Study On The Tumor-Induced Angiogenesis Using Mathematical Models

Abstract

We study angiogenesis using mathematical models describing the dynamics of tip cells. We review the basic ideas of angiogenesis models and its numerical simulation technique to produce realistic computer graphics images of sprouting angiogenesis. We examine the classical model of Anderson-Chaplain using fundamental concepts of mass transport and chemical reaction with ECM degradation included. Then we construct two kind of numerical schemes, model-faithful and model-driven ones, where new techniques of numerical simulation are introduced, such as the transient probability, particle velocity, and Boolean variables.

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