Multiscale Modeling of the Human Brain and Neurodegeneration
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Neurodegenerative diseases (NDs) are complex disorders marked by progressive loss of structure and function in the central nervous system. A common hallmark shared by many NDs is the accumulation of disease-specific misfolded proteins, such as amyloid-beta and tau in Alzheimer’s disease and α-synuclein in Parkinson’s disease. In this talk, we present a multiscale mathematical framework that combines physics-based modeling with data-driven learning to investigate the mechanisms of human brain neurodegeneration. The framework integrates models across multiple scales. We first discuss the spatio-temporal dynamics of misfolded protein propagation at the organ level using advanced mathematical models discretized with high-order discontinuous Galerkin methods on general polytopal meshes. Next, we incorporate models of cerebral waste-clearance mechanisms, which are critical to ND progression. We then introduce a coupled multiscale model to account for altered electrical signal propagation, a phenomenon often observed in neurodegenerative disorders. Finally, we validate the proposed approach through extensive numerical simulations on patient-specific brain geometries reconstructed from clinical imaging data.
