Topology of the heterogeneous nature of the extracellular matrix on stochastic modeling of tumor-induced angiogenesis.

We have modeled tumor-induced angiogenesis; our model includes the phenomena of the migratory response of endothelial cells (ECs) to tumor angiogenic factors, and the interaction of ECs with the extracellular matrix (ECM). ECs switch between growth, differentiation, motility, or apoptotic behavior in response to the local topology and composition of the ECM. Assuming the ECM medium as a statistically inhomogeneous medium (some area support sprout growth, some not), we show that the ECM can be a natural barrier to angiogenesis. We study vascular network formation for several ECM distributions and topologies, and we find an analogy with percolation. A threshold exists, under which sprouts cannot reach the tumor. During the growth of the vascular network, a competition exists between the attraction exerted by tumor and the preferred path created by the ECM. We also examined the influence of branching on the tumor vascularization. Branching is a natural phenomenon which helps the tumor become vascularized. By increasing the number of sprouts, the vascular network increases the probability of reaching the tumor, as it can explore more pathways. Our simulations show after two branching events, the vascular network is very likely to reach the tumor.