Mathematical modeling for meshwork formation of endothelial cells in fibrin gels.

Vasculogenesis is the earliest process in development for spontaneous formation of a primitive capillary network from endothelial progenitor cells. When human umbilical vein endothelial cells (HUVECs) are cultured on Matrigel, they spontaneously form a network structure which is widely used as an in vitro model of vasculogenesis. Previous studies indicated that chemotaxis or gel deformation was involved in spontaneous pattern formation. In our study, we analyzed the mechanism of vascular pattern formation using a different system, meshwork formation by HUVECs embedded in fibrin gels. Unlike the others, this experimental system resulted in a perfusable endothelial network in vitro. We quantitatively observed the dynamics of endothelial cell protrusion and developed a mathematical model for one-dimensional dynamics. We then extended the one-dimensional model to two-dimensions. The model showed that random searching by endothelial cells was sufficient to generate the observed network structure in fibrin gels.