Optimal Responses to Constrained Bolus Inputs to Models of T1D

TL;DR

This paper characterizes the optimal bolus insulin inputs in T1D models to minimize peak plasma glucose levels without causing hypoglycemia, highlighting the limits of controllability in such systems.

Contribution

It provides a mathematical characterization of optimal insulin inputs in T1D models, considering constraints and system limitations.

Findings

Optimal bolus inputs minimize maximum plasma glucose levels.

Further reduction leads to hypoglycemia.

Limits controllability of glucose regulation systems.

Abstract

We characterise the bolus insulin input which minimises the maximum plasma glucose concentration predicted by the Magdelaine and Bergman minimal models in response to any positive bounded disturbance whilst remaining above a fixed lower plasma glucose concentration. This characterisation is in terms of the maxima and minima of the plasma glucose concentration and limits the controllability of such systems. Any further attempt to lower the maximum plasma glucose concentration will result in hypoglycaemia.