Abstract

Interpretation of rate constants in the sequential metabolism of two different primary metabolites (MIA and MIB) for formation of a common, secondary metabolite (MII) after drug administration requires theoretical development of formulations that govern mass transfer during intravenous and oral administrations. Two cases (a and b) were presently considered for metabolism occurring only in the first-pass organs (intestine and liver) for flow-limited drugs and primary and secondary metabolites: (case a) wherein drug formed only the two primary metabolites, with the fractions of total body clearance that formed MIA and MIB, being denoted by f1 and f2, respectively, and (case b) wherein other additional elimination pathways for drug were present. MIA and MIB only partially formed MII (denoted by fMIA and fMIB, respectively), because provision was made for alternate elimination pathways; the fractional clearance in the formation of MII from MIA and MIB were fMIA and fMIB, respectively. Drug was metabolized to MIA than MII within the gut lumen with oral drug administration; the MIA and MII formed were further absorbed. Triangular matrices were found to result from mass transfer equations for first-order conditions with oral and intravenous administrations. Upon inversion of the matrices, the areas under the curve for drug and metabolite species were obtained after multiplication by the administered dose and division by the volume of the species considered. However, the dose-corrected area under the curve was used as the basis for comparison. Case-independent solutions were obtained for the fractions absorbed (Fa, FaMIA, FaMIB) and the availabilities (F, F(MIA), F(MIB)) of drug and the primary metabolites, and for f1, f2, f1/f2, fMIA/fMIB, and (f1fMIA)/(f2fMIB) (ratio of effective clearances of MII formation from D via MIA and MIB). Case-dependent solutions also existed. For case a (f1 + f2 = 1), the fraction of total body clearance that formed MIA (f1) or MIB (f2) was solved with the area under the curve of MII after intravenous D, MIA, and MIB administrations. For case b, however, the same constants were obtained after greater manipulation, and entailed oral administration of the metabolites. Although solutions for the ratios of f1/f2 and (f1fMIA)/(f2fMIB) were found, the fractional clearances in formation of MII from MIA (fMIA) and MIB (fMIB) were, however, not provided in both cases unless MII was completely absorbed.