Date of Award

Spring 1-1-2014

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Applied Mathematics

First Advisor

David M. Bortz

Second Advisor

Vanja Dukic

Third Advisor

Sriram Sankaranarayanan

Abstract

Diabetes cases worldwide have risen steadily over the past decades, lending urgency to the search for more efficient, effective, and personalized ways to treat the disease. Current treatment strategies, however, may fail to maintain ultradian oscillations in blood glucose concentration, an important element of a healthy alimentary system. Building upon recent successes in mathematical modeling of the human glucose insulin system, we show that both food intake and insulin therapy likely demand increasingly precise control over insulin sensitivity if oscillations at a healthy average glucose concentration are to be maintained. We then suggest guidelines and personalized treatment options for diabetic patients that maintain these oscillations. To do so, we develop a closed form criterion to indicate the presence of blood glucose oscillations in our model. We show that for a type II diabetic, both blood glucose levels can be controlled and healthy oscillations maintained when the patient gets an hour of daily exercise and is placed on a combination of Metformin and sulfonylurea drugs. We note that insulin therapy and an additional hour of exercise will reduce the patient's need for sulfonylureas. Results of a modeling analysis suggest that a typical type I diabetic's blood glucose levels can be properly controlled with a constant insulin infusion between 0.45 and 0.7 microUnits/ (ml*min). Lastly, we note that all suggested strategies rely on existing clinical techniques and established treatment measures, and so could potentially be of immediate use in the design of an artificial pancreas.

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