Hybrid control of type 1 diabetes bolus therapy

The probably best treatment of type 1 diabetes mellitus (T1DM) would be an artificial pancreas (AP). Unfortunately, AP is still not available as AP requires continuous glucose measurements and continuous insulin delivery systems which are not available. The vast majority of patients do not use any of them but instead resort to a few irregularly sampled measurements and single insulin administrations (`insulin bolus´). Choosing time and quantity of a bolus delivery is critical for the health of T1DM patients, and ideally this should be done on basis of a model. While good physiological models for populations exist, in general they can hardly be tuned to specific patients and are therefore not very useful for bolus choice. Against this background, this paper proposes to see the issue of model based bolus choice in a hybrid framework in which the continuous time meal and insulin model is replaced by a discrete parameterization which associates to each meal and bolus a function of given, patient specific shape whose amplitude depends on the respective amounts. This allows restating the standard model predictive control of the AP design by a line search method.