The STF tensors were built by computing a Wavelet trans- form of the EEG and MEGdata using a real-valued Morlet wavelet with a centre frequency of 35 Hz and N f = 100
frequency samples. The STWV tensors were constructed separately for EEG and MEG by calculating a discrete local Fourier transform over space of data selected by a spherical Blackman window function. For both modalities, we consid- ered 63 wave vector samples. Each of the resulting tensors was then decomposed individually using a slightly modified version of the SALT algorithm, yielding the lead field matri- ces of the separately treated data. Moreover, we computed the JCP decompositions of the EEG and MEG tensors using the same modified SALT algorithm. For the present source con- figuration, we used a weighting factor of w = 4 for the EEG tensor, which was chosen because of the high associated core consistency (cf. ) of the decomposed tensors. To ensure a real-valued loading matrix for the temporal characteristics of the STWV tensors, one iteration of ALS was applied after the SALT decomposition. For all cases, we assumed that the number of sources and thereby the number of CP components is known.
Abstract—Scale-free dynamics, quantified as power law spectra from magnetoencepholagraphic (MEG) recordings of Human brain activity, may play an important role in cognition and behavior. To date, their characterization remain limited to uni- variate analysis. Independently, functional connectivity analysis usually entails uncovering interactions between remote brain regions. In MEG, specific indices (e.g., Imaginary coherence ICOH and weighted Phase Lag Index wPLI) were developed to quantify phase synchronization between time series reflecting activities of distant brain regions and applied to oscillatory regimes (e.g., α-band in (8, 12) Hz). No such indices has yet been developed for scale-free brain dynamics. Here, we propose to design new indices (w-ICOH and w-wPLI) based on complex wavelet analysis, dedicated to assess functional connectivity in the scale-free regime. Using synthetic multivariate scale-free data, we illustrate the potential and efficiency of these new indices to assess phase coupling in the scale-free dynamics range. From MEGdata (36 individuals), we demonstrate that w-wPLI constitutes a highly sensitive index to capture significant and meaningful group-level changes of phase couplings in the scale-free (0.1, 1.5) Hz regime between rest and task conditions.
Fig. 3: Effective network of A 1 , left, and A 2 , right, obtained from iSDR(p=2) and MEGdata  during face recognition task. Red spheres represent center of active cortical regions. Edges represent uni/bidirectional interactions. Self-interactions are not shown for visualization clarity. Edge’s color represents its strength.
Application to real data of other mental tasks must be investigated and compared to physiological liter- ature to validate our method. Information criterion can be used to obtain the order of MAR model.
V. C ONCLUSION
This work proposed a novel multiscale phase synchroniza- tion measure for the assessment of functional connectivity in scale-free brain dynamics regime. To this end, the key intuitions of Fourier coherence based indices for oscillatory regimes, lending robustness against volume conduction effects in MEG, are combined with scale-free dynamics analysis in the complex wavelet transform domain. To the best of our knowledge, the proposed tool constitutes the only existing operational procedure for the robust quantification of phase synchronization in scale-free time series. Applied to MEGdata for 36 individuals, this tool brought evidence for the pres- ence of significant group-level scale-free FC networks, which are distinct from those classically uncovered with oscillatory regimes. It is noteworthy that only scale-free synchronization measures captured the variations in long-range phase synchro- nization between rest and task. Future work will focus on the functional role of those scale-free FC patterns.
24 within the Hierarchical Bayesian modelling (HBM) framework (Lucka et al., 2012; Strobbe et al., 2016). Lucka et al., 2012 proposed a fully-Bayesian inference method that was developed to localize focal sources, to correct depth localization, a well-known source of systematic error of many current density reconstruction methods, and to separate single sources in multiple-source scenarios. Strobbe et al., 2016 proposed a variational Bayesian approach called the multiple sparse volumetric priors (MSVP) to localize distributed sources and demonstrated the potential of a Bayesian approach to estimate the underlying sources of interictal activity. The MSVP approach seems inspired from a previously proposed method called COH-s, which was introduced in Chowdhury et al., 2013. COH-s consisted in a model combining spatially extended parcels (coming from MEM-based parcellization) and smoothness constraint as covariance components within a hierarchical Bayesian model and inference based on restricted maximum likelihood estimate (Friston et al., 2006, 2008). In Chowdhury et al., 2013 we showed that MEM was more robust and reliable than COH-s method especially in regards to the scale of the underlying parcellization. All these recently developed promising approaches should be considered in future comparative work. One main feature of the present study was not only to compare cMEM and 4-ExSo-MUSIC together but also to quantify their respective ability to retrieve the spatial extent from EEG versus MEG signals. In previous studies, when EEG and MEG source localization were compared on clinical datasets, EEG recordings used a relatively small number of electrodes (typically <64) when compared to MEG (275) (Barkley and Baumgartner, 2003; Malmivuo, 2012; Lopes da Silva, 2013). In such a context, most of these clinical studies demonstrated that source localization from MEG signals was more accurate than EEG. Yet, in line with theoretical studies (Gevins, 1993; Srinivasan et al., 1996, 1998) showing that higher spatial resolution can be obtained with closely spaced electrodes, it has been reported that a clear improvement in terms of localization accuracy can be attained in epileptic patients when EEG is acquired with high density scalp electrodes cap, typically more than 120 electrodes (Lantz and Grave de Peralta, 2003; Holmes et al., 2008, 2010; Brodbeck et al., 2011; Yamazaki et al., 2012, 2013). This is even more true when the data are processed with realistic geometry head models (Wang et al., 2011; Birot et al., 2014) using appropriate brain-to-skull conductivity ratios (Huiskamp et al., 1999; Lantz and Grave de Peralta, 2003; Wang and Ren, 2013) or by calculating the calibrated skull conductivity from EEG/MEGdata as recommended by Aydin et al., 2014.
IV. D ISCUSSION AND C ONCLUSION
In this paper, we proposed a data-driven procedure to detect perceptual thresholds using MEGdata. We proposed an innovative approach to measure decoder’s performance when working with ordered targets and demonstrated how the predictions errors can offer interesting insights on the data. Rather than using a multi-class classifier blind to targets order and with little training samples per class, we used a ridge regression with a pairwise ranking scorer. Altogether, our results suggest that decoding brain activity in a visual task may enable to reliably derive participants’ perceptual threshold changes. Additionally, decoding results in source space bring out reliable discriminative power across regions known to be implicated in the task. Future work will take into consideration additional dynamic aspects of the MEG signals, and test the
In this paper, we propose a sparse MEG/EEG source imaging approach based on regularized regression with a ℓ 2,0.5 -quasinorm penalty. We solve the non-convex optimiza-
tion problem by iterative reweighted MxNE. Each MxNE iteration is solved efficiently by combining a block coordinate descent scheme and an active set strategy. The resulting algorithm is applicable to MEG/EEG inverse problems with and without orientation constraint, running in a few seconds on real MEG/EEG problems. We provide empirical evidence using simulations and analysis of MEGdata that the proposed method outperforms MxNE in terms of active source identifi- cation and amplitude bias.
shown that the peak latency of this component is generally delayed in normal aging (Federmeier & Kutas, 2005; Giaquinto, Ranghi, & Butler, 2007).
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The event-related fields were used to perform source localization, with the maximum entropy on the mean method (MEM : Amblard, Lapalme, & Lina, 2004; Grova, et al., 2006). This method is a cortically-constrained distributed source-localization approach. The cortical surface (we used the white/gray matter boundary in a 3D surface) was segmented from each anatomical MRI scan using BrainVisa software (http://brainvisa.info/index_f.html ). We used a standard co-registration process: like all CTF-VSM MEG systems, three coils that emit signals at three different locations (nasion, left and right pre-ocular) were recorded by the MEG sensors. The positions of the coils relative to the MEG sensors were then calculated. On the processed MRI (3D reconstruction of the subject's head), we manually indicated the position of the three coils with the aid of the pictures taken during the experimental session. The position of the subject's head and the MEG sensors were then co-registered by superimposing the MEGdata and MRI image, by repositioning the coil locations from one image to the other. Approximately 4000 sources, orthogonal to the local surface, were distributed over the cortex of each hemisphere of each participant, and these sources were used in distributed source localization analyses, for each participant.
White matter fibers transfer the information between brain regions with delays that are measurable with magnetoen- cephalography and electroencephalography (M/EEG). In the context of regularizing the dynamics of M/EEG and recov- ering electrical activity of the brain from M/EEG measure- ments, this article proposes a graph representation-based framework to solve the M/EEG inverse problem, where prior information about transmission delays supported by diffusion MRI (dMRI) are included to enforce temporal smoothness. Results of the reconstruction of brain activity from simulated MEG measurements are compared to MNE, LORETA and CGS methods and we show that our approach improves MEG source localization when compared to these three state-of-the- art approaches. In addition, we show preliminary qualitative results of the proposed reconstruction method on real MEGdata for a sensory-motor task.
Let x be an 𝑀 × 1 signal vector of MEGdata measured with 𝑀 sensors, and 𝑁 is the number of grid 259
points in the ROI with grid locations r j , (j = 1, … , 𝑁). Then the source 𝐲(𝑟 𝑗 ) at any location 𝑟 𝑗 can be 260
(3) INSERM, U992, Cognitive Neuroimaging Unit, F-91191 Gif-sur-Yvette, France. 1,3 firstname.lastname@example.org , 2 email@example.com
The analysis of scale-free (i.e., 1/f power spectrum) brain ac- tivity has emerged in the last decade since it has been shown that low frequency fluctuations interact with oscillatory activity in elec- trophysiology, noticeably when exogenous factors (stimuli, task) are delivered to the human brain. However, there are some major dif- ficulties in measuring scale-free activity in neuroimaging data: they are noisy, possibly nonstationary ... Here, we make use of multifrac- tal analysis to better understand the biological meaning of scale-free activity recorded with Magnetoencephalography (MEG) data. On a cohort of 20 subjects, we demonstrate the presence of self-similarity on all sensors during rest and visually evoked activity. Also, we re- port significant multifractality on the norm of gradiometers. Finally, on the latter signals we show how self-similarity and multifractality are modulated between ongoing and evoked activity.
5.2. Experiments on MEGdata
Datasets description. The different strategies were evaluated on two publicly available MEG datasets: DS117  and Cam-CAN . DS117 provides MRI, MEG, EEG and fMRI data of 16 healthy subjects to whom were presented images of famous, unfamiliar and scrambled faces. The fusiform face area (FFA) which specializes in facial recognition activates around 170ms after stimulus [29, 34]. We pick the time point in the contrast response famous vs scrambled with the peak response for each subject within the interval 150-200ms after stimulus. Similarly, Cam-CAN provides MEG, EEG and MRI data of around 650 healthy subjects with several types of tasks. We select the youngest 32 subjects (aged between 18 years and 29 years) and use their MEG recordings to study the auditory N100 response. We average the responses of 3 stimuli: 300Hz, 600Hz and 1200Hz with a total of 60 trials. We pick the time point with the peak response within 80-120 ms after stimulus. For both datasets, the leadfield operator of each subject was obtained from their T1 MRI scan using a cortically constrained source space formed by about 2500 candidate dipoles per hemisphere. Model selection. For all lasso-type models, there exists λ max such that for λ ≥ λ max the
strategy can be extended to set thresholds separately for each sensor and mark trials as bad when a large majority of the sensors have high-amplitude artifacts. This process closely mimics how a human expert would mark a trial as bad during visual inspection.
In the rest of the paper, we detail the internals of our algorithm, compare it against various state-of- the-art methods, and position it conceptually with respect to these different approaches. For this purpose, we make use of qualitative visualization techniques as well as quantitative reports. In a major validation effort, we take advantage of cleaned up evoked response fields (ERFs) provided by the Human Connectome Project ( Larson-Prior et al. , 2013 ) enabling ground truth comparison between alternative methods. This work represents one of the first efforts in reanalysis of the MEGdata from the HCP dataset using a toolkit stack significantly different from the one employed by the HCP consortium. The convergence between our method and the HCP MEG pipelines is encouraging and testifies to the success of the community-wide open science efforts aiming at reproducible research. Naturally, we have therefore made our code available online 2 . In addition to this, we validated our algorithm on the MNE sample data ( Gramfort et al. , 2013 ), the multimodal faces dataset ( Wakeman and Henson , 2015 ), and the EEGBCI motor imagery data ( Goldberger et al. , 2000 ; Schalk et al. , 2004 ).
We present a significant extension of the Brain Imaging Data Structure (BIDS) to support the specific aspects of magnetoencephalography (MEG) data. MEG provides direct measurement of brain activity with millisecond temporal resolution and unique source imaging capabilities. So far, BIDS has provided a solution to structure the organization of magnetic resonance imaging (MRI) data, which nature and acquisition parameters are different. Despite the lack of standard data format for MEG, MEG-BIDS is a principled solution to store, organize and share the typically-large data volumes produced. It builds on BIDS for MRI, and therefore readily yields a multimodal data organization by construction. This is particularly valuable for the anatomical and functional registration of MEG source imaging with MRI. With MEG-BIDS and a growing range of software adopting the standard, the MEG community has a solution to minimize curation overheads, reduce data handling errors and optimize usage of computational resources for analytics. The standard also includes well-defined metadata, to facilitate future data harmonization and sharing efforts.
Second, the MEG and EEG communities follow the recent trend toward data-centric research in the biomedical sciences (Leonelli, 2016). This trend is characterized by the increasing volume of publicly available curated scientific data (Poldrack et al., 2017) and their reuse by teams who have not been involved in the acquisition of the data. Accordingly, new consortia keep emerging that curate large-scale MEG and EEG datasets (Niso et al., 2016; Zhang et al., 2018; Van Essen et al., 2013; Taylor et al., 2017). As a result, researchers from diverse backgrounds can now work on human electrophysiology data without having access to MEG and/or EEG acquisition infrastructure. A researcher who acquires MEGdata in a semantic auditory processing experiment with a limited number of subjects would need a di↵erent set of tools than one who studies cognitive aging employing thousands of MEG recordings from a database (Taylor et al., 2017; Van Essen et al., 2013; Niso et al., 2016). The former would use a combination of GUIs for assessment of data quality, setting annotations, scripting for preprocessing and data analysis backed by reporting tools for quality assessment. The latter would almost solely rely on scripts, emphasize automated processing (Engemann and Gramfort, 2015; Jas et al., 2017) and utilize dedicated libraries for classical machine learning (Pedregosa et al., 2011), deep learning, and specialized forms of data visualization.
are needed to constrain the solution space.
In this work, we introduce an approach which considers white matter streamlines, obtained using diffusion magnetic resonance (MR) imaging , as a source model for the MEG forward problem . To simplify the model and reduce the computational complexity we regrouped similarly shaped streamlines into bundles. The MEGdata associated with a single bundle activity was simulated. The objective was to ﬁt simulated data for each bundle and to analyze the data ﬁtting error.
Functional vs. effective connectivity
The aim of dynamic causal modeling (Friston et al., 2003) is to make inferences about the coupling among brain regions or sources and how that coupling is influenced by experimental factors. DCM uses the notion of effective connectivity, defined as the influence one neuronal system exerts over another. DCM represents a fundamental departure from existing approaches to connectivity because it employs an explicit generative model of measured brain responses that embraces their nonlinear causal architecture. The alternative to causal modeling is to simply establish statistical dependencies between activity in one brain region and another. This is referred to as functional connectivity. Functional connectivity is useful because it rests on an operational definition and eschews any arguments about how dependencies are caused. Most approaches in the EEG and MEG literature address functional connectivity, with a focus on dependencies that are expressed at a particular frequency of oscillations (i.e. coherence). See Schnitzler and Gross (2005) for a nice review. Recent advances have looked at nonlinear or generalized synchronization in the context of chaotic oscillators (e.g. Rosenblum et al 2002) and stimulus-locked responses of coupled oscillators (see Tass 2004). These characterizations often refer to phase-synchronization as a useful measure of nonlinear dependency. Another exciting development is the reformulation of coherence in terms of autoregressive models. A compelling example is reported in Brovelli et al (2004) who were able show that "synchronized beta oscillations bind multiple sensorimotor areas into a large-scale network during motor maintenance behavior and carry Granger causal influences from primary somatosensory and inferior posterior parietal cortices to motor cortex." Similar developments have been seen in functional neuroimaging with fMRI (e.g. Harrison et al., 2003; Roebroeck et al., 2005).
potential neural source to be either active for all subjects or for none of them.
Contribution. The assumption of identical functional activity across subjects is clearly not realistic. Here we investigate several multi-task regression models that relax this assumption. One of them is the multi-task Wasserstein (MTW) model . MTW is defined through an Unbalanced Optimal Transport (UOT) metric that promotes support proximity across regression coefficients. However, applying MTW to group level data assumes that the signal-to-noise ratio is the same for all subjects. We propose to build upon MTW and alleviate this problem by inferring estimates of both sources and noise variance for each subject. To do so, we follow similar ideas that lead to the concomitant Lasso [27,31,25] or the multi-task Lasso .
between the anatomical and diffusion space was obtained by using FSL .
MEG (102 magnetometers, 204 planar gradiometers) and EEG (70 electrodes) were measured simultaneously in a magnetically shielded room. The face stimuli contain three sets of 450 gray scale photographs, one third of unfamiliar people (unknown to the participants), one third of famous people and the remaining are of scrambled faces. The reader is referred to  for more details.
Compared to other methods (e.g., PREP ), we do not make the assumption that sensors must be globally bad. In fact, it can detect and repair sensors even when they are locally bad, thus saving data. Of course, with suitable modifications, the method can also be used to detect flat sensors. Note that, even though we used peak-to-peak threshold as our statistic for trials, our algorithm should work with other reasonable statistics too.