Optimal model-based insulin dosing strategy with offline and online optimization

Abstract

This paper presents the design of a model-based bolus calculator algorithm aimed at optimizing insulin therapy for patients with type 1 diabetes. The proposed concept functions as an advisory system to assist in decision-making regarding insulin administration. In contrast to traditional artificial pancreas systems based on model predictive control, which involve continuous insulin dosing and rely on frequent feedback from continuous glucose monitoring, the proposed bolus calculator processes sporadic, impulse-like inputs without requiring regularly sampled glycemia feedback. This design prioritizes simplicity and practicality for eventual clinical use. The bolus calculator is fundamentally based on the principles of mathematical modeling, prediction, and optimization. The primary objective is to minimize deviations in glycemic response from the basal glucose level by adjusting both the insulin bolus size and its timing. Mathematically, this problem can be formulated as a bivariate, mixed real-integer optimization problem. The optimal insulin bolus size was derived in closed form, reducing the problem to a univariate, constrained integer optimization focused on determining the administration time. Two variants of the bolus calculator are distinguished: the offline variant, which provides general, personalized recommendations applicable to any situation regardless of the patient’s current state, and the online variant, which offers tailored advice for each disturbance event. The online variant accounts for previously administered insulin, prior carbohydrate intake, and, when available, preprandial finger-stick glucose measurements. To mitigate the risk of hypoglycemia, additional constraints are imposed on the predicted glycemic trajectory, ensuring the recommended insulin bolus does not induce hypoglycemia. The proposed strategy was validated through simulation-based experiments and compared to ideal bolus treatment and model predictive control strategies.

Keywords

• Diabetes mellitus
• Insulin treatment
• Bolus calculator
• Optimization
• Model-based design
• Advisory system