A Discrete Mathematical Model for Angiogenesis.

Angiogenesis is the morphogenetic phenomenon in which new blood vessels emerge from an existing vascular network and configure a new network.In consideration of recent experiments with time-lapse fluorescent imaging in which vascular endothelial cells exhibit cell-mixing behavior even at a tip of newly generated vascular networks, we propose a discrete mathematical model for the dynamics of vascular endothelial cells in angiogenic morphogenesis.The model incorporates two-body interaction between endothelial cells which induces cell-mixing behavior and length of the generating blood vessel shows temporal power-law scaling behavior.Numerical simulation of the model successfully reproduces elongation and bifurcation of blood vessels in the early stage of angiogenesis.