| Summary: | <p>In the field of computational neuroscience, large-scale biophysical modelling is a bottom-up approach to study the interaction between brain structure and function. In this thesis, we propose two models of varying biophysical plausibility as a mechanistic explanations for spontaneous brain activity, as measured with magnetoencephalography (MEG). </p> <p>Mathematically, these models take the form of large systems of non-linear coupled delay-differential equations, and we implement software to numerically solve such systems efficiently. After analysing the empirical data and extracting key features of interest (relating to the temporal dynamics of measured signals), we use Bayesian optimisation to fit our models with two different parameterisation of increasing complexity: first assuming a spatially uniform brain in which the pattern of connections between cortical regions is the only source of temporal structure in the simulations; and second allowing smooth variations of intrinsic parameters across the cortical surface. Our results outperform those published in the scientific literature to date.</p> <p>We contribute an original derivation of a conductance-based model, and an in-depth analysis of the effects of intrinsic model parameters; software to build and simulate large models of delay-networks efficiently; a new approach to the exploration of high-dimensional spaces in the context of Bayesian optimisation (using space-partitioning); an original parameterisation allowing smooth spatial variations of intrinsic parameters across the cortical surface (using spherical harmonics); a novel analysis of structural brain data (from tractography), and several original methods to analyse MEG data (e.g. exploiting the Hilbert phase and extending Riemannian metrics).</p>
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