On a Keller-Segel type equation to model Brain Microvascular Endothelial Cells growth's patterns

TL;DR

This paper introduces a Keller-Segel type PDE model for brain microvascular growth patterns, offering mathematical insights and data-driven equations to understand vascular development and impairments in neurodegenerative diseases.

Contribution

It develops a new PDE model for brain microvasculature growth, integrating data-driven components and aiming to connect blood flow and biochemical processes.

Findings

The PDE reproduces observed vascular patterns.

A data-driven equation models chemoattractant dynamics.

Numerical simulations support the model's relevance.

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.