Optimal model-based insulin bolus advisor for subjects with type 1 diabetes using continuous glucose monitoring

This paper presents an optimal model-based bolus advisor aimed at improving insulin therapy for individuals with type 1 diabetes who actively utilize continuous glucose monitoring systems. The proposed approach serves as an advanced advisory system, facilitating decision-making for insulin administration. Unlike traditional artificial pancreas systems, which rely on continuous insulin delivery and equidistant control decisions at each sampling interval, this bolus advisor considers sparse and impulse-like insulin administration without the basal component, solely disturbance-triggered to optimally reject the carbohydrate intake. This bolus advisor generates personalized recommendations for the timing and dosage of insulin administration, informed by real-time glycemia measurements. The methodology considers a linear discrete-time state space model and an optimization problem based on a quadratic summation criterion to minimize the area of deviation of the preprandial-postprandial glycemia response from the target glycemia response. It can be seen as a constrained bivariate optimization problem with real-valued and integer decision variables. The proposed algorithm for constrained optimization is based on sequential quadratic interpolation and Karush-Kuhn-Tucker conditions, with the solution obtained by Newton's method. In order to take into account the past input activity and the glycemia measurements, the state of the system is estimated by the Kalman filter and involved in the problem formulation, providing feedback from the subject. The effectiveness of the proposed bolus advisor is validated through simulation experiments, showcasing its potential to enhance glycemic control and improve the overall management of type 1 diabetes.