An equation for the systemic availability of drugs undergoing simultaneous enterohepatic cycling, first-pass metabolism, and intestinal elimination.

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 (fa), the hepatic extraction ratio (E), and the fraction of extracted drug that is transported to the gallbladder for EHC (fg) according to the relationship F = f*a(1 - E)/(1 - fafgE) 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.