA96
Trabecular
0.040
0.041
0.007
0.027, 0.054
-0.16
AALM-LG
HE98
Cortical
0.037
0.036
0.011
0.014, 0.058
0.12
AALM-LG
HE98
Trabecular
0.040
0.025
0.004
0.017, 0.033
3.67
AALM-OF
CA96
Cortical
0.042
0.052
0.013
0.027, 0.077
-0.81
AALM-OF
CA96
Trabecular
0.060
0.041
0.007
0.027, 0.054
2.70
AALM-OF
HE98
Cortical
0.042
0.036
0.011
0.014, 0.058
0.53
AALM-OF
HE98
Trabecular
0.060
0.025
0.004
0.017, 0.033
8.68
CA96, Cake et al. (1996); HE98, Hernandez-Avila et al. (1998)
3
4
152
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 TABLE 4-18. CHANGES TO (O'FLAHERTY. 1995,1993) AND (LEGGETT. 1993) MODELS
2 INCORPORATED INTO AALM
Model Component
Parameter Change
AALM-LG AALM-OF
Growth
Body and tissue growth as functions of age and
body weight
X
Respiratory tract
Simulation of deposition, mucociliary
clearance and absorption of inhaled Pb based
on ICRP HRTM
X
X
GI tract
Age-dependent absorption calculated with a
continuous function rather than age array
variable
X
GI tract
GI tract
Infant GI absorption fractions optimized X
Absorption fraction adjustable by user- X
specified media-specific relative bioavailability
fractions
X
X
Tissue Pb
Age-dependent values for tissue-blood partition
coefficients
X
Tissue Pb
Bone, kidney and liver concentrations
calculated from Pb masses and tissue weights
X
Neonate
Neonatal model which sets Pb masses in blood
and tissues at birth as a function of maternal Pb
concentration
X
X
RBC
Parameters for plasma-RBC binding and
uptake optimized
X
X
GFR
Parameters for GFR adjusted to predict adult
GFR of 170 L/day/1.73m2 (120
mL/min/1.73m2) and 30% of adult in infants
(<1 year)
X
Urine Pb
Parameters for Pb transfer to urine optimized
X
X
GFR, glomerular filtration rate; GI, gastrointestinal; ICRP, International Commission of Radiological
Protection; RBC, red blood cell
153
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 TABLE 4-19. COMPARISON OF AALM-LG AND AALM-OF PREDICTIONS OF BLOOD AND
2 TISSUE PB CONCENTRATIONS
Dose
(Hg/day)
Age
(year)
Sex
Tissue
Unit
AALM-LG
AALM-OF
5
2
M
Blood
1-ig/dL
1.86
2.39
5
2
M
Bone
Mg/g
0.88
0.43
5
2
M
Kidney
Mg/g
0.06
0.08
5
2
M
Liver
Mg/g
0.14
0.09
5
40
M
Blood
1-ig/dL
0.28
0.50
5
40
M
Bone
Mg/g
0.14
0.15
5
40
M
Kidney
Mg/g
0.005
0.010
5
40
M
Liver
Mg/g
0.008
0.012
5
2
F
Blood
1-ig/dL
1.95
2.39
5
2
F
Bone
Mg/g
0.93
0.43
5
2
F
Kidney
Mg/g
0.07
0.08
5
2
F
Liver
Mg/g
0.15
0.09
5
40
F
Blood
1-ig/dL
0.36
0.50
5
40
F
Bone
Mg/g
0.20
0.15
5
40
F
Kidney
Mg/g
0.006
0.010
5
40
F
Liver
Mg/g
0.010
0.012
F, female; M, male
3
154
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 TABLE 4-20. COMPARISON OF ADULT LEAD METHODOLOGY, AALM-LG AND AALM-
2 OF PREDICTIONS OF BLOOD PB CONCENTRATIONS IN ADULTS
Parameter
Description
Units
ALM
AALM-LG
AALM-OF
PbS
Soil lead concentration
Hg/g or ppm
1000
1000
1000
BKSF
Biokinetic Slope Factor
(ig/dL per (ig/day
0.4
NA
NA
PbBo
Baseline Blood Pb
1-ig/dL
1.5
1.5
1.5
IRs
Soil Ingestion Rate
g/day
0.050
0.05
0.05
AFs, d
Absorption Fraction
--
0.12
0.048
0.048
EFs, d
Exposure Frequency
days/yr
219
219
219
ATs, d
Averaging Time
days/yr
365
365
365
PbBadult
Blood Pb Concentration
1-ig/dL
2.9
3.1
4.6
ALM, Adult Lead Methodology
3
155
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 TABLE 4-21. COMPARISON OF AALM-LG AND AALM-OF PREDICTIONS OF BLOOD AND
2 TISSUE PB CONCENTRATIONS AFTER CALIBRATING RBC PARAMETER VALUES TO
3 THE IEUBK MODEL OUTPUT
Dose
(Hg/day)
Age
(year)
Sex
Tissue
Unit
AALM-LG
AALM-OF
5
2
M
Blood
1-ig/dL
1.6
1.2
5
2
M
Bone
Mg/g
1.33
0.43
5
2
M
Kidney
Mg/g
0.10
0.08
5
2
M
Liver
Mg/g
0.21
0.09
5
40
M
Blood
1-ig/dL
0.28
0.50
5
40
M
Bone
Mg/g
0.15
0.15
5
40
M
Kidney
Mg/g
0.005
0.010
5
40
M
Liver
Mg/g
0.008
0.012
5
2
F
Blood
1-ig/dL
1.7
1.2
5
2
F
Bone
Mg/g
1.42
0.46
5
2
F
Kidney
Mg/g
0.10
0.08
5
2
F
Liver
Mg/g
0.23
0.10
5
40
F
Blood
1-ig/dL
0.36
0.55
5
40
F
Bone
Mg/g
0.20
0.14
5
40
F
Kidney
Mg/g
0.006
0.012
5
40
F
Liver
Mg/g
0.010
0.014
F, female; M, male
4
156
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 TABLE 4-22. CHANGES MADE TO THE (LEGGETT. 1993) MODEL TO CREATE AALM-
2 LG.CSL
LEGGETT
AALM-LG
Output/Functionality
Affected
Age-dependent blood volume
Age-dependent blood volume
based on O'Flahertv (1995. 1993)
Age-dependent RBC and
plasma volumes
Constant hematocrit
Age-dependent hematocrit based
on O'Flahertv fl995. 1993)
Age-dependent RBC and
plasma volumes
Adult bone mass
Age-dependent bone mass based
on O'Flahertv (1995. 1993)
Age-dependent cortical and
trabecular bone Pb
concentration
Adult kidney mass
Age-dependent kidney mass based
on O'Flahertv (1995. 1993)
Age-dependent kidney Pb
concentration
NA
Age-dependent liver mass based
on O'Flahertv (1995. 1993)
Age-dependent liver Pb
concentration
Age-dependent absorption
fraction (/'/):
• birth: 0.45
• 0.27 y: 0.45
• 1 y: 0.30
• 5 y: 0.30
• 10 y: 0.30
• 15 y: 0.30
• >25 y: 0.15
Age-dependent absorption fraction
(Fl):
• birth: 0.39
• 0.27 y: 0.39
• 1 y: 0.38
• 5 y: 0.17
• >10 y: 0.12
Absorption fraction for ingested
Pb
Absorption fraction for ingested
Pb not adjusted for RBA
Absorption fraction adjusted for
media-specific RBA
Absorption fraction of ingested
Pb
RBC Pb saturation threshold: 60
(ig/dL blood)
Maximum: 350 (ig/dL RBC
RBC Pb saturation threshold: 20
(ig/dL blood)
Maximum: 350 (ig/dL RBC
Plasma-RBC Pb relationship
Transfer rate from (d1) RBC to
diffusible plasma:
• birth: 0.462
• 0.27 y: 0.462
• 1 y: 0.462
• 5 y: 0.277
• >10 y: 0.139
Transfer rate from (d1) from RBC
to diffusible plasma:
• birth: 0.462
• 0.27 y: 0.462
• 1 y: 0.785
• 5 y: 0.499
• 10 y: 0.195
• > 15 y: 0.139
Plasma-RBC Pb relationship
Deposition fraction from
diffusible plasma to RBC (0.24)
Deposition fraction from
diffusible plasma to RBC (0.25)
Plasma-RBC relationship
Deposition fraction from
diffusible plasma to urine (30)
Deposition fraction from
diffusible plasma to urine (0)
Plasma to urine clearance
157
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
LEGGETT
AALM-LG
Output/Functionality
Affected
Transfer rate (d1) from liver to
Transfer rate (d1) from liver to
Plasma to liver Pb kinetics
diffusible plasma:
diffusible plasma:
• birth: 0.00693
• birth
: 0.00693
• 0.27 y: 0.00693
• 0.27
y: 0.00693
• 1 y: 0.00693
• ly:
0.00693
• 5 y: 0.00693
• 5 y:
0.00139
• 10 y: 0.00190
• lOy
0.000570
• 15 y: 0.00190
• 15 y
0.000570
• >25 y: 0.00190
• 25 y
0.000570
• 30 y
0.00142
• 40 y
0.00304
• 60 y
0.00342
• 90 y
0.00380
Deposition fraction from
Deposition fraction from
Urinary clearance of plasma Pb
diffusible plasma to kidney (40)
diffusible plasma to kidney (50)
Transfer rate (d1) from kidney to
Transfer rate (d1) from kidney to
Plasma to kidney Pb kinetics
diffusible plasma (RKDN2):
diffusible plasma (RKDN2):
• birth: 0.00693
• birth
: 0.000693
• 0.27 y: 0.00693
• 0.27
y: 0.000693
• 1 y: 0.00693
• ly:
0.000693
• 5 y: 0.00693
• 5 y:
0.000693
• 10 y: 0.00190
• lOy
0.000190
• 15 y: 0.00190
• 15 y
0.000190
• >25 y: 0.00190
• 25 y
0.000190
• 30 y
0.000950
• >40 y: 0.00190
Fraction of total transfer from
Fraction of total transfer from
Bone Pb retention
exchangeable bone to
exchangeable bone to
nonexchangeable bone (0.2)
nonexchangeable bone (0.6)
Transfer rate (d1) from non-
Transfer rate (d1) from non-
Bone to plasma Pb kinetics
exchangeable cortical bone to
exchangeable cortical bone to
diffusible plasma:
diffusible plasma:
• birth: 0.00822
• birth
: 0.0204
• 0.27 y: 0.00822
• 0.27
y: 0.0164
• 1 y: 0.00288
• ly:
0.00576
• 5 y: 0.00154
• 5 y:
0.00308
• 10 y: 0.000890
• lOy
0.00178
• 15 y: 0.000512
• 15 y
0.00102
• >25 y: 0.0000822
• >25 y: 0.000164
158
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
LEGGETT
AALM-LG
Output/Functionality
Affected
Transfer rate (d1) from non-
Transfer rate (d1) from non-
Bone-to-plasma Pb transfer
exchangeable trabecular bone to
exchangeable trabecular bone to
kinetics
diffusible plasma:
diffusible plasma:
• birth: 0.00822
• birth: 0.0102
• 0.27 y: 0.00822
• 0.27 y: 0.01644
• 1 y: 0.00288
• 1 y: 0.00576
• 5 y: 0.00181
• 5 y: 0.00362
• 10 y: 0.00132
• 10 y: 0.00264
• 15 y: 0.000956
• 15 y: 0.00192
• >25 y: 0.000493
• >25 y: 0.000986
— J
— J
1
2
159
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 4-1. DATA FLOW DIAGRAM FOR AALM.
AALM Data Flow
2
3
> INPUT&OUTPUT.xIsm ' i
IMPORT MACRO I I EXPORT MACRO i
OUTPUTDATA.DAT
/
OUT.M
OUTPU1
(acsIX d a1
MATRIX
ta matrix)
to the All Ages Lead Model
INPUTDATA.DAT
OUT.M
RUN SIMULATION €
IN.M
INPUTDATA
(acsIX data matrix)
RUN.M
I BLUE = xlsm I
[ RED = acsIX |
160
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 4-2. STRUCTURE OF AALM-LG MODEL.
Losses in
Hair Nails,
Skin
Other Soft Tissues
Intermediate
Turnover
Skeleton
Rapid
Turnover
Tenacious
Turnover
Cortical Volume
Non-
Exchange
Exchange
Trabecular Volume
Non-
Exchange
Exchange
Cortical
Surface
Trabecular
Surface
Kidneys
Other
Kidney
Tissue
Urinary
Path
Bladder
Contents
Diffusible
Plasma
Extra-
Vascular
4f
RBC
if
Bound
Plasma
4 ~
Brain
Sweat
Liver
Liver 2
Liver 1
RT Tract
Gl Tract
Feces
Urine
2
3 Figure is based on Leggett (1993).
4
161
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 4-3. STRUCTURE OF AALM-OF MODEL.
Air
Ingestion
Bile
Liver
Feces
Urine
Gl T ract
Blood Plasma
Well-perfused Tissues
Poorly-perfused Tissues
Kidney
Trabecular Bone
Cortical Bone
3 Figure is based on OFlahertv (1993).
4
162
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 4-4. STRUCTURE OF AALM-LG BONE MODEL.
Cortical
Bone
Surface
Exchangeable
Cortical
Bone
Volume
Trabecular
Bone
Surface
Exchangeable
Trabecular
Bone
Volume
Unexchangeable
Cortical
Bone
Volume
Nonexchangeable
Trabecular
Bone
Volume
Central
Blood
Plasma
2
3 Figure is based on Leggett (1993).
4
163
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 4-5. STRUCTURE OF AALM-OF BONE MODEL.
Trabecular
Bone
Bone formation
Bone resorption
Blood Supply to
Trabecular Bone
Metabolically
Active Cortical
Bone
Mature
Cortical
Bone
Bone formation
Bone resorption
Radial diffusion
Radial diffusion
Blood Supply to
Metabolically
Active Cortical
Bone
2
3 Figure is based on OFlahertv (1993).
4
164
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 4-6. COMPARISON OF PB (jiG) LEVELS PREDICTED FROM AALM-OF AND
2 AALM-LG FOR A CONSTANT INGESTION OF 5 jiG PB/DAY FOR AGES 0 TO 30 YEARS.
3
4
AALM-LG AALM-OF
o 1U -
1000
20 30 40
Age (yr)
200
160
120 -
80
40
AALM-LG -
- AALM-OF
A
\
^ ~ v
20 40
AGE (yr)
AALM-LG AALM-OF
800
= 600 -
400
200 I
20 30 40
AGE (yr)
60
6000
5000 -
_ 4000
Q0
=l
£ 3000
ai
c
3 2000 4
1000
0
-AALM-LG AALM-OF
20 40
Age (yr)
60
165
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 4-7. DIFFERENCES IN PB LEVELS PREDICTED FROM AALM-LG AND AALM-OF.
2
3
1.0
0.5
£
a 0.0
u_
o
-0.5
-1.0
1.0
0.5
3 0.0
iL
o.
-0.5 -f
-1.0
• Blood Pb (ug)
J 0.20 J 0.20
-0.18
-0.65
-0.64
10 20
Age (yr)
30
10
20
Age (yr)
30
1.0
0.5 -
0.0
lL
o
-0.5 4
-1.0
» Bone Pb (ug)
0.18
I • -0.07
• -0.15
-0.68
-0.63
40
10 20
Age (yr)
30
• Soft Tissue Pb (ug)
-0.90
i -0.92
' -0.79
i -0.61
-0.59
1.0
0.5
(J
I
^ 0.0
LL
o
-0.5
-1.0
40
• Total Body Pb (ug)
| 0.11
J
• -0.11
1 -0.24
: -o.6s
' -0.71
40
10
20
Age (yr)
30
40
Differences are expressed relative to the prediction from AALM-LG.
166
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 4-8. COMPARISON OF CUMULATIVE URINARY AND FECAL PB EXCRETION
2 (jiG) LEVELS PREDICTED FROM AALM-OF AND AALM-LG FOR A CONSTANT
3 INGESTION OF 5 jiG PB/DAY FOR AGES 0 TO 30 YEARS.
4
5
6000
5000
— 4000
&o
£ 3000
J 2000
1000
0
1.5
1.0
0.5
V,
o.o
LL_
O
-AALM-LG AALM-OF
20
40
Age (yr)
-0.5
-1.0
-1.5
1.31
• Urine Pb (ng)
| 0.37
| 0.21 | 0.22 f 0.19
10
20
Age (yr)
30
60
40
AALM-LG
AALM-OF
50000
40000
X! 30000
20000
10000
1.0
0.5
3 0.0
LL_
o
-0.5
-1.0
20 40
Age (yr)
~ Fecal Pb (\ig)
0.21
t 0.05, 0Q1
0.00 ~ 0.00
10
20
Age (yr)
30
40
167
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 4-9. DECLINE IN PB LEVELS FOLLOWING CESSATION OF EXPOSURE
2 PREDICTED FROM AALM-LG AND AALM-OF FOR AGES 5 AND 30 YEARS.
3
4
5
6
7
O
m
OJ
oo
<
o
CL
T3
O
_o
CO
<
o
o
CQ
1.2
1.0
0.8
0.6
0.4
0.2
0.0
AALM-LG AALM-OF
/
t
' " - -
20
30
40
Age (yr)
50
60
AALM-LG AALM-OF
AALM-LG: TI/2= 19.7 yr
AALM-OF: = 12.6 yr
Age yr
AALM-LG AALM-OF
Age (yr)
AALM-LG AALM-OF
AALM-LG: Ti/2 = 3.00 yr
cq 0.2
AALM-OF: = 2.24 yr
Age [yr
Half-times are based on applying a single exponential model to the predicted time series (i.e., Pbt=i = Pbt=o
x e"kt). The decline in blood Pb has multiple rates. In adults, the half-time for the first 50 days following
cessation of exposure is approximately 36 days in AALM-LG and 46 days in AALM-OF. The half-time
for the period 5-20 years following cessation of exposure is 12.7 years in AALM-LG and 10.9 years in
AALM-OF.
168
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 4-10. COMPARISON OF PB CONCENTRATIONS PREDICTED FROM AALM-LG
2 AND AALM-OF FOR A CONSTANT INGESTION OF 5 jiG PB/DAY FOR AGES 0 TO 30
3 YEARS.
3.5
AALM-LG
AALM-OF
3.0
2.5
a- 2.0
1.0
0.5 s -*-¦«
0.0
1.6
AALM-LG
AALM-OF
1.4
1.2
1.0
o 0.4 -4-
0.2
0.0
0 10 20 30 40 50 60 0 10 20 30 40 50 60
Age (yr) Age (yr)
0.06
AALM-LG
AALM-OF
0.05
0.04
Qfi 0.03
>. 0.02
0.01
0.00
0.12
AALM-LG
AALM-OF
0.10
0.08
ao 0.06
0.04
0.02
0.00
Age (yr) Age (yr)
4
5
169
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
FIGURE 4-11. DOSE-RESPONSE RELATIONSHIP FOR PB LEVELS AT AGE 5 YEARS
PREDICTED FROM AALM-LG AND AALM-OF.
100.0
80.0 -
w> 60.0 -
40.0 -
20.0
0.0
AALM-LG
AALM-OF
160
120 -
400 600
Pb Intake (jig/day)
1000
AALM-LG
AALM-OF
200 400 600
Pb Intake (jig/day)
1000
2.0
AALM-LG
- - AALM-OF
100
400 600
Pb Intake (|ig/day)
1000
AALM-LG
AALM-OF
a 60
0.8 1.2
Plasma Pb (ng/dL)
2.0
170
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
FIGURE 4-12. DOSE-RESPONSE RELATIONSHIP FOR PB LEVELS AT AGE 30 YEARS
PREDICTED FROM AALM-LG AND AALM-OF.
AALM-LG
AALM-OF
200
400 600
Pb Intake (ng/day)
800 1000
AALM-LG
AALM-OF
200
400 600
Pb Intake ([ig/day)
800 1000
AALM-LG
AALM-OF
100
a eo -
400 600
Pb Intake (ng/day)
1000
AALM-LG
AALM-OF
0.8 1.2
Plasma Pb (ng/dL)
2.0
171
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 4-13. GASTROINTESTINAL ABSORPTION OF PB IN THE O'FLAHERTY MODEL
2 (OF) AND LEGGETT MODEL (OF) AND AALM, OPTIMIZED TO (RYU ET AL., 1983).
0.6
•- LG (default)
0.5
— OF (default)
~ 0.4
AALM (optimized)
Ll_
0.3
Q.
0-2
0.1
0.0
0
10
20
30
40
50
Age (year)
172
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 4-14. BODY AND TISSUE GROWTH IN AALM.
Female
10 20 30 40 50 60
Age (year)
Female
20 30 40 50 60
Age (year)
2
3
Female
10 20 30 40 50 60
Age (year)
Male
Female
10 20 30 40 50 60
Age (year)
173
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 4-15. SIMULATION OF WHOLE BLOOD AND PLASMA PB IN ADULTS (SMITH ET
2 AL.. 2002; BERGDAHL ET AL.. 1999; BERGDAHL ET AL.. 1998; HERNANDEZ-AVILA ET
3 AL., 1998; BERGDAHL ET AL., 1997; SCHUTZ ET AL., 1996).
4
5
6
7
• Observations
-AALM-OF
-AALM-LG
80
0.20 0.30
Plasma Pb (us/dl)
1.2 -r
0.8
0.4
^ 00
a)
cc
-0.4
-0.8
-1.2
• AALM-LG
0.00
0.10 0.20 0.30
Plasma Pb (ng/dl)
= 60
• AALM-LG
y = 0.99x- 1,01
R2 = 0.99
¦ AALM-OF
y = 0.90x + 1.64
R2 = 0.98
/y i
20 40 60
Predicted Blood Pb (jig/dl)
0.4
-0.4
0.40
• AALM-OF
<»
. \
.!l I Tt
1
1
4
0.00
0.10 0.20 0.30
Plasma Pb (ng/dl)
0.40
Combined data for individuals (N = 406) from all studies were quantized into ranges of plasma Pb; shown
are mean and standard deviations for ranges. Upper right panel shows linear regression for predicted and
observed blood Pb concentrations. Lower panels show residuals for predictions
([predicted-observed]/standard deviation).
174
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 4-16. SIMULATION OF PLASMA-TO-URINE CLEARANCE.
(C
"C
"5
Ol
u
Ol
'¦I
¦T
25
20
15
10
AALM-LG
AALM-OF
20
40 60
Age (year)
80
100
2
3
4
Data point is mean and standard deviation for four estimates based on 32 (normal) adults (Araki et al.
1986; Manton and Cook. 1984; Manton and Mallov. 1983; Chamberlain et al.. 1978).
175
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1
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
FIGURE 4-17. SIMULATION OF POST-MORTEM SOFT TISSUE/TIBIA PB RATIOS.
0.30
Male
Female
0.25
ALLM-LG
- -AALM-OF
.9 0.20
IU
>
_l
0.05
0.00
0
20
40
60
80
100
0.25
Male
Female
0.20
AALM-LG
--AALM-OF
10
0.05
0.00
0
20
40
60
80
100
Age (yr) Age (yr)
2
3 Shown are group means for kidney (n = 8) and for liver (n = 9), based on Barry (1975).
176
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 4-18. SIMULATION OF PLASMA PB/BONE PB RATIO IN ADULTS.
0.10
0.08
Q-
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 4-19. SIMULATION OF ELIMINATION KINETICS OF PB FROM BLOOD (LEFT
2 PANEL) AND BONE (RIGHT PANEL).
3
4
5
6
AALM-LG AALM-OF NI91
AALM-LG: T1/2 = 15.4 yr
AALM-LG
- AALM-OF N 91
u 0.8
0.6 -
AALM-OF: T]y2 = 13,6 yr
o 0.4
5 10 15 20
Years from End of Exposure
5 10 15 20
Years from End of Exposure
Dotted lines show the elimination from based on the median and upper and lower 95% confidence limits
of the tri-exponential model retired Pb workers (n = 14, median age 60 years at time of retirement)
reported in Nilsson et al. (1991).
178
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 4-20. COMPARISON OF OBSERVED AND PREDICTED BLOOD PB
2 CONCENTRATIONS IN INDIVIDUALS WHO RECEIVED INGESTION DOSES OF [202PB]-
3 NITRATE (RABINOWITZ ET AL., 1976).
10
4
5
6
7
6
S 4
• Subject A
AALM LG
AALM OF
/ '"T
#• ' iN
J * 4 %
/ / j \
f / \ ^
L t A
f /
/ ' #\
' •«—
m.
0 48 96 144 192 240 288 336 384 432
Time (day)
6
'Si
P 4
2
• Subject D
AALM LG
AALM OF
/••A
fr
* ''
/•• ''
/ t
r''
m *
f
/
0 2 4 4 8 72 96 1 20 144 1 68 1 92 216 240
Time (day)
• Subject B
AALM LG
AALM OF
0 24 48 72 96 120 144 168 192 216 240
Time (day)
• Subject E
flALM LG
- - AALM OF
a 0.6
do 0.4
24 48 72 96
Time (day)
Subject A received 204 (ig/day for 104 days, Subject B received 185 (ig/day for 124 days, Subject D
received 105 (ig/day for 83 days, and Subject E received 99 (ig/day for on days 1-8 and days 42-51.
Estimated absorption fractions were 8.5% for Subject A, 6.5% for Subject B, 10.9% for Subject D and
9.1% for Subject E.
179
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 4-21. SIMULATION OF FORMULA-FED INFANTS FROM (RYU ET AL.. 1983).
Q_
m
AALM-LG
=o 12
Q_
¦o
o
o
m
100
Age (day)
200
RY83
AALM-LG
100
Age (day)
200
RY83
AALM-OF
RY83
AALM-OF
m
100 150 200 0 50 100 150 200
2 Age (day1) Age (day)
3 Data in left panels are from 25 infants fed formula from cartons (12-20 (ig/day) from age 8-196 days.
4 Data in right panels are show a subset (n = 7) that were switched to formula from cans at age 112 days
5 (60-63 (ig/day). Solid lines show simulations of the mean Pb intakes; dotted lines show simulations of
6 ±1 SD of mean intakes.
180
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 4-22. SIMULATION OF FORMULA-FED INFANTS (N = 131, AGE 91 DAYS) FROM
2 (SHERLOCK AND OUINN, 1986).
60
• SH86
— AALM-LG
- -AALM-OF
50
40
30
20
10
0
0
100
200
300
400
Pb Intake (|jg/ciay)
3
4 Blood Pb were measured and Pb intakes were estimated from duplicate diets assessed at age 91 days.
5
181
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 4-23. COMPARISON OF INITIAL AND OPTIMIZED AALM-LG AND AALM-OF
2 MODELS FOR CONTINUOUS PB INTAKE OF 5 jiG/DAY.
AALM-Lfc. AALM-OF
20 40 60
Age (year)
100
AALM-LG AALM-OF
l.G -
40 60
A(-;e (year)
ICC
AALM-LL AALM-0
40 50
Ap.e (year)
ICC
ai
3
cZ
O
c£i
AALM-LG AALM-OF
40 60
Age (year)
100
3
4
Right panels show optimized models.
182
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 4-24. COMPARISON OF INITIAL AND OPTIMIZED AALM-LG AND AALM-OF
2 MODELS FOR CONTINUOUS PB INTAKE OF 5 fiG/DAY.
o.io
E 0.06
0.02
AALM-LG AALM-OF
Age (year,"
100
0.10
0.08 -
& 0.04
0.02
AALM-LG AALM-OF
0.00
40 60
Age (year)
-AALM-LG
AALM-OF
0.15
0.05
40 60
Age (year)8
-AALM-LG
AALM-OF
0.20
0.10 -
0.05
40 60
Age (year)
4 Right panels show optimized models.
5
183
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 4-25. COMPARISON OF BLOOD PB PREDICTIONS OF AALM AND IEUBK
2 MODEL.
12
Age 2 years
AALM-OF
AALM- LG
10
IEUBK Model
t;
-o
o
o
2
0
3.5
AALM-LG
3.0
AALM-OF
2.5
• IEUBK Model
2.0
•S 15
1.0
0.5
0.0
0
2
4
6
8
10
0 10 20 30 40
Age iyearj pb |nta|
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 4-26. COMPARISON OF BLOOD PB PREDICTIONS OF AALM AND IEUBK MODEL
2 AFTER ADJUSTMENT OF RED BLOOD CELL PARAMETERS (RRBC IN AALM-LG, KBIND
3 IN AALM-OF).
2 5
AALM LG
2.0
AALM Of
• IEUBK Model
i
TD
-Q
Q_
T3
CD
C 5
0.0
0
2
4
6
8
10
Age (year)
Age 2 years
AALM-OF
AALM-LG
IEUBK Mudel
C
1C
2C
3C
4C
5C
^ Pb Intake (jig/day)
5 Upper panel shows simulations of continuous intake of 10 (ig Pb/day in dust. Lower panel shows
6 relationship between dust Pb intake and blood Pb concentration at 2 years of age. In both models, the
7 RBA for Pb in dust was assumed to be 60%. This corresponds to an absolute bioavailability of
8 approximately 20% at age 2 years in the AALM and 30% in the IEUBK model.
9
185
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 4-27. SIMULATION OF FORMULA-FED INFANTS FROM (RYU ET AL., 1983)
2 AFTER ADJUSTMENT OF RED BLOOD CELL (RRBC IN AALM-LG, KBIND IN AALM-OF).
• RY83
AALM-LG
100
Age (day)
RY 83
-AALM-OF
100
Age (day)
3
4 Data in left panels are from 25 infants fed formula from cartons (12-20 (ig/day) from age 8-196 days
5 (closed circles) and then a subset (n = 7) that were switched to formula from cans at age 112 days (60-63
6 (ig/day, closed squares). Solid lines show simulations of the mean Pb intakes; dotted lines show
7 simulations of ±1 SD of mean intakes.
8
186
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 FIGURE 4-28. SIMULATION OF FORMULA-FED INFANTS (N = 131, AGE 91 DAYS) FROM
2 (SHERLOCK AND OUINN. 1986) AFTER ADJUSTMENT OF RED BLOOD CELL (RRBC IN
3 AALM-LG, KBIND IN AALM-OF).
4
5
6
O)
70
60
50
40
£ 30
~o
o
— 20
m
10
SH86
¦AALM-LG
AALM-OF
-f
100 200 300
Pb Intake (ng/ciay)
400
Blood Pb were measured and Pb intakes were estimated from duplicate diets assessed at age 91 days.
187
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3
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7
8
9
10
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12
13
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15
16
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18
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24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
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5. REFERENCES
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Barry. PSI. (1975). A comparison of concentrations of lead in human tissues. Occup Environ Med 32:
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concentration-using-updated-pbpk-model
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lead from motor vehicles. (AERE-R9198). Berkshire, England: Transportation and Road
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Cohen. N; Eisenbud. M; Wrenn. ME. (1970). Radioactivity studies. Volume I. The retention and
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the U.S. EPA uptake/biokinetic model. (SRC TR-92-135). Syracuse, NY: Syracuse Research
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Dixon. SL; Gaitens. JM; Jacobs. DE; Strauss. W; Nagaraia. J; Pivetz. T; Wilson. JW; Ashley. PJ. (2009).
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1 APPENDIX A - EQUATIONS IN AALM.FOR
2 TABLE A-l. EQUATIONS OF THE ALL AGES LEAD MODEL (AALM.FOR)
Model
Submodel
Equation
Daily lead intake rate from air (jug/day)
Exposure
Air
For each discrete age: MrTWAdiscrete = Mr\ * fAirx + Airz * fAir2 + Air3 * fAir.t
Exposure
Air
For each discrete age: fAir:< = 1 - (fAiri + fAir2)
Exposure
Air
For each discrete age: INairdiscrete = AirTWAdiscrete * Vair
Exposure
Air
For each pulse. INairpUiS6sum — (Aivbaseline AiTpulse) ' ^air
Exposure
Air
For combined discrete and pulse: INairTotal = INairdiscrete * (l - fpuiSeair) + INairpulse * fpuiseair
Daily lead intake rate from indoor dust (jug/day)
Exposure
Dust
For each discrete age: DustTWAdiscrete = Dusti * foust, + Dust2 * fDust2 + Dust3 * fDust.t
Exposure
Dust
For each discrete age: fDush = 1 - (fDustl + fDust2)
Exposure
Dust
For each discrete age: lNdustdiscrete = DustTWAdiscrete * IRDust * RBADust
194
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Model
Submodel
Equation
Exposure
Dust
For each pulse. IN dustpUisesum (J^^stijaseiine + DustpUis e) * I Roust * R^^Dust
Exposure
Dust
For combined discrete and pulse. INdustf0f-ai IN dustdiscrete * (1 fpuise) //Vclust^* fpuise
Exposure
Dust
For each discrete age: DustTWAdiscrete = Dusti * foust, + Dust2 * fDust2 + Dust3 * fDust.t
Exposure
Dust
IRoust = IRsD * (1 — flRsoil)
Daily lead intake rate from soil (jig/day)
Exposure
Soil
For each discrete age: SoilTWAdiscrete = Soi* fSoih + Soil2 * fSoii2 + Soil3 * fSoii3
Exposure
Soil
For each discrete age: fSou3 = 1 - (fsoii, + fsoiij
Exposure
Soil
For each discrete age: INsoildiscrete = SoilTWAdiscrete * IRSou * RBADoii
Exposure
Soil
For each pulse. INsoilpUiSgsum (Soilfoaseiine SoilpUise) * IRsoii * RBAsoii
Exposure
Soil
For combined discrete and pulse: lNsoilTotai = INsoildiscrete * (1 - fpuise) + lNsoilpuise * fpUise
Exposure
Soil
IRSoil = IRSD * flRsoil
195
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Model
Submodel
Equation
Daily lead intake rate from water (jug/day)
Exposure
Water
For each discrete age: WaterTWAdisCrete = Wateri * fwateri + Water2 * fWater2 + Water3 * fWater3
Exposure
Water
For each discrete age: fWater3 = 1 - (fwateri + fwaterj
Exposure
Water
For each discrete age. 1N Will to I'd is (Tot e VVtl to 1't WA (I is (Tot e * I^water * I ^'Vvat or
Exposure
Water
For each pulse. INwaterpuiS6sum — (Waterbaseijne + WaterpUise) * IRwater * RBAwater
Exposure
Water
For combined discrete and pulse: INwaterTotal = INwaterdiscrete * (1 - fpuisewater) + INwaterpulse * fpuisewater
Daily lead intake rate from food (jug/day)
Exposure
Food
For each discrete age: FoodTotaidiscrete = Foodi + Food2 + Food3
Exposure
Food
For each discrete age: INfooddiscrete = FoodTotaldiscrete * RBAfood
Exposure
Food
For each pulse. INfoodpu[sesum (F*-"-"^baseiine Foodpu[se) * RBAf00d
Exposure
Food
For combined discrete and pulse: INfoodXotal = INfooddiscrete * (1 — fpuise) + INfoodpulse * fpuise
196
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Model
Submodel
Equation
Daily lead intake rate from other sources (jig/day)
Exposure
Other
For each discrete age: OtherXotaldiscrete = Otherl + Other2 + Other3
Exposure
Other
For each discrete age: INotherdiscrete = OtherTotaldiscrete * RBAother
Exposure
Other
For each pulse: INotherpulsesum = (Otherbaseiine + Otherpulse) * RBAother
Exposure
Other
For combined discrete and pulse: INotherTotai = INotherdiscrete * (1 — fpuise) + INotherpuise * fpuise
Daily lead intake from all sources (jig/day)
Exposure
Inhaled
For input to biokinetics: BRETH = INairtotai
Exposure
Ingested
For combined ingestion pathways: INingeStiontotal = INwater + INdust + INfood + INother
Exposure
Ingested
For input to biokinetics: EAT = INingestiontotal
BioKinetics Equations (including absorption processes)
Growth and tissue volumes (L or dL) and masses (kg)
197
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Model
Submodel
Equation
Biokinetics
Growth
WCHILD * HOWOLD WADULT
WBODY - WBIRTH + + H0W0LD 1 1 + KAppA * e(LAMBDA*WADULT*HOWOLD)
Biokinetics
Growth
AMTBLD = VBLC * WBODY * 10
Biokinetics
Growth
PLSVOL = AMTBLD * (1 - BLDHCT)
Biokinetics
Growth
RBCVOL = AMTBLD * BLDHCT
Biokinetics
Growth
BLDHCThowold<0 01 — 0.52 + HOWOLD * 14*
BLDHCTHowold>o.oi = HCTA * (1 + (0.66 - HCTA) * e-(HOWOLD-°01)*13-9)
Biokinetics
Growth
( WBODY \0'84
VK = 1000 * VKC * (WBIRTH + WCHILD + WADULT) * (—TTTT^TTT^
V WBIRTH + WCHILD + WADULT/
Biokinetics
Growth
KIDWT = VK * 1.05
Biokinetics
Growth
( WBODY \0'85
VL = 1000 * VLC * (WBIRTH + WCHILD + WADULT) * [r^-r—— —777777777^
VWBIRTH + WCHILD + WADULT/
Biokinetics
Growth
LIVWT = VL * 1.05
Biokinetics
Growth
TSKELWT = 1000 * 0.058 * WBODY121
Biokinetics
Growth
WBONE = 1000 * 0.029 * WBODY121
198
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
Biokinetics
Growth
VBONE = 1000 * 0.0168 * WBODY1188
Biokinetics
Growth
CVBONE = 0.8 * VBONE
Biokinetics
Growth
TVBONE = VBONE - CVBONE
Biokinetics
Growth
WBONE * CVBONE
CORTWT = ———;
VBONE
Biokinetics
Growth
WBONE * TVBONE
TRABWT = —————
VBONE
Deposition fractions (DF, unitless) of lead from diffusible plasma to tissue compartments
Biokinetics
DF
1.0 — TEVF — TBONE
AGESCL - i Q _ tevf _ ATB0NE
Biokinetics
DF
TURIN = AGESC * TOURIN
Biokinetics
DF
TSWET = AGESCL * TOSWET
Biokinetics
DF
TSOFO = AGESCL * TOSOFO
Biokinetics
DF
TSOF1 = AGESCL* TOSOF1
199
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
Biokinetics
DF
TSOF2 = AGESCL * TOSOF2
Biokinetics
DF
TBRAN = AGESCL * TOBRAN
Biokinetics
DF
TLVR1 = AGESCL ¦ TOLVR1
Biokinetics
DF
TKDN1 = AGESCL* TOKDN1
Biokinetics
DF
TKDN2 = AGESCL * TOKDN2
Biokinetics
DF
TRBC = AGESCL * TORBC
Biokinetics
DF
TPROT = AGESCL * TOPROT
Biokinetics
DF
( RBCONC - RBCNL\power
TOORBC = TRBC *11- „An,„An,————-
V SATRAT - RBCNL/
Biokinetics
DF
TSUM = TOORBC + TEVF + TPROT + TBONE + TURIN + TFECE + TSWET + TLVR1 + TKDN1 + TKDN2
+ TSOFO + TSOF1 + TSOF2 + TBRAN
Biokinetics
DF
1.0 - TOORBC
CF =
1.0 - TRBC
Deposition fractions (DF, unitless) of lead from diffusible plasma to tissue compartments during chelation therapy
200
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
Biokinetics
DF
TEVF = (1 - CHLEFF) * TEVF
Biokinetics
DF
TFECE = (1 - CHLEFF) * TFECE
Biokinetics
DF
TSWET = (1 - CHLEFF) * TSWET
Biokinetics
DF
TSOFO = (1 - CHLEFF) * TSOFO
Biokinetics
DF
TSOF1 = (1 - CHLEFF) * TSOF1
Biokinetics
DF
TSOF2 = (1 - CHLEFF) * TSOF2
Biokinetics
DF
TBRAN = (1 - CHLEFF) * TBRAN
Biokinetics
DF
TLVR1 = (1 - CHLEFF) * TLVR1
Biokinetics
DF
TKDN1 = (1 - CHLEFF) * TKDN1
Biokinetics
DF
TPROT = (1 - CHLEFF) * TPROT
Biokinetics
DF
TBONE = (1 - CHLEFF) * TBONE
201
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
Biokinetics
DF
TOORBC = (1 - CHLEFF) * TOORBC
Biokinetics
DF
TURIN = 1 - (TOORBC + TEVF + TPROT + TBONE + TURIN + TFECE + TSWET + TLVR1 + TKDN1 +
TKDN2 + TSOFO + TSOF1 + TSOF2 + TBRAN)
Transfer rates (day1)
Biokinetics
Plasma
RPLS = TSUM * RPLAS
Biokinetics
Plasma
BTEMP = RPLS * YPLSW
Biokinetics
Growth
TEVF * RPLS
REVF =
SIZEVF
Biokinetics
RBC
1.0 - TOORBC
CF =
1.0 -TRBC
Amount of lead (jig) in compartment at start of each integration step (Yo) and amount integrated over the step (Yw)
202
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
INRATE
Ypi —
0 RDECAY + BR1
IF DELT* OUTRATE <50:
Biokinetics
Lung
/ ( INRATE \\ ( niITr>4TC, nciTl INRATE
YR1„ = (VR1„ - (0UTRATE)) . C<-°"™TE.oELT, + qutrate
ACUTE: INRATE = 0, YR10 = R1
CHRONIC: INRATE = R1 * BRTCRN
OUTRATE = BR1 + RDECAY
IF DELT*OUTRATE>50:
1 INRATE INRATE * DELT
ypi — i ypi i
W OUTRATE ' OUTRATE OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
Lung
/I _ e(-0UTRATE*DELT) INRATE \ INRATE * DELT
YPI — 1 1 YR1 1 1
w \ OPUTRATE ' 11V"U OUTRATE J ' OUTRATE
ACUTE: INRATE = 0, YR1 = R1
CHRONIC: INRATE = R1 * BRTCRN
OUTRATE = BR1 + RDECAY
203
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT* OUTRATE >50:
INRATE
YP° -
0 OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
Lung
/ ( INRATE \\ , niITDATIj nciTl INRATE
YR20 = ( YR20 * e(-OUTRATE*DELT) +
0 \ 0 VOUTRATE// OUTRATE
ACUTE: INRATE = 0, YR2 = R2
CHRONIC: INRATE = R2 * BRTCRN
OUTRATE = BR2 + RDECAY
IF DELT* OUTRATE >50:
1 INRATE INRATE * DELT
ypo !• yp° |
W OUTRATE ' 11V"U OUTRATE OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
Lung
/I _ e(-outrate*delt) INRATE \ INRATE * DELT
ypo — [ YR° I I
w \ OUTRATE ' 11V"U OUTRATE J ' OUTRATE
ACUTE: INRATE = 0, YR2 = R2
CHRONIC: INRATE = R2 * BRTCRN
OUTRATE = BR2 + RDECAY
204
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT* OUTRATE >50:
INRATE
YP° —
0 OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
Lung
/ ( INRATE \\ , niITDATIj nciTl INRATE
YR30 = ( YR30 * e(-OUTRATE*DELT) +
0 \ 0 VOUTRATE// OUTRATE
ACUTE: INRATE = 0, YR3 = R3
CHRONIC: INRATE = R3 * BRTCRN
OUTRATE = BR3 + RDECAY
IF DELT* OUTRATE >50:
1 INRATE INRATE * DELT
ypo [ YP° 1
W OUTRATE ' OUTRATE OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
Lung
(\ - e(-outrate*delt) INRATE \ INRATE * DELT
ypo — [ YR° I I
w \ OUTRATE ' OUTRATE J ' OUTRATE
ACUTE: INRATE = 0, YR3 = R3
CHRONIC: INRATE = R3 * BRTCRN
OUTRATE = BR3 + RDECAY
205
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OURTATE >50:
INRATE
YP A
0 OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
Lung
/ ( INRATE \\ , niITDATIj nciTl INRATE
YR40 = YR40 * e(-OUTRATE*DELT) +
0 \ 0 VOUTRATE// OUTRATE
ACUTE: INRATE = 0, YR4 = R4
CHRONIC: INRATE = R4 * BRTCRN
OUTRATE = BR4 + RDECAY
IF DELT* OUTRATE >50:
1 INRATE INRATE * DELT
yp a [ YP 1 |
W OUTRATE ' 11V±U OUTRATE OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
Lung
(\ - e(-0UTRATE*DELT) INRATE \ INRATE * DELT
Yp \ — [ [ yR4 I 1
w \ OUTRATE ' 11V1U OUTRATE J ' OUTRATE
ACUTE: INRATE = 0, YR4 = R4
CHRONIC: INRATE = R4 * BRTCRN
OUTRATE = BR4 + RDECAY
206
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
Biokinetics
GI Tract
AFc2
p /vp ^
i C1 1 + 30 * e-H0W0LD
(calculated outside of Fortran code)
IF DELT*OUTRATE >50:
INRATE
YRSTMC0 =
0 OUTRATE
IF DELT* OUTRATE<5 0:
Biokinetics
GI Tract
/ ( INRATE \\ , niITr,4TC, nc.IT^ INRATE
YSTMCq = YSTMCq * g(-OUTRATE*DELT) +
0 \ 0 VOUTRATE J J OUTRATE
ACUTE: INRATE = 0, YSTMC0 = 1
CHRONIC (no inhalation): INRATE = EAT CRN
/BR1 * YR1W + BR2 * YR2W + BR3 * YR3W +\
v RR4 * YR4 /
CHRONIC (COMBINATION): INRATE = EAT CRN + CILIAR * ^
v 7 DELT
OUTRATE = GSCALE * RSTMC + RDECAY
207
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
Biokinetics
GI Tract
IF DELT*OUTRATE >50:
1 INRATE DELT
YSTMCW = * YRSTMCn + INRATE *
W OUTRATE u OUTRATE OUTRATE
IF DELT* OUTRATE <50:
(x - 6(outrate*delt) INRATE \ INRATE * DELT
YSTMCw OUTRATE 1 ^™cu qUTRATE j ' OUTRATE
ACUTE: INRATE = 0, YSTMC0 = 1
CHRONIC (no inhalation): INRATE = EAT CRN
/BR1 * YR1W + BR2 * YR2W + BR3 * YR3W +\
v RR4 * YR4 /
CHRONIC (COMBINATION): INRATE = EAT CRN + CILIAR * ^ -
v J DELT
OUTRATE = GSCALE * RSTMC + RDECAY
208
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
Biokinetics
GI Tract
IF DELT*OUTRATE >50:
INRATE
YSIC° ~ OUTRATE
IF DELT* OUTRATE <50:
/ ( INRATE \\ , miTDATP nciT^ (INRATE)
YSICq = YSICo * e(-OUTRATE*DELT) +
0 \ 0 VOUTRATE// OUTRATE
(GSCALE * RSTMC * YSTMCW) + (H1TOSI * RLVR1 * YRLVR1W) + (TFECE * CF * BTEMP)
INRATE - delt
OUTRATE = GSCALE * RSIC + RDECAY
Biokinetics
GI Tract
IF DELT*OUTRATE >50:
1 INRATE INRATE * DELT
YSICW = * YSICn +
w OUTRATE u OUTRATE OUTRATE
IF DELT* OUTRATE <50:
/I _ 6(-outrate*delt) INRATE \ INRATE * DELT
ycTp _ [ ycIC 1 1
w \ OUTRATE ' ^1VJU OUTRATE J ' OUTRATE
(GSCALE * RSTMC * YSTMCW) + (H1TOSI * RLVR1 * YRLVR1W) + (TFECE * CF * BTEMP)
INRATE - DELT
OUTRATE = GSCALE * RSIC + RSIC
209
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
INRATE
YULICn =
0 OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
GI Tract
/ ( INRATE \\ rurrBATc nciT INRATE
YULICn = YULICo * e-OUTRATE*DELT +
0 \ 0 VOUTRATE// OUTRATE
(1.0 - Fl) * GSCALE * RSIC * YSICw
INRATE = - -
DELT
OUTRATE = GSCALE * RULI + RDECAY
210
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT* OUTRATE>5 0:
1 INRATE INRATE * DELT
YULICW = * YULICn +
w OUTRATE u OUTRATE OUTRATE
IF DELT* OUTRATE<5 0:
Biokinetics
GI Tract
A - e(-°UTRATE*DELT) wttt ^ INRATE \ _ INRATE * DELT
YULICW \ OUTRATE 1 ^ULICu omRATEJ 1 OUTRATE
(1.0 - Fl) * GSCALE * RSIC * YSICW
INRATE =
DELT
OUTRATE = GSCALE * RULI + RDECAY
211
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
INRATE
YLLICq =
0 OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
GI Tract
/ ( INRATE \\ , niITDATIj nciTl INRATE
YLLICq = YLLICq * 6(-outrate*delt) +
0 \ 0 VOUTRATE// OUTRATE
GSCALE * RULI * YULICW
INRATE = -
DELT
OUTRATE = GSCALE * RLLI + RDECAY
212
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
1 INRATE INRATE * DELT
YLLICW = * YULICn +
w OUTRATE u OUTRATE OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
GI Tract
A ~ e(-°UTRATE*DELT) t ^ INRATE \ _ INRATE * DELT
YLLICW \ OUTRATE ' ^LLICu OUTRATE/' OUTRATE
GSCALE * RULI * YULICW
INRATE =
DELT
OUTRATE = GSCALE * RLLI + RDECAY
213
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
Biokinetics
Plasma
IF DELT* OUTRATE >50:
YPLSn =
INRATE
OUTRATE
IF DELT* OUTRATE <50:
/ INRATE \\ , niITDATIj nPITl (INRATE)
YPLSn = YPLSq - * e(-OUTRATE*DELT) + ^
0 1 0 VOUTRATE// OUTRATE
INRATE
/ACUTE: INRATEtissue
= < CHRONIC: INRATEtissue + CRONIC
(1.0 + CILIAR) * (BR1 * YR1W + BR2 * YR2W + BR3 * YR3W + BR4 * YR4W)
INHALATION: INRATEtissue + ¦
DELT
TISSUE RATES = RPROT * YPROTw + RRBC * YRBCW + REVF * YEVFW + RSOFO * YSOFOW * (1 - S2HAIR)
INRATEtissue —
* RSOF1 * YSOFlw + RSOF2 * YSOF2w + H1TOBL * RLVR1 * YLVR1W + RLVR2 * YLVR2
+ RKDN2 * YKDN2W + RCS2B * YCSURW + RTS2B * YTSURW + RCORT * YCVOL '
* YTVOLw + RBRAN * YBRANW + F1 * GSCALE * RSIC * YSICW
TISSUE RATES
w
w+RTRAB
DELT
OUTRATE = RPLS + RDECAY
214
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
Biokinetic
Plasma
IF DELT* OUTRATE >50:
YPLSW =
OUTRATE
INRATE INRATE * DELT
* YPLSq - + ¦
OUTRATE
OUTRATE
IF DELT* OUTRATE <50:
! _ e(-0UTRATE*DELT) INRATE \ INRATE * DELT
YPLSw = I nT^w , nnTC * YPLSq - I + ¦
RDECAY+ RPLS
INRATE
/ACUTE: INRATEtissue
RDECAY + RPLS
OUTRATE
CHRONIC: INRATEtissue + CRONIC
(1.0 + CILIAR) * (BR1 * YR1W + BR2 * YR2W + BR3 * YR3W + BR4 * YR4W)
INHALATION: INRATEtissue + ¦
DELT
TISSUE RATES = RPROT * YPROTw + RRBC * YRBCW + REVF * YEVFW + RSOFO * YSOFO^
jw * (1 - S2HAIR)
* RSOF1 * YSOFlw + RSOF2 * YSOF2w + H1TOBL * RLVR1 * YLVR1W + RLVER2 * YLVR2\
+ RKDN2 * YKDN2W + RCS2B * YCSURW + RTS2B * YTSURW + RCORT * YCVOLw + RTRAB
£w
INRATEtissue —
* YTVOLw + RBRAN * YBRANW + F1 * GSCALE * RSIC * YSICW
TISSUE RATES
DELT
OUTRATE = RPLS + RDECAY
215
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
INRATE
yproTq - 0UTRATE
IF DELT* OUTRATE <50:
Biokinetics
Plasma
Protein
/ ( INRATE \\ , miTDATP nFiTi INRATE
YPROTn = YPROTo - * e(-OUTRATE*DELT) +
0 \ 0 VOUTRATE// OUTRATE
TPROT * CF * BTEMP
INRATE = ——
DELT
OUTRATE = RPROT + RDECAY
216
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
1 INRATE INRATE * DELT
YPROTw-qutrate i \TROTu 0UTRATE ' OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
Plasma
Protein
(\ - 6(-outrate*delt) INRATE \ INRATE * DELT
YPROTW-( OUTRATE ' ^rR0Tu OUTRATE j' OUTRATE
TPROT * CF * BTEMP
INRATE = ——
DELT
OUTRATE = RDECAY + RPROT
217
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT* OUTRATE >50:
INRATE
YRBC0- 0UTRATE
IF DELT* OUTRATE <50:
Biokinetics
RBC
/ ( INRATE \\ , miTDATP nFiTi INRATE
yrbCq = yrbc0 * e(-°UTRATE*DELT) +
0 \ 0 VOUTRATE// OUTRATE
TOORBC* BTEMP
INRATE = ——
DELT
OUTRATE = RRBC + RDECAY
218
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT* OUTRATE >50:
1 INRATE INRATE * DELT
YRBCW-0UTRATE i\REC0 QUTRATE 1 OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
RBC
A - e(-°UTRATE*DELT) INRATE \ _ INRATE * DELT
YRBCW — ^ OUTRATE '^RECu QUTRATE/' OUTRATE
TOORBC* BTEMP
INRATE = ——
DELT
OUTRATE = RRB C+RDECAY
219
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
INRATE
YEVF°~ OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
EVF
/ ( INRATE \\ , miTDATP nciT^ INRATE
yevFq = yevf0 * e(-°UTRATE*DELT) +
0 \ 0 VOUTRATE// OUTRATE
TEVF * CF * BTEMP
INRATE = ——
DELT
OUTRATE = REVF + RDECAY
220
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
1 INRATE INRATE * DELT
YEVFW = * YEVFq +
w OUTRATE u OUTRATE OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
EVF
(\ - 6(-outrate*delt) INRATE \ INRATE * DELT
YEVF I i yEVF I 1
w \ OUTRATE ' ±u OUTRATE J ' OUTRATE
TEVF * CF * BTEMP
INRATE = ——
DELT
OUTRATE = REVF + RDECAY
221
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
INRATE
ybraNq - 0UTRATE
IF DELT* OUTRATE <50:
Biokinetics
Brain
/ ( INRATE \\ , miTDATP no-n INRATE
YBRANq = YBRANo - * e(-OUTRATE*DELT) +
0 \ 0 VOUTRATE// OUTRATE
TBRAN * CF * BTEMP
INRATE = ——
DELT
OUTRATE = RBRAN + RDECAY
222
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
Biokinetics
Brain
IF DELT*OUTRATE >50:
1 INRATE INRATE * DELT
YBRANW = * YBRANq +
W OUTRATE u OUTRATE OUTRATE
IF DELT* OUTRATE <50:
(\ - 6(-outrate*delt) INRATE \ INRATE * DELT
YBRANW — y OUTRATE ' ^CRANu OUTRATE/' OUTRATE
TBRAN * CF * BTEMP
INRATE = ——
DELT
OUTRATE = RBRAN + RDECAY
223
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT* OUTRATE >50:
INRATE
YKDN1° = OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
Kidney
/ ( INRATE \\ , niITDATIj nPITl INRATE
YKDNln = YKDNIq - * 6(-outrate*delt) +
0 \ 0 VOUTRATE// OUTRATE
TKDN1 * CF * BTEMP
INRATE = ——
DELT
OUTRATE = RKDN1 + RDECAY
224
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
Biokinetics
Kidney
IF DELT* OUTRATE >50:
1 INRATE INRATE * DELT
YKDN1W-0UTRATE i \KDN10 QUTRATE 1 OUTRATE
IF DELT* OUTRATE <50:
(\ - 6(-outrate*delt) INRATE \ INRATE * DELT
YKDN1W — y OUTRATE ' M*DN1" OUTRATE/' OUTRATE
TKDN1 * CF * BTEMP
INRATE = ——
DELT
OUTRATE = RKDN1 + RDECAY
225
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT* OUTRATE >50:
INRATE
YKDN2° = OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
Kidney
/ ( INRATE \\ , niITDATIj nPITl INRATE
YKDN20 = YKDN20 - * 6(-outrate*delt) +
0 \ 0 VOUTRATE// OUTRATE
TKDN2 * CF * BTEMP
INRATE = ——
DELT
OUTRATE = RKDN2 + RDECAY
226
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
Biokinetics
Kidney
IF DELT* OUTRATE >50:
1 INRATE INRATE * DELT
YKDN2W-0UTRATE i \KDN.,0 QUTRATE 1 OUTRATE
IF DELT* OUTRATE <50:
(\ - 6(-outrate*delt) INRATE \ INRATE * DELT
YKDN2W-^ OUTRATE ' OUTRATEj ' OUTRATE
TKDN2 * CF * BTEMP
INRATE = ——
DELT
OUTRATE = RKDN2 + RDECAY
227
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
INRATE
yblaDq - 0UTRATE
IF DELT* OUTRATE <50:
Biokinetics
Bladder
/ ( INRATE \\ , niiTDATc nfiTi INRATE
YBLADq = YBLADo - * e(-OUTRATE*DELT) +
0 \ 0 VOUTRATE// OUTRATE
TURIN * CF * BTEMP + RKDN1 * YKDN1W
INRATE = -
DELT
OUTRATE = RBLAD + RDECAY
228
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
1 INRATE INRATE * DELT
YBLADW = * YBLADq +
w OUTRATE u OUTRATE OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
Bladder
(\ - 6(-outrate*delt) INRATE \ INRATE * DELT
YBLADw = * YBLADn +
w \ OUTRATE u OUTRATE J OUTRATE
TURIN * CF * BTEMP + RKDN1 * YKDN1W
INRATE =
DELT
OUTRATE = RBLAD + RDECAY
229
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
INRATE
YLVRIq- 0UTRATE
IF DELT* OUTRATE <50:
Biokinetics
Liver
/ ( INRATE \\ , miTDATP nciT^ INRATE
YLVRIq = YLVRIq * e(-°UTRATE*DELT) +
0 \ 0 VOUTRATE// OUTRATE
TLVR1 * CF * BTEMP
INRATE = ——
DELT
OUTRATE = RLVR1 + RDECAY
230
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
1 INRATE INRATE * DELT
YLVR1W- QUTRATE 1 MAR10 0UTRATE 1 OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
Liver
/I - 6(-outrate*delt) INRATE \ INRATE * DELT
YLVR1W \ OUTRATE 1 MAR10 QUTRATE J ' OUTRATE
TLVR1 * CF * BTEMP
INRATE = ——
DELT
OUTRATE = RLVR1 + RDECAY
231
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
INRATE
YLVR20- 0UTRATE
IF DELT* OUTRATE <50:
Biokinetics
Liver
/ ( INRATE \\ , miTDATP nciT^ INRATE
YLVR20 = YLVR20 * e(-°UTRATE*DELT) +
0 \ 0 VOUTRATE// OUTRATE
H1TOH2 * RLVR1 * YLVR1W
INRATE = -
DELT
OUTRATE = RLVR2 + RDECAY
232
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
1 INRATE INRATE * DELT
YLVR2W- QUTRATE 1 0UTRATE 1 OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
Liver
/I - 6(-outrate*delt) INRATE \ INRATE * DELT
YLVR2W — ^ OUTRATE 1 QUTRATE J ' OUTRATE
H1TOH2 * RLVR1 * YLVR1W
INRATE =
DELT
OUTRATE = RLVR2 + RDECAY
233
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
INRATE
YSOFOq =
0 OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
Soft Tissue
/ ( INRATE \\ , niITDATIj nPITl INRATE
YSOFOq = YSOFOq - * 6(-outrate*delt) +
0 \ 0 VOUTRATE// OUTRATE
TSOFO * CF * BTEMP
INRATE = ——
DELT
OUTRATE = RSOFO + RDECAY
234
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
1 INRATE INRATE * DELT
YSOFOW = * YSOFOq +
w OUTRATE u OUTRATE OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
Soft Tissue
(\ - 6(-outrate*delt) INRATE \ INRATE * DELT
YSOFOw = * YSOFOn +
w \ OUTRATE u OUTRATE J OUTRATE
TSOFO * CF * BTEMP
INRATE = ——
DELT
OUTRATE = RSOFO + RDECAY
235
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
INRATE
ysofIq - 0UTRATE
IF DELT* OUTRATE <50:
Biokinetics
Soft Tissue
/ ( INRATE \\ , miTDATP nciT^ INRATE
YSOFlo = YSOFIq * e(-OUTRATE*DELT) +
0 \ 0 VOUTRATE// OUTRATE
TSOFOl * CF * BTEMP
INRATE = ——
DELT
OUTRATE = RSOF1 + RDECAY
236
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
1 INRATE INRATE * DELT
YS0F1W - 0UTRATE 1 ^OFlu OUTRATE1 OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
Soft Tissue
(\ - 6(-outrate*delt) INRATE \ INRATE * DELT
YSOFlw — y OUTRATE 1 ^OFlu 0UTRATE J 1 OUTRATE
TSOF1 * CF * BTEMP
INRATE = ——
DELT
OUTRATE = RSOF1 + RDECAY
237
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
INRATE
YSOF20 =
0 OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
Soft Tissue
/ ( INRATE \\ , niITDATIj nPITl INRATE
YSOF20 = YSOF20 * 6(-outrate*delt) +
0 \ 0 VOUTRATE// OUTRATE
TSOF02 * CF * BTEMP
INRATE = ——
DELT
OUTRATE = RSOF2 + RDECAY
238
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
1 INRATE INRATE * DELT
YSOF2w = * YSOF20 +
w OUTRATE u OUTRATE OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
Soft Tissue
(\ - 6(-outrate*delt) INRATE \ INRATE * DELT
YSOF2w = * YSOF2n +
w \ OUTRATE u OUTRATE J OUTRATE
TSOF2 * CF * BTEMP
INRATE = ——
DELT
OUTRATE = RSOF2 + RDECAY
239
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
INRATE
ycdiFq - 0UTRATE
IF DELT* OUTRATE <50:
Biokinetics
Bone
/ ( INRATE \\ , miTDATP nri-n INRATE
ycdiFq = ycdiFq * e(-°UTRATE*DELT) +
0 \ 0 VOUTRATE// OUTRATE
RCS2DF* YCSURW
INRATE = -
DELT
OUTRATE = RDF2CS + RDF2DC + RDECAY
240
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
1 INRATE INRATE * DELT
YCDIFW - qutrate i \CDIFu QUTRATE 1 OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
Bone
/I - 6(-outrate*delt) INRATE \ INRATE * DELT
YCDIFW \ OUTRATE 1 ^CDIFu 0UTRATE J 1 OUTRATE
RCS2DF* YCSURW
INRATE =
DELT
OUTRATE = RDF2CS + RDF2DC + RDECAY
241
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
INRATE
ycsuRq - 0UTRATE
IF DELT* OUTRATE <50:
Biokinetics
Bone
/ ( INRATE \\ , niiTDATc nfiTi INRATE
ycsuRq = ycsuRq * e(-°UTRATE*DELT) +
0 \ 0 VOUTRATE// OUTRATE
(TBONE * (1.0 - TFRAC) * CF * BTEMP * RDF2CS * YCDIFW
INRATE = - - - -
DELT
OUTRATE = RCS2B + RCS2DF + RDECAY
242
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT* OUTRATE >50:
1 INRATE INRATE * DELT
YCSURW = * YCSURq +
w OUTRATE u OUTRATE OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
Bone
(\ - 6(-outrate*delt) INRATE \ INRATE * DELT
YCSURw -y OUTRATE ' ^C"URu qUTRATE j ' OUTRATE
(TBONE * (1.0 - TFRAC) * CF * BTEMP * RDF2CS * YCDIFW
INRATE = - - -
DELT
OUTRATE = RCS2B + RCS2DF + RDECAY
243
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
INRATE
YCVOLq =
0 OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
Bone
/ ( INRATE \\ , niITDATIj nciTl INRATE
YCVOLq = YCVOLq * 6(-outrate*delt) +
0 \ 0 VOUTRATE// OUTRATE
RDF2DC * YCDIFW
INRATE = -
DELT
OUTRATE = RCORT + RDECAY
244
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT* OUTRATE >50:
1 INRATE INRATE * DELT
YCVOLw = * YCVOLq +
w OUTRATE u OUTRATE OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
Bone
(\ - e(-0UTRATE*DELT) INRATE \ INRATE * DELT
YCVOLw = * YCVOLn +
w \ OUTRATE u OUTRATE J OUTRATE
RDF2DC * YCDIFW
INRATE =
DELT
OUTRATE = RCORT + RDECAY
245
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
INRATE
ytdiFq - 0UTRATE
IF DELT* OUTRATE <50:
Biokinetics
Bone
/ ( INRATE \\ , niiTDATc nfiTi INRATE
ytdiFq = ytdiFq * e(-°UTRATE*DELT) +
0 \ 0 VOUTRATE// OUTRATE
RTS2DF * YTSURW
INRATE = -
DELT
OUTRATE = RDF2TS + RDF2DT + RDECAY
246
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
1 INRATE INRATE * DELT
YTDIFW-qutrate i \TDIFu 0UTRATE ' OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
Bone
(\ - e(-0UTRATE*DELT) INRATE \ INRATE * DELT
YTDIFw-(^ OUTRATE 1 ^TDIFu 0UTRATE J 1 OUTRATE
RTS2DF * YTSURW
INRATE =
DELT
OUTRATE = RDF2TS + RDF2DT + RDECAY
247
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
INRATE
ytsuRq - 0UTRATE
IF DELT* OUTRATE <50:
Biokinetics
Bone
/ ( INRATE \\ , miTDATP nci-n INRATE
YTSURn = YTSURo - * e(-OUTRATE*DELT) +
0 \ 0 VOUTRATE// OUTRATE
TBONE * TFRAC * CF * BTEMP * RDF2TS * YTDIFW
INRATE = -
DELT
OUTRATE = RTS2B + RTS2DF + RDECAY
248
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT* OUTRATE >50:
1 INRATE INRATE * DELT
YTSURW ~ OUTRATE ' ^T"URu OUTRATE ' OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
Bone
(\ - e(-0UTRATE*DELT) INRATE \ INRATE * DELT
YTSURw OUTRATE ' ^T"URu qUTRATE j ' OUTRATE
TBONE * TFRAC * CF * BTEMP * RDF2TS * YTDIFW
INRATE =
DELT
OUTRATE = RTS2B + RTS2DF + RDECAY
249
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT*OUTRATE >50:
INRATE
YTVOLq =
0 OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
Bone
/ ( INRATE \\ , niITDATIj nPITl INRATE
YTVOLq = YTVOLq * 6(-outrate*delt) +
0 \ 0 VOUTRATE// OUTRATE
RDF2DT * YTDIFW
INRATE = -
DELT
OUTRATE = RTRAB + RDECAY
250
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
IF DELT* OUTRATE >50:
1 INRATE INRATE * DELT
YTVOLw = * YTVOLq +
w OUTRATE u OUTRATE OUTRATE
IF DELT* OUTRATE <50:
Biokinetics
Bone
(\ - 6(-outrate*delt) INRATE \ INRATE * DELT
YTVOLw = * YTVOLn +
w \ OUTRATE u OUTRATE J OUTRATE
RDF2DT * YTDIFW
INRATE =
DELT
OUTRATE = RTRAB + RDECAY
Lead Masses in Tissues at Birth
Biokinetics
Blood
BLDMOT * BRATIO * 3
YRBC = RBCIN *
RBCIN
Biokinetics
Brain
BLDMOT * BRATIO * 3
YBRAN = BRANIN *
RBCIN
251
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
Biokinetics
Kidney
BLDMOT * BRATIO * 3
YKDN2 = RENIN *
RBCIN
Biokinetics
Liver
BLDMOT * BRATIO * 3
YLVR2 = HEPIN *
RBCIN
Biokinetics
Soft Tissue
BLDMOT * BRATIO * 3
YS0F2 = SOFIN *
RBCIN
Biokinetics
Bone
BLDMOT * BRATIO * 3
YCVOL = 0.8 * ——
RBCIN
Biokinetics
Bone
BLDMOT * BRATIO * 3
YTVOL = 0.2 * ——
RBCIN
Composite lead masses in tissues
Biokinetics
Blood
YBLUD = YPLAS + YRBC
Biokinetics
Plasma
YPLAS = YPLS + YPROT
252
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
Biokinetics
Plasma
YPLASW = YPLSW + YPROTw
Biokinetics
RBC
SUMRBC = SUMRBC + YRBCW
Biokinetics
Kidney
YKDNE = YKDNI + YKDN2
Biokinetics
Liver
YLIVR = YLVR1 + YLVR2
Biokinetics
Lung
YLUNG = YR1 + YR2 + YR3 + YR4
Biokinetics
Soft Tissue
YSOFT = YSOFO + YS0F1 + YS0F2
Biokinetics
Bone
YCORT = YCSUR + YCDIF + YCVOL
Biokinetics
Bone
YTRAB = YRSUR + YTDIF + YTVOL
Biokinetics
Bone
YSKEL = YCVOL + YTVOL + YCSUR + YTSUR + YCDIF + YTDIF
Biokinetics
Body
TB0DY1 = YPLAS + YRBC + YEVF + YSOFO + YS0F1 + YS0F2 + YBRAN + YCVOL + YTVOL + YCSUR + YTSUR
+ YCDIF + YTDIF + YKDNE + YLIVR
Biokinetics
Body
TBODY2 = TBODY1 + YR1 + YR2 + YR3 + YR4 + YBLAD + YSTMC + YSIC + YULIC + YLLIC
253
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
Fraction of lead in tissues relative to total body burden or blood
Biokinetics
Blood
YBLUD
BLDFRC =
TB0DY1
Biokinetics
Plasma
YPLAS
PLSRBC = YBLUD
Biokinetics
Plasma
100 * YPLAS
PCENT =
YBLUD
Biokinetics
Brain
YBRN
BRNFRC =
TBODY1
Biokinetics
Kidney
YKDNE
RENFRC =
TBODY1
Biokinetics
Liver
YLIVR
HEPFRC =
TBODY1
Biokinetics
Soft Tissue
YSOFT
OTHFRC =
TBODY1
Biokinetics
Bone
YSKEL
BONFRC =
TBODY1
Tissue-specific lead concentrations (jig/g or jig/dL)
Biokinetics
Blood
YBLUD
BLCONC = A,jrT^TT>
AMTBLD
Biokinetics
Plasma
YPLAS
DECPLS =
PLSVOL
254
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
Biokinetics
RBC
YRBC
RBCONC =
BLDHCT * AMTBLD
Biokinetics
Kidney
YKDNE
rencon = kidwt
Biokinetics
Liver
YLIVR
LIVCON =
LIVWT
Biokinetics
Bone
YCORT
CRTCON =
CORTWT
Biokinetics
Bone
YTRAB
TRBCON =
TRABWT
Biokinetics
Bone
YSKEL
ashcon = tskelwt
Biokinetics
Bone
CRTCON
CRTCONBM = ——
0.55
Biokinetics
Bone
TRBCON
TRBCONBM = —
0.5
Lead excretion (jug or jug/day)
Biokinetics
Urine
YURIN = YURINq + INRATE * DELT
RBLAD * YBLADW
INRATE =
DELT
URIN = YURIN - YURINq
255
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Model
Submodel
Equation
Biokinetics
Feces
YFECE = YFECEq + INRATE * DELT
GSCALE * RLLI * YLLICW
INRATE =
DELT
Biokinetics
Sweat
YSWET = YSWETq + INRATE * DELTT
TSWET * CF * BTEMP
INRATE = ——
DELT
Biokinetics
Other
YHAIR = YHAIRq + INRATE * DELT
S2HAIR * RS0F1 * YS0F1W
INRATE =
DELT
Biokinetics
Total
TOTEXC = YURIN + YFECE + YSWET + YHAIR
Clearance (day1)
Biokinetics
Urine
URINE 1
CLEAR = *
DELT YPLAS
Biokinetics
Blood
URIN 1
BCLEAR = 100 * —— * -r-—
DELT YBLUD
256
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 APPENDIX B - ALL AGES LEAD MODEL (AALM.FOR) PARAMETERS
2 TABLE B-l. ALL AGES LEAD MODEL PARAMETER DESCRIPTIONS
Variable
Units
Form
Type
Explanation
EXPOSURE MODEL PARAMETERS
Age_air_discrete
day
A
F
Age for discrete air Pb concentration
Age_air_V
day
A
F
Age for air ventilation rate
Age_dust_discrete
day
A
F
Age for discrete dust Pb concentration
AgedustIR
day
A
F
Age for dust ingestion rate
Age_food_discrete
day
A
F
Age for discrete food Pb concentration
Age_other_discrete
day
A
F
Age for discrete other Pb concentration
Age_soil_discrete
day
A
F
Age for discrete soil Pb concentration
Age_soil_IR
day
A
F
Age for indoor soil ingestion rate
Age_water_discrete
day
A
F
Age for discrete water Pb concentration
Age_water_IR
day
A
F
Age for water ingestion rate
Air_baseline
(ig/m3
C
F
Baseline air Pb concentration used in exposure
pulse train
Air i; i= 1, 2,3
(ig/m3
A
F
Air Pb concentrations for discrete exposures
Air_pulse
l-tg/m3
C
F
Air Pb concentration used in exposure pulse train
Air_discrete_weight
ed
(ig/m3
V
F
Weighted average air Pb concentrations for
discrete exposures
Dustbaseline
Mg/g
c
F
Baseline dust Pb concentration used in exposure
pulse train
Dust_i; i= 1, 2,3
Mg/g
A
F
Dust Pb concentrations for discrete exposures
Dust_pulse
Mg/g
c
F
Dust Pb concentration used in exposure pulse train
Dust_discrete_weigt
ed
Mg/g
V
F
Weighted average dust Pb concentrations for
discrete exposures
f Air i; i= 1,2,3
unitless
A
F
Fraction of discrete Air i contributing to daily air
Pb exposure
f_Dust_i; i= 1,2
unitless
A
F
Fraction of discrete Dust i contributing to daily
dust Pb exposure
f IR soil
unitless
C
F
Soil fraction of soil and dust ingestion rate (IR sd)
f_Other_i; i= 1,2,3
unitless
A
F
Fraction of discrete Other i contributing to daily
other Pb exposure
f_pulse_air
unitless
C
F
Fraction of air daily air exposure from pulse train
f_pulse_dust
unitless
C
F
Fraction of daily dust exposure from pulse train
f_pulse_other
unitless
c
F
Fraction of daily other exposure from pulse train
257
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable
Units
Form
Type
Explanation
f_pulse_soil
unitless
C
F
Fraction of daily soil exposure from pulse train
f_pulse_water
unitless
C
F
Fraction of daily water exposure from pulse train
f_Soil_i; i= 1,2
unitless
A
F
Fraction of discrete Soil i contributing to daily soil
Pb exposure
f_Water_i; i= 1,2,3
unitless
A
F
Fraction of discrete Water i contributing to daily
water Pb exposure
Foodbaseline
Mg/day
C
F
Baseline food Pb intake used in exposure pulse
train
Food_i; i= 1, 2,3
Mg/day
A
F
Food Pb intakes for discrete exposures
Food_pulse
Mg/day
C
F
Food Pb intake used in exposure pulse train
Foodtotaldiscrete
Mg/day
V
F
Total food Pb intakes for discrete exposures
IN_air_discrete
(.ig/day
V
F
Pb intake from discrete exposures to air
INairpulsc
(.ig/day
V
F
Pb intake from pulse train exposures to air
IN_air_total
l-ig/day
V
F
Pb intake from combined discrete and pulse train
exposures to air
IN_dust_discrete
(.ig/day
V
F
Pb intake from discrete exposures to dust
IN_dust_pulse
(.ig/day
V
F
Pb intake from pulse train exposures to dust
IN_dust_total
(.ig/day
V
F
Pb intake from combined discrete and pulse train
exposures to dust
IN_food_discrete
Mg/day
V
F
Pb intake from discrete exposures to food
IN_food_pulse
Mg/day
V
F
Pb intake from pulse train intakes from food
IN_food_total
Mg/day
V
F
Pb intake from combined discrete and pulse train
exposures to food
IN_inge stion_total
Mg/day
V
F
Pb intake from all ingestion exposures combined
(dust, soil, food, water, other)
IN_other_discrete
l-ig/day
V
F
Pb intake from discrete exposures to other sources
IN_other_pulse
Mg/day
V
F
Pb intake from pulse train intakes from other
sources
IN_other_total
(.ig/day
V
F
Pb intake from combined discrete and pulse train
exposures to other sources
IN_s°il_discrete
Mg/day
V
F
Pb intake from discrete exposures to soil
IN_soil_pulse
Mg/day
V
F
Pb intake from pulse train exposures to soil
IN_s°il _t°tal
Mg/day
V
F
Pb intake from combined discrete and pulse train
exposures to soil
IN_water_discrete
Mg/day
V
F
Pb intake from discrete exposures to water
IN_water_pulse
(.ig/day
V
F
Pb intake from pulse train exposures to water
IN_water_total
l-ig/day
V
F
Pb intake from combined discrete and pulse train
exposures to water
258
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable
Units
Form
Type
Explanation
IRdust
g/day
C
F
Dust ingestion rate for dust Pb exposures
IRsoil
g/day
C
F
Dust ingestion rate for soil Pb exposures
IRsd
g/day
A
F
Combined soil and dust ingestion rate for Pb
exposures
IRwater
L/day
C
F
Dust ingestion rate for water Pb exposures
Otherbaseline
fig/day
C
F
Baseline other Pb intake used in exposure pulse
train
Other_i; i= 1, 2,3
Mg/day
A
F
Food Pb intakes for discrete exposures
Other_pulse
Mg/day
C
F
Other Pb intake used in exposure pulse train
Othertotaldiscrete
Mg/day
V
F
Total other Pb intakes for discrete exposures
Pulse i_period air;
i=l,2
day
c
F
Period for pulse train exposure to air
Pulse i_period dust
; 1=1,2
day
c
F
Period for pulse train exposure to dust
Pulse i_period food
; 1=1,2
day
c
F
Period for pulse train exposure to food
Pulse_i_period_othe
r; i=l,2
day
c
F
Period for pulse train exposure to other
Pulse i_period soil;
i=l,2
day
c
F
Period for pulse train exposure to soil
Pulse_i_period_wate
r; i=l,2
day
c
F
Period for pulse train exposure to water
Pulse i width air;
i=l,2
day
c
F
Width for pulse train exposure to air
Pulse i width dust;
i=l,2
day
c
F
Width for pulse train exposure to dust
Pulse i width food;
i=l,2
day
c
F
Width for pulse train exposure to food
Pulse i width other
; 1=1,2
day
c
F
Width for pulse train exposure to other
Pulse i width soil;
i=l,2
day
c
F
Width for pulse train exposure to indoor soil
Pulseiwidthwate
r; i=l,2
day
c
F
Width for pulse train exposure to water
Pulsestartair
day
c
F
Start age for pulse train exposure to air
Pulsestartdust
day
c
F
Start age for pulse train exposure to dust
Pulsestartfood
day
c
F
Start age for pulse train exposure to food
Pulsestartother
day
c
F
Start age for pulse train exposure to other
Pulsestartsoil
day
c
F
Start age for pulse train exposure to indoor soil
259
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable
Units
Form
Type
Explanation
Pulsestartwater
day
C
F
Start age for pulse train exposure to water
Pulsestopair
day
C
F
Stop age for pulse train exposure to air
Pulsestopdust
day
C
F
Stop age for pulse train exposure to dust
Pulsestopfood
day
C
F
Stop age for pulse train exposure to food
Pulsestopother
day
C
F
Stop age for pulse train exposure to other
Pulsestopsoil
day
C
F
Stop age for pulse train exposure to soil
Pulsestopwater
day
C
F
Stop age for pulse train exposure to water
RBAdust
unitless
C
F
Relative bioavailability of dust Pb
RBA food
unitless
C
F
Relative bioavailability of food Pb
RBA other
unitless
C
F
Relative bioavailability of other Pb
RBA soil
unitless
C
F
Relative bioavailability of soil Pb
RBAwater
unitless
C
F
Relative bioavailability of water Pb
Sex
unitless
C
S
Female of male
Soil_baseline
Mg/g
C
F
Baseline dust Pb concentration used in exposure
pulse train
Soil i; i= 1, 2,3
Mg/g
A
F
Soil Pb concentrations for discrete exposures
Soil_pulse
Mg/g
C
F
Soil Pb concentration used in exposure pulse train
Soil discrete weigte
d
Mg/g
V
F
Weighted average soil Pb concentrations for
discrete exposures
Water_baseline
l-ig/L
c
F
Baseline water Pb concentration used in exposure
pulse train
Water_i; i= 1, 2,3
l-ig/L
A
F
Water Pb concentrations for discrete exposures
Water_pulse
l-ig/L
c
F
Water Pb concentration used in exposure pulse
train
Water_discrete_wei
ghted
l-ig/L
V
F
Weighted average water Pb concentrations for
discrete exposures
V_air
m3/day
A
F
Ventilation rate for air Pb exposures
BIOKINETIC MODEL PARAMETERS
AF1
unitless
A
F
Fractional absorption of Pb from small intestine -
age array (see Fl)
AGESCAL
unitless
A
F
Age scaling factor for gastrointestinal transfers -
age array (see GSCALE)
AGEYEAR
year
V
F
Age from birth in years
AMTBLD
dL
V
F
Amount of blood at time(t)
ARBLAD
day-1
A
F
Rate coefficient for Pb transfer from urinary
bladder to urine - age array (see RBLAD)
260
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable
Units
Form
Type
Explanation
ARBRAN
day"1
A
F
Rate coefficient for Pb transfer from brain to
diffusible plasma - age array (see RBRAN)
ARCORT
day"1
A
F
Rate coefficient for Pb transfer from non-
exchangeable cortical bone to diffusible plasma -
age array (see RCORT)
ARCS2B
day"1
A
F
Rate coefficient for Pb transfer from cortical bone
surface to diffusible plasma - age array (see
RCS2B)
ARCSDF
day"1
A
F
Rate coefficient for Pb transfer from cortical bone
surface to exchangeable cortical bone - age array
(see RCS2DF)
ARD2CS
day"1
A
F
Rate coefficient for Pb transfer from exchangeable
cortical bone to cortical bone surface - age array
(see RDF2CS)
ARD2DC
day"1
A
F
Rate coefficient for Pb transfer from exchangeable
cortical bone to non-exchangeable cortical bone -
age array (see RDF2DC)
ARD2DT
day"1
A
F
Rate coefficient for Pb transfer from exchangeable
trabecular bone to non-exchangeable trabecular
bone - age array (see RDF2DT)
ARD2TS
day"1
A
F
Rate coefficient for Pb transfer from exchangeable
trabecular bone to trabecular bone surface - age
array (see RDF2DS)
ARKDN2
day"1
A
F
Rate coefficient for transfer from kidney
compartment 2 to diffusible plasma - age array
(see RKDN2)
ARLVR2
day"1
A
F
Rate coefficient for Pb transfer from the slow liver
compartment 2 to diffusible plasma - age array
(see RLVR2)
ARRBC
day"1
A
F
Rate coefficient for Pb transfer from RBC to
diffusible plasma - age array (see RRBC)
ARTRAB
day"1
A
F
Rate coefficient for Pb transfer from non-
exchangeable trabecular bone to diffusible plasma
- age array (see RTRAB)
ARTS2B
day"1
A
F
Rate coefficient for Pb transfer from trabecular
bone surface to diffusible plasma - age array (see
RTS2B)
ARTSDF
day"1
A
F
Rate coefficient for Pb transfer from surface
trabecular bone to exchangeable trabecular bone -
age array (see RTS2DF)
ASHCON
Mg/g
V
F
Pb concentration in skeletal mineral
261
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable
Units
Form
Type
Explanation
ATBONE
unitless
A
F
Deposition fraction for Pb from diffusible plasma
to surface bone - age array (see TBONE)
ATBRAN
unitless
A
F
Deposition fraction for Pb from diffusible plasma
to brain - age array (see RBRAN)
ATFRAC
unitless
A
F
Fraction of diffusible plasma-to-bone deposition
that goes to trabecular surface bone - age array
(see TFRAC)
ATOSOFO
unitless
A
F
Deposition fraction for Pb from diffusible plasma
to soft tissue compartment 0 - age array (see
TOSOFO)
ATOSOF1
unitless
A
F
Deposition fraction for Pb from diffusible plasma
to soft tissue compartment 1 - age array (see
TOSOF1)
ATOSOF2
unitless
A
F
Deposition fraction for Pb from diffusible plasma
to soft tissue compartment 2 - age array (see
TOSOF2)
BCLEAR
day-1
V
F
Clearance of Pb from blood to urine
BLCONC
1-ig/dL
V
D
Pb concentration in whole blood
BLDFRC
unitless
V
F
Amount of Pb in blood as a fraction of total body
Pb
BLDHCT
unitless
V
F
Blood hematocrit
BLDMOT
1-ig/dL
C
F
Maternal blood Pb concentration
BLDVOL
dL
V
F
Blood volume as the sum of RBC and plasma
volume
BONFRC
unitless
V
F
Amount of Pb in bone as a fraction of total body
Pb
BR1
day"1
c
F
Rate coefficient for Pb transfer from RT
compartment 1 to diffusible plasma
BR2
day"1
c
F
Rate coefficient for Pb transfer from RT
compartment 2 to diffusible plasma
BR3
day"1
c
F
Rate coefficient for Pb transfer from RT
compartment 3 to diffusible plasma
BR4
day"1
c
F
Rate coefficient for Pb transfer from RT
compartment 4 to diffusible plasma
BRATIO
unitless
c
F
Child (at birth):maternal blood Pb concentration
ratio
BRETH
Mg/day
V
A
Pb intake rate age array from inhalation of Pb in air
(see IN_air_total)
BRNFRC
unitless
V
F
Amount of Pb in brain as a fraction of total body
Pb
262
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable
Units
Form
Type
Explanation
BRTCRN
fig/day
V
F
Pb intake from inhalation exposure at each age
range
BTEMP
Mg/day
V
F
Total outflow of Pb from diffusible plasma to all
compartments
CF
unitless
V
F
Factor for adjusting Pb deposition fractions from
diffusible plasma to account for non-linear uptake
of Pb in RBC
CHAGE
day
A
F
Ages at which biokinetics parameters are specified
(for each NUMAGE)
CHEL1
unitless
c
I
First day of chelation therapy
CHEL2
unitless
c
I
Last day of chelation therapy
CHLEFF
unitless
c
I
Deposition change factor due to chelation therapy
CHR
Mg
A
F
Chronic injection uptakes for each NCHRON
CILIAR
unitless
c
F
Fraction of inhaled Pb transferred to
gastrointestinal tract
CORTWT
g
V
F
cortical bone weight
CRONIC
Mg
V
F
Chronic injection intake at current integration time
step
CRTCON
Mg/g
V
F
Pb concentration in cortical bone
CRTCONBM
Mg/g
V
F
Pb concentration in cortical bone mineral
CVBONE
mL
V
F
cortical bone volume
DECLTR
1-ig/dL
V
D
Pb concentration in total blood
DECPLS
1-ig/dL
V
D
Pb concentration in diffusible plasma
DECRBC
1-ig/dL
V
D
Pb concentration in RBCs
DELTO
day
c
F
Initial integration time step
DELTA
unitless
A
F
Numerical integration cycle lengths - age array
DELT i
day
A
F
Array of integration step sizes for each NDELT
EAT
Mg/day
A
F
Pb intake rate age array from ingestion of Pb (see
IN_inge stion_total)
EATCRN
Mg/day
V
F
Pb intake from oral exposure at each age range
ENDDAY
day
c
F
Age and end of simulation
ENDPT
day
A
F
End days for chronic intakes for each NCHRON
EXPAGE
day
C
F
Age at start exposure
F1
unitless
V
F
Fractional absorption of Pb from small intestine at
time(t) (see AF1)
FLONG
unitless
A
F
Fraction of total Pb transfer from the exchangeable
bone to non-exchangeable bone
263
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable
Units
Form
Type
Explanation
GSCALE
unitless
V
F
Age scaling factor for gastrointestinal transfers at
time(t) (see AGSCL)
HALF
year
c
F
Age at which body weight is half of WCHILD
HCTA
unitless
c
F
Adult hematocrit
H1TOBL
unitless
c
F
Fraction of Pb transfer out of liver compartment 1
that goes to diffusible plasma
H1TOH2
unitless
c
F
Fraction of Pb transfer out of liver compartment 1
that goes to liver compartment 2
H1TOSI
unitless
c
F
Fraction of Pb transfer out of liver compartment 1
that goes to the small intestine
HEPFRC
unitless
V
F
Amount of Pb in liver as a fraction of total body Pb
IACUTE
unitless
c
I
Switch for acute (1) or chronic array (2) uptakes
ICHEL
unitless
c
I
Switch for chelation simulation off (0) or on (1)
ICY C_i
unitless
A
F
Number of numerical integration cycles for each
NDELT
IFETAL
unitless
c
I
Switch for fetal simulation on (1) or off (0)
INMODE
unitless
c
I
Switch for injection (0), inhalation (1), ingestion
(2), or combination (3)
IRBC
unitless
c
I
Switch for linear (0) or non-linear (1) RBC uptake
ISKIP
day
c
F
Communication interval
KAPPA
unitless
c
F
Logistic body growth parameter
KIDWT
g
V
F
Kidney weight
LAMBDA
unitless
c
F
Logistic body growth parameter
LINPUT
unitless
c
I
Switch for manual input (0) or array input (1)
LIVCON
Mg/g
V
F
Pb concentration in liver
LIVWT
g
V
F
Liver weight
NCHRON
unitless
c
F
Number of different chronic intakes
NCYCLE
unitless
c
F
Maximum number of numerical integration cycles
NDELT
unitless
c
F
Number of times the integration step changes
NUMAGE
unitless
c
F
Number of ages at which biokinetics parameter
values are specified
OTHFRC
unitless
V
F
Amount of Pb in other soft tissue as a fraction of
total body Pb
PCENT
percent
V
F
Percent of whole blood Pb in plasma
PLSRBC
unitless
V
F
Plasma fraction of Pb in whole blood
PLSVOL
dL
V
F
Plasma volume
POWER
unitless
c
F
Exponent for non-linear deposition of Pb from
diffusible plasma to RBC
264
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable
Units
Form
Type
Explanation
R1
unitless
C
F
Fraction of inhaled Pb deposited in RT
compartment 1
R2
unitless
C
F
Fraction of inhaled Pb deposited in RT
compartment 2
R3
unitless
C
F
Fraction of inhaled Pb deposited in RT
compartment 3
R4
unitless
C
F
Fraction of inhaled Pb deposited in RT
compartment 4
RBCIN
unitless
V
F
Amount of Pb in RBC as a fraction of body Pb, at
birth
RBCNL
1-ig/dL
c
F
Threshold Pb concentration in RBC for non-linear
deposition of Pb from diffusible plasma to RBC
RBCON
1-ig/dL
V
F
Concentration of Pb in RBC
RBCVOL
dL
V
F
RBC volume
RBLAD
day-1
V
F
Rate coefficient for Pb transfer from urinary
bladder to urine at time(t) (see ARB LAD)
RBRAN
day"1
V
F
Rate coefficient for Pb transfer from brain to
diffusible plasma at time(t) (see ABRAN)
RCORT
day"1
V
F
Rate coefficient for Pb transfer from non-
exchangeable cortical bone to diffusible plasma at
time(t) (see ACORT)
RCS2B
day"1
V
F
Rate coefficient for Pb transfer from cortical bone
surface to diffusible plasma at time(t) (see
ARCS2B)
RCS2DF
day"1
V
F
Rate coefficient for Pb transfer from cortical bone
surface to exchangeable cortical bone at time(t)
(see ARCSDF)
RDECAY
day"1
c
F
Rate coefficient for radioactive decay
RDF2CS
day"1
V
F
Rate coefficient for Pb transfer from exchangeable
cortical bone to cortical bone surface at time(t) (see
ARD2CS)
RDF2DC
day"1
V
F
Rate coefficient for Pb transfer from exchangeable
cortical bone to non-exchangeable cortical bone at
time(t) (see ARD2DC)
RDF2DT
day"1
V
F
Rate coefficient for Pb transfer from exchangeable
trabecular bone to non-exchangeable trabecular
bone at time(t) (see ARD2DT)
RDF2TS
day"1
V
F
Rate coefficient for Pb transfer from exchangeable
trabecular bone to trabecular bone surface at
time(t) (see ARD2TS)
265
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable
Units
Form
Type
Explanation
RDIFF
day"1
A
F
Rate coefficient for Pb transfer from exchangeable
bone (cortical or trabecular) to surface and non-
exchangeable bone - age array (see FLONG for
fraction to non-exchangeable)
RENCON
Mg/g
V
F
Pb concentration in kidney
RENFRC
unitless
V
F
Amount of Pb in kidney as a fraction of total body
Pb
REVF
day"1
V
F
Rate coefficient for transfer from diffusible plasma
to the extravascular fluid
RKDN1
day"1
c
F
Rate coefficient for transfer from kidney
compartment 1 to urinary pathway
RKDN2
day"1
V
F
Rate coefficient for transfer from kidney
compartment 2 to diffusible plasma at time(t) (see
ARKDN2)
RLLI
day"1
c
F
Rate coefficient for Pb transfer from lower large
intestine to feces
RLVR1
day"1
c
F
Rate coefficient for Pb transfer from liver
compartment 1 to small intestine or diffusible
plasma
RLVR2
day"1
V
F
Rate coefficient for Pb transfer from the slow liver
compartment 2 to diffusible plasma at time(t) (see
ARLVR2)
RPLAS
day"1
c
F
Rate coefficient for Pb transfer from diffusible
plasma to all compartments; Note: scaled to bone
surface deposition (see RPLS)
RPLS
day"1
V
F
Rate coefficient for Pb transfer from diffusible
plasma scaled to bone surface deposition (see
RPLAS)
RPROT
day"1
c
F
Rate coefficient for Pb transfer from bound plasma
to diffusible plasma
RRBC
day"1
V
F
Rate coefficient for Pb transfer from RBC to
diffusible plasma at time(t) (see ARRBC)
RSIC
day"1
c
F
Rate coefficient for Pb transfer from small intestine
to upper large intestine
RSOFO
day"1
c
F
Rate coefficient for Pb transfer from soft tissue
compartment 0 to diffusible plasma
RSOF1
day"1
c
F
Rate coefficient for Pb transfer from soft tissue
compartment 1 to diffusible plasma
RSOF2
day"1
c
F
Rate coefficient for Pb transfer from soft tissue
compartment 2 to diffusible plasma
RSTMC
day"1
c
F
Rate coefficient for Pb transfer from stomach to
small intestine
266
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable
Units
Form
Type
Explanation
RTRAB
day"1
V
F
Rate coefficient for Pb transfer from non-
exchangeable trabecular bone to diffusible plasma
at time(t) (see ARTRAB)
RTS2B
day-1
V
F
Rate coefficient for Pb transfer from trabecular
bone surface to diffusible plasma at time(t) (see
ARTS2B)
RTS2DF
day"1
V
F
Rate coefficient for Pb transfer from surface
trabecular bone to exchangeable trabecular bone at
time(t) (see ARTSDF)
RULI
day"1
c
F
Rate coefficient for Pb transfer from upper large
intestine to lower large intestine
S2HAIR
unitless
c
F
Deposition fraction for Pb from soft tissue
compartment 1 to other excreta
SATRAT
(.ig/dL
c
F
Maximum (saturating) concentration of Pb in RBC
SIGMA
Mg
V
F
Amount of Pb in all compartments
SIZEVF
unitless
c
F
Relative volume of the EVF compartment
compared to plasma (EVF/Plasma)
SOFIN
unitless
c
F
Amount of Pb in other soft tissue as a fraction of
total body Pb, at birth
SUMRBC
Mg
V
F
Cumulative amount of Pb in RBC over the
simulation
TBODY1
Mg
V
F
Pb mass in body, excluding bladder, GIT and RT
TBODY2
Mg
V
F
Pb mass in body, including bladder,
gastrointestinal tract, and RT
TBONE
unitless
V
F
Deposition fraction for Pb from diffusible plasma
to surface bone at time(t) (see ATBONE)
TBRAN
unitless
V
F
Deposition fraction for Pb from diffusible plasma
to brain at time(t) scaled to bone surface deposition
(see TOBRAN)
TEVF
unitless
c
F
Deposition fraction for Pb from diffusible plasma
to extravascular fluid
TFECE
unitless
V
F
Deposition fraction for Pb from diffusible plasma
directly to the small intestine at time(t) scaled bone
surface deposition (not including the transfer from
biliary secretion, specified by RLVR1) (see
TOFECE)
TFRAC
unitless
V
F
Fraction of diffusible plasma-to-bone deposition
that goes to trabecular surface bone at time(t); 1-
TFRAC is the fraction that goes to cortical surface
bone
267
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable
Units
Form
Type
Explanation
TKDN1
unitless
V
F
Deposition fraction for Pb from diffusible plasma
to kidney compartment 1 scaled to bone surface
deposition (see TOKDN1)
TKDN2
unitless
V
F
Deposition fraction for Pb from diffusible plasma
to liver compartment 2 scaled to bone surface
deposition (see TOKDN2)
TLVR1
unitless
V
F
Deposition fraction for Pb from diffusible plasma
to liver compartment 1 scaled to bone surface
deposition (see TOLVR1)
TOBRAN
unitless
A
F
Deposition fraction for Pb from diffusible plasma
to brain at time(t) (not scaled for bone surface
deposition - see TBRAN)
TOEVF
unitless
c
F
Deposition fraction for Pb from diffusible plasma
to extravascular fluid
TOFECE
unitless
c
F
Deposition fraction for Pb from diffusible plasma
directly to the small intestine (not including the
transfer from biliary secretion, specified by
RLVR1, not scaled to bone surface deposition -
see TFECE)
TOKDN1
unitless
c
F
Deposition fraction for Pb from diffusible plasma
to kidney compartment 1 not scaled to bone
surface deposition (see TKDN1)
TOKDN2
unitless
c
F
Deposition fraction for Pb from diffusible plasma
to kidney compartment 2 not scaled to bone
surface deposition (see TKDN2)
TOLVR1
unitless
c
F
Deposition fraction for Pb from diffusible plasma
to liver compartment 2 not scaled to bone surface
deposition (see TLVR1)
TOORBC
unitless
V
F
Deposition fraction for Pb from diffusible plasma
to RBC adjusted for capacity-limited deposition in
RBC and scaled to bone surface deposition
TOPROT
unitless
c
F
Deposition fraction for Pb from diffusible plasma
to protein-bound plasma not scaled to bone surface
deposition (see TPROT)
TORBC
unitless
c
F
Deposition fraction from diffusible plasma to RBC
not scaled to bone surface (see TRBC)
TOSOFO
unitless
A
F
Deposition fraction for Pb from diffusible plasma
to soft tissue compartment 0 at time (t), not scaled
to bone surface deposition (see TSOFO)
TOSOF1
unitless
A
F
Deposition fraction for Pb from diffusible plasma
to soft tissue compartment 1 at time (t), not scaled
to bone surface deposition (see TSOF1)
268
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable
Units
Form
Type
Explanation
TOSOF2
unitless
A
F
Deposition fraction from diffusible plasma to soft
tissue compartment 2 at time (t), not scaled to bone
surface deposition (see TSOF2)
TOSWET
unitless
C
F
Deposition fraction for Pb from diffusible plasma
to sweat not scaled to bone surface deposition (see
TSWET)
TOTEXC
Mg
V
F
Pb mass in urine, feces, sweat, hair, nails, and skin
TOURIN
unitless
c
F
Deposition fraction for Pb from diffusible plasma
to urine not scaled to bone surface deposition (see
TURIN)
TPROT
unitless
V
F
Deposition fraction for Pb from diffusible plasma
to protein-bound plasma scaled to bone surface
deposition (see TOPROT)
TRABWT
g
F
F
Trabecular bone weight
TRBC
unitless
V
F
Deposition fraction for Pb from diffusible plasma
to RBCs, below non-linear threshold, scaled to
bone surface deposition (see TORBC)
TRBCON
Mg/g
V
F
Pb concentration in trabecular bone
TRBCONBM
Mg/g
V
F
Pb concentration in trabecular bone mineral
TSKELWT
g
V
F
Skeleton weight
TSOFO
unitless
V
F
Deposition fraction for Pb from diffusible plasma
to soft tissue compartment 0 at time (t), scaled to
bone surface deposition (see TOSFO)
TSOF1
unitless
V
F
Deposition fraction for Pb from diffusible plasma
to soft tissue compartment 1 at time (t), scaled to
bone surface deposition (see TOSOF1)
TSOF2
unitless
V
F
Deposition fraction from diffusible plasma to soft
tissue compartment 2 at time (t), scaled to bone
surface deposition (see TOSF2)
TSUM
unitless
V
F
Sum of deposition fractions
(TOORBC,TEVF,TPROT,TBONE,TURIN,TFEC
E,TSWET,TLVR1 ,TKDN 1 ,TKDN2,TSOFO,TSOF
l,TSOF2,TBRAN)
TSWET
unitless
V
F
Deposition fraction for Pb from diffusible plasma
to sweat, scaled to bone surface deposition (see
TOSWET)
TURIN
unitless
V
F
Deposition fraction for Pb from diffusible plasma
to urine, scaled to bone surface deposition (see
TOURIN)
TVBONE
mL
V
F
trabecular bone volume
URIN
Mg
V
F
Amount of Pb excreted in urine during the
integration time step
269
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable
Units
Form
Type
Explanation
VBL
L
V
F
Whole blood volume
VBLC
L/kg
c
F
Blood volume fraction of body weight
VBONE
mL
V
F
bone volume
VK
mL
V
F
Kidney volume
VKC
L/kg
c
F
Kidney volume fraction of body weight
VL
mL
V
F
Liver volume
VLC
L/kg
c
F
Liver volume fraction of body weight
VLUC
L/kg
c
F
Lung volume fraction of body weight
VP
mL
V
Lung tissue volume
WADULT
kg
c
F
Maximum body weight
WBIRTH
kg
c
F
Weight at birth
WBODY
kg
V
F
Age-dependent body weight
WBONE
g
V
F
Bone weight
WCHLD
kg
c
F
Maximum body weight achieved during early
hyperbolic growth phase.
XMXAGE
day
c
F
End age for biokinetics parameter values array
(max NUMAGE)
YBLOOD
Mg
V
F
Amount of Pb in blood
YBRANo
Mg
V
F
Amount of Pb in brain at the beginning of each
integration cycle
YBRANw
Mg
V
F
Amount of Pb in the brain integrated over the time
interval DELT
YCDIFo
Mg
V
F
Amount of Pb in the exchangeable volume of
cortical bone at the beginning of each integration
cycle
YCDIFw
Mg
V
F
Amount of Pb in the exchangeable volume of
cortical bone integrated over the time interval
DELT
YCORT
Mg
V
F
Amount of Pb in cortical bone
YCSURo
Mg
V
F
Amount of Pb in cortical bone surface at the
beginning of each integration cycle
YCSURw
Mg
V
F
Amount of Pb in the cortical bone surface
integrated over the time interval DELT
YCVOLo
Mg
V
F
Amount of Pb in non-exchangeable volume of
cortical bone at the beginning of each integration
cycle
YCVOLw
Mg
V
F
Amount of Pb in the non-exchangeable volume of
cortical bone over the time interval DELT
270
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Variable
Units
Form
Type
Explanation
YEVFo
Mg
V
F
Amount of Pb in extravascular fluid at the
beginning of each integration cycle
YEVFw
Mg
Amount of extravascular fluid in the brain
integrated over the time interval DELT
YFECE
Mg
V
F
Amount of Pb excreted in feces
YHAIR
Mg
V
F
Amount of Pb excreted by routes other than feces,
sweat and urine (e.g., hair, nails, and desquamated
skin)
YKDNlo
Mg
V
F
Amount of Pb in fast-turnover kidney at the
beginning of each integration cycle
YKDN20
Mg
V
F
Amount of Pb in slow-turnover kidney at the
beginning of each integration cycle
YKDN2W
Mg
V
F
Amount of Pb in the slow-turnover over kidney the
time interval DELT
YKIDNlw
Mg
V
F
Amount of fast-turnover kidney in the brain
integrated over the time interval DELT
YLLICo
Mg
V
F
Amount of Pb in lower portion of large intestine at
the beginning of each integration cycle
YLLICw
Mg
V
F
Amount of Pb in the lower portion of large
intestine integrated over the time interval DELT
YLVRlo
Mg
V
F
Amount of Pb in fast-turnover liver at the
beginning of each integration cycle
YLVRlw
Mg
V
F
Amount of fast-turnover liver in the brain
integrated over the time interval DELT
YLVR20
Mg
V
F
Amount of Pb in slow-turnover liver at the
beginning of each integration cycle
YLVR2W
Mg
Amount of slow-turnover liver in the brain
integrated over the time interval DELT
YPLAS
Mg
V
F
Amount of Pb in plasma (diffusible plus protein
bound)
YPLASw
Mg
V
F
Amount of Pb in plasma (diffusible plus protein
bound) integrated over the time interval DELT
YPLSO
Mg
V
F
Amount of Pb in diffusible plasma (0.69 x
YPLAS) at the beginning of each integration cycle
YPLSw
Mg
V
F
Amount of Pb in diffusible plasma (0.69 x
YPLAS) integrated over the time interval DELT
YPROTo
Mg
V
F
Amount of Pb in plasma protein at the beginning of
each integration cycle
YPROTw
Mg
V
F
Amount of Pb in the plasma protein integrated over
the time interval DELT
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Variable
Units
Form
Type
Explanation
YROo
Mg
V
F
Amount of Pb in RT region 1 at the beginning of
each integration cycle
YROw
Mg
V
F
Amount of Pb in the RT region 1 integrated over
the time interval DELT
YRlo
Mg
V
F
Amount of Pb in RT region 2 at the beginning of
each integration cycle
YRlw
Mg
V
F
Amount of Pb in the RT region 2 integrated over
the time interval DELT
YR20
Mg
V
F
Amount of Pb in RT region 3 at the beginning of
each integration cycle
YR2W
Mg
V
F
Amount of Pb in the RT region 3 integrated over
the time interval DELT
YR30
Mg
V
F
Amount of Pb in RT region 4 at the beginning of
each integration cycle
YR3W
Mg
V
F
Amount of Pb in the RT region 4 integrated over
the time interval DELT
YRBCo
Mg
V
F
Amount of Pb in RBCs at the beginning of each
integration cycle
YRBCw
Mg
V
F
Amount of Pb in RBCs integrated over the time
interval DELT
YSICo
Mg
V
F
Amount of Pb in small intestine at the beginning of
each integration cycle
YSICw
Mg
V
F
Amount of Pb in the small intestine integrated over
the time interval DELT
YSKEL
Mg
V
F
Amount of Pb in bone
YSOFOo
Mg
V
F
Amount of Pb in fast-turnover soft tissue at the
beginning of each integration cycle
YSOFOw
Mg
V
F
Amount of Pb in the fast-turnover soft tissue
integrated over the time interval DELT
YSOFlo
Mg
V
F
Amount of Pb in intermediate-turnover soft tissue
at the beginning of each integration cycle
YSOFlw
Mg
V
F
Amount of Pb in the intermediate-turnover soft
tissue integrated over the time interval DELT
YSOF20
Mg
V
F
Amount of Pb in slow-turnover soft tissue at the
beginning of each integration cycle
YSOF2w
Mg
V
F
Amount of Pb in the slow-turnover soft tissue
integrated over the time interval DELT
YSOFT
Mg
V
F
Amount of Pb in soft tissues
YSTMCo
Mg
V
F
Amount of Pb in stomach at the beginning of each
integration cycle
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Variable
Units
Form
Type
Explanation
YSTMCw
Mg
V
F
Amount of Pb in the stomach integrated over the
time interval DELT
YSWET
Mg
V
F
Amount of Pb excreted in sweat
YTDIFo
Mg
V
F
Amount of Pb in exchangeable trabecular bone
surface at the beginning of each integration cycle
YTDIFw
Mg
V
F
Amount of Pb in the exchangeable trabecular bone
surface integrated over the time interval DELT
YTRAB
Mg
V
F
Amount of Pb in brain at the beginning of each
integration cycle
YTSURo
Mg
V
F
Amount of Pb in trabecular bone surface at the
beginning of each integration cycle
YTSURw
Mg
V
F
Amount of Pb in the trabecular bone surface
integrated over the time interval DELT
YTVOLo
Mg
V
F
Amount of Pb in non-exchangeable volume of
trabecular bone at the beginning of each integration
cycle
YTVOLw
Mg
V
F
Amount of Pb in the non-exchangeable volume of
trabecular bone integrated over the time interval
DELT
YULICo
Mg
V
F
Amount of Pb in upper portion of lower intestine at
the beginning of each integration cycle
YULICw
Mg
V
F
Amount of Pb in the upper portion of lower
intestine integrated over the time interval DELT
YURIN
Mg
V
F
Amount of Pb in excreted in urine
Abbreviations: A=array; C=constant; F=floating point; I=integer; S=switch; V=variable
1
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1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
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APPENDIX C - ALL AGES LEAD MODEL (AALM.FOR) EXPOSURE PARAMETER
VALUES
The AALM.FOR exposure model includes parameters that are variables (i.e., computed in mathematical
expressions), and parameters that are assigned constants or are represented by age arrays. A list of
parameters that are assigned constants or are represented by age arrays are presented in Table C-l. The
bases for values assigned to each parameter are summarized below. Parameters are presented in
alphabetical order, according to the parameter name.
Exposure variables include variables that represent the concentration of Pb in air, indoor dust, soil, food
and water, and activity factors that represent the intensity of exposure to contaminated environmental
media (e.g., water consumption rates). All exposure variables that are accessible to the user are included
in Table C-l. Default values are intended to be central tendency estimates that are representative of the
U.S. population. Sources for the default values are provided along with a brief summary of the sources.
Some exposure variables were not assigned default values. Some of these variables were considered to be
inherently site-specific and assigning default values to them would therefore be arbitrary. For others,
reliable sources of data upon which to base a default value were not identified.
In general, the activity factors were taken from the Exposure Factors Handbook (EFH: U.S. EPA. 2011).
The EFH recommendations for default values for activity factors are based on thorough reviews of the
exposure science literature and independent analyses of exposure data from surveys performed by others.
The use of the EFH-recommended default values in the AALM.FOR, when appropriate, also promotes
consistency in risk assessments performed by or for the Agency. In some cases, default values were
based on recent studies that were not included in the EFH when the studies were deemed to be sufficiently
reliable.
A strong preference was placed on basing default values for environmental concentration variables and
activity factors on data from statistical surveys that were designed to provide data representative of the
entire U.S. Equally important was ensuring that analyses of data from these surveys were done properly
to produce unbiased estimates (i.e., properly used the sampling weights in calculating estimates and
considered the complex sampling design when calculating standard errors).
AIR CONCENTRATION
AALM Variables: Air_baseline, Air_i, Air_pulse
The AALM.FOR allows the user to define multiple exposures to Pb in air. These can include up to three
discrete (i.e., age-specific) exposure concentrations, a constant baseline concentration and up to two pulse
trains in which air Pb concentration can vary at inputted durations and periods. Multiple exposures could
be used to represent exposures to air Pb in various settings such as outdoor and indoor air; air at the home,
school, workplace, or recreational sites; or continuous exposure or intermittent exposures.
Concentrations of Pb in air can be expected to vary considerably by location, depending on proximity to
local sources (U.S. EPA. 2013). Based on analysis of data from U.S. national monitoring networks
collected during the period 2008-2010, air Pb concentrations were as follows (U.S. EPA. 2013):
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1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Source Oriented
Non-source Oriented
Mean
0.21
0.012
Median
0.079
0.010
95th percentile
0.88
0.037
Units: |ig/m3
3-month rolling average, 2008-2010
Source-oriented monitors are within one mile of >0.5 ton/year emission
non-airport source or near airports in which use of leaded aviation fuels
are estimated to result in >1 tone/year emissions.
A detailed description the national monitoring networks and related data can be found in U.S. EPA
(2013).
Recommendations. Based on these data, 0.01 (.ig/nr1 is recommended as a default value for the parameter
Air baseline to represent average U.S. exposure concentrations distant from substantial emissions
sources. For simulations of populations living near emissions sources, the source-oriented average could
be used as a default for average air concentrations, however, it should be recognized that air Pb
concentrations near emission sources could vary considerably depending on the strength of the source and
other geographic and weather factors that would affect dispersion and deposition of emissions.
Although, the default values are based on measurements made of outdoor air, indoor and outdoor air Pb
concentrations are expected to be similar if indoor environments that do not have substantial indoor
sources of Pb (Clayton et al.. 1999; Robertson et al.. 1999).
INDOOR DUST LEAD CONCENTRATION
AALM Variables: Dust_baseline, Dust_i, Dust_pulse
The AALM.FOR allows the user to define multiple exposures to Pb in indoor dusts. These can include up
to three discrete (i.e., age-specific) exposure concentrations, a constant baseline concentration and up to
three pulse trains in which dust Pb concentration can vary at inputted durations and periods. These could
be used to represent exposures to Pb in various sources of dust such dusts at various locations (e.g., at the
home, school, workplace, or recreational sites); or continuous exposure or intermittent exposures.
The National Human Exposure Assessment Surveys (NHEXAS) provides data on indoor dust Pb
concentrations in statistical samples from various locations. Based on data for approximately 250
residences in EPA Region 5 (Great Lakes region), the mean Pb concentrations were as follows (Clayton
et al.. 1999):
Surface
Window Sill
463
954
(188, 738)
(481,3164)
Units: |ig/g (95% CL)
Based on NHEXAS data for approximately 119 residences in Arizona, the median Pb concentration
(XRF) was 21 jj.g/g (90th percentile: 122; Robertson et al.. 1999).
Concentrations of Pb in dusts can be expected to vary considerably by location, depending on proximity
to local sources, presence in lead-based paint, and dust cleaning practices (U.S. EPA. 2013). The National
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1 Survey of Lead and Allergens (NSLAH) conducted by the Department of Housing and Urban
2 Development; (Clickner et al.. 2002) provides data in Table 5.7 of their report on Pb in residential indoor
3 dusts for a statistical sample of U.S. residences. Based on a sample of approximately 2000 homes, the
4 mean Pb loading (fj.g/ft2) were as follows:
Floors
Window Sills
Window Troughs
(n = 3,894
(n = 2,302)
(n = 1,607)
13.6±484
195±1683
1991±12,086
Units: ng/ft2
5 Data on dust Pb loading on indoor surfaces (|_ig Pb/ft2) provide additional sources estimated of
6 indoor dust Pb concentration (U.S. EPA. 2019). An analysis of data on Pb loading collected as part of the
7 American Healthy Housing Survey (AHHS. Cox et al.. 2011) provided the following central estimates for
8 residential Pb loading and concentration (U.S. EPA. 2019):
Loading
Concentration
(jUg/ft2)
fag/g)
Median
Mean
Median Mean
0.8
1.2
107.8 175.0
9
10 Recommendations. Based on the above data, 175 jj.g/g is recommended as a default value for the
11 parameter Dust baseline to represent average U.S. exposure concentrations distant from substantial
12 current or historical emission sources (e.g., background) that could impact the indoor environment (e.g.
13 track in from contaminated soil). A value of equal to the soil Pb concentration (see section on Soil Lead
14 Concentration) is recommended for Dust baseline for simulating residences where soil derived dust is
15 the major source of indoor dust Pb (e.g. no other significant indoor sources such as paint or hobbies).
16 Indoor dust Pb concentrations in residences impacted by Pb-based paint can be expected to vary
17 considerably within and between residences and local exposure conditions should be considered to
18 establish a representative estimate.
19 SOIL LEAD CONCENTRATION
20 AALM Variables: Soil_baseline, Soil i, Soil_pulse
21 The AALM.FOR allows the user to define multiple exposures to Pb in soil. These can include up to three
22 discrete (i.e., age-specific) exposure concentrations, a constant baseline concentration and up to three
23 pulse trains in which dust Pb concentration can vary at inputted durations and periods. These could be
24 used to represent exposures to Pb in various sources of surface soil such soils at various locations (e.g., at
25 the home, school, workplace, or recreational sites); or continuous exposure or intermittent exposures.
26 Concentrations of Pb in soils can be expected to vary considerably by location, depending on proximity to
27 local sources (U.S. EPA. 2013). A study conducted by the U.S. Geological Survey measured soil Pb
28 concentrations along a 4000 km east-west transect of the U.S. (Smith et al.. 2013: Reimann et al.. 2011).
29 Sampling locations were selected to avoid local sources, including roads, buildings, power plants and
30 smelters. The mean concentrations for samples collected a depth of 0-5 cm depth (sieved at 2 mm) were
31 as follows:
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Full Transect
Statewide Average
(n = 4841)
(n = 48)
25
30
(8, 44)a
(14, 68)b
Units: |ig/g.
Statewide average is the average of state means.
ll5lh-95lh percentile range
brange
1 Data for individual U.S. states and physiographic provinces are provided in Smith et al. (2013).
2 NSLAH conducted by the Department of Housing and Urban Development; Clickner et al. (2002)
3 provide data in Table 6.3 of their report on Pb in residential soil for a statistical sample of U.S. residences.
4 Based on a sample of approximately 700 residential yards, the mean Pb concentrations (j^ig/g) were as
5 follows:
Main Entry way
Dripline 1
Dripline 2
Midyard 1
Midyard 2
235±1094
243±818
404±1613
87±195
123±360
|ig/g. mean ± SD
6 Based on data from the AHHS (Cox etal.. 2011: Clickner et al.. 2002). the following central estimates for
7 soil Pb concentration were estimated (U.S. EPA. 2019):
Housing Stock
GM
GSD
Median
Mean
Pre-1940
113.4
3.58
113.4
246.8
1940-1977
28.6
2.9
28.6
50.0
Pre-1978
26.3
3.8
26.3
64.1
GM, geometric mean, jj.g/g; GSD, geometric standard deviation
8
9 Recommendations. Based on the above data, 25 jj.g/g is recommended as a default value for the
10 parameter Soil baseline to represent average U.S. exposure concentrations distant from substantial
11 current or historical emission sources (e.g., background). Means for individual U.S. states ranged 6 to 80
12 (-ig/g. These estimates are based on measurements made in soils sieved to <2 mm and which may have
13 underestimated Pb concentration in the fine fraction (e.g. <250 (.un or <150 |_im) that is typically used to
14 represent the exposure term for the adherence to hand-to-mouth pathway used in risk assessment. The
15 value 50 jj.g/g is recommended as a value for yard soils associated with post 1940 housing stock and 250
16 jj.g/g for older housing stock.
17 WATER CONCENTRATION
18 AALM Variables: Water_baseline, Water_i, Water_pulse
19 The AALM.FOR allows the user to define multiple exposures to Pb in drinking water. These can include
20 up to three discrete (i.e., age-specific) exposure concentrations, a constant baseline concentration and up
21 to two pulse trains in which water Pb concentration can vary at inputted durations and periods. These
22 could be used to represent exposures to Pb in various exposure settings such: home, school, workplace, or
23 recreational sites; or continuous exposure or intermittent exposures.
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1 Concentrations of Pb in drinking water can be expected to vary considerably by location, depending on
2 water source, Pb in service lines and extent of plumbing corrosion (U.S. EPA. 2007a). In residences
3 served by lines containing Pb, first-draw water that has been stagnant in plumbing will tend to have a
4 higher Pb concentration than after the system has been flushed. The NHEXAS provides data on drinking
5 water Pb concentrations in statistical samples from various locations. Based on data for approximately
6 250 residences in EPA Region 5 (Great Lakes region), the mean Pb concentrations were as follows
7 (Clayton et al.. 1999):
First draw
Flushed
3.92
0.84
(3.06, 4.79)
(0.6, 1.07)
Units: jig/L (95% CL)
8 Based on NHEXAS data for approximately 82 residences in Arizona, median, 75th and 90th percentile of
9 Pb concentrations in flushed unfiltered tap water were 0.4, 0.9, and 1.3 (ig/L, respectively (O'Rourkc et
10 al.. 1999).
11 The EPA TRW analysed data tap water concentrations reported for the Six-Year Review-ICR
12 dataset. This survey conducted during the period 1998-2005 measured first-draw tap water concentration
13 in residences supplied by approximately 883 public water suppliers in the U.S. Based on this analysis, the
14 mean tap water concentrations were as follows:
Sample Mean
Population Weighted Mean
4.89
0.89
(4.38, 5.39)
(0.78, 1.01)
Units: jig/L (95% CL)
Population weighted mean is weighted for number of people
served by each supplier.
15 Based on data in Supplemental Information from Zartarian et al. (2017). the average, 95th
16 percentile and 99th percentile values from this dataset are 0.89, 2.25 and 13.27 (ig/L, respectively. The
17 following central estimates for water Pb concentration were estimated (U.S. EPA. 2019):
GM
GSD
Median
Mean
0.69
2.1
0.69
0.89
GM, geometric mean, jj.g/g; GSD, geometric standard
deviation
18
19 Recommendations. Based on the above data, 0.9 (ig/L is recommended as a default value for the
20 parameter Water baseline to represent average U.S. exposure concentrations to tap water from public
21 water supplies. This default value may not apply to local conditions that contribute to leaching of Pb into
22 tap water (e.g. Pb service lines, Pb solder, corrosion).
23 FOOD LEAD INTAKE
24 AALM Variables: Food_baseline, Food_i, Food_pulse
25 The AALM.FOR allows the user to define multiple exposures to Pb in food. These can include up to three
26 discrete (i.e., age-specific) food Pb intakes ((ig/day), a constant baseline intake and up to two pulse trains
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1 in which food Pb intake can vary at inputted durations and periods. These could be used to represent
2 exposures to Pb in various diets or sources of food (e.g., market basket, home grown produce, local fish
3 or game); or continuous exposure or intermittent exposures.
4 The rate of Pb intake from food can be expected to vary considerably depending on the diet and age. The
5 NHEXAS provides data on food Pb intakes in statistical samples from various locations (Clayton et al..
6 1999; Thomas et al.. 1999V Based on a sample for 159 residences (children and adults), the mean food
7 Pb intakes was 7.96 (ig/day (95% CL: 4.2. 11.6; Clayton etal.. 1999).
8 The EPA TRW estimated food Pb intakes in children based on data from the U.S. Food and Drug
9 Administration Total Diet Studies performed between 1995-2005 (FDA. 2007. 2006) and food
10 consumption data from the National Food Consumption Survey (NCFS) that was performed as part of the
11 Third National Health and Nutrition Examination Survey (NHANES 2003-2006). Age category mean Pb
12 intakes were as follows:
Age Category
(months)
Dietary Pb Intake
(jig/day)
0 to <12
2.26
12 to <24
1.96
24 to <36
2.13
36 to <48
2.04
40 to <60
1.95
60 to <72
2.05
72 to <84
2.22
13
14 Recommendations. Based on the above data, 10 |_ig/day is recommended as a default value for
15 Food baseline the food Pb intake in adults. This corresponds to an intake of approximately 0.14 j^ig/kg
16 bw/day which, if extrapolated to children, yield estimates that are similar to those recommended by the
17 EPA TRW, if AALM.FOR growth is assumed:
Age
(year)
Female BW
(kg)
Male BW
(kg)
Female Pb
Intake
(US/(lay)
Male Pb
Intake
(US/(lay)
1
8.9
9.4
1.2
1.3
2
12.3
12.9
1.7
1.8
3
14.6
15.3
2.0
2.1
4
16.4
17.2
2.3
2.4
5
18.0
18.8
2.5
2.6
6
19.7
20.2
2.8
2.8
7
21.7
21.8
3.0
3.1
8
24.2
23.7
3.4
3.3
9
27.7
26.1
3.9
3.7
10
32.1
29.3
4.5
4.1
15
52.5
56.4
7.3
7.9
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Age
(year)
Female BW
(kg)
Male BW
(kg)
Female Pb
Intake
(US/day)
Male Pb
Intake
(US/day)
>20
56.2
71.4
7.9
10.0
For intake 0.14 |ig/kg bw/dav.
BW, body weight
1 The above age array of food Pb intakes are recommended default values for Food i, where i would
2 represent age category baseline intakes for the average U.S. diet.
3 DUST AND SOIL INGESTION RATES
4 AALM Variables: IR sd, f_IR_s, IR dust, IR soil
5 The EPA Exposure Factors Handbook (U.S. EPA. 2017) provides the following recommendations for
6 dust and soil ingestion rates to be used in U.S. EPA risk assessments.
7
Age Category Dust Soil Dust + Soil
(g/day) (g/day) (g/day)
<6 months
0.020
0.020
0.040
6 months to 1 year
0.040
0.030
0.070
1 to <2 years
0.050
0.040
0.090
2 to <6 years
0.030
0.030
0.060
1 to 6 years
0.040
0.040
0.080
6 to <12 years
0.030
0.030
0.060
>12 years
0.020
0.010
0.030
8
9 The EPA TRW estimated combined soil and dust ingestion rates in children based on the best fit model
10 from von Lindern et al. (2016) and supported by modelled estimates from Ozkavnak et al. (2011) and
11 Wilson et al. (2013). Age category mean ingestion rates were as follows:
Age Category Soil + Dust
(months) (g/day)
Oto 12
0.086
13 to 24
0.094
25 to 36
0.067
37 to 48
0.063
49 to 60
0.067
61 to 72
0.052
73 to 84
0.055
12
13 Recommendations. Based on the Exposure Factors Handbook (U.S. EPA. 2017). the following values
14 are recommended as default values for the parameters IR dust and IR soil to represent average U.S.
15 ingestion rates in children and adults. The default values for adults may not represent activities that result
16 in intensive dermal contact with surface dusts, such as construction or excavation.
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Age
(days)
Dust Ingestion
IR_dust
(g/day)
Soil Ingestion
IR_soil
(g/day)
Combined Dust
and Soil
IR_sd
(g/day)
Soil Fraction
f_IR_soil
0
0.022
0.018
0.040
0.45
90
0.039
0.032
0.070
0.45
365
0.050
0.041
0.090
0.45
1825
0.044
0.036
0.080
0.45
3650
0.033
0.027
0.060
0.45
5475
0.017
0.014
0.030
0.45
9125
0.017
0.014
0.030
0.45
>18250
0.017
0.014
0.030
0.45
1
2 WATER INTAKE RATE
3 AALM Variables IR water
4 Water ingestion rate can be expected to vary with age, activity level and environmental factors
5 (e.g. temperature, humidity). U.S. EPA (2011) has recommended the following age-specific water
6 ingestion rates for use in EPA risk assessments of the general population:
Age
Mean Intake
95th Percentile
(mL/day)
(mL/day)
Birth to <1 mo
184
839
1 to <3 mo
227
896
3 to < 6 mo
362
1056
6 to <12 mo
360
1055
1 to <2 yr
271
837
2 to <3yr
317
877
3 to <6 yr
327
959
6 to <11 yr
414
1316
11 to <16 yr
520
1821
16 to <21 yr
573
1783
18 to <21 yr
681
2368
>21 yr
1043
2958
>65 yr
1046
2733
All ages
869
2717
7
8 The EPA TRW estimated drinking water intakes rates in children based on and analysis of data from the e
9 1994-1996 and 1998 Continuing Survey of Food Intakes by Individuals (CSFII; USDA. 2000) as
10 reported by Kahn and Stralka (2009). Age category mean ventilation rates were as follows:
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Age Category
(months)
Water Intake
(L/day)
0 to <12
0.40
12 to <24
0.43
24 to <36
0.51
36 to <48
0.54
40 to <60
0.57
60 to <72
0.60
72 to <84
0.63
1
2 Recommendations. Based on the above data, the following values are recommended as default values
3 for the parameter IR water to represent average U.S. drinking water ingestion rates in children and adults:
Age
(days)
Water Intake
(L/day)
0
0.20
90
0.30
365
0.35
1825
0.35
3650
0.45
5475
0.55
9125
0.70
>18250
1.04
4
5 VENTILATION RATE
6 AALM Variable: V air
7 The AALM.FOR assigns values for regional deposition of inhaled Pb (see parameters Bl, B2, B3, B4;
8 Appendix D and clearance in the RT (see parameter CILIAR; Appendix D). Values for these parameters
9 were based on experimental studies conducted adults who inhaled submicron particles from automobile
10 exhausts while they were sedentary. However, regional deposition and clearance in the RT (will depend
11 on numerous factors, including age and particle size, as well as various factors that affect ventilation rates
12 (m3/day) which vary with age and physical activity. The interrelationships between particle size,
13 clearance, regional deposition and ventilation rate should be considered in assigning values to these
14 parameters for simulating specific populations and exposure settings, these subjects are treated in depth in
15 ICRP (1994V
16 The ICRP (1994) has recommended the following age-specific activity weighted ventilation rates for use
17 in radiation dosimetry assessments of the general population:
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Age
Ventilation
(m3/day)
Male
Ventilation
(m3/day)
Female
Ventilation
(m3/day)
Average
3 mo
2.86
2.86
2.86
1 yr
5.2
5.2
5.2
5 yr
8.76
8.76
8.76
10 yr
15.28
15.28
15.28
15 yr
20.1
15.72
17.91
>17 yr
22.18
17.68
19.93
From ICRP (1994).
Values for children are from Table B. 16A
Values for >17 yr are for sedentary workers (Table B.16B)
1
2 The above ventilation rates can be matched to corresponding regional deposition rates, also provided in
3 ICRP (1994V
4 U.S. EPA (2011) has recommended the following age-specific activity weighted ventilation rates for use
5 in EPA risk assessments of the general population:
Age Category
Mean Ventilation
(m3/day)
95th Percentile
(m3/day)
Birth to <1 mo
3.6
7.1
1 to <3 mo
3.5
5.8
3 to < 6 mo
4.1
6.1
6 to <12 mo
5.4
8.0
Birth to <1 yr
5.4
9.2
1 to <2 yr
8.0
12.8
2 to <3yr
8.9
13.7
3 to <6 yr
10.1
13.8
6 to <11 yr
12.0
16.6
11 to <16 yr
15.2
21.9
16 to <21 yr
16.3
24.6
21 to <31 yr
15.7
21.3
31 to <41 yr
16.0
21.4
41 to 51 yr
16.0
21.2
51 to 61 yr
15.7
21.3
61 to 71 yr
14.2
18.1
71 to <81 yr
12.9
16.6
> 81 yr
12.2
15.7
6
7 The EPA TRW estimated ventilation rates in children based on and analysis of data on total energy
8 expenditure (estimated from doubly labeled water studies) and relationships between energy expenditure
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and ventilation rate (Stifclman. 2007; Brochu et al.. 2006; IOM. 2005; Lavton. 1993). Age category mean
ventilation rates were as follows:
Age Category
(months)
Ventilation Rate
(m3/day)
0 to <12
3.22
12 to <24
4.97
24 to <36
6.09
36 to <48
6.95
40 to <60
7.68
60 to <72
8.32
72 to <84
8.89
Recommendations. Based on the above data, the following values are recommended as default values
for the parameter V air to represent average U.S. ventilation rates in children and adults:
Age
(days)
Ventilation
(m3/day)
0
2.9
90
2.9
365
5.2
1825
00
00
3650
15.3
5475
17.9
9125
19.9
>18250
19.9
RBAdust. A discussion of available data on RBA of Pb in indoor dust can be found in U.S. EPA (2013).
RBA of Pb in house dusts has not been rigorously evaluated quantitatively in humans or in experimental
animal models, unlike soil (see section on RBA soil). As with soil, RBA of dust Pb can be expected to
vary depending on the Pb mineralogy, physical characteristics of the Pb in the dust (e.g., encapsulated or
exposed) and size of the Pb-bearing particles. The RBA for paint Pb mixed with soil (relative to lead
acetate) was reported to be approximately 0.72 (95% CI: 0.44, 0.98) in juvenile swine, suggesting that
paint Pb dust reaching the gastrointestinal tract maybe highly bioavailable (Casteel et al.. 2006). Several
studies have measured in vitro bioaccessibility (IVBA) of Pb in residential indoor dust; however, with
few exceptions, these have not used IVBA methods for from which RBA can be reliably predicted
(Juhasz etal.. 2011; Lu etal.. 2011; Smith etal.. 2011; Roussel et al.. 2010; Yu et al.. 2006). A study
conducted at two sites in EPA Region 7 compared Pb RBA predicted from IVBA using a prediction
method that had been validated for soil as described in U.S. EPA (2013). At the Herculaneum site, mean
RBA was 0.47 (SD 0.07, 10 samples) for indoor dust and 0.69 (SD 0.03, 12 samples) for soil. At the
Omaha site, mean Pb RBA was 0.73 (SD 0.10, 90 samples) for indoor dust and 0.70 (SD 0.10, 45
samples) for soil.
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RBA soil. A discussion of available data on RBA of Pb in soil can be found in U.S. EPA (2013). RBA of
soil Pb can be expected to vary depending on the Pb mineralogy, physical characteristics of the Pb in the
soil (e.g., encapsulated or exposed) and size of the Pb-bearing particles. The EPA TRW has
recommended a value of 60% for RBA for ingested soil Pb based on analysis of data on soil Pb RBA
estimated in bioassays of juvenile swine (Bannon et al.. 2009; Smith et al.. 2009; Casteel et al.. 2006;
Marschner et al.. 2006); and other unpublished data collected as part of site risk assessments. The soil
RBA measured in the swine assay is equivalent to the ratio of the absorbed fraction of an ingested dose of
soil Pb to that of water-soluble Pb acetate. Analysis of 31 soils (excluding galena-enriched soil, soils from
firing ranges, and soils sieved at >250 |_im) resulted in a median RBA estimate of 60% with the 5th-95th
percentile range from 11-97%; the mean RBA is 54% ±32 SD. RBA estimates for soils collected from
eight firing ranges were approximately 100% (mean =108% ± 18: Bannon et al.. 2009). The relatively
high RBA for the firing range soils may reflect the high abundance of relatively un-encapsulated lead
carbonate (30-90% abundance) and lead oxide (1-60%) in these soils. Similarly, a soil sample (low Pb
concentration) mixed with a National Institute of Standards and Technology paint standard (55% lead
carbonate, 44% lead oxide) also had a relatively high bioavailability (72%; Casteel et al.. 2006). Samples
of smelter slag, or soils contaminated with slag, had relatively low RBA (14-40%, n = 3) as did a sample
from a mine tailings pile (RBA = 6%), and a sample of finely ground galena mixed with soil (1%; Casteel
et al.. 2006). A single estimate for RBA of interior dust was 51% for a sample collected at the
Herculaneum site.
RBA food. RBA of water-soluble Pb dissolved in food is assumed to be 1. RBA of Pb in foods has not
been studied and it is possible that certain exposure settings could result in ingestion of Pb that has and
TBA <1 in association with food. For example, adherence of surface dust, soil or sediments to consumed
foods.
RBAwater. RBA of Pb dissolved in water is assumed to be 1. This is based on evidence that dissolution
of Pb from the soil/mineralogical matrix in the stomach appears to be the major process that renders soil
Pb bioaccessible for absorption in the GI tract (U.S. EPA. 2013. 2007b'). However, his may not apply to
Pb-bearing particles suspended in surface water and this may be relevant to certain exposure settings (e.g.,
incidental ingestion of suspended sediments during activities such as swimming or play near shorelines).
Recommendations. Based on the above data, the following values are recommended as default values
for the parameters RBA dust, RBA soil, RBA food, RBA water:
Medium RBA
Dustpaint" 1
Dust_soilb 0.6
Soil 0.6
Food 1
Water 1
indoor dust derived from Pb-based paint
bIndoor dust derived from soil
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1 TABLE C-l. LIST OF PARAMETERS THAT ARE ASSIGNED CONSTANTS OR ARE REPRESENTED BY AGE ARRAYS
Variable
Units
Form
Type
Explanation
Value
Reference
Air_baseline
(ig/m3
C
F
Baseline air Pb
concentration used in
exposure pulse train
0.01-0.2
(U.S. EPA. 2013)
Air i; i= 1, 2,3
(ig/m3
A
F
Air Pb
concentrations for
discrete exposures
User defined
Air_pulse
(ig/m3
C
F
Air Pb concentration
used in exposure
pulse train
User defined
Dustbaseline
Mg/g
C
F
Baseline indoor dust
Pb concentration
used in exposure
pulse train
Residential
175
(U.S. EPA. 2019)
Dust_i; i= 1, 2,3
Mg/g
A
F
Dust Pb
concentrations for
discrete exposures
User defined
Dust_pulse
Mg/g
C
F
Dust Pb
concentration used in
exposure pulse train
User defined
f Air i; i= 1,2,3
unitless
A
F
Fraction of discrete
Air_i contributing to
daily air Pb exposure
User defined
See Chapter 16 of U.S. EPA
(2011)
f_Dust_i; i= 1,2
unitless
A
F
Fraction of discrete
Dust i contributing
to daily dust Pb
exposure
User defined
See Chapter 16 of U.S. EPA
(2011)
f IR soil
unitless
C
F
Soil fraction of
combined dust and
soil ingestion rate
0.45
Based Table 5-1 of U.S.
EPA (2017)
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Variable
Units
Form
Type
Explanation
Value
Reference
f_Other_i; i= 1,2,3
unitless
A
F
Fraction of discrete
Otheri contributing
to daily other Pb
exposure
User defined
See Chapter 16 of U.S. EPA
(2013)
f_pulse_air
unitless
C
F
Fraction of air daily
air exposure from
pulse train
User defined
f_pulse_dust
unitless
C
F
Fraction of daily dust
exposure from pulse
train
User defined
f_pulse_other
unitless
c
F
Fraction of daily
other exposure from
pulse train
User defined
f_pulse_soil
unitless
c
F
Fraction of daily soil
exposure from pulse
train
User defined
f_pulse_water
unitless
c
F
Fraction of daily
water exposure from
pulse train
User defined
(Clavton et al.. 1999)
f_Water_i; i= 1,2,3
unitless
A
F
Fraction of discrete
Water_i contributing
to daily water Pb
exposure
User defined
See Chapter 16 of U.S. EPA
(2011)
Foodbaseline
Mg/day
c
F
Baseline food Pb
intake used in
exposure pulse train
10 (ig/kg bw/day
(Clavton et al.. 1999)
Food_i; i= 1, 2,3
Mg/day
A
F
Food Pb intakes for
discrete exposures
User defined
See Chapter 16 of U.S. EPA
(2011)
Food_pulse
Mg/day
C
F
Food Pb intake used
in exposure pulse
train
User defined
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Variable
Units
Form
Type
Explanation
Value
Reference
Age-day
Value
0
0.040
90
0.070
365
0.090
Combined dust and
soil ingestion rate
1825
0.080
Based Table 5-1 of U.S.
EPA (2017)
IRsd
Mg/day
A
F
3650
0.060
5475
0.030
9125
0.030
18250
0.030
25550
0.030
32850
0.030
Age-day
Value
0
0.20
90
0.30
365
0.35
Based on U.S. EPA (2011).
Table 3-1, per capita; values
Water ingestion rate
for water Pb
1825
0.35
IRwater
L/day
C
F
3650
0.45
are interpolated between
exposures
5475
0.55
ages
9125
0.70
18250
1.04
25550
1.04
32850
1.04
Baseline other Pb
Other baseline
Mg/day
C
F
intake used in
User defined
exposure pulse train
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Variable
Units
Form
Type
Explanation
Value
Reference
Other_i; i= 1, 2,3
Mg/day
A
F
Food Pb intakes for
discrete exposures
User defined
Other_pulse
Mg/day
C
F
Other Pb intake used
in exposure pulse
train
User defined
Pulse_i_period_air; i=l,2
day
C
F
Period for pulse train
exposure to air
User defined
Pulse i_period dust;
i=l,2
day
c
F
Period for pulse train
exposure to dust
User defined
Pulse i_period food;
i=l,2
day
c
F
Period for pulse train
exposure to food
User defined
Pulse i_period other;
i=l,2
day
c
F
Period for pulse train
exposure to other
User defined
Pulse_i_period_soil; i=l,2
day
c
F
Period for pulse train
exposure to soil
User defined
Pulse i_period water;
i=l,2
day
c
F
Period for pulse train
exposure to water
User defined
Pulseiwidthair; i=l,2
day
c
F
Width for pulse train
exposure to air
User defined
Pulseiwidthdust; i=l,2
day
c
F
Width for pulse train
exposure to dust
User defined
Pulse i width food;
i=l,2
day
c
F
Width for pulse train
exposure to food
User defined
Pulse i width other;
i=l,2
day
c
F
Width for pulse train
exposure to other
User defined
Pulse i width soil; i=l,2
day
c
F
Width for pulse train
exposure to soil
User defined
Pulse i width water;
i=l,2
day
c
F
Width for pulse train
exposure to water
User defined
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Variable
Units
Form
Type
Explanation
Value
Reference
Pulsestartair
day
C
F
Start age for pulse
train exposure to air
User defined
Pulsestartdust
day
C
F
Start age for pulse
train exposure to dust
User defined
Pulsestartfood
day
C
F
Start age for pulse
train exposure to
food
User defined
Pulsestartother
day
C
F
Start age for pulse
train exposure to
other
User defined
Pulsestartsoil
day
C
F
Start age for pulse
train exposure to soil
User defined
Pulsestartwater
day
C
F
Start age for pulse
train exposure to
water
User defined
Pulsestopair
day
C
F
Stop age for pulse
train exposure to air
User defined
Pulsestopdust
day
C
F
Stop age for pulse
train exposure to dust
User defined
Pulsestopfood
day
C
F
Stop age for pulse
train exposure to
food
User defined
Pulsestopother
day
C
F
Stop age for pulse
train exposure to
other
User defined
Pulsestopsoil
day
C
F
Stop age for pulse
train exposure to soil
User defined
Pulsestopwater
day
C
F
Stop age for pulse
train exposure to
water
User defined
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Variable
Units
Form
Type
Explanation
Value
Reference
RBAdust
unitless
C
F
Relative
bioavailability of
dust Pb
0.6
(U.S. EPA. 1994)
RBA food
unitless
C
F
Relative
bioavailability of
food Pb
1
Assumed to be water
soluble (U.S. EPA. 1994)
RBA other
unitless
C
F
Relative
bioavailability of
other Pb
User defined
RBA soil
unitless
C
F
Relative
bioavailability of soil
Pb
0.6
(U.S. EPA. 1994)
RBAwater
unitless
C
F
Relative
bioavailability of
water Pb
1
Assumed to be water
soluble (U.S. EPA. 1994)
Soil_baseline
Mg/g
C
F
Baseline indoor Soil
Pb concentration
used in exposure
pulse train
Background
25
(U.S. EPA. 2019: Smith et
al.. 2013)
Residential (>1940)
50
Residential (<1940)
250
Soil i; i= 1, 2,3
Mg/g
A
F
Soil Pb
concentrations for
discrete exposures
User defined
Soil_pulse
Mg/g
C
F
Soil Pb concentration
used in exposure
pulse train
User defined
Water_baseline
l-ig/L
C
F
Baseline water Pb
concentration used in
exposure pulse train
0.9
(U.S. EPA. 2019; Zartarian
et al.. 2017)
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Variable
Units
Form
Type
Explanation
Value
Reference
Water_i; i= 1, 2,3
l-ig/L
A
F
Water Pb
concentrations for
discrete exposures
User defined
See Chapter 16 of U.S. EPA
(2011)
Water_pulse
l-ig/L
C
F
Water Pb
concentration used in
exposure pulse train
User defined
Age-day
Value
0
2.9
90
2.9
365
5.2
Ventilation rate for
air Pb exposures
1825
8.8
Based on ICRP (1994); also
see Chapter 6 of U.S. EPA
V_air
m3/day
A
F
3650
15.3
5475
17.9
(2011)
9125
19.9
18250
19.9
25550
19.9
32850
19.9
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APPENDIX C REFERENCES - EXPOSURE VARIABLES (PRIMARY ONLY)
Bannon. DI; Drexler. JW; Fent. GM; Casteel. SW; Hunter. PJ; Brattin. WJ; Major. MA. (2009).
Evaluation of small arms range soils for metal contamination and lead bioavailability. Environ
Sci Technol 43: 9071-9076. http://dx.doi.org/10.1021/es901834h
Brochu. P; Ducre-Robitaille. JF; Brodeur. J. (2006). Physiological daily inhalation rates for free-living
individuals aged 1 month to 96 years, using data from doubly labeled water measurements: A
proposal for air quality criteria, standard calculations and health risk assessment. Hum Ecol Risk
Assess 12: 675-701. http://dx.doi.org/10.1080/1080703060080155Q
Casteel. SW; Weis. CP; Henningsen. GM: Brattin. WJ. (2006). Estimation of relative bioavailability of
lead in soil and soil-like materials using young swine. Environ Health Perspect 114: 1162-1171.
http://dx.doi.org/10.1289/ehp.8852
Clayton. CA; Pellizzari. ED; Whitmore. RW; Perritt. RL; Ouackenboss. JJ. (1999). National Human
Exposure Assessment Survey (NHEXAS): distributions and associations of lead, arsenic and
volatile organic compounds in EPA region 5. J Expo Anal Environ Epidemiol 9: 381-392.
Clickner. RP; Marker. D; Viet. SM; Rogers. J; Broene. P. (2002). National Survey of Lead and Allergens
in Housing. Volume I: Analysis of lead hazards. Final report. Revision 7.1. Washington, DC:
U.S. Department of Housing and Urban Development.
Cox. DC; Dewalt. G; O'Haver. R; Salatino. B. (2011). American Healthy Homes Survey: Lead and
arsenic findings. Washington, DC: U.S. Department of Housing and Urban Development.
http: //portal .hud.gov/hudportal/documents/huddoc?id=AHHS REPORT.pdf
FDA (U.S. Food and Drug Administration). (2006). Total diet study. Available online at
https://www.fda.gov/Food/FoodScienceResearch/TotalDietStudv/default.htm
FDA (U.S. Food and Drug Administration). (2007). Total diet study statistics on element results, Revision
4.1, Market baskets 1991-3 through 2004-5.
ICRP (International Commission on Radiological Protection). (1994). Human respiratory tract model for
radiological protection: A report of a task group of the International Commission on Radiological
Protection. ICRP Publication 66. New York, NY: Pergamon Press.
IOM (Institute of Medicine). (2005). Doubly Labeled water data set-Used to establish the estimated
average requirement for energy.
Juhasz. AL; Weber. J; Smith. E. (2011). Impact of soil particle size and bioaccessibility on children and
adult lead exposure in peri-urban contaminated soil. J Hazard Mater 186: 1870-1879.
http://dx.doi.Org/10.1016/i.ihazmat.2010.12.095
Kahn. HP; Stralka. K. (2009). Estimated daily average per capita water ingestion by child and adult age
categories based on USDA's 1994-1996 and 1998 continuing survey of food intakes by
individuals. J Expo Sci Environ Epidemiol 19: 396-404. http://dx.doi.org/10.1038/ies.2008.29
Lavton. DW. (1993). Metabolically consistent breathing rates for use in dose assessments. Health Phys
64: 23-36.
Lu. Y; Yin. W; Huang. L; Zhang. G; Zhao. Y. (2011). Assessment of bioaccessibility and exposure risk
of arsenic and lead in urban soils of Guangzhou City, China. Environ Geochem Health 33: 93-
102. http://dx.doi.org/10.1007/slQ653-010-9324-8
Marschner. B; Welge. P; Hack. A; Wittsiepe. J; Wilhelm. M. (2006). Comparison of soil Pb in vitro
bioaccessibility and in vivo bioavailability with Pb pools from a sequential soil extraction.
Environ Sci Technol 40: 2812-2818. http://dx.doi.org/10.1021/es051617p
O'Rourke. MK; Van De Water. PK; Jin. S; Rogan. SP; Weiss. AD; Gordon. SM; Moschandreas. DM;
Lebowitz. MP. (1999). Evaluations of primary metals from NHEXAS Arizona: distributions and
preliminary exposures. National Human Exposure Assessment Survey. J Expo Anal Environ
Epidemiol 9: 435-445.
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Ozkavnak. H; Xue. J; Zartarian. VG; Glen. G; Smith. L. (2011). Modeled estimates of soil and dust
ingestion rates for children. Risk Anal 31: 592-608. http://dx.doi.Org/10.l 11 l/j.1539-
6924.2010.01524.x
Reimann. C; Smith. DB; Woodruff. LG; Flem. B. (2011). Pb-concentrations and Pb-isotope ratios in soils
collected along an east-west transect across the United States. Appl Geochem 26: 1623-1631.
http://dx.doi.Org/10.1016/i.apgeochem.2011.04.018
Robertson. GL; Lebowitz. MP; O'Rourke. MK; Gordon. S; Moschandreas. D. (1999). The National
Human Exposure Assessment Survey (NHEXAS) study in Arizona—introduction and preliminary
results. J Expo Anal Environ Epidemiol 9: 427-434.
Roussel. H: Waterlot. C; Pelfrene. A: Pruvot. C; Mazzuca. M: Douav. F. (2010). Cd, Pb and Zn oral
bioaccessibility of urban soils contaminated in the past by atmospheric emissions from two lead
and zinc smelters. Arch Environ Contam Toxicol 58: 945-954. http://dx.doi.org/10.1007/sQ0244-
009-9425-5
Smith. DB; Cannon. WF; Woodruff. LG; Solano. F; Kilburn. JE; Fey. PL. (2013). Geochemical and
mineralogical data for soils of the conterminous United States: U.S. Geological Survey data series
801 (pp. 19). (Data Series 801). Reston, VA: U.S. Department of the Interior, U.S. Geological
Survey, http://pubs.usgs.gov/ds/801/
Smith. DM; Mielke. HW; Heneghan. JB. (2009). Subchronic lead feeding study in male rats and
micropigs. Environ Toxicol 24: 453-461. http://dx.doi.org/10.1002/tox.20448
Smith. E; Weber. J; Naidu. R; Mclaren. RG; Juhasz. AL. (2011). Assessment of lead bioaccessibility in
peri-urban contaminated soil. J Hazard Mater 186: 300-305.
http://dx.doi.Org/10.1016/i.ihazmat.2010.10.l 11
Stifelman. M. (2007). Using doubly-labeled water measurements of human energy expenditure to
estimate inhalation rates. Sci Total Environ 373: 585-590.
http://dx.doi.Org/10.1016/i.scitotenv.2006.ll.041
Thomas. K; Pellizzari. E; Berry. M. (1999). Population-based dietary intakes and tap water concentrations
for selected elements in the EPA region V National Human Exposure Assessment Survey
(NHEXAS). J Expo Anal Environ Epidemiol 9: 402-413.
http://dx.doi.org/10.1038/si.iea.7500Q51
U.S. EPA (U.S. Environmental Protection Agency). (1994). Technical support document: Parameters and
equations used in integrated exposure uptake biokinetic model for lead in children (v 099d) [EPA
Report], (EPA/54O/R-94/04O). Washington, DC.
U.S. EPA (U.S. Environmental Protection Agency). (2007a). EPA science advisory board (SAB) ad hoc
all-ages lead model review panel's peer review of the "all-ages lead model (AALM) version 1.05
(External review draft)". (EPA-SAB-07-002).
https://cfpub.epa.gov/si/si public record report.cfm?dirEntrvId=139314&Lab=NCEA
U.S. EPA (U.S. Environmental Protection Agency). (2007b). National primary drinking water regulations
for lead and copper: Short-term regulatory revisions and clarifications. Fed Reg 72: 57782-57820.
U.S. EPA (U.S. Environmental Protection Agency). (2011). Exposure factors handbook: 2011 edition
(final) [EPA Report]. (EPA/600/R-090/052F). Washington, DC: U.S. Environmental Protection
Agency, Office of Research and Development, National Center for Environmental Assessment.
http://cfpub.epa.gov/ncea/cfm/recordisplav.cfm?deid=236252
U.S. EPA (U.S. Environmental Protection Agency). (2013). Integrated science assessment for lead [EPA
Report]. (EPA/600/R-10/075F). Research Triangle Park, NC: U.S. Environmental Protection
Agency, National Center for Environmental Assessment.
http://cfpub.epa.gov/ncea/cfm/recordisplav.cfm?deid=255721
U.S. EPA (U.S. Environmental Protection Agency). (2017). Update for chapter 5 of the Exposure Factors
Handbook. Soil and dust ingestion. (EPA/600R-17/384F). Washington, DC: National Center for
Environmental Assessment, Office of Research and Development.
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U.S. EPA (U.S. Environmental Protection Agency). (2019). Technical support document for residential
dust-lead hazard standards rulemaking. Title Page. (EPA TSD LDHS).
USD A (U.S. Department of Agriculture). (2000). 1994-1996, and 1998 continuing survey of food intakes
by individuals and 1994-1996 diet and health knowledge survey.
von Lindern. I; Spalinger. S; Stifelman. ML; Stanek. LW; Bartrem. C. (2016). Estimating Children's
Soil/Dust Ingestion Rates through Retrospective Analyses of Blood Lead Biomonitoring from the
Bunker Hill Superfund Site in Idaho. Environ Health Perspect 124: 1462-1470.
http: //dx.doi .org/10.1289/ehp. 1510144
Wilson. R; Jones-Otazo. H; Petrovic. S; Mitchell. I. an; Bonvalot. Y; Williams. D; Richardson. GM.
(2013). Revisiting Dust and Soil Ingestion Rates Based on Hand-to-Mouth Transfer. Hum Ecol
Risk Assess 19: 158-188. http://dx.doi.org/10.1080/10807039.2012.6858Q7
Yu. CH; Yiin. LM; Liov. PJ. (2006). The bioaccessibility of lead (Pb) from vacuumed house dust on
carpets in urban residences. Risk Anal 26: 125-134. http://dx.doi.org/10.1111/j. 1539-
6924.2006.00710.x
Zartarian. V; Xue. J; Tornero-Velez. R; Brown. J. (2017). Children's Lead Exposure: A Multimedia
Modeling Analysis to Guide Public Health Decision-Making. Environ Health Perspect 125: n/a.
http://dx.doi.org/10.1289/EHP1605
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APPENDIX D - ALL AGES LEAD MODEL (AALM.FOR) BIOKINETICS
PARAMETER VALUES
AALM biokinetics parameters and values are listed in Table D-l. The bases for values assigned to each
parameter are summarized below. Parameters are presented in alphabetical order, according to the
parameter name.
AFC1, AFC2: Parameters used calculating age-specific absorption fraction of Pb from small intestine
(see variable F1 in Biokinetics GI Tract, Appendix A). The absorption fraction is calculated based on an
expression from O'Flahertv (1995. 1993). AFci an&AFc2 were assigned values of 0.40 and 0.28,
respectively, based on fitting simulations to data on blood Pb concentration in children (Sherlock and
Ouinn. 1986; Ryu et al.. 1983) and adults (Rabinowitz et al.. 1976) as described in Chapter 4. The values
for AFCI and AFC2 of 0.40 and 0.28, respectively, produce absorption fractions of 30-40% in infants and
during early childhood (Ziegler et al.. 1978; Alexander et al.. 1974) and 12% in adults (Maddaloni et al..
2005; U.S. EPA. 2003).
AGSCAL: Age-scaling factor for gastrointestinal transfer rates. Age-dependent values assigned to
AGSCAL are the same as those in Leggett (1993). The value of lis assigned to adults and higher values
for infants and children. This results in a slower removal kinetics in children compared to adults
(Corazziari et al.. 1985).
ARBLAD: Rate coefficient for Pb transfer from urinary bladder to urine. The value assigned to
ARBLAD is from Leggett (1993). The value of 5 d"1 for adults is based on a removal ti/2 of 0.1 days for Pb
being voided from the bladder (ICRP. 1975). which approximates a transfer rate of 0.693/0.1 d = 7 d1.
The rate coefficients for children are 7, 8, 11, 15, 12, and 12 d"1 for 15, 10, 5, and 1 year old, 3 months
old, and birth, respectively.
ARBRAN: Rate coefficient for Pb transfer from brain to diffusible plasma. The value assigned to
ARBRANis from Leggett (1993). The value of 0.00095 d"1 derives from a removal ti/2 of 2 years (0.693/2
yrs = 9.5* 10"4 d"1). The values for A BRAN and TOBRAN (deposition of 0.015% of Pb from diffusible
plasma), are based on comparison of predicted and observed brain Pb in dogs and baboons (Llovd et al..
1975; Cohen etal.. 1970) and human autopsy observations (Grandiean. 1978; Nivogi. 1974).
ARCORT: Rate coefficient for Pb transfer from non-exchangeable cortical bone to diffusible plasma.
Leggett (1993) assigned a value of 0.000082 d"1 for ACORT in adults based on the assumption that
removal of Pb from the non-exchangeable bone volume is occurs at same rate as bone resorption.
Childhood and adult rates were adopted from ICRP (1990) for bone-seeking radionuclides, based on
histomorphometric measurements taken of human ribs, iliac crest, and various long bones. By adulthood,
trabecular bone resorption is about 6-fold higher than in cortical bone. As discussed in Chapter 4, values
for children and adults were increased by a factor of 2, based on calibration of simulations of bone Pb
elimination kinetics in retired Pb workers (Nilsson et al.. 1991).
ARCS2B: Rate coefficient for Pb transfer from cortical bone surface to diffusible plasma. The value
assigned to ARCS2B is from Leggett (1993). The value of 0.5 d"1 for adults was based on model fit of
skeletal Pb data for humans (Heard and Chamberlain. 1984). baboons (Cohen etal.. 1970). and dogs
(Llovd etal.. 1975). assuming a transfer rate of 1 d"1 from bone surface and 0.5 d"1 each to plasma or
exchangeable bone volume. For children, the rate coefficient 0.65 d"1 was assigned to ARCS2B based on
the assumption that, in children, a larger fraction of Pb leaving bone surfaces goes to plasma. By analogy
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to strontium, approximately 1.25-fold more Pb transfers from bone surface to plasma in children,
compared to adults (1.25x0.5 d"1 = 0.65 d1).
ARCS2DF: Rate coefficient for Pb transfer from cortical bone surface to exchangeable cortical bone
volume. The value assigned to ARCS2DF is from Leggett (1993). The value of 0.5 d"1 in adults was based
on model fits to skeletal Pb data for humans (Heard and Chamberlain. 1984). baboons (Cohen ct al..
1970). and dogs (Llovd et al.. 1975) assuming transfer rate of 1 d"1 from bone surface and 0.5 d"1 each to
plasma or exchangeable bone volume. For children to age 15, the rate coefficient is 0.35 d1. By analogy
to strontium, approximately 1.25-fold more Pb transfers from bone surface to plasma in children,
compared to adults (1.25x0.5 d"1 = 0.65 d"1). The remaining Pb transfers to exchangeable bone volume at
a rate of 0.35 d1.
ARKDN2: Rate coefficient for transfer from kidney compartment 2 to diffusible plasma. Leggett (1993)
assigned a value of 0.0019 d"1 for adults. After parameter values for TOKDN1 and RKDN1 were set,
0.02% deposition from diffusible plasma and a removal tin of 1 year (rate coefficient: 0.693/1 yrs =
0.0019 d"1) replicated and overestimated slow renal Pb loss in humans (Heard and Chamberlain. 1984)
and animals (Llovd etal.. 1975; Cohen et al.. 1970). respectively. Rate coefficients for children ages 10-
15 years were assigned the adult value, while 0.00693 d"1 was used to represent birth to 5 years of age,
assuming a removal tin of 100 days. This assumption was needed to keep predicted Pb levels from overly
accumulating in long-term kidney compartments. These values were revised downward in the
AALM.FOR based on calibration of simulations (see Chapter 4) of post-mortem soft tissue-bone Pb
concentrations in children and adults reported by Barry (1975). The adjustments were a factor of xO.l for
ages <25 years, increasing to 0.5 at age 30 ears and 1 by age 40 years.
ARLVR2: Rate coefficient for Pb transfer from the slow liver compartment 2 to diffusible plasma.
Leggett (1993) assigned a value of 0.0019 d"1 for adults and children >10 years of age to reproduce
observations of 2% fraction of body Pb in liver of chronically exposed humans. For children ages 10-15
years, the rate coefficient was the same as adults, while 0.00693 d"1 was used for birth to 5 years of age,
assuming a removal tin of 100 days. This assumption was made to keep predicted Pb levels from overly
accumulating in long-term compartments. Values for children and adults were revised downward in the
AALM.FOR based on calibration of simulations (see Chapter 4) of post-mortem soft tissue-bone Pb
concentration ratios in children and adults reported by Barry (1975). The adjustments were a factor of 0.1
for ages <1 year, increasing progressively to 0.3 at age 10 years, 0.75 at age 30 years, 1.6 at age 40 years,
and 1.8 at 60 years.
ARRBC: Rate coefficient for Pb transfer from RBC to diffusible plasma. Leggett (1993) assigned a
value of 0.0019 for adults and children >10 years of age, based on a removal tin from RBCs to plasma of
5 days [0.693/5 days = 0.0019 d1; (Chamberlain et al.. 1978)1. For children from birth to 5 years of age,
0.00693 d"1 was assigned to provide reasonable agreement with the reference distributions of RBC levels
derived by Leggett (1993). Values for ages 1-10 years were revised upward in the AALM.FOR to
achieve alignment of Pb uptake-blood Pb concentration relationships in children predicted by the AALM
and IEUBK model (Chapter 4). The adjustments were a factor of x 1.7 at age 1 year, x 1.4 at age 5 years
and x 1.4 at age 10 years.
ARTRAB: Rate coefficient for Pb transfer from non-exchangeable trabecular bone volume to diffusible
plasma. Leggett assigned a value of 0.000493 d"1 to adults (assuming that removal of Pb from the non-
exchangeable bone volume occurs at same rate as bone resorption). Childhood and adult rates were
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adopted from ICRP (1990) for bone-seeking radionuclides, based on histomorphometric measurements
taken of human ribs, iliac crest, and various long bones. By adulthood, trabecular bone resorption is
about 6-fold higher than in cortical bone. Values for children and adults were increased by a factor of x3,
based on calibration of simulations (see Chapter 4) of bone Pb elimination kinetics in retired Pb workers
(Nilsson et al.. 1991).
ARTS2B: Rate coefficient for Pb transfer from trabecular bone surface to diffusible plasma. Values for
ARTS2B are from Leggett (1993). For adults, the value 0.5 d"1 was based on model fit to skeletal Pb data
for humans (Heard and Chamberlain. 1984). baboons (Cohen etal.. 1970). and dogs (Llovd et al.. 1975).
Assuming a total transfer rate of 1 d"1 from bone surface, a rate of 0.5 d"1 each transfers Pb to plasma or
exchangeable bone volume. The rate coefficient for children (<15 years) is 0.65 d1, based on the
assumption that, in children, a larger fraction of Pb leaves bone surfaces and goes to plasma. By analogy
to strontium, approximately 1.25-fold more Pb transfers from bone surface to plasma in children,
compared to adults (1.25x0.5 d"1 = 0.65 d1).
ARTS2DF: Rate coefficient for Pb transfer from surface trabecular bone to exchangeable trabecular
bone volume. Values for ARTS2DF are from Leggett (1993). For adults, the value 0.5 d"1 was based on
model fit to skeletal Pb data for humans (Heard and Chamberlain. 1984). baboons (Cohen et al.. 1970).
and dogs (Llovd etal.. 1975). Assuming a total transfer rate of Id"1 from bone surface, a rate of 0.5 d"1
each transfers Pb to plasma or exchangeable bone volume, the rate coefficient for children <15 years is
0.35 d"1. By analogy to strontium, approximately 1.25-fold more Pb transfers from bone surface to
plasma in children, compared to adults (1.25x0.5 d"1 = 0.65 d"1). The remaining Pb transfers to
exchangeable bone volume at a rate of 0.35 d"1.
ATBONE: Deposition fraction for Pb from diffusible plasma to surface bone. The value of 8% for
adults reproduces observations of Pb deposition to total bone of humans (Heard and Chamberlain. 1984).
baboons (Cohen et al.. 1970). and dogs (Llovd et al.. 1975). For children, the following deposition
fractions were used: 23.7% at 15 years, 17.9% at 10 years, 12.8% at 5 years, 14.4% at year, and 24% at
birth and 3 months. These values arise from the assumption that Pb deposits to bone surfaces
proportional to the rate of calcium addition, as described by Leggett (1992).
ATBRAN: Deposition fraction for Pb from diffusible plasma to brain. Values for A 1'B RAN are from
Leggett (1993). For children >5 years old and adults, the value of 0.015%, combined with a removal tin
of 2 years (0.693/2 yrs = 9.49x 10~4 d"1) were assigned based on model fit to observations of brain Pb
levels in dogs (Llovd et al.. 1975) and baboons (Cohen etal.. 1970) and human autopsy observations
(Grandiean. 1978; Nivogi. 1974). For children from birth to 1 year, the a 3-fold higher value of 0.045%
was assigned to account for the relatively larger brain mass:body weight ratio in this age range.
ATFRAC: Fraction of diffusible plasma-to-bone deposition that goes to trabecular surface bone. Values
for ATFRAC are from Leggett (1993). For adults, the value of 55.6% was assigned based on an
approximate 4-fold larger trabecular bone mass than cortical bone in humans (ICRP. 1975). and that
calcium deposits in trabecular bone are 5- to 6-fold greater than in cortical bone in humans (Leggett.
1992; Leggett et al.. 1982). The fraction transferring from diffusible plasma to cortical bone is \-TFRAC,
or 0.444. For children, the following values were assigned: 27.95% for 15 years, 25% for 10 years,
22.2% for 5 years, or 20% for birth to 3 months.
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ATOSOFO: Deposition fraction for Pb from diffusible plasma to the fast soft tissue compartment 0.
Values for ATOSOFO are from Leggett (1993). For adults, the value of 8.88%, and a removal tm of 8
hours (RSOFO) was assumed in order to replicate Pb reappearance in blood from extravascular fluid after
the first day following Pb injections in animals (Grcgus and Klaassen. 1986; Victerv et al.. 1979; Llovd et
al.. 1975; Potter et al.. 1971; Cohen et al.. 1970; Llovd etal.. 1970). For children, values of 8.38 and
8.35% were assigned to ages 5 to 15 years and birth to 1 year, respectively.
ATOSOF1: Deposition fraction for Pb from diffusible plasma to the intermediate soft tissue
compartment 1. Values for ATOSOF1 are from Leggett (1993). For adults, the value of 0.5% produced
an intermediate-rate loss of Pb from soft tissues and that aligned with blood Pb and excretion kinetics
(hair, nails, and skin) in humans (Rabinowitz et al.. 1976). A value of 1% was assigned children up to 15
years of age (Leggett. 1993).
ATOSOF2: Deposition fraction for Pb from diffusible plasma to the slow soft tissue compartment 2.
Values for ATOSOF2 are from Leggett (1993). The value of 0.1% for adults and children, along with a
retention time of at >5 years was based on comparisons of predicted and observed post-mortem soft tissue
Pb levels in chronically exposed humans (Grandiean. 1978; Nivogi. 1974).
BLDMOT: Maternal blood Pb concentration. The value 0.6 (ig/dL is based on an analysis of blood Pb
concentration data for U.S. females age 17-45 years reported in the NHANES 2009-2014 and assessed
by U.S. EPA (2017).
BR1: Rate coefficient for Pb transfer from RT compartment 1 to the gastrointestinal tract (CILIAR) or
diffusible plasma (l-CILIAR). The value assigned to BR1 is from Leggett (1993). The value of 16.6 is
based on observations of clearance of 203PbO, 203Pb(NO3)2, or 203Pb-labeled exhaust aerosols in humans
(Chamberlain et al.. 1978). in which 22% of deposited Pb was cleared from lungs with a tm of 0.8 hours.
The rate of clearance is calculated as 0.693/0.04167 days = 16.6 d"1.
BR2: Rate coefficient for Pb transfer from RT compartment 2 to the gastrointestinal tract (CILIAR) or
diffusible plasma (l-CILIAR). The value assigned to BR2 is from Leggett (1993) . The value of 5.54 is
based on observations of clearance of 203PbO, 203Pb(NO3)2, or 203Pb-labeled exhaust aerosols in humans
(Chamberlain et al.. 1978). in which 34% of deposited Pb was cleared from lungs with a tm of 2.5 hours.
The rate of clearance is calculated as 0.693/0.125 days = 5.54 d"1.
BR3: Rate coefficient for Pb transfer from RT compartment 3 to the gastrointestinal tract (CILIAR) or
diffusible plasma (l-CILIAR). The value assigned to BR3 is from Leggett (1993). The value of 1.66 d"1
was chosen based on observations of clearance of 203PbO, 203Pb(NO3)2, or 203Pb-labeled exhaust aerosols
in humans (Chamberlain et al.. 1978). in which 33% of deposited Pb was cleared from lungs with a ti/2 of
9 hours. The rate of clearance is calculated as 0.693/0.375 days = 1.66 d"1.
BR4: Rate coefficient for Pb transfer from RT compartment 4 to the gastrointestinal tract (CILIAR) or
diffusible plasma (l-CILIAR). The value assigned to BR4 is from Leggett (1993). The value of 0.347 d"1
is based on observations of clearance of 203PbO, 203Pb(NO3)2, or 203Pb-labeled exhaust aerosols in humans
(Chamberlain et al.. 1978). in which 12% of deposited Pb was cleared from lungs with ati/2 of 44 hours.
The rate coefficient is calculated as 0.693/2 days = 0.347 d1.
BRATIO: Child (at birth):maternal blood Pb concentration ratio. The value assigned to BRATIO is from
Leggett (1993). The value of 0.85 is based on studies that have compared maternal and fetal cord blood
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1 Pb concentrations which have observed cord-maternal ratios ranging from 0.7 to 1 (Baranowska-Bosiacka
2 et al.. 2016; Gulson et al.. 2016; Kavaalti et al.. 2015; Kim et al.. 2015; Baevens et al.. 2014; Chen et al..
3 2014; Kazi et al.. 2014; Reddv et al.. 2014; Amaral et al.. 2010; Kordas et al.. 2009; Patel and Prabhu.
4 2009; Carbone etal.. 1998; Gover. 1990; Graziano et al.. 1990).
5 BRETH: Pb deposition in RT (|_ig/day). Values are assigned by the user in AALM Fortran.xlsm (see
6 parameters IN air total. Appendix B).
7 CHAGE: Age years for parameters that are assigned values at specific ages. Values assigned to CHAGE
8 are from Leggett (1993).
9 CHR: Pb intake to blood (|_ig/day). for simulating injection. This parameter is in the Fortran code;
10 however, injection intakes are not simulated in the AALM.FOR.
11 CILIAR: Fraction of inhaled Pb transferred to gastrointestinal tract. A value of 4% was assigned by
12 Leggett (1993) to the fraction of total deposited Pb deposited cleared from the lung via mucociliary
13 escalation. This value is based observations that in adults approximately 95% of Pb deposited in the RT
14 was absorbed directly to blood (Wells et al.. 1977; Hursh et al.. 1969). Assuming a total deposition of
15 40% of inhaled Pb, the value for CILIAR is 1.6% (0.016 = 0.04x0.40).
16 DELTO: Starting value for numerical integration time step. The default value is 0.1 day is intended to
17 limit integration error in the calculation of blood Pb concentration to less than 5%
18 DELTi: Array of numerical integration time steps if the time step varies in the simulation. The default
19 for the AALM.FOR is to use a single time step for the simulation (0.1 day).
20 EAT: Pb ingestion (|_ig/day) for each exposure time step (NCHRON). Values are assigned by the user in
21 AALM Fortran.xlsm (see parameters IN ingestion total, Appendix B).
22 END AY: Ending day of simulation. For example, for a simulation from birth to age 60 years,
23 ENDAY=6Q * 365=21900.
24 EXP AGE: Age at start of the simulation. The default value for HXl'AGli is zero in the AALM.FOR
25 which simulates Pb biokinetics beginning at birth, with a pre-existing body Pb burden based on maternal
26 blood Pb (BLDMOT).
27 FLONG: Fraction of total Pb transfer from the exchangeable bone volume to non-exchangeable bone
28 volume. The fraction of total Pb transfer from the exchangeable bone volume to bone surface (cortical or
29 trabecular) is 1 O-FLONG. The value of 20% from Leggett (1993) was revised to 0.6, based on
30 calibration of simulations (see Chapter 4) of bone Pb elimination kinetics in retired Pb workers (Nilsson
31 etal.. 1991).
32 H1TOBL: Fraction of Pb transfer from liver compartment 1 to diffusible plasma. The value assigned to
33 H1TOBL is from Leggett (1993). Transfer out of liver compartment 1 includes 45% to diffusible plasma
34 (H1TOBL), 45% to small intestine (H1TOSI) and 10% to liver compartment 2 (H1TOH2). These
35 assumptions based on estimates of hepatic uptake and retention in humans and animals, and biliary
36 secretion in humans (Heard and Chamberlain. 1984; Llovd et al.. 1975; Cohen etal.. 1970).
37 H1TOH2: Fraction of Pb transfer from liver compartment 1 to liver compartment 2. The value assigned
38 to H1TOH2 is from Leggett (1993). Transfer out of liver compartment 1 includes 45% to diffusible
39 plasma (H1TOBL), 45% to small intestine (H1TOSI) and 10% to liver compartment 2 (H1TOH2). These
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1 assumptions based on estimates of hepatic uptake and retention in humans and animals, and biliary
2 secretion in humans (Heard and Chamberlain. 1984; Lloyd et al.. 1975; Cohen etal.. 1970).
3 H1TOSI: Fraction of Pb transfer from liver compartment 1 to the small intestine. The value assigned to
4 H1TOSI is from Leggett (1993). Transfer out of liver compartment 1 includes 45% to diffusible plasma
5 (H1TOBL), 45% to small intestine (H1TOSI) and 10% to liver compartment 2 (H1TOH2). These
6 assumptions based on estimates of hepatic uptake and retention in humans and animals, and biliary
7 secretion in humans (Heard and Chamberlain. 1984; Lloyd et al.. 1975; Cohen et al.. 1970).
8 HALF: Age at which body weight is half of WCHILD. This parameter is used in body weight and tissue
9 volume growth equations (see variables WBODY, VK, VL, Appendix A). The value assigned to WCHILD
10 is from O'Flahertv (1995. 1993).
11 HCTA: Adult hematocrit. Sex-specific values assigned to HCTA are from O'Flahertv (1995. 1993).
12 IACUTE: Switch for acute (1) or chronic array (2) uptakes. The default value is 2 in the AALM.FOR
13 which simulates chronic (i.e., repeated) daily exposures. Acute (e.g. single day exposures) can be
14 simulated with discrete exposure inputs or pulse train inputs (see Exposure Model Parameters, Appendix
15 C).
16 ICHEL: Switch for chelation simulation off (0) or on (1). The default value is 0 (no chelation). The
17 AALM Fortran.xlsm user interface does not support the chelation option.
18 IFETAL: Switch for fetal simulation on (1) or off (0). The default value is 1 which turns on calculations
19 of Pb body burden at birth based on maternal blood Pb (BLDMOT, see variables for Pb Masses at Birth,
20 Appendix A).
21 INMODE: Switch for injection (0), inhalation (1), ingestion (2), or combination (3). The default value is
22 3 which allows combined ingestion and inhalation exposures. Injection intakes are not supported in the
23 AALM.FOR.
24 IRBC: Switch for linear (0) or non-linear (1) RBC uptake. The default value is 1 which implements a
25 threshold-specified RBC uptake of Pb from plasma.
26 KAPPA: Logistic parameter for calculation of body weight (see variable WBODY in Appendix A). The
27 parameters KAPPA and LAMBDA determine the pre-adult rate of increase of body weight. The default
28 value for KAPPA is 600 (O'Flahertv. 1995. 1993).
29 LAMBDA: Logistic parameter in calculation of body weight (see variable WBODY in Appendix A). The
30 parameters KAPPA and LAMBDA determine the pre-adult rate of increase of body weight during. The
31 default value for LAMBDA is 0.017 for females and 0.0095 for males (O'Flahertv. 1995. 1993).
32 NCHRON: Number of exposure time steps, where the exposure time step is an age-day range within
33 which ingestion intake (EAT) or inhalation intake (BRETH) remains constant.
34 NCYCLE: Number of numerical integration steps for the simulation. If the numerical integration step
35 size is 0.1 day, NCYCLE is the day length of the simulation (ENDDAY)I0A day.
36 NDELT: Number of times the numerical integration time step changes during the simulation. The default
37 is 1 which applies the same time step throughout the simulation
38 NUMAGE: Number of ages (CHAGE) at which age-dependent parameters are assigned specific values.
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OUTPUTS: Variable identity numbers selected for output. This parameter is in the Fortran code;
however, is it not used in the implementation of AALM.FOR, which specifies output variables in the
AALM Fortran.xlsm file.
POWER: Exponent factor for non-linear expression for RBC deposition. The value assigned to POWER
is from Leggett (1993). The value of 1.5 was empirically derived based on data on Pb in human urine,
plasma, and blood (Minoia et al.. 1990; Iyengar and Woittiez. 1988; Somervaille et al.. 1988; SkerfVing et
al.. 1985; Manton and Cook. 1984; DeSilva. 1981; Chamberlain et al.. 1978; Schiitz and SkerfVing. 1976;
Cooper etal.. 1973).
R1: Fraction of inhaled Pb deposited in the RT compartment 1. Leggett (1993) assigned values for the
regional distribution of deposited Pb based on observations of clearance of 203PbO, 203Pb(NO3)2, or 203Pb-
labeled exhaust aerosols in humans (Chamberlain et al.. 1978). with 22% of deposited Pb cleared from
lungs. Leggett (1993) equated cleared Pb with deposited dose and rounded up to 25% for the regional
distribution to compartment 1. Assuming a total deposition of 40% of inhaled Pb (Leggett. 1993). the
value for R1 is 10% (0.08 = 0.20x0.40).
R2: Fraction of inhaled Pb deposited in the RT compartment 1, representing the tracheobronchial region.
Leggett (1993) assigned values for the regional distribution of deposited Pb based on observations of
clearance of 203PbO, 203Pb(NO3)2, or 203Pb-labeled exhaust aerosols in humans (Chamberlain et al.. 1978).
with 34% of deposited Pb cleared from lungs. Leggett (1993) equated cleared Pb with deposited dose and
rounded up to 35% for the regional distribution to compartment 2. Assuming a total deposition of 40% of
inhaled Pb, the value for R2 is 14% (0.14 = 0.35x0.40).
R3: Fraction of inhaled Pb deposited in the RT compartment 1, representing the tracheobronchial region.
Leggett (1993) assigned values for the regional distribution of deposited Pb based on observations of
clearance of 203PbO, 203Pb(NO3)2, or 203Pb-labeled exhaust aerosols in humans (Chamberlain et al.. 1978).
with 33% of deposited Pb was cleared from lungs. Leggett (1993) equated cleared Pb with deposited
dose and rounded down to 30% for the regional distribution to compartment 3. Assuming a total
deposition of 40% of inhaled Pb, the value for R3 is 12% (0.14 = 0.35x0.40).
R4: Fraction of inhaled Pb deposited in the RT compartment 1, representing the tracheobronchial region.
Leggett (1993) assigned values for the regional distribution of deposited Pb based on observations of
clearance of 203PbO, 203Pb(NO3)2, or 203Pb-labeled exhaust aerosols in humans (Chamberlain et al.. 1978).
with 12% of deposited Pb was cleared from lungs. Leggett (1993) equated cleared Pb with deposited
dose and rounded down to 10% for the regional distribution to compartment 4. Assuming a total
deposition of 40% of inhaled Pb, the value for R4 is 4% (0.04 = 0.10x0.40).
RBCNL: Threshold Pb concentration in RBCs at which non-linear deposition of Pb from diffusible
plasma to RBC occurs. Leggett (1993) assigned a value of 60 |_ig dL"1 based on an observed RBC Pb
concentration threshold above which non-linear kinetics of Pb in the body were observed (Chamberlain.
1985). The value was revised to 20 (ig/dL based on calibration to data on plasma-whole blood Pb
concentrations measured in adults (Smith et al.. 2002; Manton et al.. 2001; Bergdahl etal.. 1999;
Bergdahl etal.. 1998; Hernandez-Avila et al.. 1998; Bergdahl et al.. 1997; Schutzetal.. 1996).
RDECAY: Rate coefficient for radioactive decay of unstable Pb isotope. This parameter is set to 0 by
default in the AALM.FOR which simulates biokinetics of stable isotopes of Pb.
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4
5
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7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
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38
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
RDIFF: Rate coefficient for Pb transfer from exchangeable bone (cortical or trabecular) volume to
surface or non-exchangeable bone volume (see FLONG for fraction to non-exchangeable). The value
assigned to RDIFF is from Leggett (1993). The value of 0.0231 d"1 was based on observed rates of
removal of Pb from bone of dogs, baboons, and chronically exposed humans appears, which were similar
to removal of radium, which has a removal tin of 30 days (Leggett. 1992). resulting in a rate coefficient of
0.693/30 days = 0.00231 d1.
RKDN1: Rate coefficient for transfer from kidney compartment 1 to urinary pathway. The value
assigned to RKDN1 is from Leggett (1993). The value of 0.139 d"1 was chosen based on a removal tin of
5 days (transfer rate of 0.693/5 days = 0.139 d"1) and a deposition fraction of 2%, which predicts kidney
levels in rats and baboons (Cohen etal.. 1970) and is also consistent with human excretion data
(Campbell et al.. 1984; Chamberlain et al.. 1978; Hursh and Mercer. 1970; Booker etal.. 1969; Hursh and
Suomela. 1968).
RLLI: Rate coefficient for Pb transfer from lower large intestine to feces. The value assigned to RLLI is
from Leggett (1993). The value of 1 d"1 is from the ICRP (1979) gastrointestinal tract model.
RLVR1: Rate coefficient for Pb transfer from liver compartment 1 to small intestine or diffusible
plasma. The value assigned to RLVR1 (0.693 d"1) is from Leggett (1993). The removal tin for liver
compartment 1 is assumed to be 10 days, resulting in a rate coefficient of 0.693/10 days = 0.693 d"1. A
relatively short tin is needed to reproduce hepatic uptake and loss in humans (Chamberlain et al.. 1978).
baboons (Cohen et al.. 1970). and dogs (Llovd et al.. 1975) for the first weeks following intravenous Pb
injection.
RPLAS: Rate coefficient for Pb transfer from diffusible plasma to all compartments, scaled to bone
surface deposition. The value assigned to RPLAS is from Leggett (1993). The value of 2000 d"1 reflects
the removal of radio-Pb from plasma at about 1 minute (Campbell et al.. 1984; Wells et al.. 1977; Booker
et al.. 1969). Adjusting for rapid uptake in to RBCs and EVF, the rate becomes 1.3-1.4 min1, rounded to
2000 d1.
RPROT: Rate coefficient for Pb transfer from bound plasma to diffusible plasma. The value assigned to
RPROT is from Leggett (1993). The value of 0.139 d"1 (0.693/5 days = 0.139 d"1) is based on a removal
tin of approximately 5 days, the same as observed for plasma proteins (Orten andNeuhaus. 1982).
RSIC: Rate coefficient for Pb transfer from small intestine to upper large intestine. The value assigned
to RSIC is from Leggett (1993). The value of 6 d"1 is from the first-order transfer rate in the ICRP (1979)
gastrointestinal tract model.
RSOFO: Rate coefficient for Pb transfer from soft tissues with fast Pb clearance to diffusible plasma.
The value assigned to RSOFO is from Leggett (1993). The value of 2.079 d1, based on a removal tin of 8
hours (0.693/8 hours = 2.079 d"1) and a deposition fraction of 8.875% from diffusible plasma, reproduces
Pb reappearance in blood from EVF after the first day following Pb injections in animals (Gregus and
Klaassen. 1986; Victerv et al.. 1979; Llovd et al.. 1975; Potter et al.. 1971; Cohen etal.. 1970; Llovd et
al.. 1970).
RSOF1: Rate coefficient for Pb transfer from soft tissues with medium Pb clearance to diffusible plasma.
The value assigned to RSOF1 is from Leggett (1993). The value of 0.00693 d1, based on an removal tin
of 100 days (0.693/100 days = 0.00693 d"1) and a deposition fraction of 0.5% from diffusible plasma,
reproduces Pb reappearance in blood from EVF after the first day following Pb injections in animals
303
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3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
(Grcgus and Klaassen. 1986; Victerv et al.. 1979; Llovd et al.. 1975; Potter etal.. 1971; Cohen et al..
1970; Llovdetal.. 1970).
RSOF2: Rate coefficient for Pb transfer from soft tissues with slow Pb clearance to diffusible plasma.
The value assigned to RSOF2 (0.00038 d"1) is from Leggett (1993V Assuming no more than 0.1% of
diffusible plasma Pb is deposited into soft tissue having tenacious Pb retention, and the retention time is
at least 5 years, consistent with autopsy data for chronically exposed humans (Grandican. 1978; Nivogi.
1974).
RSTMC: Rate coefficient for Pb transfer from stomach to small intestine. The value assigned to RSTMC
is from Leggett (1993). The value of 24 d"1 is from the ICRP (1979) gastrointestinal tract model.
RULI: Rate coefficient for Pb transfer from upper large intestine to lower large intestine. The value
assigned to RULI is from Leggett (1993). The value of 1.85 d"1 is from the ICRP (1979) gastrointestinal
tract model.
S2HAIR: Fraction of Pb transfer from intermediate soft tissue (SOF2) to hair, nails, and desquamated
skin. The value assigned to S2HAIR is from Leggett (1993). The value of40% is based on observations of
3% of the Pb body burden in soft tissues and the remainder in pelt of animals at 28 days after injection
(Llovdetal.. 1975. 1970). The remaining fraction leaving SOF2 (1-S2HAIR = 60%) returns to diffusible
plasma.
SATRAT: Maximum (saturating) concentration of Pb in RBCs. The value assigned to SATRAT is from
Leggett (1993). The concentration of 350 (.ig dL"1 was assigned based on the observed upward inflection
of ratios of urinary:blood Pb and plasma:blood Pb at RBC concentrations above this level (Minoia et al..
1990; Iyengar and Woittiez. 1988; Somervaille et al.. 1988; SkerfVing et al.. 1985; Manton and Cook.
1984; DeSilva. 1981; Chamberlain et al.. 1978; Schiitz and Skerfving. 1976; Cooper etal.. 1973).
SIZEVF: Relative volume of the EVF compartment compared to plasma (EVF/Plasma). The value
assigned to SIZEVF is from Leggett (1993). The value of 3-fold was chosen because plasma Pb is about
three times that of EVF at equilibrium.
TOEVF: Deposition fraction for Pb from diffusible plasma to extravascular fluid. The value assigned to
STOEVF is from Leggett (1993). The value of 50% was based on observations of rapid return of Pb to
blood from extravascular spaces (Heard and Chamberlain. 1984; Booker etal.. 1969; Hursh and Suomcla.
1968; Stover. 1959).
TOFECE: Deposition fraction for Pb from diffusible plasma directly to the small intestine (not including
the transfer from biliary secretion, specified by RLVR1). The value assigned to TOFECE is from Leggett
(1993). The value of 0.6%, as well as Pb entering from biliary excretion (H1TOSI) was based on
observations of fecal excretion and the feces-to-urine Pb ratios in adults (Heard and Chamberlain. 1984;
Chamberlain et al.. 1978; Wells et al.. 1977).
TOKDN1: Deposition fraction for Pb from diffusible plasma to kidney compartment 1. Leggett (1993)
assigned a value of 2% and a removal tm of 5 days (RKDN1) based on observed kidney levels in rats and
baboons (Cohen et al.. 1970) that were also consistent with human excretion data (Campbell etal.. 1984;
Chamberlain et al.. 1978; Hursh and Mercer. 1970; Booker etal.. 1969; Hursh and Suomela. 1968).
Values for children and adults were revised upward in the AALM.FOR by a factor of x 1.25 based on
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1 calibration of simulations of plasma-to-urine clearance estimated for adults from data reported in (Araki
2 et al.. 1986; Manton and Cook. 1984; Manton and Mallov. 1983; Chamberlain et al.. 1978).
3 TOKDN2: Deposition fraction for Pb from diffusible plasma to kidney compartment. The value of
4 0.02% was chosen. Leggett (1993) assigned a value of 0.02% and a removal tm of 1 year (RKDN2), after
5 values for TOKDN1 and RKND1 were set, based on observations of a slow component for loss of Pb from
6 kidney in humans (Heard and Chamberlain. 1984) and animals (Llovd et al.. 1975; Cohen etal.. 1970).
7 respectively. Values for children and adults were revised upward in the AALM.FOR by a factor of x2
8 based on calibration of simulations (see Chapter 4) of post-mortem soft tissue-bone Pb concentrations in
9 children and adults reported by Barry (1975).
10 TOLVR1: Deposition fraction for Pb from diffusible plasma to liver compartment 2. The value assigned
11 to TOLVR1 is from Leggett (1993). The value of 4% was assigned based on observed uptake and
12 retention of Pb in liver in humans and animals, and biliary secretion in humans (Heard and Chamberlain.
13 1984; Llovd etal.. 1975; Cohen etal.. 1970).
14 TOPROT: Deposition fraction for Pb from diffusible plasma to protein-bound plasma. The value
15 assigned to TOPROT is from Leggett (1993). The value of 0.04% was selected to achieve (1) early
16 bifurcation of tracer Pb between plasma and RBCs, (2) observed urinary clearance of plasma Pb, (3)
17 plasma containing 0.2% of blood Pb at equilibrium, and (4) 15% ultrafilterable plasma Pb at equilibrium.
18 TORBC: Deposition fraction from diffusible plasma to RBCs. The value assigned to TORBC is from
19 Leggett (1993). The value of 24% was based on the observation that approximately one quarter of Pb
20 depositing to RBCs provides good fits to data of Hursh et al. (1969).
21 TOSWET: Deposition fraction for Pb from diffusible plasma to sweat. The value assigned to TOSWKT
22 is from Leggett (1993). The value of 0.35% was assigned based on observations of Pb excretion in sweat
23 and which was approximately 10% of urinary excretion for chronic exposure (Rabinowitz et al.. 1976).
24 TOURIN: Deposition fraction for Pb from diffusible plasma to urine. Leggett (1993) assigned a value
25 of 1.5% for TOURIN, in addition to 2% being removed from urinary path to bladder (TOKDN1), based on
26 observations of human urinary clearance (Minoia et al.. 1990; Iyengar and Woittiez. 1988; Somervaille et
27 al.. 1988; SkerfVing et al.. 1985; Chamberlain et al.. 1978; Schiitz and SkerfVing. 1976; Cooper etal..
28 1973). This parameter was set to zero in the AALM.FOR after calibration of parameter TOKDN1 to data
29 on plasma-to-urine clearance adults (Araki et al.. 1986; Manton and Cook. 1984; Manton and Mallov.
30 1983; Chamberlain et al.. 1978).
31 VBLC: Blood volume fraction of body weight. The value assigned to VBLC is from O'Flahertv (1995.
32 1993).
33 VKC: Blood volume fraction of body weight. The value assigned to VKC is from O'Flahertv (1995.
34 1993).
35 VLC: Liver volume fraction of body weight. The value assigned to VLC is from O'Flahertv (1995. 1993).
36 VLUC: Lung volume fraction of body weight. The value assigned to VLC is from O'Flahertv (1995.
37 1993).
38 WADULT: Adult maximum weight used in calculation of body weight growth (see variable WBODY in
39 Appendix A). The value assigned to WADULT is from O'Flahertv (1995. 1993).
305
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
1 WBIRTH: Weight at birth used in calculation of body weight growth (see variable WBODY in Appendix
2 A). The value assigned to WBIRTH is from O'Flahertv (1995. 1993).
3 WCHILD: Maximum body weight achieved during early hyperbolic growth phase, used in calculation of
4 body weight growth (see variable WBODY in Appendix A). The value assigned to WCHILD is from
5 O'Flahertv (1995. 1993).
6 TABLE D-l. AALM BIOKINETICS PARAMETERS AND VALUES
Parameter
Unit
Form
Type
Description
Value
Source
AFC1
unitless
C
F
Parameter used in
calculating age-specific
absorption fraction (/25 yr
1
15 yr
1.33
Age scaling factor for
10 yr
1.67
(Leeeett.
AGSCAL
unitless
A
F
gastrointestinal transfer
5 yr
1.67
1993)
rates
1 yr
1.67
0.274
yr
1.67
Birth
1.67
ARBRAN
d1
A
F
Rate coefficient for Pb
transfer from brain to
diffusible plasma
9.5E04
(Leeeett.
1993)
Age
Value
>25 yr
1.644
E-04
Rate coefficient for Pb
15 yr
1.024
E-03
(Leeeett.
1993; Nilsson
et al.. 1991)
ARCORT
d1
A
F
transfer from non-
exchangeable cortical
10 yr
1.780
E-03
bone to diffusible
plasma
5 yr
3.080
E-03
Also see
Chapter 4
1 yr
5.760
E-03
0.274
yr
1.644
E-02
306
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Parameter
Unit
Form
Type
Description
Va
ue
Source
Birth
2.040
E-02
Age
Value
>25 yr
0.50
15 yr
0.35
Rate coefficient for Pb
transfer from cortical
bone surface to
10 yr
0.35
(Leeeett.
ARCS2B
d1
A
F
5 yr
0.35
1993)
diffusible plasma.
1 yr
0.35
0.274
0.35
yr
Birth
0.35
Age
Value
>25 yr
0.50
Rate coefficient for Pb
15 yr
0.65
transfer from cortical
10 yr
0.65
(Leggett.
ARCS2DF
d1
A
F
bone surface to
exchangeable cortical
bone volume
5 yr
0.65
1993)
1 yr
0.65
0.274
yr
0.65
Birth
0.65
Age
Value
>40 yr
1.90E-
03
30 yr
9.50E-
04
25 yr
1.90E-
04
(Lessett.
1.90E-
04
Rate coefficient for
15 yr
1993; Barrv.
transfer from kidney
compartment 2 to
diffusible plasma
1975)
Also see
ARKDN2
d1
A
F
10 yr
1.90E-
04
5 yr
6.93E-
04
Chapter 4
1 yr
6.93E-
04
0.274
6.93E-
yr
04
Birth
6.93E-
04
307
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Parameter
Unit
Form
Type
Description
Va
ue
Source
Age
Value
90 yr
3.800
E-03
60 yr
3.420
E-03
40 yr
3.040
E-03
30 yr
1.425
E-03
Rate coefficient for Pb
transfer from the slow
liver compartment 2 to
diffusible plasma
25 yr
5.700
E-04
ARLVR2
d1
A
F
15 yr
5.700
E-04
10 yr
5.700
E-04
5 yr
1.386
E-03
1 yr
6.930
E-04
0.274
yr
6.930
E-04
Birth
6.930
E-04
Age
Value
>15 yr
1.390
E-01
10 yr
1.946
E-01
(Leggett.
ARRBC
d1
A
F
Rate coefficient for Pb
transfer from RBC to
5 yr
4.986
E-01
1993)
Also see
Chapter 4
diffusible plasma
1 yr
7.854
E-01
0.274
yr
4.620
E-01
Birth
4.620
E-01
Rate coefficient for Pb
Age
Value
(Lessett.
1993; Nilsson
etal.. 1991)
ARTRAB
d1
A
F
transfer from non-
exchangeable trabecular
>25 yr
9.860
E-04
bone volume to
diffusible plasma
15 yr
1.912
E-03
308
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Parameter
Unit
Form
Type
Description
Va
ue
Source
10 yr
2.640
E-03
Also see
Chapter 4
5 yr
3.620
E-03
1 yr
5.760
E-03
0.274
yr
1.644
E-02
>25 yr
2.040
E-02
Age
Value
>25 yr
0.50
15 yr
0.35
Rate coefficient for Pb
transfer from trabecular
bone surface to
10 yr
0.35
(Leggett.
ARTS2B
d1
A
F
5 yr
0.35
1993)
diffusible plasma
1 yr
0.35
0.274
0.35
yr
Birth
0.35
Age
Value
>25 yr
0.50
Rate coefficient for Pb
transfer from surface
15 yr
0.65
10 yr
0.65
(Leggett.
ARTS2DF
d1
A
F
trabecular bone to
exchangeable trabecular
bone volume
5 yr
0.65
1993)
1 yr
0.65
0.274
yr
0.65
Birth
0.65
Age
Value
>25 yr
8.00E-
02
Deposition fraction for
15 yr
2.37E-
01
(Leggett
ATBONE
unitless
A
F
Pb from diffusible
plasma to surface bone
10 yr
1.79E-
01
1993)
5 yr
1.28E-
01
1 yr
1.44E-
01
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Parameter
Unit
Form
Type
Description
Va
ue
Source
0.274
yr
2.40E-
01
Birth
2.40E-
01
Age
Value
>5 yr
1.5E0
94
ATBRAN
unitless
A
F
Deposition fraction for
Pb from diffusible
1 yr
4.5E-
04
(Leggett.
1993)
plasma to brain
0.274
yr
4.5E-
04
Birth
4.5E-
04
Age
Value
>25 yr
0.556
15 yr
0.279
Fraction of diffusible
plasma-to-bone
deposition that goes to
trabecular surface bone
10 yr
0.250
(Leggett.
ATFRAC
unitless
A
F
5 yr
0.222
1993)
1 yr
0.200
0.274
0.200
yr
Birth
0.200
Age
Value
>25 yr
8.875
E-02
15 yr
8.375
E-02
Deposition fraction for
Pb from diffusible
plasma to the fast soft
tissue compartment 0
10 yr
8.375
E-02
(Leggett.
ATOSOFO
unitless
A
F
5 yr
8.375
E-02
1993)
1 yr
8.345
E-02
0.274
yr
8.345
E-02
Birth
8.345
E-02
Deposition fraction for
Pb from diffusible
Age
Value
(Leggett.
1993)
ATOSOF1
unitless
A
F
>25 yr
0.005
plasma to the
15 yr
0.010
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Parameter
Unit
Form
Type
Description
Va
ue
Source
intermediate soft tissue
compartment 1
10 yr
0.010
5 yr
0.010
1 yr
0.010
0.274
yr
0.010
Birth
0.010
ATOSOF2
unitless
A
F
Deposition fraction for
Pb from diffusible
plasma to the slow soft
tissue compartment 2
0.001
(Leggett.
1993)
BLDMOT
1-ig/dL
C
F
Maternal blood Pb
concentration
0.6
NHANES
2009-2014;
OJ.S. EPA.
2017)
BR1
d1
C
F
Rate coefficient for Pb
transfer from RT
compartment 1 to the
gastrointestinal tract
(CILIAR) or diffusible
plasma (1-CILIAR)
16.6
(Leggett.
1993)
BR2
d1
c
F
Rate coefficient for Pb
transfer from RT
compartment 2 to the
gastrointestinal tract
(CILIAR) or diffusible
plasma (1-CILIAR)
5.54
(Leggett,
1993)
BR3
d1
c
F
Rate coefficient for Pb
transfer from RT
compartment 3 to the
gastrointestinal tract
(CILIAR) or diffusible
plasma (1-CILIAR)
1.66
(Leggett.
1993)
BR4
d1
c
F
Rate coefficient for Pb
transfer from RT
compartment 4 to the
gastrointestinal tract
(CILIAR) or diffusible
plasma (1-CILIAR)
0.347
(Leggett.
1993)
BRATIO
unitless
c
F
Child (at
birth):maternal blood
Pb concentration ratio
0.85
Multiple
references, see
summary for
BRATIO in
this Appendix
311
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Parameter
Unit
Form
Type
Description
Value
Source
BRETH
Mg/day
A
F
Pb deposition to
respiratory tract
User defined in
exposure model
NA
CHAGE
day
A
F
Age years for
parameters that are
assigned values at
specific ages
0
100
365
1825
3650
5475
9125
10950
14600
21900
32850
(Leeeett.
1993)
Also see
Chapter 4
CHR
fig/day
A
F
Pb intake to blood from
injection
Not supported
in AALM.FOR
NA
CILIAR
unitless
C
F
Fraction of inhaled Pb
transferred to
gastrointestinal tract
0.04
(Leggett.
1993: Wells et
al.. 1977;
Hursh et al..
1969)
DELTO
day
C
F
Starting value for
numerical integration
time step
0.25
Chapter 3
DELTi
day
A
F
Array of numerical
integration time steps if
the time step varies in
the simulation
0.25
Chapter 3
EAT
Mg/day
A
F
Pb ingestion ((.ig/day)
for each exposure time
step (NCHRON)
User defined in
exposure model
NA
EXPAGE
day
C
F
Age at start of the
simulation
0 (birth)
Chapter 3
FLONG
unitless
A
F
Fraction of total Pb
transfer from the
exchangeable bone
volume to non-
exchangeable bone
volume; the fraction of
total Pb transfer from
the exchangeable bone
volume to bone surface
(cortical or trabecular)
is l.O-FLONG
0.6
(Lessett.
1993.1992;
Nilsson et al..
1991; Leaaett
et al.. 1982)
Also see
Chapter 4
312
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Parameter
Unit
Form
Type
Description
Value
Source
H1TOBL
unitless
C
F
Fraction of Pb transfer
out of liver
compartment 1 that
goes to diffusible
plasma
0.45
(Leggett.
1993)
H1TOH2
unitless
C
F
Fraction of Pb transfer
out of liver
compartment 1 that
goes to liver
compartment 2
0.1
(Leggett,
1993)
H1TOSI
unitless
C
F
Fraction of Pb transfer
out of liver
compartment 1 that
goes to the small
intestine
0.45
(Leggett.
1993)
HALF
year
C
F
Age at which body
weight is half of
WCHILD
3
(O'Flahertv.
1995. 1993)
HCTA
unitless
C
F
Adult hematocrit
0.41 (female)
0.46 (male)
(O'Flahertv.
1995. 1993)
IACUTE
unitless
C
I
Switch for acute (1) or
chronic array (2)
uptake si
2
NA
ICHEL
unitless
C
I
Switch for chelation
simulation off (0) or on
(1)
0
chelation option
not supported in
AALM.FOR
NA
IFETAL
unitless
C
I
Switch for fetal
simulation on (1) or off
(0)
1
NA
INMODE
unitless
C
I
Switch for injection (0),
inhalation (1), ingestion
(2), or combination (3)
3
NA
IRBC
unitless
C
I
Switch for linear (0) or
non-linear (1) RBC
uptake
1
NA
KAPPA
unitless
C
F
Logistic parameter for
calculation of body
weight (see variable
WBODY)
600
(O'Flahertv.
1995. 1993)
LAMBDA
unitless
C
F
Logistic parameter for
calculation of body
weight (see variable
WBODY)
0.017 (female)
0.0095 (male)
(O'Flahertv.
1995. 1993)
313
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Parameter
Unit
Form
Type
Description
Value
Source
NCHRON
unitless
C
I
Number of exposure
time steps
Specified by
user in exposure
model
NA
NCYCLE
unitless
C
I
Number of numerical
integration steps for the
simulation
Specified by
user based on
length of
simulation and
step size
NA
NDELT
unitless
C
I
Number of times the
numerical integration
time step changes
during the simulation
1
NA
NUMAGE
untless
C
I
Number of ages
(CHAGE) at which age-
dependent parameters
are assigned specific
values.
1
NA
OUTPUTS
unitless
C
I
Variable identity
numbers selected for
output.-
Not supported
in AALM.FOR
NA
POWER
unitless
C
F
Exponent factor for
non-linear expression
for RBC deposition.
1.5
(Leggett,
1993)
R1
unitless
C
F
Fraction of inhaled Pb
deposited in RT
compartment 1
0.08
(Leggett.
1993)
R2
unitless
C
F
Fraction of inhaled Pb
deposited in RT
compartment 2
0.14
(Leggett.
1993)
R3
unitless
C
F
Fraction of inhaled Pb
deposited in RT
compartment 3
014
(Leggett.
1993)
R4
unitless
C
F
Fraction of inhaled Pb
deposited in RT
compartment 4
0.04
(Leggett.
1993)
RBCNL
1-ig/dL
C
F
Threshold Pb
concentration in RBC
for non-linear
deposition of Pb from
diffusible plasma to
RBC
20
(Leggett.
1993)
Also see
Chapter 4
RDECAY
d1
C
F
Rate coefficient for
radioactive decay of
unstable Pb isotope
Not supported
in AALM.FOR
NA
314
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Parameter
Unit
Form
Type
Description
Value
Source
RDIFF
d1
C
F
Rate coefficient for Pb
transfer from
exchangeable bone
(cortical or trabecular)
volume to surface or
non-exchangeable bone
volume (see FLONG
for fraction to non-
exchangeable)
0.0231
(Leggett.
1993)
RKDN1
d1
C
F
Rate coefficient for
transfer from kidney
compartment 1 to
urinary pathway
0.139
(Leggett.
1993)
RLLI
d1
C
F
Rate coefficient for Pb
transfer from lower
large intestine to feces
1
(Leggett.
1993)
RLVR1
d1
C
F
Rate coefficient for Pb
transfer from liver
compartment 1 to small
intestine or diffusible
plasma
0.0693
(Leggett.
1993)
RPLAS
d1
C
F
Rate coefficient for Pb
transfer from diffusible
plasma to all
compartments, scaled to
bone surface deposition
2000
(Leggett.
1993)
RPROT
d1
C
F
Rate coefficient for Pb
transfer from bound
plasma to diffusible
plasma
0.139
(Leggett.
1993)
RSIC
d1
C
F
Rate coefficient for Pb
transfer from small
intestine to upper large
intestine
6
(Leggett.
1993)
RSOFO
d1
C
F
Rate coefficient for Pb
transfer from soft
tissues with fast Pb
clearance to diffusible
plasma
2.079
(Leggett.
1993)
RSOF1
d1
C
F
Rate coefficient for Pb
transfer from soft
tissues with medium Pb
clearance to diffusible
plasma
0.00693
(Leggett,
1993)
315
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Parameter
Unit
Form
Type
Description
Value
Source
Rate coefficient for Pb
(Leggett.
transfer from soft
1993)
RSOF2
d1
C
F
tissues with slow Pb
clearance to diffusible
plasma
0.00038
Rate coefficient for Pb
(Leggett.
RSTMC
d1
C
F
transfer from stomach
to small intestine
24
1993)
Rate coefficient for Pb
(Leggett.
RULI
d1
C
F
transfer from upper
large intestine to lower
large intestine
1.85
1993)
Fraction of Pb transfer
(Leggett.
S2HAIR
unitless
r
17
from intermediate soft
0.4
1993)
r
tissue to hair, nails, and
desquamated skin
Maximum (saturating)
(Leggett.
SATRAT
l-tg dL1
c
F
concentration of Pb in
RBC
350
1993)
Relative volume of the
(Leggett.
SIZEVF
unitless
c
F
EVF compartment
compared to plasma
(EVF/Plasma)
3
1993)
TOEVF
unitless
T7
Deposition fraction for
Pb from diffusible
0.5
(Leggett.
1993)
t
r
plasma to extravascular
fluid
Deposition fraction for
(Leggett.
Pb from diffusible
1993)
plasma directly to the
small intestine (not
TOFECE
unitless
c
F
including the transfer
from biliary secretion,
specified by RLVR1)
not scaled to bone
surface deposition
0.006
Deposition fraction for
Pb from diffusible
(Leggett.
1993)
TOKDN1
unitless
c
F
plasma to kidney
compartment 1, not
scaled to bone surface
deposition
0.02
316
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Parameter
Unit
Form
Type
Description
Value
Source
TOKDN2
unitless
C
F
Deposition fraction for
Pb from diffusible
plasma to kidney
compartment 2, not
scaled to bone surface
deposition
0.0002
(Leggett.
1993)
TOLVR1
unitless
C
F
Deposition fraction for
Pb from diffusible
plasma to liver
compartment 2, not
scaled to bone surface
deposition
0.04
(Leggett.
1993)
TOPROT
unitless
C
F
Deposition fraction for
Pb from diffusible
plasma to protein-
bound plasma, not
scaled to bone surface
deposition
0.0004
(Leggett.
1993)
TORBC
unitless
C
F
Deposition fraction
from diffusible plasma
to RBC, not scaled to
bone surface deposition
0.24
(Leggett.
1993)
TOSWET
-
C
F
Deposition fraction for
Pb from diffusible
plasma to sweat not
scaled to bone surface
deposition, not scaled to
bone surface deposition
0.0035
(Leggett.
1993)
TOURIN
-
C
F
Deposition fraction for
Pb from diffusible
plasma to urine, not
scaled to bone surface
deposition
0.015
(Leggett,
1993)
Also see
Chapter 4
VBLC
unitless
C
F
Blood volume fraction
of body weight.
0.067
(O'Flahertv.
1995. 1993)
VKC
unitless
C
F
Kidney volume fraction
of body weight.
0.0085
(O'Flahertv.
1995. 1993)
VLC
unitless
C
F
Liver volume fraction
of body weight.
0.025
(O'Flahertv.
1995. 1993)
VLUC
unitless
C
F
Lung volume fraction
of body weight.
0.015
(O'Flahertv.
1995. 1993)
317
-------
EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
Parameter
Unit
Form
Type
Description
Value
Source
WADULT
kg
C
F
Adult maximum weight
used in calculation of
body weight growth
(see variable WBODY)
34 (female)
50 (male)
(O'Flahertv.
1995. 1993)
WBIRTH
kg
C
F
Weight at birth used in
calculation of body
weight growth (see
variable WBODY)
3.5
(O'Flahertv.
1995. 1993)
WCHILD
kg
C
F
Maximum body weight
achieved during early
hyperbolic growth
phase, used in
calculation of body
weight growth (see
variable WBODY)
22 (female)
23 (male)
(O'Flahertv.
1995. 1993)
1 A, array; C, constant; F, floating point, I, integer, NA, not applicable.
318
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EXTERNAL REVIEW DRAFT DO NOT CITE OR QUOTE
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