Performance of different synchronization measures in real data: a case study on electroencephalographic signals

Quantification of intra- and inter-cluster relations in nonstationary and noisy data

The interrelation between data channels of multivariate data sets may lead to cluster formation. Revealing the cluster structure can give important information about the underlying systems' properties. Here we investigate the features of a recent genuinely multivariate cluster detection algorithm that is suitable for time-resolved and unsupervised application to nonstationary and noisy time series. Using numerical test systems it is discussed under which conditions intra- and inter-cluster relations can be disentangled and quantified. In addition different types of errors occurring when channels are automatically attributed to clusters are investigated quantitatively. Finally, the algorithm is applied to nonstationary model time series and its time-dependent performance is compared to other cluster detection algorithms.

Evaluation of cortical connectivity during real and imagined rhythmic finger tapping

Accumulating evidence suggests the existence of a shared neural substrate between imagined and executed movements. However, a better understanding of the mechanisms involved in the motor execution and motor imagery requires knowledge of the way the co-activated brain regions interact to each other during the particular (real or imagined) motor task. Within this general framework, the aim of the present study is to investigate the cortical activation and connectivity sub-serving real and imaginary rhythmic finger tapping, from the analysis of multi-channel electroencephalogram (EEG) scalp recordings. A sequence of 250 auditory pacing stimuli has been used for both the real and imagined right finger tapping task, with a constant inter-stimulus interval of 1.5 s length. During the motor execution, healthy subjects were asked to tap in synchrony with the regular sequence of stimulus events, whereas in the imagery condition subjects imagined themselves tapping in time with the auditory cue. To improve the spatial resolution of the scalp fields and suppress unwanted interferences, the EEG data have been spatially filtered. Further, event related synchronization and desynchronization phenomena and phase synchronization analysis have been employed for the study of functionally active brain areas and their connectivity during real and imagery finger tapping. Our results show a fronto-parietal co-activation during both real and imagined movements and similar connectivity patterns among contralateral brain areas. The results support the hypothesis that functional connectivity over the contralateral hemisphere during finger tapping is preserved in imagery. The approach and results can be regarded as indicative evidences of a new strategy for recognizing imagined movements in EEG-based brain computer interface research.

Dysconnection topography in schizophrenia revealed with state-space analysis of EEG

Background

The dysconnection hypothesis has been proposed to account for pathophysiological mechanisms underlying schizophrenia. Widespread structural changes suggesting abnormal connectivity in schizophrenia have been imaged. A functional counterpart of the structural maps would be the EEG synchronization maps. However, due to the limits of currently used bivariate methods, functional correlates of dysconnection are limited to the isolated measurements of synchronization between preselected pairs of EEG signals.

Methods/Results

To reveal a whole-head synchronization topography in schizophrenia, we applied a new method of multivariate synchronization analysis called S-estimator to the resting dense-array (128 channels) EEG obtained from 14 patients and 14 controls. This method determines synchronization from the embedding dimension in a state-space domain based on the theoretical consequence of the cooperative behavior of simultaneous time series—the shrinking of the state-space embedding dimension. The S-estimator imaging revealed a specific synchronization landscape in schizophrenia patients. Its main features included bilaterally increased synchronization over temporal brain regions and decreased synchronization over the postcentral/parietal region neighboring the midline. The synchronization topography was stable over the course of several months and correlated with the severity of schizophrenia symptoms. In particular, direct correlations linked positive, negative, and general psychopathological symptoms to the hyper-synchronized temporal clusters over both hemispheres. Along with these correlations, general psychopathological symptoms inversely correlated within the hypo-synchronized postcentral midline region. While being similar to the structural maps of cortical changes in schizophrenia, the S-maps go beyond the topography limits, demonstrating a novel aspect of the abnormalities of functional cooperation: namely, regionally reduced or enhanced connectivity.

Conclusion/Significance

The new method of multivariate synchronization significantly boosts the potential of EEG as an imaging technique compatible with other imaging modalities. Its application to schizophrenia research shows that schizophrenia can be explained within the concept of neural dysconnection across and within large-scale brain networks.

Characterization of synchronization in interacting groups of oscillators: application to seizures

We investigate the emergence of synchronization in two groups of oscillators; one group acts as a synchronization source, and the other as the target. Based on phase model simulations, we construct a synchrony index (SI): a combination of intra- and intergroup synchronies. The SI characterizes the extent of induced synchrony in the population. We demonstrate the usefulness of the measure in a test case of mesial temporal lobe epilepsy: the SI can be readily calculated from standard electroencephalographic measurements. We show that the synchrony index has a statistically significant increased value for the ictal periods and that the epileptic focus can be located by identifying the most synchronous pairs of electrodes during the initial part of ictal period of the seizure. We also show that it is possible in this pilot case to differentiate clinical and subclinical seizures based on the dynamical features of the synchronization. The synchronization index was found to be a useful quantity for the characterization of "pathological hypersynchronization" within a well-characterized patient with mesial temporal lobe epilepsy and thus has potential medical value in seizure detection, localizing ability, and association with later surgical outcome.

Wavelet bispectral analysis for the study of interactions among oscillators whose basic frequencies are significantly time variable

Bispectral analysis, recently introduced as a technique for revealing time-phase relationships, is extended to make use of wavelets rather than Fourier analysis. It is thus able to encompass instantaneous phase-time dependence for the case of two or more coupled nonlinear oscillators. The method is demonstrated and evaluated by use of test signals from a pair of coupled Poincaré oscillators. It promises to be useful in a wide range of scientific contexts for studies of interacting oscillators whose basic frequencies are significantly time variable.

Estimating nonlinear interdependences in dynamical systems using cellular nonlinear networks

We propose a method for estimating nonlinear interdependences between time series using cellular nonlinear networks. Our approach is based on the nonlinear dynamics of interacting nonlinear elements. We apply it to time series of coupled nonlinear model systems and to electroencephalographic time series from an epilepsy patient, and we show that an accurate approximation of symmetric and asymmetric realizations of a nonlinear interdependence measure can be achieved, thus allowing one to detect the strength and direction of couplings.

The time course of functional coupling between human cortical motor areas during internally driven vs. externally cued movements

The functional coupling between the primary motor cortex (M1) and the supplementary motor area (SMA) in the generation of internally paced versus externally cued rhythmic movements was explored using electroencephalography (EEG). This has important implications for the study of Parkinsonian patients who demonstrate decreased ability to perform internally paced rhythmic movement tasks. In particular, the temporal evolution of the coherence between M1 and SMA was studied using a recently developed time-frequency wavelet coherence algorithm. As this approach is not reliant upon pooling data from multiple trials to form a single estimate of the coherence for each subject, a subject by subject comparison is possible to determine subject specific frequencies of interest. It was found that at certain frequencies, the coupling between M1 and SMA was increased in the internally paced versus the externally triggered movement task. At only these specific frequencies did the peak of the coherence in the internal task precede that of the peak in the external task, which was time locked with the movement onset. This suggests a dual role of the M1-SMA coupling for both movement preparation and movement execution.

Reliability of quantitative EEG features

OBJECTIVE

To investigate the reliability of several well-known quantitative EEG (qEEG) features in the elderly in the resting, eyes closed condition and study the effects of epoch length and channel derivations on reliability.

METHODS

Fifteen healthy adults, over 50 years of age, underwent 10 EEG recordings over a 2-month period. Various qEEG features derived from power spectral, coherence, entropy and complexity analysis of the EEG were computed. Reliability was quantified using an intraclass correlation coefficient.

RESULTS

The highest reliability was obtained with the average montage, reliability increased with epoch length up to 40s, longer epochs gave only marginal improvement. The reliability of the qEEG features was highest for power spectral parameters, followed by regularity measures based on entropy and complexity, coherence being least reliable.

CONCLUSIONS

Montage and epoch length had considerable effects on reliability. Several apparently unrelated regularity measures had similar stability. Reliability of coherence measures was strongly dependent on channel location and frequency bands.

SIGNIFICANCE

The reliability of regularity measures has until now received limited attention. Low reliability of coherence measures in general may limit their usefulness in the clinical setting.

Topography, independent component analysis and dipole source analysis of movement related potentials

The objective of this study was to test, in single subjects, the hypothesis that the signs of voluntary movement-related neural activity would first appear in the prefrontal region, then move to both the medial frontal and posterior parietal regions, progress to the medial primary motor area, lateralize to the contralateral primary motor area and finally involve the cerebellum (where feedback-initiated error signals are computed). Six subjects performed voluntary finger movements while DC coupled EEG was recorded from 64 scalp electrodes. Event-related potentials (ERPs) averaged on the movements were analysed both before and after independent component analysis (ICA) combined with dipole source analysis (DSA) of the independent components. Both a simple topographic analysis of undecomposed ERPs and the ICA/DSA analysis suggested that the original hypothesis was inadequate. The major departure from its predictions was that, while activity over many brain regions did appear at the expected times, it also appeared at unexpected times. Overall, the results suggest that the neuroscientific 'standard model', in which neural activity occurs sequentially in a series of discrete local areas each specialized for a particular function, may reflect the true situation less well than models in which large areas of brain shift simultaneously into and out of common activity states.

Zero delay synchronization of chaos in coupled map lattices

We show that two coupled map lattices that are mutually coupled to one another with a delay can display zero delay synchronization if they are driven by a third coupled map lattice. We analytically estimate the parametric regimes that lead to synchronization and show that the presence of mutual delays enhances synchronization to some extent. The zero delay or isochronal synchronization is reasonably robust against mismatches in the internal parameters of the coupled map lattices, and we analytically estimate the synchronization error bounds.

Relative performance of mutual information estimation methods for quantifying the dependence among short and noisy data

Commonly used dependence measures, such as linear correlation, cross-correlogram, or Kendall's tau , cannot capture the complete dependence structure in data unless the structure is restricted to linear, periodic, or monotonic. Mutual information (MI) has been frequently utilized for capturing the complete dependence structure including nonlinear dependence. Recently, several methods have been proposed for the MI estimation, such as kernel density estimators (KDEs), k -nearest neighbors (KNNs), Edgeworth approximation of differential entropy, and adaptive partitioning of the XY plane. However, outstanding gaps in the current literature have precluded the ability to effectively automate these methods, which, in turn, have caused limited adoptions by the application communities. This study attempts to address a key gap in the literature-specifically, the evaluation of the above methods to choose the best method, particularly in terms of their robustness for short and noisy data, based on comparisons with the theoretical MI estimates, which can be computed analytically, as well with linear correlation and Kendall's tau . Here we consider smaller data sizes, such as 50, 100, and 1000, and within this study we characterize 50 and 100 data points as very short and 1000 as short. We consider a broader class of functions, specifically linear, quadratic, periodic, and chaotic, contaminated with artificial noise with varying noise-to-signal ratios. Our results indicate KDEs as the best choice for very short data at relatively high noise-to-signal levels whereas the performance of KNNs is the best for very short data at relatively low noise levels as well as for short data consistently across noise levels. In addition, the optimal smoothing parameter of a Gaussian kernel appears to be the best choice for KDEs while three nearest neighbors appear optimal for KNNs. Thus, in situations where the approximate data sizes are known in advance and exploratory data analysis and/or domain knowledge can be used to provide a priori insights into the noise-to-signal ratios, the results in the paper point to a way forward for automating the process of MI estimation.

Estimate of causality between independent cortical spatial patterns during movement volition in spinal cord injured patients

Static hemodynamic or neuroelectric images of brain regions activated during particular tasks do not convey the information of how these regions communicate to each other. Cortical connectivity estimation aims at describing these interactions as connectivity patterns which hold the direction and strength of the information flow between cortical areas. In this study, we attempted to estimate the causality between distributed cortical systems during a movement volition task in preparation for execution of simple movements by a group of normal healthy subjects and by a group of Spinal Cord Injured (SCI) patients. To estimate the causality between the spatial distributed patterns of cortical activity in the frequency domain, we applied a series of processing steps on the recorded EEG data. From the high-resolution EEG recordings we estimated the cortical waveforms for the regions of interest (ROIs), each representing a selected sensor group population. The solutions of the linear inverse problem returned a series of cortical waveforms for each ROI considered and for each trial analyzed. For each subject, the cortical waveforms were then subjected to Independent Component Analysis (ICA) pre-processing. The independent components obtained by the application of the ThinICA algorithm were further processed by a Partial Directed Coherence algorithm, in order to extract the causality between spatial cortical patterns of the estimated data. The source-target cortical dependencies found in the group of normal subjects were relatively similar in all frequency bands analyzed. For the normal subjects we observed a common source pattern in an ensemble of cortical areas including the right parietal and right lip primary motor areas and bilaterally the primary foot and posterior SMA areas. The target of this cortical network, in the Granger-sense of causality, was shown to be a smaller network composed mostly by the primary foot motor areas and the posterior SMA bilaterally. In the case of the SCI population, both the source and the target cortical patterns had larger sizes than in the normal population. The source cortical areas included always the primary foot and lip motor areas, often bilaterally. In addition, the right parietal area and the bilateral premotor area 6 were also involved. Again, the patterns remained substantially stable across the different frequency bands analyzed. The target cortical patterns observed in the SCI population had larger extensions when compared to the normal ones, since in most cases they involved the bilateral activation of the primary foot movement areas as well as the SMA, the primary lip areas and the parietal cortical areas.

Directionality of coupling from bivariate time series: how to avoid false causalities and missed connections

We discuss some problems encountered in inference of directionality of coupling, or, in the case of two interacting systems, in inference of causality from bivariate time series. We identify factors and influences that can lead to either decreased test sensitivity or false detections and propose ways to cope with them in order to perform tests with high sensitivity and a low rate of false positive results.

On the meaning and interpretation of global descriptors of brain electrical activity. Including a reply to X. Pei et al

Global descriptors of the brain's electrical activity, Sigma, Phi, and Omega, provide a comprehensive characterisation of brain functional states. Recently, Pei et al. [Pei, X., Zheng, C., Zhang, A., Duan, F., Bin, G., 2005. Discussion on "Towards a quantitative characterisation of functional states of the brain: from the nonlinear methodology to the global linear description" by J. Wackermann. Int. J. Psychophysiol. 56, 201-207] discussed the effects of signal power on the global measure of spatial complexity, Omega, and suggested a modification consisting in epoch-wise and channel-wise normalisation of input data to unit power. In the present paper, the basic principles of the global approach are reviewed, and the issues of Pei et al.'s approach are assessed. The original and the modified measures of spatial complexity are compared in two case studies. Numerical simulation shows that both methods veridically estimate small numbers of signal sources, but systematically underestimate as the number increases; the modified method yields a minor relative improvement. A study on real EEG data shows that the two measures sensibly differ only where artefactual inhomogeneities in channel variances affect the data; a combined procedure, consisting in record-wise equalisation of channel variances before Omega calculations, is suggested as the optimal strategy. Differences between the original objectives of the global methodology and the proposed modifications are pointed out and critically discussed.

Detection of synchronization from univariate data using wavelet transform

A method is proposed for detecting from univariate data the presence of synchronization of a self-sustained oscillator by external driving with varying frequency. The method is based on the analysis of difference between the oscillator instantaneous phases calculated using continuous wavelet transform at time moments shifted by a certain constant value relative to each other. We apply our method to a driven asymmetric van der Pol oscillator, experimental data from a driven electronic oscillator with delayed feedback and human heartbeat time series. In the latest case, the analysis of the heart rate variability data reveals synchronous regimes between the respiration and slow oscillations in blood pressure.

Exploration of event-induced EEG phase synchronization patterns in cognitive tasks using a time–frequency-topography visualization system

In this paper, we present a method for the study of synchronization patterns measured from EEG scalp potentials in psychophysiological experiments. This method is based on various techniques: a time-frequency decomposition using sinusoidal filters which improve phase accuracy for low frequencies, a Bayesian approach for the estimation of significant synchrony changes, and a time-frequency-topography visualization technique which allows for easy exploration and provides detailed insights of a particular experiment. Particularly, we focus on in-phase synchrony using an instantaneous phase-lock measure. We also discuss some of the most common methods in the literature, focusing on their relevance to long-range synchrony analysis; this discussion includes a comparison among various synchrony measures. Finally, we present the analysis of a figure categorization experiment to illustrate our method.

Revealing direction of coupling between neuronal oscillators from time series: phase dynamics modeling versus partial directed coherence

The problem of determining directional coupling between neuronal oscillators from their time series is addressed. We compare performance of the two well-established approaches: partial directed coherence and phase dynamics modeling. They represent linear and nonlinear time series analysis techniques, respectively. In numerical experiments, we found each of them to be applicable and superior under appropriate conditions: The latter technique is superior if the observed behavior is "closer" to limit-cycle dynamics, the former is better in cases that are closer to linear stochastic processes.

Two types of phase synchronization destruction

In this paper we report that there are two different types of destruction of the phase synchronization (PS) regime of chaotic oscillators depending on the parameter mismatch as well as in the case of the classical synchronization of periodic oscillators. When the parameter mismatch of the interacting chaotic oscillators is small enough, the PS breaking takes place without the destruction of the phase coherence of chaotic attractors of oscillators. Alternatively, due to the large frequency detuning, the PS breaking is accomplished by loss of the phase coherence of the chaotic attractors.

Measures of linear and nonlinear interdependence of electrocortigram time series from evoked-response potential experiments

In this brief discussion, we consider various coupling measures applied to electrocortigram (ECoG) data. The analysis consists of both linear and nonlinear measures of coupling - or interdependence - between two ensembles of measurements collected at two electrodes in an evoked-response potential (ERP) experiment. The interdependence measures are applied to simulated time series data and experimental ECoG data. The algorithms discussed here are implemented in the interactive data language (IDL) and available for download from the authors.

A novel approach to the detection of synchronisation in EEG based on empirical mode decomposition

Transient neural assemblies mediated by synchrony in particular frequency ranges are thought to underlie cognition. We propose a new approach to their detection, using empirical mode decomposition (EMD), a data-driven approach removing the need for arbitrary bandpass filter cut-offs. Phase locking is sought between modes. We explore the features of EMD, including making a quantitative assessment of its ability to preserve phase content of signals, and proceed to develop a statistical framework with which to assess synchrony episodes. Furthermore, we propose a new approach to ensure signal decomposition using EMD. We adapt the Hilbert spectrum to a time-frequency representation of phase locking and are able to locate synchrony successfully in time and frequency between synthetic signals reminiscent of EEG. We compare our approach, which we call EMD phase locking analysis (EMDPL) with existing methods and show it to offer improved time-frequency localisation of synchrony.

General framework for phase synchronization through localized sets

We present an approach which enables one to identify phase synchronization in coupled chaotic oscillators without having to explicitly measure the phase. We show that if one defines a typical event in one oscillator and then observes another one whenever this event occurs, these observations give rise to a localized set. Our result provides a general and easy way to identify PS, which can also be used to oscillators that possess multiple time scales. We illustrate our approach in networks of chemically coupled neurons. We show that clusters of phase synchronous neurons may emerge before the onset of phase synchronization in the whole network, producing a suitable environment for information exchanging. Furthermore, we show the relation between the localized sets and the amount of information that coupled chaotic oscillator can exchange.

Interactions between cardiac, respiratory and EEG-delta oscillations in rats during anaesthesia

We hypothesized that, associated with the state of anaesthesia, characteristic changes exist in both cardio-respiratory and cerebral oscillator parameters and couplings, perhaps varying with depth of anaesthesia. Electrocardiograms (ECGs), respiration and electroencephalograms (EEGs) were recorded from two groups of 10 rats during the entire course of anaesthesia following the administration of a single bolus of ketamine-xylazine (KX group) or pentobarbital (PB group). The phase dynamics approach was then used to extract the instantaneous frequencies of heart beat, respiration and slow delta-waves (within 0.5-3.5 Hz). The amplitudes of delta- and theta-waves were analysed by use of a time-frequency representation of the EEG signal within 0.5-7.5 Hz obtained by wavelet transformation, using the Morlet mother wavelet. For the KX group, where slow delta-waves constituted the dominant spectral component, the Hilbert transform was applied to obtain the instantaneous delta-frequency. The theta-activity was spread over too wide a spectral range for its phase to be meaningfully defined. For both agents, we observed two distinct phases of anaesthesia, with a marked increase in theta-wave activity occurring on passage from a deeper phase of anaesthesia to a shallower one. In other respects, the effects of the two anaesthetics were very different. For KX anaesthesia, the two phases were separated by a marked change in all three instantaneous frequencies: stable, deep, anaesthesia with small frequency variability was followed by a sharp transition to shallow anaesthesia with large frequency variability, lasting until the animal awoke. The transition occurred 16-76 min after injection of the anaesthetic, with simultaneous reduction in the delta-wave amplitude. For PB anaesthesia, the two epochs were separated by the return of a positive response to the pinch test at 53-94 min, following which it took a further period of 45-70 min for the animal to awaken. delta-Waves were not apparent at any stage of PB anaesthesia. We applied non-linear dynamics and information theory to seek evidence of causal relationships between the cardiac, respiratory and slow delta-oscillations. We demonstrate that, for both groups, respiration drives the cardiac oscillator during deep anaesthesia. During shallow KX anaesthesia the direction either reverses, or the cardio-respiratory interaction becomes insignificant; in the deep phase, there is a unidirectional deterministic interaction of respiration with slow delta-oscillations. For PB anaesthesia, the cardio-respiratory interaction weakens during the second phase but, otherwise, there is no observable change in the interactions. We conclude that non-linear dynamics and information theory can be used to identify different stages of anaesthesia and the effects of different anaesthetics.

Synchronization likelihood with explicit time-frequency priors

Cognitive processing requires integration of information processed simultaneously in spatially distinct areas of the brain. The influence that two brain areas exert on each others activity is usually governed by an unknown function, which is likely to have nonlinear terms. If the functional relationship between activities in different areas is dominated by the nonlinear terms, linear measures of correlation may not detect the statistical interdependency satisfactorily. Therefore, algorithms for detecting nonlinear dependencies may prove invaluable for characterizing the functional coupling in certain neuronal systems, conditions or pathologies. Synchronization likelihood (SL) is a method based on the concept of generalized synchronization and detects nonlinear and linear dependencies between two signals (Stam, C.J., van Dijk, B.W., 2002. Synchronization likelihood: An unbiased measure of generalized synchronization in multivariate data sets. Physica D, 163: 236-241.). SL relies on the detection of simultaneously occurring patterns, which can be complex and widely different in the two signals. Clinical studies applying SL to electro- or magnetoencephalography (EEG/MEG) signals have shown promising results. In previous implementations of the algorithm, however, a number of parameters have lacked a rigorous definition with respect to the time-frequency characteristics of the underlying physiological processes. Here we introduce a rationale for choosing these parameters as a function of the time-frequency content of the patterns of interest. The number of parameters that can be arbitrarily chosen by the user of the SL algorithm is thereby decreased from six to two. Empirical evidence for the advantages of our proposal is given by an application to EEG data of an epileptic seizure and simulations of two unidirectionally coupled Hénon systems.

Identifying phase synchronization clusters in spatially extended dynamical systems

We investigate two recently proposed multivariate time series analysis techniques that aim at detecting phase synchronization clusters in spatially extended, nonstationary systems with regard to field applications. The starting point of both techniques is a matrix whose entries are the mean phase coherence values measured between pairs of time series. The first method is a mean-field approach which allows one to define the strength of participation of a subsystem in a single synchronization cluster. The second method is based on an eigenvalue decomposition from which a participation index is derived that characterizes the degree of involvement of a subsystem within multiple synchronization clusters. Simulating multiple clusters within a lattice of coupled Lorenz oscillators we explore the limitations and pitfalls of both methods and demonstrate (a) that the mean-field approach is relatively robust even in configurations where the single-cluster assumption is not entirely fulfilled and (b) that the eigenvalue-decomposition approach correctly identifies the simulated clusters even for low coupling strengths. Using the eigenvalue-decomposition approach we studied spatiotemporal synchronization clusters in long-lasting multichannel EEG recordings from epilepsy patients and obtained results that fully confirm findings from well established neurophysiological examination techniques. Multivariate time series analysis methods such as synchronization cluster analysis, which account for nonlinearities in the data, are expected to provide complementary information which allows one to gain deeper insights into the collective dynamics of spatially extended complex systems.

Unraveling cell processes: interference imaging interwoven with data analysis

The paper presents results on the application of interference microscopy and wavelet-analysis for cell visualization and studies of cell dynamics. We demonstrate that interference imaging of erythrocytes can reveal reorganization of the cytoskeleton and inhomogenity in the distribution of hemoglobin, and that interference imaging of neurons can show intracellular compartmentalization and submembrane structures. We investigate temporal and spatial variations of the refractive index for different cell types: isolated neurons, mast cells and erythrocytes. We show that the refractive dynamical properties differ from cell type to cell type and depend on the cellular compartment. Our results suggest that low frequency variations (0.1-0.6 Hz) result from plasma membrane processes and that higher frequency variations (20-26 Hz) are related to the movement of vesicles. Using double-wavelet analysis, we study the modulation of the 1 Hz rhythm in neurons and reveal its changes under depolarization and hyperpolarization of the plasma membrane. We conclude that interference microscopy combined with wavelet analysis is a useful technique for non-invasive cell studies, cell visualization, and investigation of plasma membrane properties.

Cortical and thalamic coherence during spike–wave seizures in WAG/Rij rats

The study examines cortico-cortical and cortico-thalamic network synchronization at the onset of spike-wave discharges (SWD) in a genetic model of absence epilepsy, WAG/Rij rats. Coherence was measured between multiple cortical areas (intracortical), reticular and rely thalamic nuclei (intrathalamic) and between the cortex and the thalamus. SWD-related increase of coherence (5-60 Hz) was found in all investigated pairs. The highest increase of coherence was around the mean frequency of SWD (8-11.5 Hz) and in the harmonic band 16-21.5 Hz with two central maxima around 10 and 20 Hz. The frequency profile of coherence was different in different intracortical networks, therefore latter were divided into local, global and transhemispheric networks. The presumable source of SWD in the somatosensory cortex and its closest surroundings formed a minimal (local) circuit, in which occurrence of SWD was facilitated by a consistent shift of network synchrony from delta to alpha/beta frequencies. Transhemispheric coherence revealed the largest increase with an additional 16 Hz peak, suggesting a crucial involvement of the corpus callosum in the pathophysiology of absence seizures. The increase in interhemispheric coherence was largest between relatively remote somatosensory or frontal areas, supporting the assumption that SWD originate from the lateral fronto-parietal cortical area.

Quantitative evaluation of linear and nonlinear methods characterizing interdependencies between brain signals

Brain functional connectivity can be characterized by the temporal evolution of correlation between signals recorded from spatially-distributed regions. It is aimed at explaining how different brain areas interact within networks involved during normal (as in cognitive tasks) or pathological (as in epilepsy) situations. Numerous techniques were introduced for assessing this connectivity. Recently, some efforts were made to compare methods performances but mainly qualitatively and for a special application. In this paper, we go further and propose a comprehensive comparison of different classes of methods (linear and nonlinear regressions, phase synchronization, and generalized synchronization) based on various simulation models. For this purpose, quantitative criteria are used: in addition to mean square error under null hypothesis (independence between two signals) and mean variance computed over all values of coupling degree in each model, we provide a criterion for comparing performances. Results show that the performances of the compared methods are highly dependent on the hypothesis regarding the underlying model for the generation of the signals. Moreover, none of them outperforms the others in all cases and the performance hierarchy is model dependent.

Spurious detection of phase synchronization in coupled nonlinear oscillators

Coupled nonlinear systems under certain conditions exhibit phase synchronization, which may change for different frequency bands or with the presence of additive system noise. In both cases, Fourier filtering is traditionally used to preprocess data. We investigate to what extent the phase synchronization of two coupled Rössler oscillators depends on (1) the broadness of their power spectrum, (2) the width of the bandpass filter, and (3) the level of added noise. We find that for identical coupling strengths, oscillators with broader power spectra exhibit weaker synchronization. Further, we find that within a broad bandwidth range, bandpass filtering reduces the effect of noise but can lead to a spurious increase in the degree of phase synchronization with narrowing bandwidth, even when the coupling between the two oscillators remains the same.

Towards a proper estimation of phase synchronization from time series

In experimental synchronization studies a continuous phase variable is commonly estimated from a scalar time series by means of its representation on the complex plane. The aim is to obtain a pair of functions [A(t), phi(t)] defining its instantaneous amplitude and phase, respectively. However, any arbitrary pair of functions cannot be considered as the amplitude and the phase of the real observable. Here, we point out some criteria that the pair [A(t), phi(t)] must observe to unambiguously define the instantaneous amplitude and phase of the observed signal. In this work, we illustrate how the complex representation may fail if the signal possesses a multi-component or a broadband spectra. We also point out a practical procedure to test whether a signal, not displaying a single oscillation at a unique frequency, has a narrow-band behavior. Implications for the study of phase interdependencies are illustrated and discussed. Phase dynamics estimated from electric brain activities recorded from an epileptic patient are also discussed.

Empirical mode decomposition and synchrogram approach to cardiorespiratory synchronization

We use the empirical mode decomposition method to decompose experimental respiratory signals into a set of intrinsic mode functions (IMFs), and consider one of these IMFs as a respiratory rhythm. We then use the Hilbert spectral analysis to calculate the instantaneous phase of the IMF. Heartbeat data are finally incorporated to construct the cardiorespiratory synchrogram, which is a visual tool for inspecting synchronization. We perform analysis on 20 data sets collected by the Harvard medical school from ten young (21-34 years old) and ten elderly (68-81 years old) rigorously screened healthy subjects. Our results support the existence of cardiorespiratory synchronization. We also investigate the origin of the cardiorespiratory synchronization by addressing the problem of correlations between regularities of respiratory and cardiac signals. Our analysis shows that regularity of respiratory signals plays a dominant role in the cardiorespiratory synchronization.

How do brain tumors alter functional connectivity? A magnetoencephalography study

OBJECTIVE

This study was undertaken to test the hypothesis that brain tumors interfere with normal brain function by disrupting functional connectivity of brain networks.

METHODS

Functional connectivity was assessed by computing the synchronization likelihood in a broad band (0.5-60Hz) or in the gamma band (30-60Hz) between all pairwise combinations of magnetoencephalography signals. Magnetoencephalography recordings were made at rest in 17 brain tumor patients and 15 healthy control subjects. For a given threshold of synchronization likelihood values, graphs of the suprathreshold connections between each magnetoencephalography channel and the others channels were built.

RESULTS

In some regions, a variable number of channels without connectivity (missing connective points) at this threshold was found. The number of missing connective points was higher in patients with brain tumors than in control subjects (p < 0.0001, broad and gamma band) and was higher for left-sided than right-sided tumors (p = 0.008, broad band; p < 0.0001, gamma band). Individual results analysis indicates that the majority of brain tumor patients display several regions with missing connective point alterations in the affected and in the contralateral hemisphere.

INTERPRETATION

Our findings suggest that brain tumors induce a loss of functional connectivity that affects multiple brain regions, and that left side brain tumors have the more severe consequences in this respect.

Enhanced synchrony in epileptiform activity? Local versus distant phase synchronization in generalized seizures

Synchronization is a fundamental characteristic of complex systems and a basic mechanism of self-organization. A traditional, accepted perspective on epileptiform activity holds that hypersynchrony covering large brain regions is a hallmark of generalized seizures. However, a few recent reports have described substantial fluctuations in synchrony before and during ictal events, thus raising questions as to the widespread synchronization notion. In this study, we used magnetoencephalographic recordings from epileptic patients with generalized seizures and normal control subjects to address the extent of the phase synchronization (phase locking) in local (neighboring) and distant cortical areas and to explore the ongoing temporal dynamics for particular ranges of frequencies at which synchrony occurs, during interictal and ictal activity. Synchronization patterns were found to differ somewhat depending on the epileptic syndrome, with primary generalized absence seizures displaying more long-range synchrony in all frequency bands studied (3-55 Hz) than generalized tonic motor seizures of secondary (symptomatic) generalized epilepsy or frontal lobe epilepsy. However, all seizures were characterized by enhanced local synchrony compared with distant synchrony. There were fluctuations in the synchrony between specific cortical areas that varied from seizure to seizure in the same patient, but in most of the seizures studied, regardless of semiology, there was a constant pattern in the dynamics of synchronization, indicating that seizures proceed by a recruitment of neighboring neuronal networks. Together, these data indicate that the concept of widespread "hypersynchronous" activity during generalized seizures may be misleading and valid only for very specific neuronal ensembles and circumstances.

Genetic components of functional connectivity in the brain: the heritability of synchronization likelihood

Cognitive functions require the integrated activity of multiple specialized, distributed brain areas. Such functional coupling depends on the existence of anatomical connections between the various brain areas as well as physiological processes whereby the activity in one area influences the activity in another area. Recently, the Synchronization Likelihood (SL) method was developed as a general method to study both linear and nonlinear aspects of coupling. In the present study the genetic architecture of the SL in different frequency bands was investigated. Using a large genetically informative sample of 569 subjects from 282 extended twin families we found that the SL is moderately to highly heritable (41-67%) especially in the alpha frequency (8-13 Hz) range. This index of functional connectivity of the brain has been associated with a number of pathological states of the brain. The significant heritability found here suggests that SL can be used to examine the genetic susceptibility to these conditions.

Lag synchrony measures dynamical processes underlying progression of seizure states

We investigate the dynamics of bursting behavior in an intact hippocampal preparation using causal entropy, an adaptive measure of lag synchrony. This analysis, together with a heuristic model of coupled bursting networks, separates experimentally observed bursting dynamics into two dynamical regimes, when bursting is driven by (1) the intranetwork dynamics of a single region, or (2) internetwork feedback between spatially disjoint neural populations. Our results suggest that the abrupt transition between these two states heralds the gradual desynchronization of bursting activity. These results illustrate how superficially homogeneous behavior across loosely coupled networks may harbor hidden, but robust, dynamical processes.

Comment on "Performance of different synchronization measures in real data: a case study on electroencephalographic signals"

We agree with Duckrow and Albano [Phys. Rev. E 67, 063901 (2003)] and Quian Quiroga [Phys. Rev. E 67, 063902 (2003)] that mutual information (MI) is a useful measure of dependence for electroencephalogram (EEG) data, but we show that the improvement seen in the performance of MI on extracting dependence trends from EEG is more dependent on the type of MI estimator rather than any embedding technique used. In an independent study we conducted in search for an optimal MI estimator, and in particular for EEG applications, we examined the performance of a number of MI estimators on the data set used by Quian Quiroga in their original study, where the performance of different dependence measures on real data was investigated [Phys. Rev. E 65, 041903 (2002)]. We show that for EEG applications the best performance among the investigated estimators is achieved by -nearest neighbors, which supports the conjecture by Quian Quiroga in Phys. Rev. E 67, 063902 (2003) that the nearest neighbor estimator is the most precise method for estimating MI.

Nonlinear dynamical analysis of EEG and MEG: review of an emerging field

Many complex and interesting phenomena in nature are due to nonlinear phenomena. The theory of nonlinear dynamical systems, also called 'chaos theory', has now progressed to a stage, where it becomes possible to study self-organization and pattern formation in the complex neuronal networks of the brain. One approach to nonlinear time series analysis consists of reconstructing, from time series of EEG or MEG, an attractor of the underlying dynamical system, and characterizing it in terms of its dimension (an estimate of the degrees of freedom of the system), or its Lyapunov exponents and entropy (reflecting unpredictability of the dynamics due to the sensitive dependence on initial conditions). More recently developed nonlinear measures characterize other features of local brain dynamics (forecasting, time asymmetry, determinism) or the nonlinear synchronization between recordings from different brain regions. Nonlinear time series has been applied to EEG and MEG of healthy subjects during no-task resting states, perceptual processing, performance of cognitive tasks and different sleep stages. Many pathologic states have been examined as well, ranging from toxic states, seizures, and psychiatric disorders to Alzheimer's, Parkinson's and Cre1utzfeldt-Jakob's disease. Interpretation of these results in terms of 'functional sources' and 'functional networks' allows the identification of three basic patterns of brain dynamics: (i) normal, ongoing dynamics during a no-task, resting state in healthy subjects; this state is characterized by a high dimensional complexity and a relatively low and fluctuating level of synchronization of the neuronal networks; (ii) hypersynchronous, highly nonlinear dynamics of epileptic seizures; (iii) dynamics of degenerative encephalopathies with an abnormally low level of between area synchronization. Only intermediate levels of rapidly fluctuating synchronization, possibly due to critical dynamics near a phase transition, are associated with normal information processing, whereas both hyper-as well as hyposynchronous states result in impaired information processing and disturbed consciousness.

Multisensory processing and oscillatory gamma responses: effects of spatial selective attention

Here we describe an EEG study investigating the interactions between multisensory (audio-visual) integration and spatial attention, using oscillatory gamma-band responses (GBRs). The results include a comparison with previously reported event-related potential (ERP) findings from the same paradigm. Unisensory-auditory (A), unisensory-visual (V), and multisensory (AV) stimuli were presented to the left and right hemispaces while subjects attended to a designated side to detect deviant target stimuli in either sensory modality. For attended multisensory stimuli we observed larger evoked GBRs approximately 40-50 ms post-stimulus over medial-frontal brain areas compared with those same multisensory stimuli when unattended. Further analysis indicated that the integration effect and its attentional enhancement may be caused in part by a stimulus-triggered phase resetting of ongoing gamma-band responses. Interestingly, no such early interaction effects (<90 ms) could be found in the ERP waveforms, suggesting that oscillatory GBRs may be more sensitive than ERPs to these early latency attention effects. Moreover, no GBR attention effects could be found for the unisensory auditory or unisensory visual stimuli, suggesting that attention particularly affects the integrative processing of audiovisual stimuli at these early latencies.

Increase in 20–50Hz (gamma frequencies) power spectrum and synchronization after chronic vagal nerve stimulation

OBJECTIVE

Though vagus nerve stimulation (VNS) is an important option in pharmaco-resistant epilepsy, its mechanism of action remains unclear. The observation that VNS desynchronised the EEG activity in animals suggested that this mechanism could be involved in VNS antiepileptic effects in humans. Indeed VNS decreases spiking bursts, whereas its effects on the EEG background remain uncertain. The objective of the present study is to investigate how VNS affects local and inter regional syncronization in different frequencies in pharmaco-resistant partial epilepsy.

METHODS

Digital recordings acquired in 11 epileptic subjects 1 year and 1 week before VNS surgery were compared with that obtained 1 month and 1 year after VNS activation. Power spectrum and synchronization were then analyzed and compared with an epileptic group of 10 patients treated with AEDs only.

RESULTS

VNS decreases the synchronization of theta frequencies (P < 0.01), whereas it increases gamma power spectrum and synchronization (< 0.001 and 0.01, respectively).

CONCLUSIONS

The reduction of theta frequencies and the increase in power spectrum and synchronization of gamma bands can be related to VNS anticonvulsant mechanism. In addition, gamma modulation could also play a seizure-independent role in improving attentional performances.

SIGNIFICANCE

These results suggest that some antiepileptic mechanisms affected by VNS can be modulated by or be the reflection of EEG changes.

Nonlinear multivariate analysis of neurophysiological signals

Multivariate time series analysis is extensively used in neurophysiology with the aim of studying the relationship between simultaneously recorded signals. Recently, advances on information theory and nonlinear dynamical systems theory have allowed the study of various types of synchronization from time series. In this work, we first describe the multivariate linear methods most commonly used in neurophysiology and show that they can be extended to assess the existence of nonlinear interdependence between signals. We then review the concepts of entropy and mutual information followed by a detailed description of nonlinear methods based on the concepts of phase synchronization, generalized synchronization and event synchronization. In all cases, we show how to apply these methods to study different kinds of neurophysiological data. Finally, we illustrate the use of multivariate surrogate data test for the assessment of the strength (strong or weak) and the type (linear or nonlinear) of interdependence between neurophysiological signals.

Drawing on mind's canvas: differences in cortical integration patterns between artists and non-artists

Our primary question was to learn whether mentally composing drawings of their own choice produce different brain electric features in artists and laymen. To this purpose, we studied multichannel electroencephalograph (EEG) signals from two broad groups (all participants were females): artists (professionally trained in visual arts) and non-artists (without any training in art). To assess the underlying synchronization, which is assumed to be the platform for general cognitive integration between different cortical regions, three measures inspired by nonlinear dynamical system theory were applied as follows: (1) index based on generalized synchronization; (2) index based on mean phase coherence; and (3) index of phase synchrony based on entropy. Results consistent over all three measures were as follows: comparing the tasks to rest, the artists showed significantly stronger short- and long-range delta band synchronization, whereas the non-artists showed enhancement in short-range beta and gamma band synchronization primarily in frontal regions; comparing the two groups during the tasks, the artists showed significantly stronger delta band synchronization and alpha band desynchronization than did the non-artists. Strong right hemispheric dominance in terms of synchronization was found in the artists. In artists, the higher synchrony in the low-frequency band is possibly due to the involvement of a more advanced long-term visual art memory and to extensive top-down processing. The results demonstrate that in artists, patterns of functional cooperation between cortical regions during mental creation of drawings were significantly different from those in non-artists.

Time-frequency characterization of interdependencies in nonstationary signals: application to epileptic EEG

For the past decades, numerous works have been dedicated to the development of signal processing methods aimed at measuring the degree of association between electroencephalographic (EEG) signals. This interdependency parameter, which may be defined in various ways, is often used to characterize a functional coupling between different brain structures or regions during either normal or pathological processes. In this paper, we focus on the time-frequency characterization of the interdependency between signals. Particularly, we propose a novel estimator of the linear relationship between nonstationary signals based on the cross correlation of narrow band filtered signals. This estimator is compared to a more classical estimator based on the coherence function. In a simulation framework, results show that it may exhibit better statistical performances (bias and variance or mean square error) when a priori knowledge about time delay between signals is available. On real data (intracerebral EEG signals), results show that this estimator may also enhance the readability of the time-frequency representation of relationship and, thus, can improve the interpretation of nonstationary interdependencies in EEG signals. Finally, we illustrate the importance of characterizing the relationship in both time and frequency domains by comparing with frequency-independent methods (linear and nonlinear).

Phase dynamics in cerebral autoregulation

Complex continuous wavelet transforms are used to study the dynamics of instantaneous phase difference delta phi between the fluctuations of arterial blood pressure (ABP) and cerebral blood flow velocity (CBFV) in a middle cerebral artery. For healthy individuals, this phase difference changes slowly over time and has an almost uniform distribution for the very low-frequency (0.02-0.07 Hz) part of the spectrum. We quantify phase dynamics with the help of the synchronization index gamma = (sin delta phi)2 + (cos delta phi)2 that may vary between 0 (uniform distribution of phase differences, so the time series are statistically independent of one another) and 1 (phase locking of ABP and CBFV, so the former drives the latter). For healthy individuals, the group-averaged index gamma has two distinct peaks, one at 0.11 Hz [gamma = 0.59 +/- 0.09] and another at 0.33 Hz (gamma = 0.55 +/- 0.17). In the very low-frequency range (0.02-0.07 Hz), phase difference variability is an inherent property of an intact autoregulation system. Consequently, the average value of the synchronization parameter in this part of the spectrum is equal to 0.13 +/- 0.03. The phase difference variability sheds new light on the nature of cerebral hemodynamics, which so far has been predominantly characterized with the help of the high-pass filter model. In this intrinsically stationary approach, based on the transfer function formalism, the efficient autoregulation is associated with the positive phase shift between oscillations of CBFV and ABP. However, the method is applicable only in the part of the spectrum (0.1-0.3 Hz) where the coherence of these signals is high. We point out that synchrony analysis through the use of wavelet transforms is more general and allows us to study nonstationary aspects of cerebral hemodynamics in the very low-frequency range where the physiological significance of autoregulation is most strongly pronounced.

Quantitative analysis of chaotic synchronization by means of coherence

We use an index of chaotic synchronization based on the averaged coherence function for the quantitative analysis of the process of the complete synchronization loss in unidirectionally coupled oscillators and maps. We demonstrate that this value manifests different stages of the synchronization breaking. It is invariant to time delay and insensitive to small noise and distortions, which can influence the accessible signals at measurements. Peculiarities of the synchronization destruction in maps and oscillators are investigated.

EEG responses to long-term audio-visual stimulation

In this study, linear and nonlinear electroencephalogram (EEG) changes due to long-term audio-visual stimulation (AVS) were investigated. In the course of 2 months, 25 repetitions of a 20-min AVS program with stimulation frequencies in the range 2-18 Hz were applied to six healthy volunteers. EEG data were recorded from six head locations during relaxed wakefulness prior to AVS. Then linear spectral measures (total power, frequency band powers, spectral edge frequency, and spectral entropy), nonlinear measures of complexity (histogram-based entropy and correlation dimension), interdependency measures (linear correlation coefficient, mutual information, and coherence), and measures of subjective assessment were estimated. Evolution of these measures during the whole experiment period was analyzed with respect to the significance of their linear regression. Our results confirm that repetitive training with audio-visual stimulation does induce changes in the electro-cortical activity of the brain. Long-term AVS significantly increased power in theta-1, theta-2, and alpha-1 bands in the frontal and central cortex locations. Total power increased in the right central region. Interhemispheric coherence in alpha-1 band displayed a significant increase between frontal parts in contrast to the decrease of both linear correlation and mutual information. Correlation dimension significantly decreased in some locations while entropy displayed an ascending trend.

Assessing interactions of linear and nonlinear neuronal sources using MEG beamformers: a proof of concept

OBJECTIVE

This study aimed to explore methods of assessing interactions between neuronal sources using MEG beamformers. However, beamformer methodology is based on the assumption of no linear long-term source interdependencies [VanVeen BD, vanDrongelen W, Yuchtman M, Suzuki A. Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Trans Biomed Eng 1997;44:867-80; Robinson SE, Vrba J. Functional neuroimaging by synthetic aperture magnetometry (SAM). In: Recent advances in Biomagnetism. Sendai: Tohoku University Press; 1999. p. 302-5]. Although such long-term correlations are not efficient and should not be anticipated in a healthy brain [Friston KJ. The labile brain. I. Neuronal transients and nonlinear coupling. Philos Trans R Soc Lond B Biol Sci 2000;355:215-36], transient correlations seem to underlie functional cortical coordination [Singer W. Neuronal synchrony: a versatile code for the definition of relations? Neuron 1999;49-65; Rodriguez E, George N, Lachaux J, Martinerie J, Renault B, Varela F. Perception's shadow: long-distance synchronization of human brain activity. Nature 1999;397:430-3; Bressler SL, Kelso J. Cortical coordination dynamics and cognition. Trends Cogn Sci 2001;5:26-36].

METHODS

Two periodic sources were simulated and the effects of transient source correlation on the spatial and temporal performance of the MEG beamformer were examined. Subsequently, the interdependencies of the reconstructed sources were investigated using coherence and phase synchronization analysis based on Mutual Information. Finally, two interacting nonlinear systems served as neuronal sources and their phase interdependencies were studied under realistic measurement conditions.

RESULTS

Both the spatial and the temporal beamformer source reconstructions were accurate as long as the transient source correlation did not exceed 30-40 percent of the duration of beamformer analysis. In addition, the interdependencies of periodic sources were preserved by the beamformer and phase synchronization of interacting nonlinear sources could be detected.

CONCLUSIONS

MEG beamformer methods in conjunction with analysis of source interdependencies could provide accurate spatial and temporal descriptions of interactions between linear and nonlinear neuronal sources.

SIGNIFICANCE

The proposed methods can be used for the study of interactions between neuronal sources.