Parameters interpretability in phenomenological-based semiphysical models. A human glucose homeostasis model

Abstract

In this thesis, the structure of a phenomenological-based semi-physical model (PBSM) of the glucose homeostasis in the human body was deduced such that its descriptive ability can be compared with the existent physiological models or maximal-like models. The PBSM of the glucose homeostasis has gathered the available physiological insight about such homeostasis by means of a systematic application of mass, energy, and momentum balances over the process systems of interest. To get a whole mathematical model of the glucose homeostasis, a model of each organ involved in such mechanism was developed like a sub-model. Once the main model structure was achieved, the specific transference mechanisms were determined according to the human physiology, providing what is known as constitutive and assessment equations, allowing to write the mathematical model in terms of the main variables in the homeostasis. Finally, a degree of freedom analysis over each mathematical model provided the information about which parameters of the model need to be identified by means of data-based or statistical procedures reported in the available literature. The sub-models give information about the clinical experimentation needed to make the mathematical model usable for real-life applications. Such a complex model deduction is seized to construct a conceptual framework about parameters interpretability to allow a particular model definition in terms of parameters with physical or physiological meaning. In this regard, a conceptual framework from a qualitative point of view was proposed to analyze and endow interpretability the parameters of the model. The concepts proposed were based on the identifiability concept reported in the literature.