Date of Award

Spring 1998

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics and Statistics

Program/Concentration

Computational and Applied Mathematics

Committee Director

John Adam

Committee Member

D. Glenn Lasseigne

Committee Member

Richard Noren

Committee Member

Roger Perry

Abstract

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 the effects of immersing a tumor into a nutrient bath. Similarly, this model could represent the addition of nutrient to the tissue surrounding a spherical tumor.

In this paper, we model several problems associated with the clinical observations noted above, and draw conclusions based on the obtained results.

DOI

10.25777/vq14-9425

ISBN

9780591815719

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