Percolation, Morphogenesis, and Burgers Dynamics in Blood Vessels Formation

TL;DR

This paper presents a model that captures the fractal and percolation behaviors observed in blood vessel formation, aligning well with experimental data and shedding light on the underlying biological processes.

Contribution

It introduces a simple, effective model that reproduces key features of blood vessel morphogenesis, including fractal growth and percolation phenomena.

Findings

Model reproduces fractal behavior at small scales

Model and experiments show percolation at large scales

Results align well with experimental data

Abstract

Experiments of in vitro formation of blood vessels show that cells randomly spread on a gel matrix autonomously organize to form a connected vascular network. We propose a simple model which reproduces many features of the biological system. We show that both the model and the real system exhibit a fractal behavior at small scales, due to the process of migration and dynamical aggregation, followed at large scale by a random percolation behavior due to the coalescence of aggregates. The results are in good agreement with the analysis performed on the experimental data.