Mathematical Insights into Alzheimer’s Disease: A Multiscale Modeling Approach

Abstract

• In this presentation, we study the progression of Alzheimer’s disease through a multiscale modeling approach. We begin by formulating a system of partial differential equations that captures the underlying biological mechanisms. The evolution of the system is analyzed within a thin porous heterogeneous medium, reflecting the complex structure of brain tissue. To address the multiscale nature of the problem, we adopt a finite element heterogeneous multiscale method (FE-HMM), which enables us to accurately approximate the macroscopic behavior by systematically incorporating microscale effects. Numerical simulations are carried out to validate the theoretical analysis and to illustrate the impact of tissue heterogeneity on disease progression.