On the prediction of glucose concentration under intra-patient variability in type 1 diabetes: A monotone systems approach

Abstract Insulin therapy in type 1 diabetes aims to mimic the pattern of endogenous insulin secretion found in healthy subjects. Glucose–insulin models are widely used in the development of new predictive control strategies in order to maintain the plasma glucose concentration within a narrow range, avoiding the risks of high or low levels of glucose in the blood. However, due to the high variability of this biological process, the exact values of the model parameters are unknown, but they can be bounded by intervals. In this work, the computation of tight glucose concentration bounds under parametric uncertainty for the development of robust prediction tools is addressed. A monotonicity analysis of the model states and parameters is performed. An analysis of critical points, state transformations and application of differential inequalities are proposed to deal with non-monotone parameters. In contrast to current methods, the guaranteed simulations for the glucose–insulin model are carried out by considering uncertainty in all the parameters and initial conditions. Furthermore, no time-discretisation is required, which helps to reduce the computational time significantly. As a result, we are able to compute a tight glucose envelope that bounds all the possible patient's glycemic responses with low computational effort.