Stochastic modeling of tumor induced angiogenesis in a heterogeneous medium, the extracellular matrix

Angiogenesis, the formation of blood vessels, is a process whereby capillary sprout are formed in response to external stimuli. We model the tumor induced angiogenesis on keys events such of migratory response of endothelial cells to tumor angiogenic factors and the local cell interaction with the extracellular matrix (ECM). We consider the ECM medium as a statistically inhomogeneous two-phase random medium. Numerical simulations of the model are presented. Using this model, we will compare the influence of ECM distribution on vascular network formation. By developing mathematical models of angiogenesis, we hope to provide a deeper insight into the mechanisms underlying angiogenesis.