An algorithm for identifiable parameters and parameter bounds for a class of cascaded mammillary models

A complex structural identifiability problem for a class of unidirectionally interconnected n-compartment linear mammillary models with multiple inputs is discussed. This class is particularly useful in the study of drug/metabolite kinetics and other interconversion kinetic processes. An explicit algorithm is developed for this model class that provides identifiable parameter combinations, parameter bounds, steady-state pool sizes, and production rates, with input forcing and output measurements in central compartments. A six-compartment model of the combined dynamics of the prohormone thyroxine (T4) and hormone triiodothyronine (T3) illustrates how physiological parameter values or their smallest ranges, such as tissue T4 to T3 conversion rates and separate T4 and T3 production rates, can be determined from stimulus-response measurements in plasma alone.