On the Identifiability of Physiological Models: Optimal Design of Clinical Tests

Physiological models are mathematical models characterized by a physiologically consistent mathematical structure (defined by the set of equations being used) and a set of model parameters to be estimated in the most precise and accurate way. However, systems in physiology and medicine are typically characterized by poor observability (i.e., possibility for the clinician to observe practically and quantify the relevant phenomena occurring in the body through clinical tests and investigations), high number of interacting and unmeasured variables (as an effect of the complexity of interactions), and poor controllability (i.e., limited capacity to drive the state of the system by acting on decision variables). All these factors may severely hinder the practical identifiability of these models, i.e., the possibility to estimate the set of parameters in a statistically satisfactory way from clinical data. Identifiability is a structural property of a model, but it is also determined by the amount of useful information that can be generated by clinical data. Hence, the importance of designing clinical protocols that allow estimating the model parameters in the quickest and more reliable way. In this chapter, we discuss how the identifiability of a physiological model can be characterized and analyzed, and how identifiability tests and model-based design of experiments (MBDoE) techniques can be exploited to tackle the identifiability issues arising from clinical tests. A case study related to the identification of physiological models of von Willebrand disease from clinical data will be presented where techniques and methods for testing the identifiability of PK models have been used.