Simulations of Endothelial Cells Clusters Migration in Angiogenesis

Abstract

Tumor angiogenesis is the process that a capillary network is formed from a pre-existing vasculature in response to chemical stimuli (tumor angiogenic factors, TAF) secreted by a solid tumor. In order to supply a growing tissue such as a solid tumor with nutrients and oxygen, the formation of the capillary network (angiogenesis) are gradually growing towards the tumor by using the migration of endothelial cells driven by chemical stimuli gradient. In this study, a continuous and discrete mathematical model are considered to examine the migration of Endothelial Cells (ECs) and the formation of vessel capillary in response to chemical stimuli concentration gradient supplied by a solid tumor, respectively. Moreover, this study is also further to investigate the effects of a series of initial ECs clusters number releasing from parent vessel on ECs migration images, ECs density distribution and their patterns of capillary network when ECs migrate across the considered domain toward the tumor. In contrast to the present study, the effect of a series of initial ECs clusters number releasing from parent vessel on angiogenesis was not addressed in previous reports of others.