Environ. Sci. Technol. 2004, 38, 5674-5681
Development of a Physiologically Based Pharmacokinetic Model for Volatile Fractions of Gasoline Using Chemical Lumping Analysis J A M E S E . D E N N I S O N , * ,† MELVIN E. ANDERSEN,‡ HARVEY J. CLEWELL,§ AND RAYMOND S. H. YANG† Quantitative and Computational Toxicology Group, Center for Environmental Toxicology & Technology, Department of Environmental and Radiological Health Sciences, Colorado State University, Ft. Collins, Colorado 80523-1860, CIIT Centers for Health Research, 6 Davis Drive, Research Triangle Park, North Carolina 27709, and Environ Corp, 602 East Georgia Avenue, Ruston, Louisiana 71270
Physiologically based pharmacokinetic (PBPK) models have often been used to describe the absorption, distribution, metabolism, and excretion of chemicals in animals but have been limited to single chemicals and simple mixtures due to the numerous parameters required in the models. To overcome the barrier to modeling more complex mixtures, we used a chemical lumping approach, used in the past in chemical engineering but not in pharmacokinetic modeling, in a rat PBPK model for gasoline hydrocarbons. Our previous gasoline model consisted of five individual components (benzene, toluene, ethylbenzene, xylene, and hexane) and a lumped chemical that included all remaining components of whole gasoline. Despite being comprised of hundreds of components, the lumped component could be described using a single set of chemical parameters that depended on the blend of gasoline. In the present study, we extend this approach to evaporative fractions of gasoline. The PBPK model described the pharmacokinetics of all of the volatility-weighted fractions of gasoline when differences in partitioning and metabolism between fractions were taken into account. Adjusting the ventilation rate parameter to account for respiratory depression at high exposures also allowed a much improved description of the data. At high exposure levels, gasoline components competitively inhibit each other’s metabolism, and the model successfully accounted for binary interactions of this type, including between the lumped component and the five other chemicals. The model serves as a first example of how the engineering concept of chemical lumping can be used in pharmacokinetics.
* Corresponding author phone: (970)491-8867; e-mail: dennison@ colostate.edu. Corresponding author address: Center for Environmental Toxicology & Technology, Colorado State University, Fort Collins, CO 80523. † Colorado State University. ‡ CIIT Centers for Health Research. § Environ Corp. 5674
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Introduction Gasoline is a large-production chemical product with significant human exposure potential (1-7). It contains several individual components that cause toxicity in humans at sufficiently high exposures (8-12). Yet, studying the toxic effects of gasoline is complicated for many reasons, including (1) toxicity studies cannot be performed on every component and every blend of gasoline; (2) interactions between components of complex mixtures such as gasoline can alter toxicity; (3) these alterations will depend on exposure concentrations and the blends of gasoline examined; and (4) exposures occur to whole gasoline and fractions of these fuels, i.e., low boiling volatiles or high-boiling residues after evaporation. Predictive approaches to toxicity of gasoline blends, such as the approach presented in this paper, will be important to understanding the fate of the chemical in organisms and the risks associated with exposures. Pharmacokinetic aspects (absorption, distribution, metabolism, and excretion) of chemical toxicity have been elucidated in recent years using physiologically based pharmacokinetic (PBPK) modeling for various animals, including humans (13-15). These models are fundamentally similar to models used for many years to describe multimedia environmental processes, i.e., groundwater models or fate and transport models (16). In simple PBPK models, the organism is conceptualized as consisting of homogeneous (well stirred) compartments between which chemicals are transported advectively (sometimes diffusively as well) by the blood. At most interfaces, equilibrium is usually assumed. In PBPK models, metabolism of chemicals is analogous to chemical reaction in multimedia models. The models are codified using equations often similar to those in multimedia compartmental models and can be solved using similar differential equation solvers. Thus, there are distinct parallels between the two model types (16). PBPK models have also been directly linked to environmental fate models (17, 18). Over the past 20 years, PBPK models have been used to evaluate a large number of individual chemicals (19) and simple chemical mixtures (14, 20, 21). Mixture models yield different results from single chemical models when chemicals interact. The most common pharmacokinetic (PK) interaction between organic chemicals is metabolic inhibition, e.g., when chemicals are metabolized by the same enzymes, they can competitively inhibit (reduce the rate of) metabolism of the other compound. Many components of gasoline have this effect on other gasoline components (22). A “biologically effective dose” can be thought of as the amount of chemical (parent chemical or metabolites) that reaches the target organ in the body where it exerts its principal effect. Recently, human health risk assessments have been frequently based on the biologically effective dose rather than the ambient exposure level since the former basis yields a measure of the true internal dose of the chemical (23, 24). Computational methods for determining the internal dose are important, particularly with compounds that may interact in the body, and can be provided by PBPK modeling (25). PBPK models therefore allow PK interactions to be taken into account when performing mixture risk assessments and have received increasing emphasis by the USEPA (26). The simple mixture models that have been developed typically describe the PKs of mixtures of two to five components (20, 21, 27). These mixture models are developed by conducting suites of experiments with all single chemicals and various combinations of the mixture, including binary, ternary, etc. combinations. A practical limit is soon reached 10.1021/es035201s CCC: $27.50
2004 American Chemical Society Published on Web 09/28/2004
FIGURE 1. Gas chromatograms of the 1/3 cut, 2/3 cut, and whole gasoline samples used in this study. BTHEX components were identified by matching the fingerprint to GC/MS analyses and retention times. All other components were quantified by comparing the total peak areas against a calibration curve. The 1/3 cut and 2/3 cut samples contain more light-end volatiles than whole gasoline and exhibit different pharmacokinetics in rats. for the size of the mixture that can be accommodated this way, a limit that is well below the number of components in gasoline that need to be included for a reasonable analysis. An alternative approach that incorporates chemical lumping into PBPK modeling has also been used to address this issue. In our previous work, we developed a PBPK model for two blends of whole gasoline that described the PKs of specific components of gasoline (n-hexane, benzene, toluene, ethylbenzene, and o-xylene (BTHEX)) and a lumped component that represented the bulk of the mixture (28). Interactions between all of the components, including the lumped components, were incorporated into the model. Chemical lumping is a purposeful modeling simplification, in which several components are handled as a single species. Various forms of chemical lumping exist. For example, if species A‚ ‚‚Z exist in the real mixture, a two-lump model can be developed with any combination of the species. The mixture could be described as consisting of Lump A and Lump B‚‚‚Z. Three or more lumps may be required, depending on the
system being described, but the principle of parsimony suggests minimizing the number of lumps in order to reduce the number of parameters required. Lumping can be perfect, if one lumping scheme can be maintained throughout the system description. Proper lumping refers to a system in which each component is wholly in one lump or another. In the previous (28) and present work, a six lump model is used. Five lumps consist of single chemicals (BTHEX), and the sixth lump consists of all remaining components. Each lump therefore is both perfect and proper. Not only is PBPK modeling analogous to various types of environmental modeling, the present model’s addition of a chemical lumping approach is analogous to the chemical lumping approach used in the chemical engineering field, and specifically in petroleum refining processes. In PBPK modeling, each chemical requires data for thermodynamic parameters (partition coefficients) and kinetic parameters (metabolism, inhibition, excretion, etc.) In particular, kinetic parameters require extensive experimentation to determine. VOL. 38, NO. 21, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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Since it is not feasible to conduct these experiments on the numerous components in gasoline, we determined a set of parameter values for a group of chemicals that are lumped together in the PK analysis. A similar approach has been used in petroleum refining and in kinetic models of environmental processes, where blends of feedstock, refined product, or pollutants are segregated into a small number of lumps according to the thermodynamic or kinetic properties of the lump (29-31). In environmental processes, advective processes (e.g., groundwater transport, wind) are analogous to blood flow. Storage in sediments or other media containing organic carbon is the corollary of uptake in the body’s fat tissue. Degradation in various media takes on similar mathematical forms to metabolism of chemicals in the liver or other organs of the PBPK model. Correlates of these processes are also present in chemical engineering processes such as petroleum refining. Hybridized parameter values are then determined for the lump, generally in an empirical manner. Our previous PBPK model (28) adequately described the PKs of whole gasoline and several individual components. However, actual inhalation exposures to “gasoline” will frequently be weighted toward the more volatile components, raising the question of whether this lumping approach would work for a low boiling fraction of gasoline. A variety of scenarios occur where persons are exposed to the more volatile components: emissions from gas tank refilling, fugitive emissions from contained products, and evaporation from spills. This wide variety of scenarios suggests that a method for predicting the PKs of gasoline components that can be adapted to different subsets of gasoline components based on volatility would be useful. The present work extended the existing model to examine a series of samples of the most volatile components of gasoline that represent the fractions of gasoline components that would be inhaled after release of gasoline to the environment.
Methods Experimental Design. The methods for this study were similar to those previously reported (28, 32) except as described below and will be summarized briefly. Experimental work was based on gas uptake pharmacokinetic studies. In these studies, a rat (male Fisher 344 weighing 190-220 g) was placed in a closed chamber experimental system. A sample of the test chemical (gasoline or fraction thereof) was injected into the system at the start of the experiment and rapidly evaporated by gentle heating to mix in the chamber atmosphere. The concentrations of chemicals in the chamber decline as the rat absorbs them from the atmosphere, so the declining concentration reflects the PKs of the chemical in the organism. When metabolism is inhibited by the presence of other chemicals, the chemical is cleared from blood more slowly, which reduces the rate of absorption of chemical from the chamber. The atmosphere in the chamber was serially sampled and analyzed by gas chromatography. Peaks corresponding to BTHEX, confirmed by GC/MS, were identified. and all remaining peaks are integrated as a whole. Intrinsic losses of chemical in the chamber were premeasured (including losses to hair and skin) and incorporated into the model as first-order rates. Carbon dioxide (CO2) expired by the animal was removed by a CO2 scrubber (Baralyme), and oxygen was replaced as consumed. Both gases were monitored with direct reading probes. Sample Preparation. A sample of gasoline was obtained from a local gasoline station (BP “Regular Unleaded”; 2/24/ 03) and maintained at 0 °C until prepared for use. One hundred milliliters of this whole gasoline was warmed gently on a hotplate until ∼33 mL evaporated. The headspace vapors were collected throughout the process in a separate flask 5676
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TABLE 1. Composition of the 1/3 Cut, 2/3 Cut, and Whole Gas Samples Used in This Study componenta
1/3 cut (%)
2/3 cut (%)
whole gas (%)
n-hexane benzene toluene ethylbenzene o-xylene lumped component
4.8 0.7 0.2 0.2 0.2 94
5.5 2.0 2.1 0.1 0.2 90
4.0 1.5 4.7 1.1 1.7 87
a
% by weight.
FIGURE 2. Structure of the PBPK model used in this study, showing the fat, liver, slowly perfused tissues (“slowly”), and rapidly perfused tissues (“rapidly”) compartments, blood flows, and lung:air equilibration. over dry ice. This sample, representing the first third of the sample to evaporate, is referred to as the “1/3 cut”. A “2/3 cut” sample was also prepared by evaporating ∼66 mL of whole gasoline and collecting the vapors. Chromatograms of these samples showed the concentration of light end components differed widely (Figure 1). The concentration of BTHEX in each sample differed greatly (Table 1) with the volatile fraction samples containing more n-hexane and less toluene, ethylbenzene, and o-xylene than the whole gas. With the 1/3 cut and 2/3 cut samples, ethylbenzene and o-xylene were below the limit of detection initially or within the first hour of the PK experiment, so they were not included as model data. For each fraction, three gas uptake experiments were performed at approximate starting concentrations of 500, 1000, and 1500 ppm. Due to rapid absorption by the animal, chemical concentrations decline during the 6-h experiment by roughly 1 to 2 orders of magnitude. Thus, the average exposure levels for the 6-h period are much lower than the initial concentration. Hence the advantage of the gas uptake experimental design over constant exposure designs: in addition to maintaining a mass balance, the gas uptake design requires fitting model behaviors over a wide range of concentrations that are differentially affected by different parameter estimates. PBPK Modeling. All PBPK modeling was performed in Berkeley Madonna, v. 8.0.2a8 (33) using a basic fourcompartment structure that has been previously used in many PBPK models (28, 34). The model (Figure 2) includes fat tissue, liver tissue, slowly perfused tissue (muscle, skin etc.), and rapidly perfused tissue (other internal organs) compartments. Metabolism is represented in the liver by a
TABLE 2. Physiological Model Parameters tissue group
volume (%BW)
flow (%QC)
liver fat richly perfused slowly perfused lung blood
3.7 .035*BW+0.205 5.4 91 - remaining 0.2
18.3 7.0 51.0 100 - remaining N/A
system parameters
flow (%QC)
cardiac output alveolar ventilation
15 L/h/kg0.74 14.9 L/h/kg0.74 13.5 L/h/kg0.74 12.5 L/h/kg0.74
low exposures medium exposures high exposures
TABLE 3. Chemical Parameters for the PBPK Modela chemical
PB
PL
PF
PS
Vmaxb
Kmc
Kic
n-hexane benzene toluene ethylbenzene o-xylene 1/3 cut 2/3 cut whole gas
2.29 17.8 18.0 42.7 44.3 1.6 2.3 3.0
2.27 0.96 4.64 1.96 2.44 3.16 3.16 3.16
69.4 22.0 56.7 36.4 42.4 80 80 80
1.27 0.58 1.54 .609 1.16 0.88 0.88 0.88
7.0 5.3 5.3 7.6 6.5 2.5 3.5 2.7
0.01 0.10 0.02 0.10 0.20 0.15 0.10 0.30
.01 .10 .02 .10 .20 .06 .20 .10
a PB ) blood:air partition coefficient (PC), PL ) liver:blood PC, PF ) fat:blood PC, PS ) slowly perfused tissue:blood PC. Richly perfused tissue:blood PC (PR) is set equal to PL by convention. Vmax is the maximum rate of metabolism, Km is the affinity constant, and Ki is the inhibitory constant. See Appendix for equations. b mg/h/kg0.74. c mg/L.
single enzyme metabolic pathway representing the predominant enzyme for initial hydrocarbon oxidation (cytochrome P450 2E1). Michaelis Menten (saturable) metabolic rate equations were used, i.e., rate of metabolism ) Vmax * [substrate]/([substrate] + Km), where Vmax is the maximum rate of metabolism and Km is the affinity constant. Inhibitors were assumed to act by competitive inhibition, modifying a substrate’s Km: Km*(1+ [inhibitor]/Ki]) where Ki is the inhibitory constant (35). The compartments are linked to an arterial blood compartment, which is in equilibrium with the chamber atmospheric concentrations for each chemical, representing the blood leaving the lung. The venous blood leaving each tissue compartment is represented as in equilibrium with the compartment. An external chamber compartment is also included for mass balance. Representative equations, based on earlier models (20, 21), are included in the Appendix. Parameter Values. Anatomical and physiological parameter values, including tissue volumes and blood flows for each compartment, were taken from the literature ((36) Table 2). Based on observations in this and other studies (37), the alveolar ventilation rate was treated as an adjustable parameter, within the range previously reported (36). Parameter values for BTHEX-specific parameters were maintained the same as in the previous gasoline PBPK model (28). For all single chemicals, partition coefficients (Table 3) were taken from the literature (38), and metabolic parameters (Vmax, Km, and Ki) were determined through optimization of single chemical and simple mixture PK data in the previous study (28). As the gasoline blends used in this study varied, the lumped chemical parameters for each blend were determined through simulation. The alveolar ventilation rate (QP), cardiac output, and Vmax were allometrically scaled to body weight0.74. Parameter Optimization. The optimization of parameter values was done by visual best-fit methods with Berkeley Madonna, an ordinary differential equation solver, followed
FIGURE 3. PBPK model for the 1/3 cut sample. Gas uptake studies (single experiments) with rats were conducted at starting concentrations of approximately 500, 1000, and 1500 ppm with serial analysis of chamber air. The PBPK model (curves) describes the decline in chemicals due to the pharmacokinetic process within the animal. In Figures 3-5, curves are simulations of the model described in this paper, and symbols are experimental data. Panels A (high exposure), B (moderate exposure), and C (low exposure). by verification with numerical methods. The optimization started with data from PK experiments with the 1/3 cut sample. First, the data for the lumped chemical in three experiments was fit by adjusting the available parameters (QP, Vmax, and Km). During this optimization with the 1/3 cut sample, it was observed that the best apparent fit was obtained by slightly decreasing QP for experiments starting at higher concentrations. This adjustment is biologically consistent with known effects of gasoline in terms of central nervous system depression and respiratory irritation, as previously noted (37). The best fits occurred with QP ) 14.9 L/h/kg0.74 for the lowest concentrations, consistent with the default values used in other PBPK models (39, 40). QP was decreased to 13.1 L/h/kg0.74 for the medium concentration and to 12.5 L/h/kg0.74 for the highest concentration, consistent with other previous reports (37). Using these rates for QP, the parameter values for Vmax and Km for the lumped VOL. 38, NO. 21, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 4. PBPK model for the 2/3 cut sample. A less volatile sample is used than in Figure 3, with proportionately less n-hexane and more toluene. The upper curve is the lumped component that includes all components except BTHEX. Ethylbenzene and o-xylene were not detected in the sample. See Figure 3 legend for details. component were determined across all three data sets (Table 3) for the 1/3 cut. After setting the parameters for QP, Vmax, and Km, the inhibitory parameter Ki was adjusted until a best fit for the other components of the mixture (BTHEX) was obtained for the three experiments. The data for the 2/3 cut and whole gasoline was simulated using a similar approach, except that QP was not reoptimized; the same values for QP at each respective concentration were used for the other blends. For optimization of the 2/3 cut and whole gasoline, the lumped chemical’s Vmax and Km were first determined. Then, the lumped chemical’s Ki was determined by fitting the BTHEX data. After each visual optimization, numerical optimization was performed constraining the parameters into the local minima ( 10% of each parameter’s fitted value. When the root-mean-square fitted value was reported to be the same (given its number of significant figures) as the visually determined parameter, the fit was considered adequate. The PBPK model was then used to determine the alteration in venous blood concentrations and the amount of each 5678
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FIGURE 5. PBPK model for whole gasoline. The model describes absorption, distribution, metabolism, including metabolic inhibition between each of the six components (BTHEX and the lumped component), and elimination of each chemical in rats. All nonBTHEX components are lumped into one component, described by hybrid parameter estimates, shown as the data and curve at the top of the plots. See Figure 3 legend for details. chemical metabolized caused by the inhibition of each chemical’s metabolism (including the lumped chemical) by each of the other chemicals, under constant exposure conditions. The exposure scenario for this analysis was a 6-h exposure to constant levels of 100-500 ppm of the 1/3 cut, 2/3 cut, and the whole gasoline.
Results and Discussion Model simulations are plotted against the PK data for each of the three experiments with each of the blends of gasoline components (Figures 3-5). The model for the 1/3 cut (Figure 3) overpredicts n-hexane at the lowest concentration (Panel C) but closely predicts n-hexane at the medium and high concentrations and other components at all concentrations. The model performs similarly with respect to the 2/3 cut (Figure 4). As indicated in the Methods section, ethylbenzene and o-xylene were not detected in the PK experiments for the 1/3 and 2/3 cuts. The simulation quality of all components were similar to that with the 1/3 cut, with n-hexane at the lowest concentration (Panel C) deviating the most. All other data sets were comparatively predicted quite well by this
FIGURE 6. Effect of metabolic inhibition on metabolism and blood concentrations in gasoline pharmacokinetics. The percent decrease in the total amount metabolized of BTHEX and the lumped component during a 6 h exposure at constant level, as determined with the PBPK model, is shown in the left panels. The percent increase in venous blood concentration in the right panels and the alterations in metabolism are dependent on the chemical and the composition of the lumped component. PBPK model. Deviations in gas uptake experiment-based PBPK models tend to increase throughout the timecourse of the data set, as the error in predicting concentrations is cumulative in nature. The whole gasoline contained quantifiable amounts of each of the BTHEX components and all could be detected in all three experiments. The model provides a close fit to the data for toluene, ethyl benzene, and the lumped component at all three exposure levels (Figure 5). The discrepancy in n-hexane simulations at lower concentrations could be due to imprecision in one of the n-hexane-specific parameter values. The parameters used for n-hexane were taken from the literature (partition coefficients (38)) or the previous study (28), where some deviations were also noted. In the previous study, a limited data set was used for model parameterization. Additional studies are being used in our lab to improve the description of the single chemical pharmacokinetics for this chemical. Another possibility lies, in part, with the partition coefficients for n-hexane. The experimentally determined value (38) was measured in vitro. However, it has been previously noted that the blood:air partition coefficient (PB) measured in vitro may differ from the apparent in vivo PB (41). Furthermore, the n-hexane model overpredicts by a greater margin at low exposure levels, which could be attributable to the impact of saturable blood binding’s effect on the measured PB, as suggested by Krishnan and co-workers (42). PB is an important parameter governing the uptake of chemical from the chamber. As the PB for some hydrocarbons
is related to vapor pressure (42), which in turn is related to molecular weight (43), we expect that the PB for the lumped component will be near the PB for that gasoline component with the median molecular weight. Indeed, a reported molecular weight of gasoline (∼95 g/mol) lies between the molecular weights of n-hexane and n-heptane (86 and 100 g/mol respectively), whose measured PBs are 2.3 and 4.75, respectively (38). Thus, our values for PB (1.6 (1/3 cut), 2.3 (2/3 cut), and 3.0 (whole gas)) are in the appropriate range. More significantly, the PB increased as the volatility of the blend decreased, as expected. Kinetic parameter estimates for the lumped component are also similar to those reported for gasoline in the previous study (28). Here, Vmax was 2.5-3.5 L/h/kg0.74 as opposed to 2.0 L/h/kg0.74 in the previous study. Km in this study (0.1-0.3 mg/L) compares well to the previous value (0.1 mg/L). Thus, the lumped component is relatively well-metabolized. Ki’s in this study (0.06 to 0.2 mg/L) also agreed with the previous value (0.1 mg/L). Ki values may vary from corresponding Kms as the mode of inhibition may not be purely competitive. The model is much less sensitive to the Ki value for BTHEX components, as they are at lower concentration than the lumped component, but an adequate representation of the pharmacokinetics of the lumped component and the inhibition of BTHEX by the lumped component indicated that Km did not equal Ki for the lumped component in each blend. Nevertheless, each blend’s Ki was in the same range as its Km, as would be expected in the case of competitive inhibition. As each cut of the whole gasoline contained VOL. 38, NO. 21, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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different proportions of components, metabolic parameters are expected to vary slightly from one lumped component to another. Sensitivity analysis indicated that the venous blood concentrations of BTHEX were generally sensitive to the alveolar ventilation rate (QP). In most PBPK models, QP is held invariant as a function of exposure level, but the absolute value of QP is selected from a wide range reported in the literature (36). In the present model, the data suggested that QP varied with exposure level not only because the model was better able to represent all data sets when QP was allowed to vary while other parameters were constrained but also because the value of QP that allowed the optimal fits varied in an orderly manner with concentration but not with blend. As many chemicals in gasoline are depressants of the central nervous system and respiratory irritants (8-12), both having the effect of reducing the ventilation rate, it is biologically plausible, or expectable, that QP should be reduced at higher exposure levels. The power and perhaps the principal purpose of PBPK models are to allow extrapolation of the model to exposure scenarios of interest. Ultimately, this gasoline PBPK model should be extrapolated to humans, but sufficient data to support such extrapolation are not available at this time. However, the model was used to determine the degree of alteration in metabolism of BTHEX in rats. Of most interest are the change in blood concentrations and the degree of reduction of BTHEX metabolism during exposure to relevant levels of gasoline in the environment. The gasoline concentration in the gas uptake chamber at the end of the PK experiment that started at the lowest concentration was approximately 150 ppm; extrapolation of this PBPK model well below this level to environmental exposure levels would be associated with greater uncertainty. However, the exposure levels for several components allowed by the U.S. Occupational Safety and Health Administration were within the exposure levels used in these studies. Also, the Threshold Limit Value for gasoline is 300 ppm over an 8-h workshift (44). Therefore, the model can be used to determine internal measurements of dose, i.e., biologically effective doses, in this range (Figure 6). Using a significance level defined as a 10% increase in a biologically effective dose (45), inhibition in gasoline was frequently found at concentrations of 200 ppm and above and occasionally at 100 ppm. The blood concentrations of ethylbenzene, o-xylene, and the lumped component tended to be affected more than n-hexane, benzene, and toluene. The 2/3 cut affected blood concentrations the least as the lumped component in this fraction was a weaker inhibitor than in the other fractions. For chemicals that have toxicity mediated through metabolites, the amount of chemical metabolized is a better marker of biologically effective dose than levels of the parent compound. For the 1/3 and 2/3 cuts, the amount metabolized is decreased for most BTHEX components at 300 ppm and above. For the whole gasoline, a decrease in the amount metabolized is seen for most components at 200 ppm and above. The present model suggests that lumping approaches will work for whole gasoline and for various volatile fractions of gasoline, such as may be inhaled by workers exposed to gasoline vapors in various workplaces. Lumping approaches could also be useful with respect to the PKs of complex mixtures via other routes of entry into the body, e.g., dermal exposures. PBPK lumping can also be applied to classical (non-PBPK) PK studies and to other complex mixtures, e.g., diesel fuel, jet fuel, combustion products (polycyclic aromatic hydrocarbon mixtures), or asphalt fumes and may serve as the basis for cumulative risk assessments of components exerting similar kinds of toxicological action within the mixture. 5680
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Acknowledgments This study was supported in part by a Cooperative Agreement from ATSDR (U61/ATU 881475) and NIEHS Quantitative Toxicology Training Grant (T32 ES07321). The assistance of Drs. M. Mumtaz, I. Dobrev, and M. Reddy and B. Cranmer and D. Dick is gratefully appreciated.
Appendix The following equations describe the chemical in the chamber and in the lung blood of the rat in the chamber: d(AC)/dt ) QP*(CX-CC) d(AP)/dt d(AP)/dt ) KL*AC CX ) CA/PB CV ) (σQi*CVi)/QC d(AB)/dt ) QC*(CV-CA) + QP*(CC-CX) CA ) AB/VB
rate of change in amount in chamber rate of loss due to nonspecific absorption concn in exhaled air concn in mixed venous blood rate of change in lung blood amount concn in arterial blood
where AC is the amount in the chamber, QP is the alveolar ventilation rate, CX is the concentration of chemical in exhaled air, CC is the concentration of chemical in the chamber, AP is the amount of chemical lost in the chamber other than due to systemic absorption by the rat, KL is the first-order loss rate constant, CA is the arterial blood concentration, PB is the blood:air partition coefficient, CV is the venous blood concentration, Qi is the blood flow rate to tissue i (fat, liver, rapidly perfused, and slowly perfused), CVi is the concentration in the venous blood leaving each tissue, QC is the total blood flow, AB is the amount in the lung blood, and VB is the volume of the lung blood. A single equation represents the description of the chemical in each tissue d(AT)/dt ) Qi*(CA-CVi) - rate of change in amount in d(AM)/dt compartments CT ) AT/VT concn in each tissue compartment CVi ) CT/PT concn in venous blood leaving tissues
where AT is the amount in each tissue, Qi is the blood flow to tissue i, CVi is the chemical concentration in the venous blood leaving tissue i, CT is the chemical concentration in each tissue, VT is the volume of each tissue, PT is the partition coefficient between the tissue and blood, and AM is the amount of chemical metabolized (liver only). In the liver, metabolism is represented
d(AM)/dt ) VMAX*CVL/(KM*(1+
∑CVi/Ki) + CVL)
where VMAX is the maximum rate of metabolism, CVL is the concentration in the venous blood leaving the liver, Km is the affinity constant for the chemical, CVi is the venous blood concentration leaving the liver for each inhibitor i, and Ki is the inhibitory constant for each inhibitor.
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Received for review October 28, 2003. Revised manuscript received August 1, 2004. Accepted August 13, 2004. ES035201S
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