Normal-mode identifiability analysis of linear compartmental systems in linear stages

Abstract

The identifiability of linear, time-invariant compartmental models from specified experiments with noise-free observations is analyzed in terms of normal modes. The formulation of the analysis reduces the problem to that of checking if a solution by a succession of linear stages is possible. This allows the information available from a proposed experiment and from prior knowledge of model parameters, primarily those taken as zero, to be checked easily for redundancy, and unique (global) identifiability established or disproved. The analysis covers any combination of impulse and step forcing, and observation of any set of state variables. Examples are given, and the new method is compared with those based on the transfer-function matrix and the Markov parameter matrix. The features giving rise to nonunique but distinct models (local identifiability) are also explained in terms of normal modes, and illustrated by examples.