Physiologically Based Pharmacokinetic Modeling of Inhalation Exposure of Humans to Dichloromethane during Moderate to Heavy Exercise

Fredrik Jonsson*,1, Frédéric Bois{dagger} and Gunnar Johanson*,{ddagger}

* Toxicology and Risk Assessment, National Institute for Working Life, S-112 79 Stockholm, Sweden; {dagger} Institut National de l'Environnement Industriel et des Risques, Verneuil en Halatte, France; and {ddagger} Department of Medical Sciences, Occupational and Environmental Medicine, Uppsala University Hospital, Sweden

Received June 20, 2000; accepted October 23, 2000


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Dichloromethane (methylene chloride, DCM) is metabolized via two pathways in humans: mixed-function oxidases (MFO) and glutathione-S-transferase (GST). Most likely, the carcinogenicity for DCM is related to metabolic activation of DCM via the GST pathway. However, as the two pathways are competing, the metabolic capacity for the MFO pathway in vivo is also of interest in risk assessment for DCM. Past estimates of MFO metabolism are based on the in vitro activity of tissue samples. The aim of the present study was to develop a population model for DCM in order to gain more knowledge on the variability of DCM inhalation toxicokinetics in humans, with main emphasis on the MFO metabolic pathway. This was done by merging published in vitro data on DCM metabolism and partitioning with inhalation toxicokinetic data (Åstrand et al., 1975, Scand. J. Work.Environ. Health 1, 78–94) from five human volunteers, using the MCMC technique within a population PBPK model. Our results indicate that the metabolic capacity for the MFO pathway in humans is slightly larger than previously estimated from four human liver samples. Furthermore, the interindividual variability of the MFO pathway in vivo is smaller among our five subjects than indicated by the in vitro samples. We also derive a Bayesian estimate of the population distribution of the MFO metabolism (median maximum metabolic rate 28, 95% confidence interval 12–66 µmol/min) that is a compromise between the information from the in vitro data and the toxicokinetic information present in the experimental data.

Key Words: dichloromethane; inhalation; pharmacokinetics; physiologically based modeling; Markov chain Monte Carlo simulations; population kinetics.


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Dichloromethane (methylene chloride, DCM) has been studied extensively over the years, due to its widespread use, coupled with carcinogenic properties in rats (Burek et al., 1984Go; IPCS, 1996Go). DCM metabolism takes place via two competing pathways: metabolism by mixed-function oxidases (MFO) (Ahmed and Anders, 1976Go), and glutathione-S-transferase T1 (GSTT1) (Kubic and Anders, 1975Go). The GSTT1 pathway is assumed to be the one associated with an increase in cancer risk (Andersen et al., 1987Go). However, at low exposure levels, the MFO pathway is dominating (Ottenwälder et al., 1989Go). Thus, population variability in DCM metabolism via both pathways is of considerable interest. At low exposure levels, the interindividual variability in total DCM metabolism mainly reflects variability in the MFO pathway. As the pathways are competing, variability in the MFO pathway would affect target dose estimates based on the amount metabolized via the GSTT1 pathway.

Andersen and coworkers developed a PBPK model for DCM in humans in order to estimate the target dose, defined as the amount metabolized by the GST pathway (Andersen et al., 1987Go). In that model, the toxicokinetics in humans was predicted from the in vitro metabolism and the in vivo toxicokinetics of DCM in three other species. The model was then validated against kinetic data from human subjects exposed to DCM at 100 and 350 ppm. The kinetic data were pooled, and the means of the DCM concentrations in the six subjects were used in the validation. Reitz and coworkers refined the model by introducing enzymatic activities determined in vitro using human and animal subcellular fractions (Reitz et al., 1988Go). The individual metabolic capacities for DCM in humans were estimated using four human liver samples (Reitz et al., 1989Go). The Andersen et al. model (1987), as subsequently modified by Reitz et al., will be referred to in this paper as the Andersen/Reitz model. Later on, variability was introduced in the metabolic parameters in the Andersen/Reitz model in order to improve the reliability of the target dose estimates (Dankovic and Bailer, 1994Go), but without validation against human data. The recent risk assessment for DCM by the U.S. Occupational Safety and Health Administration (OSHA, 1997Go) included a new PBPK analysis published by Andersen et al. (1991). However, the data used were again the aggregates for six subjects and did not allow for an assessment of interindividual variability. To our knowledge, there are no estimates of human DCM metabolism based on individual in vivo data, and thus, no reliable estimates of the population variability of DCM metabolism. This is unfortunate, as knowledge of population variability is essential in risk assessment.

Population variability in physiological pharmacokinetic parameters can be estimated from experimentally derived individual concentration–time profiles for human subjects. By combining the information in the experimental toxicokinetic data with the information from the in vitro estimates of DCM metabolism, new knowledge on population variability in target dose can be gained. One way of doing this is by Bayesian statistics. The Bayesian approach yields statistical distributions (so-called posterior distributions) of parameter values rather than single point estimates. These posterior distributions are consistent with both the experimental data and the prior assumptions (specified as so-called prior distributions for the parameters). The distributions can be approximated by random draws using so-called Markov chain Monte Carlo (MCMC) simulations (Wakefield and Smith, 1994Go). MCMC simulations have previously been linked successfully to PBPK models embedded in population frameworks (Bois et al., 1996aGo,bGo). The parameter vectors thus generated can then be used for further simulations to compute posterior distributions of quantities of interest, including target doses. The risk assessment for DCM by OSHA (1997) used techniques similar to those presented here. Although MCMC is a Monte Carlo–based technique, it should not be confused with the Monte Carlo techniques commonly employed for predictions in conjunction with PBPK models (Thomas et al., 1996Go). Regular Monte Carlo techniques can be used to estimate variability in model output (such as in target dose), but not to estimate model parameters. In contrast, MCMC is a parameter estimation technique.

Åstrand et al. (1975) exposed male volunteers to DCM vapors at rest and various levels of exercise on a bicycle ergometer. Extensive data collection was made. PBPK modeling has previously been performed on the Åstrand data set (Johanson and Näslund, 1988Go). This modeling successfully described the changes in DCM uptake and perfusion with increasing workload. However, that model did not account for interindividual variability in parameters other than intrinsic liver clearance and did not use the extensive data on DCM levels in exhaled air postexposure.

The aim of the present study was to develop a population model (Sheiner, 1984Go) for DCM in order to gain more knowledge on the variability in DCM inhalation toxicokinetics in humans, with main emphasis on the MFO metabolic pathway. This was done by merging published in vitro data on DCM metabolism and partitioning with the Åstrand toxicokinetic data (Åstrand et al., 1975Go) from five human volunteers using the MCMC technique within a population PBPK model.


    MATERIALS AND METHODS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Experimental data.
Detailed information on the experimental part is reported elsewhere (Åstrand et al., 1975Go). In brief, a total of 14 male subjects were exposed to different levels of DCM at various levels of exercise. In five of the experiments, subjects were exposed to relatively high DCM levels at a high workload (Series III in Åstrand et al., 1975). The subjects in this study group showed the highest uptake of DCM. Thus, these five experiments were deemed most suitable for assessing the maximum metabolic rate. The five subjects in Series III were all exposed to DCM at a level of 500 ppm at rest (30 min), followed by a 30-min exposure-free interval. Subsequently, subjects were exposed at the same level during exercise (30 + 30 + 30 min) at consecutive workloads of 50, 100, and 150 W, respectively. Frequent sampling of arterial blood and end-exhaled air was performed during and up to 2 h after the exposure. For end-exhaled air, sampling continued until 20 h after the exposure. In addition to the kinetic measurements, pulmonary and alveolar ventilation, oxygen uptake during exposure, initial carboxyhemoglobin (HbCO) concentration, body weight, height, and age of the subjects were recorded. The individual values for these physiological quantities were not given in the original publication of this study, but are presented in Table 1Go.


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TABLE 1 Measured Values for Some Physiological Quantities for Subjects from Åstrand et al. (1975) at Various Levels of Workload
 
All blood samples were analyzed for HbCO, as carbon monoxide (CO) is a major metabolite of DCM via the MFO pathway. However, the concentrations of HbCO did not reach a maximum during the time of monitoring in any of the subjects. Thus, the data set was considered insufficient for estimating the individual formation and elimination rates of HbCO, and the HbCO levels were not used in the analysis.

PBPK model.
The basic PBPK model used in this analysis was first published by Andersen et al. (1987) and subsequently modified by Reitz et al. (1988). A compartment for working muscle was added to the Andersen/Reitz model. This was done in order to reflect the increased perfusion of leg muscle during bicycle exercise (Johanson and Näslund, 1988Go). Thus, the present model incorporates compartments for resting muscle, working muscle, well-perfused tissue, fat, lung, and liver. The revised model is illustrated in Figure 1Go. Metabolism by the MFO pathway is believed to be saturable and is described by a maximum rate of metabolism (Vmax) and by the concentration at which the rate of metabolism is half-maximal (km). This pathway produces a rise in blood HbCO levels. The GSTT1 pathway is assumed to be nonsaturable in the present concentration range and is described in the model by a first-order rate constant (Kf). Symbols are also explained in the Appendix.



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FIG. 1. Physiologically based pharmacokinetic model for dichloromethane in exhaled air and arterial blood. Symbols are explained in Appendix.

 
Physiological parameters.
The lean body mass was calculated from measured data, as described in Table 2Go (Watson et al., 1980Go; Widdowson, 1965Go). To account for known physiological dependencies between some pharmacokinetic parameters such as between lean body weight and organ volumes, dependent parameters were linked to body weight, height, and workload via scaling functions (Cowles et al., 1971Go; Droz et al., 1989Go; Williams and Leggett, 1989Go). The scaling functions are described in Table 2Go. The sum of all volume fractions add up to lean body weight minus skeleton, 13% of lean body weight. The muscle compartment includes skin. The well-perfused compartment is calculated as the sum of brain, kidneys, and other tissues (Droz, 1992Go). A density of 1.1 was assumed in all tissues (Behnke et al., 1953Go), except for fat, for which density was assumed to be 0.92 (Fidanza et al., 1953Go).


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TABLE 2 Relationships between Physiological Variables in the Model for Dichloromethane in Humans
 
The change in blood flow to various tissues with physical workload was considered independent of body size, and calculated with the assumption that the change is proportional to the excess oxygen uptake above rest (Cotes, 1975Go). The equations used to describe the effect of physical workload (Droz et al., 1989Go) were derived according to suggested reference values (Åstrand, 1983Go) and are described in detail in Table 2Go.

Statistical computations: the Bayesian approach.
One fundament of Bayesian inference, as opposed to purely likelihood-based inference, is to incorporate the uncertainty about assumptions into the statistical analysis. That means, in this case, quantifying the prior belief about the model parameters before taking the observed data into account. In a Bayesian analysis, two forms of information are combined logically: prior knowledge about parameter values (often drawn from the scientific literature), which may be known with various degrees of confidence, and data from experimental studies. In our case, the analysis is made within the context of a PBPK model. Neither source of information alone is sufficient to fully parameterize the PBPK model. If the prior knowledge of the parameters was sufficient, the experimental data from Åstrand et al. (1975) would not have been needed at all in the present study. However, the available experimental data alone are not sufficient to estimate all the parameters of the model independently, which is why they cannot be estimated simultaneously using the maximum likelihood-based techniques often employed in empirical pharmacokinetic modeling. Fitting only two or three parameters, while using reference literature values for the others, would produce estimates that would be conditional on the assumed values of the fixed parameters. As the values of the physiological and physicochemical parameters in vivo are not known with precision, such a procedure may result in erroneous estimates of the fitted parameters. In addition, the variability in the fixed parameters is ignored, whereas the variability in the fitted ones tends to be overestimated. An additional disadvantage is that any correlations between parameters tend to be ignored or underestimated (Woodruff and Bois, 1993Go).

The Bayesian approach produces posterior estimates (in the form of distributions) of all the parameters of the PBPK model, along with information on the full joint covariance structure. The posterior distributions of the parameter values (posterior estimates) are consistent with both the experimental data and the prior information. It should be noted that if the experimental data lack any information on a certain parameter, the posterior estimate is equal to the prior estimate. Additionally, if the prior distributions are assigned to be uniform in shape (i.e., complete ignorance about plausible values), the posterior will be proportional to the likelihood of the data, and asymptotically equivalent to the standard likelihood techniques referred to above. When compared with standard analytical tools for population modeling, the Bayesian population method has been shown to be more reliable from a statistical point of view (Bennett and Wakefield, 1996Go).

The complicated high-dimensional joint posterior distribution was summarized by random draws using Metropolis-Hastings Monte Carlo sampling (Smith, 1991Go). Random draws from the prior were made in order to obtain initial parameter vectors. The individual parameter vectors were used to simultaneously simulate the experimental data for each individual, and the value of the likelihood function was calculated (see following section). The sampled values were either kept or rejected on the basis of the current value of the posterior distribution, computed by multiplying the prior by the value of the likelihood function. This procedure was iterated several thousand times, with the posterior parameter vector of one step used as prior for the next, until all parameters had reached equilibrium.

Five independent Markov chains, using different seeds for the random number generator, were run to approximate equilibrium. Convergence was monitored using the method of Gelman and Rubin (Gelman and Rubin, 1992Go), with an value lower than 1.1 as a criterion for convergence. At perfect convergence, all values should be equal to 1. An of 1.3, for example, indicates that the use of longer chains would have reduced the variance estimates by 30%. If convergence tests resulted in values greater than 1.1 during model development, additional Markov iterations were performed until acceptable convergence was obtained. Posterior distributions were obtained by running the MCMC simulations further. Each independent equilibrated Markov chain was run for 10,000 iterations while printing one iteration in ten. The MCSim software (Bois and Maszle, 1997Go) was used throughout the study.

A priori parameter distributions and data likelihood.
Alveolar ventilation was measured in the original study, and the measured values (Table 1Go) were used. Body weight and height were also measured in the original study (Table 1Go), and thus the compartment volumes could be estimated with reasonable accuracy from the measured quantities via scaling functions (Table 2Go). Interindividual variability in all tissue volumes and some blood flows was assumed to be accounted for adequately by the scaling functions (Table 2Go), based on the estimated affinity of DCM for these tissue groups. Prior distributions were assigned to all other parameters, thereby quantifying the uncertainty of these (Table 3Go).


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TABLE 3 Prior Estimates of the Scaling Coefficients for the Dichloromethane Model Parameters in Humans
 
Each component of the parameter set being estimated was assumed to be distributed lognormally in the population. During model development, normal population distribution of all parameters was also tested. Although providing very good predictions of the experimental data, the use of normal distributions produced individual posterior estimates that approached zero for the parameter governing the change in perfusion with exercise. These values were deemed very unlikely, considering the physiological literature. Thus, lognormal population distributions were used throughout the study.

The prior uncertainties of the parameters were summarized numerically by assigning a priori truncated lognormal distributions (from now on called prior estimates) to the population parameters on the basis of the literature (Bülow and Madsen, 1978Go; Gargas et al., 1989Go; Williams and Leggett, 1989Go; Åstrand, 1983Go). The choices of these values and bounds for truncation are given in Table 3Go. In the prior estimates, each parameter is characterized by its expected population mean, an uncertainty around the population mean, as well as a population standard deviation (SD), expressing the expected variability in the population.

For all tissue:air partition coefficients except blood:air, prior means were set at the value for rat (Gargas et al., 1989Go). The prior uncertainties for these coefficients were set to 1.1 on the log scale, corresponding to an approximate coefficient of variation of 10%.

Population SDs were set at higher values for the fat blood flow than for other parameters, based on published observations on variability in fat tissue perfusion (Bülow and Madsen, 1976Go; Linde et al., 1989Go; Samra et al., 1995Go).

Truncation bounds were generally set at wide intervals in order to give the model a considerable amount of freedom to explore the parameter space.

We had no information on the values of the parameters at the individual level. Thus, starting values for individual parameters were generated by sampling from the priors for the population parameters. The individual parameters were updated on the basis of their conditional distribution with respect to the population parameters and the data likelihood. The data likelihood was calculated assuming that the observations in both blood and alveolar air were associated with lognormally distributed residual errors ({epsilon}) due to intraindividual variability and measurement error. As the two types of observations have different experimental protocols, the vector {epsilon} has two elements, reflecting differing measurement errors in blood and alveolar air, respectively.


    RESULTS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
The Markov chains reached approximate convergence after 25,000 iterations. Each chain was then run for 10,000 more iterations. Every 10th iteration was printed to the output file, and thus a total of 5,000 posterior parameter vectors were produced from the five chains. Each chain took about 11 h to run on a 450-MHz personal computer running under Linux.

Figure 2Go shows the predicted versus observed values of the dependent variable for all individuals. Predictions were made using one randomly chosen parameter vector among the 5,000 vectors recorded. As the chains had reached approximate equilibrium, the fit illustrated in Figure 2Go can therefore to be considered as representative of the set.



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FIG. 2. Predicted versus observed values for all data points used in the analysis. The line of unity is also indicated. Each symbol represents one subject. Predictions were made using the last iteration of the last Markov chain in the analysis.

 
Figure 3Go presents the simulated time profiles for each subject, as predicted by one randomly chosen parameter vector out of each chain. This figure also provides a visual indication of the difference between predictions produced by parameter vectors generated during different runs. The curves are all rather close to the observed data, indicating that model predictions made using our individual posterior parameter estimates can predict the observed data with considerable precision and with little bias.



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FIG. 3. Observed (dots) and model-predicted (lines) concentration–time profiles for dichloromethane in end-exhaled air and arterial blood from all five individuals Predictions were made using parameters from the last iteration of each run.

 
The posterior estimates of the population parameters are summarized in Table 4Go. This table was generated by pooling the 5,000 parameter vectors, generated as described above. For most parameters, the posterior estimates of the population means are very close to the corresponding prior estimates. The most notable deviations are observed for the fat:air partition coefficient, which decreased from 120 to 65, and for the increase in perfusion of adipose tissue during physical exercise. The estimated increase in fat perfusion shifted from 0.03 to 0.014 l • min–1 l fat–1 • l O2 • min–1. The latter parameter is associated with a large standard error. The residuals ({epsilon}) for observations in alveolar air and blood are small, corresponding to approximate coefficients of variation (CVs) of 16 and 25%, respectively.


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TABLE 4 Summary of the Posterior Estimates of the Scaling Coefficients of the Parameters for the Model for Dichloromethane in Humans
 
Interindividual variability is quantified by the population SDs, also given in Table 4Go. A large posterior population SD of the scaling coefficient for maximum metabolic rate of the MFO pathway (VmaxC) is estimated.

The posterior estimates of the individual parameters are summarized in Table 5Go. The individual estimates of fat perfusion are notably different from the corresponding prior estimates, although all values are physiologically plausible. There is also considerable interindividual variability among the estimates of VmaxC (range of posterior estimates 2.0–4.0 µmol/min).


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TABLE 5 Summary of the Posterior Estimates of the Individual Parameters in the Model for Dichloromethane in Humans
 
The present model accounts for measurement error and intersubject variability but only to a limited extent for intrasubject variability. The parameter values should therefore be considered approximate averages over time for each individual.


    DISCUSSION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
A population model was applied to a previously published PBPK model for methylene chloride in humans. The structural model was modified in order to accommodate changes in perfusion with exercise. The model provides good descriptions of the concentrations in arterial blood and exhaled air (Figs. 2 and 3GoGo), while maintaining biologically plausible parameter values (Tables 4 and 5GoGo). Furthermore, new knowledge on the interindividual variability in human metabolic capacity for DCM in vivo was gathered. We can derive a Bayesian estimate of the population distribution of Vmax that merges the information from the prior and the information present in the experimental data. The population SD for VmaxC corresponds to Vmax values for 70-kg men of 12–66 (95% confidence interval), with a mean of 28 µmol/min (also presented in Fig. 4Go). This interval was calculated using the posterior estimate of the geometric population mean, the lognormal geometric population SD from Table 4Go and the scaling function from Table 2Go. Thus, the interval is conditional on the posterior estimate of the population mean and does not take the uncertainty around the mean into account.



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FIG. 4. Comparison of individual and population estimates of the in vivo maximum metabolic rate (Vmax) of DCM for the MFO pathway. The estimates by Dankovic and Bailer (1994) were obtained by scaling in vitro data reported by Reitz et al. (1988). The box plot shows the 2.5th, 25th, 50th, 75th, and 97.5th percentiles of our estimated population distribution.

 
In the present study, we estimate individual values of Vmax for the MFO pathway in a 70-kg man to 39–78 µmol/min (calculated using Tables 2 and 5GoGo). The highest posterior Vmax was estimated for subject A (Table 5Go). For comparison, when interindividual variability in metabolism was introduced in the Andersen/Reitz model by Dankovic and Bailer (1994), the Vmax values used were 6.7–47 µmol/min. The present individual and population estimates of Vmax for a 70-kg man are juxtaposed with the values used by Dankovic and Bailer in Figure 4Go. Our estimate for subject A is outside the Vmax range used by Dankovic and Bailer, but is not extreme. Dankovic and Bailer based their estimate of Vmax in vivo on an extrapolation of the activity in four in vitro tissue samples (Reitz et al., 1989Go). For subjects B through E, the posterior estimates of Vmax are similar to the in vitro–derived prior estimates (Fig. 4Go). As there is no known polymorphism for the cytochrome P 450 2E1 enzyme, the suggested individual Vmax values in the present paper seem reasonable. However, the enzyme is known to be inducible. Subject A, for whom the posterior estimate of Vmax was higher than for other subjects, showed a significantly higher preexposure HbCO concentration than other subjects (Table 1Go). It can be assumed that subject A was a smoker, and therefore had an increased metabolic capacity of the MFO pathway.

As our estimated individual values for Vmax are based on PBPK modeling of individual concentration–time profiles in humans, we consider the estimates quite reliable. Our individual Vmax values indicate that the metabolic capacity for the MFO pathway in vivo is higher, and associated with lower degree of interindividual variability, than estimated previously from in vitro samples. However, there is still considerable uncertainty as to the representativeness of these five young, healthy, Swedish males to the general population. In contrast, the Bayesian estimate of population variability in Vmax illustrated in Figure 4Go is based on the toxicokinetic data, plus the in vitro metabolic data from four human livers of unknown gender, age, and ethnicity, and is thus more useful for extrapolations to the general population. An even more reliable estimate of population variability in Vmax would be obtained by studying a larger and more heterogeneous population. There may also be interindividual variabilities in Vmax (or other parameters) associated with covariates such as age, ethnicity, body build, sex, or smoker status. Thus, although differences in body build may be easily incorporated into the model, extrapolations to larger, more heterogenous populations should be done with caution.

The individual posterior estimates of GST metabolism are very close to the prior estimates (Table 5Go). This indicates, as expected, that the experimental data contain very little information about the parameter governing GST metabolism (see "Statistical calculations" in the Materials and Methods section). Thus, most of the retained DCM is apparently metabolized by the oxidative pathway, even at the high exposure levels in the data set of Åstrand et al. (1975). DCM metabolized by the GST pathway would result in the appearance of metabolites such as glutathione conjugates in blood and mercapturic acid in the urine. In order to estimate GST metabolism in vivo, we would need information on the levels of these metabolites. Unfortunately, these were not monitored by Åstrand and coworkers, and we cannot derive an estimate of GST metabolism in vivo in the present study.

The individual posterior estimates of the increase in fat perfusion with exercise predict a considerably smaller increase than the prior estimate. The prior estimate was based on experiments performed at prolonged exercise (Bülow and Madsen, 1976Go). Change in fat tissue perfusion during exercise is a slow process. When Bülow and Madsen measured fat tissue perfusion during a constant workload of 120 W, fat perfusion did not reach a constant level until approximately 2 h had passed. Estimating the effect of different levels of exercise on fat perfusion with any precision using the present data set seems unfeasible and would most likely demand prolonged exposures at each level of exercise. The lack of information in the data set is also reflected in large uncertainties of the posterior estimates of the parameters governing the increase in fat perfusion during exercise, both at the population and at the individual level (Tables 4 and 5GoGo).

All posterior estimates of the individual fat:air partition coefficients are lower than the prior estimate, which was based on an in vitro estimate for rat (Gargas et al., 1989Go). The shift might be an indication that the size of the fat compartment was predicted with insufficient accuracy by the algorithms being used (Table 2Go). In reality, the fat compartment would then be smaller than predicted by the algorithm. On the other hand, fat tissue is heterogeneously perfused. Individual ranges in the perfusion of perirenal and subcutaneous fat have been reported to be 0.1–8 and 0.3–2.3 ml/min/100 g fat, respectively (Bülow and Madsen, 1978Go). The fat compartment in our model might correspond to the well-perfused portions of fat tissue. The less well-perfused portions of fat tissue would receive only a minute amount of DCM, and the washout from the less well-perfused fat tissue would not be visible until later points in time for which we have no data.

The use of MCMC simulations and of a population hierarchical model in a Bayesian context allowed us to reach deeper conclusions about toxicokinetic data and modeling practice than before. In addition to disentangling variability (inter- or intraindividual, etc.) from uncertainty and providing improved uncertainty estimates for model predictions (Bois, 1999Go, 2000aGo,bGo), PBPK/MCMC coupling also helped us with model checking.

The present study provides a Bayesian estimate of the population distribution of metabolic capacity for the MFO pathway in humans. We also detect a need to incorporate the highly variable perfusion of various kinds of fat tissue when applying the PBPK model. Our approach illustrates the importance of implementing existing knowledge on variability in these parameters into the PBPK modeling process.


    APPENDIX
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Explanation of symbols

A1 Lung:liver ratio of rate of MFO metabolism

A2 Lung:liver ratio of rate of GST metabolism

BHt Body height (cm)

blo Venous blood

BV Lean body volume (l)

BWt Body weight (kg)

C Coefficient for scaling to physiological quantity

CV Coefficient of variation

DCM Dichloromethane

exh Exhaled

FFM Fat-free mass (kg)

GSTT1 Glutathione-S-transferase T1

h Hepatic

Kf First-order rate constant for GST metabolism (min–1)

km Michaelis constant for oxidative pathway (µmol/l)

m Muscle

MCMC Markov chain Monte Carlo

MFO Mixed-function oxidases

PBPK Physiologically based pharmacokinetic

PC Partition coefficient

pul Pulmonary

Q Flow (l/min)

SD Standard deviation

TBW Total body water (l)

wm Working muscle

tot Total

V Compartment volume (l)

Vmax Maximum rate of oxidative metabolism (µmol/min)

wp Well perfused

VPR Ventilation/perfusion ratio

{Delta}VO2 Excess oxygen uptake above rest (l/min)

{epsilon} Residual error encompassing intra-individual variability and measurement error


    ACKNOWLEDGMENTS
 
This study was financially supported by the Swedish Council for Work Life Research (Grant No. RALF 1997–1039). We are grateful to Ms. Elisabeth Gullstrand for supplying the raw data from the DCM experiments.


    NOTES
 
1 To whom correspondence should be addressed. Fax: +46 8 730 33 12. E-mail: fredrik.jonsson{at}niwl.se. Back


    REFERENCES
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
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