A priori identifiability of distributed models of blood-tissue exchange

A priori identifiability deals with the uniqueness of the solution for the unknown parameters of a dynamic model from a given input-output experiment, and is a prerequisite for well posedness of parameter estimation from the data. Identifiability has been extensively investigated for lumped parameter, linear, and nonlinear dynamic models, in particular, compartmental models of biological systems. Much less attention has been devoted to distributed parameter model, in particular, those describing blood-tissue exchange, which are normally used to interpret regional multiple tracer dilution experiments. In this paper, we study a priori identifiability of distributed parameter models of transcapillary exchange, focusing first on a single capillary (one-region) model, then moving on to a single capillary-interstitial fluid (two-region) model, and finally to an organ model also describing flow heterogeneity.