Optimal Regulation of Blood Glucose Level in Type I Diabetes using Insulin and Glucagon
For Type I diabetes patients, this work provides a computational framework to optimize insulin and glucagon delivery, though it is an incremental application of existing optimal control methods to a known model.
This paper formulates and solves an optimal control problem for regulating blood glucose in Type I diabetes using insulin alone or combined with glucagon, finding that dual therapy outperforms monotherapy and that the optimal monotherapy solution resembles standard clinical practice.
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.