Identifiability and distinguishability testing via computer algebra

Abstract

This paper describes how computer algebra can be of help when studying either the identifiability of one given parametric model structure or the distinguishability of several of them. Two examples are used to briefly recall classical methods for checking model structures for these properties. The first one deals with the identifiability of model structures that are being used for describing the first-pass effect of drugs after oral administration. The second one studies the distinguishability of two nonlinear compartmental model structures with Michaelis-Menten elimination kinetics. In both cases classical methods yield a set of algebraic equations that can easily be put in polynomial form. Testing model structures for identifiability or distinguishability then amounts to characterizing the number of solutions of this set of polynomial equations. Two approaches are described for this purpose, which have been implemented using the algebraic manipulation language REDUCE. Among other things, they make it possible to prove that none of the model structures used for describing the first-pass effect is identifiable and to generate the set of all output-indistinguishable models.