Medicine and Health Sciences Commons^™

An Extensible Mathematical Model Of Glucose Metabolism, Caleb L. Adams

Mathematics & Statistics Theses & Dissertations

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 …

Mathematical Models Of Tumors And Their Remote Metastases, Carryn Bellomo

Mathematics & Statistics Theses & Dissertations

Clinical observations and indications in the literature have led us to investigate several models of tumors. For example, it has been shown that a tumor has the ability to send out anti-growth factors, or inhibitors, to keep its remote metastases from growing. Thus, we model the depleting effect of such a growth inhibitor after the removal of the primary tumor (thus removing the source) as a function of time t and distance from the original tumor r.

It has also been shown clinically that oxygen and glucose are nutrients critical to the survival and growth of tumors. Thus, we model …

Reaction-Diffusion Models Of Cancer Dispersion, Kim Yvette Ward

Mathematics & Statistics Theses & Dissertations

The phenomenological modeling of the spatial distribution and temporal evolution of one-dimensional models of cancer dispersion are studied. The models discussed pertain primarily to the transition of a tumor from an initial neoplasm to the dormant avascular state, i.e. just prior to the vascular state, whenever that may occur. Initiating the study is the mathematical analysis of a reaction-diffusion model describing the interaction between cancer cells, normal cells and growth inhibitor. The model leads to several predictions, some of which are supported by experimental data and clinical observations $\lbrack25\rbrack$. We will examine the effects of additional terms on these characteristics. …

Mathematical Models Of Chemotherapy, John Carl Panetta

Mathematics & Statistics Theses & Dissertations

Several mathematical models are developed to describe the effects of chemotherapy on both cancerous and normal tissue. Each model is defined by either a single homogeneous equation or a system of heterogeneous equations which describe the states of the normal and/or cancer cells. Periodic terms are added to model the effects of the chemotherapy. What we obtain are regions, in parameter space (dose and period), of acceptable drug regimens.

The models take into account various aspects of chemotherapy. These include, interactions between the cancer and normal tissue, cell specific chemotherapeutic drug, the use of non-constant parameters to aid in modeling …