Michaelis‐menten metabolite formation kinetics: Equations relating area under the curve and metabolite recovery to the administered dose

A computational approach which concomitantly determines the capacity‐limited rate constants of parent drug elimination and metabolite formation is presented. The approach applies both the presently derived total excretory recovery versus dose relationships of the metabolite and the AUC versus dose relationships of the parent drug to identify the parameters. Three parent drug elimination conditions were assessed: pooled first‐order, pooled Michaelis‐Menten, and parallel first‐order and pooled Michaelis–Menten kinetics. Model and parameter identification criteria are discussed. Literature data for theophylline and two of its metabolites in rats were examined to reveal pooled Michaelis–Menten elimination kinetics of theophylline and capacity‐limited formation of the metabolites. The proposed technique is useful for quantitating commonly obtained nonlinear drug disposition data such as AUC and amount of metabolites excreted.