  A two-dimensional mathematical model for dynamics of endothelial cells in
angiogenesis is investigated. Angiogenesis is a morphogenic process in which
new blood vessels emerge from an existing vascular network. Recently a
one-dimensional discrete dynamical model has been proposed to reproduce
elongation, bifurcation, and cell motility such as cell-mixing during
angiogenesis on the assumption of a simple two-body interaction between
endothelial cells. The present model is its two-dimensional extension, where
endothelial cells are represented as the ellipses with the two-body
interactions: repulsive interaction due to excluded volume effect, attractive
interaction through pseudopodia and rotation by contact. We show that the
oblateness of ellipses and the magnitude of contact rotation significantly
affect the shape of created vascular patterns and elongation of branches.
