Monotonicity-based guaranteed prediction for glucose control and supervision under intra-patient variability

The prediction of blood glucose for therapy optimization in type 1 diabetes has proved to be a difficult challenge. A main limitation is the presence of large intra-patient variability and hence, model uncertainty, which may jeopardize model individualization, both for data-based and physiological models. Interval models provide a natural framework to represent intra-patient variability in the form of interval parameters. Recent results have shown their potential in the context of glucose control, hypoglycemia risk prediction and fault detection. Interval-model-based methods rely on the prediction of envelopes containing all the possible glycemic responses according to the patient´s characterized intra-patient variability. Monotone systems theory has been successfully used for this purpose. Exact or tight glucose envelopes can be computed with mathematical guarantee and computational efficiency. A review of these methods is presented here with special focus on techniques to overcome the lack of monotonicity. The methods are illustrated with examples of different literature glucose-insulin models.