Friis-Jensen, Esben. 2007. Modeling and Simulation of Glucose-Insulin Metabolism. B. Sc. Thesis. 124 pp.
Abstract: Diabetes is a widespread disease in the western world today. Many researchers are working on methods for diagnosing and treating diabetes. A tool used for this is mathematical models of the blood glucose and insulin kinetics.
In this thesis one of the models, Bergman’s minimal model is described trough derivation and simulations. It is a model consisting of a glucose and an insulin kinetics part. The part, describing glucose kinetics has the problem that it overestimates glucose effectiveness SG and underestimates insulin sensitivity SI, which is interpretation parameters of a test called the IVGTT (Intravenous Glucose Tolerance Test).
Modifications and additions which could be done in order to describe the glucose and insulin kinetics more thoroughly is described. Based on Bergman’s minimal model, two coupled models are proposed. A coupling between the two basic parts of Bergman minimal model and a coupling between the two modified parts of Bergman’s minimal model. The basic coupling is called the original model. It can be used to describe the IVGTT for a healthy and a glucose resistant subject. Through calculation and simulation it is shown that the original model has a equilibrium problem, when a parameter p5 is less than the basal concentration Gb.
The modified coupling, which is able to describe the glucose-insulin system for a type 1 diabetic on treatment is tested for reactions to insulin injections and change in basal insulin production. A PID controller, controlling insulin delivery is implemented, and it is shown how it can be used with the modified model, in order to test it for meal disturbance.
The final conclusion of the thesis is that both coupled models have problems, but they can be used to approximately simulate the blood glucose-insulin system, if you are aware where the problems occur.
Keywords: differential equations, model, glucose, insulin, intolerance, metabolism
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