Mathematical analysis and optimal control of cancer radiotherapy

Felix Afegnui Azenui, Fayetteville State University

Abstract

The pathophysiology of cancer radiotherapy was analyzed using the principles of Pontryagin's Optimal Control Theory and the methodology of non-linear systems analysis.^ The dynamics of the cancer cells and normal cells in the cancer-bearing anatomic organ were modeled by a system of nonlinear ordinary differential equations. In particular the modulating effects of intracellular glutathione (GSH), Buthionine Sulfoxide BSO, and Misonidazole (MTSO) were incorporated using clinically plausible interaction functions. The nonlinear model equations were linearized using Hartman-Grobman Theory and the stability analysis utilized Dynamic Systems Theory.^ The Optimal Protocol for Radiotherapy was derived using Pontryagin's Optimality Principles. The investigative computer simulations were executed using clinically plausible patient parametric configurations. The findings clearly delineate criteria for cancer persistence and destruction for various cancer-patient pathological scenarios. There are no universally effective strategies that prevent ultimate progression of cancer, in spite of all research efforts. Mathematical models are used as a powerful tool in the quest for optimal therapy administration.^

Subject Area

Applied Mathematics|Health Sciences, Radiology|Health Sciences, Oncology

Recommended Citation

Azenui, Felix Afegnui, "Mathematical analysis and optimal control of cancer radiotherapy" (2012). ETD Collection for Fayetteville State University. AAI1525803.
http://digitalcommons.uncfsu.edu/dissertations/AAI1525803

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