Modelling of large-scale brain network dynamics

Like many systems in nature, the brain is a highly organised unit of interacting components. A natural way to study such systems is through the lens of mathematics, from which we may attempt to delineate the mechanisms that underlie seemingly unfathomable brain functionality using prescribed parameters and equations. In this thesis, we use large-scale neural mass network models of the human cortex to simulate brain activity. Moreover, we utilise techniques from graph, linear and weakly-coupled oscillator theory to describe the network states that are exhibited by such models. In particular, we focus on how the emergent patterns of synchrony (which are thought to be fundamental to the function of brain), or so-called functional connectivity, are dependent on the structural connectivity, which is the anatomical substrate for brain dynamics. Through large-scale network simulations and linear analysis we find that the structure--function relationship is highly dependent on-- and indeed, predictable from-- the dynamical state of individual nodes in the network, highlighting the role of dynamics in facilitating emergent functional connectivity. We take this further to consider how network states are modulated by external simulation and conduction delays, especially in relation to the influence of transcranial magnetic stimulation (TMS) on the brain's dynamics and, more generally, its role as a neuromodulator. We describe a computational framework using a recently developed next-generation neural mass model, by which trains of simulated pulses are employed to drive network dynamics into different states, which we believe may be adapted to be used to study the efficacy of TMS and to test in silico different stimulation protocols that can be used to treat neurological conditions. We then analyse more specific applications to potential effects of TMS: neural entrainment and conduction delays (which may be altered via TMS-induced plasticity). We use the theory of Lyapunov exponents to study entrainment via external stimulation and use linear analysis, as well as structural eigenmodes, to predict emergent network states due to conduction delays across long-range white matter projections