Date of Award

May 2023

Degree Type

Thesis

Degree Name

Master of Science

Department

Mathematics

First Advisor

Gabriella Pinter

Committee Members

Jeb Willenbring, Lijing Sun

Abstract

Primary brain tumors pose a serious threat to a person’s health. Gaining a deeper understanding of the dynamics of tumor growth is crucial for developing a proper treatment plan. Many computational models have been suggested to investigate the interaction between tumor cells and their surroundings. Using cellular automata is particularly promising since it integrates the features of self-organizing complex systems which allows them to properly depict local interactions between cells. The foundation of the thesis lies in the model proposed by Kansal et al. It uses four microscopic parameters, the maximum tumor extent, the base proliferative and necrotic thickness as well as the base probability of division. Based on literature review, this model has been extended through additional parameters, namely, angiogenesis (a process that forms new blood vessels), the extracellular matrix (which provides support and structure to the tumor), as well as an additional oxygen and nutrient coefficient. The result is a comprehensive model that predicts tumor growth patterns. Furthermore, the implementation of this model allows for the incorporation of additional parameters, making it possible to consider even more complex models in the future.

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