A 2D mathematical model for tumor angiogenesis: The roles of certain cells in the extra cellular matrix

Abstract

We present a 2D mathematical model of tumor angiogenesis which is an extension of the 1D model originally presented in Levine et al. (2000) [1]. Our model is connected to that 1D model by some transmission and boundary conditions which carry certain cells, the endothelials, pericytes and macrophages from the vessel wall into the extra cellular matrix. In our extended model we also include a mechanism for the action of anti-angiogenic factors such as angiostatin. We present numerical simulations in which we obtain a very good "qualitative agreement" with the time of the onset of vascularization of tumors and with the fact that the capillary tip growth accelerates as it approaches the "tumor".

Keywords: Capillary formation; Mathematical modeling; Numerical solution; Tumor angiogenesis.