A Priori Identifiability Analysis in Pharmacokinetic Experiment Design

Abstract

Mathematical modelling and dynamic identification experiments are increasingly employed in quantitative pharmacokinetic studies. This paper addresses the so-called identifiability problem which has to be faced a priori, i.e., once a certain pharmacokinetic model structure has been postulated and the input-output experiment planned, but prior to its performing. More precisely, identifiability analysis addresses the question of whether it is possible to obtain solutions for the unknown parameters of the chosen model structure from data collected via those input-output tests which can be carried out. The prerequisite value of identifiability analysis for the design of a well-posed pharmacokinetic experiment is emphasized. A precise set of identifiability definitions are given with reference to a general pharmacokinetic experiment design model. Three classes of pharmacokinetic models are discussed in some detail, namely the nonlinear saturable models, the linear or linearizable models and the linear compartmental models. Available methods for testing in practice identifiability for these three classes of experiment design models are reviewed, compared and exemplified. Connections between the identifiability property of a given model and the possibility of reconstructing/predicting system variables of interest not directly accessible to measurement, which is one of the purposes for which pharmacokinetic models are often built, are stressed.