Modelling Type 1 Diabetes Mellitus Blood Glucose Dynamics as a Monotone System

In this presentation, we study an FDA-approved Type 1 diabetes mellitus (T1DM) blood glucose dynamics simulator used in the majority of the practical studies on Artificial Pancreas (AP). We show that under some physiologically plausible assumptions, the glucoregulatory system described by the model is monotone. This means that the system generates trajectories which are monotone with respect to specific changes in initial conditions and control signals. This strong property leads to many interesting observations. By using monotonicity, for example, it becomes straightforward to compute bounds on glucose concentration subject to variations in intake of carbohydrates and insulin injections. Monotonicity also rigorously justifies recent studies on fundamental limitations in glucose control.