Cell directional persistence [corrected] and chemotaxis in vascular morphogenesis

In vertebrates, supply of oxygen and nutrients to tissues is carried out by the blood vascular system through capillary networks. Capillary patterns are closely mimicked by endothelial cells cultured on Matrigel, a preparation of basement membrane proteins. On the Matrigel surface, single randomly dispersed endothelial cells self-organize into vascular networks. The network is characterized by a typical length scale, which is independent of the initial mean density of deposed cells n over a wide range of values of n. We give here a detailed description of a mathematical model of the process which is able to reproduce several qualitative and quantitative features of in vitro vascularization experiments. Cell matter is basically modelled as an elastic fluid subjected to a specific force field depending on the concentration of a chemoattractant factor. Starting from sparse initial data, mimicking the initial conditions realized in laboratory experiments, numerical solutions reproduce characteristic network structures, similar to observed ones, whose average size is theoretically related to the finite range of chemoattractant diffusion. A possible area of application of the model is the design of properly vascularized artificial tissues.