Towards a reduced model for angiogenesis: A hybrid approach

In this communication, we introduce a new mathematical model for the angiogenesis by endothelial cells. The setup is initially formulated from the perspective of partial differential equations. In this context, we describe the spatiotemporal evolution of the cell population, the extracellular matrix macromolecules, the proteases, the tumor angiogenic factors, and the possible presence of inhibitors. However, we also present a complementary (and, in fact, more physiologically realistic) hybrid viewpoint in which the cells are treated as individual particles. As a test-bed towards the more realistic two-dimensional case, here we showcase the setup and the model in the simpler, spatially one-dimensional situation.