Alzheimer's disease is characterised by the spreading of misfolded proteins and progressive structural changes in the brain. Despite significant clinical research, understanding how microscopic protein dynamics translate into macroscopic tissue degeneration remains a major challenge. In this work, we present a three-dimensional, finite element-based computational framework to model disease progression by combining multi-protein transport and brain tissue deformation within anatomically realistic geometries. The propagation of toxic tau and amyloid-beta proteins is described using reaction-diffusion equations of the Fisher-Kolmogorov type, incorporating prion-like growth mechanisms and anisotropic transport along white matter fibre tracts. Brain atrophy is represented through a hyperelastic constitutive model driven by protein-dependent volume loss. Subject-specific simulations are achieved through an automated preprocessing pipeline that generates finite element meshes and reconstructs axonal orientation fields from medical imaging data. The model reproduces key morphological patterns observed in Alzheimer's disease and shows good quantitative agreement with longitudinal imaging measurements. Overall, the proposed framework offers an extensible computational platform for studying Alzheimer's disease progression across subject-specific brain geometries. The models developed, including the image processing framework (BrainImage2Mesh) and the coupled bio-chemo-mechanical COMSOL finite element implementation, are made freely available to download at https://mechmat.web.ox.ac.uk/codes.

翻译：阿尔茨海默病的特征在于错误折叠蛋白的扩散及大脑进行性结构变化。尽管临床研究已取得显著进展，但微观蛋白动力学如何转化为宏观组织退化仍是重大挑战。本研究提出一种基于三维有限元的计算框架，通过结合多蛋白转运与脑组织变形，在解剖学真实几何结构中模拟疾病进展。有毒tau蛋白和β-淀粉样蛋白的传播采用Fisher-Kolmogorov型反应扩散方程描述，该方程整合类朊病毒生长机制及沿白质纤维束的各向异性转运。通过蛋白浓度依赖性体积损失驱动的超弹性本构模型表征脑萎缩。个体化模拟通过自动化预处理管线实现，该管线能生成有限元网格并从医学影像数据重建轴突方向场。本模型再现了阿尔茨海默病的关键形态学模式，并与纵向影像测量结果具有良好定量一致性。总体而言，所提出的框架为研究个体化脑几何结构中的阿尔茨海默病进展提供了可扩展的计算平台。相关模型（包括图像处理框架BrainImage2Mesh及耦合生物-化学-力学的COMSOL有限元实现）已在https://mechmat.web.ox.ac.uk/codes 免费开放下载。