Identification of a pharmacokinetic two-compartment model application to the case of salicylates administered to rabbit

Abstract

The purpose of this paper is mainly the coefficient identification of a pharmacokinetic two-compartment open model with first-order absorption. This model consists of the central compartment (plasma) and the peripheral one (tissue) containing the ill site aimed by the action of the administered drug. The different phenomenons taking place between the compartments obey a first-order (linear) kinetic. This phenomenons of absorption, transfer, and elimination are characterized by their rate constants. A compartmental analysis leads to a system of coupled linear differential equations whose coefficients, the unknowns of the problem, are the above-mentioned rate constants. This system describes the transition of the drug from its administration to its action site passing through the plasma. An oral administration of a single dose is considered and the evolution of the drug concentration in the plasma is measured. These measurements, performed over time in a reduced number on the rabbit, give unique and useful information for the identification of the coefficient set appearing in the mathematical model. The identification problem is stated in terms of a constraint minimization of a cost functional, given by the quadratic error between the measured and the computed drug concentrations in the plasma. From the nonconvexity of this cost functional (existence of more than one local minimum) follows the nonuniqueness of the optimal solution of this identification problem. The minimization is performed on a minicomputer by means of a nonlinear programming method of conjugate-gradient type. The efficiency of the suggested method has been tested with measurements made on a lot of rabbits after the administration of a single dose (100 mg/kg) of aspirin in form of lysine acetylsalicylate and sodium salicylate. The administration was made, thanks to an adapted technique, by a rubber probe in two different ways: in the stomach and in the duodenum. After the model identification it was possible to study, in simulation on a computer, the effect of the metabolite/nonmetabolite drug forms as well as the effect of the drug administration site on the time course of the drug in the organism. This simulation makes it easy to have access to magnitudes, familiar to the pharmaceutical practitioner, like the half-life, the bioavailability, the clearances, the build- up of blood levels for multiple doses, etc. . . . It was possible to improve the understanding of the time course of aspirin in rabbit in comparison to the time course of its main metabolite, the sodium salicylate, and this for the same animal.