Background: Measuring spinal alignment with radiological parameters is essential in patients with spinal conditions likely to be treated surgically. These evaluations are not usually included in the radiological report. As a result, spinal surgeons commonly perform the measurement, which is time-consuming and subject to errors.
View Article and Find Full Text PDFIn 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 connectivity graph which represents the neural network, and the proximity graph which takes into account the extracellular space. Toxic proteins such as [Formula: see text] amyloid and Tau play in fact a crucial role in the development of Alzheimer's disease and, separately, have been targets of medical treatments.
View Article and Find Full Text PDFAlzheimer's disease involves widespread and progressive deposition of misfolded protein tau (), first appearing in the entorhinal cortex, coagulating in longer polymers and insoluble fibrils. There is mounting evidence for "prion-like" trans-neuronal transmission, whereby misfolded proteins cascade along neuronal pathways, giving rise to networked spread. However, the cause-effect mechanisms by which various oligomeric species are produced, aggregate, and disseminate are unknown.
View Article and Find Full Text PDFIn this article 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 malfunctioning. Two different mechanisms are assumed to be relevant for the temporal evolution of the disease: i) diffusion and agglomeration of soluble polymers of amyloid, produced by damaged neurons and ii) neuron-to-neuron prion-like transmission.
View Article and Find Full Text PDFIn this paper we present a mathematical model for the aggregation and diffusion of Aβ amyloid in the brain affected by Alzheimer's disease, at the early stage of the disease. The model is based on a classical discrete Smoluchowski aggregation equation modified to take diffusion into account. We also describe a numerical scheme and discuss the results of the simulations in the light of the recent biomedical literature.
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