Dynamic MEG-based imaging of focal neuronalcurrent sources

We describe a new approach to imaging neuronal currents from measurements of the magnetoencephalogram (MEG) and the electroencephalogram (EEG) associated with sensory, motor or cognitive brain activation. Previous approaches have concentrated on the use of weighted minimum norm inverse methods which often produce overly smoothed solutions and exhibit severe sensitivity to noise. Here we describe a Bayesian formulation in which a Gibbs prior is used to resolve ambiguities in the inverse problem.; Basic studies of functional activation reveal the sparse and localized nature of activation in the cerebral cortex. Our prior therefore specifically reflects the expectation that the current sources tend to be sparse and focal. This prior is combined with a Gaussian likelihood model for the data.; The general Bayesian framework presented allows us to introduce a broad range of information, either from other modalities or from prior physiological knowledge. This Bayesian formulation gives a complete probabilistic representation of the image, allowing us the to determine a large number of image properties (i.e., mean, variance, etc.) as well as use a variety of cost functionals on the density to find an estimate of the locations and time series amplitudes of neural sources.; We examine three cost functionals associated with this density. The maximum a posteriori method seeks to find the maximum of the joint density. We show a marginalization technique which integrates over all possible amplitudes to find a binary posterior density depending only on the on or off characteristic of each location. We show the MAP estimate over this marginalized density and show how we may approximately marginalize out all pixels except the pixel of interest, to achieve the maximizer of the posterior marginals solution.; This model is highly non-convex and involves discrete variables (indicating which pixels are active). To perform the optimization we use a continuation method based on mean field theory to guide the solution to a desirable local optimum. We demonstrate the method in application to computer generated data and realistic phantom studies and show favorable performance in comparison to minimum norm approaches.