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A two-dimensional mathematical model for dynamics of endothelial cells inangiogenesis is investigated. Angiogenesis is a morphogenic process in whichnew blood vessels emerge from an existing vascular network. Recently aone-dimensional discrete dynamical model has been proposed to reproduceelongation, bifurcation, and cell motility such as cell-mixing duringangiogenesis on the assumption of a simple two-body interaction betweenendothelial cells. The present model is its two-dimensional extension, whereendothelial cells are represented as the ellipses with the two-bodyinteractions: repulsive interaction due to excluded volume effect, attractiveinteraction through pseudopodia and rotation by contact. We show that theoblateness of ellipses and the magnitude of contact rotation significantlyaffect the shape of created vascular patterns and elongation of branches.

Pattern formation of elliptic particles by two-body interactions: a model for dynamics of endothelial cells in angiogenesis