7
PBPK Modeling White Paper: Addressing the Use of PBPK Models to Support Derivation of Acute Exposure Guideline Levels1

PREFACE

This White Paper describes the guidance that is proposed for use in the integration of physiologically based pharmacokinetic (PBPK) modeling in risk assessment in the EPA Acute Exposure Guideline Level (AEGL) program. After finalization, the guidance document will be added to the existing AEGL guidance for risk assessment activities. Therefore, the PBPK White Paper does not describe the entire methodology; rather, it describes the additional steps when PBPK modeling is undertaken within the existing risk assessment paradigm. As in any methodology, every facet of the method cannot be explicitly stated in a manner that is universally applicable to all chemicals. Where some details are not specified, the risk assessment process will be handled in accordance with the U.S. Environmental Protection Agency (EPA) document Approaches for the Application of Physiologically Based Pharmacokinetic (PBPK) Modeling and Supporting Data in Risk Assessment (EPA 2006).

1

This White Paper was prepared by James E. Dennison, of Century Environmental Hygiene; Claudia Troxel, of Oak Ridge National Laboratory; and Robert Benson, of the U.S. Environmental Protection Agency (EPA), with the assistance of numerous scientists and risk assessors. Guidance from Ernest Falke, Marquea D. King, and Iris Camacho, of the AEGL Development Team, EPA; review by Robert Young, of Oak Ridge National Laboratory; review and discussions with William Boyes, Hugh Barton, Jane Ellen Simmons, Marina Evans, and Vernon Benignus, of the EPA National Health and Environmental Effects Research Laboratory, and Hisham El-Masri, Paul Schlosser, Robert Dewoskin, and George Woodall, of the EPA National Center for Environmental Assessment; and comments from international National Advisory Committee participants Ursula Gundert-Remy and Peter Griem, of Germany, were vital in its preparation.



The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001
Copyright © National Academy of Sciences. All rights reserved.
Terms of Use and Privacy Statement



Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.

OCR for page 381
7 PBPK Modeling White Paper: Addressing the Use of PBPK Models to Support Derivation of Acute Exposure Guideline Levels1 PREFACE This White Paper describes the guidance that is proposed for use in the in- tegration of physiologically based pharmacokinetic (PBPK) modeling in risk assessment in the EPA Acute Exposure Guideline Level (AEGL) program. After finalization, the guidance document will be added to the existing AEGL guid- ance for risk assessment activities. Therefore, the PBPK White Paper does not describe the entire methodology; rather, it describes the additional steps when PBPK modeling is undertaken within the existing risk assessment paradigm. As in any methodology, every facet of the method cannot be explicitly stated in a manner that is universally applicable to all chemicals. Where some details are not specified, the risk assessment process will be handled in accordance with the U.S. Environmental Protection Agency (EPA) document Approaches for the Application of Physiologically Based Pharmacokinetic (PBPK) Modeling and Supporting Data in Risk Assessment (EPA 2006). 1 This White Paper was prepared by James E. Dennison, of Century Environmental Hygiene; Claudia Troxel, of Oak Ridge National Laboratory; and Robert Benson, of the U.S. Environmental Protection Agency (EPA), with the assistance of numerous scientists and risk assessors. Guidance from Ernest Falke, Marquea D. King, and Iris Camacho, of the AEGL Development Team, EPA; review by Robert Young, of Oak Ridge National Laboratory; review and discussions with William Boyes, Hugh Barton, Jane Ellen Sim- mons, Marina Evans, and Vernon Benignus, of the EPA National Health and Environ- mental Effects Research Laboratory, and Hisham El-Masri, Paul Schlosser, Robert De- woskin, and George Woodall, of the EPA National Center for Environmental Assessment; and comments from international National Advisory Committee participants Ursula Gundert-Remy and Peter Griem, of Germany, were vital in its preparation. 381

OCR for page 381
382 Acute Exposure Guideline Levels 1. INTRODUCTION AEGL values are developed in accordance with the Standing Operating Procedures for Developing Acute Exposure Guidelines Levels (AEGLs) for Hazardous Substances (NRC 2001). At the request of the AEGL/National Advi- sory Committee (NAC) and the AEGL Subcommittee of the Committee on Toxicology, National Academy of Sciences, this White Paper has been prepared to describe an approach for integrating the use of PBPK modeling into the de- velopment of AEGL values. PBPK modeling serves as a useful adjunct to risk assessment of systemi- cally acting chemicals by improving the basis of, or entirely allowing for, ex- trapolation of pharmacokinetics between animals and humans, extrapolation between various exposure scenarios (e.g., what exposure concentration for 10 minutes [min] results in the same internal dose produced from a 4-hour [h] ex- posure), and other types of extrapolation. As internal dose of a chemical agent is more closely associated with toxicity than is external exposure level of chemi- cals, extrapolating on the basis of internal dose is more reliable. In a sense, the use of PBPK models factors pharmacokinetic differences out of the extrapola- tion because they are handled by dose calculations instead of on the basis of an assumed equivalency followed by application of an uncertainty factor (UF) that is usually preset because of lack of knowledge about the true difference. As a result of using calculated doses, the overall uncertainty is reduced, and therefore the overall UFs may be reduced, allowing for more realistic exposure guidelines, which is the purpose in the advancement of the risk assessment process. The risk assessment process includes identifying a point of departure (POD) from toxicity studies. The POD is usually the highest exposure concen- tration that did not result in the effect under consideration and may be a no- observed-adverse-effect level (NOAEL), a lowest-observed-adverse-effect level (LOAEL) if a NOAEL is not available, a level from a benchmark dose (BMD), or another value. The POD is then divided by UFs composed of estimated uncer- tainty in interspecies extrapolation, intraspecies variability, and other factors including weakness in the toxicologic database of information on a chemical. Briefly, PBPK models are a description of the body and processes within the body (animal and human) that affect the disposition of a chemical. Disposi- tion, or pharmacokinetics, includes the processes of absorption, distribution, metabolism, and excretion of chemicals. After development with necessary pa- rameters and equations, the models calculate the concentration of the chemical (and metabolites, if necessary) in various parts of the body using exposure con- centrations as the input. The main function PBPK modeling serves in risk assessments is to pro- vide a computational biology basis for some extrapolations that need to be made in the course of the risk assessment. This process is done by using PBPK models to determine the target tissue dose in humans or the test species (EPA 2006). Historically, in the AEGL program, types of extrapolations have included ani- mal to human, within the human population, and for different periods of expo-

OCR for page 381
383 PBPK Modeling White Paper sure. Animal-to-human extrapolation occurs when human studies are not avail- able or cannot be used to determine the POD; therefore, the animal POD is used to estimate human risk. If an animal study is used, an interspecies UF is applied to the POD to guard against the likelihood that humans are more sensitive than other animals at a given exposure. The human variability issue is an extrapola- tion in the sense that the POD for a set of experimental subjects is a projection of the values that should protect most of the population. This extrapolation is offset by applying the intraspecies UF, which is intended to protect individuals who are more sensitive than those represented by the experimental data. The temporal extrapolation is performed when a POD is based on studies with dif- ferent exposure durations than the AEGL value. Thus, the value for one period is extrapolated to another exposure period. This extrapolation is currently per- formed using the ten Berge empirical formula, by holding the value constant for all exposure durations, or possibly other approaches. When PBPK modeling is used as an alternative method of extrapolation, associated UFs can be eliminated or reduced and other approaches can be sup- planted. The animal-to-human extrapolation is made directly on the basis of internal dose, so the pharmacokinetic portion of the interspecies UF can be re- duced. Temporal extrapolations, currently made by using empirical approaches, can be done with explicit calculations of the internal dose. Finally, PBPK mod- eling can be used to examine some types of intraspecies uncertainty. Many toxicity studies are performed with the human volunteer or animal effectively in a resting condition. However, humans may be stressed, working, or otherwise in an altered physiologic state during an emergency event or other scenarios where the AEGLs may be applied. Altered physiologic states signifi- cantly affect the pharmacokinetics of some chemicals. The consequent altera- tions in pharmacokinetics are not commonly addressed in a traditional risk as- sessment. PBPK modeling can be used to reduce both inter- and intraspecies uncer- tainties in human health risk assessments for chemicals. Risk assessments tradi- tionally have been performed by using the external exposure concentration, as opposed to an internal exposure concentration, as the basis for the dose-response assessment that results in the POD selection. In recent years, there has been a movement to use internal measures of exposure calculated with a PBPK model instead of external measures. Risk assessments that rely on this general concept have been performed for many chemicals, often in the cancer, chronic noncan- cer, and developmental risk assessment areas. The rationale for using PBPK modeling in these other types of risk assessments applies as well in the assess- ment of acute exposure risks. The difference between a PBPK-based and a traditional dose-response as- sessment is that the PBPK method relies on an internal measure of exposure rather than an external one. An internal measure of exposure can be thought of as the exposure of the target tissue to the chemical, or “dose.” If the dose of chemical that reaches a target tissue can be determined with reasonable accu- racy, then the pharmacokinetic issues described above can be dealt with by us-

OCR for page 381
384 Acute Exposure Guideline Levels ing known biology rather than UFs and empirical techniques. PBPK approaches are further empowered through the use of different methods for integrating the measure of dose. Depending on the chemical, the best predictor of toxicity may be the average tissue concentration of chemical, the peak concentration, the area under the curve (AUC) (concentration  time), or some other expression of con- centration. The specific integrated measure of dose is referred to as the dose metric (DM) and is selected based on the mode of toxicologic action of the chemical. PBPK models are used to determine the DM at the POD. This concen- tration would become, in effect, a pharmacokinetic POD. If the critical study involves humans, this target DM is used to determine the equivalent concentra- tion for different exposure durations or physiologic conditions. If the critical study involves animals, the pharmacokinetic POD would be determined in an animal version of the model and a human version of the model would then be used to determine the exposure concentration that results in the same DM value in human tissue. Thus, extrapolating from an animal to a human is performed with uncertainty limited to model error that is assessed during evaluation of the model. PBPK modeling can be utilized in quantifying the effect of workload (ex- ercise) on toxicity. Values for physiologic properties of the human in the model can be adjusted to account for exercise. Exposure concentrations that yield the same target tissue DM value could be determined under the exercise condition. Likewise, extrapolating to other exposure periods can be performed by deter- mining the exposure concentration under a different exposure duration that yields the same target tissue DM value. Thus, the PBPK model minimizes some sources of uncertainty by basing the risk assessment on an appropriate internal DM, so that species, temporal, and physiologic differences are explicitly taken into account. PBPK modeling is advocated and frequently used in modern risk assess- ments, but there are times when it is not appropriate. There are no set criteria, but in general PBPK models can be used for AEGL risk assessment when:  Existing PBPK models are available for a given chemical.  Existing models can be used in their current form or can be readily adapted for use.  Existing models can be adapted for the relevant species.  The ability of the model to simulate DMs (evaluation) within the con- text of their use in AEGLs is reasonable.  The PBPK models can calculate a DM that is appropriate, given the critical effect that is used in the risk assessment. Different chemicals, exposure periods, and PODs may necessitate the use of different types of models. The criteria for deciding whether a model is ac- ceptable for use in deriving AEGL values are provided in Section 4. When these criteria are not substantially met, PBPK models are not appropriate for use.

OCR for page 381
385 PBPK Modeling White Paper When they are not appropriate and available for use in deriving AEGL values, the AEGL values should be derived with existing methodologies. A mode of toxicologic action consists of both pharmacokinetic and phar- macodynamic processes. Pharmacokinetics is what the body does with the chemical, and pharmacodynamics is what the chemical does to the body. For example, if a chemical enters a tissue, binds to a receptor protein, and interferes with signal transduction, the entry into the tissue is a pharmacokinetic process and the effects are pharmacodynamic. As the two processes are often conceptu- ally separate, different models can sometimes be developed for each aspect, and the models can be linked to produce a biologically based dose-response model. While PBPK models describe the relationship between exposure and tissue dose, physiologically based pharmacodynamic (PBPD) models describe the relation- ship between tissue dose and response. The linked PBPK and PBPD models are often referred to as PBPK/PD models. In some cases, it may not be possible to develop separate PBPK and PBPD models. Some examples of PBPK/PD models include those developed for acetylcholinesterase inhibition for chlorpyrifos (Timchalk et al. 2002) and other organophosphate pesticides, glutathione deple- tion (Frederick et al. 1992), and cytotoxic responses due to intracellular acidifi- cation (Andersen et al. 2000). If such models exist for an AEGL chemical and can be incorporated into derivation of AEGLs, these models would serve to fur- ther reduce uncertainty and may reduce the pharmacodynamic portion of the UF. The methodology for using PBPK modeling in risk assessments has been described (Clewell et al. 2002). The methodology provided in this White Paper is consistent with the guidance provided by the current EPA document on the use of PBPK modeling in risk assessment (EPA 2006). This document describes the process and explores specific issues that arise in the context of AEGL devel- opment. Although not often used in the risk assessment context, under specific circumstances classical (i.e., non-physiologically based) pharmacokinetic mod- eling may be useful for performing the temporal extrapolations when a PBPK model is not available. 2. DESCRIPTION OF PBPK MODELING In this section, PBPK models are described in a general manner. Addi- tional detail may be found in various literature reviews of PBPK models (Krishnan and Andersen 1994; Leung and Paustenbach 1995; Bailer and Dankovic 1997; Reddy et al. 2005). The pharmaceutical and medical sciences have studied and used pharma- cokinetics for many years to determine appropriate doses of intentionally admin- istered chemicals and drugs (pharmaceuticals) and, to a more limited extent, evaluate the effect of unintentional exposures (accidental overdoses, poisonings, narcotics usage). In these sciences, measures of dose such as the peak concentra- tion (Cmax), time of peak concentration (Tmax), and AUC of concentration versus time have been of interest in determining the therapeutic dose. These

OCR for page 381
386 Acute Exposure Guideline Levels efforts were made after it was recognized that internal dose was a better predic- tor of therapy or toxicity than external exposures. Mathematically, measures of dose were usually determined by using curve-fitting regression methods that fit a simple empirical model to the concentration-versus-time data. The data were usually fit with formulas that replicated either a one- or a two-compartment sys- tem that represents either whole body or tissue and body water constructs. This approach served the intended pharmaceutical needs because they were usually based on relatively rich data sets, including human data from clini- cal trials. Thus, extrapolations to other exposure scenarios were not a major fac- tor in their use, as a range of doses could be studied in experimental trials. If extrapolation were needed, it could be performed in an empirical manner. PBPK models first received attention in the medical literature. As far back as the 1920s, they were described for ether, an anesthetic gas. Unfortunately, the com- putation burden in these models is such that the model could be solved only at steady state. In the 1950s and 1960s, PBPK models were described for addi- tional drugs, including the chemotherapeutic methotrexate. Later work by Fise- rova-Bergerova and others in the 1970s returned to a series of other anesthetic gases. Starting in the 1980s, PBPK models largely turned to considering envi- ronmental risk assessment, starting with work on methylene chloride and other chemicals. The classical pharmacokinetic modeling approaches used in pharmaceu- tics did not serve the needs of environmental risk assessments nearly as well, where the data are relatively less abundant. In environmental risk assessment, intentional dosing studies that cover a range of exposures are often not available. High-dose studies could be associated with morbidity and are therefore not per- missible. Experiments designed to evaluate effects of low-dose toxicity would require doses much lower than typical therapeutic doses and generally do not have large enough study populations to detect effects. Thus, risk assessments are enhanced when supported by estimates of internal tissue dose (EPA 2006). Ex- trapolating to low or high doses could be performed using proportional methods or classical pharmacokinetic methodologies. Proportional methods rely on the assumption that dose is proportional to exposure. This assumption is not the case for many exposures because of nonlinear physiologic processes such as satur- able metabolism. This issue is also a limitation of classical pharmacokinetics; that is, Cmax at a dose of 3x is often not three times the Cmax at a dose of x. Tissue responses are more closely related to the internal target tissue dose versus the external chemical compound. The PBPK model mitigates this dilemma and reduces the uncertainty in the dose-response assessment. The use of mathematical representation of the body based on first principles, meaning that the underlying construct of the body is true to life rather than entirely empirical, allows for full utilization of available data. Each compartment in the model represents an actual portion of the body, and the more important physiologic and biochemical processes are explicitly included in the mathematics of the model. However, there is simplification, such as considering major metabolic processes while ignoring minor ones. This sim-

OCR for page 381
387 PBPK Modeling White Paper plification is justified by the assumption, which can be tested, that the minor processes not included do not have a significant effect on model outcome. When all significant biologic processes are included in a model with equations that reflect the biology of the actual process, the outcome of the model will be a true representation of pharmacokinetics even when the doses are changed, so such models are a sounder basis for extrapolation. An example of the impact of using a PBPK model rather than empirical methods is provided in Figure 7-1. In this figure, the blood concentration is not directly proportional to exposure level. For example, at 8 h, the concentration of toluene in blood is about 1 milligram per liter (mg/L) after exposure to 100 parts per million (ppm); after a 1,000-ppm exposure, it exceeds 20 mg/L. The internal concentration of a chemical or a chemical’s metabolite has been referred to as tissue dose, which is considered a more salient measure of dose (DM) for a POD than the external exposure. The ultimate tissue dose ver- sus time profile is a composite event that results from all pharmacokinetic proc- esses that occur, broadly divided into the processes of absorption, distribution, metabolism, and elimination. When a chemical such as an anesthetic gas is in- haled, it is taken up through the upper respiratory passages into the deep lung. More water-soluble chemicals may be absorbed into the upper respiratory tract and may even cause toxicity in those tissues. Chemicals that persist into the deep lung are presented to the lung cells, perhaps after absorption into mucous layers. In accordance with chemical equilibrium partitioning and diffusion characteris- tics, the chemical is absorbed into lung tissue cells several layers thick and even- tually diffuses out of the tissue and into the blood, which perfuses that tissue. In the blood (and the lymph), the chemical may remain as a free compound or may bind with macromolecules and be transported to other parts of the body. 25 20 cv:1(100) Cv (mg/L) 15 cv:2(400) cv:3(700) 10 cv:4(1000) 5 0 0 2 4 6 8 10 Exposure duration (h) FIGURE 7-1 Plot of venous blood concentration (CV) of toluene (mg/L) versus time for four exposure levels (100, 400, 700, and 1,000 ppm) for up to 8 h. Based on PBPK model for toluene used for setting AEGL values for toluene.

OCR for page 381
388 Acute Exposure Guideline Levels When reaching other tissues of the body, chemicals again diffuse into cells in accordance with rates of diffusion and equilibrium partitioning. For chemicals that diffuse relatively rapidly, it is usually assumed that diffusion rates are un- important and that the concentration of the chemical in the blood leaving the tissue will be in equilibrium with the concentration in the tissue. When this as- sumption has been tested for small molecular weight hydrophobic chemicals, it has been found to be reasonable. In other cases, the rate of diffusion must be explicitly incorporated in the model. Metabolism may occur in various tissues. For some chemicals, the liver is the major metabolic organ, but a significant degree of metabolism may occur in other tissues as well. These processes are incorporated in a PBPK model by in- serting the Michaelis-Menten equation into the rate expression for concentration of chemical in the tissue. At low concentrations, the rate expression compresses to the linear rate of metabolism with tissue concentration as the variable parame- ter; at high concentrations, a zero order rate of metabolism occurs. For example, many small molecular weight organic molecules that are substrates for low- affinity constant enzyme cytochrome P-450 (CYP) 2E1 can begin to saturate the enzyme at exposure levels that are relevant to the AEGL risk assessment proc- ess. As many parallel or sequential metabolic steps as needed can be included. If the toxic agent is the parent chemical, the models are usually not set up to trace the pharmacokinetics of metabolites. However, some models are constructed to evaluate the pharmacokinetics of metabolites by including a submodel with the necessary equations and parameter values for partitioning, absorption, metabo- lism, and other biologic processes for the metabolite. A chemical may be elimi- nated via exhalation, excretion through the kidney (urine) or liver (bile), or, in a sense, metabolized. Rate expressions for any significant elimination process would be included, such as in models that have successfully simulated the ap- pearance of a metabolite in urine or feces (Gearhart et al. 1993). While the body undergoes many thousands of simultaneous processes on a macro or molecular basis, when chemical concentrations are measured in tis- sues, their pharmacokinetics are often dominated by a selected few macroscale processes. Absorption of airborne chemicals is dominated by breathing rates and equilibrium between the lung air and lung tissue blood. Distribution is domi- nated by rates of blood flow to various tissues and equilibrium in those loca- tions. Metabolism of inhaled chemicals occurs in metabolically active tissues such as the liver and can involve multiple CYP enzymes and others as well. In some cases, the data indicate that one enzyme in one principal tissue, often the liver, predominates and that an adequate model can be developed in which the contribution of other isoforms or enzymes in the principal tissue or the same or other enzymes in other tissues can reasonably be lumped with the activity of the major enzyme in the predominant tissue. In other cases, multiple enzymes and multiple metabolic tissues are sufficiently important that they should be incorpo- rated in the PBPK model. The determination of how complex the model should be must be guided by the available data for each chemical during model devel- opment. For many chemicals, PBPK models can be constructed with only a few

OCR for page 381
389 PBPK Modeling White Paper rate expressions. Likewise, the anatomy of the body can be represented simply as well. The use of PBPK modeling has been compared with results of using the ten Berge empirical equation for inhalation exposure to toluene. The specific results of this analysis are presented in Appendix A. The PBPK model was de- veloped and then used to calculate the AEGL values at each exposure duration, based on achieving the same target tissue dose at all durations (toluene in brain or equivalently in blood). The target tissue dose was derived from the key study for that AEGL. In the toluene example, the PBPK model was able to determine the AEGL value for each duration that would yield the same expected tissue dose, while the ten Berge equation yielded tissue doses that varied from the tar- get dose by a factor of 2-3. The structure of a PBPK model has anatomic and kinetic elements. Ana- tomically, the body is represented as a system of compartments connected via blood flow. Typically, compartments are established for target tissue, a lung, blood, fat tissue, and the liver. Other tissues are usually grouped into rapidly perfused and slowly perfused tissues, and some tissues are combined when the processes that occur in them are relatively similar. For example, the gastrointes- tinal tract and kidney can be classified as rapidly perfused tissues, while muscle and bone can be considered slowly perfused tissues. Alternatively, any of the lumped-compartment tissues can be separated into its own compartment. Meas- ured anatomic values for the size (volume or weight) of the tissue compartment are physiologic parameters. The sum of the tissue compartments is usually 80% to 90% of total body mass, as 10% to 20% of the body is not perfused with blood. A simple four-compartment model is shown in Figure 7-2. Ambient Environment Equilibration at lung Slowly Rapidly Fat Liver Metabolism by 2E1 Metabolism by Enzyme 2 FIGURE 7-2 Four-compartment model.

OCR for page 381
390 Acute Exposure Guideline Levels Kinetic elements of the model structure include ventilation, blood flow, and biochemical expressions for metabolism, excretion, and other processes. Unless lymph, bile, or other fluids are included in the model, the only flow rates that need to be included are alveolar ventilation and blood flows. Alveolar venti- lation is the fraction of pulmonary ventilation that reaches the gas-exchanging tissue in the deep lung. Total ventilation may be relevant for some types of models. Blood flows include cardiac output, arterial and venous blood flow, and blood flow to tissue compartments. Each of these values is taken from standard physiology literature (Brown et al. 1997) as model inputs. Biochemical expressions depend on the chemical in question. If the meta- bolic rate is significant, equations are included representing metabolism as saturable (Michaelis-Menten), first order, or second order, as indicated by ex- perimental data. Excretion of parent chemical or metabolites through the lung is handled by lung equilibration. The model does not need to compute the time course of metabolites if the DM relates to the parent compound, but if metabo- lites need to be included, excretion to feces or urine may be relevant and in some cases for the parent compound. These processes can be represented as first-order rates or by other appropriate kinetic mechanisms. This description of a simple four-compartment model is often used for lipophilic chemicals. Many other model structures have been developed to de- scribe various types of chemicals. For example, some models have more de- tailed descriptions of the lung or skin compartment (McDougal et al. 1986; Fre- derick et al. 1992) and some models have descriptions of biochemical processes such as protein binding, diffusion-limited kinetics, or enterohepatic recircula- tion. In practice, the concept of modeling parsimony should be exercised. This concept states that the model should be kept as simple as possible yet still pro- vide the information needed for the analysis. In the AEGL program, PBPK models considered may often be more complex than the four-compartment model and should be used with due regard for the parsimony principle. The PBPK model consists of a series of equations that include differential equations for the rate expressions and algebraic equations that compute other quantities. The equations were originally developed using the mass balance con- cept, which means that the amount of chemical entering a compartment equals the amount leaving or cleared from the same compartment plus the amount re- tained in the compartment. These values are expressed as a function of time. During acute exposure, the tissue concentrations are often not at steady state and therefore are significantly affected by the duration of exposure. The typical mass balance equation for a compartment is Rate of change of amount in tissue = Qi  (CA – CVi) – clearance, where Qi = blood flow to tissue i, CA = arterial blood concentration, CVi = chemical concentration in the venous blood leaving tissue i, and

OCR for page 381
391 PBPK Modeling White Paper clearance is an additional rate expression describing clearance processes, such as metabolism in the tissue. The equation determines the rate of change in amount of the chemical in the ith compartment. The mass of chemical in the compartment is determined by integrating the equation. This normally has to be done by using a numerical method for integration. In other words, the mass balance equation can be re- stated: Rate of change in the chemical amount in the tissue (mg/h) = tissue blood flow rate (L/h)  (concentration in arterial blood [mg/L] – concentration in ve- nous blood leaving the tissue [mg/L]) – rate of change in chemical amount due to metabolism in the tissue (mg/h). Additional quantities are then calculated: CT = AT/VT concentration in each tissue compartment and CVi = CT/PT concentration in venous blood leaving tissue, where CT = chemical concentration in each tissue, AT = amount in each tissue, VT = volume of each tissue, and PT = partition coefficient between the tissue and blood. Metabolism is computed by another rate equation. For Michaelis- Menten kinetics in the liver, Rate of metabolism = Vmax  CVL/(Km + CVL), where Vmax = maximum rate of metabolism, CVL = concentration in venous blood leaving the liver, and Km = affinity constant for the chemical. Other rate equations describe the uptake of chemical into lung blood by equilibration. Full versions of model codes have been provided for typical mod- els in the literature (Clewell et al. 2000). Models developed for AEGLs should be scientifically supported and documented when possible. 3. RECOMMENDATIONS FOR USE OF PBPK MODELS IN RISK ASSESSMENT The EPA and other risk assessment organizations and practitioners have advocated the use of PBPK models to support risk assessment. These recom-

OCR for page 381
436 Acute Exposure Guideline Levels perimental concentration was equivalent to an exposure to 1,000 ppm (for 20 min), but this could not be accounted for without the PBPK model. Fourth, the PBPK-based approach allows an improvement in the basis for the animal-to-human extrapolation. While this advantage was not relevant at all levels, the AEGL-3 for toluene was based on a rat-to-human extrapolation of lethality data. Some concern may exist over setting AEGLs at less than the existing per- missible exposure limits (PEL) from OSHA (200 ppm). However, the current PEL for toluene was derived from toxicologic assessment performed in the mid- 1940s. The Threshold Limit Value (TLV) was 200 ppm until adoption as a PEL in 1970 by OSHA, but the TLV was reduced to 100 ppm in the early 1970s and to 50 ppm in 1991-1992. Thus, the studies that are the basis for the AEGLs had not even been conducted when the current PEL was established, the organization that set the value that eventually became the PEL has since lowered the value two times, and the current PEL is effectively a 60-year-old standard. REFERENCES Ali, N., and R. Tardif. 1999. Toxicokinetic modeling of the combined exposure to tolu- ene and n-hexane in rats and humans. J. Occup. Health 41:95-103. Astrand, I., H. Ehrner-Samuel, A. Kilbom, and P. Ovrum. 1972. Toluene exposure. I. Concentration in alveolar air and blood at rest and during exercise. Work Environ. Health 9:119-130. Benignus, V.A., W.K. Boyes, and P.J. Bushnell. 1998. A dosimetric analysis of behav- ioral effects of acute toluene exposure in rats and humans. Toxicol. Sci. 43(2):186- 195. Brown, R.P., M.D. Delp, S.L. Lindstedt, L.R. Rhomberg, and R.P. Beliles. 1997. Physio- logical parameter values for physiologically based pharmacokinetic models. Toxi- col. Ind. Health 13(4):407-484. Bruckner, J.V., and D.A. Warren. 2001. Toxic effects of solvents and vapors. Pp. 869- 916 in Casarett and Doull's Toxicology: The Basic Science of Poisons, 6th Ed., C.D. Klaassen, ed. New York: McGraw-Hill. Bruckner, J.V., D.A. Keys, and J.W. Fisher. 2004. The Acute Exposure Guideline Level (AEGL) program: Applications of physiologically based pharmacokinetic model- ing. J. Toxicol. Environ. Health A 67(8-10):621-634. Carlsson, A. 1982. Exposure to toluene: Uptake, distribution and elimination in man. Scand. J. Work Environ. Health 8(1):43-55. Clewell, H.J., P.R. Gentry, J.M. Gearhart, B.C. Allen, and M.E. Andersen. 2001. Com- parison of cancer risk estimates for vinyl chloride using animal and human data with a PBPK model. Sci. Total Environ. 274(1-3):37-66. Csanady, G.A., and J.G. Filser. 2001. The relevance of physical activity for the kinetics of inhaled gaseous substances. Arch. Toxicol. 74(11):663-672. Dennison, J.E., M.E. Andersen, and R.S. Yang. 2003. Characterization of the pharma- cokinetics of gasoline using PBPK modeling with a complex mixtures chemical lumping approach. Inhal. Toxicol. 15(10):961-986. Digimatic. 2004. Digimatic, Version 2. FEBSoftware, Chesterfield, VA.

OCR for page 381
437 PBPK Modeling White Paper Dobrev, I.D., M.E. Andersen, and R.S. Yang. 2001. Assessing interaction thresholds for trichloroethylene in combination with tetrachloroethylene and 1,1,1- trichloroethane using gas uptake studies and PBPK modeling. Arch. Toxicol. 75(3):134-144. Droz, P.O., and J.G. Fernandez. 1977. Effect of physical workload on retention and me- tabolism of inhaled organic solvents. A comparative theoretical approach and its applications with regards to exposure monitoring. Int. Arch. Occup. Environ. Health 38(4):231-246. Fiserova-Bergerova, V., and M.L. Diaz. 1986. Determination and prediction of tissue-gas partition coefficients. Int. Arch. Occup. Environ. Health 58(1):75-87. Gamberale, F., and M. Hultengren. 1972. Toluene exposure. II. Psychophysiological functions. Work Environ. Health 9:131-139. Gargas, M.L., R.J. Burgess, D.E. Voisard, G.H. Cason, and M.E. Andersen. 1989. Parti- tion coefficients of low-molecular-weight volatile chemicals in various liquids and tissues. Toxicol. Appl. Pharmacol. 98(1):87-99. Haddad, S., R. Tardif, G. Charest-Tardif, and K. Krishnan. 1999a. Physiological model- ing of the toxicokinetic interactions in a quaternary mixture of aromatic hydrocar- bons. Toxicol. Appl. Pharmacol. 161(3):249-257. Haddad, S., R. Tardif, C. Viau, and K. Krishnan. 1999a. A modeling approach to account for toxicokinetic interactions in the calculation of biological hazard index for chemical mixtures. Toxicol. Lett. 108(2-3):303-308. Harlan 2004. Harlan Product Guide, 2003-2004. Harlan [online]. Available: http://www.harlan.com/library.html Johanson, G. 1986. Physiologically based pharmacokinetic modeling of inhaled 2- butoxyethanol in man. Toxicol. Lett. 34(1):23-31. Jonsson, F., and G. Johanson. 2001. Bayesian estimation of variability in adipose tissue blood flow in man by physiologically based pharmacokinetic modeling of inhala- tion exposure to toluene. Toxicology 157(3):177-193. Jonsson, F., F. Bois, and G. Johanson. 2001. Physiologically based pharmacokinetic modeling of inhalation exposure of humans to dichloromethane during moderate to heavy exercise. Toxicol. Sci. 59(2):209-218. Kim, H., R.S. Wang, E. Elovaara, H. Raunio, O. Pelkonen, T. Aoyama, H. Vainio, and T. Nakajima. 1997. Cytochrome P450 isozymes responsible for the metabolism of toluene and styrene in human liver microsomes. Xenobiotica 27(7):657-665. Kishi, R., I. Harabuchi, T. Ikeda, H. Yokota, and H. Miyake. 1988. Neurobehavioral effects and pharmacokinetics of toluene in rats and their relevance to man. Br. J. Ind. Med. 45(6):396-408. Krewski, D., K. Bakshi, R. Garrett, E. Falke, G. Rusch, and D. Gaylor. 2004. Develop- ment of acute exposure guideline levels for airborne exposures to hazardous sub- stances. Regul. Toxicol. Pharmacol. 39(2):184-201. Kumagai, S., I. Matsunaga, and T. Tabuchi. 1998. Effects of variation in exposure to airborne acetone and difference in work load on acetone concentrations in blood, urine, and exhaled air. Am. Ind. Hyg. Assoc. J. 59(4):242-251. Leavens, T.L., and J.A. Bond. 1996. Pharmacokinetic model describing the disposition of butadiene and styrene in mice. Toxicology 113(1-3):310-313. Mullin, L.S., and N.D. Krivanek. 1982. Comparison of unconditioned reflex and condi- tioned avoidance tests in rats exposure by inhalation to carbon monoxide, 1,1,1- trichloroethane, toluene or ethanol. Neurotoxicity 3(1):126-137.

OCR for page 381
438 Acute Exposure Guideline Levels Nakajima, T., R.S. Wang, E. Elovaara, F.J. Gonzalez, H.V. Gelboin, H. Raunio, O. Pelk- onen, H. Vainio, and T. Aoyama. 1997. Toluene metabolism by cDNA-expressed human hepatic cytochrome P450. Biochem. Pharmacol. 53(3):271-277. Pierce, C.H., R.L. Dills, M.S. Morgan, G.L. Nothstein, D.D. Shen, and D.A. Kalman. 1996a. Interindividual differences in 2H8-toluene toxicokinetics assessed by semiempirical physiologically based model. Toxicol. Appl. Pharmacol. 139(1): 49- 61. Pierce, C.H., R.L. Dills, G.W. Silvey, and D.A. Kalman. 1996b. Partition coefficients between human blood or adipose tissue and air for aromatic solvents. Scand. J. Work Environ. Health 22(2):112-118. Pierce, C.H., R.L. Dills, M.S. Morgan, P. Vicini, and D.A. Kalman. 1998. Biological monitoring of controlled toluene exposure. Int. Arch. Occup. Environ. Health 71(7):433-444. Pierce, C.H., T.A. Lewandowski, R.L. Dills, M.S. Morgan, M.A. Wessels, D.D. Shen, and D.A. Kalman. 1999. A comparison of 1H8- and 2H8-toluene toxicokinetics in men. Xenobiotica 29(1):93-108. Purcell, K.J., G.H. Cason, M.L. Gargas, M.E. Andersen, and C.C. Travis. 1990. In vivo metabolic interactions of benzene and toluene. Toxicol. Lett. 52(2):141-152. Ramsey, J.C., and M.E. Andersen. 1984. A physiologically based description of the inha- lation pharmacokinetics of styrene in rats and humans. Toxicol. Appl. Pharmacol. 73(1):159-175. Sato, A., and T. Nakajima. 1979a. Dose-dependent metabolic interaction between ben- zene and toluene in vivo and in vitro. Toxicol. Appl. Pharmacol. 48(2):249-256. Sato, A., and T. Nakajima. 1979b. Partition coefficients of some aromatic hydrocarbons and ketones in water, blood and oil. Br. J. Ind. Med. 36(3):231-234. Tardif, R., S. Lapare, K. Krishnan, and J. Brodeur. 1993. Physiologically based modeling of the toxicokinetic interaction between toluene and m-xylene in the rat. Toxicol. Appl. Pharmacol. 120(2):266-273. Tardif, R., G. Charest-Tardif, J. Brodeur, and K. Krishnan. 1997. Physiologically based pharmacokinetic modeling of a ternary mixture of alkyl benzenes in rats and hu- mans. Toxicol. Appl. Pharmacol. 144(1):120-134. Tardif, R., P.O. Droz, G. Charest-Tardif, G. Pierrehumbert, and G. Truchon. 2002. Im- pact of human variability on the biological monitoring of exposure to toluene: I. Physiologically based toxicokinetic modelling. Toxicol. Lett. 134(1-3):155-163. ten Berge, W.F., A. Zwart, and L.M. Appelman. 1986. Concentration-time mortality response relationship of irritant and systemically acting vapors and gases. J. Haz- ard. Mater. 13(3):301-309. Thrall, K.D., R.A. Gies, J. Muniz, A.D. Woodstock, and G. Higgins. 2002. Route-of- entry and brain tissue partition coefficients for common superfund contaminants. J. Toxicol. Environ. Health A 65(24):2075-2086. van Asperen, J., W.R. Rijcken, and J.H. Lammers. 2003. Application of physiologically based toxicokinetic modelling to study the impact of the exposure scenario on the toxicokinetics and the behavioural effects of toluene in rats. Toxicol. Lett. 138(1- 2):51-62. Vicini, P., C.H. Pierce, R.L. Dills, M.S. Morgan, and D.A. Kalman. 1999. Individual prior information in a physiological model of 2H8-toluene kinetics: An empirical Bayes estimation strategy. Risk Anal. 19(6):1127-1134. Vinegar, A., G.W. Jepson, and J.H. Overton. 1998. PBPK modeling of the short-term (0 to 5 min) human inhalation exposures to halogenated hydrocarbons. Inhal. Toxi- col. 10(5):411-429.

OCR for page 381
439 PBPK Modeling White Paper Abbreviations AEGL acute exposure guideline level AT amount of chemical in each tissue AUC area under the curve BMD benchmark dose BW body weight CA arterial blood concentration maximum concentration Cmax CNS central nervous system CT chemical concentration in each tissue CV venous blood concentration CVi chemical concentration in the venous blood leaving tissue i CVL concentration of chemical in venous blood leaving the liver CYP cytochrome P-450 DM dose metric EPA U.S. Environmental Protection Agency h hour KFC linear metabolism rate constant Km affinity constant for the chemical median lethal concentration LC50 LOAEL lowest-observed-adverse-effect level mg/L milligram per liter min minute NAC National Advisory Committee NOAEL no-observed-adverse-effect level NRC National Research Council OSHA Occupational Safety and Health Administration PB blood-air partition coefficient PBPD physiologically based pharmacodynamic PBPK physiologically based pharmacokinetic PEL permissible exposure limits PFA fat-air coefficient PLA liver-air coefficient

OCR for page 381
440 Acute Exposure Guideline Levels POD point of departure ppm parts per million PRA rapidly perfused air coefficient PSA slowly perfused air coefficient PT partition coefficient between the tissue and blood QCC cardiac output QFC percentage of blood flow going to fat Qi blood flow to tissue i QLC fraction of QCC to liver QPC alveolar ventilation rate QRC percentage of blood flow going to rapidly perfused tissues QSC percentage of blood flow going to slowly perfused tissues S sensitivity coefficient TLV Threshold Limit Value time (of maximum concentration) Tmax TSD technical support document UF uncertainty factor VBC fraction lung blood VFC fraction fat tissue VLC fraction liver tissue maximum rate of metabolism Vmax VmaxC maximum velocity of metabolism VRC fraction rapidly perfused VSC fraction slowly perfused VT volume of each tissue W watt

OCR for page 381
441 PBPK Modeling White Paper ATTACHMENT 1 PBPK MODEL EQUATIONS FOR TOLUENE AEGL MODEL2 This is a four-compartment model for toluene inhalation in the rat and human. ;Physiologic parameters BW = 70 ;Body weight (kg) VFC = 0.19 ;Fraction fat tissue (kg/(kg/BW)) VLC = 0.026 ;Fraction liver tissue (kg/(kg/BW)) VRC= 0.05 ;Fraction rapidly perfused (kg/(kg/BW)) VSC = 0.62 ;Fraction slowly perfused (kg/(kg/BW)) SF = .75 ;Scaling coefficient QPC = 18 ;Alveolar ventilation rate (L/h/kg) QCC = 18 ;Cardiac output (L/h/kg) QFC = 0.09 ;Fractional blood flow to fat ((L/h)/QC) QLC = 0.26 ;Fractional blood flow to liver ((L/h)/QC) QRC= 0.55 ;Fractional blood flow to rapidly perfused ((L/h)/QC) ;Chemical-specific parameters PLA = 83.6 ;Liver-air partition coefficient PFA = 1021 ;Fat-air partition coefficient PSA = 27.7 ;Slowly perfused air partition coefficient PRA = 83.6 ;Rapidly perfused air partition coefficient PB = 18 ;Blood-air partition coefficient PL = PLA/PB ;Liver-blood partition coefficient PF = PFA/PB ;Fat-blood partition coefficient PS = PSA/PB ;Slowly perfused blood partition coefficient PR = PRA/PB ;Rapidly perfused blood partition coefficient MW = 92.13 ;Molecular weight (g/mol) VMAXC = 3.44 ;Maximum velocity of metabolism (mg/h/kg) KM = 0.13 ;Michaelis-Menten (mg/L) KFC = 0.05 ;First-order rate constant ;Calculated parameters QC = QCC  BWSF ;Cardiac output QP = QPC  BWSF ;Alveolar vent VS = VSC  BW ;Volume slowly perfused tissue (L) 2 PROGRAM: Toluene, last Revision 08-11-04; J Dennison.

OCR for page 381
442 Acute Exposure Guideline Levels VF = VFC  BW ;Volume fat tissue (L) VL = VLC  BW ;Volume liver (L) VR= VRC  BW ;Volume rapidly perfused (L) VB = 0.0005  BW ;Lung blood volume (L) QF = QFC  QC ;Blood flow to fat (L/h) QL = QLC  QC ;Blood flow to liver (L/h) QS = QC – QF – QL – QR ;Blood flow to nonfat tissue (L/h) QR = QRC  QC ;Blood flow to rapidly perfused (L/h) VMAX = VMAXC  BWSF ;Maximum rate of metabolism (mg/h) KF = KFC/BW0.3 ;Linear metabolic rate ;Parameters for simulated experiment CONC = 500 ;Inhaled concentration (ppm) ;Parameters for exercise (50 W, 75 W, 100 W, 150 W) QPC50 = 53 QCC50 = 50 QLC50 = 0.13 QFC50 = 0.031 QRC50 = 0.60 QPC75 = 70 QCC75 = 59 QLC75 = 0.10 QFC75 = 0.030 QRC75 = 0.28 QPC100 = 87 QCC100 = 68.5 QLC100 = 0.076 QFC100 = 0.034 QRC100 = 0.58 QPC150 = 100 QCC150 = 79 QLC150 = 0.042 QFC150 = 0.024 QRC150 = 0.58 ;The following IF THEN statements implement the Carlsson Stage 3 exercise scenario (rest, 50 W, 100 W, 150 W) ;QPC = IF TIME >= 1.5 THEN QPC150 ELSE IF TIME >= 1.0 THEN QPC100 ELSE IF TIME >= .5 THEN QPC50 ELSE 18

OCR for page 381
443 PBPK Modeling White Paper ;QCC = IF TIME >= 1.5 THEN QCC150 ELSE IF TIME >= 1.0 THEN QCC100 ELSE IF TIME >= 0.5 THEN QCC50 ELSE 18 ;QLC = IF TIME >= 1.5 THEN QLC150 ELSE IF TIME >= 1.0 THEN QLC100 ELSE IF TIME >= 0.5 THEN QLC50 ELSE 0.26 ;QFC = IF TIME >= 1.5 THEN QFC150 ELSE IF TIME >= 1.0 THEN QFC100 ELSE IF TIME >= 0.5 THEN QFC50 ELSE 0.09 ;QRC = IF TIME >= 1.5 THEN QRC150 ELSE IF TIME >= 1.0 THEN QRC100 ELSE IF TIME >= 0.5 THEN QRC50 ELSE 0.55 ;The following IF THEN statements implement the Carlsson Stage 3 exercise scenario (rest, 50 W, 100 W, 150 W) with QPC and QCC from QCP2004 calculations ;QPC = IF TIME >= 1.5 THEN 129 ELSE IF TIME >= 1.0 THEN 88.4 ELSE IF TIME >= .5 THEN 45 ELSE 14.7 ;QCC = IF TIME >= 1.5 THEN 46.6 ELSE IF TIME >= 1.0 THEN 37.1 ELSE IF TIME >= 0.5 THEN 26 ELSE 14.4 ;QLC = IF TIME >= 1.5 THEN 0.05 ELSE IF TIME >= 1.0 THEN .076 ELSE IF TIME >= 0.5 THEN 0.13 ELSE 0.26 ;QFC = IF TIME >= 1.5 THEN 0.03 ELSE IF TIME >= 1.0 THEN 0.03 ELSE IF TIME >= 0.5 THEN 0.03 ELSE 0.09 ;QRC = IF TIME >= 1.5 THEN 0.58 ELSE IF TIME >= 1.0 THEN 0.58 ELSE IF TIME >= 0.5 THEN 0.60 ELSE 0.55 ;The following IF THEN statements implement the Astrand et al. (1972) Figure 3, Steps 1 and 2, exercise scenario (rest, 50 W) ;QPC = IF TIME >= 0.5 THEN QPC50 ELSE 18 ;QCC = IF TIME >= 0.5 THEN QCC50 ELSE 18 ;QLC = IF TIME >= 0.5 THEN QLC50 ELSE 0.26 ;QFC = IF TIME >= 0.5 THEN QFC50 ELSE 0.09 ;QRC = IF TIME >= 0.5 THEN QRC50 ELSE 0.55 ;The following IF THEN statements implement the Astrand et al. (1972) Figure 3, Steps 1 to 4, exercise scenario (rest, 50 W) ;QPC = IF TIME >= 1.08 THEN 18 ELSE IF TIME >= .55 THEN 53 ELSE 18 ;QCC = IF TIME >= 1.08 THEN 18 ELSE IF TIME >= .55 THEN 50 ELSE 18 ;QLC = IF TIME >= 1.08 THEN 0.26 ELSE IF TIME >= .55 THEN .13 ELSE 0.26 ;QFC = IF TIME >= 1.08 THEN 0.09 ELSE IF TIME >= .55 THEN 0.03 ELSE 0.09 ;QRC = IF TIME >= 1.08 THEN 0.55 ELSE IF TIME >= .55 THEN 0.6 ELSE 0.55 ;CONC = IF TIME >= 1.37 THEN 175 ELSE IF TIME >= 1.08 THEN 0 ELSE 95

OCR for page 381
444 Acute Exposure Guideline Levels ;The following IF THEN statements implement the Astrand et al. (1972) Figure 3, Steps 1 to 6, exercise scenario (rest, 50 W) ;QPC = IF TIME >= 2.4 THEN 18 ELSE IF TIME >= 1.9 THEN QPC50 ELSE IF TIME>= 1.08 THEN 18 ELSE IF TIME >= .55 THEN QPC50 ELSE 18 ;QCC = IF TIME >= 2.4 THEN 18 ELSE IF TIME >= 1.9 THEN QCC50 ELSE IF TIME >= 1.08 THEN 18 ELSE IF TIME >= .55 THEN QCC50 ELSE 18 ;QLC = IF TIME >= 2.4 THEN .26 ELSE IF TIME >= 1.9 THEN QLC50 ELSE IF TIME >= 1.08 THEN 0.26 ELSE IF TIME >= .55 THEN QLC50 ELSE 0.26 ;QFC = IF TIME >= 2.4 THEN .09 ELSE IF TIME >= 1.9 THEN QFC50 ELSE IF TIME >= 1.08 THEN 0.09 ELSE IF TIME >= .55 THEN QFC50 ELSE 0.09 ;QRC = IF TIME >= 2.4 THEN .55 ELSE IF TIME >= 1.9 THEN QRC50 ELSE IF TIME >= 1.08 THEN 0.55 ELSE IF TIME >= .55 THEN QRC50 ELSE 0.55 ;CONC = IF TIME >= 2.4 THEN 0 ELSE IF TIME >= 1.37 THEN 175 ELSE IF TIME >= 1.08 THEN 0 ELSE 95 ;The following IF THEN statements implement the Astrand et al. (1972) Figure 4 exercise scenario (75 W, 150 W, rest) ;QPC = IF TIME >= 1.17 THEN 18 ELSE IF TIME >= .5 THEN QPC150 ELSE QPC75 ;QCC = IF TIME >= 1.17 THEN 18 ELSE IF TIME >= .5 THEN QCC150 ELSE QCC75 ;QLC = IF TIME >= 1.17 THEN 0.26 ELSE IF TIME >= .5 THEN QLC150 ELSE QLC75 ;QFC = IF TIME >= 1.17 THEN 0.09 ELSE IF TIME >= .5 THEN QFC150 ELSE QFC75 ;QRC = IF TIME >= 1.17 THEN 0.55 ELSE IF TIME >= .5 THEN QRC150 ELSE QRC75 ;CONC = IF TIME >= 1 THEN 0 ELSE 105 ;The following IF THEN statements implement the Astrand et al. (1972) Figure 9 exercise scenario ;QPC = IF TIME >= 1.4 THEN 18 ELSE IF TIME >= 0.92 THEN 53 ELSE IF TIME >= .5 THEN 18 ELSE 18 ;QCC = IF TIME >= 1.4 THEN 18 ELSE IF TIME >= 0.92 THEN 50 ELSE IF TIME >= 0.5 THEN 18 ELSE 18 ;QLC = IF TIME >= 1.4 THEN 0.26 ELSE IF TIME >= 0.92 THEN .13 ELSE IF TIME >= 0.5 THEN 0.26 ELSE 0.26 ;QFC = IF TIME >= 1.4 THEN 0.09 ELSE IF TIME >= 0.92 THEN 0.03 ELSE IF TIME >= 0.5 THEN 0.09 ELSE 0.09

OCR for page 381
445 PBPK Modeling White Paper ;QRC = IF TIME >= 1.4 THEN 0.55 ELSE IF TIME >= 0.92 THEN 0.6 ELSE IF TIME >= 0.5 THEN 0.55 ELSE 0.55 ;CONC = IF TIME >= 1.4 THEN 0 ELSE IF TIME >= .92 THEN 200 ELSE IF TIME >= .5 THEN 0 ELSE 200 ;The following IF THEN statements implement the Gamberale and Hultengren (1972) experiment (Figure 1) ;CONC = IF TIME >= 1.08 THEN 714 ELSE IF TIME >= .75 THEN 501 ELSE IF TIME >= .67 THEN 0 ELSE IF TIME >= .33 THEN 300 ELSE 100 CIX = CONC  MW/24,450 ;Exposure concentration (mg/L) LENGTH = 4 ;Length of inhalation exposure (h) INTERVAL = 8 CI = CIX  (mod(time,interval)<=length) method RK4 ;Rosenbrock stiff solver starttime = 0 ;start integration stoptime = 8 ;end integration dtmin = 0.0001 ;minimum (and initial) step size dtmax = 1 ;maximum step size tolerance = 0.0001 ;error tolerance for stiff solver dtout = 0.1 ;communication interval (optional) deltaT = stepsize ;allows plotting step sizes used as deltaT (optional) display cv, ca, vlc, vrc, vfc, vsc, qfc, qlc, qrc, sf, dose, mass, massbal, pfa, pla, psa, pra display length, bw, qpc, qcc, pb, vfc, km, vmaxc, interval, kfc display cl, cr, cxppm, ci, conc, af, as, ar, al ;INTEGRATIONS ;Chemical in blood AB' = QP  (CI – CX) + QC  (CV– CA) INIT AB = 0 CA = AB/VB CV = (QF  CVF + QR  CVR + QL  CVL + QS  CVS)/QC ;Mixed venous (mg/L) ;Exhaled chemical

OCR for page 381
446 Acute Exposure Guideline Levels CX = CA/PB ;Alveolar (mg/L) CXPPM = CX  24,450/MW ;Chemical in slowly perfused compartment AS' = QS  (CA – CVS) ;(mg/h) init AS = 0. ;(mg) CS = AS/VS ;(mg/L) CVS = CS/PS ;Venous blood (mg/L) Chemical in fat compartment AF' = QF  (CA – CVF) ;(mg/h) init AF = 0 ;(mg) CF = AF/VF ;(mg/L) CVF = CF/PF ;Venous blood (mg/L) ;Chemical in rapidly perfused compartment AR' = QR  (CA – CVR) ;(mg/h) init AR = 0 ;(mg) CR = AR/VR ;(mg/L) CVR = CR/PR ;Venous blood (mg/L) ;Chemical in liver compartment AL' = QL  (CA – CVL) – AM' ;(mg/h) init AL = 0 ;(mg) CL = AL/VL ;(mg/L) CVL = CL/PL ;Venous blood (mg/L) ;Metabolism AMS' = VMAX  CVL/(KM + CVL) ;Saturable metabolism (mg/h) init AMS = 0 AML' = KF  CVL ;Linear metabolism (mg/h) init AML = 0 AM' = AMS' + AML' ;Total metabolism init AM = 0 ;Mass balance DOSE' = QP  (CI – CX) ;Net absorption (mg/h) init DOSE = 0 ;Net absorption (mg) MASS = AF + AS + AL + AM + AR + AB ;In tissues + metabolized (mg) MASSBAL = DOSE – MASS + 1