It is well appreciated that many dynamical processes such as transport and waves take place in the brain.

These are generated by mechanisms relying on various physical principles: action potential along the axon, protein transport in intracellular and extracellular space through diffusion, electrophysiological depolarization waves in cortical spreading depression, and cell motion in cancer. Yet, they all share constraints related to tissue heterogeneity, complicated cortical geometry, and the topology of the human brain connectome. In particular, it has been proposed that neurodegenerative diseases are related to the transport and amplification of toxic protein along axonal pathways. From an initial seeding region, we will show that proteins propagate like fronts to the rest of the brain. In turn, these toxic proteins damage neuronal tissues and therefore affect the natural oscillatory dynamics of the brain.Therefore, by coupling these two processes, we can better understand the evolution of cognitive functions during dementia by studying nonlinear waves arising from neuronal mass models on evolving networks.

Short Bio:

Alain Goriely is statutory Professor of Mathematical Modelling at the University of Oxford and a member of the Mathematical Institute. He is Director of the Oxford Centre for Industrial and Applied Mathematics and Director of the Brain and Mechanics Lab. He is a Fellow of St. Catherine’s College, and a Fellow of the Royal Society of London.