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| A Multiscale Coupled Reaction-Diffusion Model of Amyloid-Beta and Tau Pathology in Alzheimer's Disease |
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| KeyWord:Alzheimer's disease, amyloid-beta, tau pathology, reaction-diffu-sion models, neurodegeneration, mathematical modeling |
| Author Name | Affiliation | | Aytekin Enver | Graduate School of Natural and Applied Sciences, Department of Mathematics, Gazi University, Besevler, 06550, T\"{u}rkiye | | Fatma Ayaz | Department of Mathematics, Gazi University, Besevler, 06550, T\"{u}rkiye | | Deniz Eylem Yal\c{c}\i{}nkaya | Department of Neurology, Ankara Private Koru Hospital, Kavaklidere, 06550, T\"{u}rkiye |
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| Abstract: |
| Alzheimer's disease (AD) is a progressive neurodegenerative disorder characterized by the accumulation of amyloid-beta (A$\beta$) plaques and tau neurofibrillary tangles (NFTs), as well as by chronic neuroinflammation and blood-brain barrier (BBB) dysfunction. Although these pathological features are well known, their complex interactions remain poorly understood. This study proposes a comprehensive multiscale coupled reaction-diffusion model composed of 13 partial differential equations to simulate the spatio-temporal dynamics of A$\beta$ and tau pathology, neuroinflammatory responses, BBB integrity, and neuronal degeneration. The model captures biochemical reaction kinetics, diffusion-driven propagation, and regulatory feedback among key cellular components, including microglia, astrocytes, and cytokines. Furthermore, the effects of therapeutic interventions, such as anti-amyloid drugs and dietary modifications, are incorporated to assess their influence on disease progression. Numerical simulations using finite difference methods provide insights into how these factors contribute to or mitigate AD pathogenesis. The results support the potential of mathematical modeling as a tool to understand disease mechanisms and evaluate treatment strategies. |
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