The role of beta-amyloid and tau proteins in Alzheimer's disease: a mathematical model on graph

TL;DR

This paper introduces a novel mathematical model representing the brain as two interconnected graphs to study the progression of Alzheimer's disease, emphasizing the synergistic effects of beta-amyloid and tau proteins.

Contribution

It presents a new graph-based modeling approach that captures the diffusion of toxic proteins and their interactions in Alzheimer's disease progression.

Findings

The model confirms the importance of protein synergy in disease development.

Numerical tests support the relevance of the proposed hypotheses.

The approach offers a new perspective for understanding Alzheimer's mechanisms.

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-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.