||Model Predictive Control for Insulin Administration in People with Type 1 Diabetes
||Nærum, Miriam M.N.
||Jørgensen, John Bagterp (Scientific Computing, Department of Informatics and Mathematical Modeling, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
||Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark
||People with type 1 diabetes are unable to regulate their blood glucose concentration
because they do not produce insulin. The non-linear Hovorka model
is used to simulate the responses of blood glucose concentration, when meals
are consumed and insulin is injected subcutaneously. First the theory of the
Hovorka model is presented, by describing the three parts of the model: Carbohydrate
absorption from meals, subcutaneous insulin injection and absorption,
and the gluco-regulatory system.
Then model predictive control (MPC) is described. MPC-based algorithms
attempt to regulate the blood glucose concentration by manipulating the insulin
infusion rate based on predictions of future glucose trends. MPC can use three
different prediction models: ARX, ARX, and EARX. The theory of these
models is examined. Futhermore the theory of a possible improvement of MPC,
asymmetric penalty function MPC, is derived.
The Hovorka model is used to calculate the appropriate basal insulin infusion
rate. This is the delivery rate of insulin that results in a steady-state glucose
concentration at normaglycemia, the optimal glucose concentration level. From
the calculation it is observed that the basal insulin infusion rate is linearly
dependent on the weight of the patient. Next, the Hovorka model is used to
inspect the importance of the duration of meals. It is evident that the glucose
concentrations obtained, when a meal is consumed over long and short durations,
are almost the same.
In order to obtain a realistic view of the Hovorka model, simulations are made
with meals from a typical day. First insulin boluses found with trial and error
are used, and then simulations are made using MPC.
||Technical University of Denmark (DTU) : Kgs. Lyngby, Denmark
Creation date: 2010-07-01
Update date: 2010-07-01