Physiologically Based Pharmacokinetic Models for the Systemic Transport of Trichloroethylene

Abstract

Three physiologically based pharmacokinetic (PBPK) models for thesystemic transport of inhaled trichloroethylene (TCE) are presented.The major focus ofthese modeling efforts is the disposition of TCE in the adiposetissue, where TCE is known to accumulate. Adipose tissue is highly heterogeneous, with wide variations in fat cell size, lipid composition, blood flow rates and cellpermeability. Since TCE is highly lipophilic, the uneven distributionof lipids in the adipose tissue may lead to an uneven distribution of TCEwithin the fat. These physiological characteristics suggest that thedynamics of TCE in the adipose tissue may depend on spatial variations within the tissue itself.

The first PBPK model for inhaled TCE presented here is a system ofordinary differential equations which includes the standardperfusion-limited compartmental model for each of the adipose, brain,kidney, liver, muscle and remaining tissue compartments.Model simulations predict relatively rapiddecreases in TCE fat concentrations following exposure, which may notreflect the accumulation and relative persistence of TCE inside the fattissue. The second PBPK model is identical to the first except forthe adipose tissue compartment, which is modeled as a diffusion-limited compartment.Although this model yields various concentration profiles for TCE inthe adipose tissue depending on the value of the permeabilitycoefficient, this model may not be physically appropriate for TCE,which is highly lipophilic and has a low molecular weight. Moreover,neither of these two PBPK models is able to capture spatialvariation of TCE concentrations in adipose tissue as suggested bythe physiology.

The third model we present is a hybrid PBPK model with adispersion-type model for the transport of TCE in the adipose tissue. Thedispersion model is designed to account for the heterogeneities within fattissue, as well as the corresponding spatial variation of TCE concentrationsthat may occur. This partial differential equation model is based onthe dispersion model of Roberts and Rowland for hepatic uptake andelimination, adapted here for the specific physiology of adipose tissue.

Theoretical results are given for the well-posedness of a generalclass of abstract nonlinear parabolic systems which includes the TCEPBPK-hybrid model as a special case. Moreover, theoretical issues related to associated general least squares estimation problems are addressed,including the standard type of deterministic problem and aprobability-based identification problem that incorporates variability inparameters across a population. We also establish thetheoretical convergence of the Galerkin approximations used in our numericalschemes.

The qualitative behavior of the TCE PBPK-hybrid model is studied usingmodel simulations and parameter estimation techniques. In general, theTCE PBPK-hybrid model can generate various predictions of the dynamicsof TCE in adipose tissue by varying the adipose model parameters.These predictions include simulations that are similar to the expectedbehavior of TCE in the adipose tissue, which involves a rapid increaseof TCE adipocyte concentrations during the exposure period, followed by aslow decay of TCE levels over several hours.

Results are presented for several types of parameter estimationproblems associatedwith the TCE PBPK-hybrid model. We test theseestimation strategies using two types of simulated data: observationsrepresenting TCE concentrations from a single individual, andobservations that simulateinter-individual variability. The latter type of data, which iscommonly found in experiments related to toxicokinetics, assumesvariability in the parameters across a population, and may includeobservations from multiple individuals. Using both deterministic andprobability-based estimation techniques, we demonstrate thatthe probability-based estimation strategiesthat incorporate variability in the parameters may be best suited forestimating adipose model parameters that vary across the population.