Synchronisation and propagation in human cortical networks

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The idea of modelling the brain as a complex network is now well established. However, the emergence of functional brain states, via the interaction of large interconnected neuronal populations, remains poorly understood. This hinders understanding of pathological brain states, and their therapeutic manipulation. This project aims to employ computational and mathematical techniques to shed light on the relationship between structure and function, and with particular application to Transcranial Magnetic Stimulation (TMS), a non-invasive treatment for depression, schizophrenia and chronic pain, whose neurological mechanism remains unknown. To achieve this, we will utilise direct simulation of neural mass models (that provide a coarse-grained description of neural population behaviour) posed on physiological brain networks, together with a range of complementary mathematical approaches that will build up a picture of the structure-function relationship. Mathematical techniques include: study of the network instabilities of equilibria that give rise to neural oscillations, weakly coupled oscillator analyses to describe phase-locked states beyond the onset of oscillations, consideration of false bifurcations (where the shape of network limit-cycle oscillations undergoes a qualitative change) and graph theoretical interrogation of structure-function networks, including multiplex approaches. Insights from these studies will inform how changes in the parameters of TMS delivery (frequency, amplitude, target region etc.) affect resultant functional networks to help understand treatment design for optimisation of TMS therapy.