A whole-brain model of amyloid beta accumulation and cerebral hypoperfusion in Alzheimer's disease

TL;DR

The paper tackles the coupled dynamics of amyloid-beta accumulation and cerebral blood flow disruption in Alzheimer's disease by integrating a heterodimer amyloid-β kinetics model with a three-network porous-medium perfusion framework. It employs a high-order discontinuous Galerkin discretization in space and an implicit Euler scheme in time to solve a parabolic–elliptic IBVP on patient-specific brain geometries. A key mathematical insight is the reproduction-number threshold $R_0 = \frac{k_0 k_{12}}{k_1 \tilde{k}_1}$ that determines the existence of a positive pathogenic equilibrium. Numerical experiments reveal that sufficiently large A seeds or localized hypoperfusion can trigger brain-wide disease outbreaks, while smaller perturbations remain benign, consistent with a two-hit vascular hypothesis. The framework provides a computation-driven context for evaluating interventions targeting either amyloid-β dynamics or vascular function in Alzheimer's disease, and underscores the importance of coupling vascular and protein-aggregation processes in brain-scale models.

Abstract

Accumulation of amyloid beta proteins is a defining feature of Alzheimer's disease, and is usually accompanied by cerebrovascular pathology. Evidence suggests that amyloid beta and cerebrovascular pathology are mutually reinforcing; in particular, amyloid beta suppresses perfusion by constricting capillaries, and hypoperfusion promotes the production of amyloid beta. Here, we propose a whole-brain model coupling amyloid beta and blood vessel through a hybrid model consisting of a reaction-diffusion system for the protein dynamics and porous-medium model of blood flow within and between vascular networks: arterial, capillary and venous. We discretize the resulting parabolic--elliptic system of PDEs by means of a high-order discontinuous Galerkin method in space and an implicit Euler scheme in time. Simulations in realistic brain geometries demonstrate the emergence of multistability, implying that a sufficiently large pathogenic protein seeds is necessary to trigger disease outbreak. Motivated by the "two-hit vascular hypothesis" of Alzheimer's disease that hypoperfusive vascular damage triggers amyloid beta pathology, we also demonstrate that localized hypoperfusion, in response to injury, can destabilize the healthy steady state and trigger brain-wide disease outbreak.

Figures (12)

• Figure 1: Synthetic representation of the article structure. Description of the A--vascular interaction in AD (left panel), patients-specific geometry (right panel), and mathematical models and resulting numerical simulations (center panel).
• Figure 2: Test Case 1: Pressures computed in healthy conditions in the domain $\Omega$. We report the arterial $p_\mathrm{A}$ (upper-left), capillary $p_\mathrm{C}$ (upper-right), and venous $p_\mathrm{V}$ (lower-left) pressures and the healthy CBF rate $Q_\mathrm{H}=\frac{\beta_\mathrm{AC}}{\rho}(p_\mathrm{A}-p_\mathrm{C})$ (lower right).
• Figure 3: Numerical solution for Test Case 1 with large seeding region. Misfolded proteins $\tilde{u}$ (first row), healthy proteins $u$ (second row), and reduction of CBF (third row). Disease propagation succeeds.
• Figure 4: Numerical solution for Test Case 1 with small seeding region. Disease propagation fails.
• Figure 5: Numerical solution for Test Case 2 with large injury site. Localized injury triggers disease spread.