Optimal Meal Time after Bolusing for Type 1 Diabetes Patients under Meal Uncertainties
Nandi, S., Singh, T., Singla, P., and Mastrandrea, L.
2017 American Control Conference, May 24-May 26, Seattle, Washington.
The focus of this paper is on the characterization of the uncertainties in the evolving states of a diabetic model, to permit a study of the impact of the time interval between insulin bolusing and meal initiation on hypo- and hyperglycemic events. A polynomial chaos based approach is used to characterize the independent uncertainties in the initial condition and meal size. Galerkin projection of the resulting equations reduce the stochastic differential equations to a set of deterministic equations. This forms the framework to optimize for the post bolusing time to initiate the meal. Two cost functions are considered which correspond to the postprandial hypoand hyperglycemic excursions of the blood glucose. Numerical results from the minimal Bergman model suggest a 13 and 14 minute interval between bolusing and the initiation of the meal.