Elsevier

NeuroImage

Volume 100, 15 October 2014, Pages 715-724
NeuroImage

Technical Note
Multiple sparse volumetric priors for distributed EEG source reconstruction

https://doi.org/10.1016/j.neuroimage.2014.06.076Get rights and content

Highlights

  • We revist the Multiple Sparse Priors algorithm for EEG source reconstruction.

  • We extend the scope of the algorithm to volumetric forward models.

  • We propose a technique to construct volumetric sparse regions using region growing.

  • Using ERP data and MR images of 12 subjects we illustrate the proposed method.

  • We found very strong evidence in favor this method.

Abstract

We revisit the multiple sparse priors (MSP) algorithm implemented in the statistical parametric mapping software (SPM) for distributed EEG source reconstruction (Friston et al., 2008). In the present implementation, multiple cortical patches are introduced as source priors based on a dipole source space restricted to a cortical surface mesh. In this note, we present a technique to construct volumetric cortical regions to introduce as source priors by restricting the dipole source space to a segmented gray matter layer and using a region growing approach. This extension allows to reconstruct brain structures besides the cortical surface and facilitates the use of more realistic volumetric head models including more layers, such as cerebrospinal fluid (CSF), compared to the standard 3-layered scalp-skull-brain head models. We illustrated the technique with ERP data and anatomical MR images in 12 subjects. Based on the segmented gray matter for each of the subjects, cortical regions were created and introduced as source priors for MSP-inversion assuming two types of head models. The standard 3-layered scalp–skull–brain head models and extended 4-layered head models including CSF. We compared these models with the current implementation by assessing the free energy corresponding with each of the reconstructions using Bayesian model selection for group studies. Strong evidence was found in favor of the volumetric MSP approach compared to the MSP approach based on cortical patches for both types of head models. Overall, the strongest evidence was found in favor of the volumetric MSP reconstructions based on the extended head models including CSF. These results were verified by comparing the reconstructed activity. The use of volumetric cortical regions as source priors is a useful complement to the present implementation as it allows to introduce more complex head models and volumetric source priors in future studies.

Introduction

In this note we present a new application of hierarchical or empirical Bayes for distributed EEG source reconstruction. We depart from the parametric empirical Bayesian (PEB) framework used in the Statistical Parametric Mapping software (SPM) package (Wellcome Trust Centre for Neuroimaging, London, UK). Within the framework, the multiple sparse priors (MSP) algorithm is the state-of-the-art inverse technique. Depending on the EEG data, the algorithm allows the automatic selection of multiple cortical sources with compact spatial support that are specified in terms of empirical priors (Friston et al., 2008).

In the present implementation of the MSP algorithm, multiple cortical patches of sources are constructed based on a source space of dipoles constrained to a cortical surface mesh (Mattout et al., 2007) and the field propagation of the surface patches is calculated based on a 3-layered scalp–skull–brain head model (Henson et al., 2009). Constraining the dipolar sources to a cortical mesh does not allow the reconstruction of brain activity besides the cortical surface. Moreover, it is not straightforward to use more complex head models that extend the 3-layered model with extra layers such as cerebrospinal fluid (CSF). Because the dipoles are located on the boundary between the CSF and the brain, they will either be located inside the CSF or brain compartment which does not satisfy the restrictions to the source space of commonly used numerical methods, such as the boundary element method (Mosher et al., 1999), finite difference method (Hallez et al., 2005, Vanrumste et al., 2001) or finite element method (Wolters et al., 2002), to properly calculate the dipole field propagation (Stenroos and Nenonen, 2012, Strobbe et al., 2014).

In this work, we propose a technique to construct volumetric regions based on a dipole source space restricted to gray matter, segmented from an anatomical MR image, and using a region growing technique. This approach allows the inclusion of more prior information about the anatomy and shape of the sources and does not require the extraction of the cortical surface. It opens up the possibility to use the MSP algorithm to reconstruct brain structures besides the cortical surface and facilitates the use of more realistic volumetric head models including cerebrospinal fluid (CSF) compared to the currently used 3-layered scalp–skull–brain head models.

To illustrate the volumetric MSP approach, we used realistic ERP datasets and anatomical MR images in 12 subjects. Based on the segmented gray matter for each of the subjects, cortical regions were created and introduced as source priors for MSP-inversion assuming two types of head models. For every subject, a 3-layered volumetric subject specific head model was constructed. Also extended 4-layered head models including CSF were built to investigate the influence of increasing the head model complexity. We compared with the present implementation by assessing the free energy corresponding with the reconstructions using Bayesian model selection for group studies (Rigoux et al., 2013, Stephan et al., 2009). The reconstructed activity was also compared with the results of previous studies using similar ERP datasets (Mijović et al., 2012).

In the first section of this paper, we will briefly present the PEB framework and the MSP algorithm. We will explain how we extended the currently used approach based on cortical patches to volumetric regions and subsequently describe how the different head models used in this study were constructed. Next, we explain how we compared the models using Bayesian model selection and verified the reconstructed activity. We conclude with a discussion of the benefits and potential of using volumetric source priors.

Section snippets

Distributed EEG source reconstruction

Assume that we represent the EEG measurements as a multivariate linear model involving a distributed source model with fixed positions and orientations (Dale and Sereno, 1992):V=LJ+ϵwhere VNc×Nt is the EEG dataset of Nc channels and Nt time samples, JNd×Nt is the amplitude of Nd current dipoles with fixed orientations, ϵNc×Nt is the zero mean Gaussian noise and LNc×Nd is the lead field matrix linking the source amplitudes in J to the electrical scalp potentials in V. The lead field

Bayesian model comparison

In Fig. 5, the log Bayes factors are shown, computed as differences in free energy (F) corresponding with the reconstructions based on the considered models for each stimulus condition and every subject. In the first row, we compared the 3-layered models assuming volumetric regions, Vol3lay, with the 3-layered models assuming cortical surface patches, Surf3lay. In the second row, the 4-layered models assuming volumetric regions, Vol4lay were compared with the Surf3lay models. The Vol4lay models

Discussion

We have extended the current application of the multiple sparse priors algorithm (Friston et al., 2008) from sparse surface based priors to volumetric sparse regions. This extension provides the ability to use the MSP algorithm to reconstruct brain structures besides the cortical surface and opens up the ability to introduce more advanced volumetric head models based on volumetric forward modeling approaches using finite differences (Vanrumste et al., 2001), finite elements (Wolters et al., 2002

Software note

The described methods in this technical note are freely available. Please contact the authors for the scripts. We are currently working on a toolbox to integrate volumetric forward models into the SPM framework.

Acknowledgments

Research supported by Research Council KUL: GOA MaNet, PFV/10/002 (OPTEC), Flemish Government FWO projects: G.0427.10N (Integrated EEG-fMRI), IWT-TBM080658-MRI (EEG-fMRI), iMinds, and Belgian Federal Science Policy Office: IUAP P7/(DYSCO, ‘Dynamical systems, control and optimization’, 2012–2017). This work was carried out using the Stevin Supercomputer Infrastructure at Ghent University, funded by Ghent University, the Hercules Foundation and the Flemish Government Department EWI.

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