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We develop a new methodology for determining the location and dynamics ofbrain activity from combined magnetoencephalography (MEG) andelectroencephalography (EEG) data. The resulting inverse problem is ill-posedand is one of the most difficult problems in neuroimaging data analysis. In ourdevelopment we propose a solution that combines the data from three differentmodalities, MRI, MEG, and EEG, together. We propose a new Bayesian spatialfinite mixture model that builds on the mesostate-space model developed byDaunizeau and Friston (2007). Our new model incorporates two major extensions:(i) We combine EEG and MEG data together and formulate a joint model fordealing with the two modalities simultaneously; (ii) we incorporate the Pottsmodel to represent the spatial dependence in an allocation process thatpartitions the cortical surface into a small number of latent states termedmesostates. The cortical surface is obtained from MRI. We formulate the newspatiotemporal model and derive an efficient procedure for simultaneous pointestimation and model selection based on the iterated conditional modesalgorithm combined with local polynomial smoothing. The proposed method resultsin a novel estimator for the number of mixture components and is able to selectactive brain regions which correspond to active variables in a high-dimensionaldynamic linear model. The methodology is investigated using synthetic data andsimulation studies and then demonstrated on an application examining the neuralresponse to the perception of scrambled faces. R software implementing themethodology along with several sample datasets are available at the followingGitHub repository https://github.com/v2south/PottsMix.

A Potts-Mixture Spatiotemporal Joint Model for Combined MEG and EEG Data