Optimal Regulation of Blood Glucose Level in Type I Diabetes using Insulin and Glucagon

TL;DR

This paper develops an optimal control framework for regulating blood glucose in Type I diabetes using insulin alone or combined with glucagon, demonstrating improved regulation with dual therapy over monotherapy.

Contribution

It introduces a nonlinear optimal control approach for dual hormone therapy, showing its advantages over standard insulin-only methods.

Findings

Dual therapy better maintains glucose levels than insulin alone.

Optimal control solutions align with existing insulin timing strategies.

Proposes an ad-hoc dosage and timing rule for hormone delivery.

Abstract

The Glucose-Insulin-Glucagon nonlinear model [1-4] accurately describes how the body responds to exogenously supplied insulin and glucagon in patients affected by Type I diabetes. Based on this model, we design infusion rates of either insulin (monotherapy) or insulin and glucagon (dual therapy) that can optimally maintain the blood glucose level within desired limits after consumption of a meal and prevent the onset of both hypoglycemia and hyperglycemia. This problem is formulated as a nonlinear optimal control problem, which we solve using the numerical optimal control package PSOPT. Interestingly, in the case of monotherapy, we find the optimal solution is close to the standard method of insulin based glucose regulation, which is to assume a variable amount of insulin half an hour before each meal. We also find that the optimal dual therapy (that uses both insulin and glucagon) is better able to regulate glucose as compared to using insulin alone. We also propose an ad-hoc rule for both the dosage and the time of delivery of insulin and glucagon.