Numerical methods for a PDE system modeling tumor angiogenesis

Undergraduate Honors Thesis

Citations

Citeable URL: https://scholar.colorado.edu/concern/undergraduate_honors_theses/3f462699g

Abstract

This thesis is centered on the foundation needed for performing numerical simulations of a partial differential system (PDE) of reaction-diffusion equations modeling tumor growth in two dimensions. It includes the derivation of a particular PDE system modeling chemotaxis with a generalized logistic growth of the cell population density, and original results on the one-dimensional case. In particular, we show the effect of the generalized logistic growth on the population density of the organism. The second part of this thesis lays down the foundation needed to extend the numerical simulations to a two-dimensional Euclidean framework, confirming the accuracy of results through various numerical and analytical methods. The results of this work may pave the way to a deeper understanding of tumor angiogenesis over curved organ surfaces.

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