Author Type

Graduate Student

Date of Award

2016

Document Type

Thesis

Publication Status

Version of Record

Submission Date

October 2026

Thesis/Dissertation Advisor [Chair]

Kalantzis, Georgios

Abstract

The purpose of this research is to validate various forms of mathematical modeling of glioblastoma multiforme (GBM) expressed as differential equations, numerically. The first work was involved in the numerical solution of the reaction-convection model, efficacy of which is expressed in terms of survival time. It was calculated using simple numerical scheme for the standard-of-care treatment in clinics which includes surgery followed by the radiation and chemotherapy. Survival time using all treatment options increased significantly to 57 weeks compared to that of surgery close to 14 weeks. It was also observed that survival time increased significantly to 90 weeks if tumor is totally resected. In reaction-diffusion model using simple numerical scheme, tumor cell density patterns due to variation in patient specific tumor parameters such as net proliferation rate and diffusion coefficient were computed. Significant differences were observed in the patterns while using dominant diffusion and proliferation rate separately. Numerical solution of the tumor growth model under the anti-angiogenic therapy revealed some impacts in optimum tumor growth control however it was not significant.

Extent

96 p.

Comments

Includes bibliography.|Thesis (M.S.)--Florida Atlantic University, 2016.|FAU Electronic Theses and Dissertations Collection|Includes bibliography.

Identifier

FA00004703

Format

pdf

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