Pattern formation of vascular network in a mathematical model of angiogenesis

TL;DR

This paper presents a mathematical model of angiogenesis that captures vascular network pattern formation based on endothelial cell dynamics, bifurcation, and vessel reconnection, aligning with experimental observations.

Contribution

The study introduces a novel mathematical model incorporating vessel reconnection and multifractal analysis to better understand angiogenesis pattern formation.

Findings

Pattern formation depends on endothelial cell supply rate and vessel connectivity.

Reconnection of blood vessels affects island size distribution in the network.

Multifractal analysis characterizes the complexity of vascular patterns.

Abstract

We discuss the characteristics of the patterns of the vascular networks in a mathematical model for angiogenesis. Based on recent in vitro experiments, this mathematical model assumes that the elongation and bifurcation of blood vessels during angiogenesis are determined by the density of endothelial cells at the tip of the vascular network, and describes the dynamical changes in vascular network formation using a system of simultaneous ordinary differential equations. The pattern of formation strongly depends on the supply rate of endothelial cells by cell division, the branching angle, and also on the connectivity of vessels. By introducing reconnection of blood vessels, the statistical distribution of the size of islands in the network is discussed with respect to bifurcation angles and elongation factor distributions. The characteristics of the obtained patterns are analysed using multifractal dimension and other techniques.