Bayesian inverse analysis of neuromagnetic data using cortically constrained multiple dipoles

Abstract

A recently introduced Bayesian model for magnetoencephalographic (MEG) data consistently localized multiple simulated dipoles with the help of marginalization of spatiotemporal background noise covariance structure in the analysis [Jun et al., (2005): Neuroimage 28:84-98]. Here, we elaborated this model to include subject's individual brain surface reconstructions with cortical location and orientation constraints. To enable efficient Markov chain Monte Carlo sampling of the dipole locations, we adopted a parametrization of the source space surfaces with two continuous variables (i.e., spherical angle coordinates). Prior to analysis, we simplified the likelihood by exploiting only a small set of independent measurement combinations obtained by singular value decomposition of the gain matrix, which also makes the sampler significantly faster. We analyzed both realistically simulated and empirical MEG data recorded during simple auditory and visual stimulation. The results show that our model produces reasonable solutions and adequate data fits without much manual interaction. However, the rigid cortical constraints seemed to make the utilized scheme challenging as the sampler did not switch modes of the dipoles efficiently. This is problematic in the presence of evidently highly multimodal posterior distribution, and especially in the relative quantitative comparison of the different modes. To overcome the difficulties with the present model, we propose the use of loose orientation constraints and combined model of prelocalization utilizing the hierarchical minimum-norm estimate and multiple dipole sampling scheme.

Automatic fMRI‐guided MEG multidipole localization for visual responses

“…3A). The simulated dipolar sources had a 20-nAm strength and different time courses with realistic measurement noise added based on empirical data [see, Auranen et al, 2007]. By slightly varying the location of two sources (2-3 mm along the cortex) the orientation changed significantly enough to make some of the sources barely visible in MEG sensors due to their almost radial orientation (S1r and S2r).…”

“…To avoid shifting the focus from the novel idea of utilizing fMRI data for guiding the MCMC-based algorithm, and to keep the manuscript straightforward, we do not duplicate the model formulation from [Auranen et al, 2007]. Here, the simulated and empirical data were analyzed with this previously described model with modifications so that the fMRI-guidance in the form of proposal distributions in the reversible jump Markov chain Monte Carlo and Metropolis-Hastings parts of the sampling procedure could be used [see, next section and Auranen et al, 2007, for details].…”

“…If the sampler does not switch well between modes, it is very difficult to validly compare the probability mass of the different solution modes (i.e., inverse estimates) as samples from the different chains are not typically directly comparable. Previously, we implemented cortical orientation and location constraints to a Bayesian dipole analysis model introduced by Jun et al [2005] and showed that it provides reasonable inverse estimates with little manual intervention [Auranen et al, 2007]. However, the convergence of the Markov chain was rather slow and the sampler did not switch optimally between different modes, thus hampering full Bayesian posterior analysis.…”

“…In this article, we incorporate fMRI data to our cortically constrained MEG inverse dipole sampling method [Auranen et al, 2007], not by directly seeding the model or by using strict priors, but by introducing fMRI-based proposal distributions that are used to suggest MCMC jumps to more likely activated cortical locations. This yields an fMRI-guided MEG inverse model, which we first verify by simulations designed to test the ability of our fMRI-guided dipole sampling to produce improved localization results and faster convergence than the model without fMRI-guidance.…”

“…As our previous model [Auranen et al, 2007] produces reasonable estimates with sources far apart from each other, we wanted to test the model in a particularly difficult situation, namely to scan the locations of human visual system, in which the sources are known to be adjacent [Vanni et al, 2004b] making the inverse estimation challenging. We specifically hypothesize that with simulated data, the convergence of the sampling procedure is faster and the results are both qualitatively and quantitatively improved with the fMRI-guided MEG inverse dipole modeling.…”