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.