An understanding of flow- and diffusion-limited vs. carrier-mediated hepatic transport: a simulation study

Concentration-dependent changes in the hepatic extraction ratio E and tissue accumulation of drugs were examined in a simulation study, wherein plasma protein binding, flow, and mode of entry were altered. A tubular flow model that described carrier-mediated (influx: Kml = 20 microM, Vmax1 = 1000 nmol min-1; efflux, Km2 = 200 microM, Vmax2 = 250 nmol min-1), flow-limited (influx clearance CLin = efflux clearance CLef = 50 ml min-1), or diffusion-limited (CLin = CLef = 0.1 ml min-1) hepatocytic entry was employed; drug removal was solely via biliary excretion (Km3 = 100 microM, Vmax3 = 1500 nmol min-1). Other parameter space and the combination of carrier-mediated transport and passive diffusion were also explored. Increased plasma protein binding reduced the hepatic extraction of the substrate, and in some instances, constituted the rate-controlling factor, especially at lower input concentrations for which tighter binding existed. Increased flow rate also brought about a reduction in E, affecting E almost inversely when values of E were low (e.g., for the diffusion-limited case or at higher input concentration). Tissue accumulation patterns and the apparent tissue distribution equilibrium ratio, i.e., tissue to plasma unbound concentration ratio Kp, differed among the systems. The behavior of Kp may be used as an identifier for the mode of drug transport: A declining (concave-down) Kp curve or a parabolic Kp that approached unity with input concentration (Cln) is associated with carrier-mediated entry; a rising Kp curve that approaches unity with Cln suggests flow limitation; and a waning concave-up Kp curve of very low magnitude represents diffusion limitation. Since the unbound tissue concentration (Ct) differs from the logarithmic average of the unbound input and output concentrations in plasma (Cu) for carrier-mediated and diffusion-limited systems, excretion parameters may be obtained only upon fitting of the overall excretion rate vs. Ct in the Michaelis-Menten equation; whereas when data are fitted with Cu, the rate-limiting step, influx, or deviations of influx, efflux, and excretion, will be obtained. When Ct equals Cu, as in flow-limited systems, accurate excretion parameters will be provided with the fitting of data against either Ct or Cu.