Date of Award

Spring 2011

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics and Statistics

Program/Concentration

Computational and Applied Mathematics

Committee Director

John A. Adam

Committee Member

D, Glenn Lasseigne

Committee Member

Hideaki Kaneko

Committee Member

Gordon Melrose

Committee Member

Holly Gaff

Abstract

The American Diabetes Association reports that diabetes is the fifth leading cause of death by disease in the United States. An estimated 23.6 million individuals, or seven percent of the population, have diabetes. Nearly one-third are unaware that they have the disease. The total of the direct and indirect medical costs associated with diabetes in 2007 was projected to be $174 billion, or approximately one out of every ten health care dollars.

One must understand the glucose regulatory system of the healthy body to understand diabetes. Blood glucose concentration returns to a constant level after eating and is maintained during exercise. With thousands of chemical reactions involved in the process, a complete mathematical model is not yet realistic. Proposed here is the evolution of a model beginning with a three-variable model of glucose, insulin, and glucagon and ending with its extension to the four-variable model incorporating the additional interdependent mechanics of hepatic glycogen. The three-variable model mimics the return of blood glucose levels to a constant, or basal, state; however, this model is consistent only with short-term dynamics since it excludes consideration of finite energy stores. Thus, the extension includes the effects of a finite store of hepatic glycogen. The solution of the four-variable model demonstrates the short-term return of glucose concentration to near basal levels despite the constant energy usage which draws upon the glycogen stores. Long-term glucose homeostasis is explained by investigating the storage of a glucose load in the postprandial period and dispersion of stored glucose during the extended postprandial period.

Increased hepatic glucose production in people with diabetes is thought to be the driving mechanism for increased basal glucose levels. Analysis of this model indicates the genesis of this phenomenon. Elevated prandial glucose and insulin levels associated with insulin resistance increase the glycogen-storage levels above normal which then increase hepatic glucose production in the postprandial period. Increased energy input exasperates this problem, but only in insulin resistant individuals. This simple model suggests that Type II diabetes results from insulin resistance more than from overeating.

DOI

10.25777/5tvx-td93

ISBN

9781124664002

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