相关论文: A discontinuous Galerkin method for the three-dime…
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 semilinear parabolic partial differential equations describing the…
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 pathologies, such as Alzheimer's. In this work, we discuss…
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 $\alpha$-synuclein and Amyloid-$\beta$, related to Parkinson's and…
This spreading of prion proteins is at the basis of brain neurodegeneration. This paper deals with the numerical modelling of the misfolding process of $\alpha$-synuclein in Parkinson's disease. We introduce and analyze a discontinuous…
Epilepsy is a clinical neurological disorder characterized by recurrent and spontaneous seizures consisting of abnormal high-frequency electrical activity in the brain. In this condition, the transmembrane potential dynamics are…
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, with applications to neurodegenerative disorders. This…
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 MPET model can comprehensively describe functional changes…
Many neurodegenerative diseases are related to the propagation and accumulation of toxic proteins throughout the brain. The lesions created by aggregates of these toxic proteins further lead to cell death and accelerated tissue atrophy. A…
For hyperbolic conservation laws, traditional methods and physics-informed neural networks (PINNs) often encounter difficulties in capturing sharp discontinuities and maintaining temporal consistency. To address these challenges, we…
This work presents a structure-preserving, high-order, unconditionally stable numerical method for approximating the solution to the Fisher-Kolmogorov equation on polytopic meshes, with a particular focus on its application in simulating…
The quasi-static multiple network poroelastic theory (MPET) model, first introduced in the context of geomechanics, has recently found new applications in medicine. In practice, the parameters in the MPET equations can vary over several…
Alzheimer's disease is characterised by the spreading of misfolded proteins and progressive structural changes in the brain. Despite significant clinical research, understanding how microscopic protein dynamics translate into macroscopic…
Neurodegenerative diseases are associated with the assembly of specific proteins into oligomers and fibrillar aggregates. At the brain scale, these protein assemblies can diffuse through the brain and seed other regions, creating an…
Neurodegenerative diseases are closely associated with the amplification and invasion of toxic proteins. In particular Alzheimer's disease is characterized by the systematic progression of amyloid-$\beta$ and $\tau$-proteins in the brain.…
Alzheimer's disease (AD) is a complex neurodegenerative disorder characterized by the progressive accumulation of misfolded proteins, leading to cognitive decline. This study presents a novel stochastic modelling approach to simulate the…
We present and analyze a high-order discontinuous Galerkin method for the space discretization of the wave propagation model in thermo-poroelastic media. The proposed scheme supports general polytopal grids. Stability analysis and…
Prion-like proteins play crucial parts in biological processes in organisms ranging from yeast to humans. For instance, many neurodegenerative diseases are believed to be caused by the production of prion-like proteins in neural tissue. As…
Prion-like propagation of misfolded proteins is a key mechanism underlying the progression of neurodegenerative diseases such as Alzheimer's disease. In previous work, we introduced the HeMiTo framework, describing these prion-like dynamics…
Integro-differential equations, analyzed in this work, comprise an important class of models of continuum media with nonlocal interactions. Examples include peridynamics, population and opinion dynamics, the spread of disease models, and…
Alzheimer's disease is the most common neurodegenerative disorder. Its pathological development is connected with the misfolding and accumulation of two toxic proteins: amyloid-beta and tau proteins. Mathematical models provide a valuable…