Building a structured model of a complex pharmacokinetic system with time delays

This paper presents a description of the procedure for building a structured model of a complex pharmacokinetic system on using its transfer function. The example employed is that of the pharmacokinetic system based on gentamicin plasma concentrations after intravenous and intratracheal administration to guinea pigs, describing the pathway of the drug into the systemic circulation after the extravascular injection mentioned. The structured model selected consisted of a submodel of a proportional linear subsystem, two submodels of simple linear dynamic subsystems with time constants of 0.135 +/- 0.065 hr (95% I.C.) and 0.052 +/- 0.049 hr, and two submodels of parallel subsystems with time delays of 0.25 +/- 0.046 hr and 1.135 +/- 0.288 hr, connected in serial. Two estimates of the mean residence time of the total amount of gentamicin in the system, i.e., 0.347 and 0.335 hr, were obtained, based on the system frequency and structured model, respectively. From the methodological point of view, our paper demonstrates the efficiency of combination of modelling in the frequency and in the time domain, designed to facilitate studies of pharmacokinetic systems.