A Physiologically Based Pharmacokinetic Model for Methyl tert-Butyl Ether in Humans: Implementing Sensitivity and Variability Analyses

Amy Collins Licata*,{dagger},1, Wolfgang Dekant{ddagger}, Charles E. Smith{dagger} and Susan J. Borghoff*,2

* CIIT Centers for Health Research, 6 Davis Drive, P. O. Box 12137, Research Triangle Park, North Carolina 27709-2137; {dagger} Biomathematics Graduate Program, Department of Statistics, Box 8203, North Carolina State University, Raleigh, North Carolina 27695; and {ddagger} Institut fur Toxikologie, Universitat Würzburg, Versbacher Str. 9, 97078 Würzburg, Germany

Received January 9, 2001; accepted May 1, 2001


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Methyl tert-butyl ether (MTBE) is added to gasoline to reduce carbon monoxide and ozone precursors from automobile emissions. The objectives of this study were to verify the ability of a physiologically based pharmacokinetic (PBPK) model to predict MTBE blood levels in humans and to investigate the effect of variability in the metabolism of MTBE and its influence on the predicted MTBE blood levels. The model structure for MTBE was flow-limited and had six essential compartments: lung, liver, rapidly perfused tissues, slowly perfused tissues, fat, and kidney. In this model, two pathways of metabolism are described to occur in the liver by Michaelis-Menten kinetics. Metabolic rate constants were measured in vitro using human liver microsomes and extrapolated to in vivo whole-body metabolism. Model predictions were compared with data on blood levels of MTBE taken from humans during and after a 1-h inhalation exposure to 1.7 ppm MTBE and after 4-h inhalation exposures to 4 or 40 ppm MTBE. The PBPK model accurately predicted MTBE pharmacokinetics at the high and low MTBE exposure concentrations for all time points. At the intermediate MTBE exposure concentration, however, the model underpredicted early time points while adequately predicting later time points. Results of the sensitivity analysis indicated that the influence of metabolic parameters on model output was dependent on MTBE exposure concentration. Subsequent variability analysis indicated that there was more variability in the actual measured MTBE blood levels than in the blood levels predicted by the PBPK model when using the range of metabolic parameters measured in vitro in human liver samples. By incorporating an understanding of the metabolic processes, this PBPK model can be used to predict blood levels of MTBE, which is important in determining target tissue dose estimates for risk assessment.

Key Words: physiologically based pharmacokinetic (PBPK) model; methyl tert-butyl ether (MTBE); sensitivity analysis; variability analysis.


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
By enacting a specific requirement from the 1990 Clean Air Amendments, Congress mandated that changes be made to reformulate gasoline in an effort to reduce carbon monoxide (CO) and ozone (O3), two key National Ambient Air Quality Standard (NAAQS) pollutants (HEI, 1996Go). Two gasoline programs have been implemented in which oxygenates are added to gasoline to increase the oxygen content of fuel. The first gasoline program, as an effort to reduce CO from automobile emissions, is in effect in the wintertime where oxygenated gasoline contains a minimum of 2.7% oxygen by weight (HEI, 1996Go). The second program is a year-round reformulated gasoline program to reduce emission of O3 precursors. Reformulated gasoline contains at least 2% oxygen by weight. The gasoline additive methyl tert-butyl ether (MTBE) is the most frequently used oxygenate; 15% MTBE is added to wintertime gas and 11% to reformulated gas (HEI, 1996Go). While the purpose of using these oxygenates in gasoline is to achieve or maintain compliance with the NAAQS, concern has been raised regarding the potential health effects of exposure to MTBE. Exposure to MTBE can be both occupational and nonoccupational. For manufacturing and distribution workers, service station attendants, and auto mechanics, occupational exposure can occur at any point in the manufacture, transportation, distribution, or use of MTBE and gasoline containing MTBE. For the general public, MTBE exposure via inhalation can occur from evaporative gasoline emissions and incomplete gasoline combustion at levels from 2–10 ppm MTBE at 2–5 minute intervals (U.S. EPA, 1996Go).

Several studies have been conducted to evaluate the potential health effects of MTBE in humans and rodents. Data from acute inhalation exposures indicate that MTBE is not highly toxic to rodents (Constantini, 1993Go). In chronic inhalation studies, however, MTBE caused renal tumors in male Fischer 344 rats and hepatic tumors in female CD-1 mice (Bird et al., 1997Go). Oral administration of MTBE to Sprague-Dawley rats increased Leydig cell tumors in males and lymphohematopoietic tumors in females (Belpoggi et al., 1995Go). To assess acute responses from humans, various evaluations have been made. Several individuals complained of headaches, nausea, and sensory irritations from breathing fumes associated with MTBE-oxygenated gasoline (Moolenaar et al., 1994Go; White et al., 1995Go). Yet, epidemiological studies and human clinical studies (Amberg et al., 1999Go; Cain et al., 1996Go; Mohr et al., 1994Go; Nihlén et al., 1998Go; Prah et al., 1994Go) do not indicate any significant adverse health effects from exposure to MTBE.

Experimental studies indicate that both rats and humans metabolize MTBE in the liver by two cytochrome P450 (CYP) enzymes (Brady et al., 1990Go; Hong et al., 1997Go; Poet and Borghoff, 1998Go). In rats, MTBE is oxidized by CYP2B1 and CYP2E1 (Brady et al., 1990Go). In humans, one pathway appears to be a low-affinity, high-capacity pathway and correlates with the specific isoform CYP2A6 (Poet and Borghoff, 1998Go). There is high variability associated with CYP2A6 in the human population (Koenigs et al., 1997Go; Pelkonen and Raunio, 1995Go). The other pathway is a high-affinity, low-capacity pathway, which correlates with CYP2E1 activity (Poet and Borghoff, 1998Go). Previous studies have suggested that certain individuals may be sensitive to environmental chemicals due to differences in ability to metabolize these chemicals (Hong et al., 1997Go, 1999Go). Therefore understanding the variation associated with metabolizing enzymes is an important factor in determining an individual's susceptibility to environmental chemicals (Faustman and Omenn, 1996Go).

In a previously developed physiologically based pharmacokinetic (PBPK) model for MTBE in rats, in vivo metabolic rate constants were estimated from gas uptake studies (Borghoff et al., 1996Go). Subsequently, this rodent model was scaled to humans to predict human data from inhalation exposure to MTBE by incorporating human physiological and anatomical parameters and allometrically scaling metabolic rate parameters (Cain et al., 1996Go). Even though this model was able to predict human MTBE blood levels during exposure, it underpredicted postexposure data. Some PBPK model parameters, such as tissue:blood partition coefficients, are relatively constant across species (Krishnan and Andersen, 1994Go); while other parameters, such as alveolar ventilation rate, vary coherently across species (Krishnan and Andersen, 1994Go). Metabolic rate parameters do not scale accurately from species to species (Gillette, 1985Go; Krishnan and Andersen, 1994Go). Allometric scaling between species for metabolic rate constants seems to be insufficient to describe MTBE postexposure data. The data collected after an inhalation exposure is greatly influenced by metabolism (Clewell et al., 1994Go). Metabolic rate constants for MTBE were determined in vitro using rat and human liver microsomes (Poet and Borghoff, 1998Go). The in vitro metabolic rate constants, measured using rat microsomes, were able to predict whole-body metabolism in the rats. This strongly suggests that in vitro metabolic constants measured in human microsomes would be able to predict whole-body metabolism in humans.

The primary objective of this study was to verify the ability of a PBPK model to predict MTBE blood levels in humans. Another objective of this work was to investigate the effect of variability in the metabolism of MTBE and its influence on the predicted MTBE blood levels. A formal sensitivity analysis was used to determine the relative importance of metabolic parameters to PBPK model output. Specifically, the sensitivity analysis was used to determine the MTBE inhalation exposure concentrations in which MTBE blood levels were greatly influenced by the metabolic parameters. This PBPK model was then used to evaluate the contribution of the various metabolic pathways at different exposure concentrations. A statistical variability analysis was used to investigate how the highly variable high-capacity, low-affinity metabolic pathway affects model output following various exposure concentrations. An improved PBPK model for MTBE that incorporates an understanding of the metabolic processes will be useful in developing a more accurate exposure-dose relationship in humans.


    MATERIALS AND METHODS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
PBPK model development.
The existing PBPK model for MTBE (Borghoff et al., 1996Go) was refined by incorporating MTBE-specific parameters values that were experimentally measured in human tissues, such as partition coefficients and metabolic rate constants. Fundamental assumptions underlying the PBPK model for MTBE were taken from a flow-limited model for volatile chemicals (Ramsey and Anderson, 1984). The MTBE PBPK model had 6 essential compartments: lung, liver, rapidly perfused tissues, slowly perfused tissues, fat, and kidney (Fig. 1Go). In this model, the metabolism of MTBE was described to take place in the liver by 2 pathways that followed Michaelis-Menten kinetics.



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FIG. 1. Schematic diagram of a physiologically based pharmacokinetic model used to describe the disposition of MTBE.

 
The commercial software packages MATLAB® (The MathWorks, Inc., Natick, MA) and Simulink®, a companion program to MATLAB®, were used during model development and simulation. In the model development process, a Simulink® graphical user interface (GUI) was utilized for building the MTBE PBPK model as block diagrams. The model equations (Appendix), both the ordinary differential equations (ODE) and algebraic equations, were implicitly defined in these blocks. The ODEs were used to explain the change in amount of MTBE over time. For numerical integration, the MATLAB® ODE solver "ode15s" (Gear-type stiff solver) was chosen because this variable-order, multistep integration algorithm is particularly designed to work well with stiff systems, such as a PBPK model that has both very fast and very slow dynamics.

Human-specific model parameters.
In the model equations, the species-specific physiological and anatomical parameters used were taken from Brown et al. (1997) (Table 1Go). Individual body weights and volumes of fat were measured in the Amberg et al. (1999) study and used accordingly with this source of experimental human data. Since individual values for body weights and volumes of fat were not measured by Cain et al. (1996), mean body weight and mean volume of fat calculated from the Amberg et al. (1999) study were used with the Cain et al. (1996) experimental human data. Organ volumes were scaled to body weight (Clewell et al., 1999Go). The parameters of cardiac output, alveolar ventilation rate, and Michaelis-Menten maximum rate of metabolism were scaled with three-fourths power of body weight for intraspecies extrapolations (Andersen et al., 1987Go; Clewell et al., 1999Go).


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TABLE 1 Physiological and Anatomical Parameters Incorporated into the Model Describing MTBE Disposition
 
Chemical-specific model parameters: Partition coefficients.
Chemical-specific partition coefficients for MTBE in humans are listed in Table 2Go. The blood:air partition coefficient was analyzed from pooled samples based on 5 male and 5 female volunteers (Nihlén et al., 1995Go). Also in this study, the muscle:blood partition coefficient was calculated from tissue composition (Nihlén et al., 1995Go). Partition coefficients were determined for MTBE in human kidney and adipose tissue using the vial-equilibration technique described by Gargas et al. (1989). Kidney and fat samples were obtained from accident victims (International Institute for the Advancement of Medicine, Exton, PA). These tissues became available for research based on complications of identifying a proper recipient for transplant. Five out of the 6 kidney samples had been perfused with and stored for 24 h in VialspanTM (Dupont, Wilmington, DE) transplant media at 4°C. Once these kidneys were determined not to be appropriate for transplant purposes, they were then stored frozen at –70°C. All the samples of adipose tissue were from 3 male donors (ages 18, 34, and 54), whereas 3 of the kidney tissue samples were from male donors (ages 21, 65, and 69) and 3 from female donors (ages 38, 44, and 66). The partition coefficients of MTBE in kidney and adipose tissue were measured in tissue homogenates at 37°C and also in samples preheated at 60°C for 1 h to inhibit any possible metabolism or potential protein binding. Modifications in the vial equilibration method described by Gargas et al. (1989) were made only in using an additional control to account for partitioning differences between saline (used for nonperfused tissues) and the VialspanTM perfusion media. Kidneys that had been perfused with VialspanTM were homogenized in VialspanTM and the control was VialspanTM instead of saline.


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TABLE 2 Partition Coefficients for MTBE
 
The partition coefficient of MTBE in the kidney was used to represent the partition coefficients for the kidney, rapidly perfused tissues, and liver. The partition coefficient of MTBE in muscle was used to represent the partition coefficient for slowly perfused tissues (Nihlén et al., 1995Go). The tissue:blood partition coefficients (PiMTBE) used throughout the model were calculated by dividing the tissue:air partition coefficients by the equilibrium blood:air partition coefficient (PbMTBE).

Chemical-specific model parameters: Metabolic rate constants.
In a study conducted by Poet and Borghoff (1998), MTBE in vitro metabolic rate constants were determined using liver microsomes from 10 human subjects, 5 males and 5 females. The metabolism of MTBE was measured using a 2-compartment vial equilibration system, where MTBE activity correlated with 2 specific P450 marker substrate activities. One P450 isoform corresponded to a low-affinity, high-capacity pathway, and the other P450 isoform corresponded to a high-affinity, low-capacity pathway (Poet and Borghoff, 1998Go). In this model, the low-affinity, high-capacity pathway was denoted as pathway 1 with the Michaelis-Menten metabolic parameters Vmax CMTBE,1 and KMMTBE,1; the high-affinity, low-capacity pathway was denoted as pathway 2 with Vmax CMTBE,2 and KMMTBE,2 as its Michaelis-Menten metabolic parameters. These metabolic parameters, listed in Table 3Go, were extrapolated to in vivo whole-body metabolism based on microsomal protein content, body weight, and liver weight as a percentage of body weight. In Table 3Go, maximum and minimum metabolic values are shown to illustrate the variability for each of the 4 parameters.


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TABLE 3 In Vivo Rate Constants for Hepatic Metabolism of MTBE
 
Source of experimental human data.
Six human volunteers, 3 males and 3 females, were exposed to 2 concentrations of MTBE by inhalation (Amberg et al., 1999Go). The 6 volunteers were exposed to 4 ppm MTBE for 4 h and 4 weeks later the same 6 volunteers were exposed to a higher MTBE concentration of 40 ppm for 4 h. The parameters of body weight and fractional volume of fat were measured in each of the volunteers. Blood was collected postexposure via the antecubital vein. The MTBE concentrations in the blood were quantified by gas chromatography-mass spectrometry.

In another study, human volunteers were exposed to MTBE via inhalation. Four individuals, 2 males and 2 females, were exposed for 1 h to 1.7 ppm MTBE (Cain et al., 1996Go). Blood samples, from the antecubital vein, were taken before, during, and after the exposure. MTBE levels were measured in the venous blood using gas chromatography-mass spectrometry. The PBPK model was used to predict this Cain data set, along with the Amberg et al. (1999) data.

Metabolic parameter estimation.
During the parameter estimation procedure, the built-in routine "fmincon" from the MATLAB® Optimization Toolbox was used. This routine, with the Sequential Quadratic Programming (SQP) optimization algorithm, was utilized to find the constrained minimum of the objective function. Maximization of the objective function was achieved when using "-objective function." Since maximum likelihood techniques were used during parameter estimation, the objective function was the log likelihood function (LLF) of the form:

where zi,j was the measured value of the jth response for the ith data point, fi,j was the predicted value of the jth response for the ith data point, {gamma}j was the heteroscedasticity parameter for the jth response variables (set to 2, which denotes constant coefficient of variation and relative error), r was the number of measured response variables, and nj was the number of measurements of the jth system responses (data points). The heteroscedasticity parameter {gamma}j is also known as the weighting parameter. When setting this value to 2 during optimizations, an estimate of the standard deviation for a given measured response variable will be proportional to the predicted value for that measured response variable.

Using maximum likelihood techniques, 4 metabolic parameters (Vmax CMTBE,1, KMMTBE,1, Vmax CMTBE,2, and KMMTBE,2), describing 2 pathways of MTBE metabolism, were estimated by pooling the data (simultaneously evaluating all data sets) from the 3 human pharmacokinetic inhalation studies (Amberg et al., 1999Go; Cain et al., 1996Go). The maximum and minimum in vivo scaled values were used as the upper and lower bounds, respectively. The optimum metabolic parameter values were the best-fit estimates based on maximum likelihood techniques; therefore these values are known as maximum likelihood estimates (MLE) (Table 3Go).

Sensitivity analysis.
A sensitivity analysis was implemented to evaluate the relative importance of model parameters on model output at various times and concentrations. The model parameters investigated included partition coefficients, compartment blood flows, compartment volumes, and metabolic parameters. The key model parameters of interest were the 4 Michaelis-Menten metabolic parameters (Vmax CMTBE,1, KMMTBE,1, Vmax CMTBE,2, and KMMTBE,2), with predicted MTBE blood levels as the PBPK model output.

Sensitivity coefficients (SC) were obtained using the partial derivatives of model output with respect to model parameters (Clewell et al., 1994Go; Evans et al., 1994Go). These SC were calculated using the central difference method:

where {partial} is the partial derivative, Y is the PBPK model output (predicted MTBE blood levels) as a function of pi and t, pi is the exclusive ith parameter (Vmax CMTBE,1, KMMTBE,1, Vmax CMTBE,2, and KMMTBE,2) that was investigated while all other parameters were held at constant values, t is the independent run variable (time), and {Delta} is the change in the parameter pi (5% change). Log-normalized (ln) SC are: [{partial} ln Y(pi, t)/{partial} ln pi] {cong} [SC* (pi/Y(pi, t))].

The normalized SC represented the percentage change in the model output due to a percentage change in the distinct parameter value. For the 4 metabolic parameters, their log-normalized SC were directly comparable to one another. The log-normalized SC ranged in values between positive and negative one for all 3 concentrations, 40, 4, and 1.7 ppm. The larger normalized SC, those with values near positive or negative one, were associated with the model parameter greatly influencing model output. A model parameter that has smaller normalized SC, those with values near zero, would not be that important in generating model output. Negative normalized SC indicate that a decrease in model output has occurred when there is an increase in the specific parameter evaluated, or vice versa. On the other hand, positive normalized SC occur when both the model output and the model parameter increase, or decrease, together.

Variability analysis.
Measured in vitro and scaled to in vivo, the metabolic parameter Vmax CMTBE,1 was highly variable with a 25-fold difference between the maximum and minimum values. To assess how this 25-fold difference would impact MTBE blood levels, a variability analysis was conducted. This analysis was used to evaluate the variability of the scaled in vivo metabolic parameters Vmax CMTBE,1, KMMTBE,1, Vmax CMTBE,2, and KMMTBE,2 (Poet and Borghoff, 1998Go), along with the variability of the experimental data, measured MTBE blood levels (Amberg et al., 1999Go; Cain et al., 1996Go). A coefficient of variation (CV), also known as a coefficient of variability, is a relative measure of spread that can be used to assess variability from different experiments (Steel and Torrie, 1980Go), such as measurements of MTBE metabolic parameters (Poet and Borghoff, 1998Go) and measurements of MTBE blood levels following an MTBE inhalation exposure (Amberg et al., 1999Go; Cain et al., 1996Go). The CV, a ratio of sample standard deviation over the sample mean (CV = s/), was used to compare the variability of the model output with the variability of the experimental data (Amberg et al., 1999Go; Cain et al., 1996Go). The CV generated from the scaled in vivo metabolic parameters could not be directly compared with the experimental data CV because these are 2 different metrics. Yet the PBPK model output CV, focusing solely on the variability of the metabolic parameters, is comparable with the experimental data CV. These 2 quantities were directly compared because the PBPK model output is predicted MTBE blood levels and the experimental data are measured MTBE blood levels.

For the experimental data at MTBE exposure concentrations of 40, 4, or 1.7 ppm (Amberg et al., 1999Go; Cain et al., 1996Go), an empirical CV, with the sample mean and the sample standard deviation, was calculated at each time point. For the PBPK model output, the CV was calculated by approximation using propagation of error formulas (Vardeman, 1994). The approximate mean (EU) (Vardeman, 1994) was given by:

where E represented mean, Y(Ep1, Ep2, ... , Epn) was the model output evaluated using the mean values of the parameters (p1, p2, ... , pn), and n was the number of parameters investigated in the variability analysis. The overall PBPK model output approximate variance was based on both the variability of the parameter values and the model output sensitivity to changes in these parameters over time. Thus, the approximate variance (VarU) (Vardeman, 1994) of the PBPK model output was calculated by:

where Var represents variance, [{partial}Y(pi, t)/{partial}pi]2 are SC for respective ith parameter (see earlier Sensitivity Analysis section) raised to the second power, Var(pi) is the variance for the respective ith parameter, and n is the number of parameters investigated in the variability analysis. If the ith and jth parameters are not independent, the term [({partial}Y(pi, t)/{partial}pi) • ({partial}Y(pj, t)/{partial}pj)] Cov (pi, pj) can be added to the approximate variance formula. After obtaining the approximate mean and approximate variance at each time point, the CV for the PBPK model output, focusing on the parameters of interest, was calculated as follows:

The empirical CV calculated from the actual measured MTBE blood levels was compared with the approximate CV from the model output, focusing on the variability of the metabolic parameters.


    RESULTS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Model Predictions of Measured MTBE Blood Levels
The scaled in vivo metabolic parameters, Vmax CMTBE,1, KMMTBE,1, Vmax CMTBE,2, and KMMTBE,2, were used as initial values in the numerical maximum likelihood estimation procedure. The MLE were obtained by pooling (simultaneously evaluating all data sets) the 3 inhalation pharmacokinetic studies (Amberg et al., 1999Go; Cain et al., 1996Go). Incorporating the MLE for the 4 metabolic parameters (Vmax CMTBE,1 = 34.5, KMMTBE,1 = 61.4, Vmax CMTBE,2 = 8.6, and KMMTBE,2 = 5.0) and literature or experimentally determined values for all other parameters, PBPK model predictions were compared to data on measured blood levels of MTBE taken from humans during and after a 1-h inhalation exposure to 1.7 ppm MTBE (Cain et al., 1996Go), and after 4-h inhalation exposures to 4 or 40 ppm MTBE (Amberg et al., 1999Go). For the 40 and 4 ppm inhalation study (Amberg et al., 1999Go), the individual measurements of body weights and volumes of fat for the 6 volunteers were used for the respective volunteers during the parameter estimation procedure. Yet, for both the 40 and 4 ppm data, the mean body weight and the mean volume of fat were used to generate the PBPK model predictions. The PBPK model accurately predicted MTBE blood levels following a 4-h inhalation exposure at the high MTBE exposure level (40 ppm) (Fig. 2AGo). At the intermediate MTBE exposure level (4 ppm), however, the PBPK model underpredicted early time points following a 4-h inhalation exposure (Fig. 2BGo). At the low MTBE exposure level (1.7 ppm), the model was able to predict the data collected during and following the 1-h inhalation exposure (Fig. 2CGo).



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FIG. 2. Experimental data (symbols) and model predictions (curves) for the concentration of MTBE after a 4-h inhalation exposure to 40 (A) or 4 (B) ppm MTBE (Amberg et al., 1999) and during and after a 1-h inhalation exposure to 1.7 (C) ppm MTBE (Cain et al., 1996). Physiological and chemical parameter values used in the model (Fig. 1Go) are listed in Tables 1–3GoGoGo. The maximum likelihood estimates (MLE), as listed in Table 3Go, for the 4 metabolic parameters were used in these predictions.

 
Sensitivity Analysis
A sensitivity analysis, using the central difference method, was conducted on the 4 metabolic parameters, Vmax CMTBE,1, KMMTBE,1, Vmax CMTBE,2, and KMMTBE,2, to evaluate their influence in generating model output, namely predicted MTBE blood levels. Each metabolic parameter was analyzed individually, while all other parameters were held at their respective mean values. The sensitivity analysis was run at the exposure scenario identical to that of the pharmacokinetic data that were modeled (Amberg et al., 1999Go; Cain et al., 1996Go). There was an overall time and concentration-dependent sensitivity of predicted MTBE venous blood levels (model output) to the metabolic parameters. Model output at the high concentration (40 ppm, 4-h inhalation) was more sensitive to pathway 1 metabolic parameters, Vmax CMTBE,1 and KMMTBE,1, which correspond to a high-capacity, low-affinity pathway (Fig. 3AGo). On the contrary, at the lower concentrations (4 ppm, 4-h inhalation and 1.7 ppm, 1-h inhalation), the model output was more sensitive to pathway 2 metabolic parameters, Vmax CMTBE,2, and KMMTBE,2 (Figs. 3B and 3CGoGo). Pathway 2 corresponds to the low-capacity, high-affinity pathway. For the 2 metabolic pathways, the normalized SC for the respective Vmax CMTBE,1 or 2 and KMMTBE,1 or 2 are inversely related due to the Michaelis-Menten equation that was used to describe saturable metabolism. In this equation (Appendix), the metabolic parameters are represented as a ratio. Unlike during the exposure, the normalized SC for the metabolic parameters are numerically large at the end of the exposure phase because metabolism plays an important role in clearance during postexposure (Clewell et al., 1994Go).



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FIG. 3. Normalized sensitivity coefficients (SC) for metabolic parameters (VMAXC1, KM1, VMAXC2, KM2) at 40 ppm, 4-h inhalation (A), 4 ppm, 4-h inhalation (B), or 1.7 ppm, 1-h inhalation (C). The PBPK model output is predicted MTBE venous blood levels. The symbols are not data points but representations used to differentiate the normalized SC for the 4 different metabolic parameters.

 
Even though the objective of this exercise was to focus on the influence of the metabolic parameters in generating model output, a sensitivity analysis was also performed on other model parameters. During exposure, the model output was more sensitive to changes in the blood:air partition coefficient (PbMTBE) and the alveolar ventilation rate (Qalv) than to changes in metabolic parameters, most likely due to the data being collected from inhalation studies (Amberg et al., 1999Go; Cain et al., 1996Go). At low exposure concentrations, overall model output is less sensitive to changes in the metabolic parameters and more sensitive to changes in the following parameters: blood:air partition coefficient (PbMTBE), alveolar ventilation rate (Qalv), cardiac output (Qt), the fat:blood partition coefficient (PfMTBE), and blood flow to fat (Qf). At high exposure concentrations, the metabolic parameters, when compared with other model parameters, have the most influence on model output.

Model Prediction of Amount Metabolized
The MTBE PBPK model was used to predict the amount of MTBE metabolized by the 2 different pathways. These model predictions were used to evaluate the contribution of the high-capacity, low-affinity metabolic pathway versus the low-capacity, high-affinity metabolic pathway to the MTBE blood levels following exposure to various concentrations of MTBE. Model output was generated using a description of a 4-h inhalation exposure to various concentrations of MTBE. A range of MTBE concentrations, 100, 40, 12, or 4 ppm, was used to examine the contribution of the 2 different pathways to the amount of MTBE metabolized. At the higher concentrations, 100 (Fig. 4AGo) and 40 (Fig. 4BGo) ppm, pathway 1, the high-capacity, low-affinity pathway, had a larger contribution to the amount of MTBE metabolized. At 12 ppm (Fig. 4CGo), both pathways appear to contribute equally to the amount of MTBE metabolized over time. The low-capacity, high-affinity pathway had a larger contribution to the amount of MTBE metabolized at the lower concentration of 4 ppm (Fig. 4DGo) and, as expected, the high-capacity, low-affinity pathway was more important at high exposure concentrations (Figs. 4A and 4BGoGo). The model was used to evaluate exposure concentrations at which pathway 1 would be most significant. For the general public, typical MTBE inhalation exposures are 2–10 ppm at 2–5 min intervals (U.S. EPA, 1996Go). While a 4-h exposure duration was used for comparison with the current experimental study, other temporal durations and exposure levels could be investigated with the model, depending on the exposure scenario of interest.



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FIG. 4. Using the PBPK model, the amount of MTBE predicted to be metabolized over time by the 2 different metabolic pathways following a 4-h inhalation exposure period at 100 (A), 40 (B), 12 (C), or 4 (D) ppm MTBE. The solid curve represents the amount metabolized by pathway 1, the high-capacity, low-affinity pathway. The dotted curve represents the amount metabolized by pathway 2, the low-capacity, high-affinity pathway.

 
Variability Analysis
A high variability (Table 3Go) was found in the Vmax CMTBE,1 metabolic parameter where there was approximately a 25-fold difference in 10 individuals between the maximum and minimum values (Poet and Borghoff, 1998Go). The other 3 parameters had less variability (Table 3Go): KMMTBE,1 had approximately a 2-fold difference, Vmax CMTBE,2 had approximately a 4-fold difference, and KMMTBE,2 had approximately a 2.5-fold difference (Poet and Borghoff, 1998Go). Using the 25-fold range (maximum, mean, and minimum values as listed in Table 3Go) of Vmax CMTBE,1, model predictions were compared to data (Fig. 5Go) on measured MTBE blood levels after a 4-h inhalation exposure to 40 or 4 ppm MTBE (Amberg et al., 1999Go), and during and after a 1-h inhalation exposure to 1.7 ppm MTBE (Cain et al., 1996Go). In these model predictions (Fig. 5Go), the mean values for the other 3 metabolic parameters (KMMTBE,1, Vmax CMTBE,2, and KMMTBE,2), were used; therefore the predictions solely illustrate the variability of Vmax CMTBE,1 . This 25-fold difference in Vmax CMTBE,1 generates approximately a 1.4-fold difference in peak blood levels at all 3 exposure concentrations at the end of the exposure (Fig. 5Go).



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FIG. 5. Experimental data (symbols) and model predictions (curves) using the 25-fold range (Poet and Borghoff, 1998) of Vmax CMTBE,1 solid curve, minimum value; dashed curve, mean value; dotted curve, maximum value) for the concentration of MTBE after a 4-h inhalation exposure to 40 (A) or 4 (B) ppm MTBE (Amberg et al., 1999), and during and after a 1-h inhalation exposure to 1.7 (C) ppm MTBE (Cain et al., 1996). The mean values for the other 3 metabolic parameters (KMMTBE,1, Vmax CMTBE,2, KMMTBE,2) were used in these predictions to illustrate the range of Vmax CMTBE,1 on model predictions. Physiological and chemical parameter values used in the model (Fig. 1Go) are listed in Tables 1–3GoGoGo.

 
To quantitatively understand how this variability of the metabolic parameters influences model output, a variability analysis was conducted. With this analysis, CV, a ratio of sample standard deviation over the sample mean, was used to compare the variability of the model output with the variability of the experimental data (Amberg et al., 1999Go; Cain et al., 1996Go). To evaluate the variability of each of the 2 metabolic pathways, a CV for the model output (predicted MTBE blood levels) was generated for each of the pathways and individually compared with the CV for the experimental data (measured MTBE blood levels).

For the experimental data at each time point, the empirical CV was directly calculated from the sample mean and sample standard deviation. Conversely, for the model output, the CV at each time point was obtained by approximation using propagation of error formulas (Vardeman, 1994). Specifically, the approximate mean (EU) and approximate variance (VarU) calculated (Appendix) for the PBPK model focusing on the variability of pathway 1 (Vmax CMTBE,1 and KMMTBE,1) or focusing on the variability of pathway 2 (Vmax CMTBE,2 and KMMTBE,2). To obtain the approximate mean and approximate variance for the PBPK model output, the mean and variance of the in vivo scaled values (Table 3Go) for Vmax CMTBE,1 and KMMTBE,1 (pathway 1) and Vmax CMTBE,2 and KMMTBE,2 (pathway 2) (Poet and Borghoff, 1998Go) were incorporated. The approximate mean (EU1) focusing on the variability of pathway 1 metabolic parameters and the approximate mean (EU2) focusing on the variability of pathway 2 metabolic parameters were equivalent since the mean values of the metabolic parameters were used in this analysis. The approximate variance (VarU1or2) was based on both the variability of these metabolic parameters and sensitivity of model output to changes in these parameters (Fig. 3Go). The PBPK model output CV was calculated from the approximate mean and the approximate variance (Appendix).

For each of the 2 metabolic pathways, the PBPK model output CV, focusing on the variability of pathway 1 parameters (Vmax CMTBE,1 and KMMTBE,1) or focusing on the variability of pathway 2 parameters (Vmax CMTBE,2 and KMMTBE,2), was compared with the CV of the experimental data at 40 (Fig. 6AGo), 4 (Fig. 6BGo), and 1.7 (Fig. 6CGo) ppm MTBE (Amberg et al., 1999Go; Cain et al., 1996Go). In general, at all 3 concentrations, 40, 4, and 1.7 ppm, there was more variability, over time, in the actual measured MTBE blood levels than in the model predictions of MTBE blood concentrations, when the variability is focused on pathway 1 or pathway 2 metabolic parameters. Even though the metabolic parameter Vmax CMTBE,1 had a 25-fold difference between the maximum and minimum in vivo values, this high variability, combined with the low variability from the other pathway 1 metabolic parameter (KMMTBE,1) to generate the model output CV for pathway 1, was still less than the variability in the experimental data, the measured MTBE blood level CV (Fig. 6Go).



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FIG. 6. Variability analysis, over time, tested under the condition of a 40-ppm, 4-h inhalation exposure (A), 4-ppm, 4-h inhalation exposure (B), and 1.7-ppm, 1-h inhalation exposure (C). The coefficient of variation (CV) of the experimental data (measured MTBE blood levels) is represented by solid diamonds. The CV of the PBPK model output (predicted MTBE blood levels) focusing solely on the variability of pathway 1 metabolic parameters (Vmax CMTBE,1 and KMMTBE,1) is represented by open circles. The CV of the PBPK model output (predicted MTBE blood levels) focusing solely on the variability of pathway 2 metabolic parameters (Vmax CMTBE,2 and KMMTBE,2) is represented by open triangles.

 
Since CV is a ratio of 2 averages, the standard deviation over the mean, the sample mean () of the experimental data (measured MTBE blood levels) and the approximate mean (EU1or2) of the model output (predicted MTBE blood levels) should be similar to appropriately use this measure of spread to assess variability. For each of the 3 concentrations (40, 4, or 1.7 ppm) that were investigated in this variability analysis, the sample means and the approximate means, over time, were generally the same for the respective concentrations. Therefore, there were no limitations in using CV as an appropriate measure of variability.


    DISCUSSION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
After incorporating estimated metabolic parameters and literature-determined or experimentally-determined values for all other parameters, the PBPK model was used to test its ability to predict blood levels measured in humans exposed to 1.7 ppm MTBE for 1 h, and 40 or 4 ppm MTBE for 4 h. At the 40- and 1.7-ppm exposure concentrations, the model accurately predicted measured MTBE blood levels for all time points. Yet, at the 4-ppm exposure concentration, although the model accurately predicted later time points, it underpredicted early time points immediately following the 4-h exposure. Since there is strong agreement between the model and the data at both the high and low exposure concentrations, the model structure appears to be adequate. Also, through the model validation processes presented in this work, specifically the sensitivity and variability analyses, the MTBE PBPK model structure appeared to be sufficient to predict MTBE blood levels during and following inhalation exposures to MTBE. Collecting more data before and after exposure may provide greater insight to further evaluate the model structure and may help to explain the lack of fit following the 4 ppm, 4-h exposure scenario.

There is concern for this disagreement between the data and model prediction. In Licata (2000), this model misspecification at the 4 ppm exposure concentration was investigated using several different modeling approaches. These alternative modeling approaches included incorporating the Hill Equation to describe metabolism, investigating different breathing rates at different exposure concentrations, evaluating the contribution of urinary elimination, determining the appropriate model response that corresponds with the MTBE blood concentration data, scaling by minimizing sum of squares, and estimating an input dose (Licata, 2000Go). Of the model alternatives described in Licata (2000), only scaling by minimizing the sum of squares and estimating the input dose produced agreement between the model and 4 ppm data, while not deteriorating the fit of the model to the 40 or 1.7 ppm data. These 2 approaches do not have clear biological interpretations; yet, additional laboratory experiments may indicate otherwise. The collection of more data, especially during and immediately following various inhalation exposures, may provide greater insight to the overall agreement between model predictions and experimental data.

By incorporating estimated metabolic parameters, which were obtained by using human in vivo scaled values as bounds and pooling the inhalation exposure data (40, 4, and 1.7 ppm), the fit of the model to the 1.7-ppm data (Cain et al., 1996Go) is adequate as determined by a mean square error (MSE). According to the MSE, the current fit of the model to the data is an improvement over the fit that was obtained in the previously developed MTBE PBPK model (Borghoff et al., 1996Go). When predicting the 1.7-ppm human data, this original model (Borghoff et al., 1996Go) used scaled metabolic rate constants that were estimated from rodent gas uptake studies. Ideally, metabolic parameters would be obtained in the species of interest, rather than scaling these parameter values from species to species (Gillette, 1985Go; Krishnan and Andersen, 1994Go).

The MTBE PBPK model incorporated 2 metabolic pathways because experimental studies indicate that humans metabolize MTBE in the liver by 2 different CYP enzymes (Hong et al., 1997Go; Poet and Borghoff, 1998Go). Model predictions suggested that the enzyme in pathway 1 would metabolize a greater percentage of MTBE at higher concentrations (69% at 100 ppm, 58% at 40 ppm, and 46% at 4 ppm at time = 20 h) and the enzyme in pathway 2 a greater percentage of MTBE at lower concentrations (32% at 100 ppm, 42% at 40 ppm, and 53% at 4 ppm, at time = 20 h). The first pathway, correlating with the specific isoform CYP2A6, is a low-affinity, high-capacity enzyme (Poet and Borghoff, 1998Go). In contrast, the second pathway is a high-affinity, low-capacity enzyme and correlates with CYP2E1 activity (Poet and Borghoff, 1998Go). A similar study in human liver microsomes (Duescher and Elfarra, 1994Go) was conducted on 1,3-butadiene; and, uptake of this chemical, like MTBE, is primarily by inhalation from environmental exposure through automobile fuel (Himmelstein et al., 1997Go). Duescher and Elfarra (1994) demonstrated that metabolism by CYP2A6 is predominate at higher concentrations, while metabolism by CYP2E1 is predominate at lower concentrations. As supporting evidence that CYP2A6 is more important at high exposure concentrations and CYP2E1 is more important at low exposure concentrations, the sensitivity analysis demonstrated that the high-capacity, low-affinity (pathway 1) metabolic parameters (Vmax CMTBE,1 and KMMTBE,1) greatly influenced model output at the 40-ppm exposure concentration; and the low-capacity, high-affinity (pathway 2) mtabolic parameters (Vmax CMTBE,2 and KMMTBE,2) have more influence on model output at the lower exposure concentrations of 4 and 1.7 ppm (Fig. 3Go). Therefore this sensitivity analysis indicated that there is overall time- and concentration-dependent sensitivity of model output (predicted MTBE blood levels) to metabolic parameters. This is not surprising information; however, the model provides a tool that can be used to investigate various exposure levels where different pathways play a predominant role.

At lower exposure concentrations used for human experiments, such as 1.7 and 4 ppm, the Michaelis-Menten term may be well approximated by a linear term. While at the higher exposure concentrations, such as 40 ppm in the human study and especially concentrations used in rodent studies, its nonlinear functional form largely determines the temporal behavior of the measured dose. The nonlinear Michaelis-Menten term accounts for high-dose/low-dose extrapolation because metabolism becomes saturated at high exposure concentrations, but can collapse to linear at low exposure concentrations (Licata, 2000Go). Also, Poet and Borghoff (1998) indicated that the metabolism of MTBE followed Michaelis-Menten kinetics. For some low-level environmental scenarios, a linearization of time-weighted average values of model outputs of interest in PBPK models has proven useful (Bogen, 1988Go; Bogen and McKone, 1988Go; Bogen and Hall, 1989Go).

The variability found in the MTBE in vitro metabolic parameters (Poet and Borghoff, 1998Go) is similar to the variability found in metabolic parameters obtained in other human in vitro liver microsomal studies. For instance, in the Koenigs et al. (1997) study, 12 human livers were analyzed to determine the CYP2A6 metabolic values where the KM parameter had a 4-fold variation and the Vmax C had a 36-fold variation. To determine CYP2E1 metabolic values, Powell et al. (1998), using 16 human livers, demonstrated that this isoform has low variability where the KM parameter had a 2.5-fold variation and the Vmax C had a 4-fold variation. The variability in the CYP2A6 (Koenigs et al., 1997Go) and CYP2E1 (Powell et al., 1998Go) metabolic parameters is consistent with the variability determined in the Poet and Borghoff (1998) study using 10 human livers. These studies (Koenigs et al., 1997Go; Powell et al., 1998Go) support the high variability associated with the Vmax C parameter in the CYP2A6 pathway and that the other 3 metabolic parameters have low variability. Yet, even though Vmax CMTBE,1, has approximately a 25-fold difference between the maximum and minimum values (Poet and Borghoff, 1998Go), the variability analysis at 40, 4, and 1.7 ppm indicated that there was more variability in the actual MTBE blood levels of different people exposed than in the blood levels predicted by the PBPK model, when the variability is focused on the CYP2A6 or CYP2E1 pathway.

The variability analysis outlined here can be used for other PBPK models to compare the variability of experimentally measured model parameters with the variability of the experimental data that are modeled. This analysis, along with sensitivity and uncertainty analyses, can be used to examine model parameters during the model validation process. Although variability and uncertainty have been used in similar circumstances, they describe completely different phenomena (Grassman et al., 1998Go), but all model parameters will include both. Uncertainty is the lack of knowledge about a parameter value and can be addressed through Monte Carlo techniques (Krewski et al., 1995Go; Krishnan and Andersen, 1994Go; Vose, 1996), whereas variability is a range of values for a parameter expected among individuals within a given population and can be evaluated through a variability analysis using approximation methods, as presented in this work. For a linearized model, the propagation of error variance formula is exact, not an approximation. If the distribution of the variability in parameters is known and the model is highly nonlinear, a Monte Carlo strategy may be preferable to the propagation of error formulas used here. Critics of present risk assessment procedures state the need for a better understanding and assessment of uncertainty and variability (Bogen and Spear, 1987Go; National Research Council, 1994Go).

Several sources (Hong et al., 1997Go, 1999Go) suggest that the 25-fold difference in metabolic activity (CYP2A6) is a major concern. Yet, these model investigations imply that the variability in the MTBE metabolic rate parameters within the human population does not appear to have a significant impact on blood levels at low MTBE exposure concentrations, particularly those within a range of concentrations to which the general public would be exposed via inhalation. By incorporating an understanding of the underlying metabolic processes, this model can be used to predict blood levels of MTBE given an external MTBE exposure concentration, which is important in determining dose estimates for risk assessment.


    APPENDIX
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Terms, Equations, and Formulas Used in the Model
Definition of Terms Used in the Model
i = ith compartment or tissue.

t = Time (h).

AiMTBE = Amount (µmol) of MTBE in tissue or compartment i, where AiMTBE = CiMTBEVi

CiMTBE = Concentration (µmol/liter) of MTBE in compartment or tissue i.

Cv,iMTBE = Concentration (µmol/liter) of MTBE in the venous blood v exiting compartment or tissue i. In this venous equilibrium model, the venous blood concentration is at equilibrium with the free concentration of MTBE in tissue i. The Cv,iMTBE relationship with the tissue/blood partition coefficient is as follows:

(Ramsey and Andersen, 1984Go).

CaMTBE = Concentration (µmol/liter) of MTBE in the arterial blood.

PiMTBE = Equilibrium tissue:blood partition coefficient for MTBE in tissue i.

PbMTBE = Equilibrium blood:alveolar air partition coefficient for MTBE in blood b.

Vi = Volume (liter) of tissue or compartment i.

a = Arterial blood.

alv = Gas-exchange region of the lung, which has no volume, where

inh = Inhalation exposure, there is an infinitely large volume when there is an open chamber.

f = Fat compartment.

k = Kidney compartment.

l = Liver compartment.

r = Rapidly perfused compartment (organs that have high blood flow, for instance, brain and intestines).

s = Slowly perfused compartment (organs that have low blood flow, for instance, muscle and skin).

v = Venous blood.

Qt = Total cardiac output (liter/kg-h), where

Qi = Blood flow (liter/h) to perfusing tissue i.

Qalv = Alveolar ventilation (liter/kg-h), where

VmaxMTBE,1 or 2 = Maximum rate (µmol/h) of metabolism of MTBE, in the liver through pathway 1 or 2, where

KMMTBE,1 or 2 = Apparent enzyme affinity (µmol/liter) for MTBE, in the liver, through pathway 1 or 2. This is also known as the Michaelis-Menten constant or the affinity constant.

Ordinary Differential Equations





Algebraic Equations
The lung compartment in the MTBE model consists of lung blood and alveolar space. The differential equation for the lung is:

There are several simplifying assumptions for the lung compartment: no storage of the toxin in the lung, continuous ventilation, and rapid equilibration of toxic vapor in the lung between blood and alveolar air (Ramsey and Andersen, 1984Go). With these assumptions, a steady-state equation can be derived to calculate the MTBE arterial blood concentration:

The mixed venous blood concentration of MTBE is calculated with the following equation:

This equation for the concentration of MTBE in mixed venous blood is PBPK model output (predicted MTBE blood levels), since blood was sampled from the antecubital vein in the MTBE inhalation studies (Amberg et al., 1999Go; Cain et al., 1996Go).

Propagation of Error Formulas—Approximate Mean and Approximate Variance
The approximate mean (EU1) and approximate variance (VarU1) of the PBPK model focusing on the variability of pathway 1 (Vmax CMTBE,1 and KMMTBE,1) was calculated as follows:

and

where

and

The approximate mean (EU2) and approximate variance (VarU2) of the PBPK model focusing on the variability of pathway 2 (Vmax CMTBE,2 and KMMTBE,2) was calculated as follows:

and

where

and

In this case, a covariance term is not needed in the calculation of approximate variance for pathway 1 or pathway 2 because the interparameter covariance is negligible and the respective parameters are assumed to be independent. Whether focusing on the variability of the metabolic parameters of pathway 1 or pathway 2, the PBPK model output CV was calculated from the approximate mean and the approximate variance as follows:

, where the subscripts indicate the respective metabolic pathways that were examined.


    ACKNOWLEDGMENTS
 
We are thankful for valuable discussions and review of this manuscript from CIIT staff, particularly Drs. Gregory Kedderis, Barbara Kuyper, and Paul Schlosser. We are grateful for the technical expertise of Mr. John Murphy (CIIT). A.C.L. was supported by Science to Achieve Results (STAR) Graduate Fellowship from the United States Environmental Protection Agency.


    NOTES
 
1 Present address: Research Triangle Institute, 3040 Cornwallis Rd., P. O. Box 12194, Research Triangle Park, NC 27709-2194. Back

2 To whom correspondence should be addressed. Fax: (919) 558-1300. E-mail: borghoff{at}ciit.org. Back


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