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

TL;DR

This paper introduces a two-dimensional mathematical model for endothelial cell dynamics in angiogenesis, focusing on how cell shape and contact interactions influence vascular pattern formation.

Contribution

It extends a previous one-dimensional model to two dimensions, incorporating elliptic cell shapes and contact rotation effects to better simulate angiogenic processes.

Findings

Elliptic cell shape affects vascular pattern morphology.

Contact rotation influences branch elongation.

Model reproduces key features of angiogenesis patterns.

Abstract

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.