A differential equation model is formulated that describes the dynamics of glucose concentration in blood circulation. The model accounts for the intake of food, expenditure of calories and the control of glucose levels by insulin and glucagon. These and other hormones affect the blood glucose level in various ways. In this study only main effects are taken into consideration. Moreover, by making a quasi-steady state approximation the model is reduced to a single nonlinear differential equation of which parameters are fit to data from healthy subjects. Feedback provided by insulin plays a key role in the control of the blood glucose level. Reduced β-cell function and insulin resistance may hamper this process. With the present model it is shown how by closed-loop control these defects, in an organic way, can be compensated with continuous infusion of exogenous insulin.
Biomathematics; Mathematical models; Differential equations; Blood sugar
Citation: Pilot Scholars Version (Modified MLA Style)
Grasman, Johan; Callender, Hannah L.; and Mensink, Marco, "Proportional Insulin Infusion in Closed-Loop Control of Blood Glucose" (2017). Mathematics Faculty Publications and Presentations. 14.