An Equation for the Systemic Availability of Drugs Undergoing Simultaneous Enterohepatic Cycling, First-Pass Metabolism, and Intestinal Elimination

Abstract

A relationship between systemic availability and its determinants has been derived for a physiologically realistic model of drug disposition that includes enterohepatic cycling (EHC), gallbladder emptying (with an arbitrary time course), first-pass metabolism to noncycling metabolites, and fecal excretion. Systemic availability (F) has been shown to be determined by the fraction of the dose initially absorbed (f _a*), the fraction of the drug excreted into the GI tract that is reabsorbed with each cycle (f _a), the hepatic extraction ratio (E), and the fraction of extracted drug that is transported to the gallbladder for EHC (f _g) according to the relationship F = f _a*(1 −E/(1 − f _a f _g E) The implications of the above relationship are that (1) systemic availability is dependent on EHC, (2) values of F calculated to be greater than unity cannot be explained simply by the presence of EHC, (3) calculations of E based on the usual expression F = f _a* (1 − E) are erroneous for drugs subject to EHC, and (4) a compound that has a high systemic availability and is subject to EHC is not necessarily inefficiently metabolized. The quantitative interrelationship of systemic availability and its determinants is illustrated using a contour plot. Slices through the surface are used to demonstrate that the presence of EHC changes the sensitivity of F to changes in E.