On a Keller-Segel type equation to model Brain Microvascular Endothelial Cells growth's patterns
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911637456289792 |
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| author | Ambrosio, B Garroudji, A Fitzsimons, S. Zaag, H Elahi, F. M. |
| author_facet | Ambrosio, B Garroudji, A Fitzsimons, S. Zaag, H Elahi, F. M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25180 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On a Keller-Segel type equation to model Brain Microvascular Endothelial Cells growth's patterns Ambrosio, B Garroudji, A Fitzsimons, S. Zaag, H Elahi, F. M. Dynamical Systems Quantitative Methods 35K57, 92C17, 35D92, 92C15, 35B36, 35K55, 92B05 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. |
| title | On a Keller-Segel type equation to model Brain Microvascular Endothelial Cells growth's patterns |
| topic | Dynamical Systems Quantitative Methods 35K57, 92C17, 35D92, 92C15, 35B36, 35K55, 92B05 |
| url | https://arxiv.org/abs/2604.25180 |