MEG Source Localization under Multiple Constraints: An Extended Bayesian Framework

Abstract

To use Electroencephalography (EEG) and Magnetoencephalography (MEG) as functional brain 3D imaging techniques, identifiable distributed source models are required. The reconstruction of EEG/ MEG sources rests on inverting these models and is ill-posed because the solution does not depend continuously on the data and there is no unique solution in the absence of prior information or constraints. We have described a general framework that can account for several priors in a common inverse solution. An empirical Bayesian framework based on hierarchical linear models was proposed for the analysis of functional neuroimaging data [Friston, K., Penny, W., Phillips, C., Kiebel, S., Hinton, G., Ashburner, J., 2002. Classical and Bayesian inference in neuroimaging: theory. NeuroImage 16, 465 -483] and was evaluated recently in the context of EEG [Phillips, C., Mattout, J., Rugg, M.D., Maquet, P., Friston, K., 2005. An empirical Bayesian solution to the source reconstruction problem in EEG. NeuroImage 24, 997 -1011]. The approach consists of estimating the expected source distribution and its conditional variance that is constrained by an empirically determined mixture of prior variance components. Estimation uses Expectation-Maximization (EM) to give the Restricted Maximum Likelihood (ReML) estimate of the variance components (in terms of hyperparameters) and the Maximum A Posteriori (MAP) estimate of the source parameters. In this paper, we extend the framework to compare different combinations of priors, using a second level of inference based on Bayesian model selection. Using MonteCarlo simulations, ReML is first compared to a classic Weighted Minimum Norm (WMN) solution under a single constraint. Then, the ReML estimates are evaluated using various combinations of priors. Both standard criterion and ROC-based measures were used to assess localization and detection performance. The empirical Bayes approach proved useful as: (1) ReML was significantly better than WMN for single priors; (2) valid location priors improved ReML source localization; (3) invalid location priors did not significantly impair performance. Finally, we show how model selection, using the logevidence, can be used to select the best combination of priors. This enables a global strategy for multiple prior-based regularization of the MEG/EEG source reconstruction. D

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

“…By allowing the prior precisions to be optimised as free parameters, we are effectively optimising the balance between data and priors. This is an important aspect of hierarchical Bayesian models, which we have exploited in the context of parametric empirical Bayes models previously (e.g., Mattout et al, 2006;Phillips et al, 2002). It was also used by Sato et al (2004) to implement automatic relevance determination (ARD) to 'switch off' redundant sources in an imaging context.…”

“…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.…”

fMRI–EEG integrated cortical source imaging by use of time-variant spatial constraints

“…Depending on different EEG source models, the fMRI map can be used to constrain the locations of multiple current dipoles, namely the fMRI-constrained dipole fitting (Ahlfors et al, 1999;Korvenoja et al, 1999;Fujimaki et al, 2002;Vanni et al, 2004), or to constrain the distributed source distribution over the folded cortical surface or in the 3-D brain volume, namely the fMRI-constrained current density imaging (George et al, 1995;Liu et al, 1998;Dale et al, 2000;Wagner et al, 2000;Babiloni et al, 2005;Ahlfors and Simpson, 2004;Sato et al, 2004;Phillips et al, 2005;Liu et al, 2006b;Mattout et al, 2006).…”

“…Existing methods for the fMRI-constrained current density imaging have been implemented under different frameworks such as Wiener estimation (Dale and Sereno, 1993;Liu et al, 1998;Dale et al, 2000), weighted minimum norm (Wagner et al, 2000;Babiloni et al, 2005;Ahlfors and Simpson et al, 2004), Bayesian estimation (Sato et al, 2004;Phillips et al, 2005;Mattout et al, 2006) and Twomey regularization (Liu et al, 2006b). …”

A Unified Bayesian Framework for MEG/EEG Source Imaging

“…In this scenario, candidate priors are distinguished by a set of flexible hyperparameters γ that must be estimated via a variety of data-driven iterative procedures. Examples include hierarchical covariance component models [12], [24], [31], automatic relevance determination (ARD) [22], [26], [33], [34], [41], and several related variational Bayesian methods [13], [14], [27], [29], [36], [38].…”