Implications and Limitations of Ideal Insulin Administration for People with Type 1 Diabetes

In this paper we use open-loop constrained non-linear optimal control to compute insulin administration profiles for people with type 1 diabetes. The algorithm is a multiple shooting algorithm based on sequential quadratic programming (SQP) for optimisation and an explicit Dormand-Prince Runge-Kutta method (DOPRI54) for numerical integration and sensitivity computation. We describe the numerical details of the constrained non-linear optimal control algorithm. The Hovorka model is used to describe a person with type 1 diabetes. We use the model and the algorithm to compute insulin administration profiles for people with type 1 diabetes in the cases with and without meal announcement in advance. The case with advance meal announcement results in almost perfect glucose control, but is undesirable as an insulin therapy due to the fact that most of the meal-related insulin is injected before the meal is actually taken. In the second, more realistic case, information about the meal is provided to the controller as the meal is taken. In this case, the optimal insulin administration profile is characterised by bolus-like injections of insulin coincident with the meals. These results indicate that, for certain conditions, insulin pens may be able to provide glucose control comparable to that of insulin pumps.