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Amyloid beta peptides (A\b{eta}), implicated in Alzheimers disease (AD), interact with the cellular membrane and induce amyloid toxicity. The composition of cellular membranes changes in aging and AD. We designed multi component lipid…
We consider a stochastic model describing the spiking activity of a countable set of neurons spatially organized into a homogeneous tree of degree $d$, $d \geq 2$; the degree of a neuron is just the number of connections it has. Roughly,…
Recent discovery by Perutz et al. of the physical structure of the amyloid that accumulates in neurons in certain neurodegenerative diseases like Alzheimer's disease or Huntington's disease, suggests novel mechanism of consciousness…
Alzheimer's disease causes severe neurodegeneration in the brain that leads to a certain death. The defining factor is the formation of extracellular senile amyloid plaques in the brain. However, therapeutic approaches to remove them have…
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…
Intrinsically disordered proteins (IDPs), such as amyloid polypeptide (IAPP), beta-amyloid (A\b{eta}), and {\alpha}-synuclein are linked to the insurgence of type 2 diabetes, Alzheimer's, and Parkinson's diseases, respectively. Common…
Alzheimer's disease (AD) is a neurodegenerative disease characterized by dementia and memory loss in the elderly population. The amyloid-$\beta$ peptide (A$\beta$ 1-42) is one of the main pathogenic factors in AD and is known to cause…
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…
It is well-known that the formation of amyloid fiber may cause invertible damage to cells, while the underlying mechanism has not been fully uncovered. In this paper, we construct a mathematical model, consisting of infinite ODEs in the…
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…
Over the past thirty years, researchers have highlighted the role played by a class of proteins or polypeptides that forms pathogenic amyloid aggregates in vivo, including i) the amyloid Abeta peptide, which is known to form senile plaques…
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 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…
Alzheimer's disease (AD) is a neurodegenerative disorder that is beginning with amyloidosis, followed by neuronal loss and deterioration in structure, function, and cognition. The accumulation of amyloid-beta in the brain, measured through…
Diabetic neuropathy is a disorder characterized by impaired nerve function and reduction of the number of epidermal nerve fibers per epidermal surface. Additionally, as neuropathy related nerve fiber loss and regrowth progresses over time,…
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…
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…
Experimental evidence suggests that the folding and aggregation of the amyloid $\beta$-protein (A$\beta$) into oligomers is a key pathogenetic event in Alzheimer's disease (AD). Inhibiting the pathologic folding and oligomerization of…
Inspired by recent suggestions that the Alzheimer's amyloid beta peptide (A beta) can insert into cell membranes and form harmful ion channels, we model insertion of the 40 and 42 residue forms of the peptide into cell membranes using a…
The loss of neuronal cells in the central nervous system may happen in numerous neurodegenerative illnesses. Alzheimer's Disease (AD) is an intricate, irreversible, dynamic neurodegenerative sickness. It is the main source of age-related…