Indistinguishability and identifiability analysis of linear compartmental models

DISTING: A web application for fast algorithmic computation of alternative indistinguishable linear compartmental models

BACKGROUND AND OBJECTIVES

We describe and illustrate use of DISTING, a novel web application for computing alternative structurally identifiable linear compartmental models that are input-output indistinguishable from a postulated linear compartmental model. Several computer packages are available for analysing the structural identifiability of such models, but DISTING is the first to be made available for assessing indistinguishability.

METHODS

The computational algorithms embedded in DISTING are based on advanced versions of established geometric and algebraic properties of linear compartmental models, embedded in a user-friendly graphic model user interface. Novel computational tools greatly speed up the overall procedure. These include algorithms for Jacobian matrix reduction, submatrix rank reduction, and parallelization of candidate rank computations in symbolic matrix analysis.

RESULTS

The application of DISTING to three postulated models with respectively two, three and four compartments is given. The 2-compartment example is used to illustrate the indistinguishability problem; the original (unidentifiable) model is found to have two structurally identifiable models that are indistinguishable from it. The 3-compartment example has three structurally identifiable indistinguishable models. It is found from DISTING that the four-compartment example has five structurally identifiable models indistinguishable from the original postulated model. This example shows that care is needed when dealing with models that have two or more compartments which are neither perturbed nor observed, because the numbering of these compartments may be arbitrary.

CONCLUSIONS

DISTING is universally and freely available via the Internet. It is easy to use and circumvents tedious and complicated algebraic analysis previously done by hand.

MAMCAT: an expert system for distinguishing between mammillary and catenary compartmental models

MAMCAT is a user-friendly, interactive, graphics-based PC program for addressing a common compartmental model discrimination problem in the framework of model indistinguishability theory: can mammillary and catenary models of the same order be distinguished from each other? The software is designed to teach the theory and solve specific problems. The user is guided step-by-step through definitions, examples, theory and problem solution. Topological properties are used first to screen out some distinguishable models and thereby reduce the number of candidates for indistinguishability. Transfer function analysis is then used to explore the remaining candidates. Analytical results for up to 5-compartment models are given and a more general algorithm is induced from these results.