Introducing carbohydrates suggestions and corrective boluses administrations in Artificial Pancreas by Model Predictive Control

Type 1 diabetes (T1D) is characterized by the absence of insulin production and thus by an impaired glycaemia control. T1D therapy consists in providing insulin to the patient, aiming to maintain the blood glucose level in euglycaemia (i.e., between 70 and 180 mg/dl), counteracting hyperglycaemia, but without incurring in hypoglycaemic events, which can lead to severe consequences in the short term. This is not trivial, due to disturbing factors and given the pharmacokinetics and pharmacodynamics of exogenous insulin. The Artificial Pancreas (AP) is a new technology for the automation and the optimization of basal insulin administration, which works by a closed-loop algorithm that controls the functioning of an insulin pump, basing on the measurements provided by a glucose sensor. The objective of this work is to improve the quality of glycaemia control, by adding in AP the possibility to suggest carbohydrates assumptions and the administration of corrective insulin boluses, by using the Model Predictive Control (MPC) algorithm. The idea is to strengthen the counteraction of hypo- and hyperglycaemia, respectively. To model the quantity of CHO to be suggested and the capability of the algorithm to choose whether to deliver a bolus or not, a series of Boolean support variables is needed and has to be included in the control problem. Therefore, our approach involves the resolution of a Mixed Integer Quadratic Programming (MIQP) problem, which the MPC’s control problem can be reformulated as. To evaluate the performances of the resultant system (the triple-action MPC AP), we resort to the UVa/Padova T1D Simulator®, an accurate model of a T1D patient's metabolism, which was accepted by the U.S. FDA (Food and Drug Administration) as a substitute of animal trials for preclinical testing of T1D therapies, and is integrated with a population of realistic virtual subjects to perform the trials on. We compare our approach with a state-of-the-art strategy (the single-action MPC AP), which only manages the basal insulin delivery, and an advanced technique (the dual-action MPC AP), which, in addition, can suggest carbohydrates intakes. The results show how the triple-action MPC AP outperforms both the single-action- and the dual-action MPC AP, with an increment of the average time in euglycaemia of more than 9% and almost 3%, respectively, with the optimal parametrization. Adopting a suboptimal tuning, inferred by using hyperparameters’ regression models, our approach still outperforms the single-action technique, with an increase of the time in euglycaemia of almost 5%, and shows slightly better performances with respect to the dual-action MPC AP, as well.