Square root law model for the delivery and intestinal absorption of drugs: a case of hydrophilic captopril

Abstract

The in vivo release and absorption of drugs are dependent on the interplay between many factors related to compound, formulation, and physiological properties. The mathematical models of oral drug absorption attempt to strike a balance between a complete description that takes into consideration as many independent factors as possible, and simple models that operate with fewer parameters, based mainly on critical factors. The latter models are by far more robust and easier to apply to predict the extent and sometimes even the rate of absorption. The present paper attempted to develop a simple model to describe the time course of absorption of the hydrophilic drug captopril (CPT) at the early phases of absorption, with implications mainly in the induction and early stages of achieving its therapeutic effect. As a phenomenological model, the instantaneous release of CPT was considered in the gastrointestinal fluid, leading to a constant drug concentration for a prolonged time, followed by a ‘long path diffusion’ inside the intestinal wall and a very low concentration at the interface intestinal wall-blood. These conditions regarding CPT concentration were translated into initial and boundary mathematical conditions for the diffusion equation in the intestinal wall. The solution of the diffusion equation led in the end to a square root law describing the dependence between the fraction of the drug absorbed and time. The model was successfully applied to data obtained in five bioequivalence studies: three comparing plasma levels achieved after the administration of a single dose of CPT 50 mg, one evaluating CPT pharmacokinetics after a 100 mg dose, and a fifth comparing CPT pharmacokinetics of two fixed-dose combinations of CPT 50 mg and hydrochlorothiazide 25 mg.