A general Bayesian treatment for MEG source reconstruction incorporating lead field uncertainty

Abstract

There is uncertainty introduced when a cortical surface based model derived from an anatomical MRI is used to reconstruct neural activity with MEG data. This is a specific case of a problem with uncertainty in parameters on which M/EEG lead fields depend non-linearly. Here we present a general mathematical treatment of any such problem with a particular focus on co-registration. We use a Metropolis search followed by Bayesian Model Averaging over multiple sparse prior source inversions with different headlocation/orientation parameters. Based on MEG data alone we can locate the cortex to within 4 mm at empirically realistic signal to noise ratios. We also show that this process gives improved posterior distributions on the estimated current distributions, and can be extended to make inference on the locations of local maxima by providing confidence intervals for each source.

Flexible head-casts for high spatial precision MEG

“…However, the high SNR recordings mean that this framework can be used to directly test between different forward models (e.g. the head in different positions, see (López et al, 2012)) delivering an accuracy measure that encompasses the complete source reconstruction pathway.…”

Data-driven forward model inference for EEG brain imaging

“…The latter would hinder a grid search for the optimal forward model due to the 'curse of dimensionality' and optimization techniques such as Bayesian schemes, e.g. BayesOpt [62] or Metropolis search combined with BMA [48] would become necessary. The database can be further extended by adding head geometries for more subjects using large anatomical scan databases such as the Biomedical Informatics Research Network [63].…”

“…2, the free energy provides optimal data fit while penalizing complexity. We optimize the free energy with respect to both the source configuration as well as the forward model representation, as similarly done in [48]. We apply a source localization procedure based on a statistical model whose prior favors sparse solutions; the so-called Variational Garrote [33,34,35,36], described in Appendix A.…”

Non-linear Parameter Estimates from Non-stationary MEG Data

“…Generally, source estimation can be expressed by the expected value of the posterior source activity distribution, which can be computed from the input data using the Bayes' theorem, as follows: $Pfalse(\mathbf{J}|\mathbf{Y}false)=Pfalse(\mathbf{Y}|\mathbf{J}false)Pfalse(\mathbf{J}false)/Pfalse(\mathbf{Y}false).$ As outlined in Lopez et al (2012), we can incorporate uncertainty about anatomical assumptions of the head model, that is, L = L ( h ), where h denotes the set of anatomical parameters (in this case the head-position data). Thus, the source reconstructed solution is rewritten in the form:…”