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

- Several computer packages are available for analysing structural identifiability, for both linear and nonlinear models used in biomedicine.
- Structural indistinguishability is a much less well understood problem and until now, no computer packages have been available for its analysis.
- For linear models, it consists of finding all other models within a given class which are indistinguishable from a given (postulated) model.
- Unless it is realised that there are alternative structures that provide an equally good model, erroneous conclusions can easily be reached.
- DISTING uses novel computational tools for analysing indistinguishability and is freely available on the Web, in a user-friendly interface.

Background and objectivesWe 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.MethodsThe 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.ResultsThe 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.ConclusionsDISTING is universally and freely available via the Internet. It is easy to use and circumvents tedious and complicated algebraic analysis previously done by hand.