Tau Protein Propagation, Atrophy, and Shrinkage in Alzheimer's Brain

Objective: Alzheimer’s disease (AD) is characterized by the spread of tau and amyloid β (Aβ) pathology, progressive brain atrophy, and eventual tissue deformation. Yet, most computational models treat these processes separately. Here, we develop a fully coupled multiphysics framework that simulates in a single subject specific head mesh the spatiotemporal evolution of pro- tein aggregation, concentration dependent tissue shrinkage, and the resulting biomechanical stresses. Methods: A 12 region finite element mesh was segmented from T1 weighted MRI and DTI tractography. Two protein species (cTAU, cAB) follow an anisotropic diffusion reaction equation with prion like logistic kinetics and cross promotion (Aβ accelerates tau aggregation). Atrophy is driven by a domain ODE where the volume fraction θ decays exponentially, with a sharp sigmoidal enhancement once cTAU exceeds a critical threshold (ccrit=0.2). The solid mechanics problem uses a nearly in- compressible Neo Hookean hyperelastic model with stiffness degradation proportional to θ and region specific Lamé parame- ters. The entire system is solved transiently over 20 years using a segregated solver (PARDISO/MUMPS). Results: Tau spreads from the entorhinal cortex along white matter tracts to the hippocampus and temporal cortex (Braak stage III IV by 10 years), while Aβ remains more diffuse. Cross promotion accelerates tau kinetics, reducing time to hippocampal involvement by ~3 years. Atrophy is highest in entorhinal cortex (θ≈0.78 at 20 years), with total brain volume loss of 5-7%. Atrophy induced shrinkage generates von Mises stresses of 1.5–3.0 kPa in white matter and ventricular expansion of 10-15%. Simulated annual volume changes agree with ADNI data for MCI converters (hippocampus: −4.1% vs. −3.8±1.2%/ year). Sensitivity analysis identifies axial diffusion (Daxn) and baseline atrophy rate (G0) as dominant controls. Conclusion: This multiphysics framework captures the interdependent evolution of protein pathology, tissue loss, and mechanical stress in AD. It provides a quantitative tool to test mechanistic hypotheses, predict patient specific trajectories, and evaluate biomechanical consequences of neurodegeneration. Limitations include single subject anatomy and a coarse mesh (error ~8%), positioning this as a proof of concept for future population scale studies.