Phase shift invariant imaging of coherent sources (PSIICOS) from MEG data

Characterization of Second-Order Mixing Effects in Reconstructed Cross-Spectra of Random Neural Fields

Functional connectivity in electroencephalography (EEG) and magnetoencephalography (MEG) data is commonly assessed by using measures that are insensitive to instantaneously interacting sources and as such would not give rise to false positive interactions caused by instantaneous mixing of true source signals (first-order mixing). Recent studies, however, have drawn attention to the fact that such measures are still susceptible to instantaneous mixing from lagged sources (i.e. second-order mixing) and that this can lead to a large number of false positive interactions. In this study we relate first- and second-order mixing effects on the cross-spectra of reconstructed source activity to the properties of the resolution operators that are used for the reconstruction. We derive two identities that relate first- and second-order mixing effects to the transformation properties of measurement and source configurations and exploit them to establish several basic properties of signal mixing. First, we provide a characterization of the configurations that are maximally and minimally sensitive to second-order mixing. It turns out that second-order mixing effects are maximal when the measurement locations are far apart and the sources coincide with the measurement locations. Second, we provide a description of second-order mixing effects in the vicinity of the measurement locations in terms of the local geometry of the point-spread functions of the resolution operator. Third, we derive a version of Lagrange's identity for cross-talk functions that establishes the existence of a trade-off between the magnitude of first- and second-order mixing effects. It also shows that, whereas the magnitude of first-order mixing is determined by the inner product of cross-talk functions, the magnitude of second-order mixing is determined by a generalized cross-product of cross-talk functions (the wedge product) which leads to an intuitive geometric understanding of the trade-off. All results are derived within the general framework of random neural fields on cortical manifolds.

Tuning Minimum-Norm regularization parameters for optimal MEG connectivity estimation

The accurate characterization of cortical functional connectivity from Magnetoencephalography (MEG) data remains a challenging problem due to the subjective nature of the analysis, which requires several decisions at each step of the analysis pipeline, such as the choice of a source estimation algorithm, a connectivity metric and a cortical parcellation, to name but a few. Recent studies have emphasized the importance of selecting the regularization parameter in minimum norm estimates with caution, as variations in its value can result in significant differences in connectivity estimates. In particular, the amount of regularization that is optimal for MEG source estimation can actually be suboptimal for coherence-based MEG connectivity analysis. In this study, we expand upon previous work by examining a broader range of commonly used connectivity metrics, including the imaginary part of coherence, corrected imaginary part of Phase Locking Value, and weighted Phase Lag Index, within a larger and more realistic simulation scenario. Our results show that the best estimate of connectivity is achieved using a regularization parameter that is 1 or 2 orders of magnitude smaller than the one that yields the best source estimation. This remarkable difference may imply that previous work assessing source-space connectivity using minimum-norm may have benefited from using less regularization, as this may have helped reduce false positives. Importantly, we provide the code for MEG data simulation and analysis, offering the research community a valuable open source tool for informed selections of the regularization parameter when using minimum-norm for source space connectivity analyses.

PSIICOS projection optimality for EEG and MEG based functional coupling detection

Functional connectivity is crucial for cognitive processes in the healthy brain and serves as a marker for a range of neuropathological conditions. Non-invasive exploration of functional coupling using temporally resolved techniques such as MEG allows for a unique opportunity of exploring this fundamental brain mechanism. The indirect nature of MEG measurements complicates the estimation of functional coupling due to the volume conduction and spatial leakage effects. In the previous work (Ossadtchi et al., 2018), we introduced PSIICOS, a method that for the first time allowed us to suppress the volume conduction effect and yet retain information about functional networks whose nodes are coupled with close to zero or zero mutual phase lag. In this paper, we demonstrate analytically that the PSIICOS projection is optimal in achieving a controllable trade-off between suppressing mutual spatial leakage and retaining information about zero- or close to zero-phase coupled networks. We also derive an alternative solution using the regularization-based inverse of the mutual spatial leakage matrix and show its equivalence to the original PSIICOS. We then discuss how PSIICOS solution to the functional connectivity estimation problem can be incorporated into the conventional source estimation framework. Instead of sources, the unknowns are the elementary dyadic networks and their activation time series are formalized by the corresponding source-space cross-spectral coefficients. This view on connectivity estimation as a regression problem opens up new opportunities for formulating a set of principled estimators based on the rich intuition accumulated in the neuroimaging community.

Modified covariance beamformer for solving MEG inverse problem in the environment with correlated sources

Magnetoencephalography (MEG) is a neuroimaging method ideally suited for non-invasive studies of brain dynamics. MEG's spatial resolution critically depends on the approach used to solve the ill-posed inverse problem in order to transform sensor signals into cortical activation maps. Over recent years non-globally optimized solutions based on the use of adaptive beamformers (BF) gained popularity. When operating in the environment with a small number of uncorrelated sources the BFs perform optimally and yield high spatial resolution. However, the BFs are known to fail when dealing with correlated sources acting like poorly tuned spatial filters with low signal-to-noise ratio (SNR) of the output timeseries and often meaningless cortical maps of power distribution. This fact poses a serious limitation on the broader use of this promising technique especially since fundamental mechanisms of brain functioning, its inherent symmetry and task-based experimental paradigms result into a great deal of correlation in the activity of cortical sources. To cope with this problem, we developed a novel data covariance modification approach that allows for building beamformers that maintain high spatial resolution when operating in the environments with correlated sources. At the core of our method is a projection operation applied to the vectorized sensor-space covariance matrix. This projection does not remove the activity of the correlated sources from the sensor-space covariance matrix but rather selectively handles their contributions to the covariance matrix and creates a sufficiently accurate approximation of an ideal data covariance that could hypothetically be observed should these sources be uncorrelated. Since the projection operation is reciprocal to the PSIICOS method developed by us earlier (Ossadtchi et al., 2018) we refer to the family of algorithms presented here as ReciPSIICOS. We assess the performance of the novel approach using realistically simulated MEG data and show its superior performance in comparison to the classical BF approaches and well established MNE as a method immune to source synchrony by design. We have also applied our approach to the MEG datasets from the two experiments involving two different auditory tasks. The analysis of experimental MEG datasets showed that beamformers from ReciPSIICOS family, but not the classical BF, discovered the expected bilateral focal sources in the primary auditory cortex and detected motor cortex activity associated with the audio-motor task. In most cases MNE managed well but as expected produced more spatially diffuse source distributions. Notably, ReciPSIICOS beamformers yielded cortical activity estimates with SNR several times higher than that obtained with the classical BF, which may indirectly indicate the severeness of the signal cancellation problem when applying classical beamformers to MEG signals generated by synchronous sources.

Lag-invariant detection of interactions in spatially-extended systems using linear inverse modeling

Measurements on physical systems result from the systems' activity being converted into sensor measurements by a forward model. In a number of cases, inversion of the forward model is extremely sensitive to perturbations such as sensor noise or numerical errors in the forward model. Regularization is then required, which introduces bias in the reconstruction of the systems' activity. One domain in which this is particularly problematic is the reconstruction of interactions in spatially-extended complex systems such as the human brain. Brain interactions can be reconstructed from non-invasive measurements such as electroencephalography (EEG) or magnetoencephalography (MEG), whose forward models are linear and instantaneous, but have large null-spaces and high condition numbers. This leads to incomplete unmixing of the forward models and hence to spurious interactions. This motivated the development of interaction measures that are exclusively sensitive to lagged, i.e. delayed interactions. The drawback of such measures is that they only detect interactions that have sufficiently large lags and this introduces bias in reconstructed brain networks. We introduce three estimators for linear interactions in spatially-extended systems that are uniformly sensitive to all lags. We derive some basic properties of and relationships between the estimators and evaluate their performance using numerical simulations from a simple benchmark model.

Alpha Band Resting-State EEG Connectivity Is Associated With Non-verbal Intelligence

The aim of the present study was to investigate whether EEG resting state connectivity correlates with intelligence. One-hundred and sixty five participants took part in the study. Six minutes of eyes closed EEG resting state was recorded for each participant. Graph theoretical connectivity metrics were calculated separately for two well-established synchronization measures [weighted Phase Lag Index (wPLI) and Imaginary Coherence (iMCOH)] and for sensor- and source EEG space. Non-verbal intelligence was measured with Raven's Progressive Matrices. In line with the Neural Efficiency Hypothesis, path lengths characteristics of the brain networks (Average and Characteristic Path lengths, Diameter and Closeness Centrality) within alpha band range were significantly correlated with non-verbal intelligence for sensor space but no for source space. According to our results, variance in non-verbal intelligence measure can be mainly explained by the graph metrics built from the networks that include both weak and strong connections between the nodes.