A Numerical Simulation of Tumor Angiogenesis

A mathematical model of tumor angiogenesis, regulated by vascular endothelial growth factor (VEGF) and angiopoietins (Ang-1, Ang-2), is presented. The Overture numerical simulation of this model is developed, and the result analysis shows the characteristics of the density changing of endothelial cells, vascular endothelial growth factor and angiopoietins in the extra-cellular matrix in tumor angiogenesis. There is a discussion of the simulation results of the model under four different situations, which shows the different roles of VEGF, Ang-1, Ang-2 and their relationship in tumor angiogenesis.