Multi-Objective Optimal Regulation of Glucose Concentration in Type I Diabetes Mellitus

Abstract

Type I, or insulin-dependent diabetes mellitus, is a chronic disease in which insulin is not adequately produced by the pancreatic β-cells, which leads to a high glucose concentration. In practice, external insulin delivery is the only method to deal with this disease. To this end, a multi-objective optimal control for insulin delivery is introduced in this paper. Three conflicting objectives, including minimizing the risk of hypoglycemia and hyperglycemia, and reducing the amount of injected insulin, are considered. These objectives are minimized simultaneously while tuning the closed-loop system parameters that include the design details of the linear-quadratic regulator (LQR) and estimator speed of convergence. The lower and upper bounds of the LQR setup parameters are determined by Bryson’s rule taking into account the nominal glucose range (70−160 mg/dL) and maximum and minimum pump infusion rates (0.0024−15 mU/min). The lower and upper bounds of the estimator convergence speed are chosen such that the estimator is faster than the fastest mode of the closed-loop system. For computer simulations, Bergman’s minimal model, which is one of the commonly used models, is employed to simulate glucose-insulin dynamics in Type-I diabetic patients. The optimization problem is solved by the nondominated sorting genetic algorithm (NSGA-II), one of the widely used algorithms in solving multi-objective optimization problems (MOPs). The optimal solutions in terms of the Pareto set and its image, the Pareto front, are obtained and analyzed. The results show that the MOP solution introduces many optimal options from which the decision-maker can choose to implement. Furthermore, under high initial glucose levels, parametric variations of Bergman’s model, and external disturbance, the optimal control performance are tested to show that the system can bring glucose levels quickly to the desired value regardless of high initial glucose concentrations, can efficiently work for different patients, and is robust against irregular snacks or meals.