Evaluating in vivo data for drug metabolism and transport: lessons from Kirchhoff's Laws

Mechanistic models of hepatic clearance have been evaluated for more than 50 years, with the first author of this mini-review serving as a co-author of the first paper proposing such a model. However, published quality experimental data are only consistent with the first of these models, designated as the well-stirred model, despite the universal recognition that this model is physiologically unrepresentative of what occurs with respect to liver metabolism and transport. Within the last 3 years, our laboratory has recognized that it is possible to derive clearance equations employing the concepts of Kirchhoff's Laws from physics, independent of the differential equation approach that has been utilized to derive reaction rates in chemistry. Here we review our published studies showing that the equation previously believed to be the well-stirred model, when hepatic basolateral transporters are not clinically relevant, is in fact the general equation for hepatic clearance when only systemic drug concentrations are measured, explaining why all experimental data fit this equation. To demonstrate that the equations deriving the mechanistic models of hepatic elimination for the past 50 years are not valid, we show that when calculating Kp_uu, the ratio of unbound drug concentration in the liver to the unbound concentration of drug in the systemic circulation, for the well-stirred, parallel tube and dispersion models, Kp_uu surprisingly can never exceed 1 and is a function of F_H, the hepatic bioavailability following oral dosing. We believe that knowledgeable drug metabolism scientist and clinical pharmacologist will agree that this outcome is nonsensical.