Stochastic Modelling of Human EEG: Application to Epilepsy Diagnosis

This PhD project aims to understand the role of structured random data in recordings of the brain's electrical activity that are used clinically to diagnose epilepsy. The project will develop mathematical models and theories using principles of nonlinear dynamical systems and stochastic processes including differential equations, mean field theory, bifurcation analysis and random matrix theory. In this context, mean field theory and stochastic differential equations can be used to formalise this problem, whereby the dependence structure (effectively the coupling between different brain regions as measured through statistical independencies of the EEG) can be represented as a matrix of random variables. Working in close co-operation with theoreticians and clinicians we will have access to data with which to explore how predictions of the developed models might inform new approaches to diagnosis of epilepsy.