Optimal regulation of blood glucose level in Type I diabetes using insulin and glucagon

Abstract

The Glucose-Insulin-Glucagon nonlinear model 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 . 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.

Data-driven optimized control of the COVID-19 epidemics

“…Following previous work by the authors 42 , 43 , we use pseudo-spectral optimal control (see Supplementary Note 7 ) to compute solutions for the problem formulated in Eqs. ( 2 ), ( 4 ), ( 5 ), ( 6 ).…”

“…In addition, we did not account for the cost associated with medical treatments, which is important yet significantly smaller than the cost of shutting down the economical activities of the entire society 10 . Our approach can be easily generalized to other more complex, more realistic types of objective functions, see e.g., 42 , 43 . Different from this study, these objective functions may also be specific to given regions or try to capture a particular socio-economical model of interest.…”

Data-driven Optimized Control of the COVID-19 Epidemics

“…Following previous work by the authors [40, 39], we use pseudo-spectral optimal control (see Supplementary Note 7) to compute solutions for the problem formulated in Eqs. (2),(4),(5),(6).…”

Mathematical Model of Glucagon Kinetics for the Assessment of Insulin-Mediated Glucagon Inhibition During an Oral Glucose Tolerance Test

“…As previously outlined, some mathematical models were developed with the aim to investigate glucagon secretion at cellular level (12)(13)(14)(15)(16)(17)(18)(19)(20)(21), whereas other models, more similarly to ours, were developed for whole-body analyses, but mainly for simulation purposes rather than for clinical applications (22)(23)(24)(25). Other studies presented models of glucagon kinetics for possible clinical applications, but they were focused on the analysis of glucagon administered exogenously, or for the analysis of the not common glucagon challenge test (26)(27)(28)(29). The study having more aspects in common with ours is that of Kelly et al (30).…”