Large-scale neural dynamics: simple and complex.
We review the use of neural field models for modelling the brain at the large scales necessary for interpreting EEG, fMRI, MEG and optical imaging data. Albeit a framework that is limited to coarse-grained or mean-field activity, neural field models provide a framework for unifying data from different imaging modalities. Starting with a description of neural mass models, we build to spatially extend cortical models of layered two-dimensional sheets with long range axonal connections mediating synaptic interactions. Reformulations of the fundamental non-local mathematical model in terms of more familiar local differential (brain wave) equations are described. Techniques for the analysis of such models, including how to determine the onset of spatio-temporal pattern forming instabilities, are reviewed. Extensions of the basic formalism to treat refractoriness, adaptive feedback and inhomogeneous connectivity are described along with open challenges for the development of multi-scale models that can integrate macroscopic models at large spatial scales with models at the microscopic scale.
Coombes
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School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK. stephen.coombes@nottingham.ac.uk
D000818:Animals; D001921:Brain / Q000502:physiology*; D001931:Brain Mapping / Q000379:methods*; D004569:Electroencephalography; D006801:Humans; D007090:Image Interpretation, Computer-Assisted / Q000379:methods; D008279:Magnetic Resonance Imaging; D015225:Magnetoencephalography; D008959:Models, Neurological; D008962:Models, Theoretical; D012815:Signal Processing, Computer-Assisted