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We introduce a mathematical model of the in vivo progression of Alzheimer's disease with focus on the role of prions in memory impairment. Our model consists of differential equations that describe the dynamic formation of {\beta}-amyloid…
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…
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…
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,…
We employ the Hopfield model as a simplified framework to explore both the memory deficits and the biochemical processes characteristic of Alzheimer's disease. By simulating neuronal death and synaptic degradation through increasing the…
The association of epileptic activity and Alzheimer's disease (AD) has been increasingly reported in both clinical and experimental studies, suggesting that amyloid-$\beta$ accumulation may directly affect neuronal excitability. Capturing…
Pre-symptomatic (or Preclinical) Alzheimer's Disease is defined by biomarker evidence of fibrillar amyloid beta pathology in the absence of clinical symptoms. Clinical trials in this early phase of disease are challenging due to the slow…
Alzheimer's disease (AD) is driven by the accumulation of amyloid-beta (Abeta) proteins in the brain, leading to memory loss and cognitive decline. While monoclonal antibodies targeting Abetahave been approved, optimizing their use to…
Recent experiments with amyloid-beta (Abeta) peptide suggest that formation of toxic oligomers may be an important contribution to the onset of Alzheimer's disease. The toxicity of Abeta oligomers depends on their structure, which is…
Alzheimer's disease (AD) persists as a paramount challenge in neurological research, characterized by the pathological hallmarks of amyloid-$\beta$ (A$\beta$) plaques and neurofibrillary tangles composed of hyperphosphorylated tau. This…
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…
Alzheimer's disease (AD) persists as a paramount challenge in neurological research, characterized by the pathological hallmarks of amyloid-beta (Abeta) plaques and neurofibrillary tangles composed of hyperphosphorylated tau. This review…
Alzheimer's disease is a human brain disease that affects a significant fraction of the population by causing problems with short-term memory, thinking, spatial orientation and behavior, memory loss and other intellectual abilities. Up to…
Alzheimer's disease (AD) is a common form of dementia observed in the elderly due to neurodegenerative disorder and dysfunction. This arises from alterations in synaptic functioning of neurons leading to cognitive impairment and memory…
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 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…
Alzheimer's disease is a progressive neurodegenerative disorder that primarily affects cognitive functions such as memory, thinking, and behavior. In this disease, there is a critical phase, mild cognitive impairment, that is really…
Alzheimer's disease (AD) is a neurodegenerative disorder and the most common cause of dementia in the elderly. The extracellular accumulation of amyloid-$\beta$ (A$\beta$) in senile plaques is a principal event in the pathogenesis and there…
Alzheimer's disease (AD) is a progressive neurodegenerative disorder that severely impairs survival and quality of life. While anti-amyloid beta (Abeta) therapies can slow disease progression, their efficacy depends on personalized dosing…
Disease progression modeling provides a robust framework to identify long-term disease trajectories from short-term biomarker data. It is a valuable tool to gain a deeper understanding of diseases with a long disease trajectory, such as…