Mathematics, the Mind and Alzheimer’s disease: Systematical progression on brain graphs #

Prama Putra, Alain Goriely

14:10 Tuesday in 4Q56.

Part of the New mathematical approaches in the life sciences session.

Abstract #

Neurodegenerative diseases, Alzheimer’s disease (AD) in particular, present a clear challenge to modern medicine due to the brain’s delicate in vivo environment and limited insight from the human whole nervous system. Mathematical network models of dementia, such as AD, offer a path forward that can be deployed using the multitude of anatomical brain-graph data from real human patients. The dynamical processes of the model support front-like propagation on networks, where an initial localized perturbation grows and systematically invades all nodes in the network. The main question is to understand its overall dynamics. For instance, if a process starts at a seed location, how long will it take to appear at other locations, and then develop through a full-scale invasion, leading to dementia in the brain? The arrival-time problem, which consists in determining the time it takes for a quantity of interest to reach a certain level at each node, greatly depends on the coupling dynamics between nodes. In this talk, I address a question to extract estimates for the dynamics motivated by the study of toxic protein propagation in neurodegenerative diseases: if a single node is seeded at a small concentration, when will other nodes reach the same initial concentration? My research demonstrates that different estimates can give important insights to understand the dynamics and, in particular, analytical methods to estimate and compute the arrival times are extremely powerful and can capture essential features in AD.