Novel multivariate methods to track frequency shifts of neural oscillations in EEG/MEG recordings.

Instantaneous and peak frequency changes in neural oscillations have been linked to many perceptual, motor, and cognitive processes. Yet, the majority of such studies have been performed in sensor space and only occasionally in source space. Furthermore, both terms have been used interchangeably in the literature, although they do not reflect the same aspect of neural oscillations. In this paper, we discuss the relation between instantaneous frequency, peak frequency, and local frequency, the latter also known as spectral centroid. Furthermore, we propose and validate three different methods to extract source signals from multichannel data whose (instantaneous, local, or peak) frequency estimate is maximally correlated to an experimental variable of interest. Results show that the local frequency might be a better estimate of frequency variability than instantaneous frequency under conditions with low signal-to-noise ratio. Additionally, the source separation methods based on local and peak frequency estimates, called LFD and PFD respectively, provide more stable estimates than the decomposition based on instantaneous frequency. In particular, LFD and PFD are able to recover the sources of interest in simulations performed with a realistic head model, providing higher correlations with an experimental variable than multiple linear regression. Finally, we also tested all decomposition methods on real EEG data from a steady-state visual evoked potential paradigm and show that the recovered sources are located in areas similar to those previously reported in other studies, thus providing further validation of the proposed methods.

Canonical maximization of coherence: A novel tool for investigation of neuronal interactions between two datasets.

Synchronization between oscillatory signals is considered to be one of the main mechanisms through which neuronal populations interact with each other. It is conventionally studied with mass-bivariate measures utilizing either sensor-to-sensor or voxel-to-voxel signals. However, none of these approaches aims at maximizing synchronization, especially when two multichannel datasets are present. Examples include cortico-muscular coherence (CMC), cortico-subcortical interactions or hyperscanning (where electroencephalographic EEG/magnetoencephalographic MEG activity is recorded simultaneously from two or more subjects). For all of these cases, a method which could find two spatial projections maximizing the strength of synchronization would be desirable. Here we present such method for the maximization of coherence between two sets of EEG/MEG/EMG (electromyographic)/LFP (local field potential) recordings. We refer to it as canonical Coherence (caCOH). caCOH maximizes the absolute value of the coherence between the two multivariate spaces in the frequency domain. This allows very fast optimization for many frequency bins. Apart from presenting details of the caCOH algorithm, we test its efficacy with simulations using realistic head modelling and focus on the application of caCOH to the detection of cortico-muscular coherence. For this, we used diverse multichannel EEG and EMG recordings and demonstrate the ability of caCOH to extract complex patterns of CMC distributed across spatial and frequency domains. Finally, we indicate other scenarios where caCOH can be used for the extraction of neuronal interactions.

Using reciprocity for relating the simulation of transcranial current stimulation to the EEG forward problem.

To explore the relationship between transcranial current stimulation (tCS) and the electroencephalography (EEG) forward problem, we investigate and compare accuracy and efficiency of a reciprocal and a direct EEG forward approach for dipolar primary current sources both based on the finite element method (FEM), namely the adjoint approach (AA) and the partial integration approach in conjunction with a transfer matrix concept (PI). By analyzing numerical results, comparing to analytically derived EEG forward potentials and estimating computational complexity in spherical shell models, AA turns out to be essentially identical to PI. It is then proven that AA and PI are also algebraically identical even for general head models. This relation offers a direct link between the EEG forward problem and tCS. We then demonstrate how the quasi-analytical EEG forward solutions in sphere models can be used to validate the numerical accuracies of FEM-based tCS simulation approaches. These approaches differ with respect to the ease with which they can be employed for realistic head modeling based on MRI-derived segmentations. We show that while the accuracy of the most easy to realize approach based on regular hexahedral elements is already quite high, it can be significantly improved if a geometry-adaptation of the elements is employed in conjunction with an isoparametric FEM approach. While the latter approach does not involve any additional difficulties for the user, it reaches the high accuracies of surface-segmentation based tetrahedral FEM, which is considerably more difficult to implement and topologically less flexible in practice. Finally, in a highly realistic head volume conductor model and when compared to the regular alternative, the geometry-adapted hexahedral FEM is shown to result in significant changes in tCS current flow orientation and magnitude up to 45° and a factor of 1.66, respectively.

Third order spectral analysis robust to mixing artifacts for mapping cross-frequency interactions in EEG/MEG.

We present a novel approach to the third order spectral analysis, commonly called bispectral analysis, of electroencephalographic (EEG) and magnetoencephalographic (MEG) data for studying cross-frequency functional brain connectivity. The main obstacle in estimating functional connectivity from EEG and MEG measurements lies in the signals being a largely unknown mixture of the activities of the underlying brain sources. This often constitutes a severe confounder and heavily affects the detection of brain source interactions. To overcome this problem, we previously developed metrics based on the properties of the imaginary part of coherency. Here, we generalize these properties from the linear to the nonlinear case. Specifically, we propose a metric based on an antisymmetric combination of cross-bispectra, which we demonstrate to be robust to mixing artifacts. Moreover, our metric provides complex-valued quantities that give the opportunity to study phase relationships between brain sources. The effectiveness of the method is first demonstrated on simulated EEG data. The proposed approach shows a reduced sensitivity to mixing artifacts when compared with a traditional bispectral metric. It also exhibits a better performance in extracting phase relationships between sources than the imaginary part of the cross-spectrum for delayed interactions. The method is then applied to real EEG data recorded during resting state. A cross-frequency interaction is observed between brain sources at 10Hz and 20Hz, i.e., for alpha and beta rhythms. This interaction is then projected from signal to source level by using a fit-based procedure. This approach highlights a 10-20Hz dominant interaction localized in an occipito-parieto-central network.

Functional and effective connectivity in subthalamic local field potential recordings of patients with Parkinson's disease.

In Parkinson's disease (PD) levodopa-associated changes in the power and long-range temporal correlations of beta oscillations have been demonstrated, yet the presence and modulation of genuine connectivity in local field potentials (LFP) recorded from the subthalamic nucleus (STN) remains an open question. The present study investigated LFP recorded bilaterally from the STN at wakeful rest in ten patients with PD after overnight withdrawal of levodopa (OFF) and after a single dose levodopa administration (ON). We utilized connectivity measures being insensitive to volume conduction (functional connectivity: non-zero imaginary part of coherency; effective connectivity: phase-slope index). We demonstrated the presence of neuronal interactions in the frequency range of 10-30 Hz in STN-LFP without a preferential directionality of interactions between different contacts along the electrode tracks. While the direction of neuronal interactions per se was preserved after levodopa administration, functional connectivity and the ventral-dorsal information flow were modulated by medication. The OFF-ON differences in functional connectivity were correlated with the levodopa-induced improvement in clinical Unified Parkinson's Disease Rating Scale scores. We hypothesize that regional neuronal interactions, as reflected in STN-LFP connectivity, might represent a basis for the intra-nuclear spatial specificity of deep brain stimulation. Moreover, our results suggest the potential use of volume conduction-insensitive measures of connectivity in STN-LFP as a marker of clinical motor symptoms in PD.

Frequency specific interactions of MEG resting state activity within and across brain networks as revealed by the multivariate interaction measure.

Resting state networks (RSNs) are sets of brain regions exhibiting temporally coherent activity fluctuations in the absence of imposed task structure. RSNs have been extensively studied with fMRI in the infra-slow frequency range (nominally <10(-1)Hz). The topography of fMRI RSNs reflects stationary temporal correlation over minutes. However, neuronal communication occurs on a much faster time scale, at frequencies nominally in the range of 10(0)-10(2)Hz. We examined phase-shifted interactions in the delta (2-3.5 Hz), theta (4-7 Hz), alpha (8-12 Hz) and beta (13-30 Hz) frequency bands of resting-state source space MEG signals. These analyses were conducted between nodes of the dorsal attention network (DAN), one of the most robust RSNs, and between the DAN and other networks. Phase shifted interactions were mapped by the multivariate interaction measure (MIM), a measure of true interaction constructed from the maximization of imaginary coherency in the virtual channels comprised of voxel signals in source space. Non-zero-phase interactions occurred between homologous left and right hemisphere regions of the DAN in the delta and alpha frequency bands. Even stronger non-zero-phase interactions were detected between networks. Visual regions bilaterally showed phase-shifted interactions in the alpha band with regions of the DAN. Bilateral somatomotor regions interacted with DAN nodes in the beta band. These results demonstrate the existence of consistent, frequency specific phase-shifted interactions on a millisecond time scale between cortical regions within RSN as well as across RSNs.

A cartesian time--frequency approach to reveal brain interaction dynamics.

The study of large-scale interactions from magnetoencephalographic data based on the magnitude of the complex coherence computed at channel level is a widely used method to track the coupling between neural signals. Traditionally, a measure based on the magnitude of the complex coherence estimated by Fourier analysis, has been used under the assumption that the neural signals are stationary. Here, we split the complex coherence in its real and imaginary parts and focus on the latter with the advantage that the imaginary part is insensitive to spurious connectivity resulting from volume conducted "self interaction". Furthermore, interacting sources alone contribute to a non-vanishing imaginary part of the complex coherence whereas the contribute of non-interacting sources is also mapped from the magnitude of the complex coherence. Since it has been extensively shown that non-stationary stochastic processes contribute to the generation of neural signals, it is fundamental to be able to define interaction measures that are able to follow the temporal variations in the coupling between neural signals. To this purpose time-frequency domain techniques to estimate the magnitude of the complex coherence have been developed in the past decades. Similarly, we extend the analysis of the imaginary part of complex coherence to the time-frequency domain, by using the short-time Fourier transform to analyze the complex coherence as a function of time. In this way, it is possible to get an indication about the dynamic of the underlying source interaction pattern by looking at channel level interactions without the bias introduced by artifactual self-interaction by volume conduction or by the contribute of non-interacting sources. Furthermore, the corresponding imaginary part of the cross-spectrogram can be used to estimate interactions on a source level by localizing pools of sources interacting at a given frequency and by characterizing their dynamics. The method has been applied to magnetoencephalographic data from a cross-modal visual auditory stimulation and provided evidence for the involvement of temporal and occipital areas in the integrated information processing for simultaneous audio-visual stimulation. Furthermore, the source interaction pattern shows a variation in time that reflects a dynamical synchronization of the involved brain sources in the frequency bands of interest.

The use of standardized infinity reference in EEG coherency studies.

The study of large scale interactions in the brain from EEG signals is a promising method for the identification of functional networks. However, the validity of a large scale parameter is limited by two factors: the use of a non-neutral reference and the artifactual self-interactions between the measured EEG signals introduced by volume conduction. In this paper, we propose an approach to study large scale EEG coherency in which these factors are eliminated. Artifactual self-interaction by volume conduction is eliminated by using the imaginary part of the complex coherency as a measure of interaction and the Reference Electrode Standardization Technique (REST) is used for the approximate standardization of the reference of scalp EEG recordings to a point at infinity that, being far from all possible neural sources, acts like a neutral virtual reference. The application of our approach to simulated and real EEG data shows that the detection of interaction, as opposed to artifacts due to reference and volume conduction, is a goal that can be achieved from the study of a large scale parameter.

Small-world networks and functional connectivity in Alzheimer's disease.

We investigated whether functional brain networks are abnormally organized in Alzheimer's disease (AD). To this end, graph theoretical analysis was applied to matrices of functional connectivity of beta band-filtered electroencephalography (EEG) channels, in 15 Alzheimer patients and 13 control subjects. Correlations between all pairwise combinations of EEG channels were determined with the synchronization likelihood. The resulting synchronization matrices were converted to graphs by applying a threshold, and cluster coefficients and path lengths were computed as a function of threshold or as a function of degree K. For a wide range of thresholds, the characteristic path length L was significantly longer in the Alzheimer patients, whereas the cluster coefficient C showed no significant changes. This pattern was still present when L and C were computed as a function of K. A longer path length with a relatively preserved cluster coefficient suggests a loss of complexity and a less optimal organization. The present study provides further support for the presence of "small-world" features in functional brain networks and demonstrates that AD is characterized by a loss of small-world network characteristics. Graph theoretical analysis may be a useful approach to study the complexity of patterns of interrelations between EEG channels.

Noise reduction in magnetocardiography by singular value decomposition and independent component analysis.

In the routine recording of magnetocardiograms (MCGs), it is necessary to underline the problem of noise cancellation. Source separation has often been suggested to solve this problem. In this paper, blind source separation (BSS), by means of singular value decomposition (SVD) and independent component analysis (ICA), was used for noise reduction in MCG data to improve the signal to noise ratio. Special techniques, based on statistical parameters, for identifying noise and disturbances, have been introduced to automatically eliminate noise-related and disturbance-related components before reconstructing cleaned data sets. The results show that ICA and SVD can detect and remove a variety of noise and artefact sources from MCG data, as well as from stress MCG.

Using independent component analysis for noise reduction of magnetocardiographic data in case of exercise with an ergometer.

In 1992, Brockmeier et al. showed that there is a strong difference in magnetocardiography (MCG)-detected field distribution generated by the heart at rest and under stress. To study the possible clinical applications of this finding, it is convenient to avoid pharmacological stress and to perform stress MCG (SMCG) using conventional physical stress with an ergometer. When using a non-magnetic ergometer, the MCG recordings under physical stress are more noisy due to the unavoidable movement artefacts from the patient and from the residual artefacts of the ergometer. To remove these artefacts a denoising was performed using independent component analysis (ICA) in a new implementation. This work shows that with ICA in this special implementation it is becoming feasible to extract heart signals from SMCG data recorded during ergometer exercise.

Localization of realistic cortical activity in MEG using current multipoles.

We present a novel approach to MEG source estimation based on a regularized first-order multipole solution. The Gaussian regularizing prior is obtained by calculation of the sample mean and covariance matrix for the equivalent moments of realistic simulated cortical activity. We compare the regularized multipole localization framework to the classical dipole and general multipole source estimation methods by evaluating the ability of all three solutions to localize the centroids of physiologically plausible patches of activity simulated on the surface of a human cerebral cortex. The results, obtained with a realistic sensor configuration, a spherical head model, and given in terms of field and localization error, depict the performance of the dipolar and multipolar models as a function of variable source surface area (50-500 mm(2)), noise conditions (20, 10, and 5 dB SNR), source orientation (0-90 degrees ), and source depth (3-11 cm). We show that as the sources increase in size, they become less accurately modeled as current dipoles. The regularized multipole systematically outperforms the single dipole model, increasingly so as the spatial extent of the sources increases. In addition, our simulations demonstrate that as the orientation of the sources becomes more radial, dipole localization accuracy decreases substantially, while the performance of the regularized multipole model is far less sensitive to orientation and even succeeds in localizing quasi-radial source configurations. Furthermore, our results show that the multipole model is able to localize superficial sources with higher accuracy than the current dipole. These results indicate that the regularized multipole solution may be an attractive alternative to current-dipole-based source estimation methods in MEG.

Localizing brain interactions from rhythmic EEG/MEG data.

The interpretation of MEG/EEG data in terms of brain connectivity is largely obscured by artefacts of volume conduction, i.e. by the fact that a single source is observable in many channels. Here, we analyze a measure which is insensitive to spurious connectivity arising from volume conducted "self-interaction". For rhythmic data such a measure can be given by the imaginary part of the cross-spectrum between EEG/MEG channels. For the derivation we essentially exploit that a signal is not time-lagged to itself. To localize the sources of this observed interaction we fit a model cross-spectrum consisting of N interacting dipoles to the sample cross-spectrum. The relation to the maximum likelihood estimator will be discussed in detail. The method is illustrated for MEG data of human alpha rhythm in eyes closed condition. The eigenvalues of the imaginary cross-spectrum clearly indicate the presence of at least 4 necessarily interacting sources. Fits of 2 to 6 dipoles in a realistic volume conductor all resulted in locations scattered in the mesial part of the occipital lobe.

Partial signal space projection for artefact removal in MEG measurements: a theoretical analysis.

Standard methods for artefact removal in MEG or EEG measurements consist of rejection of either corrupted epochs or signal space projection (SSP). We propose to combine the two methods by applying SSP only in corrupted epochs and thus using both temporal and spatial information. This partial signal space projection necessarily results in smaller variances for the source localization. Formulae for dipole localization errors as a function of fraction of corrupted epochs are derived and verified in Monte Carlo simulations of MEG measurements corrupted with eye artefacts. A theoretical analysis of various measuring devices, classes of artefact and locations of dipole of interest shows that the proposed method leads to significant improvement for frontal signal dipoles and for 30-80% corrupted epochs.

Noise robust estimates of correlation dimension and K2 entropy.

Using Gaussian kernels to define the correlation sum we derive simple formulas that correct the noise bias in estimates of the correlation dimension and K2 entropy of chaotic time series. The corrections are only based on the difference of correlation dimensions for adjacent embedding dimensions and hence preserve the full functional dependencies on both the scale parameter and embedding dimension. It is shown theoretically that the estimates, which are derived for additive white Gaussian noise, are also robust for moderately colored noise. Simulations underline the usefulness of the proposed correction schemes. It is demonstrated that the method gives satisfactory results also for non-Gaussian and dynamical noise.

Independent short-term variability of spike-like (600 Hz) and postsynaptic (N20) cerebral SEP components.

Human scalp-derived somatosensory evoked potentials (SEP) elicited by median nerve stimulation contain an early (20 ms latency) high-frequency (600 Hz) wavelet burst which is supposed to reflect non-invasively the timing of rapidly repeating population spikes in thalamocortical afferences and/or the receiving neocortical cell populations. This burst is superimposed onto the slower (< or = 100 Hz) primary cortical response (N20) representing intracortically generated postsynaptic events. The present study addressed the temporal dynamics and correlation of these response components in awake human subjects and found that at a 3 min time scale the burst response was significantly more variable than the concomitant N20, and that the burst and N20 varied independently of each other. Thus, wavelet burst and N20 represent parallel and partly independent steps in sensory processing at cortical input stages in awake human subjects. We propose that the N20 represents a stable somatosensory input whereas the more fluctuating high-frequency burst could index variable modes of processing, such as a floating focus of attention.

Current multipole expansion to estimate lateral extent of neuronal activity: a theoretical analysis.

High-resolution magnetoencephalography (MEG) allows for a detailed description of focal neuronal current sources going far beyond the dipole approximation which merely indicates the center and magnitude of neuronal activity. Higher order multipole coefficients can be related to other bulk properties, like spatial extent or curvature. The possibility and limitations of measuring spatial extent by interpreting reconstructed multipole coefficients was tested under realistic noise conditions and for model misspecifications; for this analysis the primary cortical response ("N20") to electric median nerve stimulation was modeled by a one dimensional source distribution. The forward calculation was done analytically up to octapolar order for a spherical volume conductor. The multipole expansion is shown to estimate the lateral source extent with negligible bias; this estimate is to first-order stable against additional source features, like gyral curvature or spatial extent in a second direction (gyral depth, neuronal length). For a dipole moment of 20 nAm a lateral extent of 2 cm can be detected for a realistic noise level with large but experimentally still reasonable effort. Approximating a realistic head model by a sphere results in errors larger than the extent to be estimated; accordingly, studies on human cortical evoked responses will require multipole fitting in realistic head models.

Rapid recovery (20 ms) of human 600 Hz electroencephalographic wavelets after double stimulation of sensory nerves.

Non-invasive scalp-recordings of human somatosensory evoked potentials (SEP) contain high-frequency (600 Hz) wavelet bursts, presumably generated by synchronized thalamocortical and/or intracortical population spikes. Here, double pulse stimulation (interval 20 ms) in 12 healthy subjects revealed significantly different burst recovery for mixed vs. sensory-only nerves. For median nerves the second burst response was decreased (11/11 subjects), possibly due to interfering reafferent (e.g. muscle spindle) input. In contrast, for sensory-only superficial radial nerves (containing less fibers than median nerves), weak bursts were detected in 6/11 subjects and were found fully recovered in 4/6 subjects. This potential for rapid burst recovery at 20 ms intervals renders contributions from neurons emitting bursts based on slowly recovering low-threshold calcium spikes unlikely and favors the generation of macroscopic SEP bursts by specialized cell populations, e.g. inhibitory interneurons and/or chattering cells the latter of which are capable to discharge rapidly repeating (50 Hz) high-frequency (600 Hz) bursts of fast sodium spikes.

Artifact reduction in magnetoneurography based on time-delayed second-order correlations.

Artifacts in magnetoneurography data due to endogenous biological noise sources, like the cardiac signal, can be four orders of magnitude higher than the signal of interest. Therefore, it is important to establish effective artifact reduction methods. We propose a blind source separation algorithm using only second-order temporal correlations for cleaning biomagnetic measurements of evoked responses in the peripheral nervous system. The algorithm showed its efficiency by eliminating disturbances originating from biological and technical noise sources and successfully extracting the signal of interest. This yields a significant improvement of the neuro-magnetic source analysis.