Modeling of Blood Glucose Dynamics to Automate Personalized Insulin Therapy for Patients with Type 1 Diabetes Mellitus

The paper discusses the basic principles of automating personalized insulin therapy systems for patients with type 1 diabetes mellitus based on a combination of adaptive control of basal insulin and model predictive control. The study focuses on predicting blood glucose to calculate the optimal parameters of insulin boluses administered in response to a meal. The current knowledge about the physiological processes that affect blood glucose is analyzed and an approach is proposed to describe the compartments of the mathematical model of glucose regulation in the body, including the processes of glycogenolysis and glycogenogenesis, glucose transport into cells and renal glucose excretion based on the Michaelis-Menten kinetics. Since the mathematical model is a stiff system of nonlinear differential equations, numerical integration methods are analyzed, among which the LSODA algorithm has shown the highest rate with high accuracy. To calculate the parameters of a two-wave insulin bolus, the COBYLA multivariate optimization method is proposed. The combination of these methods can significantly improve the efficacy of the insulin response mainly to high-carbohydrate meals with a low calculation time.