Variational Bayesian inversion of the equivalent current dipole model in EEG/MEG

Abstract

In magneto-and electroencephalography (M/EEG), spatial modelling of sensor data is necessary to make inferences about underlying brain activity. Most source reconstruction techniques belong to one of two approaches: point source models, which explain the data with a small number of equivalent current dipoles and distributed source or imaging models, which use thousands of dipoles. Much methodological research has been devoted to developing sophisticated Bayesian source imaging inversion schemes, while dipoles have received less such attention. Dipole models have their advantages; they are often appropriate summaries of evoked responses or helpful first approximations. Here, we propose a variational Bayesian algorithm that enables the fast Bayesian inversion of dipole models. The approach allows for specification of priors on all the model parameters. The posterior distributions can be used to form Bayesian confidence intervals for interesting parameters, like dipole locations. Furthermore, competing models (e.g., models with different numbers of dipoles) can be compared using their evidence or marginal likelihood. Using synthetic data, we found the scheme provides accurate dipole localizations. We illustrate the advantage of our Bayesian scheme, using a multi-subject EEG auditory study, where we compare competing models for the generation of the N100 component. © 2007 Elsevier Inc. All rights reserved. Keywords: EEG; MEG; Equivalent current dipole; Variational Bayes IntroductionThe analysis of evoked responses using magneto-and electroencephalography (M/EEG) can proceed in several ways. If one is interested in inferring the locations of M/EEG generators within brain space, one has to solve the inverse spatial problem (Baillet et al., 2001). There are two main approaches to estimating sources from observed sensor data. The first assumes that sensor data can be explained by a small set of equivalent current dipoles. The inversion of this model amounts to a nonlinear optimization problem, because the forward model is nonlinear in dipole location (Mosher et al., 1992). Recently, the source reconstruction problem has been addressed by placing many dipoles in brain space, and using constraints on the solution to make it unique; for example (Baillet and Garnero, 1997;Mattout et al., 2006;Phillips et al., 2005). This approach is attractive, because it produces images of brain activity comparable to other imaging modalities and it eschews subjective constraints on the inversion. For imaging solutions, most constraints can be motivated by anatomical and physiological arguments, e.g., smoothness constraints and approximate location priors, based on regional activity in functional magnetic resonance imaging (fMRI). Traditional few-dipole solutions, however, are usually regarded as depending too much on user-specified modelling decisions; like the number of dipoles and their initial locations. Mathematically, it can be argued that the inversion of dipole models is a harder problem than inversion of distributed models, becaus...

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