A Frequency Response Method for Pharmacokinetic Model Identification

Abstract

A mathematical model must be constructed in order for either body fluid measurements of drug concentration or pharmacological response intensity data to be useful for computation of the time course of systemic drug bioavailability. For linear compartment models the time course of either drug concentration or pharmacological response is represented by a sum of exponentials. The usual method for establishing such models involves the use of some form of nonlinear least-squares estimation technique. For systems of order higher than first, such techniques are often cumbersome, time consuming, and in some cases inadequate. A general frequency response technique commonly used in systems engineering applications, pulse testing, has been successfully applied to pharmacological data for model identification. The method is general and can be applied equally well to blood or urine data. Theoretical descriptions of both the nonlinear least-squares estimation technique in the time domain and the frequency domain estimation technique are presented here. The frequency response data obtained by pulse testing are fitted with accurate model parameters by using a nonlinear least-squares estimation technique in the frequency domain. However, the number of parameters which must be determined, is decreased when modelling in the frequency domain. This results in decreased computation time. For example, the least-squares time domain technique required 25 and 190 seconds of computation time for second- and third-order models, respectively, while the frequency domain technique required 8 and 10 seconds for the same models.