Asymptotics and bioavailability in a 17-compartment pharmacokinetic model with enterohepatic circulation and remetabolization

A 17-compartment linear pharmacokinetic model is designed, describing the complex process of enterohepatic circulation as a superposition of the net (remetabolizationfree) enterohepatic circulation, and remetabolization with subsequent intestinal absorption of the parent drug. Basically, the model is built by doubling the model describing the circulation of the parent drug in the body, so that the remetabolizable metabolite circulates in a model of the same structure as does the parent compound. The two submodels are cross-connected with arrows denoting the transition of the particular substance into the complementary part of the complex model.Asymptotic properties of the model are investigated, in particular, explicit formulas for its pharmacokinetic endpoints are given using the elements of its transition probability matrix. Conversely, taking account of the effect of bile cannulation, intravenous, intraportal and oral administration of the drug, as well as of the intravenous and intraportal administration of the remetabolizable metabolite, the transition probabilities of the system are determined in terms of certain measurable pharmacokinetic endpoints and the flow rates through the kidneys, liver and the cardiac output.Finally, the influence of the enterohepatic circulation and remetabolization process on bioavailability is examined. In particular, the inclusion–exclusion formula is derived, expressing its joint efficiency (defined as the relative increase of bioavailability) by means of the efficiencies of the net enterohepatic circulation and of the remetabolization process.