54 citations · 150 across the 23 of their papers we have counts for
25 papers
A weighted polygonal discontinuous Galerkin method for hierarchically coupled reaction-diffusion systems with cubic interactions
Mattia Corti
We develop and analyse a symmetric weighted interior penalty polytopal discontinuous Galerkin (SWIP-PolyDG) method for multi-species reaction--diffusion systems with nonlinear reac…
A stability-preserving polytopal discontinuous Galerkin method for the Fisher-Kolmogorov model with applications to neurodegenerative disease modelling
Paola Francesca Antonietti, Francesca Bonizzoni, Mattia Corti +3
The Fisher--Kolmogorov equation models the spatio-temporal evolution of interacting biological species and is extensively employed in fields such as ecology, population dynamics, a…
The lymph 2.0 library: p-adaptive algorithms and parallel assembly strategies for polytopal DG methods
Paola F. Antonietti, Mattia Corti, Caterina B. Leimer Saglio +1
This work presents a new release of the lymph 2.0 library, an open-source MATLAB framework for high-order discontinuous Galerkin discretizations on general polytopal meshes. The ly…
Optimized high-order IMEX-RK schemes for degenerate diffusion-reaction problems with application to travelling waves phenomena
Paola F. Antonietti, Mattia Corti, Giuseppe Orlando
We study a class of IMplicit-EXplicit Runge--Kutta (IMEX-RK) schemes for the numerical approximation of reaction and diffusion-reaction problems arising in a variety of biological…
High-fidelity and Network-based Spatio-temporal Mathematical Models of Alzheimer's Disease Progression and their Validation Against PET-SUVR Imaging Data
Beatrice Caon, Mattia Corti, Francesca Bonizzoni +1
Alzheimer's disease is the most common neurodegenerative disorder. Its pathological development is connected with the misfolding and accumulation of two toxic proteins: amyloid-bet…
A whole-brain model of amyloid beta accumulation and cerebral hypoperfusion in Alzheimer's disease
Mattia Corti, Andrew Ahern, Alain Goriely +2
Accumulation of amyloid beta proteins is a defining feature of Alzheimer's disease, and is usually accompanied by cerebrovascular pathology. Evidence suggests that amyloid beta and…
On the Compact Discontinuous Galerkin method for polytopal meshes
Mattia Corti, Sergio Gómez
The Compact Discontinuous Galerkin method was introduced by Peraire and Persson in (SIAM J. Sci. Comput., 30, 1806-1824, 2008). In this work, we present the stability and convergen…
A novel mathematical and computational framework of amyloid-beta triggered seizure dynamics in Alzheimer's disease
Caterina B. Leimer Saglio, Mattia Corti, Stefano Pagani +1
The association of epileptic activity and Alzheimer's disease (AD) has been increasingly reported in both clinical and experimental studies, suggesting that amyloid- accumulatio…
Structure-preserving local discontinuous Galerkin discretization of conformational conversion systems
Paola F. Antonietti, Mattia Corti, Sergio Gómez +1
We investigate a two-state conformational conversion system and introduce a novel structure-preserving numerical scheme that couples a local discontinuous Galerkin space discretiza…
A structure-preserving LDG discretization of the Fisher-Kolmogorov equation for modeling neurodegenerative diseases
Paola F. Antonietti, Mattia Corti, Sergio Gómez +1
This work presents a structure-preserving, high-order, unconditionally stable numerical method for approximating the solution to the Fisher-Kolmogorov equation on polytopic meshes,…
A coupled mathematical and numerical model for protein spreading and tissue atrophy, applied to Alzheimer's disease
Valentina Pederzoli, Mattia Corti, Davide Riccobelli +1
The aim of this paper is to introduce, analyse and test in practice a new mathematical model describing the interplay between biological tissue atrophy driven by pathogen diffusion…
Unified discontinuous Galerkin analysis of a thermo/poro-viscoelasticity model
Stefano Bonetti, Mattia Corti
We present and analyze a discontinuous Galerkin method for the numerical modeling of a Kelvin-Voigt thermo/poro-viscoelastic problem. We present the derivation of the model and we…
A discontinuous Galerkin method for the three-dimensional heterodimer model with application to prion-like proteins' dynamics
Paola F. Antonietti, Mattia Corti, Giacomo Lorenzon
Neurocognitive disorders, such as Alzheimer's and Parkinson's, have a wide social impact. These proteinopathies involve misfolded proteins accumulating into neurotoxic aggregates.…
Polytopal mesh agglomeration via geometrical deep learning for three-dimensional heterogeneous domains
Paola F. Antonietti, Mattia Corti, Gabriele Martinelli
Agglomeration techniques can be successfully employed to reduce the computational costs of numerical simulations and stand at the basis of multilevel algebraic solvers. To automati…
Exploring tau protein and amyloid-beta propagation: a sensitivity analysis of mathematical models based on biological data
Mattia Corti
Alzheimer's disease is the most common dementia worldwide. Its pathological development is well known to be connected with the accumulation of two toxic proteins: tau protein and a…
Numerical modelling of protein misfolding in neurodegenerative diseases: a computational study
Paola F. Antonietti, Mattia Corti
The spreading of misfolded proteins is a known hallmark in some neurodegenerative diseases, known as proteinopathies. A significant example is the tau protein, associated with many…
A high-order discontinuous Galerkin method for the numerical modeling of epileptic seizures
Caterina Beatrice Leimer Saglio, Stefano Pagani, Mattia Corti +1
Epilepsy is a clinical neurological disorder characterized by recurrent and spontaneous seizures consisting of abnormal high-frequency electrical activity in the brain. In this con…
lymph: discontinuous poLYtopal methods for Multi-PHysics differential problems
Paola F. Antonietti, Stefano Bonetti, Michele Botti +3
We present the library lymph for the finite element numerical discretization of coupled multi-physics problems. lymph is a Matlab library for the discretization of partial differen…
Polytopal discontinuous Galerkin discretization of brain multiphysics flow dynamics
Ivan Fumagalli, Mattia Corti, Nicola Parolini +1
A comprehensive mathematical model of the multiphysics flow of blood and Cerebrospinal Fluid (CSF) in the brain can be expressed as the coupling of a poromechanics system and Stoke…
Discontinuous Galerkin approximations of the heterodimer model for protein-protein interaction
Paola F. Antonietti, Francesca Bonizzoni, Mattia Corti +1
Mathematical models of protein-protein dynamics, such as the heterodimer model, play a crucial role in understanding many physical phenomena. This model is a system of two semiline…
Structure Preserving Polytopal Discontinuous Galerkin Methods for the Numerical Modeling of Neurodegenerative Diseases
Mattia Corti, Francesca Bonizzoni, Paola F. Antonietti
Many neurodegenerative diseases are connected to the spreading of misfolded prionic proteins. In this paper, we analyse the process of misfolding and spreading of both -synuclei…
Uncertainty Quantification for Fisher-Kolmogorov Equation on Graphs with Application to Patient-Specific Alzheimer Disease
Mattia Corti, Francesca Bonizzoni, Paola F. Antonietti +1
The Fisher-Kolmogorov equation is a diffusion-reaction PDE that is used to model the accumulation of prionic proteins, which are responsible for many different neurological disorde…
Discontinuous Galerkin Methods for Fisher-Kolmogorov Equation with Application to -Synuclein Spreading in Parkinson's Disease
Mattia Corti, Francesca Bonizzoni, Luca Dede' +2
This spreading of prion proteins is at the basis of brain neurodegeneration. This paper deals with the numerical modelling of the misfolding process of -synuclein in Parkinson's…
Numerical Modelling of the Brain Poromechanics by High-Order Discontinuous Galerkin Methods
Mattia Corti, Paola F. Antonietti, Luca Dede' +1
We introduce and analyze a discontinuous Galerkin method for the numerical modelling of the equations of Multiple-Network Poroelastic Theory (MPET) in the dynamic formulation. The…