Angiogenesis is a complex process where biological signals, such as the activation of signaling pathways by the binding of VEGF to its receptors at the cell membrane, are converted into mechanical forces originating cell movement. The endothelial cells then reorganize spatially into tubular structures that are able support the flow of blood and that respond to blood pressure and shear stress by altering their number, shape and size. Therefore, a mathematical description of sprouting angiogenesis has to take into consideration biological signals as well as relevant physical processes. We model sprouting events in angiogenesis using a continuum model that takes into account the tissue elasticity and the forces exerted by the cells in the sprout. We demonstrate that the endothelial cell proliferation has to be regulated by the local mechanical stress for a well-formed vascular sprout. The force exerted at the tip cell induces an increase in the stress, which determines the locations with higher endothelial cell proliferation. The model also permits a new look into how anastomosis events are controlled by the local tissue displacements. Our results highlight the ability of mathematical models to suggest relevant hypotheses with respect to the role of forces in sprouting, hence underlining the necessary collaboration between modeling and molecular biology techniques to improve the current state-of-the-art.

angiogenesis; elasticity;