BraiNum is a research project carried out at the MOX Laboratory (Department of Mathematics, Politecnico di Milano) devoted to the mathematical modeling and numerical simulation of the brain and the central nervous system, with a strong emphasis on medical applications and industrial impact in computational medicine. The project aims to develop quantitative, predictive models of brain physiology and pathology, leveraging advanced numerical methods, such as high-order finite elements and discontinuous Galerkin, high-performance scientific computing, computational learning techniques, and uncertainty quantification.
BraiNum tackles the brain’s remarkable anatomical, physical, and multiscale complexity: from the propagation of electrical signals on millisecond time scales to the dynamics of blood and cerebrospinal fluid, and up to long‑term tissue remodeling and the diffusion of misfolded proteins over years or decades. The group develops multiscale and multiphysics models to describe brain mechanics, fluid circulation, and the spread of proteins such as amyloid‑beta, tau, and α‑synuclein in neurodegeneration, including Alzheimer’s and Parkinson’s diseases, on complex three‑dimensional geometries and connectome-based graphs. Moreover, machine-learning models are developed to leverage multimodal clinical datasets and improve patient stratification and prognostic predictions.
Key roles are played by innovative discretization techniques on polytopal meshes, structure‑preserving discontinuous Galerkin schemes, and p-adaptivity strategies, which enable the efficient solution of strongly heterogeneous problems with sharp fronts in realistic geometries. These methods are implemented in dedicated high‑performance computing codes designed for scalability, robustness, and reusability.