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Motivated by the biologically important and complex phenomena of A\beta\ peptide aggregation in Alzheimer's disease, we introduce a model and simulation methodology for studying protein aggregation that includes extra-cellular aggregation,…
Background. Alzheimer's disease and related dementia (ADRD) are characterized by multiple and progressive anatomo clinical changes. Yet, modeling changes over disease course from cohort data is challenging as the usual timescales are…
Alzheimer's disease (AD) is a prominent, worldwide, age-related neurodegenerative disease that currently has no systemic treatment. Strong evidence suggests that permeable amyloid-beta peptide (Abeta) oligomers, astrogliosis and reactive…
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…
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…
Amyloid-$\beta$ (A$\beta$) plaques in conjunction with hyperphosphorylated tau proteins in the form of neurofibrillary tangles are the two neuropathological hallmarks of Alzheimer's disease. It is well-known that the identification of…
The abnormal aggregation of extracellular amyloid-$\beta$ (A\beta) in senile plaques resulting in calcium (Ca^{+2}) dyshomeostasis is one of the primary symptoms of Alzheimer's disease (AD). Significant research efforts have been devoted in…
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…
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 is a progressive neurological disorder characterized by cognitive impairment and memory loss. With the increasing aging population, the incidence of AD is continuously rising, making early diagnosis and intervention an…
As other neurodegenerative diseases, Alzheimer's disease, the most frequent dementia in the elderly, is characterized by multiple progressive impairments in the brain structure and in clinical functions such as cognitive functioning and…
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…
Currently, many studies of Alzheimer's disease (AD) are investigating the neurobiological factors behind the acquisition of beta-amyloid (A), pathologic tau (T), and neurodegeneration ([N]) biomarkers from neuroimages. However, a…
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 the first part of this paper we review a mathematical model for the onset and progression of Alzheimer's disease (AD) that was developed in subsequent steps over several years. The model is meant to describe the evolution of AD in vivo.…
The preclinical stage of many neurodegenerative diseases can span decades before symptoms become apparent. Understanding the sequence of preclinical biomarker changes provides a critical opportunity for early diagnosis and effective…
Alzheimer's disease (AD) is a progressive and irreversible brain disorder that unfolds over the course of 30 years. Therefore, it is critical to capture the disease progression in an early stage such that intervention can be applied before…
Uncovering the heterogeneity in the disease progression of Alzheimer's is a key factor to disease understanding and treatment development, so that interventions can be tailored to target the subgroups that will benefit most from the…
Predicting the risk of clinical progression from cognitively normal (CN) status to mild cognitive impairment (MCI) or Alzheimer's disease (AD) is critical for early intervention in Alzheimer's disease (AD). Traditional survival models often…
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…