Mathematical neuroscience: from neural fields to neuroimagingTools Ross, James (2025) Mathematical neuroscience: from neural fields to neuroimaging. PhD thesis, University of Nottingham.
AbstractModern non-invasive techniques for probing human brain activity, such as magnetoencephalography (MEG), offer high temporal resolution and continuously improving spatial resolution, providing an increasingly detailed view of brain function. These advancements enable the development of sophisticated mathematical models to better understand the mechanisms underlying spatio-temporal neuroimaging signals. This thesis enhances the biological accuracy of neural mass, field, and network models by incorporating a variety of key biological features, improving their utility in understanding brain function. We make use of various neural models, including mean-field models derived from networks of single neurons, which allow for tracking neuronal synchrony and incorporating biological features such as gap junctions at the cellular level. A model incorporating dendritic depth allows more direct measures of local field potentials (LFP) and electroencephalography (EEG) signals. Furthermore, models integrating gap-junctions and extracellular ion concentrations are developed, providing insights into the relationship between extracellular activity and neuronal dynamics—a subject particularly relevant to epilepsy research. An optimisation algorithm is also developed and utilised to fit these models to real data.
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