Related papers: A computational framework to predict the spreading…
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…
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…
Mathematical modeling offers a valuable approach to understanding Alzheimers disease (AD) given its complexity, unknown causes, and lack of effective treatments. Models, once validated, offer a powerful tool to test medical hypotheses that…
It is well known that today nearly one in six of the world's population has to deal with neurodegenerative disorders. While a number of medical devices have been developed for the detection, prevention, and treatments of such disorders,…
Alzheimer's disease involves progressive tau accumulation and spread, leading to regional brain atrophy and disruption of large-scale functional networks. While tau propagation and tissue degeneration have been widely modeled, how atrophy…
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 amyloid-$\beta$. Mathematical models and numerical…
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 propose a mathematical model for the onset and progression of Alzheimer's disease based on transport and diffusion equations. We treat brain neurons as a continuous medium and structure them by their degree of malfunctioning. Three…
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.…
In this paper we propose a mathematical model for the onset and progression of Alzheimer's disease based on transport and diffusion equations. We regard brain neurons as a continuous medium, and structure them by their degree of…
In this Note we study a mathematical model for the progression of Alzheimer's Disease in the human brain. The novelty of our approach consists in the representation of the brain as two superposed graphs where toxic proteins diffuse, the…
Misfolded tau proteins play a critical role in the progression and pathology of Alzheimer's disease. Recent studies suggest that the spatio-temporal pattern of misfolded tau follows a reaction-diffusion type equation. However, the precise…
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…
Alzheimer's disease (AD) is characterized by progressive microstructural deterioration in brain tissue, yet conventional imaging and histopathology often lack the sensitivity needed to detect subtle early-stage changes. Here, we present a…
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…
Alzheimer's disease (AD) is characterized by complex and largely unknown progression dynamics affecting the brain's morphology. Although the disease evolution spans decades, to date we cannot rely on long-term data to model the pathological…
In this study we propose a deformation-based framework to jointly model the influence of aging and Alzheimer's disease (AD) on the brain morphological evolution. Our approach combines a spatio-temporal description of both processes into a…
One of the hallmarks of Alzheimer's disease (AD) is the accumulation and spread of toxic aggregates of tau protein. The progression of AD tau pathology is thought to be highly stereotyped, which is in part due to the fact that tau can…
Biomechanical modeling of tissue deformation can be used to simulate different scenarios of longitudinal brain evolution. In this work,we present a deep learning framework for hyper-elastic strain modelling of brain atrophy, during healthy…
We propose a topological framework to study the evolution of Alzheimer's disease, the most common neurodegenerative disease. The modeling of this disease starts with the representation of the brain connectivity as a graph and the seeding of…