Connecting sensitivity, identifiability and interpretability of a glucose minimal model

Abstract

Mathematical models have increased their applications in physiology, control and systems science, and biomedical engineering because they offer the opportunity to examine the structure and behavior of complex physiological systems. In addition, they provide a concise description of complex dynamic processes, indicating ways to improve experimental design and allowing the testing of hypotheses related to physiological structure. When building a mathematical model, it is important to assess the impact of different factors on the overall behavior of the system being modeled and to determine which variables have the most significant influence on the system. Properties such as identifiability, sensitivity, and interpretability in mathematical models are crucial for representing real-world phenomena. In this paper, a sensitivity, structural identifiability, and qualitative parameter interpretability analysis is carried out in a new version of the minimal model of the glucose-insulin system proposed by Bergman. The aim was to evaluate the structure of this new mathematical model and the existing relationship among sensitivity, identifiability, and interpretability of the model parameters. The findings demonstrated the connection between the properties of sensitivity, structural identifiability, and parameter interpretability, which provide important details about the model structure.