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Two Dimensional Models Of Tumor Angiogenesis , Serdal Pamuk Jan 2000

Two Dimensional Models Of Tumor Angiogenesis , Serdal Pamuk

Retrospective Theses and Dissertations

Angiogenesis, the formation of new capillaries from pre-existing vessels, is essential for tumor progression. It is critical for the growth of primary cancers. In this thesis we present a new approach to angiogenesis, based on the theory of reinforced random walks, coupled with a Michaelis-Menten type mechanism. This views the endothelial cell receptors as the catalyst for transforming angiogenic factor into proteolytic enzyme in order to model the first stage. In our model we use a curvature-induced proliferation term for the endothelial cell equation. Our numerical results indicate that the proliferation of endothelial cells is high at the tip. Also ...