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

Area of Science:

• Mathematical Biology
• Neuroscience
• Computational Fluid Dynamics

Background:

• Brain microvasculature exhibits complex growth patterns.
• Understanding these patterns is crucial for neurodegenerative disease research.
• Existing models may not fully capture the dynamics of microvascular development.

Purpose of the Study:

• To present a novel partial differential equation (PDE) model of the Keller-Segel (KS) type for brain microvasculature growth.
• To provide mathematical insights into pattern formation mechanisms.
• To develop a comprehensive mathematical framework linking vascular dynamics to neurodegeneration.

Main Methods:

• Development of a Keller-Segel (KS) type partial differential equation (PDE).
• Derivation of a data-driven equation for chemoattractant temporal evolution.
• Mathematical analysis and numerical simulations of the model.
• Integration of blood flow and biochemical process modeling.

Main Results:

• The proposed PDE model successfully reproduces observed patterns in brain microvasculature growth.
• Mathematical insights into the mechanisms driving pattern emergence were provided.
• A data-driven equation was derived, ensuring consistent chemoattractant dynamics.
• A comprehensive modeling framework was advanced.

Conclusions:

• The developed mathematical framework offers a novel approach to studying brain microvasculature.
• This model can elucidate the role of vascular impairments in neurodegenerative diseases.
• Further research can refine the model for clinical applications in understanding and potentially treating neurodegeneration.