United States Office of Superfund Remediation EPA 9285.7-42 Environmental Protection and Technology Innovation May 2007 Agency 540-K-01-005 System Requirements and Design for the Integrated Exposure Uptake Biokinetic Model for Lead in Children (IEUBK) Windowsฎ Prepared for The Technical Review Workgroup for Metals and Asbestos (TRW) Prepared by Syracuse Research Corporation 6225 Running Ridge Road North Syracuse, NY 13212 ------- SYSTEM REQUIREMENTS AND DESIGN FOR lEUBKwiN Disclaimer This document has been reviewed in accordance with U.S. EPA policy and is approved for publication. Mention of trade names or commercial products does not constitute endorsement or recommendation. ------- SYSTEM REQUIREMENTS AND DESIGN FOR lEUBKwiN U.S. Environmental Protection Agency Technical Review Workgroup for Metals and Asbestos Members The members of the TRW Lead Committee are technical staff from EPA Regions, Office of Solid Waste and Emergency Response (OSWER) Headquarters, and Office of Research and Development National Center for Environmental Assessment (ORD/NCEA). Lead Committee members generally have an active interest and recognized scientific expertise in metals or asbestos risk assessment. For more information see: http://www. epa.gov/superfund/lead/trw.htm ------- SYSTEM REQUIREMENTS AND DESIGN FOR lEUBKwiN This page intentionally left blank. ------- SYSTEM REQUIREMENTS AND DESIGN FOR lEUBKwiN v Table of Contents Disclaimer ii Members iii Table of Contents v List of Tables vii List of Figures ix 1.0 Introduction 1 1.1 Purpose 1 1.2 Background 1 1.3 Scope 1 1.4 Approach 2 1.5 System References 3 1.6 Terms and Abbreviations 3 1.7 Referenced Documents 4 1.8 Organization of This Document 5 2.0 System Requirements 7 2.1 System Definition 7 2.1.1 System Concept and Purpose 7 2.1.2 System Sizing and Timing Requirements 7 2.1.3 Design Standards 7 2.1.4 Design Constraints and Assumptions 7 2.2 System Hardware and Software Requirements 8 2.3 Functional Requirements 8 2.3.1 Exposure Component 14 2.3. 2.3. 2.3. 2.3. 2.3. 2.3. .1 Air Lead Exposure Module 14 .2 Dietary Lead Exposure Module 15 .3 Water Lead Exposure Module 18 .4 Soil Lead Exposure Module 19 .5 Dust Lead Exposure Module 20 .6 Exposure Component Parameters 23 2.3.2 Uptake Component 30 2.3.3 Biokinetic Component 32 2.3.4 Probability Distribution Component 33 3.0 Software Detail Design 35 3.1 Overall Design Description 35 3.1.1 Local Data 35 3.1.2 Control 35 3.1.3 Error Handling 35 3.1.4 Data Conversion 36 3.1.5 Test Structure 36 3.1.6 Manual Procedures 36 3.2 Exposure Component 36 ------- SYSTEM REQUIREMENTS AND DESIGN FOR lEUBKwiN 3.2.1 Air Lead Exposure Module 37 3.2.2 Dietary Lead Exposure Module 38 3.2.3 Water Lead Exposure Module 39 3.2.4 Soil/Dust Lead Exposure Module 40 3.2.5 Maternal Lead Exposure Module 41 3.2.6 Other Lead Exposure Module 41 3.2.7 GI/Bioavailability Module 42 3.3 Uptake Component 42 3.4 Biokinetic Component 42 4.0 Documentation for the lEUBKwin 43 ------- SYSTEM REQUIREMENTS AND DESIGN FOR lEUBKwiN vii List of Tables Table 1. Terms and Abbreviations 4 Table 2. Values for the new consumption variables that were added to version 1, build 264 17 ------- SYSTEM REQUIREMENTS AND DESIGN FOR lEUBKwiN viii This page intentionally left blank. ------- SYSTEM REQUIREMENTS AND DESIGN FOR lEUBKwiN List of Figures Figure 1. System Life Cycle 3 Figure 2. Biological Structure of the lEUBKwin Model 9 Figure 3. Mathematical Structure of the lEUBKwin Model 10 Figure 4. Iterative Procedure for Determining Compartmental Lead Masses in Biokinetic Component 13 ------- SYSTEM REQUIREMENTS AND DESIGN FOR lEUBKwiN This page intentionally left blank. ------- SYSTEM REQUIREMENTS AND DESIGN FOR THE lEUBKwiN 1.0 Introduction 1.1 PURPOSE This System Requirements and Design document is an all-inclusive synopsis of the requirements for the development of the Integrated Exposure Uptake Biokinetic Model for Lead in Children (TEUBK). It documents the design and implementation of the software, and is intended as a reference which can be used in the future for model enhancement or modification. The requirements portion of this document describes, in detail, the parameters and equations that are used in the lEUBKwin model. The design portion describes the structure and details of the design of the model. 1.2 BACKGROUND The IEUBK model is a standalone, personal computer (PC)-compatible software package. The model allows the user to estimate a plausible distribution of blood lead concentrations for a hypothetical child or population of children. This distribution is centered on the geometric mean blood lead concentration which is predicted from available information about the child and his/her exposure to lead. From this distribution, the model estimates the probability that a child's blood lead concentration will exceed a certain level of concern (either user-selected or default). The user also can explore possible changes in exposure media that would alter the probability that blood lead concentrations would be above this level. The model should be viewed as a tool for making rapid calculations and recalculations of an extremely complex set of equations that include exposure, uptake, and biokinetic parameters. The model was originally developed as a tool for determining site-specific cleanup levels. The Office of Solid Waste and Emergency Response (OSWER) hopes to base the U.S. Environmental Protection Agency (EPA) lead guidance, directives (e.g., the Lead Directive), and future rulemaking on the results produced by the IEUBK model. The IEUBK model has been recommended as a risk assessment tool to support the implementation of the July 14, 1994, OSWER Interim Directive on Revised Soil Lead Guidance for CERCLA Sites andRCRA Facilities. The model uses four interrelated components (exposure, uptake, biokinetics, and probability distributions) to estimate blood lead levels in children exposed to contaminated media. 1.3 SCOPE This System Requirements and Design document encompasses both the intent and purpose of the IEUBK model as well as the programming details, documenting all facets of the program. Rather than incorporate duplicative material, this document references additional sources of information about the model. This document is not intended as a user's guide, which is available as standalone document. ------- SYSTEM REQUIREMENTS AND DESIGN FOR THE lEUBKwiN 1.4 APPROACH This document represents a particular step in the information system life cycle. As stated in the OSWER System Life Cycle Management Guidance (April 1988): "Life cycle management represents a structured approach to solving an information management problem ... starting with the initial identification of the problem, progressing through the building or acquisition of a solution, and ending with the final disposition of the solution at the end of its useful life." Figure 1 illustrates the five major phases and the stages of the system life cycle which are as follows: Initiation Concept Definition and Design Development and Implementation (including testing) Operation (stages include production, evaluation, and archive) The OSWER System Life Cycle is designed to allow flexibility in system development while at the same time providing distinct steps to follow in each phase. Each step has clearly defined: Objectives (major accomplishments) Key decisions (related to project approach, project execution, and project continuation) Products (primarily documentation, but can include other written material and the system itself) The OSWER System Life Cycle Management Guidance includes descriptions of each phase and discussion of the various steps involved in the phase. Outlines are provided for the system documentation requirements which are included in the products within each phase. In reference to the IEUBK model, the life cycle began with system conception and included system design, development, and implementation. Currently, the lEUBKwin model is in the operation stage, in which the system definition, design, development, and implementation phases are repeated. ------- SYSTEM REQUIREMENTS AND DESIGN FOR THE lEUBKwiN INITIATION SYSTEM LIFE CYCLE DEFINITION AND DESIGN OPERATION DEVELOPMENT AND IMPLEMENTATION Production Implementation Development Figure 1. System Life Cycle 1.5 SYSTEM REFERENCES The primary reference for the lEUBKwin model version 1.1 is earlier versions of the IEUBK model software (versions 0.99d and version 1.0). References include the U.S. EPA documents listed in Section 1.7. 1.6 TERMS AND ABBREVIATIONS A number of terms, acronyms, and abbreviations are used throughout this document. Acronyms and abbreviations are identified in parentheses following the first usage of the term. Terms and abbreviations used often in this document are listed in the table below: ------- SYSTEM REQUIREMENTS AND DESIGN FOR THE lEUBKwiN Table 1. Terms and Abbreviations TERM Comprehensive Environmental Response, Compensation, and Liability Act CERCLA cubic meters Disk Operating System deciliter Environmental Protection Agency gastrointestinal gram Independent Verification and Validation Integrated Exposure Uptake Biokinetic Model for Lead in Children Integrated Exposure Uptake Biokinetic Model for Lead in Children Windows version liters micro Office of Solid Waste and Emergency Response Resource Conservation an d Recovery A c/RCRA lead Technical Review Workgroup for Lead Technical Support Document ABBREVIATION m3 DOS dL EPA GI g IV&V IEUBK lEUBKwin L H OSWER Pb TRW TSD 1.7 REFERENCED DOCUMENTS The documents listed below served as references for developing the lEUBKwin model. Correspondence between the IEUBK Lead Model Source Code and Technical Support Document: Parameters and Equations Used in the Integrated Exposure Uptake Biokinetic Model for Lead in Children (version 0.99d), prepared by Battelle for EPA Office of Pollution Prevention and Toxics, September 30, 1994. EPA System Design and Development Guidance, June 1989. Guidance Manual for the Integrated Exposure Uptake Biokinetic Model for Lead in Children, Publication Number, 9285.7-15-1, EPA/540/R-93/081, PB93-963510, February 1994. ------- SYSTEM REQUIREMENTS AND DESIGN FOR THE lEUBKwiN Phase I Report for the Independent Verification and Validation (IV&V) of the Integrated Exposure Uptake Biokinetic (IEUBK) Model for Lead in Children, Vols. I and II, prepared by SAIC for EPA Office of Solid Waste and Emergency Response, Novembers, 1995. Technical Support Document: Parameters and Equations Used in the Integrated Exposure Uptake Biokinetic (IEUBK) Model for Lead in Children (version 0.99d), Publication Number 9285.7-22, EPA 540/R-94/040, PB 94-963505, December 1994. OSWER System Life Cycle Management Guidance. OSWER 9028.00, April 1988. In addition to the documents listed above, the TRW Lead Committee web site has guidance and recommendations pertinent to lead risk assessment for hazardous waste sites (www.epa.gov/superfund/lead). 1.8 ORGANIZATION OF THIS DOCUMENT This document is divided into the following five chapters with four appendices: 1.0 Introduction 2.0 System Requirements 3.0 Software Detailed Design 4.0 Documentation for the lEUBKwin Appendix A Equations and Parameters in the lEUBKwin Model Appendix B Data Crosswalk for the lEUBKwin Model Appendix C lEUBKwin Parameter Dictionary ------- SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN This page intentionally left blank. ------- SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN 2.0 System Requirements 2.1 SYSTEM DEFINITION In terms of functionality, the lEUBKwin model is essentially the same as earlier versions of the model (version 0.99d and version 1.0). The primary difference is that the lEUBKwin model version 1.1 incorporates updates to several model variables (i.e., dietary data and maternal blood lead concentration) and addresses a discrepancy with the equations used to fit the bone growth data (to a single continuous equation). As this task was solely a conversion effort, no attempt was made to modify the program code substantively. 2.1.1 System Concept and Purpose In order to predict the likely distribution of blood lead concentrations for children between the ages of 6 months and 7 years exposed to lead in environmental media, the lEUBKwin model combines estimates of lead intake from lead in air, water, soil, dust, diet, and other ingested environmental media with an absorption model for the uptake of lead from the lung or gastrointestinal tract, and a biokinetic model of lead distribution and elimination from a child's body. 2.1.2 System Sizing and Timing Requirements The lEUBKwin model is a standalone program that must be capable of performing on a desktop personal computer. For easy distribution and installation, the system should be able to be downloaded via the Internet. 2.1.3 Design Standards The design standards from the EPA System Design and Development Guidance June 1989 were followed in developing the IEUBK. In addition the changes to lEUBKwin were made according to the Capability Maturity Model Implementation (CMMI). CMMI is an evaluation tool used by government contractors to perform a contracted software project. At the time of development, the contractor developing the software was at CMM level 3. The CMM Level 3 credential demonstrates that SRC's software engineering solutions establish consistency across the organization, which enables result-oriented outcomes for SRC staff and customers. 2.1.4 Design Constraints and Assumptions EPA required that the lEUBKwin model be portable. Consequently, it was important to efficiently recede the lEUBKwin model. This feature makes distribution of the model both ------- SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN inexpensive and easy. The compiler program, Visual C++ version 6.0, was selected as the development tool. This feature makes the lEUBKwin model portable in selected 32-bit Windows environments (Windows 98/ME, Windows 2000, and Windows NT). 2.2 SYSTEM HARDWARE AND SOFTWARE REQUIREMENTS The lEUBKwin model is designed to operate on a specific hardware platform with one of a limited number of operating systems installed. The optimal hardware and software requirements are shown below. Recommended for Optimum Performance: Pentium Processor 200 MHZ (or higher) 32MB RAM 10MB Disk space 32-bit Windows Operating System 2.3 FUNCTIONAL REQUIREMENTS Figures 2 and 3 are graphical illustrations of the biological and mathematical structures, respectively, of the lEUBKwin model. The biological structure in Figure 2 shows how lead can move from the environment of a hypothetical child into the child's blood, while the mathematical structure in Figure 3 shows the parameters and calculations necessary to determine the child's blood lead concentration. Exposure, uptake, and biokinetic components are clearly delineated in the figures and correspond to functions of the lEUBKwin model. Each of these components, plus a fourth componentProbability Distributionis briefly described below. Beginning in Section 2.3.1, each of the components is described in more detail, from a functional perspective. For each component, these later sections address its purpose, the functions performed in terms of the mathematical equations involved, and the interface between that component and the others. Descriptions of the database used by each component are not included in these sections because neither the model components nor the lEUBKwin model use separate databases. Refer to the lEUBKwin model Parameter Dictionary for details about the database. Similarly, a network interface for the components is not addressed; the components are contained within an overall program that is implemented as a standalone system. ------- SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN c o a. E o O 3 OT O Q. X LU Lungs Gl Tract c 0) c o Q. E o O 0) ^ Lungs Gl Tract Plasma Extra-Cellular Fluid -f-J I O E n O o frabecular Cortical '^ Bone Bone 0) ^ 0 ( 1 ^~..~ ~ ^. . Red Other Blood Kidney Soft Liver Cells Tissues Environmental Media Body Compartments Elimination Pools of the Body Body Compartment or Elimination Pool Required in More Than One Component Figure 2. Biological Structure of the lEUBKwin Model. ------- 10 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN Exposure Component ^T Media-Specific ^r ^T Consumption Rates ^r \ < r ^ i Media-Specific Lead Intake Rates 1 ^T Media-Specific ^r S Lead Concentration ^r ^^^^^^^^~^^^ y 1 / Uptake Component Max Abs Coeff and ^r ^r Passive/Active Ratio ^r ^r 1 < Total Available Lead Intake Rate | < 1 < Absorption ^V Coefficients >^ | < 1 Media-Specific Lead Intake Rates > | ^ /* 1 Saturation Factor | 1 Lead Uptake Rates 7 / Child's Body /^ Weight /^ 1 y s^\ \ < Maternal Blood Lead ^^ / Weights and Volumes Concentration >^ ^^ of Body Compartments Biokinetic Component yv i i Compartment Lead ^^ / Masses at Birth >^ ^^ ^^^^^^ < < _| 1 1 Compartmental Lead Transfer Times Compartmental Lead Masses 1 PbB \ >\ / y ^-S Total Lead S S Uptake S y y y Input Only Calculations and Input Calculations Required in More Than One Component Figure 3. Mathematical Structure of the lEUBKwin Model. ------- 11 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN Exposure Component As indicated in Figure 2, the exposure component relates environmental lead concentrations to the intake rate at which lead enters the child's body via the gastrointestinal (GI) tract and lungs. The environmental media that serve as lead sources for the child are air, which enters the body through the lungs, and diet, dust, paint, soil, water, and other media which enter the body through the GI tract. As indicated in Figure 3, the exposure component converts media-specific consumption rates (in m3/day, g/day, or L/day) and media-specific lead concentrations (in jig Pb/m3, jig Pb/g, jig Pb/L), to media-specific lead intake rates (in jig Pb/day). The media-specific consumption rates and lead concentrations can be modified by the user using site specific data. The general equation relating the consumption rates and lead concentrations to the lead intake rate is: Lead Intake Rate = Media Lead Concentration * Media Intake Rate In this manner, the exposure component determines how much lead enters the child's body and stores that information in a set of media-specific lead intake rates. Uptake Component As indicated in Figure 2, the uptake component relates lead intake into the lungs or GI tract determined in the exposure component to the uptake of lead from the exposed membrane into the child's blood, for children at each age. Lead that enters through the lungs is either absorbed into the blood plasma through the lungs, transferred to the GI tract, or eliminated from the body via exhaled air. Very small particles may move directly into the blood plasma or may be eliminated from the body via exhaled air. Most of the lead found in the human body enters through the GI tract, either through direct ingestion or by movement from the nose, throat or lung structures. Lead that enters the body through the GI tract is either absorbed into the blood plasma or eliminated from the gut with other waste as feces. As indicated in Figure 3, the uptake component converts the media-specific lead intake rates produced by the exposure component into media-specific lead uptake rates (jig/day) for the blood plasma. The total lead uptake (jig/day) from the GI tract is estimated as the sum of two components, one passive (represented by a first order, linear relationship), the second active (represented by a saturable, nonlinear relationship). These two components are intended to represent two different mechanisms of lead absorption, an approach which is in accord with the limited data available in humans and animals, and also by analogy, with what is known about calcium uptake from the gut. First, the total lead "available" for uptake from the gut is defined as the sum, across all media, of the media-specific intake rate multiplied by the estimated low-dose fractional absorption for that medium. A passive absorption coefficient defines the dose-independent fraction of the available lead that is absorbed by the passive absorption pathway, and allows calculation of the rate of absorption via that pathway. The rate of absorption of the remaining available lead by the active pathway is calculated using a non-linear relationship that allows for saturable absorption. ------- 12 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN Biokinetic Component As indicated in Figure 2, the biokinetic component models the transfer of absorbed lead between blood and other tissues, or elimination of lead from the body via urine, feces, skin, hair, and nails. The biokinetic component of the IEUBK model is structured as a compartmental model of the human body with transfer times between compartments as basic model building elements. The compartmental structure of the IEUBK model was developed by identifying the anatomical components of the body critical to lead uptake, storage, and elimination, and the routes or pathways between these compartments. This compartmental scheme includes a central body compartment, six peripheral body compartments, and three elimination pools. The blood plasma is combined with the body's accessible extracellular fluid (ECF) to form the central plasma/ECF body compartment. Separate body compartments are used to model the trabecular bone, cortical bone, red blood cells, kidney, and liver. The remainder of the body tissues is included in the "other soft tissues" peripheral body compartment. Three elimination pathways are included in the biokinetic model: pathways from the central plasma/ECF compartment to the urinary pool, from the compartment for other soft tissues to skin, hair, and nails, and from the liver to the feces. As indicated in Figure 3, the biokinetic component converts the total lead uptake rate produced by the uptake component into an input to the blood plasma/ECF. Transfer coefficients are used to model movement of lead between internal compartments and to the excretion pathway. These quantities are then combined with the total lead uptake rate to determine lead masses in each of the body compartments. The lead in the plasma portion of the central/ECF compartment is added to the lead in the red blood cells to determine the blood lead concentration. The iterative nature of the calculations in the biokinetic component is illustrated in Figure 4. The period of exposure, 0 to 84 months, is divided into a number of equal time steps (within the range of 15 minutes to one month) that are set by the user. During each iteration, compartmental lead masses at the beginning of a time step are combined with the total lead uptake, inter- compartmental transfers, and quantities of excretion during the time step to estimate compartmental lead masses at the end of the time step. The compartmental lead transfer times during the time step are key parameters in these calculations. The compartmental lead masses at the end of the time step then become the compartmental lead masses at the beginning of the next time step and the iterative process continues. The iterative process is initiated by determining the compartmental lead masses at birth from the maternal blood lead concentration and data on the relative concentrations of lead in different tissues of stillborn fetuses. The model calculates all of the compartmental contents from 0 to 84 months; and reports blood lead concentrations from 6 to 84 months. ------- 13 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN /Total Lead Uptake \ \ During Time Step / /Compartmental Leack ( Masses at Beginning V \ of Time Step / /\ /Compartmental Leac ^TransferTimes During \ Time Step Compartmental Lead Masses at End of Time Step Figure 4. Iterative Procedure for Determining Compartmental Lead Masses in Biokinetic Component. ------- 14 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN Probability Distribution Component The probability distribution component of the model estimates a plausible distribution of blood lead concentrations. The distribution is centered on the geometric mean blood lead concentration for a hypothetical child or population of children. The distribution can be displayed graphically, or the data can be downloaded into another software program for statistical analysis. Descriptive statistics and Plot/Graph are functions of PBSTAT, which uses files with the "*.asc" extension, which are generated from the DOS IEUBK model. To use these functions in the Windows batch mode data, files which have the extension "*.txt", must be renamed with the file extension to "*.asc" using File Manager or Windows Explorer. The Batch Mode text results file (*.txt) generated from the lEUBKwin model can be used in the DOS version of PBSTAT by renaming the file extension from *.txt to *.asc in File Manager or Windows Explorer. Note that the *.asc file generated by lEUBKwin will have to be modified for PBSTAT: all the headers must be removed except for the ID FAM BLK line; The P (PbB>C) data column must also be removed; the data should begin on line 4. 2.3.1 Exposure Component The exposure component of the lEUBKwin model converts media-specific consumption rates and media-specific lead concentrations to media-specific lead intake rates. The media that are included in the exposure component are air, diet, water, soil, dust and paint. The equations that govern these model calculations are listed and discussed below. In these equations, the lead intake rates for air, diet, household dust, alternate source dust, soil, water, and other ingested media are denoted by INAIR[AGE], INDIET[AGE], INDUST[AGE], INDUSTA[AGE], INSOIL[AGE], INWATER[AGE], and INOTHER[AGE], respectively. The notation "[AGE]" indicates that these intake rates change with the age, t, of the child. All lead intake rates are in units of g Pb/day. Once calculated, media-specific lead intake rates serve as inputs to the uptake component. In the sections below, the calculations required to determine the lead intake rates are discussed by media. 2.3.1.1 Air Lead Exposure Module The air lead exposure module considers both indoor and outdoor air lead exposure for determining the child's overall air lead exposure. The outdoor air lead concentration [air_concentration[AGE]] is specified by the user. The indoor air lead concentration [IndoorConc[AGE]] is determined according to Equation E-l as a user-specified, constant percentage [Indoorpercent] of the outdoor air lead concentration. A time-weighted average air lead concentration [TWA[AGE]] is determined according to Equation E-2 where the indoor and outdoor air lead concentrations are weighted by the user-specified, age-dependent number of hours per day that a child spends outdoors [time_out[AGE]]. Finally, the lead intake from air, INAIR[AGE], is calculated according to Equation E-3 as the product of the time-weighted air lead concentration and a user-specified, age-dependent ventilation rate [vent_rate[AGE]]. ------- 15 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN IndoorConc[AGE] = 0.01 * indoorpercent * air_concentration[AGE] (E-l) [time outfAGEl * air concentrationlAGEll + J24 - (time outlAGEl) * IndoorConcfAGEll _ . TWA[AGE] = ฑ =l- * = l- ^L i =l- ^ l- ^ (E-2) 24 INAIR[AGE] = TWA[AGE] * vent_rate[AGE] (E-3) 2.3.1.2 Dietary Lead Exposure Module Dietary lead exposure, or the lead intake rate from diet [INDIET[AGE]], is determined by one of two methods: (1) direct specification, or (2) the alternative diet model. Under direct specification, INDIET[AGE] is set equal to a user-specified, age-dependent lead intake rate for diet [diet_intake[AGE]], as indicated in Equation E-4a: INDIET[AGE] = diet_intake[AGE] (E-4a) Under the alternative diet model, INDIET[AGE] is calculated as the sum of the lead intake rates for meat, vegetables, fruit, and other sources. The first three categories are sub-divided as follows: Meat - non-game animal (InMeat[AGE]) - game animal (InGame[AGE]) - fish (InFish[AGE]) Vegetables - canned (InCanVeg[AGEJ) - fresh (InFrVeg[AGE]) - home-grown (InHomeVeg[AGE]) Fruit - canned (InCanFruit[AGE]) - fresh (InFrFruit[AGE]) - home-grown (InHomeFruitfAGEJ) ------- 16 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN INDIET[AGE] = DietTotal[AGE] = InMeat[AGE] + InGame[AGE] + InFish[AGE] + InCanVeg[AGE] + InFrVeg[AGE] + InHomeVeg[AGE] + InCanFruit[AGE] + InFrFruit[AGE] + InHomeFruit[AGE] + InOtherDiettAGE]1 (E-4b) InOtherDiet[AGE] = InDairy[AGE] + InJuice[AGE] + InNuts[AGE] + InBread[AGE] + InPasta[AGE] + InBeverage[AGE] + InCandy[AGE] + InSauce[AGE] + InFormula[AGE] + Mnfant[AGE] (E-4c) Under the alternative diet intake calculation, each of the terms of Equations E-4b and E-4c are calculated as the product of the lead concentration for that food category and the food consumption rate for that category, as shown in Equations E-4d through E-4r. beverage[AGE] = beverageConc * beverage_Consump[AGE] (E-4d) bread[AGE] = breadConc * bread_Consump[AGE] (E-4e) can_fruit[AGE] = canFruitConc * canFruit_Consump[AGE] (E-4f) can_veg[AGE] = canVegConc * canVeg_Consump[AGE] (E-4g) candy[AGE] = candyConc * candy_Consump[AGE] (E-4h) dairy[AGE] = dairyConc * dairy_Consump[AGE] (E-4i) f_fruit[AGE] = fFruitConc * fFruit_Consump[AGE] (E-4j) f_veg[AGE] = fVegConc * fVeg_Consump[AGE] (E-4k) formula[AGE] = formulaConc * formula_Consump[AGE] (E-41) infant[AGE] = infantConc * infant_Consump[AGE] (E-4m) juices[AGE] = juiceConc * juice_Consump[AGE] (E-4n) meat[AGE] = meatConc * meat_Consump[AGE] (E-4o) nuts[AGE] = nutsConc * nuts_Consump[AGE] (E-4p) pasta[AGE] = pastaConc * pasta_Consump[AGE] (E-4q) sauce[AGE] = sauceConc * sauce_Consump[AGE] (E-4r) The within-age sum of the dietary lead intake variables1, which are defined by Equations E-4d through E-4r, equal the default dietary lead intake represented by diet_intake[AGE]. The values for the concentration and consumption rate parameters that appear in E-4d through E-4r are assigned in the code and are not accessible to the user. The values for concentration are based on the TRW's analysis of the Food and Drug Administration (FDA) total diet study data from market basket samples that were collected from 1995-2003 (FDA, 2006). The values for consumption were derived from the food concentration values that appeared (but were not used) in the IEUBK DOS model (v. 0.99d) code, and the values of the food intake parameters that were used in the IEUBK Windows model code up to Version 1.0, Build 263. 1 The values for the dietary lead intake variables were formerly assigned directly in the code in Version 1.0, Build 263 and earlier versions, including the DOS versions. In Windows Version 1.0, Build 264, the concentration and consumption rate parameters that appear in Equation E-4d through E-4r were added to clarify how the values for dietary intake were derived, and to make the code easier to update as new information on food residue concentration and consumption rates become available. ------- 17 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN With the exception of InOtherDiet[AGE]2, which only uses default values, the terms on the right- hand side of the equal sign of Equation E-4b are defined in Equations E-5a through E-51. In Equations E-5a through E-51 the model allows the user to vary local dietary factors (e.g., home grown vegetables, fruits, game animals and fish) that may influence overall lead exposure. The user specifies the fraction of total food category consumption represented by each food source. However, the total quantity of food consumption from each category (meat, vegetables, fruit) is a model constant. Because the total quantity of food consumption for each food category is a constant, it is recommended that users do not make changes to dietary lead intake variables in combination with alternate dietary exposures. In Equations E-5a through E-5e, the traditional supermarket portion of the dietary lead intake rate is calculated as the sum of the products of each consumption fraction and the specific lead intake for that category of food. The consumption fraction is calculated as a complement of the user defined nonsupermarket fraction [i.e., 1 - user defined nonsupermarket fraction]: meatFraction = 1 - userFishFraction - userGameFraction (E-5a) vegFraction = 1 - userVegFraction (E-5b) fruitFraction = 1 - userFruitFraction (E-5c) InMeat[AGE] = meatFraction * meat[AGE] (E-5d) InCanVeg[AGE] = vegFraction/2 * can_veg[AGE] (E-5e) InFrVeg[AGE] = vegFraction/2 * f_veg[AGE] (E-5f) InCanFruit[AGE] = fruitFraction/2 * can_fruit[AGE] (E-5g) InFrFruit[AGE] = fruitFraction/2 * f_fruit[AGE] (E-5h) Table 2. Values for the new consumption variables that were added to IEUBK. [AGE] 12345 6 7 beverage_Consump[AGE] 87.993 116.487 209.677 194.982 177.061 183.333 188.710 bread_Consump[AGE] 4.992 15.862 13.311 16.639 19.967 22.629 27.898 candy_Consump[AGE] 9.955 11.273 32.909 24.409 16.000 14.818 12.455 canFruit_Consump[AGE] 13.941 8.183 8.145 7.691 7.236 7.460 7.906 canVeg_Consump[AGE] 0.668 2.274 2.563 2.662 2.771 2.626 2.356 dairy_Consump[AGE] 41.784 35.321 38.527 38.327 38.176 40.631 45.591 ffruit_Consump[AGE] 2.495 12.540 11.196 11.196 11.452 12.988 16.059 formula_Consump[AGE] 45.153 22.975 0.797 0.000 0.000 0.000 0.000 fveg_Consump[AGE] 8.773 15.945 28.156 27.623 27.030 29.164 33.373 infant_Consump[AGE] 131.767 66.905 1.634 0.000 0.000 0.000 0.000 juice_Consump[AGE] 2.018 11.656 15.692 15.692 15.692 19.646 27.471 meat_Consump[AGE] 12.500 29.605 38.111 40.930 43.750 47.368 54.558 nuts_Consump[AGE] 0.087 0.962 0.875 0.962 0.962 0.962 0.875 pasta_Consump[AGE] 10.409 18.902 26.263 25.915 25.566 27.134 30.183 sauce_Consump[AGE] 1.647 4.784 5.569 6.902 8.157 8.235 8.235 In Equations E-5i through E-51, the lead intake rate is calculated as the product of the user- defined nonsupermarket consumption fraction, and a consumption rate for that category of food: For the sake of simplification, the term InOtherDiet[AGE] is used in the text to represent components of the diet other than meat, fruit, vegetables, fish, or game (this term does not actually appear in the code). These other dietary components are modeled as InDairy, InJuice, InNuts, InBread, InPasta, InBeverage, InCandy, InSauce, InFormula, and Inlnfant. The values for these parameters are defined in the program code for the model and cannot be modified by the user. The values of these parameters are the same whether alternate dietary values are used. ------- 18 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN InHomeFruit[AGE] = userFruitFraction * (canFruit_Consump[AGE] + fFruit_Consump [AGE]) * UserFruitConc (E-5i) InHomeVeg[AGE] = userVegFraction * (canVeg_Consump[AGE] + fVeg_Consump[AGE]) * UserVegConc (E-5J) InFish[AGE] = userFishFraction * meat_consump[AGE] * UserFishConc (E-5k) InGame[AGE] = userGameFraction * meat_consump[AGE] * UserGameConc (E-51) In Equations E-5m through E-5v, the terms of InOtherDiet[AGE] are defined. All these terms have default values in the model. See Appendix B, the Data Crosswalk for the lEUBKwin model, for the default values. InDairy [AGE] = dairy [AGE] E-5m InJuice [AGE] = juices [AGE] E-5n InNuts[AGE] = nuts[AGE] E-5o InBread[AGE] = bread[AGE] E-5p InPasta[AGE] = pasta[AGE] E-5q InBeverage[AGE] = beverage [AGE] E-5r InCandy[AGE] = candy[AGE] E-5s InSauce[AGE] = sauce[AGE] E-5t InFormula[AGE] = formula[AGE] E-5u Mnfant[AGE] = infant[AGE] E-5v 2.3.1.3 Water Lead Exposure Module Water lead exposure is determined by one of two methods: (1) direct specification, or (2) an alternative water lead concentration model. For direct specification, as indicated in Equation E-6a, INWATER[AGE] is calculated as the product of a user-specified, age-dependent water consumption rate [water_consumption[AGE]] and a user-specified, constant water lead concentration [constant_water_conc]. INWATER[AGE] = water_consumption[AGE] * constant_water_conc (E-6a) For the alternative water model, as indicated in Equation E-6b, INWATER[AGE] is calculated as the product of the same user-specified, age-dependent water consumption rate [water_consumption[AGE]] and a constant water lead concentration that is calculated as a weighted average of user-specified, constant water lead concentrations from the first draw on a home faucet [FirstDrawConc], a flushed faucet at home [HomeFlushedConc], and a water fountain outside the home [FountainConc]. These concentrations are weighted by user-specified, ------- 19 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN constant fractions of consumed water that are first-draw water [FirstDrawFraction], home flushed water [HomeFlushedFraction], and fountain water [FountainFraction]. As indicated in Equation E-7, HomeFlushedFraction is calculated by subtracting the other two fractions from 1. INWATER[AGE] = water_consumption[AGEJ* ^HomeFlushedConc * HomeFlushedFraction FirstDrawConc * FirstDrawFraction + FountainConc * FountainFraction (E-6b) HomeFlushedFraction = 1 - (FirstDrawFraction - FountainFraction) (E-7) 2.3.1.4 Soil Lead Exposure Module Equation E-8a is used to determine the soil lead exposure for each of the following 'constant outdoor soil lead concentration' conditions: Multiple source analysis and constant outdoor soil lead concentration Variable indoor dust lead concentration and constant outdoor soil lead concentration Constant indoor dust lead concentration and constant outdoor soil lead concentration INSOIL[AGE] = constant_soil_conc[AGE] * soil_ingested[AGE] * (0.01 * weight_soil) (E-8a) where: constant_soil_conc[AGE] = the constant user-specified soil lead concentration soil_ingested[AGE] = the user-specified age-dependent soil and dust ingestion rate 0.01 * weight_soil = a user-specified constant fraction of soil and dust ingested that is soil. However, if none of the three conditions specified above are applicable, Equation E-8b is used to determine the soil lead exposure. Equation E-8b is only applicable if one of the following 'variable outdoor soil lead concentration' conditions exists: Multiple source analysis and variable outdoor soil lead concentration Variable indoor dust lead concentration and variable outdoor soil lead concentration Constant indoor dust lead concentration and variable outdoor soil lead concentration INSOIL[AGE] =soil_content[AGE]* soil_ingested[AGE] * (0.01 * weight_soil) (E-8b) where: soil_content[AGE] = the user-specified age-dependent outdoor soil lead concentration soil_ingested[AGE] = the user-specified age-dependent soil and dust ingestion rate 0.01 *weight_soil = a user-specified constant fraction of soil and dust ingested that is soil ------- 20 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN Outdoor soil lead concentration can be specified in an age-dependent manner in the soil/dust data input window. 2.3.1.5 Dust Lead Exposure Module Dust lead exposure is determined by one of two methods: (1) direct specification, or (2) an alternative dust model. For direct specification, as indicated in Equations E-9a, the baseline dust lead intake, INDUST[AGE], is calculated as the product of a user-specified dust concentration [constant_dust_conc], user-specified age-dependent soil and dust ingestion rate [soil_ingested[AGE]], and the fraction of soil and dust ingestion that is in the form of dust [0.01 * (100 - weight_soil)]. When using the direct specification, the alternative source dust lead intake [INDUSTA[AGE]], is set to zero. Equation E-9a is used if one of the following conditions exists: Constant indoor dust lead concentration and constant outdoor soil lead concentration Constant indoor dust lead concentration and variable outdoor soil lead concentration INDUST[AGE] = constant_dust_conc[AGE] * soil_ingested[AGE] * [0.01 * (100 - weight_soil)] (E-9a) where: constant_dust_conc[AGE] = the user-specified dust lead concentration soil_ingested[AGE] = the user-specified, age-dependent soil and dust ingestion rate [0.01 * (100 - weight_soil)] = the fraction of soil and dust ingestion that is in the form of dust The alternative dust sources component has two specifications: The indoor dust lead concentration is calculated as a sum of contributions from soil and air, either constant or age-dependent (specific calculations are not shown here, please refer to the Appendix A). The indoor dust lead intake [INDUSTA[AGE]] is calculated as the sum of contributions from several additional sources as indicated by Equation E-9c. Only a fraction of dust lead exposure is assumed to come from residential dust. When data are available, the remainder of the dust lead is assumed to come from separately estimated dust sources including: -Secondary exposure to leaded dust carried home from the workplace [OCCUP[AGE]] -Leaded dust at school or pre-school [SCHOOL[AGE]] -Leaded dust at other non-school daycare facilities [DAYCARE[AGE]] -Leaded dust from secondary homes (e.g., grandparents) [SECHOME[AGE]] -Leaded dust from deteriorating interior paint [OTHER[AGE]] ------- 21 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN Equations E-9b and E-9c are used in determining the household indoor dust lead concentration [INDUST[AGE]] and alternative indoor dust lead intake [INDUSTA[AGE]] if multiple source analysis and alternate indoor dust lead sources are used. INDUST[AGE] = DustTotal[AGE] * (soil_indoor[AGE] * HouseFraction) (E-9b) INDUSTA[AGE] = OCCUP[AGE] + SCHOOL[AGE] + DAYCARE[AGE] + SECHOME[AGE] + OTHER[AGE] (E- 9c) In Equation E-9b, INDUST[AGE] is the product of the age-dependent dust ingestion rate [DustTotal[AGE]] (see Equation E-10), an age-dependent indoor household dust lead concentration [soil_indoor[AGE]] (see Equation E-l la), and the fraction of dust exposure that is from residential dust [HouseFraction] (see Equation E-9.5). The following equations are used to determine the household indoor dust lead intake and alternative indoor dust lead intake if one of the following conditions exists: Multiple source analysis and constant outdoor soil lead concentration Multiple source analysis and variable outdoor soil lead concentration INDUST[AGE] = soil_indoor[AGE] * soil_ingested[AGE] * [0.01 * (100 - weight_soil)] (E-9d) where: soil_indoor[AGE] is derived from either Equation E-l la or E-l Ib soil_ingested[AGE] is derived from either Equation E-l la or E-l Ib [0.01 * (100 - weight_soil)] = the fraction of soil and dust ingestion that is in the form of dust In Equation E-10, Dust_Total[AGE] is the product of an age-dependent soil and dust ingestion rate [soil_ingested[AGE]] and the user-specified constant fraction of soil and dust ingested that is dust [0.01 * (100 - weight_soil)]. DustTotal[AGE] = soil_ingested[AGE] * [0.01 * (100 - weight_soil)] (E-10) Equation E-l 1 has many variations depending on the conditions that exist. In Equation E-l la, soil_indoor[AGE] is calculated as a sum of contributions from soil and air. soil_indoor[AGE] = (contrib_percent *soil_content[AGE]) + (multiply_factor * air_concentration[AGE]) (E-l la) The contribution from soil is the product of a user-specified, constant ratio of dust to soil lead concentrations [contrib_percent] and the user-specified, age-dependent outdoor soil lead concentration [soil_content[AGE]]. Similarly, the contribution from air is the product of a user- specified, constant ratio of dust to air lead concentrations [multiply_factor] and the user- specified, age-dependent outdoor air concentration [air_concentration[AGE]]. This equation only applies if both multiple source analysis and variable outdoor soil lead concentration is used in determining INDUST[AGE]. ------- 22 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN Equation E-l Ib is applicable if both multiple source analysis and constant outdoor soil lead concentration are used. The parameter constant_soil_conc[AGE] replaces the parameter soil_content[AGE] and uses the default value for outdoor soil lead concentration instead of a user-specified value. soil_indoor[AGE] = (contrib_percent * constant_soil_conc[AGE]) + (multiply_factor * air_concentration[AGE]) (E-l Ib) Equation E-9e applies if one of the following conditions exists: Variable indoor dust lead concentration and constant outdoor soil lead concentration Variable indoor dust lead concentration and variable outdoor soil lead concentration INDUST[AGE] = dust_indoor[AGE] * soil_ingested[AGE] * (0.01 * (100 - weight_soil)) (E-9e) where: dust_indoor[AGE] = the user-specified age-dependent indoor dust concentration soil_ingested[AGE] = the user-specified age-dependent soil and dust ingestion rate (0.01 * (100 - weight_soil)) = the fraction of soil and dust ingestion that is in the form of dust Equation E-l Ic is applicable when user-specified, variable household indoor dust lead concentrations are used in conjunction with either constant or variable, user-specified outdoor soil lead concentrations to determine INDUST[AGE] (see Equation E-9e). soil_indoor[AGE] = dust_indoor[AGE] (E-llc) where: dust_indoor[AGE] = user-specified age-dependent indoor dust lead concentration soil_indoor[AGE] = constant_dust_conc[AGE] (E-l Id) where: constant_dust_conc[AGE] = default or user-specified constant value for indoor dust lead concentration As indicated in Equation E-9.5, HouseFraction is determined by subtracting from 1, the total of the user-specified, constant fractions of dust ingested that come from the parent's occupation [OccupFraction], school [SchoolFraction], daycare [DaycareFraction], secondary homes [SecHomeFraction], and paint [OtherFraction]. The sum of all source fractions cannot exceed 1.0. As indicated in Equation E-9c, INDUSTA[AGE] is the sum of the lead intake rates from all five alternative sources. The individual lead intake rates for the alternative sources are defined in Equations E-12a through E-12e. In these equations, the lead intake rate is the product of the age- dependent, dust ingestion rate [DustTotal[AGE]], the user-specified, constant fraction of dust ingested that comes from that source (OccupFraction, SchoolFraction, DaycareFraction, ------- 23 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN SecHomeFraction, or OtherFraction), and the user-specified, constant dust lead concentration for dust from that source (OccupConc, SchoolConc, DaycareConc, SecHomeConc, or OtherConc). HouseFraction = 1 - (OccupFraction - SchoolFraction - DaycareFraction - SecHomeFraction - OtherFraction) (E- 9.5) OCCUP[AGE] = DustTotal[AGE] * OccupFraction * OccupConc (E-12a) SCHOOL [AGE] = DustTotal[AGE] * SchoolFraction * SchoolConc (E-12b) DAYCARE[AGE] = DustTotal[AGE] * DaycareFraction * DaycareConc (E-12c) SECHOME[AGE] = DustTotal[AGE] * SecHomeFraction * SecHomeConc (E-12d) OTHER[AGE] = DustTotal[AGE] * OtherFraction *OtherConc (E-12e) 2.3.1.6 Exposure Component Parameters For diet, water, and dust exposures, the user may choose from two or more methods of calculating exposure. Each of these exposure pathways has both concentration and intake parameter default values built into the IEUBK model that can be used to calculate default exposure levels. The following sections contain information on the default values for concentration and intake for air, diet, water, soil, and dust. ------- 24 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN Parameter Values for Air The default values for indoorpercent, air_concentration[AGE], time_out[AGE], and vent_rate[AGE] result in the default values shown in the following table: ' ' _ PARAMETER IndoorConc[AGE] 0.03 TWA[AGE] 0.03 0.03 0.03 0.04 0.04 0.04 0.04 INAIR[AGE] 0.11 0.19 0.21 0.21 0.29 0.29 DEFAULT VALUE . - (ig/m3 1-7 3 (ig/m3 1 6 (ig/m3 9 (ig/m3 2 (ig/m3 2 (ig/m3 2 (ig/m3 2 (ig/m3 0.07 (ig/day (ig/day (ig/day (ig/day (ig/day (ig/day (ig/day . AGE INTERVAL . . (year), . 2 3 4 5 6 7 1 2 3 4 5 6 7 ------- 25 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN Parameter Values for Diet The default values for the lead intake rate from diet are shown in the following table: PARAMETER / INDIET[AGE] (Direct specification) INDIETfAGE]1 (Alternative diet specification) DEFAULT VALUE 4ซ%f) 2.26 1.96 2.13 2.04 1.95 2.05 2.22 2.26 1.96 2.13 2.04 1.95 2.05 2.22 AGE INTERVAL ifear)/ 1 2 3 4 5 6 7 1 2 3 4 5 6 7 The model assumes no consumption of game animal meat, fish, home-grown vegetables or home-grown fruit unless specified by the user. ------- 26 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN Parameter Values for Water Using the default values for water_consumption[AGE] and constant_water_conc results in the default values shown in the following table: PARAMETER ' '/ INWATER[AGE] (Direct Specification) INWATER[AGE] (Alternative Water Model) DEFAULT VALUE / difftftg)/ 0.80 2.00 2.08 2.12 2.20 2.32 2.36 0.77 1.92 2.00 2.04 2.12 2.23 2.27 AGE INTERVAL ^ / * / - tyeJjr) 1 2 3 4 5 6 7 1 2 3 4 5 6 7 ------- 27 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN Parameter Values for Soil Using the default values for constant_soil_conc[AGE], soil_ingested[AGE], and weight_soil results in the default values shown in the following table: ". '_'_'_ PARAMETER _' _ '_ *, Soil-derived exterior dust ingestion rate 60.7 60.7 45.0 40.5 38.2 INSOIL[AGE] 7.65 12.1 12.1 12.1 9.00 8.10 7.65 ' , DEFAULT VALUE 38.25 mg/day 60.75 mg/day 5 mg/day 5 mg/day 0 mg/day 0 mg/day 5 mg/day Mg/day 5 Mg/day 5 Mg/day 5 Mg/day Mg/day Mg/day Mg/day ,; : : v,r, vAGEINTERVAL : . , (fear)' 1 2 3 4 5 6 7 1 2 3 4 5 6 7 ------- 28 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN Parameter Values for Dust Using the default values for soil_ingested[AGE], percent_soil, and dust_indoor[AGE] results in the default values shown in the following table: ". '_'_'_ PARAMETER _' _ '_ *, DustTotal[AGE] 46.75 74.2 74.2 74.2 55.0 49.5 46.7 INDUST[AGE] 9.35 14.8 14.8 14.8 11.0 9.90 9.35 INDUSTA[AGE] 0 ' , DEFAULT VALUE mg/day 5 mg/day 5 mg/day 5 mg/day 0 mg/day 0 mg/day 5 mg/day Mg/day 5 Mg/day 5 Mg/day 5 Mg/day 0 Mg/day Mg/day Mg/day Mg/day ,; : : v,r, vAGEINTERVAL : . , (fear)' 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1-7 ------- 29 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN Parameter Values for Alternative Dust The default values for the alternative dust module are as shown in the following table: ' . PARAMETER - DustTotal[AGE] 46.75 74.2 74.2 74.2 55.0 49.5 46.7 soil_indoor[AGE] INDUST[AGE] 8.42 13.3 13.3 13.3 9.90 8.91 8.42 INDUSTA[AGE] 0 'DEFAULT VALUE' mg/day 5 mg/day 5 mg/day 5 mg/day 0 mg/day 0 mg/day 5 mg/day 150 |ig/g (ig/day 7 (ig/day 7 (ig/day 7 (ig/day Mg/day (ig/day (ig/day (ig/day AGE INTERVAL- . ', ' * (year) ,; 1 2 3 4 5 6 7 1-7 1 2 3 4 5 6 7 1-7 ------- 30 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN 2.3.2 Uptake Component The uptake component models the manner in which lead intake (lead that has entered the child's body through ingestion or inhalation) is either transferred to the child's blood plasma or eliminated from the body. The equations that govern the uptake of lead into the blood plasma are discussed in this section. As noted in the previous section describing the exposure component of the lEUBKwin model, the notation [AGE] following a parameter name indicates that the parameter changes with the age of the child. The total of the lead uptake rates is the primary input to the biokinetic component of the model. The fraction of lead intake that is actually absorbed into a child's system is known as the absorption fraction. The lEUBKwin model is structured so that the media-specific absorption fractions are constant at typical blood lead concentrations of concern. The media-specific absorption fractions include: ABSF for dietary lead absorption ABSD for dust lead absorption ABSS for soil lead absorption ABSW for drinking water lead absorption ABSO for paint chips lead absorption In the absence of saturation effects, total lead absorption is equal to the sum of media-specific absorption values where absorption from each media is equal to the intake rate multiplied by the absorption fraction for that media. This quantity is denoted AVINTAKE, and is calculated using the Equation U-2: AVINTAKE = (ABSD * INDUST[AGE]) + (ABSD * INDUSTA[AGE]) + (ABSF * INDIET[AGE]) + (ABSF * INOTHER[AGE]) + (ABSS * INSOIL[AGE]) + (ABSW * INWATER[AGE]) (U-2) To more accurately model lead uptake at higher intake rates, absorption fractions must be modified to separate non-saturable and saturable components. At doses where saturation of absorption is important, the actual uptake of lead will be less than AVINTAKE[AGE]. Lead uptake by the passive pathway is assumed to be linearly proportional to intake at all dose levels. The user parameter PAF is the fraction of the total net absorption at low intake rates that is attributable to non-saturable processes. Specifically, the lead uptake by the passive pathway is equal to: PAF * AVINTAKE[AGE] The lEUBKwin model assumes that the fraction of absorbed lead intake that is absorbed by non- saturable processes is the same for all media. At low doses, the quantity of lead absorbed by the saturable pathway is: (1-PAF) * AVINTAKE[AGE] ------- 31 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN However, at higher doses, only a certain fraction of this amount will be absorbed. The key parameter in this relationship is SATUPTAKE[AGE], which represents the level of available intake (AVINTAKE) at which the saturable pathway uptake reaches half of its maximum value. This half-saturation parameter depends on the age [AGE] of the child. The user can modify the value of SATUPTAKE[AGE] at age t = 24 months, denoted SATINTAKE2, through the GI/Bioavailability selection from the Parameter Input menu. From SATINTAKE2, the IEUBK model calculates SATUPTAKE[AGE] for all ages using Equation U-3. The parameter WTBODY(24) in the IEUBK model source code has a default value of 12.3. SATUPTAKE[MONTH] = SATUPTAKE2 * WTBODY [MONTH] WTBODY[24] (U-3) The fraction of potential saturable pathway uptake that is actually absorbed is given by: AVINTAKE[AGE] 1 + SA TUPTAKE[AGE], Thus, the amount of lead that is absorbed by saturable processes is calculated as: (i - PAFS) * A VINTAKE[AGE] 1 + AVINTAKE[AGE] ^ SATUPTAKE[AGE\) Total lead uptake from a medium is given by the sum of the active and passive components of uptake. Media-specific uptake rates are calculated using the same proportions as total intake. For example, the non-saturable uptake component for soil is given by: INSOILfAGE] *ABSS *AVS * PAFS where, PAFS = PAF for soil (see below) Whereas the saturable uptake component for soil is: (i - PAFS) * INSOIL[AGE] * ABSS * A vs ( AVINTAKE[AGE] ^ \^SATUPTAKE[AGE]} Uptake rates for other media are calculated in the same way. ------- 32 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN The absorption coefficients for each medium (diet, water, dust, paint, soil, and alternate dust) are listed in Appendix A as Equations U-la through U-lf. The saturable uptake component for each medium is assigned a unique variable name in the source code: PAFD for diet, PAFW for water, PAFD for dust and alternate dust, PAFS for soil, and PAFP for paint. The saturable uptake component for each medium is set to a constant value except for air. The absorption coefficient for air (air_absorp[AGEJ) varies with age; it is listed in Appendix A as Equation U-4. With the absorption coefficient for each medium, the total monthly lead uptake can be calculated using EquationU-5. UPTAKE[MONTH] = 30*(UPDIET[MONTH] + UP WATER [MONTH] + UPDUST[MONTH] + UPSOIL [MONTH] + UPDUSTA [MONTH] + UPOTHER[MONTH] + UP AIR[MONTH]) (U-5) where: 30 = conversion factor from daily media-specific uptakes to monthly total uptake 2.3.3 Biokinetic Component Based on the total lead uptake rate (UPTAKE[MONTH]), the biokinetic component of the lEUBKwin model calculates age-dependent lead masses in each of the body compartments (plasma-extra-cellular fluid (ECF), liver, kidney, trabecular bone, cortical bone, and other soft tissue). The concentration of lead in blood is then calculated by dividing mass of lead in the blood plasma and red blood cells by the volume of blood. The calculations in the biokinetic module occur sequentially, beginning with a determination of the volumes and weights of specific compartments in a child's body, as a function of age. Next, the transfer times of lead between the compartments and through elimination pathways are estimated. Initial compartmental lead masses and an initial blood lead concentration are calculated for a newborn child. Then successive values are calculated for the compartmental lead masses and blood lead concentration of a child at each iteration time. These calculations are performed for a child from birth to age 84 months. The equations for compartmental lead transfer times are listed in Appendix A as Equations B-la through B-lh, B-2a through B-2o, and B-2.5. Equation B-2.5, as written in lEUBKwin model source code, indicates an age-dependent array for MRBC[STEPS]. The source code was taken directly from the IEUBK model (version 0.99d); thus, lEUBKwin model results are the same as those computed from the equation as written in the IEUBK model (version 0.99d) source code. The parameter WTBODY(24) in Equations B-la through B-le has a default value of 12.3 in the model source code. For simplification purposes, storage arrays (ResCoef and ALLOMET) are used in the IEUBK model source code to store parameter and constant values in Equations B-la through B-lg, B-2a, and B-3. The exponent, 0.333, in Equations B-la through B-le is stored in the ALLOMET array. Parameters such as TBLUR(24), TBLLIV(24), TBLOTH(24), TBLKID(24), TBLBONE(24), RATFECUR, and RATOUTFEC in Equations B-la through B-lg and constants in Equations B-2a and B-3 are stored in the ResCoef array in the IEUBK model source code. The equations for blood to plasma_ECF lead mass ratio, fluid volumes and organ weights, difference equations, tissue lead masses and blood lead concentration at birth, ------- 33 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN compartmental lead masses, and blood lead concentration are B-3, B-4a through B-4d, B-5a through B-5m, B-6.5a through B-6.51, B-7a through B-7i, B-8a through B-9i, and B-lOa through B-lOc, respectively (see Appendix A). In the lEUBKwin model source code, the parameters in Equations B-8a through B-lOa are set up as vectors that store 84 monthly values. The source code computes two values for each parameter, one for the current time step and one for the previous time step. These parameters are updated at the end of each time step. The difference in the implementation of these parameters in the lEUBKwin model source code does not affect the results of the model. 2.3.4 Probability Distribution Component The fourth component of the lEUBKwin model estimates, for a hypothetical child or population of children, a plausible distribution of blood lead concentrations centered on the geometric mean blood lead concentration predicted by the model from available information about children's exposure to lead. From this distribution, the lEUBKwin model calculates the probability that children's blood lead concentrations will exceed the user-selected level of concern. Risk estimation and plotting of probability distributions requires the selection of two parameters, the blood lead level of concern (cutoff level) and the Geometric Standard Deviation (GSD). A value of 10 |ig/dL is generally used as the blood lead level of concern and 1.6 for the GSD, but other values can be selected by the user. The user should note that results obtained from this version of lEUBKwin may differ slightly from results obtained from the 0.99d version and earlier versions of lEUBKwin (versions 244 and earlier). In this version of lEUBKwin (and all versions since version 1.0 (build 245), the algorithms have been revised so that the same algorithm is used in the batch and single modes. The current version of the model uses the polynomial function. This approach is more accurate (error <10"8), more stable (i.e., it is not affected by the integration interval), and is more computationally efficient (i.e., iterative calculations are not needed to achieve a low error rate). ------- 34 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN P(X) = 1 - Z(x](blt + b2t2 + b/ + b4t4 + b5t5}+- E (x) In (PbBcutoff)-]n(GM) __ 1 Ifx< 0 then P (cutoff) = 1 P(x) Ifx> 0 then P (cutoff) = P(x) where: (x)< 7.510'8 (error) p = 0.2316419 bi = 0.319381530 b2 =-0.356563782 b3 = 1.781477937 b4 =-1.82125578 b5 = 1.330274429 ------- 35 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN 3.0 Software Detail Design The detailed design of the lEUBKwin model is presented in this section. For each component and its associated modules, the inputs, processing in terms of calculations, and outputs are presented in table form. 3.1 OVERALL DESIGN DESCRIPTION To design the lEUBKwin model, a series of menus was created from which the user can select screens for input of specific values appropriate to the situation that is being modeled. In general, the inputs, processing, and outputs are similar for all the model componentsExposure, Uptake, Biokinetic, and Probability Distribution. The inputs are values entered by the user or passed from the previous component. The processing performed is the solving of the algorithm for the particular component using the calculations identified in the requirements section (as determined by scientific research). The output is the values passed to the following component, used as input to the graphing routine, or the graph itself. 3.1.1 Local Data The model uses local data only when the user calls up saved data as input to a graph. In addition, some of the components contain values that are coded internally, and which are accessed during the processing of algorithms. 3.1.2 Control As a standalone system, internal control of the program is not a major issue. The system is dependent on the user entering adequate, valid, and complete data; once the model runs are initiated, the model runs as designed and tested. 3.1.3 Error Handling The errors encountered by the lEUBKwin model are those relating to data input. When the user enters data that is invalid in terms of range or format, the system displays error messages which prompt the user to enter valid data. These are included in the lEUBKwin model's source code for every data input window for each model component. In addition, the lEUBKwin model displays a warning message in the model output when the predicted blood lead concentration exceeds 30 |ig/dL, the calibrated and empirical validation limit for predicted blood lead (Zaragoza, L. and Hogan, K., 1998. The Integrated Exposure Uptake Biokinetic Model for Lead in Children: Independent Validation and Verification. ------- 36 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN Environmental Health Perspectives 106 (supplement 6): 1555). However, empirical validation of the model did not address situations where the predicted blood lead concentration exceeds 30 |ig/dL; therefore, such results must be interpreted with caution. 3.1.4 Data Conversion In the lEUBKwin model, all parameters are allowed to be entered to six digits. All output values of the float type are controlled at 3 significant digits after the decimal except for blood lead concentration which is controlled to one significant figure after decimal point. 3.1.5 Test Structure The testing structure for the lEUBKwin model is described in section 4.0. 3.1.6 Manual Procedures The lEUBKwin model has a significant number of manual procedures simply because it is designed as a Windows system. The manual procedures include using the computer's mouse to select menus and to make selections from those menus. Once the selection has been made, the user must use the mouse and keyboard to input the required data. For saving results to a file, or identifying a previous results file as input to a graph, the user is prompted to enter the appropriate filenames. Output data from the batch mode runs are ASCII files that can be loaded into almost any statistical analysis package or spreadsheet program that the user may want to use. The lEUBKwin batch mode output files will require little or no editing before being imported into other programs, unless the missing value code () is incompatible with the user's package. It is recommended that the user apply a variety of graphical and statistical techniques in evaluating the output of batch mode model runs. 3.2 EXPOSURE COMPONENT The various media exposure modules are presented in the following subsections. For each exposure module, the inputs are listed along with descriptions of the sequential functions that occur in processing. ------- 37 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN 3.2.1 Air Lead Exposure Module Inputs (from the Air Data Window): air_absorp[0], air_absorp[l], air_absorp[2], air_absorp[3], air_absorp[4], air_absorp[5], air_absorp[6], time_out[0], time_out[l], time_out[2], time_out[3], time_out[4], time_out[5], time_out[6], vent_rate[0], vent_rate[l], vent_rate[2], vent_rate[3], vent_rate[4], vent_rate[5], vent_rate[6], air_concentration[0], air_concentration[l], air_concentration[2], air_concentration[3], air_concentration[4], air_concentration[5], air_concentration[6], indoorpercent ClassName.Function CAir.Check_Data_Valid() CAir.UpdateDataQ CAir.Air_TakeData() CAir.Calc_INAIRO CAir.Write_Data_File() Description Checks whether input data is within the acceptable range. If not, the user is prompted that invalid data was entered and to try again. Updates and stores data temporarily in a file called "Air.tmp." UpdateDataQ takes the user input data to the application. Opens and reads data from "Air.tmp" or "Air.inp." The file "Air.inp" stores default values for each of the variables listed under Inputs. Numeric values for air absorpfO], air absorpfl], air absorp[2], air absorp[3], air absorp[4], air_absorp[5], air_absorp[6], time_out[0], time_out[l], time_out[2], time_out[3], time_out[4], time out[5], time out[6], vent rate[0], vent ratefl], vent rate[2], vent rate[3], vent rate[4], vent rate[5],vent rate[6], air concentrationfO], air concentration]!], air concentration[2], air_concentration[3], air_concentration[4], air_concentration[5], and air_concentration[6] are stored in the following arrays: air absorp [AGE], time out[ AGE], vent ratefAGE], and air_concentration[AGE] . Calculates rNAIR[AGE] using Equations E-l through E-3. Writes input data to a temporary file. ------- 38 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN 3.2.2 Dietary Lead Exposure Module Inputs (from the Dietary Data Window): diet_intake[0], diet_intake[l], diet_intake[2], diet_intake[3], diet_intake[4], diet_intake[5], diet_intake[6], YesNo_AltemativeDiet, UserFishConc, userFishFracPercent, UserFruitConc, userFruitFracPercent, UserGameConc, userGameFracPercent, UserVegConc, userVegFracPercent, userFishFraction, userVegFraction, userFruitFraction, userGameFraction Class Name.Function CDiet. Check_Data_Valid() CDiet-UpdateDataQ CDiet.Diet_TakeData() CDiet.Calc_INDIETO CDiet. Write_Data_FileO Description Checks whether input data is within the acceptable range. If not, the user is prompted that invalid data was entered and to try again. Updates and stores data temporarily in a file called "Diet.tmp." UpdateDataQ takes the user input data to the application. Percent values for userFruitFracPercent, userGameFracPercent, userFishFracPercent, and userVegFracPercent are converted to their decimal fraction equivalent. Opens and reads data from "Diet.tmp" or "Diet.inp." The file "Diet.inp" stores default values for each of the variables listed under Inputs. Numeric values for m diet intakefO], diet intakefl], diet intake[2], diet intake[3], diet_intake[4], diet_intake[5], and diet_intake[6] are stored in the array diet_intake[AGE]. Calculates INDIETfAGE] whose value depends on the value of YesNo AltemativeDiet. If YesNo AlternativeDiet=0, INDIET[AGE] is calculated using Equation E-4a; otherwise, INDIET[AGE] is calculated using Equations E-4b and E-5d through E-51. Writes input data to a temporary file. ------- 39 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN 3.2.3 Water Lead Exposure Module Inputs (from the Water Data Window): constant_water_conc, water_consumption[0], water_consumption[l], water_consumption[2], water_consumption[3], water_consumption[4], water_consumption[5], water_consumption[6], FirstDrawConc, HomeFlushedConc, FountainConc, FirstDrawPercent, FountainPercent, FountainFraction, FirstDrawFraction, YesNo AltemativeWater. Class Name.Function C Water. Check_Data_ValidQ CWater.UpdateDataQ CWater.Water_TakeData() CWater. Calc_INWATERO CWater.Write_Data_File() Description Checks whether input data is within the acceptable range. If not, the user is prompted that invalid data was entered and to try again. Updates and stores data temporarily in a file called "Water.tmp." UpdateDataQ takes the user input data to the application. Percent values for FirstDrawPercent and FountainPercent are converted to their decimal fraction equivalent. Opens and reads data from "Water.tmp" or "Water.inp." The file "Water.inp" stores default values for each of the variables listed under Inputs. Numeric values for water_consumption[0], water_consumption[l], water consumption[2], water consumption[3], water consumption[4], water_consumption[5], and water_consumption[6] are stored in the array water consumptionfAGE]. Calculates INWATER[AGE] whose value depends on the value of YesNo_AlternativeWater. If YesNo_AltemativeWate r= 0, INWATER[AGE] is calculated using Equation E-6a; otherwise, INWATER[AGE] is calculated using Equations E-6b and E-7. Writes input data to a temporary file. ------- 40 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN 3.2.4 Soil/Dust Lead Exposure Module Inputs (from the Soil/Dust Window): weight_soil, soil_indoor[0], soil_indoor[l], soil_indoor[2], soil_indoor[3], soil_indoor[4], soil_indoor[5], soil_indoor[6], soil_content[0], soil_content[l], soil_content[2], soil_content[3], soil_content[4], soil_content[5], soil_content[6], soil_ingested[0], soil_ingested[l], soil_ingested[2], soil_ingested[3], soil_ingested[4], soil_ingested[5], soil_ingested[6], contrib_percent, multiply_factor, OtherConc, OtherFraction, SchoolConc, SchoolFraction, SecHomeConc, SecHomeFraction, DaycareConc, DaycareFraction, OccupConc, OccupFraction, AvgMultiSrc, HouseFraction, constant_soil_conc[0], constant_soil_conc[l], constant_soil_conc[2], constant_soil_conc[3], constant_soil_conc[4], constant_soil_conc[5], constant_soil_conc[5], constant_dust_conc[0], constant_dust_conc[l], constant_dust_conc[2], constant_dust_conc[3], constant_dust_conc[4], constant_dust_conc[5], constant_dust_conc[6], air_concentration[0], air_concentration[l], air_concentration[2], air_concentration[3], air_concentration[4], air_concentration[5], air_concentration[6], const_outdoor_soil, const_indoor_dust, dust_indoor[0], dust_indoor[l], dust_indoor[2], dust_indoor[3], dust_indoor[4], dust_indoor[5], dust_indoor[6], vary_indoor, vary_outdoor Class Name. Function CSoil. Check_Data_Valid() CSoiLUpdateDataQ CSoil. Soil_TakeData() CSoil. CalcJNSOILQ CSoil. Write_Data_FileO CSoil. GetExtraDataQ CSoil. MSA_TakeData() Description Checks whether input data is within the acceptable range. If not, the user is prompted that invalid data was entered and to try again. Updates and stores data temporarily in a file called "Soil.tmp." UpdateDataQ takes the user input data to the application. Percent values for DaycareFracPercent, OccupFracPercent, OtherFracPercent, SchoolFracPercent, SecHomeFracPercent, and HouseFracPercent are converted to their decimal fraction equivalent. Opens and reads data from "Soil.tmp" or "Soil.inp." The file "Soil.inp" stores default values for each of the variables listed under Inputs. Numeric values for soil indoorfO], soil indoorfl], soil indoor[2], soil indoor[3], soil_indoor[4], soil_indoor[5], soil_indoor[6], soil_content[0], soil_content[l], soil content[2], soil content[3], soil content[4], soil content[5], soil content[6], soil ingestedfO], soil ingestedfl], soil ingested[2], soil ingested[2], soil ingested[3], soil_ingested[4], soil_ingested[5], and soil_ingested[6] are stored in the following arrays: soil indoorf AGE], soil contentf AGE], and soil ingestedfAGE] . Calculates INSOIL[AGE], INDUST[AGE], and INDUSTA[AGE] whose values depend on the values of m_altsrc, vary_indoor, vary_outdoor. Writes input data to a temporary file. Takes data from the air module and MSA. Takes data from the MSA. ------- 41 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN 3.2.5 Maternal Lead Exposure Module Inputs (from the Maternal Data Window): PBBLDMAT Class Name.Function CMaternal. Check_Data_ValidQ CMaternaLUpdateDataO CMaternal. Maternal_TakeDataQ CMaternal. Write_Data_File() Description Checks whether input-data is within the acceptable range. If not, the that invalid data was entered and to try again. Updates and stores data temporarily in a file called "Matemal.tmp." takes the user input data to the application. user is prompted UpdateDataQ Opens and reads data from "Matemal.tmp" or "Maternal.inp." The file "Maternal. inp" stores default values for each of the variables listed under Inputs. Writes input data to a temporary file. 3.2.6 Other Lead Exposure Module Inputs (from the Alternate Source Data Window): other_intake[0], other_intake[l], other_intake[2], other_intake[3], other_intake[4], other_intake[5], other_intake[6]. Class Name.Function COther.Check_Data_Valid() COther.UpdateDataO COther.Other_TakeDataQ COther.Write_Data_FileQ Description Checks whether input data is within the acceptable range. If not, the user is prompted that invalid data was entered and to try again. Updates and stores data temporarily in a file called "Other. tmp." UpdateDataQ takes the user input data to the application. Opens and reads data from "Other.tmp" or "Other.inp." The file "Other.inp" stores default values for each of the variables listed under Inputs. Numeric values for other_intake[0], other_intake[l], other_intake[2], other_intake[3], other intake[4], other intake[5], and other intake[6] are stored in the array other_intake|AGE]. Writes input data to a temporary file. ------- 42 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN 3.2.7 GI/Bioavailability Module Inputs (from the Alternate Source Data Window): ABSD Percent, ABSF Percent, ABSO Percent, ABSS Percent, ABSW Percent, PAFs, SATINTAKE2. Class Name.Function CGiBio.Check_Data_Valid() CGiBio.UpdateDataO CGiBio.Other_TakeData() CGiBio.Write_Data_FileQ Description Checks whether input data is within the acceptable range. If not, the user is prompted that invalid data was entered and to try again. Updates and stores data temporarily in a file called "GiBio.tmp." UpdateDataQ takes the user input data to the application. Opens and reads data from "GiBio.tmp" or "GiBio.inp." The file "GiBio.inp" stores default values for each of the variables listed under Inputs. Writes input data to a temporary file. 3.3 UPTAKE COMPONENT The inputs to the Uptake component are listed below along with a description of the function that occurs in the model processing. Inputs: These variables were derived from the Exposure Component of the model: INAIR[AGE], INSOIL[AGE], INDUST[AGE], INDUSTA[AGE], INWATER[AGE], INDIET[AGE], INOTHER[AGE], PBBLDMAT ClassName.Function BaseComp.Calc_UPTAKE() Description Calculates the values forUPAIR[MONTH], UPDIET[MONTH], UPDUST[MONTH], UPDUSTA[MONTH], UPSOIL [MONTH], UPWATER[MONTH], UPOTHER[MONTH], and UPTAKE[MONTH] using Equations U-la through U-lf, U-2, U-3,U-4,andU-5. 3.4 BIOKINETIC COMPONENT The inputs to the Biokinetic component are listed below along with a description of the function that occurs in the model processing. Inputs: This variable was derived from the Uptake Component of the model: UPTAKE[MONTH] Class Name.Function Description BaseComp.Calc_Biokinetic() Calculates the lead masses in each body compartments (MPLECF[2], MPLASM[2], MRBC[2], MLIVER[2], MKIDNEY[2], MOTHER[2], MTRAB[2], and MCORT[2]) using the difference equations B-6.5a through B-6.5i and intermediate equations B-la through B-lh, B-2a through B-2o, B-2.5, B-3, B-4a through B-4d, B-5a through B-5m, B- 6.5a through B-6.5i, B-7a through B-7i, B-8a through B-8d, B-9a through B-9i, and B-lOa through B-lOc. ------- 43 SYSTEM REQUIREMENTS AND DESIGN FORTHEIEUBKWIN 4.0 Documentation for the lEUBKwin Several documents are required as documentation for the lEUBKwin model. The System Requirements and Design is designed for use by programmers. By contrast, The User's Guide will be widely used by end users of the lEUBKwin model. The system documentation for the lEUBKwin model includes the following: System Requirements and Design Specifications Complete printout of the IEUBK model source code Data Crosswalk These documents were prepared according to the OSWER System Life Cycle Management Guidance (April 1988) and CMMI (Level 3). The audience for these documents will be programmers. The purpose of these documents was to demonstrate that the receding of the IEUBK model was performed correctly and to document the receding effort to satisfy challenges, questions, and concerns from Congress as well as PRP litigation. The system documentation will also be an important reference for the future in the event that enhancements to the lEUBKwin model are necessary. Changes to the lEUBKwin model may occur because of changes in the scientific understanding that affect equations or defaults in the current model source code (e.g., the changes to variable values that prompted the development of lEUBKwin version 1.1). The detailed design documentation will assist future designers and programmers with system maintenance by clearly defining the current system requirements and technical design. ------- APPENDIX A EQUATIONS AND PARAMETERS IN THE lEUBKwin MODEL ------- This page intentionally left blank. ------- The parameters and equations presented here are not a line by line documentation of the lEUBKwin model source code. Although most of the symbols and notations are identical to the model source code, some notations may differ but are mathematically equivalent. The equations and parameters presented in this document have been simplified for clarity. All the equations, with the exception of those listed below, were taken from the Technical Support Document (TSD): Parameters and Equations Used in the Integrated Exposure Uptake Biokinetic (IEUBK) Model for Lead in Children (v 0.99d) [December 1994]. The TSD (December 1994) is an update of the TSD (July 1994) and was prepared and reviewed by the Technical Review Workgroup for Metals and Asbestos (TRW). Appendix A consists of three tables which contain the equations used in the lEUBKwin model. Exposure equations are listed in Table A-l. Tables A-2 and A-3 contain the equations for the uptake and biokinetic components, respectively. Within each table, similar equations or equations which combine to achieve a common purpose are grouped together. For example, in Table A-l, the equation groups are defined by the different environmental media. ------- TABLE A-l. EQUATIONS OF THE EXPOSURE MODEL COMPONENT GROUP Air Lead Dietary Lead NUMBER E-l E-2 E-3 E-4a or E-4b E-4c EQUATION IndoorConc[AGE] = 0.01 * indoorpercent * air_concentration[AGE] TWA[AGE] = [time_out[AGEJ* air_concentration[AGEJ]+ [(24 - time_out[AGE]) * IndoorConc[AGE]] 24 INAIR[AGE] = TWA[AGE] * vent_rate[AGE] INDIET[AGE] = diet_intake[AGE] or INDIET[AGE] = DietTotal[AGE] = InOtherDiet[AGE]+ InMeat[AGE] + InGame[AGE] + InFish[AGE] + InCanVeg[AGE] + InFrVeg[AGE] InHomeVeg[AGE] + InCanFrait[AGE] + InFrFruit[AGE] + InHomeFrait[AGE] InOtherDiet[AGE] = InDairy[AGE] + InJuice[AGE] + InNuts[AGE] + InBread[AGE] + InPasta[AGE] + InBeverage[AGE] + InCandy[AGE] InSauce[AGE] + InFormula[AGE] + InInfant[AGE] Note: Italicized variables are not parameters in the model. These variables are only intermediate variables. [AGE] = 0-7 years; [MONTH] = 0-84; [NS] = iteration period expressed as a fraction of one day; [STEPS] = The time step is selected by the user. It is used in the biokinetic component of the model in combination with compartmental transfer times to calculate the distribution of lead among bodily tissues. A-4 ------- TABLE A-l. EQUATIONS OF THE EXPOSURE MODEL COMPONENT GROUP Dietary Lead (continued) NUMBER E-4d E-4e E-4f E-4g E-4h E-4i E-4J E-4k E-41 E-4m E-4n E-4o E-4p E-4q E-4r E-5a E-5b E-5c EQUATION beverage [AGE] = beverageConc * beverage_Consump[AGE] bread[AGE] =breadConc * bread_Consump[AGE] can_fruit[AGE] = canFruitConc * canFruit_Consump[AGE] can_veg[AGE] = canVegConc * CanVeg_Consump[AGE] candy [AGE] = candyConc * candy_Consump[AGE] dairy[AGE] = dairyConc * dairy_Consump[AGE] f_fruit[AGE] = fFraitConc * fFrait_Consump[AGE] f_veg[AGE] =lYegConc * lYeg_Consump[AGE] formula[AGE] = formulaConc * formula_Consump[AGE] infant[AGE] = infantConc * infant_Consump[AGE] juices[AGE] =juiceConc * juice_Consump[AGE] meat[AGE] = meatConc * meat_consump[AGE] or meat_Consump[AGE] nuts[AGE] =nutsConc * nuts_Consump[AGE] pasta[AGE] = pastaConc * pasta_Consump[AGE] sauce [AGE] = sauceConc * sauce_Consump[AGE] meatFraction = 1 - userFishFraction - userGameFraction vegFraction = 1 - userVegFraction fruitFraction = 1 - userFruitFraction Note: Italicized variables are not parameters in the model. These variables are only intermediate variables. [AGE] = 0-7 years; [MONTH] = 0-84; [NS] = iteration period expressed as a fraction of one day; [STEPS] = The time step is selected by the user. It is used in the biokinetic component of the model in combination with compartmental transfer times to calculate the distribution of lead among bodily tissues. A-5 ------- TABLE A-l. EQUATIONS OF THE EXPOSURE MODEL COMPONENT GROUP Dietary Lead (continued) NUMBER E-5d E-5e E-5f E-5g E-5h E-5i E-5J E-5k E-51 E-5m E-5n E-5o E-5p E-5q E-5r E-5s E-5t E-5u E-5v EQUATION InMeat[AGE] = meatFraction * meat[AGE] InCanVeg[AGE] = vegFraction/2 * can_veg[AGE] InFrVeg[AGE] = vegFraction/2 * f_veg[AGE] InCanFrait[AGE] = fraitFraction/2 * can_frait[AGE] InFrFrait[AGE] = fraitFraction/2 * f_frait[AGE] InHomeFrait[AGE] = userFraitFraction * (canFrait_Consump[AGE] + fFrait_Consump [AGE]) * UserFraitConc InHomeVeg[AGE] = userVegFraction * (canVeg_Consump[AGE] + fVeg_Consump[AGE]) * UserVegConc InFish[AGE] = userFishFraction * meat_consump[AGE] * UserFishConc InGame[AGE] = userGameFraction * meat_consump[AGE] * UserGameConc InDairy[AGE] = Dairy[AGE] InJuice[AGE] = Juices [AGE] InNuts[AGE] = Nuts[AGE] InBread[AGE] = Bread[AGE] InPasta[AGE] = Pasta[AGE] InBeverage[AGE] = Beverage[AGE] InCandy[AGE] = Candy[AGE] InSauce[AGE] = Sauce[AGE] InFormula[AGE] = Formula[AGE] Mnfant[AGE] = Infant[AGE] Note: Italicized variables are not parameters in the model. These variables are only intermediate variables. [AGE] = 0-7 years; [MONTH] = 0-84; [NS] = iteration period expressed as a fraction of one day; [STEPS] = The time step is selected by the user. It is used in the biokinetic component of the model in combination with compartmental transfer times to calculate the distribution of lead among bodily tissues. A-6 ------- TABLE A-l. EQUATIONS OF THE EXPOSURE MODEL COMPONENT GROUP NUMBER EQUATION Water Lead E-6a INWATER[AGE] = water_consumption[AGE] * constant_water_conc or E-6b or INWATER[AGE] = water_consumption[AGE] * (HomeFlushedConc * HomeFlushedFraction + FirstDrawConc * FirstDrawFraction + FountainConc * FountainFraction) E-7 HomeFlushedFraction = 1 - FirstDrawFraction - FountainFraction Soil Lead E-8a INSOIL[AGE] = constant_soil_conc[AGE] * soil_ingested[AGE] * (0.01 * weight_soil) or or E-8b INSOIL[AGE] =soil_content[AGE]* soil_ingested[AGE] * (0.01 * weight_soil) Dust Lead E-9a INDUST[AGE] = constant_dust_conc[AGE] * soil_ingested[AGE] * (0.01 * (100 - weight_soil)) E-9b INDUST[AGE] = DustTotal[AGE] * soil_indoor[AGE] * HouseFraction E-9c INDUSTA[AGE] = OCCUP[AGE] + SCHOOL[AGE] + DAYCARE[AGE] + SECHOME[AGE] + OTHER[AGE] E-9d INDUST[AGE] = soil_indoor[AGE] * soil_ingested[AGE] * (0.01 * (100 - weight_soil)) E-9e INDUST[AGE] = dust_indoor[AGE] * soil_ingested[AGE] * (0.01 * (100 - weight_soil)) E-9.5 HouseFraction = 1 (OccupFraction - SchoolFraction - DaycareFraction - SecHomeFraction OtherFraction) E-10 DustTotal[AGE] = soil_ingested[AGE] * (0.01 * (100 - weight_soil)) E-l la soil_indoor[AGE] = (contrib_percent *soil_content[AGE]) + (multiply_factor * air_concentration[AGE]) E-l Ib soil_indoor[AGE] = (contrib_percent * constant_soil_conc[AGE]) + (multiply_factor * air_concentration[AGE]) E-l Ic soil_indoor[AGE] = dust_indoor[AGE] E-l Id soil_indoor[AGE] = constant_dust_conc[AGE] Note: Italicized variables are not parameters in the model. These variables are only intermediate variables. [AGE] = 0-7 years; [MONTH] = 0-84; [NS] = iteration period expressed as a fraction of one day; [STEPS] = The time step is selected by the user. It is used in the biokinetic component of the model in combination with compartmental transfer times to calculate the distribution of lead among bodily tissues. A-7 ------- TABLE A-l. EQUATIONS OF THE EXPOSURE MODEL COMPONENT GROUP NUMBER EQUATION Dust Lead E-12a OCCUP[AGE] = DustTotal[AGE] * OccupFraction * OccupConc E-12b SCHOOL[AGE] = DustTotal[AGE] * SchoolFraction * SchoolConc E-12c DAYCARE[AGE] = DustTotal[AGE] * DaycareFraction * DaycareConc E-12d SECHOME[AGE] = DustTotal[AGE] * SecHomeFraction * SecHomeConc E-12e OTHER[AGE] = DustTotal[AGE] * OtherFraction *OtherConc Note: Italicized variables are not parameters in the model. These variables are only intermediate variables. [AGE] = 0-7 years; [MONTH] = 0-84; [NS] = iteration period expressed as a fraction of one day; [STEPS] = The time step is selected by the user. It is used in the biokinetic component of the model in combination with compartmental transfer times to calculate the distribution of lead among bodily tissues. A-8 ------- TABLE A-2. EQUATIONS OF THE UPTAKE MODEL COMPONENT GROUP NUMBER EQUATION Absorption Coefficients, Passive Uptakes Dust Lead (continued) U-la U-lb U-lc U-ld U-le Note: In calculating uptake, first, medium-specific passive uptakes are calculated using equations Ula-Ulf, then, the medium-specific passive uptake values are updated with the inclusion of the active uptake contribution using equations Ulg-Ull. UPDIET[MONTH]=PAFF*ABSF*AVF*INDIET[AGE] UPWATER[MONTH]=PAFW*ABSW*AVW*INWATER[AGE] UPDUST[MONTH]=PAFD*ABSD*AVD*INDUST[AGE] UPDUSTA[MONTH]=PAFD*ABSD*AVD*INDUSTA[AGE] UPSOIL[MONTH]=PAFS*ABSS*AVS*INSOIL[AGE] Absorption Coefficients, Active Uptakes Dust Lead (continued) U-lg U-lh UPDIET [MONTH 1- UPDIET [MONTH 1 , (l ~ PAFF)* ABSF * AW * INฐIET [AฐE] Ul DIL 1 [MON 1 II J Ul DIL I [MON I II J 1 ^ AVINTAKE [MONTH J |_ SATUPTAKE [MONTH ] J UTW'TEP [HONTIll UTW'TEP [HONTIll , (!-pAFW)*ABSW *AVW *INWATER[AGE] L J L J AVINTAKE MONTH 1 i L SATUPTAKE [MONTH ] J Note: Italicized variables are not parameters in the model. These variables are only intermediate variables. [AGE] = 0-7 years; [MONTH] = 0-84; [NS] = iteration period expressed as a fraction of one day; [STEPS] = The time step is selected by the user. It is used in the biokinetic component of the model in combination with compartmental transfer times to calculate the distribution of lead among bodily tissues. A-9 ------- TABLE A-2. EQUATIONS OF THE UPTAKE MODEL COMPONENT GROUP Total Lead Uptake NUMBER U-li U-lj U-lk U-2 U-3 U-4 U-5 EQUATION UPDU'T[MONTHl-UPDU'T[MONTHl , (1-?)* ABSD* AVD* INDUST[AGE] UPDUSILMONIHJ UPDUSI[MONIHJI j + AYINTAKEJMONTH] |_ SATUPTAKE[MONTH] J UTDUT-fMOmTll UPD^T* [MONTIll , (l ^0)* ABSD* AVD* INDUS TA[AGE] U1DU.L4MONIIIJ UIDU.MMONIIIJI ^ AVINTAKE|MONTH] |_ SATUPTAKE[MONTH] J UPซOIL[MOOTHl- UPซOIL[MONTHl i (l-pAFS)*ABSS*AVS*INSOIL[AGE] Ul uOIL|MON 1 HJ Ul uOIL[MON 1 HJ i ^ AVINTAKE[MONTHj L + SATUPTAKE[MONTH] J AVINTAKE = ABSD * INDUST[AGE] + ABSD * INDUSTA[AGE] + ABSS * INSOIL[AGE] + ABSF * INDIET[AGE] + ABSO * INOTHER[AGE] + ABSW * INWATER[AGE] r n [ WTBODY [MONTH 1 1 QATTTPTATfF ATONTTT 1 ATTTPTATfF'1 * L J [ WTBODY [24 J J UPAIR[MONTH] = air_absorp[AGE] * 0.01 * INAIR[AGE] UPTAKE[MONTH] = 30 * {(UPDIET[MONTH] + UPWATER[MONTH] + UPDUST[MONTH] + UPSOIL[MONTH] + UPDUSTA[MONTH] + UPOTHER[MONTH] + UPAIR[MONTH]} Note: Italicized variables are not parameters in the model. These variables are only intermediate variables. [AGE] = 0-7 years; [MONTH] = 0-84; [NS] = iteration period expressed as a fraction of one day; [STEPS] = The time step is selected by the user. It is used in the biokinetic component of the model in combination with compartmental transfer times to calculate the distribution of lead among bodily tissues. A-10 ------- TABLE A-3. EQUATIONS OF THE BIOKINETIC MODEL COMPONENT GROUP NUMBER EQUATION Compartmental Lead Transfer Times B-la B-lb B-lc B-ld B-le B-lf B-lg x r -,-.0333 f -, r -, (WTBODYlMONTHl) TPT TTT? hVfrVMTTT TPTTTPM.ll* L J ^ WTBODY|24] ) x r ,-.0333 T -, r i f WTBODYlMONTHl 1 TPT T TVIMVYMTTH TPT T TVM.ll* L J ^ WTBODY|24] ) x r -,-.0333 r -, r I f WTBODYlMONTHl 1 TPT rVTTT IVfryMTTT TPTOTTTMj.1* L J ^ WTBODY[24j ) x r ,-.0333 r -I r -I f WTBODYlMONTHl) TPT TfTH ATOTsITTT TPT Tf TH ">.! 1* L J ^ WTBODY|24] ) x r -,-.0333 r T r I f WTBODYlMONTHl ) TPT PrVNTF IVfryMTTT TPT POXTT7M A 1* L J ^ WTBODY[24j ) TBLFEC[MONTH] = RATFECUR * TBLUR[MONTH] TBLOUT[MONTH] = RATOUTFEC * TBLFEC[MONTH] Note: Italicized variables are not parameters in the model. These variables are only intermediate variables. [AGE] = 0-7 years; [MONTH] = 0-84; [NS] = iteration period expressed as a fraction of one day; [STEPS] = The time step is selected by the user. It is used in the biokinetic component of the model in combination with compartmental transfer times to calculate the distribution of lead among bodily tissues. A-ll ------- TABLE A-3. EQUATIONS OF THE BIOKINETIC MODEL COMPONENT GROUP Compartmental Lead Transfer Times (continued) NUMBER B-lh B-2a B-2b B-2c B-2d B-2e B-2f EQUATION r n r n r n (WTTRAB [MONTH 1 + WTCORT [MONTH 1} TPrปTTTPT MO>TTTT PPPrปTT7PT MO>TTTT * TPT PO>TT7 MO>TTTT * l L J L a ( VOLBLOOD [MONTH J^ L I 10 J J TPLRBC = 0. 1 TRPPPT TPT RPP* R 'XTPT PT L (0.55 + 0.73)J r i TBLUR [MONTH! TPT T TT? 1 "N irYMTT T RATBLPL r n TBLLIV[MONTH! TPT T TV > TrปrTTT L J RATBLPL TLrTL[MONTIll-CRLP'EL[MONTIll- TBLLIV[MONTH] ฑ WTLIVERfMONTH] TLI.TLLMONTIIJ CRLI .'ELLMONTIIJ ^ TBLLIv[MONTHj , VOLBLOOD[MONTH]^ [ TBLFEC[MONTH]J [ 10 J TT TVFFP FMOMTH 1 rPT R'PT rMO>ITTTl*TPTFFPrMO>ITTTl* lljlvtK [MUM IH J lLI\thC[MONlHJ CkLI\EL[MONlHJ lELtbC [MON1H J /VOLBLOOD [MQNTH ]^ LI 10 JJ Note: Italicized variables are not parameters in the model. These variables are only intermediate variables. [AGE] = 0-7 years; [MONTH] = 0-84; [NS] = iteration period expressed as a fraction of one day; [STEPS] = The time step is selected by the user. It is used in the biokinetic component of the model in combination with compartmental transfer times to calculate the distribution of lead among bodily tissues. A-12 ------- TABLE A-3. EQUATIONS OF THE BIOKINETIC MODEL COMPONENT GROUP Compartmental Lead Transfer Times (continued) NUMBER B-2g B-2h B-2i B-2j B-2k B-21 B-2m EQUATION r -i TBLKID[MONTH! RATBLPL TFTDPT fMONTHl - PP FTDRT fMONTHl * TRT FTrfMONTHl * KlUJNH ^MUJN 1 HJ imiJF4MumHj u^iiJB4MumHj iBLmqMuwmj ^VOLBLOOIjMONTH^ [I 10 JJ r -, TBLBONE[MONTH] TPT TP AP IVfryMTTT L J (0.2 * RATBLPL) TTRABPL[MONTH] = TBONEBL[MONTH] r -, TBLBONE[MONTH] TPT POP T IV f rVMTT T L J (0.8* RATBLPL) TCORTPL[MONTH] = TBONEBL[MONTH] r n TBLOTHfMONTHl TPT fYTTT ATONTTT L J RATBLPL Note: Italicized variables are not parameters in the model. These variables are only intermediate variables. [AGE] = 0-7 years; [MONTH] = 0-84; [NS] = iteration period expressed as a fraction of one day; [STEPS] = The time step is selected by the user. It is used in the biokinetic component of the model in combination with compartmental transfer times to calculate the distribution of lead among bodily tissues. A-13 ------- TABLE A-3. EQUATIONS OF THE BIOKINETIC MODEL COMPONENT GROUP NUMBER EQUATION Compartmental Lead Transfer Times (continued) B-2n TOTHPL[MONTH] = CROTHBI^MONTH]^ TBLOTH[MONTH] TBLOTH[MONTH]N TBLOUlfMONTHJ^ 1- WTOTHER[MONTH] ' VOLBLOOI^MONTHp 10 B-2o TOTHOUT[MONTH] = CROTHBL[MONTH]* TBLOUT[MONTH]- WTOTHER [MONTH] ' VOLBLOOD[MONTH] 10 B-2.5 TPLRBC2[STEPS] = TPLRBC 1- MRBC[STEPS] (VOLRBC([MONTH] -1)/ CONRBC) Blood to Plasma- ECF Lead Mass Ratio B-3 RATBLPL = 100 Fluid Volumes and Organ Weights B-4a B-4b B-4c B-4d CRKIDBL[MONTH] = 0.777 + [2.35 * {1 - exp(-0.0468*[MONTH])}] CRLIVBL[MONTH] = 1.1 + [3.5 * {1 - exp(-0.0462*[MONTH])}] CRBONEBL[MONTH] = 6.0 + [215.0 * {1 - exp(-0.000942*[MONTH])}] CROTHBL[MONTH] = 0.931 + [0.437 * {1 - exp(-0.00749*[MONTH])}] Note: Italicized variables are not parameters in the model. These variables are only intermediate variables. [AGE] = 0-7 years; [MONTH] = 0-84; [NS] = iteration period expressed as a fraction of one day; [STEPS] = The time step is selected by the user. It is used in the biokinetic component of the model in combination with compartmental transfer times to calculate the distribution of lead among bodily tissues. A-14 ------- TABLE A-3. EQUATIONS OF THE BIOKINETIC MODEL COMPONENT GROUP Fluid Volumes and Organ Weights (continued) NUMBER B-5a B-5b B-5c B-5d B-5e B-5f EQUATION r n 10.67 \7C\\ PT fWMAfrVMTTT [ ([MONTH] -6.87H 1 I rvrv' ^ [_ ( 7.09 J_ r i 4-31 \/l"~VT PP PA TOMTIT i V LmXJ3LJlVHJJN 111 1 r ff 1 \-i ' [ ([MONTH] -6.45)1 1 1 rt-rJ ^L J ' ^ i i cxp-, , [_ ( 10.0 JJ r i 6.46 VfVT PT AQAT ATONTTT j ([MONTH]-6.8l)l L L 5.74 J_ 21.86 { ([MONTH] -88. is)| L I 26-73 J J 26.47 f ([MONTH]- 129.6 i)J 1 , r-T,J ^L J 'I i I cxp-, [ [ 25.98 J J 8.83 f ([MONTH] -65.66)1 i , r,,nj ^L j 'i 1 I cxp-, , i 23.62 JJ VOLECF[MONTH] = 0.73 * VOLBLOOD[MONTH] [~l V O-Lj-D-LjOO-OIJVlO-N 1 rd 1 J 10 WTPOTWrMONTHl 8'375 I 11.261 1 J n f ([MONTHJ-3.80)1 [ ([MONTH J- 48. 76)1 L [ 3.60 JJ L [ 20.63 JJ Note: Italicized variables are not parameters in the model. These variables are only intermediate variables. [AGE] = 0-7 years; [MONTH] = 0-84; [NS] = iteration period expressed as a fraction of one day; [STEPS] = The time step is selected by the user. It is used in the biokinetic component of the model in combination with compartmental transfer times to calculate the distribution of lead among bodily tissues. A-15 ------- TABLE A-3. EQUATIONS OF THE BIOKINETIC MODEL COMPONENT GROUP Fluid Volumes and Organ Weights (continued) NUMBER B-5g B-5h B-5i B-5J B-5k B-51 EQUATION WTBONE[MONTH] =0.111* WTBODY[MONTH] [MONTH] <12 months = 0.838 + 0.02 * [MONTH] [MONTH] >12 months WTCORT = 0.8*WTBONE[MONTH] WTTRAB = 0.2*WTBONE[MONTH] WTT^ TFiMF vri\/TfYNJTT-M WTT TVT7T? I'lV/mTJT'P'l 0.050 f ([MONTH! -5.24)] f ([is i , ) M. J /( i ) M. 1 4.24 \\ [_ ( 0.261 f ([MONTH! -9.82)] 1 _l_ r-TT-n > ^L J * * 1 _l_ / t-r { 3.67 JJ [_ 0.106 /IONTH]-65.37)| 34.11 JJ 0.584 [ ([MONTH]- 55. 6s)| 1 37.64 jJ WTOTHER[MONTH] = WTBODY[MONTH] - WTKIDNEY[MONTH] B-5m WTBLOOD[MONTH] - WTLIVER[MONTH] - WTTRAB[MONTH] - WTCORT[MONTH] - WTBLOOD[MONTH] - WTECF[MONTH] VOLBLOOD[MONTH! 1 0% * L J 10 NOTE: The following equations (B-6a to B-61) represent the correct mathematical specification. These differential equations are translated into difference equations employing the backward Euler solution in the series B-6.5a to B-6.51 (an algebraic rearrangement presented for ease of interpretation). The calculations are shown in B-9a B9i. Compartmental Lead Masses (Differential Equations) Note: Italicized variables are not parameters in the model. These variables are only intermediate variables. [AGE] = 0-7 years; [MONTH] = 0-84; [NS] = iteration period expressed as a fraction of one day; [STEPS] = The time step is selected by the user. It is used in the biokinetic component of the model in combination with compartmental transfer times to calculate the distribution of lead among bodily tissues. A-16 ------- TABLE A-3. EQUATIONS OF THE BIOKINETIC MODEL COMPONENT GROUP Compartmental Lead Masses (Differential Equations) (continued) INFL NUMBER B-6a B-6b EQUATION dMPLECF(STEPS)/dt = UPTAKE(STEPS) + INFLOW(STEPS) - OUTFLOW(STEPS) / x MLIVERfsTEPsl MKIDNEYfsTEPsl MOTHER(sTEPs) MTRAB(sTEPs) MCORlfsTEPsl MRBcfsTEPsl OTilOTFP^I _i_ _i_ _i_ _i_ _i_ WVฐ1L1ฐ/- r 1+ r 1+ r 1+ r 1+ r 1 + TLIVPL[MONTHJ TKIDPL[MONTH| TOTHPL[MONTHJ TTRABPL[MONTHJ TCORTPL[MONTHJ TRBCPL B-6c MPLECI[STEPs| * B-6d B-6e B-6f 1 1 1 1 1 1 i TPLUE[MONTH| TPLLI"\[MONTLJ TPLKII[MONTH| TPLOTI|MONTH| TPLTRAI|MONTH| TPLCOR|MONTH| TPLRBC2 dMRBC[STEPS] f MPLECF[STEPS] * ns^ l( ns \ dt \ TPLRBC2 }/\ ^TRBCPL) dMLIVER[STEPS] MPLECF[STEPS] r -, [ 1 1 1 MLI\rER CTEPC * I dt TPLLIV[MONTH] iV^"v^vL-^^j |^TLIVpL[MoNTrH] TLIVFEC[MONTH]J dMKIDNEY[STEPSJ MPLECp[STEPS] MKIDNEY[STEPS] dt TPLKID[MONTH] TKIDPL[MONTH] Note: Italicized variables are not parameters in the model. These variables are only intermediate variables. [AGE] = 0-7 years; [MONTH] = 0-84; [NS] = iteration period expressed as a fraction of one day; [STEPS] = The time step is selected by the user. It is used in the biokinetic component of the model in combination with compartmental transfer times to calculate the distribution of lead among bodily tissues. A-17 ------- TABLE A-3. EQUATIONS OF THE BIOKINETIC MODEL COMPONENT GROUP Compartmental Lead Masses (Differential Equations) (continued) NUMBER B-6g B-6h B-6i B-6.5a B-6.5b INFLOw[sTEPf B-6.5c MPLECF[STEPS] EQUATION dMOTHERJSTEPSl MPLECpfSTEPS] r i l~ 1 1 1 MOTHER CTEPC 1* I dt TPLOTH [MONTH] ^^^L- -j ^TOTHPL [MONTH] TOTHOUT[MONTH]J dMTRAB[STEPS] MPLECp[STEPS] MTRAB[STEPS] dt TPLTRAB[MONTH] TTRABPL[MONTH] dMCORT[sTEPs] MPLECp[sTEPs] MCORT[STEPS] dt TPLCORT[MONTH] TCORTPL [MONTH] MPLECF[STEPS]-(MPLECF[STEPS]-NS) r n r n r n L J v L J ' TTPTATtTF ATOTsJTTT i TMFT O\AHQTFPQ OTTTFT OW QTFPQ NS n MLIVER[STEPS] MKIDNE^STEPS] MOTHER[STEPS] MTRAB[STEPS] MCORT[STEPS] MRBC[STEPS] ^\ ^ ^ ^ ^ ^ 'J - r n+ r n+ r n+ r n+ r n + TLIVPL[MONTHJ TKIDPL[MONTHJ TOTHPL[MONTHJ TTRABPL|MONTH| TCORTPL[MONTHJ TRBCPL [i i i i i ill TPLUR[MONTH] TPLLIV[MONTH] TPLKID[MONTHJ TPLOTH[MONTHJ TPLTRAB[MONTHJ TPLCORT [MONTH] TPLRBC2J Note: Italicized variables are not parameters in the model. These variables are only intermediate variables. [AGE] = 0-7 years; [MONTH] = 0-84; [NS] = iteration period expressed as a fraction of one day; [STEPS] = The time step is selected by the user. It is used in the biokinetic component of the model in combination with compartmental transfer times to calculate the distribution of lead among bodily tissues. A-18 ------- TABLE A-3. EQUATIONS OF THE BIOKINETIC MODEL COMPONENT GROUP Compartmental Lead Masses (Differential Equations) (continued) NUMBER B-6.5d EQUATION MRBC[STEPS] - (MRBC[STEPS] - NS) MPLECF[STEPS] MRBC[STEPS] NS TPLRBC2 TRBCPL B-6.5e MLIVER[STEPS]-(MLIVER[STEPS]-NS) MPLECF[STEPS] ^^[0^0] J 1 , 1 NS TPLLIV[MONTH] ' "J LTLIWL[MONTHJ TLIWEC[MONTHJJ B-6.5f B-6.5g MKIDNEY[STEPS] - (MKIDNEY[STEPS] - NS) MPLECF[STEPS] MKIDNEY[STEPS] NS TPLKID[MONTH] TKIDPL[MONTH] MOTHEPJSTEPS1-(MOTHEPJSTEPS1-NS) MPLECpfsTEPsl r 1 f 1 L J V L J / LJ ATMTTTTTP IPTTTPP 1 * _L 1 MONTH] [TOTHPL [MONTH] TOTHOUT [MONTH JJ B-6.5h B-6.5i MTRAB[STEPS]-(MTRAB[STEPS]-NS) MPLECF[STEPS] MTRAB[STEPS] NS TPLTRAB[MONTH] TTRABPL[MONTH] MCORT[STEPS] - (MCORT[STEPS] - NS) MPLECF[STEPS] MCORT[STEPS] NS TPLCORT[MONTH] TCORTPL[MONTH] Note: Italicized variables are not parameters in the model. These variables are only intermediate variables. [AGE] = 0-7 years; [MONTH] = 0-84; [NS] = iteration period expressed as a fraction of one day; [STEPS] = The time step is selected by the user. It is used in the biokinetic component of the model in combination with compartmental transfer times to calculate the distribution of lead among bodily tissues. A-19 ------- TABLE A-3. EQUATIONS OF THE BIOKINETIC MODEL COMPONENT GROUP NUMBER Tissue Lead Masses and Blood Lead Concentration at Birth B-7a B-7b B-7c EQUATION NOTE: Equations B-7b, B-7c, and B-7d represent the distribution of fetal blood lead, derived from the mother's blood lead, at birth. In this simplified form, these equations are numerically equivalent to the following equations that more precisely represent the distribution of lead at birth. The difference in these two sets of equations is insignificant after 2-3 iteration steps. / / N / y. ( TPLRBC^ PPPT nn * Ivrvr PT AQATIH I_L vrvr Dppln II* XTC MPTrrrfrA ^ ' Ivll LUCr 1 U 1 . / \\ ( TRBCPL(O) ] 1 NS J f \ i i \ i \\ [ f TPLRBC(o)^~| MRRPIOI PRPJ DO * (VOT PT A'xMlO) I VOT P.RMO II* 1 04.16 [_ ^TRBCPL(0)JJ / s. MPLECF(O) A TPT AQATInl v/ 0.416 PBBLDO = 0.85 * PBBLDMAT / / \ / \\ TTPLRBC^ / s. PPPT T-jn * fvrvr PT AQATIH i_u vrvr PPPIH 11* *n 7 TTPTHI MPTrrrfrA V NS j iv ii i^ncr i u i . , ,. . f TRBCPL(O) TPLRBC 1 t NS NS J pppr T-in * 1 \^OT PT AQ"M"ini i VrVTPPPmll* ^ ' XTO ^Tprrfn^l ^ NS ; 1V1KJ3CIU 1 . , . . f TRBCPL(O) TPLRBC 1 t NS NS J Note: Italicized variables are not parameters in the model. These variables are only intermediate variables. [AGE] = 0-7 years; [MONTH] = 0-84; [NS] = iteration period expressed as a fraction of one day; [STEPS] = The time step is selected by the user. It is used in the biokinetic component of the model in combination with compartmental transfer times to calculate the distribution of lead among bodily tissues. A-20 ------- TABLE A-3. EQUATIONS OF THE BIOKINETIC MODEL COMPONENT GROUP Tissue Lead Masses and Blood Lead Concentration at Birth (continued SUMl[sTj NUMBER B-7d B-7e B-7f B-7g B-7h B-7i B-8a B-8b EQUATION / s. MPLECF(O) A TPT A Ql\ Tl O 1 v ' (1.7 - HCTO) MCORT(O) = 78.9 * PBBLDO * WTCORT(O) MKIDNEY(O) = 10.6 * PBBLDO * WTKIDNEY(O) MLIVER(O) = 13.0 * PBBLDO * WTLIVER(O) MOTHER(O) = 16.0 * PBBLDO * WTOTHER(O) MTRAB(O) = 51.2 * PBBLDO * WTTRAB(O) A T T^io^f no i IMPLECFJSTEPS - NS] + (UPTAKE[MONTH]/STEPS) + SUMS] [ i + (NS * SUMI) - (NS * SUNG)] 1 1 1 1 1 1 1 1 7PL[/ซ[A/CWm] TPLRBC2 TPLLIV\_MONTH\ TPLKID\_MONTH\ TPLOTH\_MONTH\ TPLTRAB\_MONTH\ TPLCORT\_MONTH\ Note: Italicized variables are not parameters in the model. These variables are only intermediate variables. [AGE] = 0-7 years; [MONTH] = 0-84; [NS] = iteration period expressed as a fraction of one day; [STEPS] = The time step is selected by the user. It is used in the biokinetic component of the model in combination with compartmental transfer times to calculate the distribution of lead among bodily tissues. A-21 ------- TABLE A-3. EQUATIONS OF THE BIOKINETIC MODEL COMPONENT GROUP Compartmental Lead Masses (Solution Algorithm) NUMBER B-8c B-8d EQUATION r -i 1 1 SU\f ^ 1 STEPS \ + (TRBCPL ~] r -, ( TLIVPL\MONTH] TLIVPL\MONTH] ~] TPfPRr") * i 1 77V J jTf \\ fn\TTT * L J j- L J j_ 1 V NS ) {_ NS TLIVALL[MONTH\ ) i i r -i ( TKIDPL \MONTH ^ ( TOTHPL MONTH \ TOTHPL MONTH \ ^ V NS j V NS TOTHALL j I I r n ( TTRABPL\MONTH] ^ r n ( TCORTPL\MONTH] ^ TPT TT? An\ A fD\TTTT 1 * _i_ 1 TPT fDHTl A -fD\TTTT 1 * _i_ 1 ^ AS J ^ AS J r n M?5C([STEPS1-AS') MZ/FE/?([s7EPsl- Aซ) WT/T ฐT/7Pฐ VL J / \L J / oL/A7 J[o_//i7 >j J , N /" F 1 \ 1 x\ 1 1 1 I 1 ^ -1 ' r n ' -1- ^ NS j { NS TLIVALL[MONTH\ j MKIDNEY ([STEPS] - NS) MOTHER ([sTEPs] - NS) ( TKIDPL\MONTH ^ ( TOTHPL\MONTH\ TOTHPL MONTH\ ^ j_i _L j_i V NS ) V J^ TOTHALL ) MTRAB ([STEPS ] - NS ) MCORT ([STEPS ] - NS ) (TTRABPL [MONTH ] "] (TCORTPL ([MONTH ]) ^ 1 A^S ll) ( NS ll) Note: Italicized variables are not parameters in the model. These variables are only intermediate variables. [AGE] = 0-7 years; [MONTH] = 0-84; [NS] = iteration period expressed as a fraction of one day; [STEPS] = The time step is selected by the user. It is used in the biokinetic component of the model in combination with compartmental transfer times to calculate the distribution of lead among bodily tissues. A-22 ------- TABLE A-3. EQUATIONS OF THE BIOKINETIC MODEL COMPONENT GROUP Compartmental Lead Masses (Solution Algorithm) (continued) NUMBER B-9a B-9b B-9c EQUATION i\ i \ [ r i ( NS \\ MPPPI QTTnPQ "MQ 1 _u MPT TnPF QTTnPC 1* r -, ^TPLRBC2j MPPP CLTT7PCL NS j i |_* TRBCPL] ATT TAT7!?! r^TFP0! Mil i ATPT FPFl [^TFP0! 1 * r , (TPLUV([MONTH\)J 1V1T T\/T7T? QTFPQ i, NS [ TLIVALL([MOA^777])J fr i T r i ( NS ^iTl ATKTPiMPV QTPPQ "MQ i MPT FPF QTPPQ 1* 1 I TPLKID|MONTH| J J TifFrnMTTV CLTFPCL NS j _i_ [ TKIDPL[MONTH]J Note: Italicized variables are not parameters in the model. These variables are only intermediate variables. [AGE] = 0-7 years; [MONTH] = 0-84; [NS] = iteration period expressed as a fraction of one day; [STEPS] = The time step is selected by the user. It is used in the biokinetic component of the model in combination with compartmental transfer times to calculate the distribution of lead among bodily tissues. A-23 ------- TABLE A-3. EQUATIONS OF THE BIOKINETIC MODEL COMPONENT GROUP Compartmental Lead Masses (Solution Algorithm) (continued) NUMBER B-9d B-9e B-9f B-9g B-9h EQUATION /T 1 \ /T 1\ I NS 1 ATOTTTT7D 1 1 ^TTTP*? \ XTC 1 _i_ A TDT 17^171 1 C'TTTP'? II* /r 1X I TPLOTmMCwm ) J NS i _i_ |_ TOTHALLj f\ i \ r i ( NS ^ r n I TPLTRAB MONTH J TVTriMPTlฃi1TFPr' 1 L -1 L J NS TTRABPL [MONTH] ATPfVPTf r^TPPQl Mil i ATPT FPFTlTFPll* r -. I TPLCORT[MONTH|J 1\TPORT llTFPlI NS ^ i [" ' TCORTPL [MONTH]] r -, MPLECF[STEPS]*VOLPLASM[MONTH] 1VTPT AC1VTCTFPC L J L J VOLECF[MONTH] + VOLPLASM[MONTH] i TYOTTT" -1 7" 7" lUlllALL r- - 1 1 TClTfTPT \ A/rnAfTfT \ Tr>TfTr>TTT\ AjnMTfT \ Note: Italicized variables are not parameters in the model. These variables are only intermediate variables. [AGE] = 0-7 years; [MONTH] = 0-84; [NS] = iteration period expressed as a fraction of one day; [STEPS] = The time step is selected by the user. It is used in the biokinetic component of the model in combination with compartmental transfer times to calculate the distribution of lead among bodily tissues. A-24 ------- TABLE A-3. EQUATIONS OF THE BIOKINETIC MODEL COMPONENT GROUP Compartmental Lead Masses (Solution Algorithm) (continued) Blood Lead Concentration NUMBER B-9i B-lOa B-lOb B-lOc EQUATION TT T\7A T T \<\TT7P<\\ [_TLIVPL[MONTH] TLIVFEC[MONTH]\ NOTE: Equation B-lOa is computed by a cumulative loop r n STFPS MRBCfSTEPSl + MPLASMfSTEPSl PT nnn KTFPI! blhl^b L J L J L VOLBLOOD([MONTH]-I) NS = I/iterations per day STEPS = 30 / NS = iterations per month PBBLOODEND([MONTH]) = BLOOD[STEPS]/STEPS Note: Italicized variables are not parameters in the model. These variables are only intermediate variables. [AGE] = 0-7 years; [MONTH] = 0-84; [NS] = iteration period expressed as a fraction of one day; [STEPS] = The time step is selected by the user. It is used in the biokinetic component of the model in combination with compartmental transfer times to calculate the distribution of lead among bodily tissues. A-25 ------- APPENDIX B DATA CROSSWALK FOR THE lEUBKwin MODEL ------- This page intentionally left blank. ------- The following table contains parameter names and associated values or equations for the Integrated Exposure Uptake and Biokinetic Model for Lead in Children (IEUBK). Parameter names are listed alphabetically, with corresponding model components (e.g., exposure). The parameters in italics are user inputs. These parameters are member variables (objects) of a data window in the lEUBKwin model. The values in the following table are shown with three figures after the decimal point. The lEUBKwin model output is reported to three figures after the decimal except for the blood lead concentration which is reported to one figure after the decimal point. In the lEUBKwin model, the true precision of a calculation is determined by the least precise input value. In addition, for some input parameters, the model will warn users if an input is entered which is not biologically plausible or relevant (e.g., 3 million parts per million [ppm] or -1 ppm). B-l ------- Data Crosswalk for the lEUBKwin Model Component(s) Uptake Uptake Uptake Uptake Uptake Exposure Exposure Biokinetic Uptake Uptake Exposure Exposure Uptake Uptake Uptake Uptake Exposure Exposure Exposure Biokinetic Probability Distribution Exposure Parameter Name V.I.I ABSD ABSF ABSO ABSS ABSW air_absorp[AGE] air_concentration[AGE] ALLOMET[15] AVD AW AvgHouseDust AvgMultiSrc AVINTAKE[MONTH] AWO AVS AVW beverage[AGE] bevera beverageConc beverage_Consump[AGE] BLOOD[STEPS] blood[t] blood[t] bread[AGE] V.1.0 ABSD ABSF ABSO ABSS ABSW air_absorp[AGE] air_concentration[AGE] 0.1 ALLOMET[15] AVD AW AvgHouseDust AvgMultiSrc UPPOTEN AW AVS AVW ;e[AGE] BLOOD[STEPS] bread[AGE] Equation No.(s) or Default Values V.I.I 0.300 0.500 0.000 0.300 0.500 32.000 10 0.333 1.000 1.000 150.000* 150.000 U-lg-l,U-2 1.000 1.000 1.000 E-4d 0.002109 87.993 116.487 209.677 194.982 177.061 183.333 188.710 B-10a,c None E-4e V.1.0 0.300 0.500 0.000 0.300 0.500 32.000 0.100 0.333 1.000 1.000 150.000* 150.000 U-lg-l,U-2 1.000 1.000 1.000 0.491 0.650 1.170 1.088 0.988 1.023 1.053 B-10a,c None 0.090 0.286 0.240 0.300 0.360 0.408 0.503 B-2 ------- Data Crosswalk for the lEUBKwin Model Component(s) Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Biokinetic Parameter Name V.I.I breadConc bread_Consump[AGE] Can_fruit[AGE] canFruitConc canFruit_Consump[AGE] candy [AGE] candyConc Candy _Consump[AGE] canVegConc canVeg_Consump[AGE] CONRBC V.1.0 can_fruit[AGE] candy [AGE] CONRBC Equation No.(s) or Default Values V.I.I 0.008927 4.992 15.862 13.311 16.639 19.967 22.629 27.898 E-4f 0.023873 13.941 8.183 8.145 7.691 7.236 7.460 7.906 E-4h 0.011554 9.955 11.273 32.909 24.409 16.000 14.818 12.455 0.004003 0.668 2.274 2.563 2.662 2.771 2.626 2.356 1200.000 V.1.0 1.811 1.063 1.058 0.999 0.940 0.969 1.027 0.219 0.248 0.724 0.537 0.352 0.326 0.274 1200.000 B-3 ------- Data Crosswalk for the lEUBKwin Model Component(s) Exposure Exposure Exposure Exposure Exposure Exposure Exposure Biokinetic Biokinetic Biokinetic Biokinetic Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Biokinetic Exposure Parameter Name V.I.I constant dust conc[AGE] constant indoor dust constant outdoor dust constant outdoor soil constant soil conc[AGE] constant_water_conc contrib_percent CRBONEBL[MONTH] CRKIDBL[MONTH] CRLIVBL[MONTH] CROTHBL[MONTH] Cutoff dairy [AGE] dairyConc dairy _Consump[AGE] DAYCARE[AGE] DaycareConc DaycareFraction diet_intake[AGE] DietTotal[AGE] DOTHER[0] dust_indoor[AGE] V.1.0 constant dust conc[AGE] constant indoor dust constant outdoor dust constant outdoor soil constant soil conc[AGE] constant_water_conc contrib_percent CRBONEBL[MONTH] CRKIDBL[MONTH] CRLIVBL[MONTH] CROTHBL[MONTH] Cutoff dairy [AGE] DAYCARE[AGE] DaycareConc DaycareFraction diet_intake[AGE] DietTotal[AGE] DOTHER[0] None dust_indoor[AGE] Equation No.(s) or Default Values V.I.I 200.000 200.000 200.000 200.000 200.000 4.000 0.700 B-lh,B-4c B-2h, B-4a B-2e,f, B-4b B-2n,o, B-4d 10 E-4i 0.004476 41.784 35.321 38.527 38.327 38.176 40.631 45.591 E-9c,E-12c 200.000 0.000 2.26 1.96 2.13 2.04 1.95 2.05 2.22 E-4b 200.000 V.1.0 200.000 200.000 200.000 200.000 200.000 4.000 0.700 B-lh, B-4c B-2h, B-4a B-2e,f, B-4b B-2n,o, B-4d 10 0.834 0.705 0.769 0.765 0.762 0.811 0.910 E-9c,E-12c 200.000 0.000 5.530 5.780 6.490 6.240 6.010 6.340 7.000 E-4b None 200.000 B-4 ------- Data Crosswalk for the lEUBKwin Model Component(s) Exposure Biokinetic Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Parameter Name V.I.I DustTotal[AGE] EXPR[0] f_fruit[AGE] fFruitConc fFruit_Consump[AGE] FirstDrawConc FirstDrawFraction formula[AGE] formulaConc formula_Consump[AGE] FountainConc FountainFraction fruitFraction F_veg[AGE] V.1.0 DustTotal[AGE] EXPR[0] f_fruit[AGE] FirstDrawConc FirstDrawFraction formula[AGE] FountainConc FountainFraction fruitFraction f_veg[AGE] Equation No.(s) or Default Values V.I.I E-9b,E-10, E-12a-e None E-4J 0.004462 2.495 12.540 11.196 11.196 11.452 12.988 16.059 4.000 0.500 E-41 0.002433 45.153 22.975 0.797 0.000 0.000 0.000 0.000 10.000 0.150 E-5c E-4k V.1.0 E-9b,E-10, E-12a-e None 0.039 0.196 0.175 0.175 0.179 0.203 0.251 4.000 0.500 0.340 0.173 0.006 0.000 0.000 0.000 0.000 10.000 0.150 E-5c 0.148 0.269 0.475 0.466 0.456 0.492 0.563 B-5 ------- Data Crosswalk for the lEUBKwin Model Component(s) Exposure Exposure Probability Distribution Probability Distribution Biokinetic Exposure Exposure Exposure Exposure Exposure Exposure, Uptake Exposure Exposure Exposure Exposure Exposure Exposure Exposure, Uptake Exposure Exposure Parameter Name V.I.I fVegConc fVeg_Consump[AGE] geo_mean GSD HCTO HomeFlushedConc HomeFlushedFraction HouseFraction INAIRfAGEJ InBeverage[AGE] InBread[AGE] InCandy[AGE] InCanFruit[AGE] InCanVeg[AGE] InDairy[AGE] INDIET[AGE] IndoorConc[AGE] indoorpercent V.1.0 geo_mean GSD HCTO home fruit consumpfAGE] home veg consumpfAGE] HomeFlushedConc HomeFlushedFraction HouseFraction INAIRfAGEJ InBeverage[AGE] InBread[AGE] InCandy[AGE] InCanFruit[AGE] InCanVeg[AGE] InDairy[AGE] INDIET[AGE] IndoorConc[AGE] indoorpercent Equation No.(s) or Default Values V.I.I 0.006719 8.773 15.945 28.156 27.623 27.030 29.164 33.373 None 1.000 0.000 1.000 E-3, U-4 E-4c, E-5r E-4c, E-5p E-4c, E-5s E-4b, E-5g E-4b, E-5e E-4c, E-5m E-4a,b, U-la,gU-2 E-l,E-2 30.000 V.1.0 None 1.600 0.450 38.481 69.000 63.166 61.672 61.848 67.907 80.024 56.840 106.500 155.750 157.340 158.930 172.500 199.650 1.000 0.000 1.000 E-3, U-4 E-4c, E-5o E-4c, E-5m E-4c, E-5p E-4b, E-5d E-4b, E-5b E-4c, E-5j E-4a,b, U-la,gU-2 E-l,E-2 30.000 B-6 ------- Data Crosswalk for the lEUBKwin Model Component(s) Exposure, Uptake Exposure, Uptake Exposure Exposure Exposure Exposure Biokinetic INFL Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure, Uptake Parameter Name V.I.I INDUSTA[AGE] INDUST[AGE] infant[AGE] infantConc infant_Consump[AGE] InFish[AGE] OW[STEPS] InFormula[AGE] InFrFruit[AGE] InFrVeg[AGE] InGame[AGE] InHomeFruit[AGE] InHomeVeg[AGE] InInfant[AGE] InJuice[AGE] InMeat[AGE] InNuts[AGE] INOTHER[AGE] InOtherDietfAGE]1 InOt InPasta[AGE] InSauce[AGE] INSOIL[AGE] INSOII V.1.0 INDUSTA[AGE] INDUST[AGE] infant[AGE] InHomeFish[AGE] INFLOW[STEPS] InFormula[AGE] InFrFruit[AGE] InFrVeg[AGE] InGame[AGE] InHomeFruit[AGE] InHomeVeg[AGE] Mnfant[AGE] InJuice[AGE] InMeat[AGE] InNuts[AGE] INOTHER[AGE] 0.000 ierDiet[AGE] InPasta[AGE] InSauce[AGE] ,[AGE] Equation No.(s) or Default Values V.I.I E-9c, U-ld,j,U-2 E-9a,b,e U-lc,I,U-2 E-4m 0.004047 131.767 66.905 1.634 0.000 0.000 0.000 0.000 E-4b, E-5k B-6a,b, B-6.5a,b E-4c, E-5u E-4b, E-5h E-4b, E-5f E-4b, E-51 E-4b, E-5i E-4b, E-5j E-4c, E-5v E-4c, E-5n E-4b, E-5d E-4c, E-5o E-4b,c E-4c, E-5q E-4c, E-5t E-8a,b, U-le,k,U-2 V.1.0 E-9c, U-ldj,U-2 E-9a,b,e U-lc,I,U-2 1.294 0.655 0.016 0.000 0.000 0.000 0.000 E-4b, E-5h B-6a,b, B-6.5a,b E-4c, E-5r E-4b, E-5e E-4b, E-5c E-4b, E-5i E-4b, E-5f E-4b, E-5g E-4c, E-5s E-4c, E-5k E-4b, E-5a E-4c, E-5i 0.000 E-4b,c E-4c, E-5n E-4c, E-5q E-8a,b, U-le,k,U-2 'Does not actually appear in Windows version source code. B-7 ------- Data Crosswalk for the lEUBKwin Model Component(s) Exposure, Uptake Exposure Exposure Exposure Biokinetic Biokinetic Biokinetic Exposure Exposure Exposure Exposure Parameter Name V.I.I INWATER[AGE] juices[AGE] juiceConc juice_Consump[AGE] KPLECF[0] MCORT[0] MCORT[STEPS] meat[AGE] meatConc meat_Consump[AGE] meat_Consump[AGE] V.1.0 INWATER[AGE] juices[AGE] KPLECF[0] MCORT[0] MCORT[STEPS] meat[AGE] fish[AGE] Equation No.(s) or Default Values V.I.I E-6a,b, U-lb,h,U-2 E-4n 0.004292 2.018 11.656 15.692 15.692 15.692 19.646 27.471 . B-7e B-6b,i, B-6.5b,i, B-7e, B-8d, B-9e,f E-4o 0.007822 12.500 29.605 38.111 40.930 43.750 47.368 54.558 12.500 29.605 38.111 40.930 43.750 47.368 54.558 V.1.0 E-6a,b, U-lb,h, U-2 0.049 0.283 0.381 0.381 0.381 0.477 0.667 . B-7e B-6b,i, B-6.5b,i, B-7e, B-8d, B-9e,f 0.226 0.630 0.811 0.871 0.931 1.008 1.161 29.551 87.477 95.700 101.570 107.441 111.948 120.961 B-8 ------- Data Crosswalk for the lEUBKwin Model Component(s) Exposure Exposure Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic MPL Biokinetic Biokinetic MPL Biokinetic Biokinetic Biokinetic Biokinetic Exposure Biokinetic Parameter Name V.I.I meat_Consump[AGE] meatFraction MKIDNEY[0] MKIDNEY[STEPS] MLIVER[0] MLIVEI MLIVER[STEPS] MOTHER[0] MOTHER[STEPS] MPLASM[0] ASM[STEPS] MPLECF[0] ECF[STEPS] MRBC[0] MRBC[STEPS] MTRAB[0] MTRAB [STEPS] multiply _factor NBCORT V.1.0 game[t] meatFraction MKIDNEY[0] MKIDNEY[STEPS] 40] B-7g MLIVER[STEPS] MOTHER[0] MOTHER[STEPS] MPLASM[0] MPLASM[STEPS] MPLECF[0] MPLECF[STEPS] MRBC[0] MRBC[STEPS] MTRAB[0] MTRAB[STEPS] multiply _factor NBCORT Equation No.(s) or Default Values V.I.I 12.500 29.605 38.111 40.930 43.750 47.368 54.558 E-5a B-7f B-6b,f, B-6.5b,f, B-7f, B-8d, B-9c B-6b,e, B-6.5b,e, B-7g, B-8d, B-9b B-7h B-6b,g, B-6.5b,g, B-7h, B-8d, B-9d B-7d B-7d, B-9g, B-lOa B-7b,d B-6a,c-i, B-6.5a,c-i, B-7b,d, B-8a, B-9a-g B-7c B-6b,d, B-6.5b,d, B-7c, B-8d, B-9a,B-10a B-7i B-6b,h, B-6.5b,h, B-7i, B-8d, B-9e 0.400 V.1.0 29.551 87.477 95.700 101.570 107.441 111.948 120.961 E-5a B-7f B-6b,f, B-6.5b,f, B-7f, B-8d, B-9c B-7g B-6b,e, B-6.5b,e, B-7g, B-8d, B-9b B-7h B-6b,g, B-6.5b,g, B-7h, B-8d, B-9d B-7d B-7d, B-9g, B-lOa B-7b,d B-6a,c-i, B-6.5a,c-i, B-7b,d, B-8a, B-9a-g B-7c B-6b,d, B-6.5b,d, B-7c, B-8d, B-9a,B-10a B-7i B-6b,h, B-6.5b,h, B-7i, B-8d, B-9e 100.000 0.400 B-9 ------- Data Crosswalk for the lEUBKwin Model Component(s) Biokinetic Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Biokinetic Uptake Uptake Uptake Uptake Uptake Exposure Exposure Parameter Name V.I.I NBTRAB nuts[AGE] nutsConc nuts_Consump[AGE] OCCUP[AGE] OccupConc OccupFraction OTHER[AGE] OtherConc OtherFraction other_intake OUTFLOW[STEPS] PAFD PAFF PAFP PAFS PAFW pasta[AGE] pastaConc V.1.0 NBTRAB nuts[AGE] OCCUP[AGE] OccupConc OccupFraction OTHER[AGE] OtherConc OtherFraction other_intake OUTFLOW[STEPS] PAFD PAFF PAFP PAFS PAFW pasta[AGE] Equation No.(s) or Default Values V.I.I 0.200 E-4p 0.005798 0.087 0.962 0.875 0.962 0.962 0.962 0.875 E-9c,E-12a E-9c, E-12e 0.000 0.000 B-6a,c, B-6.5a,c E-4q 0.006163 V.1.0 0.200 0.0010 0.0110 0.0100 0.0110 0.0110 0.0110 0.0100 E-9c,E-12a 1200.000 0.000 E-9c,E-12e 1200.000 0.000 0.000 B-6a,c, B-6.5a,c 0.200 0.200 0.200 0.200 0.200 0.239 0.434 0.603 0.595 0.587 0.623 0.693 B-10 ------- Data Crosswalk for the lEUBKwin Model Component(s) Exposure Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Uptake Uptake Exposure Parameter Name V.I.I pasta_Consump[AGE] PBBLDO PBBLDMAT PBBLOODEND[MONTH] RATBLPL RATFECUR RATOUTFEC RCORTO RECSUM[STEPS] REC: ResCoef[15] RKIDNEYO RLIVERO ROTHERO RTRABO SATINTAKE2 SATUPTAKE[MONTH] Sy sauce[AGE] V.1.0 PBBLDO PBBLDMAT PBBLOODEND[MONTH] RATBLPL RATFECUR RATOUTFEC RCORTO >UM[0] ResCoef[15] RKIDNEYO RLIVERO ROTHERO RTRABO SATINTAKE2 ,TUPTAKE[MONTH] sauce[AGE] Equation No.(s) or Default Values V.I.I 10.409 18.902 26.263 25.915 25.566 27.134 30.183 B-7a,b,c,e-i 1.0 B-lOc U-lg-l,U-3 E-4r V.1.0 B-7a,b,c,e-i 2.500 B-lOc 100.000 0.750 0.750 78.900 None 0.100 20.000 10.000 10.000 10.000 1.000 100.000 0.750 0.750 0.000 0.000 0.000 0.000 0.000 0.000 10.600 13.000 16.000 51.200 100.000 U-lg-l,U-3 0.021 0.061 0.071 0.088 0.104 0.105 0.105 B-ll ------- Data Crosswalk for the lEUBKwin Model Component(s) Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Biokinetic Biokinetic SUM Biokinetic SUM Biokinetic SUM Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Parameter Name V.I.I sauceConc Sauce_Consump[AGE] SCHOOL[AGE] SchoolConc SchoolFraction SECHOME[AGE] SecHomeConc SecHomeFraction soil_content[AGE] soilj soil_indoor[AGE] soil_ingested[AGE] STEPS 1[ST EPS] 2[ST EPS] 3[ST EPS] TBLBONE TBLFEC TBLKID TBLLIV TBLOTH TBLOUT TBLUR TBONEBL TCORTPL[MONTH] V.1.0 SCHOOL[AGE] SchoolConc SchoolFraction SECHOME[AGE] SecHomeConc SecHomeFraction ontent[AGE] soil_indoor[AGE] soil_ingested[AGE] STEPS SUM1 [STEPS] SUM2[STEPS] SUMS [STEPS] TBLBONE[MONTH] TBLFEC[MONTH] TBLKID[MONTH] TBLLIV[MONTH] TBLOTH[MONTH] TBLOUT[MONTH] B-lg TBLUR[MONTH] TBONEBL[MONTH] TCORTPL[MONTH] Equation No.(s) or Default Values V.I.I 0.010215 1.647 4.784 5.569 6.902 8.157 8.235 8.235 E-9c, E-12d E-9c, E-12d E-9b,d, E-lla-d B-lOb B-8a,b B-8a,c B-8a,d B-le,h,B-2i,k B-lf,g,B-2e,f B-ld,gB-2g,h B-lb,B-2d,e B-lc,B-2m,n B-2n,o B-la,f,B-2c B-lh,B-2j,l B-21, B-6b,i, B-6.5b,i, B-8c,d, B-9f V.1.0 E-9c,E-12d 200.000 0.000 E-9c,E-12d 200.000 0.000 200.000 E-9b,d, E-lla-d 0.085 0.135 0.135 0.135 0.100 0.090 0.085 B-lOb B-8a,b B-8a,c B-8a,d B-le,h,B-2i,k B-lf,g,B-2e,f B-ld,g B-2g,h B-lb,B-2d,e B-lc,B-2m,n B-lg,B-2n,o B-la,f,B-2c B-lh, B-2j,l B-21, B-6b,i, B-6.5b,i, B-8c,d, B-9f B-12 ------- Data Crosswalk for the lEUBKwin Model Component(s) Exposure Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Exposure Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Parameter Name V.I.I time_out[AGE] TimeSteps TKIDPL[MONTH] TLIVALL TLIWEC[MONTH] TLIWL[MONTH] TotAltSource TOTHALL TOTHOUT[MONTH] TOTHPL[MONTH] TPLCORT[MONTH] TPLKID[MONTH] TPLLIV[MONTH] TPLOTH[MONTH] TPLRBC TPLRBC2 V.1.0 time_out[AGE] TimeSteps TKIDPL[MONTH] TLIVALL TLIWEC[MONTH] TLIWL[MONTH] TotAltSource TOTHALL[MONTH] TOTHOUT[MONTH] TOTHPL[MONTH] TPLCORT[MONTH] TPLKID[MONTH] TPLLIV[MONTH] TPLOTH[MONTH] TPLRBC TPLRBC2 [STEPS] Equation No.(s) or Default Values V.I.I B-2h, B-6b,f, B-6.5b,f, B-8c,d, B-9c B-8c,d, B-9b,i B-2e,f, B-4i, B-6e, B-6.5e B-2e, B-6b,e, B-6.5b,e, B-8c,d, B-9i Internal verification ofE-9.5 B-8c,d, B-9d,h B-2o, B-6g, B-6.5g,B-9h B-2n, B-6b,g, B-6.5b,g, B-8c,d, B-9h B-2k, B-6c,i, B-6.5c,i, B-8b,c, B-9e,f B-2g, B-6c,f, B-6.5c,f, B-8b,c, B-9c B-2d, B-6c,e, B-6.5c,e,B-8b,c, B-9b B-2m, B-6c,g, B-6.5c,g, B-8b,c, B-9d B-2a,b, B-2.5, B-7b,c B-2.5,B-5, B-6c,d, B-6.5c,d, B-8b,c, B-9a V.1.0 1.000 2.000 3.000 4.000 4.000 4.000 4.000 1/6 B-2h, B-6b,f, B-6.5b,f, B-8c,d, B-9c B-8c,d, B-9b,i B-2e,f, B-4i, B-6e, B-6.5e B-2e, B-6b,e, B-6.5b,e, B-8c,d, B-9i Internal verification ofE-9.5 B-8c,d, B-9d,h B-2o, B-6g, B-6.5g, B-9h B-2n, B-6b,g, B-6.5b,g, B-8c,d, B-9h B-2k, B-6c,i, B-6.5c,i, B-8b,c, B-9e,f B-2g, B-6c,f, B-6.5c,f, B-8b,c, B-9c B-2d, B-6c,e, B-6.5c,e, B-8b,c, B-9b B-2m, B-6c,g, B-6.5c,g, B-8b,c, B-9d B-2a,b, B-2.5, B-7b,c B-2.5,B-5, B-6c,d, B-6.5c,d, B-8b,c, B-9a B-13 ------- Data Crosswalk for the lEUBKwin Model Component(s) Biokinetic Biokinetic Biokinetic Biokinetic Exposure Uptake Uptake Uptake Uptake Uptake Uptake Biokinetic Uptake Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Exposure Parameter Name V.I.I TPLTRAB[MONTH] TPLUR[MONTH] TRBCPL TTRABPL[MONTH] TWA[AGE] UPAIR[MONTH] UPDIET[MONTH] UPDUSTA[MONTH] UPDUST[MONTH] UPOTHER[MONTH] UPSOIL[MONTH] UPTAKE[MONTH] UPWATER[MONTH] UserFishConc userFishFraction UserFruitConc userFruitFraction UserGameConc userGameFraction UserVegConc userVegFraction vary_indoor vary_outdoor vegFraction V.1.0 TPLTRAB [MONTH] TPLUR[MONTH] TRBCPL TTRABPL[MONTH] TWA[AGE] UPAIR[MONTH] UPDIET[MONTH] UPDUSTA[MONTH] UPDUST[MONTH] UPOTHER[MONTH] UPSOIL[MONTH] UPTAKE[MONTH] UPWATER[MONTH] UserFishConc userFishFraction UserFruitConc userFruitFraction UserGameConc userGameFraction UserVegConc userVegFraction vary_indoor vary_outdoor vegFraction Equation No.(s) or Default Values V.I.I B-2i, B-6c,h, B-6.5c,h, B-8b,c, B-9e B-2c, B-6c, B-6.5c,B-8b B-2b, B-6b,d, B-6.5b,d, B-7b,c B-8c,d, B-9a B-2j,B-6b,h, B-6.5b,h, B-8c,d, B-9e E-2, E-3 U-4, U-5 U-la,gU-5 U-ldj,U-5 U-lc,iU-5 U-lf,U-5 U-le,k,U-5 U-5, B-6a, B-6.5a,B-8a U-lb,h,U-5 E-5b V.1.0 B-2i, B-6c,h, B-6.5c,h, B-8b,c, B-9e B-2c, B-6c, B-6.5c,B-8b B-2b, B-6b,d, B-6.5b,d, B-7b,c B-8c,d, B-9a B-2j,B-6b,h, B-6.5b,h, B-8c,d, B-9e E-2, E-3 U-4, U-5 U-la,gU-5 U-ld,j,U-5 U-lc,iU-5 U-lf,U-5 U-le,k,U-5 U-5, B-6a, B-6.5a,B-8a U-lb,h, U-5 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 E-5b B-14 ------- Data Crosswalk for the lEUBKwin Model Component(s) Exposure Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Exposure Exposure Biokinetic Uptake, Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Biokinetic Parameter Name V.I.I vent_rate[AGE] VOLBLOOD[MONTH] VOLECF[MONTH] VOLPLASM[0] VOLPLASM[MONTH] VOL VOLRBC[MONTH] water_consumption[AGE] w weight_soil WTBLOOD[MONTH] WTBODY[MONTH] WTBONE[MONTH] WTCORT[0] WTCORT[MONTH] WTECF[MONTH] WTKIDNEY[0] WTKIDNEY[MONTH] WTLIVER[0] WTLIVER[MONTH] WTOTHER[0] WTOTHER[MONTH] WTTRAB[0] WTTRAB [MONTH] V.1.0 vent_rate[AGE] VOLBLOOD[MONTH] VOLECF[MONTH] VOLPLASM[0] B-7b,c VOLPLASM[MONTH] VOLRBC(O) VOLRBC[MONTH] ater_consumption[AGE] weight_soil WTBLOOD[MONTH] B-5 WTBODY[MONTH] WTBONE[MONTH] WTCORT[0] B-7e WTCORT[MONTH] B-lh WTECF[MONTH] WTKIDNEY[0] WTKIDNEY[MONTH] WTLIVER[0] WTLIVER[MONTH] WTOTHER[0] B-7h WTOTHER[MONTH] WTTRAB[0] WTTRAB[MONTH] Equation No.(s) or Default Values V.I.I B-lh, B-2e,f,h,n,o, B-5a,d,e,m, B-lOa B-5d, B-9g B-5c, B-7b,c, B-9g B-7b,c B-2.5,B-5b m U-3,B-la-e, B-5f,g,l B-5g,h,i B-5h,l, B-7e B-5e,l B-7f B-2h, B-5j,l, B-7f B-7g B-2e,f, B-5k,l, B-7g B-2n,o, B-51, B-7h B-7i B-lh,B-5i,l,B-7i V.1.0 2.000 3.000 5.000 5.000 5.000 7.000 7.000 B-lh, B-2e,f,h,n,o, B-5a,d,e,m, B-lOa B-5d, B-9g B-7b,c B-5c, B-7b,c, B-9g B-7b,c B-2.5,B-5b 0.200 0.500 0.520 0.530 0.550 0.580 0.590 45.000 B-51,m U-3,B-la-e, B-5f,g,l B-5g,h,i B-7e B-lh,B-5h,l,B-7e B-5e,l B-7f B-2h,B-5j,l,B-7f B-7g B-2e,f, B-5k,l, B-7g B-7h B-2n,o, B-51, B-7h B-7i B-lh, B-5i,l, B-7i B-15 ------- APPENDIX C lEUBKwin PARAMETER DICTIONARY ------- This page intentionally left blank ------- DESCRIPTION OF PARAMETERS IN THE lEUBKwin MODEL Parameter Name ABSD ABSF ABSO ABSS ABSW air absorp[AGE] air concentration[AGE] ALLOMET[15] AVD AVF AvgHouseDust Description Total absorption for dust at low saturation (maximum absorption coefficient, active) Total absorption for food at low saturation (maximum absorption coefficient, active) Fraction absorption from paint ingested at low saturation (maximum absorption coefficient, active) Fraction absorption from soil at low saturation (maximum absorption coefficient, active) Total absorption for water at low saturation (maximum absorption coefficient, active) Net percentage of lung absorption of air lead Outdoor air lead concentration Storage array Fraction available for dust Fraction available for food/diet Average household dust concentration Default Value or Equation Number 0.300 0.500 0.000 0.300 0.500 32.000 0.100 0.333 1.000 1.000 150.000 Units unitless unitless unitless unitless unitless % Ug/m3 unitless unitless unitless Hg/g Age Range (mos) 0-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 lorE E E E E E E E I I I I Basis for Values/Equations Based on U.S. EPA (1989a). Based on U.S. EPA (1989a). Based on the default condition that there is no source of lead paint for ingestion in the household. Based on U.S. EPA (1989a). Based on U.S. EPA (1989a). Deposition efficiencies of airborne lead particles were estimated by U.S. EPA (1989a). A respiratory deposition/absorption rate of 25% to 45% is reported for young children living in non-point source areas while a rate of 42% is calculated for those living near point sources. An intermediate value of 32% was chosen. Based on the lower end of the range 0. 1-0.3 jig Pb/m3 that is reported for outdoor air lead concentration in U.S. cities without lead point sources (U.S. EPA, 1989a). Stores variable and constant values. The exponent, 0.333, in Equations B-lathrough B-le is stored in this array. Variable added for later flexibility in describing the absorption process; has no effect in current algorithm. Variable added for later flexibility in describing the absorption process; has no effect in current algorithm. Value calculated/assigned based on alternate dust lead sources (e.g., day care, sechome, paint, school, and workplace). Equation Where Used U-2 U-la,g, U-2 U-2 U-le,k, U-2 U-lb,h, U-2 U-4 E-l, E-2, E-lla,b B-la-B-le u-icAij U-la,g Note: I = internal model parameter; E = external, user-spec if led parameter ------- Parameter Name AvgMultiSrc AVINTAKE [MONTH] AVO AVS AVW beverage[AGE] beverageConc beverage Consump[AGE] BLOOD[STEPS] Description Multiple Source Analysis average Available intake Fraction available for paint Fraction available for soil Fraction available for water Lead intake from beverages by age Lead concentration in beverages Daily consumption of beverages Blood lead concentration Default Value or Equation Number 150.000 U-2 1.000 1.000 1.000 E-4d 0.002109 87.993 116.487 209.677 194.982 177.061 183.333 188.710 B-10a,c Units Hg/g ug/day unitless unitless unitless ug/day Hg*g grams/day ug/dL Age Range (mos) 0-84 0-84 0-84 0-84 0-84 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-84 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-84 lorE I I I I I I E E I Basis for Values/Equations Based on the contribution of lead from soil, air and alternate indoor sources (such as day care, sechome, paint, school, and workplace). The amount of lead that is available for intake. Variable added for later flexibility in describing the absorption process; has no effect in current algorithm. Variable added for later flexibility in describing the absorption process; has no effect in current algorithm. Variable added for later flexibility in describing the absorption process; has no effect in current algorithm. U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. U. S. Food and Drug Administration Center for Food Safety and Applied Nutrition Office of Plant and Dairy Foods and Beverages (May 16, 2006). Available online: http://www.cfsan.fda.gov/~comm/tds-toc.html U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. Quantity consumed based on Pennington (1983). Summation variable used to get the average blood lead concentration for monthly period. Equation Where Used U-lg,h,i,j,k,l, U-2 U-lf,l U-le,k U-lb,h E-5o E-4d E-4d B-10a,c Note: I = internal model parameter; E = external, user-specified parameter ------- Parameter Name bread[AGE] breadConc bread Consump[AGE] can fruit[AGE] canFruitConc canFruit Consump[AGE] Description Lead intake from breads by age Lead concentration in bread Daily consumption of bread Lead intake from canned fruit, when fruit is consumed only in canned form, at age range Lead concentration in canned fruit Daily consumption of canned fruit Default Value or Equation Number E-4e 0.008927 4.992 15.862 13.311 16.639 19.967 22.629 27.898 E-4f 0.023873 13.941 8.183 8.145 7.691 7.236 7.460 7.906 Units ug/day ug/kg grams/day ug/day ug/kg grams/day Age Range (mos) 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-84 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-84 0-11 12-23 24-35 36-47 48-59 60-71 72-84 lorE I E E I E E Basis for Values/Equations U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. U. S. Food and Drug Administration Center for Food Safety and Applied Nutrition Office of Plant and Dairy Foods and Beverages (May 16, 2006). Available online: http://www.cfsan.fda.gov/~comm/tds-toc.html U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. Quantity consumed based on Pennington (1983). U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. U. S. Food and Drug Administration Center for Food Safety and Applied Nutrition Office of Plant and Dairy Foods and Beverages (May 16, 2006). Available online: http://www.cfsan.fda.gov/~comm/tds-toc.html U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. Quantity consumed based on Pennington (1983). Equation Where Used E-5m E-4e E-4e E-5d E-4f E-4f Note: I = internal model parameter; E = external, user-specified parameter ------- Parameter Name can veg[AGE] candy[AGE] candyConc candy Consump[AGE] canVegConc canVeg Consump[AGE] Description Lead intake from canned vegetables, when vegetable is consumed only in canned form, by age Lead intake from candies by age Lead concentration in candy Daily consumption of candy Lead concentration in canned vegetables Daily consumption of canned vegetables Default Value or Equation Number E-4g E-4h 0.011554 9.955 11.273 32.909 24.409 16.000 14.818 12.455 0.004003 0.668 2.274 2.563 2.662 2.771 2.626 2.356 Units ug/day ug/day Hg*g grams/day Hg*g grams/day Age Range (mos) 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-84 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-84 0-11 12-23 24-35 36-47 48-59 60-71 72-84 lorE I I E E E E Basis for Values/Equations U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. U. S. Food and Drug Administration Center for Food Safety and Applied Nutrition Office of Plant and Dairy Foods and Beverages (May 16, 2006). Available online: http://www.cfsan.fda.gov/~comm/tds-toc.html U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. U. S. Food and Drug Administration Center for Food Safety and Applied Nutrition Office of Plant and Dairy Foods and Beverages (May 16, 2006). Available online: http://www.cfsan.fda.gov/~comm/tds-toc.html U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. Quantity consumed based on Pennington (1983). U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. Quantity consumed based on Pennington (1983). Equation Where Used E-5b E-5p E-4h E-4h E-4g E-4g Note: I = internal model parameter; E = external, user-specified parameter ------- Parameter Name CONRBC constant dust conc[AGE] constant indoor dust constant outdoor dust constant outdoor soil constant soil cone [AGE] constant water cone contrib_percent CRBONEBL[MONTH] Description Maximum lead concentration capacity of Dust lead concentration at age range Constant indoor dust lead concentration at age range Constant outdoor dust lead concentration at age range Constant outdoor soil lead concentration at age range Soil lead concentration at age range Water lead concentration at age range Ratio of indoor dust lead concentration to Ratio of lead concentration (ug/kg) in bone to blood lead concentration (ug/L) at age range Default Value or Equation Number 1200.000 200.000 200.000 200.000 200.000 200.000 4.000 0.700 B-4c Units ug/dL "g/g ug/g ug/g ug/g Ug/g ug/L Ug/g per ug/g L/kg Age Range (mos) 0-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 lorE I E E E E E E E I Basis for Values/Equations Based on Marcus' (1983) reanalysis of infant baboon data from Mallon (1983). See Marcus (1985a) for assessment of form of relationship and estimates from data on human adults [data from deSilva, 1981a,b; Manton and Malloy, 1983; and Manton and Cook 1984]; and infant and juvenile baboons (Mallon, 1983). Air Quality Criteria Document for Lead (U.S. EPA, 1986). Air Quality Criteria Document for Lead (U.S. EPA, 1986). Air Quality Criteria Document for Lead (U.S. EPA, 1986). Air Quality Criteria Document for Lead (U.S. EPA, 1986) Air Quality Criteria Document for Lead (U.S. EPA, 1986). Based on analysis of data from the American Water Works Service Co. (Marcus, 1989) Analysis of soil and dust data from 1983 East Helena study (U.S. EPA, 1989a). Additional information on this variable can be obtained from the MSD short sheet (EPA 540-F-008, OSWER 9285.7-34 [June 1998]) available on the TRW website. Data in Barry (1981) were used. Bone lead concentration was calculated as an arithmetic average of the concentrations in the rib, tibia, and calvaria. The blood lead concentrations were taken directly from the study. Concentrations in each of the following eight age groups were considered: stillbirths, 0-12 days, 1-11 mos, 1-5 yrs, 6-9 yrs, 11-16 yrs, adult (men), and adult (women). Ages 0 and 40 yrs were assumed for stillbirths and adults, respectively. Equation Where Used B-2.5 E-9a, E-lld -D -D -D E-8a E-6a E-lla,b B-lh, B-4c Note: I = internal model parameter; E = external, user-specified parameter ------- Parameter Name CRKIDBL[MONTH] CRLIVBL[MONTH] CROTHBL[MONTH] Cutoff Description Ratio of lead concentration (ug/kg) in kidney to blood lead concentration (ugL) at age range Ratio of lead concentration (ug/kg) in liver to blood lead concentration (ug/L) at age range Ratio of lead concentration (ug/kg) in other soft tissue to blood lead concentration (ug/L) at age range Blood lead level of concern Default Value or Equation Number B-4a B-4b B-4d 10 Units L/kg L/kg L/kg ug/dL Age Range (mos) 0-84 0-84 0-84 0-84 lorE I I I E Basis for Values/Equations Data in Barry (1981) were used. Lead concentrations in kidney (combined values for cortex and medulla) and blood were taken directly from the study. Concentrations in each of the following eight age groups were considered: stillbirths, 0-12 days, 1-11 mos, 1-5 yrs, 6-9 yrs, 11-16 yrs, adult (men), and adult (women). Ages 0 and 40 yrs were assumed for stillbirths and adults, respectively. Data in Barry (1981) were used. Lead concentrations in liver and blood were taken directly from the study. Concentrations in each of the following eight age groups were considered: stillbirths, 0-12 days, 1-11 mos, 1-5 yrs, 6-9 yrs, 11-16 yrs, adult (men), and adult (women). Ages 0 and 40 yrs were assumed for stillbirths and adults, respectively. Data in Barry (1981) were used. Lead concentration ratio for soft tissues was calculated as a weighted arithmetic average of concentration ratios for muscle (53.8%), fat (24.0%), skin (9.4%), dense connective tissue (4.4%), brain (2.7%), GI tract (2.3%), lung (1.9%), heart (0.7%), spleen (0.3%), pancreas (0.2%), and aorta (0.2%), where the weights applied are given in parentheses. The weight associated with each soft tissue component was equal to the weight of the component (kg) divided by weight of all soft tissues (kg). These weights were estimated from Schroeder and Tipton (1968) and are assumed to apply in the range 0-84 months of age. Concentrations in each of the following eight age groups were considered: stillbirths, 0-12 days, 1-11 mos, 1-5 yrs, 6-9 yrs, 11-16 yrs, adult (men), and adult (women). Ages 0 and 40 yrs were assumed for stillbirths and adults, respectively. USEPA, 1986, 1990; CDC, 1991. Equation Where Used B-2h, B-4a B-2e,f, B-4b B-2n,o, B-4d -D Note: I = internal model parameter; E = external, user-specified parameter ------- Parameter Name dairy[AGE] dairyConc dairy Consump[AGE] DAYCARE[AGE] DaycareConc DaycareFraction diet intake [AGE] DietTotal[AGE] Description Lead intake from dairy products by age Lead concentration in dairy products Daily consumption of dairy products Dust lead intake from daycare Dust lead concentration from daycare Fraction of total dust ingested daily from daycare dust User-specified diet lead intake by age Total dietary intake at age range Default Value or Equation Number E-4i 0.004476 41.784 35.321 38.527 38.327 38.176 40.631 45.591 E-12c 200.000 0.000 2.26 1.96 2.13 2.04 1.95 2.05 2.22 E-4b Units jig/day Hg*g grams/day ug/day Hg/g unitless ug/day ug/day Age Range (mos) 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-84 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-84 0-84 0-84 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-84 lorE I E E I E E E I Basis for Values/Equations U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. U. S. Food and Drug Administration Center for Food Safety and Applied Nutrition Office of Plant and Dairy Foods and Beverages (May 16, 2006). Available online: http://www.cfsan.fda.gov/~comm/tds-toc.html U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. Quantity consumed based on Pennington (1983). Simple combination of the total amount of dust ingested daily, fraction of total dust ingested as daycare dust, and dust lead concentration at daycare. Based on the assumption that default daycare dust concentrations are the same as default residence dust concentrations. Based on the default assumption that the child does not attend daycare. U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. U. S. Food and Drug Administration Center for Food Safety and Applied Nutrition Office of Plant and Dairy Foods and Beverages (May 16, 2006). Available online: http://www.cfsan.fda.gov/~comm/tds-toc.html Sum of all dietary sources; same as INDIET[AGE]. Equation Where Used E-5J E-4i E-4i E-9c, E-12c E-12c E-9.5, E-12c E-4a E-4b Note: I = internal model parameter; E = external, user-specified parameter ------- Parameter Name dust indoor[AGE] DustTotal[AGE] EXPR[0] f_fruit[AGE] fFruitConc fFruit Consump[AGE] f_veg[AGE] fYegConc Description User-specified indoor dust concentration at age range Daily amount of dust ingested at age range The available capacity of the red blood cells to carry lead; i.e.,1 - lead concentration in RBC at birth Lead intake from fresh fruit, if no home- grown fruit is consumed, by age Lead concentration in fresh fruits Daily consumption of fresh fruit Lead intake from fresh vegetables, if no home-grown vegetables are consumed, by age Lead concentration in fresh vegetables Default Value or Equation Number 200.000 E-10 B-7i E-4J 0.004462 2.495 12.540 11.196 11.196 11.452 12.988 16.059 E-4k 0.006719 Units "g/g g/day unitless ug/day Hg*g grams/day Ug/day "g*g Age Range (mos) 0-84 0-84 0 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-84 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-84 lorE E I I I E E I E Basis for Values/Equations Under alternate dust sources model, based on assumption that both soil and outdoor air contribute to indoor dust lead. Simple combination of total amount of soil and dust ingested daily and fraction of this combined ingestion that is dust alone. Calculated value. U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. U. S. Food and Drug Administration Center for Food Safety and Applied Nutrition Office of Plant and Dairy Foods and Beverages (May 16, 2006). Available online: http://www.cfsan.fda.gov/~comm/tds-toc.html U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. Quantity consumed based on Pennington (1983). U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. U. S. Food and Drug Administration Center for Food Safety and Applied Nutrition Office of Plant and Dairy Foods and Beverages (May 16, 2006). Available online: http://www.cfsan.fda.gov/~comm/tds-toc.html U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. Equation Where Used E-llc E-9b, E-10, E-12a-e B-7i E-5e E-4J E-4J E-5c E-4k Note: I = internal model parameter; E = external, user-specified parameter 10 ------- Parameter Name fYeg_Consump [AGE] FirstDrawConc FirstDrawFraction formula[AGE] formulaConc formula Consump[AGE] FountainConc FountainFraction Description Daily consumption of fresh vegetables First draw water lead concentration Fraction of total water consumed daily as first draw Lead intake from baby formula by age Lead concentration in formula Daily consumption of formula Fountain water lead concentration Fraction of total water consumed daily from water fountains Default Value or Equation Number 8.773 15.945 28.156 27.623 27.030 29.164 33.373 4.000 0.50000 E-41 0.002433 45.153 22.975 0.797 0.000 0.000 0.000 0.000 10.000 0.150 Units grams/day Ug/L unitless Ug/day ug/kg grams/day ug/L unitless Age Range (mos) 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-84 0-84 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-84 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-84 0-84 lorE E E E I E E E E Basis for Values/Equations Quantity consumed based on Pennington (1983). Based on analysis of data from the American Water Works Service Co. (Marcus, 1989). Conservative value corresponding to consumption largely after four fours stagnation time was used (e.g., early morning or late afternoon). U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. U. S. Food and Drug Administration Center for Food Safety and Applied Nutrition Office of Plant and Dairy Foods and Beverages (May 16, 2006). Available online: http://www.cfsan.fda.gov/~comm/tds-toc.html U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. Quantity consumed based on Pennington (1983). Default assumption is that the drinking fountain has a lead-lined reservoir, but that consumption is not always first draw. Therefore, a value was selected from the range of 5-25 ug/L. A default value was based on 4-6 trips to the water fountain at 40-50 mL per trip. Equation Where Used E-4k E-6b E-6b, E-7 E-5r E-41 E-41 E-6b E-6b, E-7 Note: I = internal model parameter; E = external, user-specified parameter 11 ------- Parameter Name fruitFraction geo mean GSD HCTO HomeFlushedConc HomeFlushedFraction HouseFraction INAIR[AGE] InBeverage[AGE] InBread[AGE] InCandy[AGE] InCanFruit[AGE] InCanVeg[AGE] InDairy[AGE] Description Fraction of fruit consumption that is derived from market basket (i.e., total fruit consumption - user-grown) Geometric Mean Geometric Standard Deviation Hematocrit at birth Home flushed water lead concentration Fraction of home flushed water Fraction of dust exposure that is from residential dust Air lead intake at age range Lead intake from beverages at age range Lead intake from bread at age range Lead intake from candy at age range Lead intake from canned fruit at age range Lead intake from canned vegetables at age range Lead intake from dairy products at age range Default Value or Equation Number E-5c -D 1.600 0.450 1.000 0.000 1.000 E-3 E-5o E-5m E-5p E-5d E-5b E-5J Units unitless ug/dL unitless % ug/L unitless unitless ug/day ug/day Ug/day ug/day ug/day ug/day ug/day Age Range (mos) 0-84 -D 0-84 0 0-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 lorE E I E I E E E I I I I I I I Basis for Values/Equations Calculated value. Calculated value. U.S. EPA, 1994. Data from Silve et al. (1987); also Spector (1956) and Altman and Dittmer (1973). Based on analysis of data from the American Water Works Service Co. (Marcus, 1989). Based on the assumption that the sum of all residential water fractions cannot exceed 1 . Based on the assumption that the sum of all residential dust fractions cannot exceed 1 . Product of average air lead concentration and ventilation rate. Product of total beverage consumed, and the lead concentration in beverage(s). Product of total bread consumed, and the lead concentration in bread(s). Product of total amount of candy consumed, and the lead concentration in the candy Product of the fraction of non-home grown fruits consumed daily, and lead intake from canned fruits when fruits are consumed only in canned form. Product of the fraction of vegetables consumed daily as non-home grown, and lead intake from canned vegetables when vegetables are consumed only in canned form. Product of total amount of dairy products consumed, and the lead concentration in the dairy products. Equation Where Used E-5g, E-5h -D -D B-7b,d E-6b E-6b, E-7 E-9.5, E-9b E-3, U-4 E-4c, E-5o E-4c, E-5m E-4c, E-5p E-4b, E-5d E-4b, E-5b E-4c, E-5J Note: I = internal model parameter; E = external, user-specified parameter 12 ------- Parameter Name InDairy[AGE] INDIET[AGE] IndoorConc[AGE] indoorpercent INDUST[AGE] INDUSTA[AGE] infant[AGE] Description Lead intake from dairy products by age Dietary lead intake at age range Indoor air lead concentration at age range Ratio of indoor dust lead concentration to corresponding outdoor concentration Household dust lead intake at age range Lead intake from alternate dust sources at age range Lead intake from infant food by age Default Value or Equation Number E-5m E-4a or E-4b E-l 30.000 E-9a or E-9b,d E-9c or E-9d E-4m Units ug Pb/day ug/day ug/m3 % ug/day ug/day ug/day Age Range (mos) 0-84 0-84 0-84 0-84 0-84 0-84 0-11 12-23 24-35 36-47 48-59 60-71 72-84 lorE E I I E I I I Basis for Values/Equations U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. U. S. Food and Drug Administration Center for Food Safety and Applied Nutrition Office of Plant and Dairy Foods and Beverages (May 16, 2006). Available online: http://www.cfsan.fda.gov/~comm/tds-toc.html Two options are provided. Default option - Considers composite diet lead intake. Alternate option - Combines lead intake from several individual components of diet. Algebraic expression of relationship. Based on homes near lead point sources. The default value is reported in OAQPS (U.S. EPA, 1989a, pp A- 1) and is estimated by Cohen and Cohen (1980). Two options are provided. Default option - Assumes that all dust lead exposure is from the household. Alternate option - Considers dust lead exposure from several alternative sources as well. Two options are provided. Default option - Assumes that lead intake from alternate sources is zero. Alternate option - Combines lead intake from several alternate sources. U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. U. S. Food and Drug Administration Center for Food Safety and Applied Nutrition Office of Plant and Dairy Foods and Beverages (May 16, 2006). Available online: http://www.cfsan.fda.gov/~comm/tds-toc.html Equation Where Used E-4c E-4a,b U-la,g, U-2 E-l, E-2 E-l E-9a,b,e U-lc,i, U-2 E-9c U-ld,j, U-2 E-5s Note: I = internal model parameter; E = external, user-specified parameter 13 ------- Parameter Name infantConc infant Consump[AGE] InFish[AGE] INFLOW[STEPS] InFormula[AGE] InFrFruit[AGE] InFrVeg[AGE] InGame[AGE] InHomeFrait[AGE] InHomeVeg[AGE] InInfant[AGE] InJuice[AGE] Description Concentration of lead in infant food Daily consumption of infant (baby) food Lead intake from fish at age range Lead input to ECF-plasma pool from organs Lead intake from infant formula at age range Lead intake from non-home grown fresh fruits at age range Lead intake from non-home grown fresh vegetables at age range Lead intake from game animal meat at age range Lead intake from home grown fruits at age range Lead intake from home grown vegetables at age range Lead intake from infant food at age range Lead intake from juice at age range Default Value or Equation Number 0.004047 131.767 66.905 1.634 0.000 0.000 0.000 0.000 E-5h B-6a,b B-6.5a,b E-5r E-5e E-5c E-5i E-5f E-5g E-5s E-5k Units Hg*g grams/day ug/day ug/day ug/day ug/day ug/day ug/day ug/day Ug/day ug/day ug/day Age Range (mos) 0-84 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 lorE E E I I I I I I I I I I Basis for Values/Equations U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. Quantity consumed based on Pennington (1983). Product of total meat consumed daily, fraction of meat consumed a locally caught fish, and lead concentration in fish. Tissue lead masses and blood lead concentration at birth. Product of total infant formula consumed daily, and the lead concentration in the formula. Product of the fraction of fruits consumed daily as non-home grown and lead intake from fresh fruits. Product of the fraction of vegetables consumed daily as non-home grown and lead intake from fresh vegetables. Product of total meat consumed daily, fraction of meat consumed as game animal meat, and lead concentration in game animal meat. Product of total amount of fruit consumed daily, fraction of fruit consumed as home grown, and lead concentration in home grown fruit. Product of total amount of vegetable consumed daily, fraction of vegetables consumed as home grown, and lead concentration in home grown vegetables. Product of total amount of infant food consumed daily, and the lead concentration in the infant food. Product of total amount of juice consumed daily, and the lead concentration in juice. Equation Where Used E-4m E-4m E-4b, E-5k B-6a,b B-6.5a,b E-4c, E-5r E-4b, E-5e E-4b, E-5c E-4b, E-5i E-4b, E-5f E-4b, E-5g E-4c, E-5s E-4c, E-5k Note: I = internal model parameter; E = external, user-specified parameter 14 ------- Parameter Name InMeat[AGE] InNuts[AGE] INOTHER[AGE] InOtherDiet[AGE] InPasta[AGE] InSauce[AGE] INSOIL[AGE] INWATER[AGE] Description Lead intake from non-game and non-fish meat at age range Lead intake from nuts at age range Combined other sources of ingested lead, such as paint chips, ethnic medicines, etc., at age range Combined lead intake from dairy food, juice, nuts, beverage, pasta, bread, sauce, candy, infant and formula food at age range Lead intake from pasta at age range Lead intake from sauces at age range Soil lead intake at age range Water lead intake at age range Default Value or Equation Number E-5a E-51 0.000 E-4c E-5n E-5q E-8a,b E-6a or E-6b Units ug/day ug/day ug/day ug/day ug/day Ug/day ug/day ug/day Age Range (mos) 0-84 0-84 0-84 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-84 0-84 0-84 0-84 lorE I I I I I I I I Basis for Values/Equations Product of total amount of meat consumed daily, fraction of meat consumed as non-game and non-fish meat, and lead concentration in non-game and non-fish meat. Product of total amount of nuts consumed daily, and the lead concentration in nuts. Assumes no other sources of ingested lead. Sum of the amounts of lead ingested in food items not substituted by the calculation of exposure to lead in home grown fruits and vegetables, wild game or fish. U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. U. S. Food and Drug Administration Center for Food Safety and Applied Nutrition Office of Plant and Dairy Foods and Beverages (May 16, 2006). Available online: http://www.cfsan.fda.gov/~comm/tds-toc.html Product of total amount of pasta consumed daily, and the lead concentration in pasta. Product of total amount of sauce consumed daily, and the lead concentration in sauce. Simple combination of total amount of soil and dust ingested daily, fraction of this combined ingestion that is soil alone, and lead concentration in soil. Two options are provided. Default option - Simple combination of water consumed daily and a constant water lead concentration. Alternate option - Water lead concentration depends on contribution from several individual sources of water. Equation Where Used E-4b, E-5a E-4c, E-51 U-ld,f,l, U-2 E-4b, E-4c E-4c, E-5n E-4c, E-5q E-8a,b U-le,k, U-2 E-6a,b U-lb,h, U-2 Note: I = internal model parameter; E = external, user-specified parameter 15 ------- Parameter Name juices [AGE] juiceConc juice Consump[AGE] KPLECF[0] MCORT[STEPS] Description Lead intake from juices by age Concentration of lead in juice Daily consumption of juice total elimination rate from ECF-plasma pool Mass of lead in cortical bone at age range (solutions algorithm) Default Value or Equation Number E-4n 0.004292 2.018 11.656 15.692 15.692 15.692 19.646 27.471 - B-7e and B-9f Units ug/day ug/kg grams/day unitless ซ Age Range (mos) 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-84 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-84 0 and 0-84 lorE I E E I Basis for Values/Equations U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. U. S. Food and Drug Administration Center for Food Safety and Applied Nutrition Office of Plant and Dairy Foods and Beverages (May 16, 2006). Available online: http://www.cfsan.fda.gov/~comm/tds-toc.html U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. Quantity consumed based on Pennington (1983). 0 months - Simple combination of an assumed bone to blood lead concentration ratio, blood lead concentration, and weight of cortical bone. Basis for value of bone to blood lead concentration ratio was human autopsy data (Barry, 1981). 0-84 months - Application of the Backward Euler solution algorithm to the system of differential equations (B-6a-B-6i in Table A-3). Both cases above assume that the cortical bone to blood lead concentration ratio is equal to the bone (composite) to blood lead concentration ratio. Equation Where Used E-5k E-4n E-4n - B-6b,i, B-6.5b,i, B-7e, B-8d, B-9e,f Note: I = internal model parameter; E = external, user-specified parameter 16 ------- Parameter Name meat[AGE] meatConc meat consump[AGE] meatFraction MKIDNEY[STEPS] MLIVER[STEPS] Description Lead intake from meat if no game meat or fish is consumed at age range Concentration of lead in meat Consumption of meat at age range Fraction of meat consumption that is derived from market basket (i.e., total meat consumption - user-caught fish and game) Mass of lead in kidney at age range (solutions algorithm) Mass of lead in liver at age range (solutions algorithm) Default Value or Equation Number E-4o 0.007822 12.500 29.605 38.111 40.930 43.750 47.368 54.558 E-5a B-7f and B-9c B-7g and B-9b Units ug/day Hg*g g/day unitless ug ug Age Range (mos) 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-84 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-84 0 and 0-84 0 and 0-84 lorE I E I E I I Basis for Values/Equations U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. U. S. Food and Drug Administration Center for Food Safety and Applied Nutrition Office of Plant and Dairy Foods and Beverages (May 16, 2006). Available online: http://www.cfsan.fda.gov/~comm/tds-toc.html U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. Quantity consumed based on Pennington (1983). Calculated value. 0 months - Simple combination of an assumed kidney to blood lead concentration ratio, blood lead concentration, and weight of kidney. Basis for the value of the kidney to blood lead concentration ratio was human autopsy data (Barry, 1981). 0-84 months - Application of the Backward Euler solution algorithm to the system of differential equations (B-6a-B-6i in Table A-3). 0 months - Simple combination of an assumed liver to blood lead concentration ratio, blood lead concentration, and weight of the liver. Basis for the value of the liver to blood lead concentration ratio was human autopsy data (Barry, 1981). 0-84 months - Application of the Backward Euler solution algorithm to the system of differential equations (B-6a-B-6i in Table A-3). Equation Where Used E-4o, E-5a E-4o E-5k,l E-5d B-6b,f, B-6.5b,f, B-7f, B-8d, B-9c B-6b,e, B-6.5b,e, B-7g, B-8d, B-9b Note: I = internal model parameter; E = external, user-specified parameter 17 ------- Parameter Name MOTHER[STEPS] MPLASM[STEPS] MPLECF[STEPS] MRBC[STEPS] Description Mass of lead in soft tissues at age range (solutions algorithm) Mass of lead in plasma pool at age range (solutions algorithm) Mass of lead in plasma-extra-cellular fluid (plasma-ECF) at age range (solutions algorithm) Mass of lead in red blood cells at age range (solutions algorithm) Default Value or Equation Number B-7h and B-9d B-7d and B-9g B-7b and B-8a B-7c and B-9a Units Hg Hg "g "g Age Range (mos) 0 and 0-84 0 and 0-84 0 and 0-84 0 and 0-84 lorE I I I I Basis for Values/Equations 0 months - Simple combination of an assumed soft tissue to blood lead concentration ratio, blood lead concentration, and weight of the soft tissues at birth. Basis for the value of soft tissue to blood lead concentration ratio was human autopsy data (Barry et al, 1981), using total lead and total weight of other tissue. 0-84 months - Application of the Backward Euler solution algorithm to the system of differential equations (B-6a-B-6i in Table A-3). 0 months - Simple combination of the mass of lead in blood and red blood cells. 0-84 months - Based on the assumption that the lead concentration in plasma-extracellular fluid (ECF) is equal to the lead concentration in the plasma. 0 months - Based on two assumptions. (1) masses of lead in plasma-ECF and red blood cells are in kinetic quasi-equilibrium, and; (2) lead concentration in the plasma-ECF is equal to lead concentration in the plasma. 0-84 months - Application of the Backward Euler solution algorithm to the system of differential equations (B-6a-B-6i in Table A-3). 0 months - Based on the assumption that the masses of lead in plasma-ECF and red blood cells are in kinetic quasi-equilibrium. 0-84 months - Application of the Backward Euler solution algorithm to the system of differential equations (B-6a -B-6i in Table A-3). Equation Where Used B-6b,g, B-6.5b,g, B-7h, B-8d, B-9d B-7d, B-9g, B-lOa B-6a,c-i, B-6.5a,c-i, B-7b,d, B-8a, B-9a,b,c,d,e,f,g B-6b,d, B-6.5b,d, B-7c, B-8d, B-9a, B-lOa Note: I = internal model parameter; E = external, user-specified parameter 18 ------- Parameter Name MTRAB[STEPS] multiply factor NBCORT NBTRAB nuts [AGE] nutsConc Description Mass of lead in trabecular bone at age range (solutions algorithm) Ratio of in-door dust lead concentration to air lead concentration Variable for tissue lead masses and blood lead concentration at birth Variable for tissue lead masses and blood lead concentration at birth Lead intake from nuts by age Lead concentration in nuts Default Value or Equation Number B-7i and B-9e 100.000 0.400 0.200 E-4p 0.005798 Units "g Ug/g per , 3 ug/m unitless unitless mg/day "g*g Age Range (mos) 0 and 0-84 0-84 0 0 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-84 lorE I E I I I E Basis for Values/Equations 0 months - Simple combination of an assumed bone to blood lead concentration ratio, blood lead concentration, and weight of trabecular bone. Basis for the value of bone to blood lead concentration ratio was human autopsy data (Barry, 1981). 0-84 months - Application of the Backward Euler solution algorithm to the system of differential equations (B-6a-B-6i in Table A-3). Both cases above assume that trabecular bone to blood lead concentration ratio is equal to bone (composite) to blood lead concentration ratio. Analyses of the 1983 East Helena study (in U.S. EPA, 1989a, Appendix B-8) suggest about 267 ug/g increment of lead in dust for each ug/m3 lead in air. A much smaller factor of 100 ug/g dust lead per ug/m3 is assumed for non-smelter community exposure. [Variable can exceed 100.] Variable constant. Variable constant. U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. U. S. Food and Drug Administration Center for Food Safety and Applied Nutrition Office of Plant and Dairy Foods and Beverages (May 16, 2006). Available online: http://www.cfsan.fda.gov/~comm/tds-toc.html U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. Equation Where Used B-6b,h, B-6.5b,h, B-7i, B-8d, B-9e E-lla,b -D -D E-51 E-4p Note: I = internal model parameter; E = external, user-specified parameter 19 ------- Parameter Name nuts Consump[AGE] NS OCCUP[AGE] OccupConc OccupFraction OTHER[AGE] OtherConc OtherFraction other intake OUTFLOW[STEPS] Description Daily consumption of nuts Length of time interval in solution algorithm Dust lead intake from secondary occupation at age range Secondary occupation dust lead concentration Fraction of total dust ingested as secondary occupation dust Dust lead intake from other home exposure source at age range Lead concentration in house dust containing lead based paint Fraction of total dust ingested that results from lead- based home paint Lead intake from other media Lead output from the ECF-plasma pool from organs Default Value or Equation Number 0.087 0.962 0.875 0.962 0.962 0.962 0.875 1/6 E-12a 1200.000 0.000 E-12e 1200.000 0.000 0 B-6a,c B-6.5a,c Units grams/day days Mg/day "g/g unitless Mg/day "g/g unitless ug/day Mg/day Age Range (mos) 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 lorE E E I E E I E E I I Basis for Values/Equations Quantity consumed based on Pennington (1983). This user-selectable parameter is available mainly for adjusting the model run time to the speed of the computer. Newer, faster computers can run the model at the shortest timestep (15 min) in less than one minute. The default value, 4 hours, is based on a tradeoff between numerical accuracy of results and computer run-time. Except in the case of extreme exposure scenarios, there is no difference in the numerical accuracy at any user selectable value for timestep. Simple combination of amount of dust ingested, fraction of the total dust ingested as secondary occupational dust, and lead concentration in secondary occupational dust. Air Quality Criteria Document for Lead (U.S. EPA, 1986). The default condition is that there is no adult in the residence who works at a lead-related job. e.g., Simple combination of amount of dust ingested daily, fraction of the total dust ingested as lead-based home paint, and lead concentration in lead-based home paint. Air Quality Criteria Document for Lead (U.S. EPA, 1986). The default is that lead paint is not actively contributing to house dust. User defined. Calculated value. Equation Where Used E-4p B-6.5a,d-i, B-7b,c, B-8a,c,d, B-9a-f, B-lOb E-9c, E-12a E-12a E-9.5, E-12a E-9c, E-12e E-12e E-9.5 E-12e -D B-6a,c, B-6.5a,c Note: I = internal model parameter; E = external, user-specified parameter 20 ------- Parameter Name PAFD PAFF PAFP PAFS PAFW pasta[AGE] pastaConc pasta Consump[AGE] PBBLDO PBBLDMAT PBBLOODEND[MONTH ] RATBLPL RATFECUR Description Fraction of total absorption as passive absorption for dust, diet, paint, soil, and water at low dose Lead intake from pasta by age Concentration of lead in pasta Daily consumption of lead Lead concentration in blood Maternal blood lead concentration at childbirth Lead concentration in blood at age range Ratio of lead mass in blood to lead mass in plasma-ECF Ratio of endogenous fecal lead elimination rate to urinary lead elimination rate Default Value or Equation Number 0.200 E-4q 0.006163 10.409 18.902 26.263 25.915 25.566 27.134 30.183 B-7a 1.0 B-lOc 100.000 0.750 Units unitless Mg/day Hg*g grams/day ug/dL ug/dL ug/dL unitless unitless Age Range (mos) 0-84 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-84 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0 adult 0-84 0-84 0-84 lorE E I E E I E I I I Basis for Values/Equations Based on in vitro everted rat intestine data (Aungst and Fung, 1981), reanalyses (Marcus, 1994) of infant baboon data (Mallon, 1983), and infant duplicate diet study (Sherlock and Quinn, 1986). U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. U. S. Food and Drug Administration Center for Food Safety and Applied Nutrition Office of Plant and Dairy Foods and Beverages (May 16, 2006). Available online: http://www.cfsan.fda.gov/~comm/tds-toc.html U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. Quantity consumed based on Pennington (1983). Based on 85% of maternal blood lead concentration (U.S. EPA, 1989a). Based on TRW analysis of 1999-2002 NHANES data. Simple combination of the blood lead concentrations determined in each iteration in the solution algorithm between the previous month and that month. Based on the lower end of the 50-500 range for the red cell/plasma lead concentration ratio recommended in Diamond and O'Flaherty (1992a). Assume child ratio is larger than the adult ratio; values derived from a reanalysis of data from Ziegler et al. (1978) and Rabinowitz and Wetherill (1973). Equation Where Used U-la-1 E-5n E-4q E-4q B-7a,b,c, e-i B-7a B-lOc B-2b-d,g,i,k,m, B-3 B-lf Note: I = internal model parameter; E = external, user-specified parameter 21 ------- Parameter Name RATOUTFEC RCORTO RECSUM[STEPS] ResCoef[15] RKIDNEYO RLIVERO ROTHERO RTRABO S ATUPTAKE [MONTH] Description Ratio of elimination rate via soft tissues to endogenous fecal lead elimination rate Variable for tissue lead masses and blood lead concentration at birth Lead transfer time from plasma-ECF to all compartments except plasma Stores parameter values that are used in various equations in the biokinetic module Variable for tissue lead masses and blood lead concentration at birth Variable for tissue lead masses and blood lead concentration at birth Variable for tissue lead masses and blood lead concentration at birth Variable for tissue lead masses and blood lead concentration at birth Half saturation absorbable lead intake at age range Default Value or Equation Number 0.750 78.900 -D 0.100 20.000 10.000 10.000 10.000 1.000 100.000 0.750 0.750 0.000 0.000 0.000 0.000 0.000 0.000 10.600 13.000 16.000 51.200 U-3 Units unitless unitless days - unitless unitless unitless unitless Mg/day Age Range (mos) 0-84 0 0-84 0 0 0 0 0-84 lorE I I I I I I I I I Basis for Values/Equations Within the range of values derived from a reanalysis of data from Ziegler et al. (1978) and Rabinowitz and Wetherill (1973). Variable constant. Calculated value Calculated value Variable constant. Variable constant. Variable constant. Variable constant. Assumed proportional to the weight of body. The coefficient of proportionality is assumed to depend on the estimate of the variable for a 24 month old and the corresponding body weight. Equation Where Used B-lg -D -D B-la-g; B-2a; B-3 -D -D -D -D U-lg-1, U-3 Note: I = internal model parameter; E = external, user-specified parameter 22 ------- Parameter Name SATUPTAKE2 sauce [AGE] sauceConc sauce Consump[AGE] SCHOOL[AGE] SchoolConc SchoolFraction SECHOME[AGE] SecHomeConc SecHomeFraction Description Half saturation absorbable lead intake for a 2-year-old Lead intake from sauces by age Concentration of lead in tomato sauce Daily consumption of tomato sauce Dust lead intake from school at age range Dust lead concentration at school Fraction of total dust ingested daily as school dust Dust lead intake at secondary home at age range Secondary home dust lead concentration Fraction of total dust ingested daily as secondary home dust Default Value or Equation Number 100.000 E-4r 0.010215 1.647 4.784 5.569 6.902 8.157 8.235 8.235 E-12b 200.000 0.000 E-12d 200.000 0.000 Units Mg/day mg/day Hg*g grams/day Mg/day Hg/g unitless Mg/day Hg/g unitless Age Range (mos) 0-84 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-84 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-84 0-84 0-84 0-84 0-84 0-84 lorE E I E E I E E I E E Basis for Values/Equations Extrapolated from reanalysis of human infant data (Sherlock and Quinn, 1986) and infant baboon data (Mallon, 1983). U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. U. S. Food and Drug Administration Center for Food Safety and Applied Nutrition Office of Plant and Dairy Foods and Beverages (May 16, 2006). Available online: http://www.cfsan.fda.gov/~comm/tds-toc.html U.S. Food and Drug Administration (FDA). 2006. Total Diet Study. Quantity consumed based on Pennington (1983). Simple combination of amount of dust ingested daily, the fraction of total dust ingested daily as school dust, and lead concentration in dust at school. By default, this dust lead concentration is set to the same as the residential dust lead concentration. Based on the default assumption that children are not in school. Simple combination of amount of dust ingested daily, fraction of dust ingested daily as secondary home dust, and lead concentration in dust at the secondary home. Based on the assumption that dust lead concentration in a secondary home is the same as the default dust lead concentration in the primary home. Based on the default assumption that the child does not spend a significant amount of time in a secondary home. Equation Where Used U-3 E-5q E-4r E-4r E-9c, E-12d E-12b E-9.5, E-12b E-9c, E-12d E-12d E-9.5, E-12d Note: I = internal model parameter; E = external, user-specified parameter 23 ------- Parameter Name soil content[AGE] soil indoor[AGE] soil ingested[AGE] STEPS SUM 1 [STEPS] SUM2[STEPS] SUM3 [STEPS] TBLBONE TBLBONE is not an array Description Outdoor soil lead concentration Indoor household dust lead concentration at age range Soil and dust (combined) consumption at age range Iterations per month Compartmental lead masses solution algorithm Compartmental lead masses solution algorithm Compartmental lead masses solution algorithm Lead transfer time from blood to bone at age range Default Value or Equation Number 200.000 E-lla-d 0.085 0.135 0.135 0.135 0.100 0.090 0.085 B-lOb B-8b B-8c B-8d B-le Units "g/g "g/g g/day days -D -D -D days Age Range (mos) 0-84 0-84 0-11 12-23 24-35 36-47 48-59 60-71 72-84 -D 0-84 0-84 0-84 0-84 lorE E E E I I I I I Basis for Values/Equations Upper bound value for a plausible urban background soil lead concentration (U.S. EPA, 1989a; HUD, 1990). Under alternate dust sources model, based on assumption that both soil and outdoor air contribute to indoor dust lead. Based on values reported in OAQPS report (U.S. EPA, 1989a, pp. A-16). The values reported were estimated for children, ages 12-48 mos, by several authors such as Binder et al. (1986) and Clausing et al. (1987). Sedman (1987) extrapolated these estimates to those for children, ages 0-84 months. Iteration interval. For Backward Euler calculation. Intermediate variables for Equations B-8b to B-8d. For Backward Euler calculation. Intermediate variables for Equations B-8b to B-8d. For Backward Euler calculation. Intermediate variables for Equations B-8b to B-8d. 24 months - Initialization is keyed to the 24 month old child, based in part on information from Heard and Chamberlain (1982) for adults, and O'Flaherty (1992). Once the concentration ratios are fixed, the exact value of this variable, within a wide range of possible values, has little effect on the blood lead value. 0-84 months - Assumed proportional body surface area. The coefficient of proportionality is assumed to depend on an estimate of the variable for a 24 month old and the corresponding body surface area. Also, it is assumed that body surface area varies as 1/3 power of the weight of body based on Mordenti (1986). Equation Where Used E-8b, E-lla E-9b,d, E-lla-d E-8a,b, E-9a,d,e, E-10 B-lOb B-8a,b B-8a,c B-8a,d B-le,h, B-2i,k Note: I = internal model parameter; E = external, user-specified parameter 24 ------- Parameter Name TBLFEC TBLFEC is not an array TBLKID TBLKID is not an array TBLLIV TBLLIV is not an array Description Lead transfer time from blood to feces at age range Lead transfer time from blood to kidney at age range Lead transfer time from blood to liver at age range Default Value or Equation Number B-lf i ft 1U and B-ld 10 and B-lb Units days days days Age Range (mos) 0-84 0-84 0-84 lorE I I I Basis for Values/Equations Simple combination of an assumed ratio of urinary lead elimination rate to endogenous fecal lead elimination rate, and lead transfer time from blood to urine (See RATFECUR). The ratio of elimination rates was estimated for adults using Chamberlain et al. (1978) and Chamberlain (1985) and is assumed to apply to ages 0-84 months. 24 months - Initialization is keyed to the 24 month old child, based in part on information from Heard and Chamberlain (1982) for adults, and O'Flaherty (1992). Once the concentration ratios are fixed, the exact value of this variable, within a wide range of possible values, has little effect on the blood lead value. 0-84 months - Assumed proportional body surface area. The coefficient of proportionality is assumed to depend on an estimate of the variable for a 24 month old and the corresponding body surface area. Also, it is assumed that body surface area varies as 1/3 power of the weight of body based on Mordenti (1986). 24 months - Initialization is keyed to the 24 month old child, based in part on information from Heard and Chamberlain (1982) for adults, and O'Flaherty (1992). Once the concentration ratios are fixed, the exact value of this variable, within a wide range of possible values, has little effect on the blood lead value. 0-84 months - Assumed proportional body surface area. The coefficient of proportionality is assumed to depend on an estimate of the variable for a 24 month old and the corresponding body surface area. Also, it is assumed that body surface area varies as 1/3 power of the weight of body based on Mordenti (1986). Equation Where Used B-lf,g, B-2e,f B-ld,g, B-2g,h B-lb, B-2d,e Note: I = internal model parameter; E = external, user-specified parameter 25 ------- Parameter Name TBLOTH TBLOTH is not an array TBLOUT TBLOUT is not an array Description Lead transfer time from blood to other soft tissue at age range Lead transfer time from blood to elimination pool via soft tissue at age range Default Value or Equation Number 10 and B-lc B-la U Ifc Units days days Age Range (mos) 0-84 0-84 lorE I I Basis for Values/Equations 24 months - Initialization is keyed to the 24 month old child, based in part on information from Heard and Chamberlain (1982) for adults, and O'Flaherty (1992). Once the concentration ratios are fixed, the exact value of this variable, within a wide range of possible values, has little effect on the blood lead value. 0-84 months - Assumed proportional body surface area. The coefficient of proportionality is assumed to depend on an estimate of the variable for a 24 month old and the corresponding body surface area. Also, it is assumed that body surface area varies as 1/3 power of the weight of body based on Mordenti (1986). Simple combination of an assumed ratio of elimination rate via soft tissues to endogenous fecal lead elimination rate, times the lead transfer time from blood to feces (See RATOUTFEC). Equation Where Used B-lc B-2m,n B-lg, B-2n,o Note: I = internal model parameter; E = external, user-specified parameter 26 ------- Parameter Name TBLUR TBLUR is not an array TBONEBL TBONEBL is not an array TCORTPL[MONTH] Description Lead transfer time from blood to urine at age range Lead transfer time from bone to blood at age range Lead transfer time from cortical bone to plasma-ECF at age range Default Value or Equation Number 20 and B-la B-lh B-21 Units days days days Age Range (mos) 0-84 0-84 0-84 lorE I I I Basis for Values/Equations 24 months - Assumed proportional to body surface area. The coefficient of proportionality is assumed to depend on an adult estimate for the variable and the corresponding body surface area. The adult estimate of 39 days was obtained using Araki et al. (1986a, 1986b, 1987), Assenato et al. (1986), Campbell etal. (1981), Carton etal. (1987), Chamberlain etal. (1978), Folashade etal. (1991), Heard and Chamberlain (1982), He et al. (1988), Kawaii et al. (1983), Kehoe (1961), Koster et al. (1989), Manton and Malloy (1983), Rabinowitz and Wetherill (1973), Rabinowitz et al. (1976), and Yokoyama et al. (1985). 0-84 months - Assumed proportional body surface area. The coefficient of proportionality is assumed to depend on an estimate of the variable for a 24 month old and the corresponding body surface area. Both cases above assume that (a) body surface area varies as 1/3 power of weight of body based on Mordenti (1986) and (b) respectively, 70 kg and 12.3 kg are standard adult and 24-month-old body weights based on Spector (1956). Since glomerular filtration rate (GFR) is proportional to body surface area for ages > 24-month based on Weil (1955), surface area scaling is equivalent to scaling by GFR for ages >24 months. Based on the assumption that masses of lead in bone and blood are in kinetic quasi-equilibrium. Based on the assumption that the cortical and trabecular bone pools have similar lead kinetics for children younger than 84 months. Equation Where Used B-la,f, B-2c B-lh, B-2j,l B-21, B-6b,i, B-6.5b,i, B-8c,d, B-9f Note: I = internal model parameter; E = external, user-specified parameter 27 ------- Parameter Name time_out[AGE] TKIDPL[MONTH] TLIVALL TLIVFEC[MONTH] TLIVPL[MONTH] TotAltSource TOTHALL TOTHOUT[MONTH] Description Time spent outdoors by age Lead transfer time from kidney to plasma- ECF at age range Lead transfer time from liver to all tissues for SUM2 Lead transfer time from liver to feces at age range Lead transfer time from liver to plasma- ECF at age range Fractional percent due to all secondary sources Lead transfer time from other soft tissues to all tissues for SUM2 Lead transfer time from soft tissues to elimination pool at age range Default Value or Equation Number 1.000 2.000 3.000 4.000 4.000 4.000 4.000 B-2h B-9i B-2e B-2f None B-9h B-2o Units Hr/day days days days days % days days Age Range (mos) 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-84 0-84 0-84 0-84 -D 0-84 0-84 lorE E I I I I I I I Basis for Values/Equations Values are reported in the OAQPS staff report (U.S. EPA, 1989a, p. A-2) and the IEUBK Technical Support Document (U.S. EPA, 1990a). The values have been derived from a literature review (Pope, 1985). Based on the assumption that the lead transfer time from kidney to blood is equal to the lead transfer time from kidney to plasma-ECF. Average transition time from liver to all tissues from SUM2. Based on the assumption that the masses of lead in liver and blood are in kinetic quasi-equilibrium. Based on the assumption that the lead transfer time from liver to blood is equal to the lead transfer time from liver to plasma-ECF. Total fractional percent due to all secondary sources. Average transition time from other soft tissues to all tissues from SUM2. Based on the assumption that the masses of lead in soft tissues and blood are in kinetic quasi-equilibrium. Equation Where Used E-2 B-2h, B-6b,f, B-6.5b,f, B-8c,d, B-9c B-8c,d, B-9b,i B-2e,f, B-4i, B-6e, B-6.5e B-2e, B-6b,e, B-6.5b,e, B-8c,d, B-9i B8c,d B-9d,h B-8c,d, B-9d,h B-2o, B-6g, B-6.5g, B-8c,d, B-9h Note: I = internal model parameter; E = external, user-specified parameter 28 ------- Parameter Name TOTHPL[MONTH] TPLCORT[MONTH] TPLKID[MONTH] TPLLIV[MONTH] TPLOTH[MONTH] TPLRBC Description Lead transfer time from soft tissues to plasma-ECF at age range Lead transfer time from plasma-ECF to cortical bone at age range Lead transfer time from plasma-ECF to kidney at age range Lead transfer time from plasma-ECF to liver at age range Lead transfer time from plasma-ECF to soft tissues at age range Lead transfer time from plasma-ECF to red blood cells for SUM2 Default Value or Equation Number B-2n B-2k B-2g B-2d B-2m 0.100 Units days days days days days days Age Range (mos) 0-84 0-84 0-84 0-84 0-84 0-84 lorE I I I I I I Basis for Values/Equations Based on the assumption that the lead transfer time from soft tissues to blood is equal to the lead transfer time from soft tissues to plasma-ECF. Based on the following assumptions: The rate at which lead leaves the plasma-ECF to reach the bone is proportional to the rate at which lead leaves the blood to reach the same pool. The cortical and trabecular bone pools have similar lead kinetics for children younger than 84 months. The cortical bone is 80% of the weight of bone based on Leggett et al. (1982). Based on the assumption that the rate at which lead leaves the plasma-ECF to reach the kidney is proportional to the rate at which lead leaves the blood to reach the same pool. Based on the assumption that the rate at which lead leaves the plasma-ECF to reach the liver is proportional to the rate at which lead leaves the blood to reach the same pool. Based on the assumption that the rate at which lead leaves the plasma-ECF to reach the soft tissues is proportional to the rate which lead leaves the blood to reach the same pool. Initialization value of 0. 1 was assigned as plausible nominal value reflecting best professional judgement on appropriate time scale for composite process of transfer of lead through the red blood cell membrane to lead binding components. Equation Where Used B-2n, B-6b,g, B-6.5b,g, B-8c,d, B-9h B-2k, B-6c,i, B-6.5c,i, B-8b,c, B-9e,f B-2g, B-6c,f, B-6.5c,f, B-8b,c, B-9c B-2d, B-6c,e, B-6.5c,e, B-8b, B-9b B-2m, B-6c,g, B-6.5c,g, B-8b,c, B-9d B-2a,b, B-2.5, B-7b,c Note: I = internal model parameter; E = external, user-specified parameter 29 ------- Parameter Name TPLRBC2 TPLTRAB[MONTH] TPLUR[MONTH] TRBCPL TTRABPL[MONTH] TWA[AGE] UPAIR[MONTH] Description Lead transfer time from plasma- ECF to red blood cells constrained by the maximum capacity of red blood cell lead concentration at age range Lead transfer time from plasma- ECF to trabecular bone at age range Lead transfer time from plasma-ECF to urine at age range Lead transfer time from red blood cells to plasma-ECF Lead transfer time from trabecular bone to plasma-ECF fluid at age range Time weighted average air lead concentration at age range Air lead uptake at age range Default Value or Equation Number B-2.5 B-2i B-2c B-2b B-2J E-2 U-4 Units days days days days days ug/m3 Mg/day Age Range (mos) 0-84 0-84 0-84 0-84 0-84 0-84 0-84 lorE I I I I I I I Basis for Values/Equations Simple combination of the lead transfer time from plasma-ECF to red blood cells, and the ratio of red blood cell lead concentration to the corresponding maximum concentration. Based on Marcus (1985a) and reanalysis of infant baboon data. Based on the following assumptions: The rate at which lead leaves the plasma-ECF to reach the bone is proportional to the rate at which lead leaves the blood to reach the same pool. The cortical and trabecular bone pools have similar lead kinetics. The trabecular bone is 20% of the weight of bone based on Leggett et al. (1982). Based on the assumption that the rate at which lead leaves the plasma-extra-cellular fluid to reach the urine pool is proportional to the rate at which lead leaves the blood to reach the same pool. Based on the assumption that the transfer time out of red blood cells is similar at all ages, since mean red cell value is similar. Based on the assumption that the cortical and trabecular bone pools have similar lead kinetics for children younger than 84 months. Simple combination of outdoor and indoor air lead concentrations and the number of hours spent outdoors. Simple combination of media-specific lead intake and the corresponding net absorption coefficient. Equation Where Used B-2.5, B-6c,d, B-6.5c,d, B-8b,c, B-9a B-2i, B-6c,h, B-6.5c,h, B-8b,c, B-9e B-2c, B-6c, B-6.5c, B-8b B-2b, B-6b,d, B-6.5b,d, B-7b,c, B-8c,d, B-9a B-2J, B-6b,h, B-6.5b,h, B-8c,d, B-9e E-2, E-3 U-4, U-5 Note: I = internal model parameter; E = external, user-specified parameter 30 ------- Parameter Name UPDIET[MONTH] UPDUSTA[MONTH] UPDUST[MONTH] UPSOIL[MONTH] UPTAKE[MONTH] UPWATER[MONTH] UserFishConc userFishFraction UserFruitConc userFruitFraction UserGameConc userGameFraction UserVegConc userVegFraction vary indoor vary outdoor Description Diet lead uptake at age range Lead uptake rate from alternate sources at age range Dust lead uptake at age range Soil lead uptake at age range Total lead uptake at age range Water lead uptake at age range Lead concentration in fish Fraction of total meat consumed as fish Lead concentration in home grown fruits Fraction of total fruits consumed as home grown fruits Lead concentration in game animal meat Fraction of total meat consumed as game animal meat excluding fish Lead concentration in home grown vegetables Fraction of total vegetables consumed as home grown vegetables Indoor soil lead concentration Outdoor soil lead concentration Default Value or Equation Number U-la U-lf U-lc U-le U-5 U-lb 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -D -D Units Mg/day Mg/day Mg/day Mg/day ug/mo Mg/day "g/g unitless Hg/g unitless Hg/g unitless Hg/g unitless Hg/g "g/g Age Range (mos) 0-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 lorE I I I I I I E E E E E E E E E E Basis for Values/Equations Simple combination of media-specific lead intake and the corresponding net absorption coefficient. Simple combination of media-specific lead intake and the corresponding net absorption coefficient. Simple combination of media-specific lead intake and the corresponding net absorption coefficient. Simple combination of media-specific lead intake and the corresponding net absorption coefficient. Simple combination of the media-specific daily lead uptake rates, translated to a monthly rate. Simple combination of media-specific lead intake and the corresponding net absorption coefficient. Based on the assumption that locally caught fish are consumed jig Pb/g fish as prepared. Based on the assumption that locally caught fish are consumed. Based on the assumption that home grown fruits are consumed ug Pb/g fruit as prepared. Based on the assumption that home grown fruits are consumed. Based on the assumption that game meat is consumed ug Pb/g game as prepared. Based on the assumption that game meat is consumed. Based on the assumption that home grown vegetables are consumed jig Pb/g vegetables as prepared. Based on the assumption that home grown vegetables are consumed. User specified. User specified. Equation Where Used U-la,g, U-5 U-ldj, U-5 U-lc,i, U-5 U-le,k, U-5 B-6a, B-6.5a, B-8a, U-5 U-lb,h, U-5 E-5h E-5a,h E-5f E-5d,e,f E-5i E-5a,i E-5g E-5b,c,g -D -D Note: I = internal model parameter; E = external, user-specified parameter 31 ------- Parameter Name vegFraction vent_rate[AGE] VOLBLOOD[MONTH] VOLECF[MONTH] VOLPLASM[MONTH] VOLRBC[MONTH] water consumption[AGE] Description Fraction of vegetable consumption that is derived from market basket (i.e., total vegetable consumption - user-grown) Ventilation rate at age range Volume of blood at age range Volume of extra-cellular fluid (ECF) at age range Volume of plasma at age range Volume of red blood cells at age range Daily amount of water consumed at age range Default Value or Equation Number E-5b 2.000 3.000 5.000 5.000 5.000 7.000 7.000 B-5a B-5d B-5c B-5b 0.200 0.500 0.520 0.530 0.550 0.580 0.590 Units unitless M3/day dL dL dL dL L/day Age Range (mos) 0-84 0-11 12-23 24-35 36-47 48-59 60-71 72-84 0-84 0-84 0-84 0-84 0-11 12-23 24-35 36-47 48-59 60-71 72-84 lorE E E I I I I E Basis for Values/Equations Calculated value. Values are reported in the OAQPS report (U.S. EPA, 1989a, pp. A-3) and the IEUBK Technical Support Document (U.S. EPA 1990a). These estimates are based on body size in combination with smoothed data from Phalen et al. (1985). Statistical fitting of data from Silve et al. (1987), Spector (1956). and Altman and Dittmer (1973) The volume of extracellular fluid that exchanges rapidly with plasma is estimated to be 73% of the blood volume based on Rabinowitz (1976). This additional volume of distribution is assumed to be the volume of the extra-cellular fluid pool, which is the difference between the volume of the distribution and the blood volume. Statistical fit to VOLBLOOD(MONTH) - VOLRBC(MONTH) Statistical fit to hematocrit x blood volume. Exposure Factors Handbook (U.S. EPA, 1989b). Equation Where Used E-5e, E-5f E-3 B-lh, B-2e,f,h,n,o, B-5a,d,e, m, B-lOa B-5d, B-9g B-5c, B-7b,c, B-9g B-2.5, B-5b E-6a,b Note: I = internal model parameter; E = external, user-specified parameter 32 ------- Parameter Name weight soil WTBLOOD[MONTH] WTBODY[MONTH] WTBONE[MONTH] WTCORT[MONTH] WTECF[MONTH] WTKIDNEY[MONTH] WTLIVER[MONTH] WTOTHER[MONTH] WTTRAB[MONTH] Description Percentage of total soil and dust ingestion that is soil Weight of blood at age range Weight of body at age range Weight of bone at age range Weight of cortical bone at age range Weight of extra-cellular fluid (ECF) in lead volume distribution at age range Weight of kidney at age range Weight of liver at age range Weight of other tissues at age range Weight of trabecular bone at age range Default Value or Equation Number 45.000 B-5m B-5f B-5g B-5h B-5e B-5J B-5k B-51 B-5i Units % kg kg kg kg kg kg kg kg kg Age Range (mos) 0-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 0-84 lorE E I I I I I I I I I Basis for Values/Equations IEUBK Guidance Manual, Section 2.3 (U.S. EPA, 1994). Based on a blood density of 1.056 kg/L (Spector 1956). Statistical fitting of data from Silve et al. (1987); also Spector (1956) and Altaian and Dittmer (1973). Also, body weight of 24 month old is assumed to be 12.3 kg (Spector 1956). WTBONE[MONTH] =0.111 * WTBODY[MONTH] [MONTH] <12 months = 0.838 + 0.02 * [MONTH] Assumed to be 80% of the weight of the bone based on Leggettefa/. (1982). Based on an assumed ECF density approximately the same as water, of 1.0 kg/L. Statistical fitting of data from Silve et al. (1987); also Spector (1956) and Altaian and Dittmer (1973). Also, body weight of 24 month old is assumed to be 12.3 kg (Spector, 1956). Statistical fitting of data from Silve et al. (1987); also Spector (1956) and Altaian and Dittmer (1973). Also, body weight of 24 month old is assumed to be 12.3 kg (Spector, 1956). Simple combination of the weight of body and the weights of kidney, liver, bone, blood, and extra- cellular fluid. Assumed to be 20% of the weight of the bone based on Leggett et al. (1982). Equation Where Used E-8a,b, E-9a,d,e, E-10 B-51,m B-la-e, B-5f,g,l, U-3 B-5g-i B-lh, B-5h,l, B-7e B-5e,l B-2h, B-5j,l, B-7f B-2e,f, B-5k,l, B-7g B-2n,o, B-51, B-7h B-lh,l, B-7i Note: I = internal model parameter; E = external, user-specified parameter 33 ------- REFERENCES Altaian, P.L. and D.S. Dittmer (eds). 1973. Biological Data Book, 2nd Ed., Bethesda, MD. Fed. Amer. Soc. Exper. Biol. 195-201. Araki, S., H. Aono, and K. Murata. 1986a. Adjustment of Urinary Concentration to Urinary Volume in Relation to Erythrocyte and Plasma Concentration: An Evaluation of Urinary Heavy Metals and Organic Substances. Arch. Environ. Hlth. 41(3): 171-177. Araki, S., H. Aono, K. Yokoyama, and K. Murata. 1986b. Filterable Plasma Concentration, Glomerular Filtration, Tubular Balance, and Renal Clearance of Heavy Metals and Organic Substances in Metal Workers. Arch. Environ. Hlth . 41(4): 216- 221. Araki, S., K. Murata, and H. Aono. 1987. Central and Peripheral Nervous System Dysfunction in Workers Exposed to Lead, Zinc and Copper. Int. Arch. Occup. Environ. Health. 59: 177-187. Assenato, G., C. Paci, M. Baser, R. Molinini, R.G. Candela, B.M. Altamura, and R. Giorgino. 1986. Sperm Count Suppression Without Endocrine Dysfunction In Lead-Exposed Men. Arch. Environ. Hlth. 41(6): 387-390. Aungst, B.J. and H. Fung. 1981. Kinetic characterization of in vitro lead transport across the rat small intestine. Toxicol. Appl. Pharmacol. 61: 39-57. Barry,P.S.I. 1981. Concentrations of Lead in the Tissuesof Children, British Journal of Industrial Medicine. 38: 61-71. Binder, S., D. Sokal, and D. Maughan. 1986. Estimating soil ingestion: The use of tracer elements in estimating the amount of soil ingested by young children. Arch. Environ. Health. 41:341-345. Campbell, B.C., H.L. Elliott, and P.A. Meredith. 1981. Lead Exposure and Renal Failure: Does Renal Insufficiency Influence Lead Kinetics. Toxicology Letters. 9:121-124. Carton, A., A. Maradona, and M. Arribas. 1987. Acute-Subacute Lead Poisoning: Clinical Findings and Comparative Study of Diagnostic Tests. Arch. Intern. Med. 147:697-703. Center for Disease Control and Prevention (CDC). 1991. Preventing lead poisoning in young children. Chamberlain, A.C. 1985. Prediction of response of blood lead to airborne and dietary lead from voluntary experiments with lead isotopes. Proc. R. Soc. London B. 224:149-182. Chamberlain, A.C., MJ. Heard, P. Little, D. Newton, A.C. Wells, and R.D. Wiffen. 1978. Investigations into lead from motor vehicles. Report of Work at Environmental and Medical Sciences Division, AERE, Harwell, HL78/4122 (C. 10). Clausing, P., B. Brunekreef, and J. H. van Wijnen. 1987. A method for estimating soil ingestion by children. Int. Arch. Occup. Environ. Health. 59: 73-82. DeSilva, P.E. 1981a. Lead in plasma ~ Its analysis and biological significance. Thesis for Master of Public Health. University of Sydney, Australia. DeSilva, P.E. 1981b. Determination of lead in plasma and studies on its relationship to lead in erythrocytes. Brit. J. Industr. Med. 38:209-217. Diamond, G.L. and E.J. O'Flaherty. 1992a. Review of the default value for lead blood-to-urine transfer coefficient (TRBCPL, TPLRBC) in the US EPA Uptake/Biokinetic Model. Report to U.S. Environmental Protection Agency, ECAO/CINC from Syracuse Research Corporation under Contract No. 68-10-0043, SRC TR-92-134. Folashade, O.O. and G.W. Crockford. 1991. Sweat Lead Levels in Persons with High Blood Lead Levels: Experimental Evaluation of Blood Lead by Ingestion of Lead Chloride. The Science of the Total Environment 108: 235-242. 34 ------- Harley, N.H. and T.H. Kneip. 1985. An integrated metabolic model for lead in humans of all ages. Final report to U.S. Environmental Protection Agency, from New York University, Department Environmental Medicine, Contract No. B44899. He, F., S. Zhang, G. Li, J. Huang, and Y. 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