On a Keller-Segel type equation to model Brain Microvascular Endothelial Cells growth's patterns
Dynamical Systems
2026-05-04 v2 Quantitative Methods
Abstract
This article presents a partial differential equation (PDE) of Keller-Segel (KS) type that reproduces patterns commonly observed during the growth of brain microvasculature. We provide mathematical insights into the mechanisms underlying the emergence of these patterns. In addition, we derive a data-driven equation that ensures a consistent temporal evolution of the chemoattractant associated with the observed microvascular dynamics. Beyond numerical simulations, the aim of this study is to advance a comprehensive mathematical modeling framework, spanning blood flow in cerebral arterial networks to biochemical processes, in order to better understand how vascular impairments may contribute to neurodegenerative diseases.
Keywords
Cite
@article{arxiv.2604.25180,
title = {On a Keller-Segel type equation to model Brain Microvascular Endothelial Cells growth's patterns},
author = {B Ambrosio and A Garroudji and S. Fitzsimons and H Zaag and F. M. Elahi},
journal= {arXiv preprint arXiv:2604.25180},
year = {2026}
}