On a Keller-Segel type equation to model Brain Microvascular Endothelial Cells growth's patterns
B Ambrosio, A Garroudji, S Fitzsimons, H Zaag, F. M. Elahi
TLDR
This paper introduces a Keller-Segel type PDE to model and understand brain microvascular growth patterns, providing mathematical insights.
Key contributions
- Introduces a Keller-Segel PDE modeling brain microvascular growth patterns.
- Offers mathematical insights into the mechanisms of pattern emergence.
- Develops a data-driven equation for chemoattractant temporal evolution.
- Contributes to a broad framework for understanding neurodegenerative diseases.
Why it matters
This paper advances mathematical modeling of brain microvasculature, crucial for understanding its complex growth. By linking these models to neurodegenerative diseases, it opens new avenues for research into vascular impairments. This could lead to better insights into disease progression.
Original 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.
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