Structural identifiability of strongly connected biological compartmental systems

The paper deals with the evaluation of the a priori possibility of estimating the unknown parameters of a system having a known structure via an input-output experiment (structural identifiability). The problem is analysed with reference to biological compartmental systems (and precisely to a specific but largely representative class of these systems, i.e. the so-called strongly connected compartment systems). The analysis is developed by using concepts and methods of system theory and particularly the concepts of 'controllability' and observability (i.e. the possibility of influencing the behaviour of the whole system by the input and of estimating it from the output). Two new theorems are proved concerning the necessary and sufficient conditions for the observability and controllability of strongly connected compartmental systems. On the basis of these theorems, a structural identifiability criterion is established and a digital-computer implementation technique for this criterion is given. Some typical tracer-analysis experiments on biological compartmental systems are analysed with the aim of evaluating how many and which parameters of the considered model can be estimated through the chosen input-output experiments. © 1975 International Federation for Medical & Biological Engineering.