Mechanistic interpretation of EEG by mapping parameters of neural mass models

Understanding the link between network structure and the dynamics that can emerge is a fundamental question in dynamical systems with applications across many different fields including biology. Neuroscience is a particular application area where the link between network structure and dynamics is fundamental to advancing our understanding
of healthy and abnormal processes. A particularly interesting example is epilepsy, where brain networks can give rise to state switches in dynamics between normal and abnormal states, when seizures occur. The changes in dynamics are visible in clinical recordings and have been modelled using various ordinary and stochastic differential equations. Optimization tools have also been developed to identify perturbations to the network that will render it incapable of generating seizures. However, these are brute force and computationally expensive methods, so we wish to build more efficient approaches that will help to explore the relationship between networks and dynamics. The goal of this project is to develop a combination of tools from dynamical systems and machine learning in order to further our understanding of the link between network structure and state-switching dynamics. Here we will explore different models of spiking dynamics to quantify the propensity of networks to generate seizures. We will complement this work by exploring different methods to quantify dynamics over variations in system parameters. Combining statistical emulation and adaptive sampling methods should help to optimize this process.