Theoretical Considerations for Direct Translation of Unbound Liver-to-Plasma Partition Coefficient from In Vitro to In Vivo

There is considerable interest in developing methods to predict the asymmetric distribution of unbound drug into tissues. The liver is of particular interest due to the multitude of expressed transporters with potential implications for pharmacokinetics, pharmacodynamics, and toxicology. Empirical correlations of in vitro unbound hepatocyte-to-media partition coefficient (in vitro Kpuu) and in vivo unbound liver-to-plasma partition coefficient (in vivo Kpuu) have been reported without considering the theoretical aspects which might confound the interpretation of such observations. To understand the theoretical basis for the translation of Kpuu between in vitro and in vivo systems, we simulated in vitro hepatocyte and in vivo liver Kpuu values using mechanistic mathematical models of these systems. Theoretical comparisons of steady-state Kpuu between in vitro and in vivo systems were performed using liver models which assumed a number of segments ranging from one (i.e., a permeability-limited well-stirred model) to infinity (i.e., a permeability-limited parallel tube model). Using a five-segment model, the effect of zonal differences in metabolism was also explored in this context. The results across the range of examined models indicated that theoretical differences between in vitro and in vivo Kpuu estimates exist and are expected to increase with an increasing degree of extraction across the liver. However, differences were relatively small using what is perhaps the most physiologically relevant, permeability-limited parallel tube model, suggesting that direct correlations are reasonably valid and that the permeability-limited parallel tube model is perhaps the most appropriate physiologically based pharmacokinetic (PBPK) construct for supporting studies of this nature.