Reduced hypoglycemia risk in insulin bolus therapy using asymmetric cost functions

A healthy glucose regulatory metabolism keeps blood glucose concentration in a relatively small range by producing insulin to store excessive blood glucose in the liver and other mechanisms, in particular glucagon, to release glucose from the liver into the blood if necessary. Type 1 diabetic patients do not have sufficient endogenous insulin and have to compensate its lack by external administrations. This paper is concerned with the multiple daily insulin injections (MDII) case. Insufficient insulin administration leads to high blood glucose values which cause dangerous long term effects, while excessive insulin can lead to very low glucose concentrations and, as a consequence, coma. Therefore, the control problem solved by the patient can be described in terms of a constrained optimal problem with input and state constraints, this being probably the cause of the large interest in the use of model predictive control (MPC) for this problem. Unfortunately, to respect the output constraint problem, MPC needs models, and diabetes models tend to be very imprecise. Against this background, this paper proposes to use an asymmetric cost function to replace the output constraints. A simulation study is used to assess the potential advantage in terms of sensitivity to model error and thus the hypoglycaemia risk associated to the use of MPC in this therapy.