Robustness Properties of Optimal Insulin Bolus Administrations for Type 1 Diabetes

Type 1 diabetic patients compensate the lack of endogenous insulin by basal delivery and bolus injections at meal-times. Exact dosage of the bolus amount is critical to keep the blood glucose both below the maximum limits and above the hypoglycaemia critical values. Determination of the optimal dosage would require information which in general is not available to the patient, who uses empirical rules of thumb to choose the dosage. Closed loop control is often viewed as a way to improve diabetes therapy, but the majority of publications is concerned with continuous blood glucose measurements and insulin delivery by pumps, even though the vast majority of patients uses single strip measurements and bolus insulin administration. This paper is concerned with this class of patients and is based on the use of model predictive techniques extended to approximate continuous control output signals by single control moves in time. The paper shows that substituting continuous measurement and insulin delivery with discrete values leads to a suboptimal control performance, but that this decrease is not essential if compared with estimation errors of model parameters, patient inputs and/or measurements. Furthermore, the approach proposed shows in simulation sufficient robustness margins. Computations are done with an extended Bergman model tuned on available data of type 1 diabetic patients.