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.

We develop mathematical and computational models to investigate neuronal activity under physiological and pathological conditions, with particular attention to epilepsy and cerebral ischemia. Our research combines neuronal electrophysiology, ionic dynamics, cellular metabolism, and tissue-scale signal propagation within multiscale and multiphysics frameworks.

Our research investigates:

• Neuronal electrophysiology and seizure propagation: mathematical models of membrane potential, ionic currents, and neuronal excitability, coupled with tissue-scale descriptions of electrical signal propagation in grey and white matter.
• Electro-metabolic coupling and cerebral ischemia: interactions between neuronal activity, oxygen availability, cellular metabolism, ionic-pump function, extracellular ionic concentrations, and cellular swelling under energy-deprived conditions.
• Multiphysics and multiscale coupling: integration of fast electrophysiological dynamics with slower biochemical and metabolic processes, including the effects of amyloid-beta accumulation on calcium regulation, neuronal excitability, and seizure onset.
• Advanced high-order numerical methods: discontinuous Galerkin methods on polygonal and polyhedral meshes, space- and time-adaptive strategies, and element-wise p-adaptivity for accurately resolving sharp electrical wavefronts while reducing computational cost.
• Efficient solvers and high-performance computing: scalable non-overlapping Schwarz preconditioners, parallel assembly strategies, and computational tools for realistic and patient-specific brain geometries.

These models and numerical methods aim to clarify the mechanisms underlying pathological neuronal activity and provide reliable computational tools for studying disease progression and, in the longer term, supporting patient-specific prediction and treatment planning.

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