| Summary: | Diabetes mellitus is one of the deadliest diseases affecting millions of people worldwide. Due to ethical issues, physiological restrictions and high expenses of human experimentation, mathematical modeling is a popular alternative approach in obtaining reliable information on a disease in a safe and cost effective way. In this thesis, I have developed and expanded a compartmental model of blood glucose regulation for type II diabetes mellitus based on a former detailed physiological model for healthy human subjects. The original model considers the interactions of glucose, insulin and glucagon on regulating the blood sugar. I have expanded the model by eliminating the main drawback of the original model which was its limitation on the route of glucose entrance to the body only to the intravenous glucose injection. I have added a model of glucose absorption in the gastrointestinal tract and incorporated the stimulatory hormonal effects of incretins on pancreatic insulin secretion followed by oral glucose intake. The parameters of the expanded model are estimated and the results of the model are validated using available clinical data sets taken from diabetic and healthy subjects. The estimation of model parameters is accomplished through solving nonlinear optimization problems. To obtain more information about the medical status of the subjects, I have designed some in silico tests based on the existing clinical tests, applied them to the model, and analyzed the model results. To accommodate model uncertainties and measurement noises, noise effects are included into the states and outputs of the model and a filtering method called particle filters is employed to estimate the hidden states of the model. The estimated model states are used to calculate the glucose metabolic rates which in turn provide more information about the medical condition of the patients. Another contribution of the type II diabetes model is developing a pharmacokinetic-pharmacodynamic model to study pharmaceutic impact of different medications on diabetes treatment. A preliminary study on metformin treatment on diabetic patients is performed using the developed type II diabetes model.
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