Nonlinearity in cancer dose-response relationships can result from saturation of a metabolic pathway. When an activation pathway is saturated, the dose response relationship can plateau at a level less than 100% lifetime risk, as in the frequently noted (1, 8, 89) case of vinyl chloride (88). When a detoxification or de-activation pathway saturates, the classic hockey stick dose-response curve can result. Data permitting, these effects can be formally taken into account through physiologically based pharmacokinetic (PBPK) modeling. The aim of the PBPK model in cancer risk prediction is to obtain a better estimate of effective dose than the administered dose, using model parameters measured in or estimated from experiments subsidiary to the bioassay. A cancer dose-response relationship for the bioassay or occupational dataset can then be expressed in terms of effective dose. If sufficient information and understanding permits the development of a PBPK model for the exposure circumstance and individuals for which risk is to be predicted, exposure can be related to effective dose. A third relationship can then be developed—risk as a function of exposure. This relationship is theoretically more reliable than that obtained through analyses based solely on administered dose, and for this reason, PBPK models have been used in cross-species, route, and dose extrapolations. However, because of incomplete understanding of critical factors (e.g., identity of the active metabolite or activation pathway) and appropriate model structure, or uncertain parameter estimates, the reliability of predictions has been questioned for a variety of PBPK applications (36, 90-92).

The PBPK models represent the body as compartments, related to one another in series or in parallel. Figure 6 depicts the PBPK model that has been used for various organic solvents (e.g., perchloroethylene [93-95], styrene [96]). The model in this case is composed of compartments for fat tissue, richly perfused tissue, poorly perfused tissue, a (volumeless) gas/blood exchange unit, and a liver metabolizing group. Tissues in which the chemical concentration changes at roughly the same rate are often grouped together (1, 94), with some tissues tracked separately because of degree of metabolism (e.g., liver) or bioaccumulation. Compartments are typically characterized by a partition coefficient describing the affinity of a chemical for two different media (such as blood/fat or blood/air), tissue volume, blood flow, and, if applicable, metabolic parameters (Fig. 7).

Mathematically, a series of differential equations describe the change in tissue concentration over time, due to transport to tissue by blood flow, uptake by and elimination from tissue according to partition coefficients, and metabolism within the tissue. Use of PBPK modeling in cancer risk prediction requires the identification of the activation pathway associated with carcinogenesis and of a kinetic model (for example, Michaelis-Menten). Data needed to populate the model include compartment partition coefficients, blood flows, tissue volumes, and metabolic parameters.

Physiologically based pharmacokinetics models have the advantage over classical pharmacokinetic models of being interpretable in biological terms. However, experience has shown that extrapolation with these models (across dose levels, routes, or species) involves considerable uncertainty, with the appropriate model structure and activation pathway frequently unknown despite considerable study and critical parameters uncharacterized. An illustration of these points is provided by early models of perchloroethylene (93-95). These models assumed that activation occurred through cytochrome P450 oxidation, confined to the liver, with the active metabolite unstable and not transported far; yet leukemia and kidney cancer are observed experimentally in the rat and there is suggestive evidence for non-liver target sites in humans (97). Although it had been suspected earlier (95), glutathione conjugation is now recognized as an important metabolic pathway, with the formation of S-(trichlorovinyl)glutathione, which is cleaved to S-(trichlorovinyl)-L-cysteine, and again cleaved in the kidney to dichlorothioketene, which can react with cellular macromolecules (98). S-(trichlorovinyl)-L-cysteine may also react with water to form dichloroacetic acid, an animal liver carcinogen. With respect to model structure, for 10 different PBPK models of perchloroethyl-ene, discrepancies were noted between data and predicted levels associated with the P450 pathway (91). It was proposed that more sophisticated models accounting for heterogeneity of the fat compartment or intertissue diffusion between fat

Fig. 7. Schematic representation of a physiologically based pharmacokinetic model. For each compartment i, change in chemical concentration is described mathematically by mass balance differential equations defined by blood flow rates, partition coefficient (Pi), volume (Vi), and if metabolism occurs in the compartment, metabolic coefficients (e.g., Vmax and Km).

Fig. 7. Schematic representation of a physiologically based pharmacokinetic model. For each compartment i, change in chemical concentration is described mathematically by mass balance differential equations defined by blood flow rates, partition coefficient (Pi), volume (Vi), and if metabolism occurs in the compartment, metabolic coefficients (e.g., Vmax and Km).

and muscle groups would result in better predictions (91). Various researchers have noted the sensitivity of the PBPK models for perchloroethylene to selection of metabolic parameters (90, 93, 99) and partition coefficients (90, 93).

Partition coefficients for PBPK models are frequently determined in vitro by using tissue homogenates and are often assumed to be the same in different species. However, they may not reflect partitioning into the organ in vivo, and significant species differences have been observed for some tissues (100, 101). Metabolic parameters, Km and Vmax, often cannot be estimated independently, introducing further error. Formal statistical procedures are usually not used to derive parameters from in vivo studies, and in vitro estimates can be inaccurate. Finally, the models typically are not independently validated. Some of these limitations have been addressed experimentally and through uncertainty analyses within a formal statistical (92-94, 102) or qualitative (91, 95) framework. The general problem of model validation can be addressed in part through the introduction of biomarker components in occupational studies. The application of a Bayesian framework to PBPK analyses for the integration of different types of data with varying levels of uncertainty is a promising technique under development (92, 94). The large range of estimates for perchloroethylene metabolized at relatively low levels of exposure (at 1 ppm, estimates of 2% to 86% metabolism [95]) was partially resolved through application of Bayesian techniques to a controlled study of healthy male volunteers exposed to relatively high levels for 4 hours and subsequently followed up. A characterization of high-dose kinetics in this group was provided by data collected near the time of exposure, whereas low-dose kinetics were characterized over subsequent days. The analyses described the varying degree of metabolism among the individual volunteers and the uncertainty in those estimates.

Although the accuracy of PBPK models for low dose and across species predictions can often be questioned, these models play a valuable role in hypothesis testing and exploratory analyses.

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