The formation of a functional vascular network depends on biological, chemical, and physical processes being extremely well coordinated. Among them, the mechanical properties of the extracellular matrix and cell adhesion are fundamental to achieve a functional network of endothelial cells, able to fully cover a required domain. By the use of a Cellular Potts Model and Finite Element Method it is shown that there exists a range of values of endothelial traction forces, cell-cell adhesion, and matrix rigidities where the network can spontaneously be formed, and its properties are characterized. We obtain the analytical relation that the minimum traction force required for cell network formation must obey. This minimum value for the traction force is approximately independent on the considered cell number and cell-cell adhesion. We quantify how these two parameters influence the morphology of the resulting networks (size and number of meshes).

• Received 25 August 2017
• Revised 11 December 2017

DOI:https://doi.org/10.1103/PhysRevE.97.012408