Individual Prior Information in a Physiological Model of 2H8‐Toluene Kinetics: An Empirical Bayes Estimation Strategy

Abstract

Physiologically‐based toxicokinetic (PBTK) models are widely used to quantify whole‐body kinetics of various substances. However, since they attempt to reproduce anatomical structures and physiological events, they have ahigh number of parameters. Their identification from kinetic data alone is often impossible, and other information about the parameters is needed to render the model identifiable. The most commonly used approach consists of independently measuring, or taking fom literature sources, some of the parameters, fixing them in the kinetic model, and then performing model identification on a reduced number of less certain parameters. This results in a substantial reduction of the degrees of freedom of the model. In this study, we show that this method results in final estimates of the free parameters whose precision is overestimated. We then compared this approach with an empirical Bayes approach, which takes into account not only the mean value, but also the error associated with the independently determined parameters. Blood and breath 2H8‐ toluene washout curves, obtained in17 subjects, were analyzed with a previously presented PBTK model suitable for person‐specific dosimetry. Model parameters with the greatest effect onpredicted levels were alveolar ventilation rate QPC, fat tissue fraction VFC, blood air partition coefficient Kb, fraction of cardiac output to fat Qa/co and rate of extrahepatic metabolismVmax.p. Differences in the measured and Bayesian‐fitted values of QPC, VFc and Kb were significant (p < 0.05), andthe precision of the fitted values Vmax.p and Qa/co went from 11 ± 5% to 75 ± 170% (NS) and from 8 ± 2% to 9 ± 2% (p < 0.05) respectively. The empirical Bayes approach did not result in less reliable parameter estimates: rather, it pointed out that the precision of parameter estimates can be overly optimistic when other parameters in the model, eitherdirectly measured or taken from literature sources, are treated as known without error. In conclusion, an empirical Bayes approach to parameter estimation resulted in a better model fit, different final parameter estimates, and more realistic parameter precisions.