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

Abstract

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.

A physiological view and structures of mean residence times

“…in the Laplace (s) domain (Yamaoka et al 1978;Ďurišová et al 1995). In the last step the physiologically realistic structures of MRT po and MRT im are determined, using Eqs.…”

“…ADME is a well-known acronym in pharmacokinetics (see e.g., Eddershaw et al 2000). A design of an ADME related dynamic system is a simple procedure, it can be performed in the following way: a function approximating a drug input into the body is used as an input to an ADME related dynamic system, and a function approximating a response of the body to the drug input is used as an output of ADME related dynamic system (Ďurišová et al 1995;Dedík and Ďurišová 1996;Ďurišová and Dedík 1997;Tvrdoňová et al 2009). Thereafter, the ADME related dynamic systems are simply called "the dynamic systems".…”

“…Therefore, several studies described investigations of the dynamic process associated with drug fate and disposition with the aid of dynamic systems. The investigations were performed in the following way: (a) dynamic systems were defined, (b) optimal circulatory models of the dynamic systems were selected through the Akaike information criterion (Akaike 1974) and (c) parameters of the optimal models were estimated (Ďurišová et al 1995;Ďurišová and Dedík 1997;Dedik et al 2009). …”

Physiologically Based Structure of Mean Residence Time

“…(2) The use of the method described previously [4, 7] and a theoretical example in which it was assumed that the drug was administered in an intravenous bolus dose to a hypothetical subject.…”

“…(7) The use of the general equation (1), the circulatory model developed, and the method described previously [4] to identify the MRT structure.…”