相关论文: Exploring tau protein and amyloid-beta propagation…
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 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…
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…
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…
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…
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 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…
Aggregates of misfolded tau proteins (or just 'tau' for brevity) play a crucial role in the progression of Alzheimer's disease (AD) as they correlate with cell death and accelerated tissue atrophy. Longitudinal positron emission tomography…
We propose a method that uses a two-species ordinary differential equation (ODE) model to characterize misfolded tau (or simply tau) protein spreading in Alzheimer's disease (AD) and calibrates it from clinical data. The unknown model…
Alzheimer's disease (AD) is a common neurodegenerative disorder nowadays. Amyloid-beta (A$\beta$) and tau proteins are among the main contributors to the development or propagation of AD. In AD, A$\beta$ proteins clump together to form…
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 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.…
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…
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 disorders. Likely, the most important and studied misfolded protein…
Three major biomarkers: beta-amyloid (A), pathologic tau (T), and neurodegeneration (N), are recognized as valid proxies for neuropathologic changes of Alzheimer's disease. While there are extensive studies on cerebrospinal fluids…
Background: Despite the striking efforts in investigating neurobiological factors behind the acquisition of amyloid-\b{eta} (A), protein tau (T), and neurodegeneration ([N]) biomarkers, the mechanistic pathways of how AT[N] biomarkers…
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 cerebrovascular pathology are mutually reinforcing; in…
In this note, we apply the theory of stochastic homogenization to find the asymptotic behavior of the solution of a set of Smoluchowski's coagulation-diffusion equations with non-homogeneous Neumann boundary conditions. This system is meant…
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…
Alzheimer's disease (AD) is a complex neurodegenerative disorder characterized by the accumulation of amyloid-beta (A$\beta$) and phosphorylated tau (p-tau) proteins, leading to cognitive decline measured by the Alzheimer's Disease…