Identifiability and interval identifiability of mammillary and catenary compartmental models with some known rate constants

The identifiability problem is addressed for n-compartment linear mammillary and catenary models, for the common case of input and output in the first compartment and prior information about one or more model rate constants. We first define the concept of independent constraints and show that n-compartment linear mammillary or catenary models are uniquely identifiable under n-1 independent constraints. Closed-form algorithms for bounding the constrained parameter space are then developed algebraically, and their validity is confirmed using an independent approach, namely joint estimation of the parameters of all uniquely identifiable submodels of the original multicompartmental model. For the noise-free (deterministic) case, the major effects of additional parameter knowledge are to narrow the bounds of rate constants that remain unidentifiable, as well as to possibly render others identifiable. When noisy data are considered, the means of the bounds of rate constants that remain unidentifiable are also narrowed, but the variances of some of these bound estimates increase. This unexpected result was verified by Monte Carlo simulation of several different models, using both normally and lognormally distributed data assumptions. Extensions and some consequences of this analysis useful for model discrimination and experiment design applications are also noted.