Blood glucose regulation with stochastic optimal control for insulin-dependent diabetic patients

Abstract

Diabetes is a disease resulting from the impaired mechanism of insulin secretion from the pancreas, which prevents glucose from entering the cells and being utilized and leads to wide swings of blood sugar and many complications such as heart disease and stroke, kidney disease and amputations. In order to prevent these complications and achieve a better quality of life for diabetic patients, effective regulation of blood glucose is essential. This study aims to achieve a better blood glucose control profile by incorporating the time-dependent uncertainties in diabetic patient parameters into formulations of optimal control using a novel approach which originates from finance literature. The time-dependent uncertainties are represented using stochastic processes called Ito processes and the mathematical formulation for this problem is presented. The usefulness of this approach is shown using experimental data from a diabetic patient and stochastic and deterministic optimal control profiles are computed. The stochastic profile results in fewer variations in blood glucose from the reference value of 4.5 mmol/L as compared to the deterministic profile in the presence of parametric uncertainty. This method holds a lot of promise in reducing the wide swings of blood glucose observed in diabetic patients and preventing possible complications of diabetes.