A model of angiogenesis during tumor growth

Angiogenesis is the process by which new blood vessels form from preexisting ones. This is crucial in tumor growth, linking the phases of avascular growth, which is usually harmless, to vascular growth. which can be potentially fatal. We analyze a simple angiogenesis model that incorporates the most important aspects that give rise to capillary sprouts that emerge from a blood vessel as a result of endothelial cells migration in response to chemotactic stimuli produced by angiogenic factors and the haptotactic interaction between endothelial cells and fibronectin found in the extracellular matrix. The angiogenic process is modeled by analyzing the spatio-temporal dynamics described by a system of reaction-difussion equations. The evolution was studied from two geometric perspectives: (i) a tumor line, which represents large tumors, and (ii) a small tumor with a radius of ∼1mm. We also showed that chemotaxis and haptotaxis in the cell migration process must be present to reasonably describe the angiogenesis process.