Analysing and interpreting neuroimaging data using mathematical frameworks for network dynamics

Modern non-invasive probes of human brain activity, such as magneto-encephalography, give high temporal resolution and increasingly improved spatial resolution. With such a detailed picture of the workings of the brain, it becomes possible to use mathematical modelling to establish increasingly complete mechanistic theories of spatio-temporal neuroimaging signals. There is an ever-expanding toolkit of mathematical techniques for addressing the dynamics of oscillatory neural networks allowing for the analysis of the interplay between local population dynamics and structural network connectivity in shaping emergent spatial functional connectivity patterns. This project will be primarily mathematical in nature, making use of notions from nonlinear dynamical systems and network theory, such as coupled-oscillator theory and phase-amplitude network dynamics. Using experimental data and data from the output of dynamical systems on networks with appropriate connectivities, we will obtain insights on structural connectivity (the underlying network) versus functional connectivity (constructed from similarity of real time series or from time-series output of oscillator models on networks). The project will focus in particular on developing techniques for the analysis of dynamics on "multi-layer networks" to better understand functional connectivity within and between frequency bands of neural oscillations.