The computational modeling of the Central Nervous System (CNS) entails several challenges:

• anatomic complexity: cerebral gyri and sulci, ventricles, vasculature, and ducti
• multiphysics: electrophysiology, blood supply and perfusion, dynamics of the cerebrospinal fluid (CSF), protein distribution and clearance, long-term remodeling
• multiscale: from single cell (neuron firing, axon mechanical remodeling, …) to the whole organ (signal propagation, blood and CSF dynamics, cerebral tissue poroelasticity, prion clearance, …); from milliseconds (electrical activation) to decades (neurodegeneration and remodeling)

Modeling of:

• CSF flow: waste clearance and its impairment in neurodegeneration (time scale: seconds/minutes)
• distribution of misfolded proteins (time scale: years)
• neural axon degeneration and brain remodeling (time scale: decades)

• anatomic complexity: cerebral gyri and sulci, ventricles, vasculature, and ducti
• multiphysics: electrophysiology, blood supply and perfusion, dynamics of the cerebrospinal fluid (CSF), protein distribution and clearance, long-term remodeling
• multiscale: from single cell (neuron firing, axon mechanical remodeling, …) to the whole organ (signal propagation, blood and CSF dynamics, cerebral tissue poroelasticity, prion clearance, …); from milliseconds (electrical activation) to decades (neurodegeneration and remodeling)

Numerical modelling of epileptic seizures. Epilepsy is a clinical neurological disorder characterized by recurrent and spontaneous seizures generating an abnormal high-frequency electrical activity of the brain. Despite several clinical studies that have permitted the development of specific pharmacological and surgical treatments to control the onset of seizures there is still an open debate on the mechanisms and optimal patient-specific treatment. We consider the bidomain model to mathematically describe seizure evolution in the grey and white matter, coupled with specific ionic models for neuronal modelling in which the different dynamics of the potential and ionic currents are considered. The mathematical model is discretized by means of discontinuous Galerkin methods. Suitable (space-time) adaptive schemes are proposed to exploit the flexibility of the numerical approach to better describe the sharp propagating fronts that characterize seizure propagation. The numerical results provide insights into the mechanisms underlying seizures and might, in the future, support precision medicine, thanks to methods capable of predicting patient-specific behaviour and suggesting optimal treatment.

• Antonietti P.F., Bonizzoni F., Corti M., Dall’Olio A., Discontinuous Galerkin approximations of the heterodimer model for protein–protein interaction. Computer Methods in Applied Mechanics and Engineering, 431:117282 (2024) https://doi.org/10.1016/j.cma.2024.117282 

• Corti M., Exploring tau protein and amyloid-beta propagation: A sensitivity analysis of mathematical models based on biological data. Brain Multiphysics 7:100098 (2024) https://doi.org/10.1016/j.brain.2024.100098
• Corti M., Bonizzoni F., Antonietti P.F., Structure Preserving Polytopal Discontinuous Galerkin Methods for the Numerical Modeling of Neurodegenerative Diseases.
  Journal of Scientific Computing 100(39) (2024) https://doi.org/10.1007/s10915-024-02581-7 

• Fumagalli I., Corti M., Parolini N, Antonietti P. F., Polytopal discontinuous Galerkin discretization of brain multiphysics flow dynamics, Journal of Computational Physics 513:113115 (2024) https://doi.org/10.1016/j.jcp.2024.113115 

• Corti M., Bonizzoni F., Antonietti P.F., Quarteroni A.M., Uncertainty quantification for Fisher-Kolmogorov equation on graphs with application to patient-specific Alzheimer’s disease. ESAIM: Mathematical Modelling and Numerical Analysis, in press (2023) https://doi.org/10.1051/m2an/2023095  

• Corti M., Bonizzoni F., Dede’ L., Quarteroni A.M., Antonietti P.F., Discontinuous Galerkin methods for Fisher–Kolmogorov equation with application to α-synuclein spreading in Parkinson’s disease. Computer Methods in Applied Mechanics and Engineering 417:116450 (2023) https://doi.org/10.1016/j.cma.2023.116450  

• Corti M., Antonietti P.F., Dede’ L., Quarteroni A., Numerical modeling of the brain poromechanics by high-order discontinuous Galerkin methods.
  Mathematical Models and Methods in Applied Sciences 33(08):1577-1609 (2023) https://doi.org/10.1142/S0218202523500367 

Preprints

• Antonietti P.F., Corti M.; Lorenzon G., A discontinuous Galerkin method for the three-dimensional heterodimer model with application to prion-like proteins’ dynamics (2024) https://arxiv.org/abs/2407.16065  

• Antonietti P.F., Bonetti S., Botti M., Corti M., Fumagalli I., Mazzieri I., lymph: discontinuous poLYtopal methods for Multi-PHysics differential problems (2024) https://arxiv.org/abs/2401.13376 

• Antonietti P.F., Corti M., Numerical modelling of protein misfolding in neurodegenerative diseases: a computational study (2024) https://arxiv.org/abs/2401.15747  

• Fumagalli I., Parolini N., Verani M., A posteriori error analysis for a coupled Stokes-poroelastic system with multiple compartments (2024) https://arxiv.org/abs/2407.09659 

• Fumagalli I., Discontinuous Galerkin method for a three-dimensional coupled fluid-poroelastic model with applications to brain fluid mechanics (2024) https://arxiv.org/abs/2406.14041  

• Leimer Saglio C.B., Pagani S., Corti M., Antonietti, P.F., A high-order discontinuous Galerkin method for the numerical modeling of epileptic seizures (2024) https://arXiv.org/abs/2401.14310