Dynamics of waste proteins in brain tissue: numerical insights into Alzheimer's risk factors

Over the last few decades, research has indicated that the build-up of waste proteins, like amyloid-β (Aβ), in the brain's interstitial spaces are linked to neurodegenerative diseases, such as Alzheimer's, but the details of how such proteins are removed from the brain is actively debated. One major component of the challenge in predicting and treating neurodegenerative diseases is the complexity of Aβ dynamics: Aβ monomers are produced as a natural consequence of metabolism, but they readily aggregate into heavier species, eventually forming plaques, which are a hallmark signature of many neurodegenerative diseases. We have developed a numerical model to investigate the aggregation and clearance mechanisms of Aβ in the interstitial spaces of the brain. The model describes the volume-averaged fluid flow between the perivascular spaces (fluid-filled spaces surrounding certain blood vessels) of the penetrating arterioles and venules in a segment of brain interstitium. Our numerical approach solves N coupled advection-diffusion-aggregation equations to model the production, aggregation, and fragmentation of N species of Aβ, where N ≥ 50. We simulate 50 Aβ species in order to investigate the protein-length dependence of clearance and aggregation. We then quantify the importance of several factors, including initial concentration, boundary conditions, Péclet number, and aggregation and fragmentation rates, to determine which factors promote or inhibit protein clearance. Our preliminary results provide novel insight into several known risk factors for Alzheimer's disease and cognitive decline.