* CIIT Centers for Health Research, 6 Davis Drive, P. O. Box 12137, Research Triangle Park, North Carolina 27709-2137;
Biomathematics Graduate Program, Department of Statistics, Box 8203, North Carolina State University, Raleigh, North Carolina 27695; and
Institut fur Toxikologie, Universitat Würzburg, Versbacher Str. 9, 97078 Würzburg, Germany
Received January 9, 2001; accepted May 1, 2001
![]() |
ABSTRACT |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Key Words: physiologically based pharmacokinetic (PBPK) model; methyl tert-butyl ether (MTBE); sensitivity analysis; variability analysis.
![]() |
INTRODUCTION |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
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, 1993). 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., 1997
). Oral administration of MTBE to Sprague-Dawley rats increased Leydig cell tumors in males and lymphohematopoietic tumors in females (Belpoggi et al., 1995
). 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., 1994
; White et al., 1995
). Yet, epidemiological studies and human clinical studies (Amberg et al., 1999
; Cain et al., 1996
; Mohr et al., 1994
; Nihlén et al., 1998
; Prah et al., 1994
) 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., 1990; Hong et al., 1997
; Poet and Borghoff, 1998
). In rats, MTBE is oxidized by CYP2B1 and CYP2E1 (Brady et al., 1990
). In humans, one pathway appears to be a low-affinity, high-capacity pathway and correlates with the specific isoform CYP2A6 (Poet and Borghoff, 1998
). There is high variability associated with CYP2A6 in the human population (Koenigs et al., 1997
; Pelkonen and Raunio, 1995
). The other pathway is a high-affinity, low-capacity pathway, which correlates with CYP2E1 activity (Poet and Borghoff, 1998
). 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., 1997
, 1999
). Therefore understanding the variation associated with metabolizing enzymes is an important factor in determining an individual's susceptibility to environmental chemicals (Faustman and Omenn, 1996
).
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., 1996). 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., 1996
). 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, 1994
); while other parameters, such as alveolar ventilation rate, vary coherently across species (Krishnan and Andersen, 1994
). Metabolic rate parameters do not scale accurately from species to species (Gillette, 1985
; Krishnan and Andersen, 1994
). 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., 1994
). Metabolic rate constants for MTBE were determined in vitro using rat and human liver microsomes (Poet and Borghoff, 1998
). 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 |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
|
Human-specific model parameters.
In the model equations, the species-specific physiological and anatomical parameters used were taken from Brown et al. (1997) (Table 1). 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., 1999
). 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., 1987
; Clewell et al., 1999
).
|
|
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, 1998). 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 3
, 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 3
, maximum and minimum metabolic values are shown to illustrate the variability for each of the 4 parameters.
|
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., 1996). 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:
![]() |
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., 1999; Cain et al., 1996
). 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 3
).
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., 1994; Evans et al., 1994
). These SC were calculated using the central difference method:
![]() |
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, 1998), along with the variability of the experimental data, measured MTBE blood levels (Amberg et al., 1999
; Cain et al., 1996
). 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, 1980
), such as measurements of MTBE metabolic parameters (Poet and Borghoff, 1998
) and measurements of MTBE blood levels following an MTBE inhalation exposure (Amberg et al., 1999
; Cain et al., 1996
). 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., 1999
; Cain et al., 1996
). 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., 1999; Cain et al., 1996
), 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:
![]() |
![]() |
![]() |
![]() |
RESULTS |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
|
|
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. 4A) and 40 (Fig. 4B
) ppm, pathway 1, the high-capacity, low-affinity pathway, had a larger contribution to the amount of MTBE metabolized. At 12 ppm (Fig. 4C
), 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. 4D
) and, as expected, the high-capacity, low-affinity pathway was more important at high exposure concentrations (Figs. 4A and 4B
). 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 210 ppm at 25 min intervals (U.S. EPA, 1996
). 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.
|
|
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 3) for Vmax CMTBE,1 and KMMTBE,1 (pathway 1) and Vmax CMTBE,2 and KMMTBE,2 (pathway 2) (Poet and Borghoff, 1998
) 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. 3
). 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. 6A), 4 (Fig. 6B
), and 1.7 (Fig. 6C
) ppm MTBE (Amberg et al., 1999
; Cain et al., 1996
). 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. 6
).
|
![]() |
DISCUSSION |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
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, 2000). 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., 1996) 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., 1996
). When predicting the 1.7-ppm human data, this original model (Borghoff et al., 1996
) 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, 1985
; Krishnan and Andersen, 1994
).
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., 1997; Poet and Borghoff, 1998
). 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, 1998
). In contrast, the second pathway is a high-affinity, low-capacity enzyme and correlates with CYP2E1 activity (Poet and Borghoff, 1998
). A similar study in human liver microsomes (Duescher and Elfarra, 1994
) 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., 1997
). 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. 3
). 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, 2000). 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, 1988
; Bogen and McKone, 1988
; Bogen and Hall, 1989
).
The variability found in the MTBE in vitro metabolic parameters (Poet and Borghoff, 1998) 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., 1997
) and CYP2E1 (Powell et al., 1998
) metabolic parameters is consistent with the variability determined in the Poet and Borghoff (1998) study using 10 human livers. These studies (Koenigs et al., 1997
; Powell et al., 1998
) 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, 1998
), 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., 1998), 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., 1995
; Krishnan and Andersen, 1994
; 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, 1987
; National Research Council, 1994
).
Several sources (Hong et al., 1997, 1999
) 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 |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
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:
![]() |
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
![]() |
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:
![]() |
![]() |
![]() |
Propagation of Error FormulasApproximate 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:
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
ACKNOWLEDGMENTS |
---|
![]() |
NOTES |
---|
2 To whom correspondence should be addressed. Fax: (919) 558-1300. E-mail: borghoff{at}ciit.org.
![]() |
REFERENCES |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Andersen, M. E., Clewell, H. J., III, Gargas, M. L., Smith, F. A., and Reitz, R. H. (1987). Physiologically based pharmacokinetics and the risk assessment process for methylene chloride. Toxicol. Appl. Pharmacol. 87, 185205.[ISI][Medline]
Belpoggi, F., Soffritti, M., and Maltoni, C. (1995). Methyl-tertiary-butyl ether (MTBE)a gasoline additive causes testicular and lymphohaematopoietic cancers in rats. Toxicol. Ind. Health. 11, 119149.[ISI][Medline]
Bird, M. G., Burleigh-Flayer, H. D., Chun, J. S., Douglas, J. F., Kneiss, J. J., and Andrews, L. S. (1997). Oncogenicity studies of inhaled methyl tertiary-butyl ether (MTBE) in CD-1 mice and F-344 rats. J. Appl. Toxicol. 17(1), S45S55.
Bogen, K. T. (1988). Pharmacokinetics for regulatory risk analysis: The case of trichloroethylene. Regul. Toxicol. Pharmacol. 8, 447466.[ISI][Medline]
Bogen, K. T., and McKone, T. E. (1988). Linking indoor air and pharmacokinetic models to assess tetrachloroethylene risk. Risk Anal. 8, 509520.[ISI][Medline]
Bogen, K. T., and Hall, L. C. (1989). Pharmacokinetics for regulatory risk analysis: The case of 1,1,1-trichloroethane (methyl chloroform). Regul. Toxicol. Pharmacol. 10, 2650.[ISI][Medline]
Bogen, K. T., and Spear, R. C. (1987). Integrating uncertainty and interindividual variability in environmental risk assessment. Risk Anal. 7, 427436.[ISI][Medline]
Borghoff, S. J., Murphy, J. E., and Medinsky, M. A. (1996). Development of a physiologically based pharmacokinetic model for methyl tertiary-butyl ether and tertiary-butanol in male Fischer-344 rats. Fundam. Appl. Toxicol. 30, 264275.[ISI][Medline]
Brady, J. F., Xiao, F., Ning, S. M., and Yang, C. S. (1990). Metabolism of methyl tertiary-butyl ether by rat hepatic microsomes. Arch. Toxicol. 64, 157160.[ISI][Medline]
Brown, R. P., Delp, M. D., Lindstedt, S. L., Rhomberg, L. R., and Beliles, R. P. (1997). Physiological parameter values for physiologically based pharmacokinetic models. Toxicol. Ind. Health 13, 407484.[ISI][Medline]
Cain, W. S., Leaderer, B. P., Ginsberg, G. L., Andrews, L., S., Cometto-Muniz, J. E., Gent, J. F., Buck, M., Berglund, L. G., Mohsenin, V., Monahan, E., and Kjaergaard, S. (1996). Acute exposure to low-level methyl tertiary-butyl ether (MTBE): Human reactions and pharmacokinetic response. Inhal. Toxicol. 8, 2148.[ISI]
Clewell, H. J., Gearhart, J. M., Gentry, P. R., Covington, T. R., VanLandingham, C. B., Crump, K. S., and Shipp, A. M. (1999). Evaluation of the uncertainty in an oral reference dose for methylmercury due to interindividual variability in pharmacokinetics. Risk Anal. 19(4), 547558.
Clewell, H. J., Lee, T., and Carpenter, R. L. (1994). Sensitivity of physiologically based pharmacokinetic models to variation in model parameters: Methylene chloride. Risk Anal. 14(4), 521531.
Constantini, M. G. (1993). Health effects of oxygenated fuels. Environ. Health Perspect. 101(6), 151160.
Duescher, R. J., and Elfarra, A. A. (1994). Human liver microsomes are efficient catalysts of 1,3-butadiene oxidation: evidence for major roles by cytochromes P450 2A6 and 2E1. Arch. Biochem. Biophys. 311(2), 342349.
Evans, M. V., Crank, W. D., Yang, H. M., and Simmons, J. E. (1994). Applications of sensitivity analysis to a physiologically based pharmacokinetic model for carbon tetrachloride in rats. Toxicol. Appl. Pharmacol. 128, 3644.[ISI][Medline]
Faustman, E. M., and Omenn, G. S. (1996). Risk assessment. In Casarett & Doull's Toxicology: The Basic Science of Poisons (C. D. Klaassen, Ed.), pp. 7588. McGraw-Hill, New York.
Gargas, M. L., Burgess, R. J., Voisard, D. E., Carson, G. H., and Andersen, M. E. (1989). Partition coefficients of low-molecular-weight volatile chemicals in various liquids and tissues. Toxicol. Appl. Pharmacol. 98, 8799.[ISI][Medline]
Gillette, J. R. (1985). Biological variation: The unsolvable problem in quantitative extrapolation from laboratory animals and other surrogate systems to human populations. In Banbury Report 19: Risk Quantitation and Regulatory Policy (D. G. Hoel, R. A. Merrill, and F. P. Perea, Eds.), pp. 199209. Cold Spring Harbor Laboratory Press, Cold Spring Harbor, NY.
Grassman, J. A., Kimmel, C. A., and Neumann, D. A. (1998). Accounting for variability in responsiveness in human health risk assessment. In Human Variability in Response to Chemical Exposures (D. A. Neumann and C. A. Kimmel, Eds.), pp. 126. CRC Press, Washington, DC.
HEI (1996). The Potential Health Effects of Oxygenates Added to Gasoline: A Review of the Current Literature (A Special Report of the Institute's Oxygenates Evaluation Committee). Health Effects Institute, Cambridge, MA.
Himmelstein, M. W., Acquavella, J. F., Recio, L., Medinsky, M. A., and Bond, J. A. (1997). Toxicology and epidemiology of 1,3-butadiene. Crit. Rev. Toxicol. 27(1), 1108.
Hong, J. -Y., Wang, Y. -Y., Bondoc, F. Y., Lee, M., Yang, C. S., Hu, W. -Y., and Pan, J. (1999). Metabolism of methyl tert-butyl ether and other gasoline ethers by human liver microsomes and heterologously expressed human cytochromes P450: Identification of CYP2A6 as a major catalyst. Toxicol. Appl. Pharmacol. 160, 4348.[ISI][Medline]
Hong, J. -Y., Yang, C. S., Lee, M., Wang, Y. -Y., Huang, W. -Q., Tan, Y., Patten, C. J., and Bondoc, F. Y. (1997). Role of cytochrome P450 in the metabolism of methyl tert-butyl ether in human livers. Arch. Toxicol. 71, 266269.[ISI][Medline]
Koenigs, L. L., Peter, R. M., Thompson, S. J., Rettie, A. E., and Trager, W. F. (1997). Mechanism-based inactivation of human liver cytochrome P450 2A6 by 8-methoxypsoralen. Drug Metab. Dispos. 25(12), 14071415.
Krewski, D., Wang, Y., Bartlett, S., and Krishnan, K. (1995). Uncertainty, variability, and sensitivity analyses in physiological pharmacokinetic models. J. Biopharm. Stat. 5(3), 245271.
Krishnan, K., and Andersen, M. E. (1994). Physiologically based pharmacokinetic modeling in toxicology. In Principles and Methods of Toxicology (A. W. Hayes, Ed.), pp. 149188. Raven Press, New York.
Licata, A. C. (2000). Physiologically based pharmacokinetic models for gasoline oxygenates: Implementing statistical and mathematical analyses. Ph.D. Dissertation, North Carolina State University, Raleigh, NC.
Medinsky, M. A., Leavens, T. L., Csanády, G. A., Gargas, M. L., and Bond, J. A. (1994). In vivo metabolism of butadiene by mice and rats: A comparison of physiological model predictions and experimental data. Carcinogenesis. 15, 13291340.[Abstract]
Mohr, S. N., Fiedler, N., Weisel, C., and Kelly-McNeil, K. (1994). Health effects of MTBE among New Jersey garage workers. Inhal. Toxicol. 6, 553562.[ISI]
Moolenaar, R. L., Heffin, B. J., Ashley, D. L., Middaugh, J. P., and Etzel, R. A. (1994). Methyl tertiary butyl ether in human blood after exposure to oxygenated fuel in Fairbanks, Alaska. Arch. Environ. Health. 49, 402409.[ISI][Medline]
National Research Council (1994). Science and Judgement in Risk Assessment. Taylor & Francis, Washington, DC.
Nihlén, A., Löf, A., and Johanson, G. (1995). Liquid/air partition coefficients of methyl and ethyl t-butyl ethers, t-amyl methyl ether, and t-butyl alcohol. J. Expo. Anal. Environ. Epidemiol. 5(4), 573582.
Nihlén, A., Wålinder, R., Löf, A., and Johanson, G. (1998). Experimental exposure to methyl tertiary-butyl ether: II. Acute effects in humans. Toxicol. Appl. Pharmacol. 148, 281287.[ISI][Medline]
Pearce, R. E., McIntyre, C. J., Madan, A., Sanzgiri, U., Draper, A. J., Bullock, P. L., Cook, D. C., Burton, L. A., Latham, J., Nevins, C., Parkinson, A. (1996). Effects of freezing, thawing, and storing human liver microsomes on cytochrome P450 activity. Arch. Biochem. Biophys. 331(2), 145169.
Pelkonen, O., and Raunio, H. (1995). Individual expression of carcinogen-metabolizing enzymes: Cytochrome P4502A. J. Occup. Environ. Med. 37(1), 1924.
Poet, T. S., and Borghoff, S. J. (1998). Metabolism of methyl t-butyl ether in human liver microsomes. Toxicol. Sci. 42, 1S [Abstract No. 464].[Abstract]
Powell, H., Kitteringham, N. R., Pirmohamed, M., Smith, D. A., and Park, B. K. (1998). Expression of cytochrome P4502E1 in human liver: Assessment by mRNA, genotype and phenotype. Pharmacogenetics 8, 411421.[ISI][Medline]
Prah, J. D., Goldstein, G. M., Devlin, R., Otto, D., Ashley, D., House, D., Cohen, K. L., and Gerrity, T. (1994). Sensory, symptomatic, inflammatory, and ocular responses to and the metabolism of methyl tertiary butyl ether in a controlled human exposure experiment. Inhal. Toxicol. 6, 521538.[ISI]
Ramsey, J. C., and Andersen, M. E. (1984). A physiologically based description of the inhalation pharmacokinetics of styrene monomer in rats and humans. Toxicol. Appl. Pharmacol. 73, 159175.[ISI][Medline]
Steel, R. G. D., and Torrie, J. H. (1980). Principles and Procedures of Statistics: A Biometrical Approach. McGraw-Hill, New York.
U.S. EPA (1996). Oxyfuels Information Needs, [U.S. EPA/600/R-96/069]. U.S. Environmental Protection Agency, Research Triangle Park, NC.
Vardeman, Stephen B. (1994). Statistics for Engineering Problem Solving. PWS Pub. Co., Boston.
Vose, David (1996). Quantitative Risk Analysis: A Guide to Monte Carlo Simulation Modelling. John Wiley & Sons, Ltd., Chichester, England.
White, M. C., Johnson, C. A., Ashley, D. L., Buchta, T. M., and Pelletier, D. J. (1995). Exposure to methyl tertiary-butyl ether from oxygenated gasoline in Stamford, Connecticut. Arch. Environ. Health. 50, 183189.[ISI][Medline]