Waves on a folded brain

Project description

The human brain has a wonderfully folded cortex with regions of both negative and positive curvature at gyri and sulci respectively. As the state of the brain changes waves of electrical activity spread and scatter through this complicated surface geometry. This project will focus on the mathematical modelling of realistic cortical tissue and the analysis of wave propagation and scattering using techniques from dynamical systems theory and scientific computation.

In more detail the project will consider models of neural activity represented by non-local integro-differential equations posed on both idealised and human realistic cortical structures. The former will allow the development of analytical tools to understand the role of tissue heterogeneity and disorder in sculpting wave dynamics, such as the recently developed interface approach [1]. The latter will extend this so-called neural field approach [2] using cortical meshes from human connectome databases, making extensive use of spectral and finite element methods

This applied mathematical project will be facilitated by interaction with colleagues from the Sir Peter Mansfield Imaging Centre. As well as exposing the PhD student to rich neuroimaging data-sets collected locally using cutting edge magnetoencephalography techniques, the project will contribute to our understanding of cortical waves in the functioning of the human brain.