Analysis of the Change in the Blood Concentration-Time Profile Caused by Complex Drug-Drug Interactions in the Liver Considering the Enterohepatic Circulation: Examining Whether the Inhibition Constants for Uptake, Metabolism, and Biliary Excretion Can be

Hypothetical substrates undergoing transporter-mediated hepatic uptake, metabolism, and enterohepatic circulation with different rate-determining processes with a combination of inhibition constants (Ki) for hepatic uptake, metabolism, and biliary excretion processes were generated with a constant Ki for uptake and incorporated into a physiologically based pharmacokinetic model. Analyses of the kinetic model suggested that the fraction of substrates excreted in the bile to the total elimination by the liver (fbile) can be estimated under certain conditions from kinetic analyses of their blood concentration-time profiles. Using the generated time profiles of substrates with and without coadministration of inhibitors, various pharmacokinetic parameters involving fbile and Ki for the hepatic uptake, metabolism, and biliary excretion of drugs were back-calculated by fitting. Comparing parameters obtained with the original parameter sets by fitting, the Ki were found to be well estimated under the following conditions: the initial estimates for inhibition constants were relatively good, which corresponds to the case for obtaining reliable in vitro inhibition constants. In conclusion, the integration of top-down analyses with bottom-up estimates (experimental determination) of inhibition constants can be used to estimate in vivo inhibition constants and fbile reliably.