The role of physiologically based toxicokinetic models in biologically based risk assessment.

Biologically-based cancer risk assessment relies on mathematical models that represent the toxicokinetics and toxicodynamics of the xenobiotic in the body. Physiologically-based toxicokinetic (PBTK) models are used as a tool for predicting the target tissue dose of a xenobiotic from different routes of exposure, extrapolating from high doses to low doses and extrapolating between species. This paper reviews the role of PBTK models and their limitations in biologically-based risk assessment.

Mathematical modeling of skin papilloma data in SENCAR mice.

Published data from SENCAR mice were analyzed to elucidate mechanisms underlying the formation of chemically induced skin papillomas. The experimental data followed a two-step protocol using 7,12-dimethylbenz[a]anthracene (DMBA) for initiation and 12-O-tetradecanoylphorbol-13-acetate (TPA) for promotion. The two-mutation model of Ellwein and Cohen was used to simulate the data. In this model, probabilities of stem cell birth and death along with initiation and increased cell division are allowed to vary in time. We incorporated a pulse dose with exponential decay to represent the effect of DMBA on the probability of initiation over time, and a summation of pulse doses to represent the repeated topical applications of TPA and its effect on cell division and cell death. We fitted the model to the papilloma and carcinoma data sequentially, and indirectly determined the dependence of model parameters on the administered dose of DMBA and TPA. The occurrence of chemically induced epidermal hyperplasia is a fundamental assumption in our fits of the papilloma data. We found a delay in the onset of normal and initiated cell death relative to the enhancement of cell division rates. In addition, the model parameters display a nonlinear dependence on the dose of DMBA or TPA administered.

Interspecies extrapolation of physiological pharmacokinetic parameter distributions.

Three methods (multiplicative, additive, and allometric) were developed to extrapolate physiological model parameter distributions across species, specifically from rats to humans. In the multiplicative approach, the rat model parameters are multiplied by the ratio of the mean values between humans and rats. Additive scaling of the distributions is defined by adding the difference between the average human value and the average rat value to each rat value. Finally, allometric scaling relies on established extrapolation relationships using power functions of body weight. A physiologically-based pharmacokinetic model was fitted independently to rat and human benzene disposition data. Human model parameters obtained by extrapolation and by fitting were used to predict the total bone marrow exposure to benzene and the quantity of metabolites produced in bone marrow. We found that extrapolations poorly predict the human data relative to the human model. In addition, the prediction performance depends largely on the quantity of interest. The extrapolated models underpredict bone marrow exposure to benzene relative to the human model. Yet, predictions of the quantity of metabolite produced in bone marrow are closer to the human model predictions. These results indicate that the multiplicative and allometric techniques were able to extrapolate the model parameter distributions, but also that rats do not provide a good kinetic model of benzene disposition in humans.

Benzene toxicokinetics in humans: exposure of bone marrow to metabolites.

A three compartment physiologically based toxicokinetic model was fitted to human data on benzene disposition. Two separate groups of model parameter derivations were obtained, depending on which data sets were being fitted. The model was then used to simulate five environmental or occupational exposures. Predicted values of the total bone marrow exposure to benzene and cumulative quantity of metabolites produced by the bone marrow were generated for each scenario. The relation between cumulative quantity of metabolites produced by the bone marrow and continuous benzene exposure was also investigated in detail for simulated inhalation exposure concentrations ranging from 0.0039 ppm to 150 ppm. At the level of environmental exposures, no dose rate effect was found for either model. The occupational exposures led to only slight dose rate effects. A 32 ppm exposure for 15 minutes predicted consistently higher values than a 1 ppm exposure for eight hours for the total exposure of bone marrow to benzene and the cumulative quantity of metabolites produced by the bone marrow. The general relation between the cumulative quantity of metabolites produced by the bone marrow and the inhalation concentration of benzene is not linear. An inflection point exists in some cases leading to a slightly S shaped curve. At environmental levels (0.0039-10 ppm) the curve bends upward, and it saturates at high experimental exposures (greater than 100 ppm).