Indistinguishability and identifiability analysis of linear compartmental models

Two compartmental model structures are said to be indistinguishable if they have the same input-output properties. In cases in which available a priori information is not sufficient to specify a unique compartmental model structure, indistinguishable model structures may have to be generated and their attributes examined for relevance. An algorithm is developed that, for a given compartmental model, investigates the complete set of models with the same number of compartments and the same input-output structure as the original model, applies geometrical rules necessary for indistinguishable models, and test models meeting the geometrical criteria for equality of transfer functions. Identifiability is also checked in the algorithm. The software consists of three programs. Program 1 determines the number of locally identifiable parameters. Program 2 applies several geometrical rules that eliminate many (generally most) of the candidate models. Program 3 checks the equality between system transfer functions of the original model and models being tested. Ranks of Jacobian matrices and submatrices and other criteria are used to check patterns of moment invariants and local identifiability. Structural controllability and structural observability are checked throughout the programs. The approach was successfully used to corroborate results from examples investigated by others.