We develop mathematical and computational models for the study of neurodegenerative diseases, with a particular focus on Alzheimer’s and Parkinson’s disease.

Our research investigates:

• CSF and brain fluid dynamics, including coupled fluid–poroelastic models of CSF flow, intracranial pressure, tissue deformation, and mechanisms related to fluid and solute clearance.
• Protein misfolding and spreading, through reaction–diffusion, heterodimer, and network-based models for amyloid-beta, tau, and alpha-synuclein propagation.
• Long-term disease multiphysics progression, by coupling protein accumulation with tissue atrophy and cerebral hypoperfusion.
• Patient-specific and data-driven modeling, using brain connectomes, neuroimaging data, uncertainty quantification, and machine-learning-based dynamical models.

These processes span different time scales: seconds to minutes for fluid dynamics, years for pathological protein propagation, and years to decades for atrophy and disease progression. Our computational framework combines anatomically informed brain models advanced numerical methods for complex multiphysics and multiscale problems.

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.

Computational mechanical modeling of the spinal column.
Spinal disorders, such as low back pain, degenerative disc disease, spondylosis, disc herniation, have a huge impact on a patient’s quality of life and are one of the leading causes of disability worldwide. In severe cases, surgical intervention (e.g., spinal fusion, microdiscectomy, or osteotomy) is the only clinical treatment, and both its planning and the post-intervention rehabilitation strongly rely on imaging data (MRI and/or X-ray). Based on such patient-specific data, computational modeling can complement it by anticipating the mechanical response to treatment, thus providing a virtual testing platform to identify the optimal treatment among several surgical procedures. We model the complex anatomical system of the spine accounting for the rheology of the different components (vertebrae, intervertebral discs, and ligaments), and we employ state-of-the-art numerical methods for its computational simulation