A Complete Extension of Classical Hepatic Clearance Models Using Fractional Distribution Parameter f_d in Physiologically Based Pharmacokinetics

The classical organ clearance models have been proposed to relate the plasma clearance CL_p to probable mechanism(s) of hepatic clearance. However, the classical models assume the intrinsic capability of drug elimination (CL_u,int) that is physically segregated from the vascular blood but directly acts upon the unbound drug concentration in the blood (f_ubC_avg), and do not handle the transit-time delay between the inlet/outlet concentrations in their closed-form clearance equations. Therefore, we propose unified model structures that can address the internal blood concentration patterns of clearance organs in a more mechanistic/physiological manner, based on the fractional distribution parameter f_d operative in PBPK. The basic partial/ordinary differential equations for four classical models are revisited/modified to yield a more complete set of extended clearance models, i.e., the Rattle, Sieve, Tube, and Jar models, which are the counterparts of the dispersion, series-compartment, parallel-tube, and well-stirred models. We demonstrate the feasibility of applying the resulting extended models to isolated perfused rat liver data for 11 compounds and an example dataset for in vitro-in vivo extrapolation of the intrinsic to the systemic clearances. Based on their feasibilities to handle such real data, these models may serve as an improved basis for applying clearance models in the future.