Exploring Equilibrium Points in a Long-term Glucose-insulin Model for Type I Diabetes: MPC Application in Automated Insulin Delivery Systems Using Functional Insulin Therapy Tools

Abstract:

This study explores a novel approach to regulate blood glucose levels in individuals with type I diabetes, employing the widely used model predictive control (MPC) strategy in type 1 diabetes mellitus therapy and clinical trials. The MPC algorithm is implemented based on Magdelaine’s long-term glucose-insulin model, which encompasses real-life characteristics often absent in other prevalent models. The control strategy is evaluated through simulations involving 10 virtual patients from existing literature. The simulations encompass fasting scenarios and a closed-loop control scenario involving three meals. MPC results are compared to those of the “optimal” conventional insulin daily injections therapy (open-loop treatment), especially under “aggressive conditions” including elevated initial blood glucose levels, substantial carbohydrate intake, closely spaced meal times, and incorporating a time delay between plasma glucose concentration and its subcutaneous measurement. The MPC algorithm demonstrated remarkable efficacy in glycemic control for 80% of patients, achieving an average time-in-range percentage exceeding 80% with no hypoglycemic episodes. This aligns with the American Diabetes Association’s recommendation of spending at least 70% of the time in the target range for effective glycemic control and maintaining an average time spent in hypoglycemia of less than 4%. However, the same MPC controller exhibited suboptimal performance for two patients, with an average time spent in hypoglycemia exceeding 8%. These findings underscore the need for individualized adjustments of MPC parameters or alternative control strategies to optimize glycemic management in all patients.

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