Nonlinear synchronization in EEG and whole-head MEG recordings of healthy subjects

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.

Attention modulates hemispheric differences in functional connectivity: evidence from MEG recordings

The present study examined intrahemispheric functional connectivity during rest and dichotic listening in 8 male and 9 female healthy young adults measured with magnetoencephalography (MEG). Generalized synchronization within the separate hemispheres was estimated by means of the synchronization likelihood that is sensitive to linear as well as non-linear coupling of MEG signals. We found higher functional intrahemispheric connectivity of frontal and temporal areas within the right as compared to the left hemisphere in the lower and higher theta band during rest and in the lower theta band during dichotic listening. In addition, higher synchronization in the lower theta band correlated with better task performance. In the upper alpha band, hemispheric differences in intrahemispheric connectivity of the frontal regions were found to be modulated by focused attention instructions. That is, attention to the right ear exaggerates the pattern of higher synchronization likelihood for the right frontal region, while attention to the left ear has an opposite effect. We found higher intrahemispheric connectivity in males compared to females as shown by higher synchronization in the lower alpha band. Taken together, our results reflect a physiological basis for functional hemispheric laterality and support the general assumption of sex differences in brain organization. Furthermore, in addition to studies that show that controlled attention processes modulate activation of the frontal areas, our study indicates that attention modulates ipsilateral functional connectivity in the frontal areas. This supports the idea of a supervisory role for the frontal cortex in attention processes.

Multiple sclerosis patients show a highly significant decrease in alpha band interhemispheric synchronization measured using MEG

MEG data were acquired from a group of relapsing-remitting multiple sclerosis (MS) patients and a group of healthy controls, using an eyes-closed no-task condition. An interhemispheric coherence measure (IHCM), reflecting the synchronization between the left and right hemispheres, showed a decrease in the patients, particularly in the alpha band. No comparable differences were seen in the alpha band power or its distribution over the head. The observed difference is in agreement with a reduced long-range connectivity in the brains of MS patients. The IHCM was found to be reproducible in controls over a period of more than 15 months. Further studies should investigate whether MEG derived synchronization measures may be useful as markers for MS disease load.

Evoked phase synchronization between adjacent high-density electrodes in human scalp EEG: Duration and time course related to behavior

OBJECTIVE

Data from a previous event-related potential (ERP) study in visual-perceptual grouping [Nikolaev AR, van Leeuwen C. Flexibility in spatial and non-spatial feature grouping: an event-related potentials study. Brain Res Cogn Brain Res 2004;22:13-25] were re-analyzed to identify event-related dynamics of phase-synchronization.

METHODS

In 20 Hz activity, uniform spreading of phase synchronization in closely spaced (approximately 2 cm) scalp electrodes appears and disappears spontaneously. The lengths of synchronized activity intervals and how they vary as a function of stimulus presentation were compared between task and control conditions.

RESULTS

Synchronization reached a maximum in the task condition about 180 ms post-stimulus onset, coinciding with the peak N180 ERP marking the deployment of task-specific attention. Synchronized intervals were longer in the task than in the control condition. Long (above 80 ms) intervals occurred at a stable rate before and just after stimulus onset, but steeply decreased 200-400 ms afterwards.

CONCLUSIONS

Perceptual tasks lead to longer synchronized intervals in early visual areas. Attention deployment resets the ongoing synchronization. Event-related activity, besides low-frequency ERP, consists of high-frequency short and long synchronized intervals corresponding to evoked bursts and ongoing oscillations, respectively.

SIGNIFICANCE

High-density scalp recorded EEG revealed synchronization dynamics in a local, early visual area of cortex that can be interpreted as modulation of spontaneous ongoing task-related processes by attention.

Imaging the dynamics of the auditory steady-state evoked response

This study used magnetoencephalography (MEG) to examine the dynamic patterns of neural activity underlying the auditory steady-state response. We examined the continuous time-series of responses to a 32-Hz amplitude modulation. Fluctuations in the amplitude of the evoked response were found to be mediated by non-linear interactions with oscillatory processes both at the same source, in the alpha and beta frequency bands, and in the opposite hemisphere.

Estimation of the effective and functional human cortical connectivity with structural equation modeling and directed transfer function applied to high-resolution EEG

Different brain imaging devices are presently available to provide images of the human functional cortical activity, based on hemodynamic, metabolic or electromagnetic measurements. However, static images of brain regions activated during particular tasks do not convey the information of how these regions are interconnected. The concept of brain connectivity plays a central role in the neuroscience, and different definitions of connectivity, functional and effective, have been adopted in literature. While the functional connectivity is defined as the temporal coherence among the activities of different brain areas, the effective connectivity is defined as the simplest brain circuit that would produce the same temporal relationship as observed experimentally among cortical sites. The structural equation modeling (SEM) is the most used method to estimate effective connectivity in neuroscience, and its typical application is on data related to brain hemodynamic behavior tested by functional magnetic resonance imaging (fMRI), whereas the directed transfer function (DTF) method is a frequency-domain approach based on both a multivariate autoregressive (MVAR) modeling of time series and on the concept of Granger causality. This study presents advanced methods for the estimation of cortical connectivity by applying SEM and DTF on the cortical signals estimated from high-resolution electroencephalography (EEG) recordings, since these signals exhibit a higher spatial resolution than conventional cerebral electromagnetic measures. To estimate correctly the cortical signals, we used a subject's multicompartment head model (scalp, skull, dura mater, cortex) constructed from individual MRI, a distributed source model and a regularized linear inverse source estimates of cortical current density. Before the application of SEM and DTF methodology to the cortical waveforms estimated from high-resolution EEG data, we performed a simulation study, in which different main factors (signal-to-noise ratio, SNR, and simulated cortical activity duration, LENGTH) were systematically manipulated in the generation of test signals, and the errors in the estimated connectivity were evaluated by the analysis of variance (ANOVA). The statistical analysis returned that during simulations, both SEM and DTF estimators were able to correctly estimate the imposed connectivity patterns under reasonable operative conditions, that is, when data exhibit an SNR of at least 3 and a LENGTH of at least 75 s of nonconsecutive EEG recordings at 64 Hz of sampling rate. Hence, effective and functional connectivity patterns of cortical activity can be effectively estimated under general conditions met in any practical EEG recordings, by combining high-resolution EEG techniques and linear inverse estimation with SEM or DTF methods. We conclude that the estimation of cortical connectivity can be performed not only with hemodynamic measurements, but also with EEG signals treated with advanced computational techniques.

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.

Phase transitions in the neuropercolation model of neural populations with mixed local and non-local interactions

We model the dynamical behavior of the neuropil, the densely interconnected neural tissue in the cortex, using neuropercolation approach. Neuropercolation generalizes phase transitions modeled by percolation theory of random graphs, motivated by properties of neurons and neural populations. The generalization includes (1) a noisy component in the percolation rule, (2) a novel depression function in addition to the usual arousal function, (3) non-local interactions among nodes arranged on a multi-dimensional lattice. This paper investigates the role of non-local (axonal) connections in generating and modulating phase transitions of collective activity in the neuropil. We derived a relationship between critical values of the noise level and non-locality parameter to control the onset of phase transitions. Finally, we propose a potential interpretation of ontogenetic development of the neuropil maintaining a dynamical state at the edge of criticality.

A field-theoretic approach to understanding scale-free neocortical dynamics

A mesoscopic field-theoretic approach is compared with neural network and brain imaging approaches to understanding brain dynamics. Analysis of high spatiotemporal resolution rabbit electroencephalogram (EEG) reveals neural fields in the form of spatial patterns in amplitude (AM) and phase (PM) modulation of gamma and beta carrier waves that serve to classify EEGs from trials with differing conditioned stimuli (CS+/-). Paleocortex exemplified by olfactory EEG has one AM-PM pattern at a time that forms by an input-dependent phase transition. Neocortex shows multiple overlapping AM-PM patterns before and during presentation of CSs. Modeling suggests that neocortex is stabilized in a scale-free state of self-organized criticality, enabling cooperative domains to form virtually instantaneously by phase transitions ranging in size from a few hypercolumns to an entire hemisphere. Self-organized local domains precede formation of global domains that supervene and contribute global modulations to local domains. This mechanism is proposed to explain Gestalt formation in perception.

Synchronized firing of FitzHugh-Nagumo neurons by noise

We investigate the influence of noise on synchronization between the spiking activities of neurons with external impulsive forces. We first analyze the dependence of the synchronized firing on the amplitude and the angular frequency of the impulsive force in the noise-free system. Three cases (regular spiking, traveling wave, and chaotic spiking) with low synchronized firing are chosen to study effects due to noise. In each case we find that small noise can be a promoter of synchronization phenomena in neural activities, by choosing an appropriate noise intensity acting on some of the neurons.

Dynamics of a neural system with a multiscale architecture

The architecture of the brain is characterized by a modular organization repeated across a hierarchy of spatial scales-neurons, minicolumns, cortical columns, functional brain regions, and so on. It is important to consider that the processes governing neural dynamics at any given scale are not only determined by the behaviour of other neural structures at that scale, but also by the emergent behaviour of smaller scales, and the constraining influence of activity at larger scales. In this paper, we introduce a theoretical framework for neural systems in which the dynamics are nested within a multiscale architecture. In essence, the dynamics at each scale are determined by a coupled ensemble of nonlinear oscillators, which embody the principle scale-specific neurobiological processes. The dynamics at larger scales are 'slaved' to the emergent behaviour of smaller scales through a coupling function that depends on a multiscale wavelet decomposition. The approach is first explicated mathematically. Numerical examples are then given to illustrate phenomena such as between-scale bifurcations, and how synchronization in small-scale structures influences the dynamics in larger structures in an intuitive manner that cannot be captured by existing modelling approaches. A framework for relating the dynamical behaviour of the system to measured observables is presented and further extensions to capture wave phenomena and mode coupling are suggested.

Age Distribution of MEG Spontaneous Theta Activity in Healthy Subjects

This study investigates the possible relevance of distribution and age variation of spontaneous theta activity (4-8 Hz) in normal subjects using magnetoencephalography (MEG) recordings. Spontaneous theta was recorded with a 151-channel MEG in healthy subjects; moreover, in a group of 10 subjects, simultaneous MEG-EEG was recorded in order to compare the two methods. Theta was divided in two sub-bands: T(A) (4-6 Hz) and T(B) (6-8 Hz). The pre-processed data were transformed into the frequency domain by Fast Fourier Transform (FFT)-based software by subdividing the data in epochs of 5 sec, on which FFT amplitudes are computed. Moreover, on all trials a simple model of a single electric current embedded in a spherically symmetric conductor was fitted automatically to the magnetic fields and projected onto an averaged MRI. The results obtained show that FFT-based theta power spectrum was distributed in adults with the highest power over the posterior parietal and occipital areas with T(B) dominance. The dipole analysis resulted in a mid-sagittal distribution, though the youngest group displayed theta dipoles fitting more posteriorly respect to the adults and the elderly. These results suggest that spontaneous theta activity is a diffuse and pervasive rhythm which shows some different topographical distribution among the age groups. Whether the prevalent posterior distribution of theta is the expression of distinct networks or the outcome of complex dynamics are questions of possible relevance in the organization of higher order processes.

Assessment of EEG synchronization based on state-space analysis

Cortical computation involves the formation of cooperative neuronal assemblies characterized by synchronous oscillatory activity. A traditional method for the identification of synchronous neuronal assemblies has been the coherence analysis of EEG signals. Here, we suggest a new method called S estimator, whereby cortical synchrony is defined from the embedding dimension in a state-space. We first validated the method on clusters of chaotic coupled oscillators and compared its performance to that of other methods for assessing synchronization. Then nine adult subjects were studied with high-density EEG recordings, while they viewed in the two hemifields (hence with separate hemispheres) identical sinusoidal gratings either arranged collinearly and moving together, or orthogonally oriented and moving at 90 degrees . The estimated synchronization increased with the collinear gratings over a cluster of occipital electrodes spanning both hemispheres, whereas over temporo-parietal regions of both hemispheres, it decreased with the same stimulus and it increased with the orthogonal gratings. Separate calculations for different EEG frequencies showed that the occipital clusters involved synchronization in the beta band and the temporal clusters in the alpha band. The gamma band appeared to be insensitive to stimulus diversity. Different stimulus configurations, therefore, appear to cause a complex rearrangement of synchronous neuronal assemblies distributed over the cortex, in particular over the visual cortex.

Assessing cortical functional connectivity by linear inverse estimation and directed transfer function: simulations and application to real data

OBJECTIVE

To test a technique called Directed Transfer Function (DTF) for the estimation of human cortical connectivity, by means of simulation study and human study, using high resolution EEG recordings related to finger movements.

METHODS

The method of the Directed Transfer Function (DTF) is a frequency-domain approach, based on a multivariate autoregressive modeling of time series and on the concept of Granger causality. Since the spreading of the potential from the cortex to the sensors makes it difficult to infer the relation between the spatial patterns on the sensor space and those on the cortical sites, we propose the use of the DTF method on cortical signals estimated from high resolution EEG recordings, which exhibit a higher spatial resolution than conventional cerebral electromagnetic measures. The simulation study was followed by an analysis of variance (ANOVA) of the results obtained for different levels of Signal to Noise Ratio (SNR) and temporal length, as they have been systematically imposed on simulated signals. The whole methodology was then applied to high resolution EEG data recorded during a visually paced finger movement.

RESULTS

The statistical analysis performed returns that during simulations, DTF is able to estimate correctly the imposed connectivity patterns under reasonable operative conditions, i.e. when data exhibit a SNR of at least 3 and a length of at least 75 s of non-consecutive recordings at 64 Hz of sampling rate, equivalent, more generally, to 4800 data samples.

CONCLUSIONS

Functional connectivity patterns of cortical activity can be effectively estimated under general conditions met in any practical EEG recordings, by combining high resolution EEG techniques, linear inverse estimation and the DTF method.

SIGNIFICANCE

The estimation of cortical connectivity can be performed not only with hemodynamic measurements, by using functional MRI recordings, but also with modern EEG recordings treated with advanced computational techniques.

Neural networks involved in mathematical thinking: evidence from linear and non-linear analysis of electroencephalographic activity

Using linear and non-linear methods, electroencephalographic (EEG) signals were measured at various brain regions to provide information regarding patterns of local and coordinated activity during performance of three arithmetic tasks (number comparison, single-digit multiplication, and two-digit multiplication) and two control tasks that did not require arithmetic operations. It was hypothesized that these measures would reveal the engagement of local and increasingly complex cortical networks as a function of task specificity and complexity. Results indicated regionally increased neuronal signalling as a function of task complexity at frontal, temporal and parietal brain regions, although more robust task-related changes in EEG-indices of activation were derived over the left hemisphere. Both linear and non-linear indices of synchronization among EEG signals recorded from over different brain regions were consistent with the notion of more "local" processing for the number comparison task. Conversely, multiplication tasks were associated with a widespread pattern of distant signal synchronizations, which could potentially indicate increased demands for neural networks cooperation during performance of tasks that involve a greater number of cognitive operations.

An information integration theory of consciousness

BACKGROUND

Consciousness poses two main problems. The first is understanding the conditions that determine to what extent a system has conscious experience. For instance, why is our consciousness generated by certain parts of our brain, such as the thalamocortical system, and not by other parts, such as the cerebellum? And why are we conscious during wakefulness and much less so during dreamless sleep? The second problem is understanding the conditions that determine what kind of consciousness a system has. For example, why do specific parts of the brain contribute specific qualities to our conscious experience, such as vision and audition?

PRESENTATION OF THE HYPOTHESIS

This paper presents a theory about what consciousness is and how it can be measured. According to the theory, consciousness corresponds to the capacity of a system to integrate information. This claim is motivated by two key phenomenological properties of consciousness: differentiation - the availability of a very large number of conscious experiences; and integration - the unity of each such experience. The theory states that the quantity of consciousness available to a system can be measured as the Phi value of a complex of elements. Phi is the amount of causally effective information that can be integrated across the informational weakest link of a subset of elements. A complex is a subset of elements with Phi>0 that is not part of a subset of higher Phi. The theory also claims that the quality of consciousness is determined by the informational relationships among the elements of a complex, which are specified by the values of effective information among them. Finally, each particular conscious experience is specified by the value, at any given time, of the variables mediating informational interactions among the elements of a complex.

TESTING THE HYPOTHESIS

The information integration theory accounts, in a principled manner, for several neurobiological observations concerning consciousness. As shown here, these include the association of consciousness with certain neural systems rather than with others; the fact that neural processes underlying consciousness can influence or be influenced by neural processes that remain unconscious; the reduction of consciousness during dreamless sleep and generalized seizures; and the time requirements on neural interactions that support consciousness.

IMPLICATIONS OF THE HYPOTHESIS

The theory entails that consciousness is a fundamental quantity, that it is graded, that it is present in infants and animals, and that it should be possible to build conscious artifacts.

Spatiotemporal wavelet resampling for functional neuroimaging data

The study of dynamic interdependences between brain regions is currently a very active research field. For any connectivity study, it is important to determine whether correlations between two selected brain regions are statistically significant or only chance effects due to non-specific correlations present throughout the data. In this report, we present a wavelet-based non-parametric technique for testing the null hypothesis that the correlations are typical of the data set and not unique to the regions of interest. This is achieved through spatiotemporal resampling of the data in the wavelet domain. Two functional MRI data sets were analysed: (1) Data from 8 healthy human subjects viewing a checkerboard image, and (2) "Null" data obtained from 3 healthy human subjects, resting with eyes closed. It was demonstrated that constrained resampling of the data in the wavelet domain allows construction of bootstrapped data with four essential properties: (1) Spatial and temporal correlations within and between slices are preserved, (2) The irregular geometry of the intracranial images is maintained, (3) There is adequate type I error control, and (4) Expected experiment-induced correlations are identified. The limitations and possible extensions of the proposed technique are discussed.

"Dynamic" connectivity in neural systems: theoretical and empirical considerations

The study of functional interdependences between brain regions is a rapidly growing focus of neuroscience research. This endeavor has been greatly facilitated by the appearance of a number of innovative methodologies for the examination of neurophysiological and neuroimaging data. The aim of this article is to present an overview of dynamical measures of interdependence and contrast these with statistical measures that have been more widely employed. We first review the motivation, conceptual basis, and experimental approach of dynamical measures of interdependence and their application to the study of neural systems. A consideration of boot-strap "surrogate data" techniques, which facilitate hypothesis testing of dynamical measures, is then used to clarify the difference between dynamical and statistical measures of interdependence. An overview of some of the most active research areas such as the study of the "synchronization manifold," dynamical interdependence in neurophysiology data and the putative role of nonlinear desynchronization is then given. We conclude by suggesting that techniques based on dynamical interdependence--or "dynamical connectivity"--show significant potential for extracting meaningful information from functional neuroimaging data.

Disturbed fluctuations of resting state EEG synchronization in Alzheimer's disease

OBJECTIVE

We examined the hypothesis that cognitive dysfunction in Alzheimer's disease is associated with abnormal spontaneous fluctuations of EEG synchronization levels during an eyes-closed resting state.

METHODS

EEGs were recorded during an eyes-closed resting state in Alzheimer patients (N=24; 9 males; mean age 76.3 years; SD 7.8; range 59-86) and non-demented subjects with subjective memory complaints (N=19; 9 males; mean age 76.1 years; SD 6.7; range: 67-89). The mean level of synchronization was determined in different frequency bands with the synchronization likelihood and fluctuations of the synchronization level were analysed with detrended fluctuation analysis (DFA).

RESULTS

The mean level of EEG synchronization was lower in Alzheimer patients in the upper alpha (10-13Hz) and beta (13-30Hz) band. Spontaneous fluctuations of synchronization were diminished in Alzheimer patients in the lower alpha (8-10Hz) and beta bands. In patients as well as controls the synchronization fluctuations showed a scale-free pattern.

CONCLUSIONS

Alzheimer's disease is characterized both by a lower mean level of functional connectivity as well as by diminished fluctuations in the level of synchronization. The dynamics of these fluctuations in patients and controls was scale-free which might point to self-organized criticality of neural networks in the brain.

SIGNIFICANCE

Impaired functional connectivity can manifest itself not only in decreased levels of synchronization but also in disturbed fluctuations of synchronization levels.

Interdependency between heart rate variability and sleep EEG: linear/non-linear?

OBJECTIVE

To investigate whether the interdependency between heart rate variability (HRV) and sleep electroencephalogram (EEG) power spectra is linear or non-linear.

METHODS

Heart rate and sleep EEG signals were recorded in 8 healthy young men. Spectral analysis was applied to electrocardiogram and EEG sleep recordings. Synchronization likelihood was computed over the first 3 non-rapid eye movement-rapid eye movement sleep cycles between normalized high frequency of RR intervals (RRI) and all electroencephalographic frequency bands. Comparison to surrogate data of different types was used to attest statistical significance of the coupling between RRI and EEG power bands and its linear or non-linear character.

RESULTS

Synchronization likelihood values were statistically greater than univariate surrogate synchronization for all sleep bands both at the individual and the group levels. With reference to multivariate surrogates, synchronization values were statistically greater at the group level and, in a majority of cases, for individual comparison except for sigma and beta bands.

CONCLUSIONS

While all electroencephalographic power bands are linked to normalized high frequency RRI band, this interdependency is non-linear for delta, theta and alpha bands.

SIGNIFICANCE

Non-linear description is required to capture the full interdependent dynamics of HRV and sleep EEG power bands.

Abnormal EEG synchronisation in heavily drinking students

OBJECTIVE

In alcoholics, grey and white brain matter is damaged. In addition, functional brain connectivity as measured by EEG coherence is abnormal. We investigated whether heavily drinking students, although drinking for a shorter period than alcoholics, already show differences in functional connectivity compared to light-drinking controls.

METHODS

EEG was recorded in 11 light and 11 heavy male student drinkers during eyes closed, and eyes closed plus mental rehearsal of pictures. Functional connectivity was assessed with the Synchronisation Likelihood method.

RESULTS

Heavily drinking students had more synchronisation in the theta (4-8 Hz) and gamma (30-45 Hz) band than lightly drinking students during eyes closed, both with and without a mental-rehearsal task.

CONCLUSIONS

Heavy student drinkers have increases in EEG synchronisation that are indicative of changes in hippocampal-neocortical connectivity.

SIGNIFICANCE

Heavy student drinkers show differences in functional connectivity as compared to their lightly drinking counterparts, even though they have a relatively short drinking history.

Origin, structure, and role of background EEG activity. Part 1. Analytic amplitude

OBJECTIVE

To explain the neural mechanisms of spontaneous EEG by measuring the spatiotemporal patterns of synchrony among beta-gamma oscillations during perception.

METHODS

EEGs were measured from 8 x 8 (5.6 x 5.6 mm2) arrays fixed on the surfaces of primary sensory areas in rabbits that were trained to discriminate visual, auditory or tactile conditioned stimuli (CSs) eliciting conditioned responses (CRs). EEG preprocessing was by (i) bandpass filtering to extract the beta-gamma range (deleting theta-alpha); (ii) low-pass spatial filtering (not high-pass Laplacians used for localization), (iii) spatial averaging (not time averaging used for evoked potentials), and (iv) close spacing of 64 electrodes for simultaneous recording in each area (not sampling single signals from several areas); (v) novel algorithms were devised to measure synchrony and spatial pattern stability by calculating variances among patterns in 64-space derived from the 8 x 8 arrays (not by fitting equivalent dipoles). These methodological differences are crucial for the proposed new perspective on EEG.

RESULTS

Spatial patterns of beta-gamma EEG emerged following sudden jumps in cortical activity called 'state transitions'. Each transition began with an abrupt phase re-setting to a new value on every channel, followed sequentially by re-synchronization, spatial pattern stabilization, and a dramatic increase in pattern amplitude. State transitions recurred at varying intervals in the theta range. A novel parameter was devised to estimate the perceptual information in the beta-gamma EEG, which disclosed 2-4 patterns with high information content in the CS-CR interval on each trial; each began with a state transition and lasted approximately 0.1 s.

CONCLUSIONS

The function of each primary sensory neocortex was discontinuous; discrete spatial patterns occurred in frames like those in cinema. The frames before and after the CS-CR interval had low content.

SIGNIFICANCE

Derivation and interpretation of unit data in studies of perception might benefit from using multichannel EEG recordings to define distinctive epochs that are demarcated by state transitions of neocortical dynamics in the CS-CR intervals, particularly in consideration of the possibility that EEG may reveal recurring episodes of exchange and sharing of perceptual information among multiple sensory cortices. Simultaneously recorded, multichannel beta-gamma EEG might assist in the interpretation of images derived by fMRI, since high beta-gamma EEG amplitudes imply high rates of energy utilization. The spatial pattern intermittency provides a tag to distinguish gamma bursts from contaminating EMG activity in scalp recording in order to establish beta-gamma recording as a standard clinical tool. Finally, EEG cannot fail to have a major impact on brain theory.

Scale-free dynamics of global functional connectivity in the human brain

Higher brain functions depend upon the rapid creation and dissolution of ever changing synchronous cell assemblies. We examine the hypothesis that the dynamics of this process displays scale-free, self-similar properties. EEGs (19 channels, average reference, sample frequency 500 Hz) of 15 healthy subjects (10 men; mean age 22.5 years) were analyzed during eyes-closed and eyes-open no-task conditions. Mean level of synchronization as a function of time was estimated with the synchronization likelihood for five frequency bands (0.5-4, 4-8, 8-13, 13-30, and 30-48 Hz). Scaling in these time series was investigated with detrended fluctuation analysis (DFA). DFA analysis of global synchronization time series showed scale-free characteristics, suggesting neuronal dynamics do not necessarily have a characteristic time constant. The scaling exponent as determined with DFA differed significantly for different frequency bands and conditions. The exponent was close to 1.5 for low frequencies (delta, theta, and alpha) and close to 1 for beta and gamma bands. Eye opening decreased the exponent, in particular in alpha and beta bands. Fluctuations of EEG synchronization in delta, theta, alpha, beta, and gamma bands exhibit scale-free dynamics in eyes-closed as well as eyes-open no-task states. The decrease in the scaling exponent following eye opening reflects a relative preponderance of rapid fluctuations with respect to slow changes in the mean synchronization level. The existence of scaling suggests that the underlying dynamics may display self-organized criticality, possibly representing a near-optimal state for information processing.

Different EEG frequency band synchronization during nocturnal frontal lobe seizures

OBJECTIVE

In this article we describe the course of synchronization between different EEG channels during nocturnal seizures in one patient with nocturnal frontal lobe epilepsy (NFLE).

METHODS

The functional interactions between the different EEG channels during the nocturnal seizures were analyzed by means of the so-called synchronization likelihood (SL). SL is a measure of the dynamical interdependencies between a time series (EEG channel) and one or more other time series. In contrast to coherence, SL measures linear as well as non-linear interdependencies and it can do so as a function of time, making it suitable for non-stationary time series.

RESULTS

The main result of our single-patient study is the demonstration of a significant hyper-synchronization during NFLE seizures in the 8-12 Hz band which seems to be stopped by an increase in synchronization in the 0.5-4 Hz band, towards the end of each ictal episode.

CONCLUSIONS

We suggest that a self-inhibiting complex mechanism might be responsible for the termination of ictal episodes which might take place at the level of the cortical layers and might involve mainly pyramidal neurons.

SIGNIFICANCE

This study shows that advanced EEG analysis methods can help the current understanding of ictal manifestations of NFLE.

Functional connectivity patterns of human magnetoencephalographic recordings: a 'small-world' network?

EEG and MEG (magnetoencephalography) are widely used to study functional connectivity between different brain regions. We address the question whether such connectivity patterns display an optimal organization for information processing. MEG recordings of five healthy human subjects were converted to sparsely connected graphs (N=126; k=15) by applying a suitable threshold to the N * N matrix of synchronization strengths. For intermediate frequencies (8-30 Hz) the synchronization patterns were similar to those of an ordered graph with a consistent drop of synchronization strength as a function of distance. For low (<8 Hz) and high (>30 Hz) frequency bands the synchronization patterns displayed the features of a so-called 'small-world' network. This might reflect an optimal organization pattern for information processing, connecting any two brain area by only a small number of intermediate steps.

A novel method for the topographic analysis of neural activity reveals formation and dissolution of 'Dynamic Cell Assemblies'

The study of synchronous oscillations in neural systems is a very active area of research. However, cognitive function may depend more crucially upon a dynamic alternation between synchronous and desynchronous activity rather than synchronous behaviour per se. The principle aim of this study is to develop and validate a novel method of quantifying this complex process. The method permits a direct mapping of phase synchronous dynamics and desynchronizing bursts in the spatial and temporal domains. Two data sets are analyzed: Numeric data from a model of a sparsely coupled neural cell assembly and experimental data consisting of scalp-recorded EEG from 40 human subjects. In the numeric data, the approach enables the demonstration of complex relationships between cluster size and temporal duration that cannot be detected with other methods. Dynamic patterns of phase-clustering and desynchronization are also demonstrated in the experimental data. It is further shown that in a significant proportion of the recordings, the pattern of dynamics exhibits nonlinear structure. We argue that this procedure provides a 'natural partitioning' of ongoing brain dynamics into topographically distinct synchronous epochs which may be integral to the brain's adaptive function. In particular, the character of transitions between consecutive synchronous epochs may reflect important aspects of information processing and cognitive flexibility.

Evaluation of different measures of functional connectivity using a neural mass model

We use a neural mass model to address some important issues in characterising functional integration among remote cortical areas using magnetoencephalography or electroencephalography (MEG or EEG). In a previous paper [Neuroimage (in press)], we showed how the coupling among cortical areas can modulate the MEG or EEG spectrum and synchronise oscillatory dynamics. In this work, we exploit the model further by evaluating different measures of statistical dependencies (i.e., functional connectivity) among MEG or EEG signals that are mediated by neuronal coupling. We have examined linear and nonlinear methods, including phase synchronisation. Our results show that each method can detect coupling but with different sensitivity profiles that depended on (i) the frequency specificity of the interaction (broad vs. narrow band) and (ii) the nature of the coupling (linear vs. nonlinear). Our analyses suggest that methods based on the concept of generalised synchronisation are the most sensitive when interactions encompass different frequencies (broadband analyses). In the context of narrow-band analyses, mutual information was found to be the most sensitive way to disclose frequency-specific couplings. Measures based on generalised synchronisation and phase synchronisation are the most sensitive to nonlinear coupling. These different sensitivity profiles mean that the choice of coupling measures can have dramatic effects on the cortical networks identified. We illustrate this using a single-subject MEG study of binocular rivalry and highlight the greater recovery of statistical dependencies among cortical areas in the beta band when mutual information is used.

A disturbance of nonlinear interdependence in scalp EEG of subjects with first episode schizophrenia

It has been proposed that schizophrenia arises through a disturbance of coupling between large-scale cortical systems. This "disconnection hypothesis" is tested by applying a measure of dynamical interdependence to scalp EEG data. EEG data were collected from 40 subjects with a first episode of schizophrenia and 40 matched healthy controls. An algorithm for the detection of dynamical interdependence was applied to six pairs of bipolar electrodes in each subject. The topographic organization of the interdependence was calculated and served as the principle measure of cortical integration. The rate of occurrence of dynamical interdependence did not statistically differ between subject groups at any of the sites. However, the topography across the scalp was significantly different between the two groups. Specifically, nonlinear interdependence tended to occur in larger concurrent "clusters" across the scalp in schizophrenia than in the healthy subjects. This disturbance was reflected most strongly in left intrahemispheric coupling and did not differ significantly according to symptomatology. Medication dose and subject arousal were not observed to be confounding factors. The study of dynamical interdependence in scalp EEG data does not support a straightforward interpretation of the disconnection hypothesis-that there is a decrease in the strength of functional coupling between adjacent cortical regions. Rather, it suggests a dysregulation in the organization of dynamical interactions across supraregional brain systems.