Bispectral pairwise interacting source analysis for identifying systems of cross-frequency interacting brain sources from electroencephalographic or magnetoencephalographic signals

A bicoherence approach to analyze multi-dimensional cross-frequency coupling in EEG/MEG data

We introduce a blockwise generalisation of the Antisymmetric Cross-Bicoherence (ACB), a statistical method based on bispectral analysis. The Multi-dimensional ACB (MACB) is an approach that aims at detecting quadratic lagged phase-interactions between vector time series in the frequency domain. Such a coupling can be empirically observed in functional neuroimaging data, e.g., in electro/magnetoencephalographic signals. MACB is invariant under orthogonal trasformations of the data, which makes it independent, e.g., on the choice of the physical coordinate system in the neuro-electromagnetic inverse procedure. In extensive synthetic experiments, we prove that MACB performance is significantly better than that obtained by ACB. Specifically, the shorter the data length, or the higher the dimension of the single data space, the larger the difference between the two methods.

Brain-to-brain communication during musical improvisation: a performance case study

Understanding and predicting others' actions in ecological settings is an important research goal in social neuroscience. Here, we deployed a mobile brain-body imaging (MoBI) methodology to analyze inter-brain communication between professional musicians during a live jazz performance. Specifically, bispectral analysis was conducted to assess the synchronization of scalp electroencephalographic (EEG) signals from three expert musicians during a three-part 45 minute jazz performance, during which a new musician joined every five minutes. The bispectrum was estimated for all musician dyads, electrode combinations, and five frequency bands. The results showed higher bispectrum in the beta and gamma frequency bands (13-50 Hz) when more musicians performed together, and when they played a musical phrase synchronously. Positive bispectrum amplitude changes were found approximately three seconds prior to the identified synchronized performance events suggesting preparatory cortical activity predictive of concerted behavioral action. Moreover, a higher amount of synchronized EEG activity, across electrode regions, was observed as more musicians performed, with inter-brain synchronization between the temporal, parietal, and occipital regions the most frequent. Increased synchrony between the musicians' brain activity reflects shared multi-sensory processing and movement intention in a musical improvisation task.

Looking through the windows: a study about the dependency of phase-coupling estimates on the data length

OBJECTIVE

Being able to characterize functional connectivity (FC) state dynamics in a real-time setting, such as in brain-computer interface, neurofeedback or closed-loop neurostimulation frameworks, requires the rapid detection of the statistical dependencies that quantify FC in short windows of data. The aim of this study is to characterize, through extensive realistic simulations, the reliability of FC estimation as a function of the data length. In particular, we focused on FC as measured by phase-coupling (PC) of neuronal oscillations, one of the most functionally relevant neural coupling modes.

APPROACH

We generated synthetic data corresponding to different scenarios by varying the data length, the signal-to-noise ratio, the phase difference value, the spectral analysis approach (Hilbert or Fourier) and the fractional bandwidth. We compared seven PC metrics, i.e. imaginary part of phase locking value (PLV), PLV of orthogonalized signals, phase lag index (PLI), debiased weighted PLI, imaginary part of coherency, coherence of orthogonalized signals and lagged coherence.

MAIN RESULTS

Our findings show that, for a signal-to-noise-ratio of at least 10 dB, a data window that contains 5 to 8 cycles of the oscillation of interest (e.g. a 500-800ms window at 10Hz) is generally required to achieve reliable PC estimates. In general, Hilbert-based approaches were associated with higher performance than Fourier-based approaches. Furthermore, the results suggest that, when the analysis is performed in a narrow frequency range, a larger window is required.

SIGNIFICANCE

The achieved results pave the way to the introduction of best-practice guidelines to be followed when a real-time frequency-specific PC assessment is at target.

Nonlinear System Identification of Neural Systems from Neurophysiological Signals

The human nervous system is one of the most complicated systems in nature. Complex nonlinear behaviours have been shown from the single neuron level to the system level. For decades, linear connectivity analysis methods, such as correlation, coherence and Granger causality, have been extensively used to assess the neural connectivities and input-output interconnections in neural systems. Recent studies indicate that these linear methods can only capture a certain amount of neural activities and functional relationships, and therefore cannot describe neural behaviours in a precise or complete way. In this review, we highlight recent advances in nonlinear system identification of neural systems, corresponding time and frequency domain analysis, and novel neural connectivity measures based on nonlinear system identification techniques. We argue that nonlinear modelling and analysis are necessary to study neuronal processing and signal transfer in neural systems quantitatively. These approaches can hopefully provide new insights to advance our understanding of neurophysiological mechanisms underlying neural functions. These nonlinear approaches also have the potential to produce sensitive biomarkers to facilitate the development of precision diagnostic tools for evaluating neurological disorders and the effects of targeted intervention.

Nonlinear interaction decomposition (NID): A method for separation of cross-frequency coupled sources in human brain

Cross-frequency coupling (CFC) between neuronal oscillations reflects an integration of spatially and spectrally distributed information in the brain. Here, we propose a novel framework for detecting such interactions in Magneto- and Electroencephalography (MEG/EEG), which we refer to as Nonlinear Interaction Decomposition (NID). In contrast to all previous methods for separation of cross-frequency (CF) sources in the brain, we propose that the extraction of nonlinearly interacting oscillations can be based on the statistical properties of their linear mixtures. The main idea of NID is that nonlinearly coupled brain oscillations can be mixed in such a way that the resulting linear mixture has a non-Gaussian distribution. We evaluate this argument analytically for amplitude-modulated narrow-band oscillations which are either phase-phase or amplitude-amplitude CF coupled. We validated NID extensively with simulated EEG obtained with realistic head modelling. The method extracted nonlinearly interacting components reliably even at SNRs as small as -15 dB. Additionally, we applied NID to the resting-state EEG of 81 subjects to characterize CF phase-phase coupling between alpha and beta oscillations. The extracted sources were located in temporal, parietal and frontal areas, demonstrating the existence of diverse local and distant nonlinear interactions in resting-state EEG data. All codes are available publicly via GitHub.

Brain Functional Connectivity Through Phase Coupling of Neuronal Oscillations: A Perspective From Magnetoencephalography

Magnetoencephalography has gained an increasing importance in systems neuroscience thanks to the possibility it offers of unraveling brain networks at time-scales relevant to behavior, i.e., frequencies in the 1-100 Hz range, with sufficient spatial resolution. In the first part of this review, we describe, in a unified mathematical framework, a large set of metrics used to estimate MEG functional connectivity at the same or at different frequencies. The different metrics are presented according to their characteristics: same-frequency or cross-frequency, univariate or multivariate, directed or undirected. We focus on phase coupling metrics given that phase coupling of neuronal oscillations is a putative mechanism for inter-areal communication, and that MEG is an ideal tool to non-invasively detect such coupling. In the second part of this review, we present examples of the use of specific phase methods on real MEG data in the context of resting state, visuospatial attention and working memory. Overall, the results of the studies provide evidence for frequency specific and/or cross-frequency brain circuits which partially overlap with brain networks as identified by hemodynamic-based imaging techniques, such as functional Magnetic Resonance (fMRI). Additionally, the relation of these functional brain circuits to anatomy and to behavior highlights the usefulness of MEG phase coupling in systems neuroscience studies. In conclusion, we believe that the field of MEG functional connectivity has made substantial steps forward in the recent years and is now ready for bringing the study of brain networks to a more mechanistic understanding.

The impact of improved MEG-MRI co-registration on MEG connectivity analysis

Co-registration between structural head images and functional MEG data is needed for anatomically-informed MEG data analysis. Despite the efforts to minimize the co-registration error, conventional landmark- and surface-based strategies for co-registering head and MEG device coordinates achieve an accuracy of typically 5-10 mm. Recent advances in instrumentation and technical solutions, such as the development of hybrid ultra-low-field (ULF) MRI-MEG devices or the use of 3D-printed individualized foam head-casts, promise unprecedented co-registration accuracy, i.e., 2 mm or better. In the present study, we assess through simulations the impact of such an improved co-registration on MEG connectivity analysis. We generated synthetic MEG recordings for pairs of connected cortical sources with variable locations. We then assessed the capability to reconstruct source-level connectivity from these recordings for 0-15-mm co-registration error, three levels of head modeling detail (one-, three- and four-compartment models), two source estimation techniques (linearly constrained minimum-variance beamforming and minimum-norm estimation MNE) and five separate connectivity metrics (imaginary coherency, phase-locking value, amplitude-envelope correlation, phase-slope index and frequency-domain Granger causality). We found that beamforming can better take advantage of an accurate co-registration than MNE. Specifically, when the co-registration error was smaller than 3 mm, the relative error in connectivity estimates was down to one-third of that observed with typical co-registration errors. MNE provided stable results for a wide range of co-registration errors, while the performance of beamforming rapidly degraded as the co-registration error increased. Furthermore, we found that even moderate co-registration errors (>6 mm, on average) essentially decrease the difference of four- and three- or one-compartment models. Hence, a precise co-registration is important if one wants to take full advantage of highly accurate head models for connectivity analysis. We conclude that an improved co-registration will be beneficial for reliable connectivity analysis and effective use of highly accurate head models in future MEG connectivity studies.

The blessing of Dimensionality: Feature Selection outperforms functional connectivity-based feature transformation to classify ADHD subjects from EEG patterns of phase synchronisation

Functional connectivity (FC) characterizes brain activity from a multivariate set of N brain signals by means of an NxN matrix A, whose elements estimate the dependence within each possible pair of signals. Such matrix can be used as a feature vector for (un)supervised subject classification. Yet if N is large, A is highly dimensional. Little is known on the effect that different strategies to reduce its dimensionality may have on its classification ability. Here, we apply different machine learning algorithms to classify 33 children (age [6-14 years]) into two groups (healthy controls and Attention Deficit Hyperactivity Disorder patients) using EEG FC patterns obtained from two phase synchronisation indices. We found that the classification is highly successful (around 95%) if the whole matrix A is taken into account, and the relevant features are selected using machine learning methods. However, if FC algorithms are applied instead to transform A into a lower dimensionality matrix, the classification rate drops to less than 80%. We conclude that, for the purpose of pattern classification, the relevant features should be selected among the elements of A by using appropriate machine learning algorithms.

Reliability of EEG Interactions Differs between Measures and Is Specific for Neurological Diseases

Alterations of interaction (connectivity) of the EEG reflect pathological processes in patients with neurologic disorders. Nevertheless, it is questionable whether these patterns are reliable over time in different measures of interaction and whether this reliability of the measures is the same across different patient populations. In order to address this topic we examined 22 patients with mild cognitive impairment, five patients with subjective cognitive complaints, six patients with right-lateralized temporal lobe epilepsy, seven patients with left lateralized temporal lobe epilepsy, and 20 healthy controls. We calculated 14 measures of interaction from two EEG-recordings separated by 2 weeks. In order to characterize test-retest reliability, we correlated these measures for each group and compared the correlations between measures and between groups. We found that both measures of interaction as well as groups differed from each other in terms of reliability. The strongest correlation coefficients were found for spectrum, coherence, and full frequency directed transfer function (average rho > 0.9). In the delta (2–4 Hz) range, reliability was lower for mild cognitive impairment compared to healthy controls and left lateralized temporal lobe epilepsy. In the beta (13–30 Hz), gamma (31–80 Hz), and high gamma (81–125 Hz) frequency ranges we found decreased reliability in subjective cognitive complaints compared to mild cognitive impairment. In the gamma and high gamma range we found increased reliability in left lateralized temporal lobe epilepsy patients compared to healthy controls. Our results emphasize the importance of documenting reliability of measures of interaction, which may vary considerably between measures, but also between patient populations. We suggest that studies claiming clinical usefulness of measures of interaction should provide information on the reliability of the results. In addition, differences between patient groups in reliability of interactions in the EEG indicate the potential of reliability to serve as a new biomarker for pathological memory decline as well as for epilepsy. While the brain concert of information flow is generally variable, high reliability, and thus, low variability may reflect abnormal firing patterns.

Objective quality assessment of stereoscopic images with vertical disparity using EEG

OBJECTIVE

Neurophysiological correlates of vertical disparity in 3D images are studied in an objective approach using EEG technique. These disparities are known to negatively affect the quality of experience and to cause visual discomfort in stereoscopic visualizations.

APPROACH

We have presented four conditions to subjects: one in 2D and three conditions in 3D, one without vertical disparity and two with different vertical disparity levels. Event related potentials (ERPs) are measured for each condition and the differences between ERP components are studied. Analysis is also performed on the induced potentials in the time frequency domain.

MAIN RESULTS

Results show that there is a significant increase in the amplitude of P1 components in 3D conditions in comparison to 2D. These results are consistent with previous studies which have shown that P1 amplitude increases due to the depth perception in 3D compared to 2D. However the amplitude is significantly smaller for maximum vertical disparity (3D-3) in comparison to 3D with no vertical disparity. Our results therefore suggest that the vertical disparity in 3D-3 condition decreases the perception of depth compared to other 3D conditions and the amplitude of P1 component can be used as a discriminative feature.

SIGNIFICANCE

The results show that the P1 component increases in amplitude due to the depth perception in the 3D stimuli compared to the 2D stimulus. On the other hand the vertical disparity in the stereoscopic images is studied here. We suggest that the amplitude of P1 component is modulated with this parameter and decreases due to the decrease in the perception of depth.

Non-linear Analysis of Scalp EEG by Using Bispectra: The Effect of the Reference Choice

Bispectral analysis is a signal processing technique that makes it possible to capture the non-linear and non-Gaussian properties of the EEG signals. It has found various applications in EEG research and clinical practice, including the assessment of anesthetic depth, the identification of epileptic seizures, and more recently, the evaluation of non-linear cross-frequency brain functional connectivity. However, the validity and reliability of the indices drawn from bispectral analysis of EEG signals are potentially biased by the use of a non-neutral EEG reference. The present study aims at investigating the effects of the reference choice on the analysis of the non-linear features of EEG signals through bicoherence, as well as on the estimation of cross-frequency EEG connectivity through two different non-linear measures, i.e., the cross-bicoherence and the antisymmetric cross-bicoherence. To this end, four commonly used reference schemes were considered: the vertex electrode (Cz), the digitally linked mastoids, the average reference, and the Reference Electrode Standardization Technique (REST). The reference effects were assessed both in simulations and in a real EEG experiment. The simulations allowed to investigated: (i) the effects of the electrode density on the performance of the above references in the estimation of bispectral measures; and (ii) the effects of the head model accuracy in the performance of the REST. For real data, the EEG signals recorded from 10 subjects during eyes open resting state were examined, and the distortions induced by the reference choice in the patterns of alpha-beta bicoherence, cross-bicoherence, and antisymmetric cross-bicoherence were assessed. The results showed significant differences in the findings depending on the chosen reference, with the REST providing superior performance than all the other references in approximating the ideal neutral reference. In conclusion, this study highlights the importance of considering the effects of the reference choice in the interpretation and comparison of the results of bispectral analysis of scalp EEG.