The role of A$$\beta $$ and Tau proteins in Alzheimer’s disease: a mathematical model on graphs

Abstract

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 connectivity graph which represents the neural network, and the proximity graph which takes into account the extracellular space. Toxic proteins such as $$\beta $$ β amyloid and Tau play in fact a crucial role in the development of Alzheimer’s disease and, separately, have been targets of medical treatments. Recent biomedical literature stresses the potential impact of the synergetic action of these proteins. We numerically test various modelling hypotheses which confirm the relevance of this synergy.

Reactive oxygen species may cause amyloid beta aggregation by free radical polymerization

“…These models include the mass balance of various species, for example, monomers and fibrils. The model equations for predicting the concentration of different species are, generally, either set of ordinary differential equations (ODEs) 30,59 or a complicated Smoluchowski‐type set of partial differential equations (PDEs) 34,53,60,61 . PDEs also incorporate the diffusion and transport of the fibrils.…”

Directionality bias underpins divergent spatiotemporal progression of Alzheimer-related tauopathy in mouse models

“…For this purpose, we used as our base model our previous mathematical network transmission (NT) models of pathology spread along anatomical connectivity successfully recapitulate the spatiotemporal regional volumetric loss in patients’ brains. These models show great promise in predicting later disease patterns from early timepoints Raj et al (2012 , 2015 ); Zhou et al (2012) ; Iturria-Medina (2013) ; Weickenmeier et al (2018) ; Bertsch et al (2023) .…”