Elsevier

Journal of Neuroscience Methods

Volume 226, 15 April 2014, Pages 147-160
Journal of Neuroscience Methods

Basic Neuroscience
Sparse weightings for collapsing inverse solutions to cortical parcellations optimize M/EEG source reconstruction accuracy

https://doi.org/10.1016/j.jneumeth.2014.01.031Get rights and content

Highlights

  • We introduce an optimized weighting operator for collapsing M/EEG inverse solutions.

  • Operator-optimization enhances source reconstruction accuracy.

  • Optimization increases true positive rate of inter-parcel interaction mapping.

  • Optimized operator is robust against changes in source topography.

  • The approach yields increased intra-parcel coherence in real and simulated data.

Abstract

Background

Source-reconstructed magneto- and electroencephalography (M/EEG) are promising tools for investigating the human functional connectome. To reduce data, decrease noise, and obtain results directly comparable to magnetic resonance imaging (MRI), M/EEG source data can be collapsed into a cortical parcellation. For most collapsing approaches, however, it remains unclear if collapsed parcel time series accurately represent the coherent source dynamics within each parcel.

New method

We introduce a collapse-weighting-operator optimization approach that maximizes parcel fidelity, i.e., the phase correlation between original source dynamics and collapsed parcel time series, and thereby the accuracy with which the source dynamics are retained in forward and inverse modeling.

Results

The sparse, optimized weighting operator increased parcel fidelity 57–73% and true positive rate of interaction mapping from 0.33 to 0.84 in comparison to a non-sparse weighting approach. These improvements were robust for variable source topographies and parcellation resolutions. Critically, in real inverse-modeled MEG data, the optimized operator yielded close-to-perfect intra-parcel coherence.

Comparison with existing methods

Previous suggestions for obtaining parcel time series include averaging all source time series within each anatomical parcel or using exclusively the time series of the voxel with maximum power. These methods are sensitive to signal heterogeneity and outlier sources. The approach advanced here avoids these problems.

Conclusions

The optimized operator is suitable for collapsing real source-reconstructed M/EEG data into any cortical parcellation. The enhanced time series reconstruction fidelity yields improved accuracy of subsequent analyses of both local dynamics and large-scale interaction mapping.

Introduction

Mapping the human connectome, i.e., creating a comprehensive map of the structural and functional networks of the brain is one of the key challenges in neuroscience (Sporns, 2013a, Van Essen and Ugurbil, 2012). To date, a vast majority of connectomics research has utilized magnetic resonance imaging (MRI) for either mapping structural connectivity with diffusion tensor or diffusion spectrum imaging (DTI, DSI) (Hagmann et al., 2008) or functional connectivity through functional MRI (fMRI) of blood-oxygenation-level dependent (BOLD) signals (Cammoun et al., 2012, Power et al., 2011). These data show that both the structural and functional connectomes are intricately structured, hierarchically modular, small-world networks (Hagmann et al., 2008, Power et al., 2011). Much less, however, is known about the electrophysiological substrates of the intrinsic functional connectivity. This connectivity comprises the human electrophysiological connectome that can be estimated from both phase and amplitude dynamics of neuronal activity recorded with millisecond resolution by using either separate (MEG and EEG) or concurrent (M/EEG) magneto- and electroencephalography. Importantly, when MEG and EEG recordings are combined with source reconstruction the neuronal activity and interactions can be localized (Gross et al., 2001, Gross et al., 2004, Palva et al., 2010, Palva and Palva, 2012b). Both independent-components analysis (ICA) (Brookes et al., 2011, de Pasquale et al., 2012) and all-to-all connectivity analyses (Hipp et al., 2012) of source modeled MEG data demonstrate that amplitude–amplitude correlations of neuronal oscillations show spatial patterns similar to those of the resting-state networks of BOLD connectivity. MEG is hence a promising method for investigating inter-areal interactions that define the human electrophysiological connectome. The accuracy of the inverse modeling methods used in source reconstruction is critical for all MEG studies, and particularly for mapping the inter-areal interactions. However, the accuracy of MEG-data based interaction studies is restricted by signal mixing as each MEG measurement channel detects a linear mixture of activity of multiple cortical sources that is impossible to fully disentangle with source modeling (Palva and Palva, 2012b, Schoffelen and Gross, 2009).

Inverse modeling can be used to estimate source time series from M/EEG sensor data. For example, cortically constrained minimum-norm-estimate (MNE) (Hamalainen and Sarvas, 1989, Lin et al., 2006) yields time series of 6000–8000 sources, “vertices”, covering the cortical surface. Considering that M/EEG have only some hundreds of sensors and even less degrees of freedom, these sources are highly redundant. Thus, to decrease redundancy and improve signal-to-noise ratio (SNR), and also to analyze M/EEG data in a form that is directly comparable with MRI studies, the vertex time series should be collapsed into time series of some hundreds of cortical areas, “parcels”, that can be obtained as a weighted average of the vertex time series (Palva et al., 2010, Palva et al., 2011).

In the present study, we present an approach for optimizing the weights for collapsing inverse-modeled M/EEG data into cortical parcellations. To this end, we quantify the accuracy of parcellated M/EEG source time series with “fidelity”; phase correlation of original simulated vertex time series and collapsed parcel time series. Optimized weights for the collapse operator are achieved by maximizing the parcel fidelity. As an outcome, the time series of each parcel form a coherent cluster and their original dynamics are better retained after inverse modeling than without such optimization. Optimization improved not only the phase reconstruction but in a comparable manner also the estimation of amplitude time series. We also demonstrate that the enhanced parcel fidelity yielded by optimal collapse weighting operators improve the accuracy of inter-areal interaction analyses, which is essential in studies mapping functional connectivity or addressing the functional significance of the inter-areal neuronal interactions.

Section snippets

Subjects and recordings

The optimized inverse collapse weighting operator was validated using both simulated and real data. T1-weighted anatomical MRI scans of 13 healthy volunteers (29 ± 6 years of age, mean ± SD, 7 females) were obtained at a resolution of a ≤1 mm × 1 mm × 1 mm with a 1.5-T MRI scanner (Siemens, Germany) and used to create an anatomical reconstruction of the cortical surface and an anatomical parcellation (see Section 2.2). The noise covariance matrix required to create inverse operators was obtained from

Optimization leads to a sparse collapse weighting operator

In the present work, we used forward and inverse modeling to simulate M/EEG data analysis: vertex time series simulated in source space (to which we refer as “original” time series) were forward modeled to obtain a simulated M/EEG measurement, and inverse modeled and collapsed to obtain the parcel time series. We defined parcel fidelity (f) as the phase correlation between the original time series of the vertices within a parcel and the collapsed parcel time series, and parcel infidelity (i) as

Discussion

In the present study, we have addressed the problem of parcellating inverse-modeled M/EEG data in an optimal way. Our approach was to find an optimal weighting operator for collapsing inverse solutions to maximize source time-series reconstruction fidelity, i.e., phase correlation between original and source-reconstructed parcel time series in any cortical parcellation. We found that the optimized weighting operator increased the true positive rate in all-to-all interaction mapping by enhancing

Acknowledgments

This work was funded by Academy of Finland Grants 253130 and 256472 (to J.M.P.) and 1126967 (to S.P.), University of Helsinki Research Funds (S.P.), and the Sigrid Juselius Foundation (S.P. and J.M.P.).

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    Present address: Department of Biomedical Engineering and Computational Science, Aalto University School of Science, P.O. Box 12200, FI-00076, Finland.

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