Mathematical Models with Delays for Glucose-Insulin Regulation and Applications in Artificial Pancreas

Abstract

A closed-loop insulin delivery system could potentially be the ultimate solution for blood glucose control. Control algorithm regulating external insulin infusion based on the models of glucose-insulin system is indispensable for a blood glucose regulation device. A new two-compartment model with two explicit delays was developed to investigate the oscillatory behavior of glucose-insulin system. Seven parameters of the model were studied for their influence on oscillatory behavior and lags in glucose-insulin system. The model was modified to include two absorption channels and local insulin degradation for external insulin injections, fitted to clinical data by adjusting six parameters using nonlinear least squares method, and compared with existing model. Model Predictive Control was applied with the two models to evaluate the performance of glucose control. Glucose level was demonstrated to be regulated to the desired level quickly on these models.