A Mathematical Modeling of Angiogenesis

Abstract

Abstract. We investigate a simple mathematical model for angiogenesis. From recent time-lapse imaging experiments on the dynamics of endothelial cells (ECs) in angiogenesis, we suppose that elongation and bifurcation of neogenetic vessel is determined by only the density of ECs near the tip, and introduce a model described by nonlinear simultaneous differential equations. We also incorporate proliferation of ECs and activation factor such as VEGF and show the exact solutions to that model and numerical simulations.