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This study develops a partial differential equation based on the Keller-Segel mathematical framework to model the growth patterns of brain microvascular endothelial cells. The researchers provide mathematical analysis of the mechanisms that produce these patterns and derive a data-driven equation describing the temporal evolution of chemoattractants involved in microvascular dynamics. The work aims to contribute to a comprehensive mathematical framework connecting blood flow in cerebral arteries to biochemical processes relevant to neurodegenerative diseases.
Why it matters
Understanding the mathematical principles governing brain microvasculature growth could help researchers identify how vascular impairments contribute to neurodegenerative diseases. This modeling approach may eventually support the development of diagnostic tools or therapeutic strategies targeting cerebrovascular dysfunction in conditions like Alzheimer's disease or vascular dementia.
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⚠️ Preprint – Noch nicht peer-reviewed
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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.
Source: On a Keller-Segel type equation to model Brain Microvascular Endothelial Cells growth's patterns