Mathematical Models and State Observation of the Glucose-Insulin Homeostasis

This paper explores the possibility of using an asymptotic state observer for the real-time reconstruction of insulin blood concentration in an individual by using only measurements of the glucose blood concentration. The interest in this topic relies on the fact that the glucose measurements are much more economical and faster then the insulin measurements. An algorithm providing reliable insulin concentrations in real-time is essential for the realization of an “artificial pancreas”, an automatic device aimed to infuse the required amount of insulin into the circulatory system of a diabetic patient. An important issue for a good observer design is the determination of satisfactory models of the glucose-insulin homeostasis. Different models have been considered and discussed in this paper. For all models presented an asymptotic state observer has been constructed and numerical simulations have been successfully carried out.