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.
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