Distributed-delay Models of the Glucose-Insulin Homeostasis and Asymptotic State Observation

In this paper the problem of the real-time reconstruction of plasma insulin concentration by using only blood glucose measurements is investigated. For the purpose of the reconstruction of the insulinemia a good model of the glucose-insuline homeostasis is required. The most known model describing the glucose-insuline homeostasis is the so called Minimal Model, created for the interpretation of the Intra Venous Glucose Tolerance Test (IVGTT). In a previous work the authors investigated the use of the Minimal Model and of some its modifications for the construction of state observers aimed to the rebuilding of the insulinemia. In this paper the use of more sophisticated models, containing distributed-delay kernel, are considered for the observer design. Simulation results are reported in order to validate the developed theory.