Formal Verification of a Multi-Basal Insulin Infusion Control Model

Abstract

The artificial pancreas concept automates the delivery of insulin to patients with type-1 diabetes, sensing the blood glucose levels through a continuous glucose monitor (CGM) and using an insulin infusion pump to deliver insulin. Formally verifying control algorithms against physiological models of the patient is an important challenge. In this paper, we present a case study of a simple hybrid multi-basal control system that switches to different preset insulin delivery rates over various ranges of blood glucose levels. We use the DallaMan model for modeling the physiology of the patient and a hybrid automaton model of the controller. First, we reduce the problem state space and replace nonpolynomial terms by approximations with very small errors in order to simplify the model. Nevertheless, the model still remains nonlinear with up to 9 state variables. Reachability analysis on this hybrid model is used to verify that the blood glucose levels remain within a safe range overnight. This poses challenges, including (a) the model exhibits many discrete jumps in a relatively small time interval, and (b) the entire time horizon corresponding to a full night is 720 minutes, wherein the controller time period is 5 minutes. To overcome these difficulties, we propose methods to effectively handle timetriggered jumps and merge flowpipes over the same time interval. The evaluation shows that the performance can be improved with the new techniques.