Reduction and lumping of physiologically based pharmacokinetic models:: Prediction of the disposition of fentanyl and pethidine in humans by successively simplified models

Physiologically based pharmacokinetic (PBPK) models can be used to predict drug disposition in humans from animal data and the influence of disease or other changes in physiology on the pharmacokinetics of a drug. The potential usefulness of a PBPK model must however be balanced against the considerable effort needed for its development. Proposed methods to simplify PBPK modeling include predicting the necessary tissue: blood partition coefficients (k(p)) from physicochemical data on the drug instead of determining them in vivo, formal lumping of model compartments, and replacing the various k(p) values of the organs and tissues by only two values, for "fat'' and "lean'' tissues, respectively. The aim of this study was to investigate the effects of simplifying complex PBPK models on their ability to predict drug disposition in humans. Arterial plasma concentration curves of fentanyl and pethidine were simulated by means of a number of successively reduced models. Median absolute prediction errors were used to evaluate the performance of each model, in relation to arterial plasma concentration data from clinical studies, and the Wilcoxon matched pairs test was used for comparison of predictions. An originally diffusion-limited model for fentanyl was simplified to perfusion-limitation, and this model was either lumped, reducing 11 organ/tissue compartments to six, or changed to a model based on only two k(p) values, those of fat (used for fat and lungs) and muscle (used for all other tissues). None of these simplifications appreciably changed the predictions of arterial drug concentrations in the 10 patients. Perfusion-limited models for pethidine were set up using either experimentally determined [Gabrielsson et al. 1986] or theoretically calculated [Davis and Mapleson 1993] k(p) values, and predictions using the former were found to be significantly better. Lumping of the models did not appreciably change the predictions; however, going from a full set of k(p) values to only two ("fat'' and "lean'') had an adverse effect. Using a k(p) for lungs determined either in rats or indirectly in humans [Persson et al. 1988], i.e., a total of three k(p) values, improved these predictions. In conclusion, this study strongly suggested that complex PBPK models for lipophilic basic drugs may be considerably reduced with marginal loss of power to predict standard plasma pharmacokinetics in humans. Determination of only two or three k(p) values instead of a "full'' set can mean an important reduction of experimental work to define a basic model. Organs of particular pharmacological or toxicological interest should of course be investigated separately as needed. This study also suggests and applies a simple method for statistical evaluation of the predictions of PBPK models.