Factors affecting the identifiability of compartmental models

The identifiability of compartmental models is analysed through a series of examples which have been used to describe physiological or pharmacokinetic processes. Emphasis is placed on aspects of experimental identifiability which have hitherto received little attention in identifiability analysis. It is shown that where a single-input, single-output experiment results in non-identifiability or local identifiability, it is often possible to improve the situation by measuring more responses or simultaneously perturbing more inputs. Identifiability is then shown usually to depend on whether the observation gains are known and on the shape of the inputs, when more than one is applied. The relative merits of the Laplace transform and normal mode methods of analysing identifiability are discussed and illustrated with a substantial example. The identifiability analysis of a nonlinear compartmental model, with state-dependent rate coefficients, is presented. It is shown that inclusion of a neglected (nonlinear) relationship can make a previously non-identifiable model uniquely identifiable.