Effects of technological delay on insulin and blood glucose in a physiological model

Abstract

In this paper, a physiological model of invasive blood-glucose (BG) measurement is employed to consider the diabetic treatment by the external auxiliary system, i.e., artificial pancreas (AP). For such system, there are two time delays, i.e., technological and liver's physiological delay, where the former comes from external auxiliary system with the active pancreas inputting. The technological delay and the infection degree of patients are considered as two controlled parameters to regulate the BG level of patients. This two parameters can also lead to the non-resonant double Hopf bifurcations. The classification and unfolding for the non-resonant double Hopf bifurcation are performed in terms of non-linear dynamics. The results show that such controlled parameters are very important. They can determine the efficiency for the diabetic treatment. It implies whether the diabetic patients recover or are still tormented by the simple or complex glucose fluctuation. The results have also been promising applications on analyzing, predicting and optimizing the medical outcome, evaluating the medical risk and feasibility. The physiological meaning in this paper is that one is able to achieve the better medical outcomes for the different patients by controlling the technological delay qualitatively.