By 2030, an estimated 78 million people will be living with Alzheimer’s disease (AD). Despite decades of research, clinical trials continue to face failure rates exceeding $95\%$, highlighting the need for improved mechanistic understanding of disease progression and therapeutic response. Mathematical modelling provides a framework to integrate biological processes across scales and enable...
Mathematical models can be used to verify medical hypotheses and quantify the mechanisms of the progression of neurological pathologies like Alzheimer's disease. In this work, we are interested in elucidating the spread of misfolded tau protein, a critical hallmark of Alzheimer's disease, alongside amyloid $\beta$ protein, while taking the synergistic interaction between the two proteins into...
Pathological accumulations of hyperphosphorylated tau protein aggregates, known as neurofibrillary tangles, are detected in several neurodegenerative tauopathies, including Alzheimer's disease \cite{GS:2017}. Tau is a highly soluble, natively unfolded protein which is predominantly located in the axons of neurons of the central nervous system. Here, its physiological function is to support...
Astrocytes are glial cells essential for brain homeostasis, acting as metabolic mediators that couple cerebral blood flow and nutrient uptake to neuronal energy demands. In Alzheimer’s disease (AD), progressive neurodegeneration is accompanied by profound alterations in astrocyte morphology and metabolism. Reactive transformation leads to significant structural remodeling and metabolic...
Mathematical modelling is an important tool for understanding a complex pathology such as Alzheimers disease (AD). Quantitative models enable to formalize hypotheses about key factors such as the dynamics of proteins ($A\beta$ and $\tau$) and inflammation, providing insights difficult to obtain through experiments alone. To this purpose many different and possibly complementary approaches can...
