Human brain alpha rhythm: nonlinear oscillation or filtered noise?

Increased neurocardiological interplay after mindfulness meditation: a brain oscillation-based approach

Background

Brain oscillations facilitate interaction within the brain network and between the brain and heart activities, and the alpha wave, as a prominent brain oscillation, plays a major role in these coherent activities. We hypothesize that mindfully breathing can make the brain and heart activities more coherent in terms of increased connectivity between the electroencephalogram (EEG) and electrocardiogram (ECG) signals.

Methods

Eleven participants (28-52 years) attended 8 weeks of Mindfulness Based Stress Reduction (MBSR) training. EEG and ECG data of two states of mindful breathing and rest, both eye-closed, were recorded before and after the training. EEGLAB was used to analyze the alpha band (8-12 Hz) power, alpha peak frequency (APF), peak power and coherence. FMRIB toolbox was used to extract the ECG data. Heart coherence (HC) and heartbeat evoked potential (HEP) were calculated for further correlation analysis.

Results

After 8 weeks of MBSR training, the correlation between APF and HC increased significantly in the middle frontal region and bilateral temporal regions. The correlation between alpha coherence and heart coherence had similar changes, while alpha peak power did not reflect such changes. In contrast, spectrum analysis alone did not show difference before and after MBSR training.

Conclusion

The brain works in rhythmic oscillation, and this rhythmic connection becomes more coherent with cardiac activity after 8 weeks of MBSR training. Individual APF is relatively stable and its interplay with cardiac activity may be a more sensitive index than power spectrum by monitoring the brain-heart connection. This preliminary study has important implications for the neuroscientific measurement of meditative practice.

Resting state electroencephalography (EEG) correlates with children's language skills: Evidence from sentence repetition

Spontaneous neural oscillatory activity reflects the brain's functional architecture and has previously been shown to correlate with perceptual, motor and executive skills. The current study used resting state electroencephalography to examine the relationship between spontaneous neural oscillatory activity and children's language skills. Participants in the study were 52 English-speaking children aged around 10-years. Language was assessed using a sentence repetition task. The main analysis revealed resting state theta power negatively correlated with this task. No significant correlations were found in the other studied frequency bands (delta, alpha, beta, gamma). As part of typical brain development, spontaneous theta power declines across childhood and adolescence. The negative correlation observed in this study may therefore be indicating children's language skills are related to the maturation of theta oscillations. More generally, the study provides further evidence that oscillatory activity in the developing brain, even at rest, is reliably associated with children's language skills.

A Waveform-Independent Measure of Recurrent Neural Activity

Rhythmic neural activity, so-called oscillations, plays a key role in neural information transmission, processing, and storage. Neural oscillations in distinct frequency bands are central to physiological brain function, and alterations thereof have been associated with several neurological and psychiatric disorders. The most common methods to analyze neural oscillations, e.g., short-time Fourier transform or wavelet analysis, assume that measured neural activity is composed of a series of symmetric prototypical waveforms, e.g., sinusoids. However, usually, the models generating the signal, including waveform shapes of experimentally measured neural activity are unknown. Decomposing asymmetric waveforms of nonlinear origin using these classic methods may result in spurious harmonics visible in the estimated frequency spectra. Here, we introduce a new method for capturing rhythmic brain activity based on recurrences of similar states in phase-space. This method allows for a time-resolved estimation of amplitude fluctuations of recurrent activity irrespective of or specific to waveform shapes. The algorithm is derived from the well-established field of recurrence analysis, which, in comparison to Fourier-based analysis, is still very uncommon in neuroscience. In this paper, we show its advantages and limitations in comparison to short-time Fourier transform and wavelet convolution using periodic signals of different waveform shapes. Furthermore, we demonstrate its application using experimental data, i.e., intracranial and noninvasive electrophysiological recordings from the human motor cortex of one epilepsy patient and one healthy adult, respectively.

Dynamic origin of spike and wave discharges in the brain

Spike and wave discharges are the main electrographic characteristic of a number of epileptic brain disorders including childhood absence epilepsy and photosensitive epilepsy. The basic dynamic mechanism that underlies the occurrence of these abnormal electrical patterns in the brain is not well understood. The current paper aims to provide a dynamic explanation for features and generation mechanism of spike and wave discharges in the brain. The main proposition of this study is that epileptic seizures could be interpreted as a resonance phenomenon rather than a limit cycle behavior. To shows this, a revised version of Jansen-Rit neural mass model is employed. The system can switch between monostable and bistable regimes, which are considered in this paper as wake and sleep states of the brain, respectively. In particular, it is shown that, in monostable region, the model can depict the alpha rhythm and alpha rhythm suppression due to mental activity. Frequency responses of the model near the bistable regime demonstrate that high amplitude harmonic excitation may lead to spike and wave like oscillations. Based on the computational results and the concept of stochastic resonance, a model for absence epilepsy is presented which can simulate spontaneous transitions between ictal and interictal states. Finally, it is shown that spike and wave discharges during epileptic seizures can be explained as a resonance phenomenon in a nonlinear system.

A new description of epileptic seizures based on dynamic analysis of a thalamocortical model

Increasing evidence suggests that the brain dynamics can be interpreted from the viewpoint of nonlinear dynamical systems. The aim of this paper is to investigate the behavior of a thalamocortical model from this perspective. The model includes both cortical and sensory inputs that can affect the dynamic nature of the model. Driving response of the model subjected to various harmonic stimulations is considered to identify the effects of stimulus parameters on the cortical output. Detailed numerical studies including phase portraits, Poincare maps and bifurcation diagrams reveal a wide range of complex dynamics including period doubling and chaos in the output. Transition between different states can occur as the stimulation parameters are changed. In addition, the amplitude jump phenomena and hysteresis are shown to be possible as a result of the bending in the frequency response curve. These results suggest that the jump phenomenon due to the brain nonlinear resonance can be responsible for the transitions between ictal and interictal states.

Nonlinear Origin of SSVEP Spectra-A Combined Experimental and Modeling Study

Steady state visual evoked potentials (SSVEPs) are steady state oscillatory potentials elicited in the electroencephalogram (EEG) by flicker stimulation. The frequency of these responses maches the frequency of the stimulation and of its harmonics and subharmonics. In this study, we investigated the origin of the harmonic and subharmonic components of SSVEPs, which are not well understood. We applied both sine and square wave visual stimulation at 5 and 15 Hz to human subjects and analyzed the properties of the fundamental responses and harmonically related components. In order to interpret the results, we used the well-established neural mass model that consists of interacting populations of excitatory and inhibitory cortical neurons. In our study, this model provided a simple explanation for the origin of SSVEP spectra, and showed that their harmonic and subharmonic components are a natural consequence of the nonlinear properties of neuronal populations and the resonant properties of the modeled network. The model also predicted multiples of subharmonic responses, which were subsequently confirmed using experimental data.

Rod Driven Frequency Entrainment and Resonance Phenomena

A controversy exists on photic driving in the human visual cortex evoked by intermittent photic stimulation. Frequency entrainment and resonance phenomena are reported for frequencies higher than 12 Hz in some studies while missing in others. We hypothesized that this might be due to different experimental conditions, since both high and low intensity light stimulation were used. However, most studies do not report radiometric measurements, which makes it impossible to categorize the stimulation according to photopic, mesopic, and scotopic vision. Low intensity light stimulation might lead to scotopic vision, where rod perception dominates. In this study, we investigated photic driving for rod-dominated visual input under scotopic conditions. Twelve healthy volunteers were stimulated with low intensity light flashes at 20 stimulation frequencies, leading to rod activation only. The frequencies were multiples of the individual alpha frequency (α) of each volunteer in the range from 0.40 to 2.30(∗)α. Three hundred and six-channel whole head magnetoencephalography recordings were analyzed in time, frequency, and spatiotemporal domains with the Topographic Matching Pursuit algorithm. We found resonance phenomena and frequency entrainment for stimulations at or close to the individual alpha frequency (0.90-1.10(∗)α) and half of the alpha frequency (0.40-0.55(∗)α). No signs of resonance and frequency entrainment phenomena were revealed around 2.00(∗)α. Instead, on-responses at the beginning and off-responses at the end of each stimulation train were observed for the first time in a photic driving experiment at frequencies of 1.30-2.30(∗)α, indicating that the flicker fusion threshold was reached. All results, the resonance and entrainment as well as the fusion effects, provide evidence for rod-dominated photic driving in the visual cortex.

Endogenous and Rapid Serial Visual Presentation-induced Alpha Band Oscillations in the Attentional Blink

The attentional blink (AB) is a deficit in conscious perception of the second of two targets if it follows the first within 200–500 msec. The AB phenomenon has been linked to pre-target oscillatory alpha activity. However, this is based on paradigms that use a rapid serial visual presentation (RSVP) stimulus stream in which the targets are embedded. This distracter stream is usually presented at a frequency of 10 Hz and thus generates a steady-state visual-evoked potential (ssVEP) at the center of the alpha frequency band. This makes the interpretation of alpha findings in the AB difficult. To be able to relate these findings either to the presence of the ssVEP or to an effect of endogenously generated alpha activity, we compared AB paradigms with and without different pre-target distracter streams. The distracter stream was always presented at 12 Hz, and power and intertrial phase coherence were analyzed in the alpha range (8–12 Hz). Without a distracter stream alpha power dropped before target presentation, whereas coherence did not change. Presence of a distracter stream was linked to stronger pre-target power reduction and increased coherence, which were both modulated by distracter stream characteristics. With regard to the AB results indicated that, whereas ssVEP-related power tended to be higher when both targets were detected, endogenous alpha power tended to be lower. We argue that the pattern of results indicates that in the pre-target interval several processes act in parallel. The balance between these processes relates to the occurrence of an AB.

Abnormal late visual responses and alpha oscillations in neurofibromatosis type 1: a link to visual and attention deficits

Background

Neurofibromatosis type 1 (NF1) affects several areas of cognitive function including visual processing and attention. We investigated the neural mechanisms underlying the visual deficits of children and adolescents with NF1 by studying visual evoked potentials (VEPs) and brain oscillations during visual stimulation and rest periods.

Methods

Electroencephalogram/event-related potential (EEG/ERP) responses were measured during visual processing (NF1 n = 17; controls n = 19) and idle periods with eyes closed and eyes open (NF1 n = 12; controls n = 14). Visual stimulation was chosen to bias activation of the three detection mechanisms: achromatic, red-green and blue-yellow.

Results

We found significant differences between the groups for late chromatic VEPs and a specific enhancement in the amplitude of the parieto-occipital alpha amplitude both during visual stimulation and idle periods. Alpha modulation and the negative influence of alpha oscillations in visual performance were found in both groups.

Conclusions

Our findings suggest abnormal later stages of visual processing and enhanced amplitude of alpha oscillations supporting the existence of deficits in basic sensory processing in NF1. Given the link between alpha oscillations, visual perception and attention, these results indicate a neural mechanism that might underlie the visual sensitivity deficits and increased lapses of attention observed in individuals with NF1.

Alpha entrainment is responsible for the attentional blink phenomenon

The attentional blink phenomenon is the reduced ability to report a second target (T2) after identifying a first target (T1) in a rapid serial visual presentation (RSVP) of stimuli (e.g., letters), which are presented at approximately 10 items per second. Several explanations have been proposed, which focus primarily on cognitive aspects, such as attentional filter-, capacity limitation- and retrieval failure-processes. Here, we focus on the hypothesis that an entrainment of alpha oscillations (with a frequency of about 10Hz) is a critical factor for the attentional blink phenomenon. Our hypothesis is based on the fact that item presentation rate in the RSVP typically lies in the alpha frequency range and is motivated by theories assuming an inhibitory function for alpha. We predict that entrainment--during the time window of T2 presentation--is larger for attentional blink (AB) items (when T2 cannot be reported) than for NoAB trials (when T2 cannot be reported). The results support our hypothesis and show that alpha entrainment as measured by the amplitude of the alpha evoked response and the extent of alpha phase concentration is larger for AB than for NoAB trials. Together with the lack of differences in alpha power these findings demonstrate that the differences between AB and NoAB trials--during presentation onset of T2--are due to an entrainment of alpha phase and not due to an amplitude modulation. Thus, we conclude that alpha entrainment may be considered the critical factor underlying the attentional blink phenomenon.

Modeling brain resonance phenomena using a neural mass model

Stimulation with rhythmic light flicker (photic driving) plays an important role in the diagnosis of schizophrenia, mood disorder, migraine, and epilepsy. In particular, the adjustment of spontaneous brain rhythms to the stimulus frequency (entrainment) is used to assess the functional flexibility of the brain. We aim to gain deeper understanding of the mechanisms underlying this technique and to predict the effects of stimulus frequency and intensity. For this purpose, a modified Jansen and Rit neural mass model (NMM) of a cortical circuit is used. This mean field model has been designed to strike a balance between mathematical simplicity and biological plausibility. We reproduced the entrainment phenomenon observed in EEG during a photic driving experiment. More generally, we demonstrate that such a single area model can already yield very complex dynamics, including chaos, for biologically plausible parameter ranges. We chart the entire parameter space by means of characteristic Lyapunov spectra and Kaplan-Yorke dimension as well as time series and power spectra. Rhythmic and chaotic brain states were found virtually next to each other, such that small parameter changes can give rise to switching from one to another. Strikingly, this characteristic pattern of unpredictability generated by the model was matched to the experimental data with reasonable accuracy. These findings confirm that the NMM is a useful model of brain dynamics during photic driving. In this context, it can be used to study the mechanisms of, for example, perception and epileptic seizure generation. In particular, it enabled us to make predictions regarding the stimulus amplitude in further experiments for improving the entrainment effect.

Neuroscience aims to understand the enormously complex function of the normal and diseased brain. This, in turn, is the key to explaining human behavior and to developing novel diagnostic and therapeutic procedures. We develop and use models of mean activity in a single brain area, which provide a balance between tractability and plausibility. We use such a model to explain the resonance phenomenon in a photic driving experiment, which is routinely applied in the diagnosis of various diseases including epilepsy, migraine, schizophrenia and depression. Based on the model, we make predictions on the outcome of similar resonance experiments with periodic stimulation of the patients or participants. Our results are important for researchers and clinicians analyzing brain or behavioral data following periodic input.

Dynamics underlying spontaneous human alpha oscillations: a data-driven approach

Although the cognitive and clinical correlates of spontaneous human alpha oscillations as recorded with electroencephalography (EEG) or magnetoencephalography (MEG) are well documented, the dynamics underlying these oscillations is still a matter of debate. This study proposes a data-driven method to reveal the dynamics of these oscillations. It demonstrates that spontaneous human alpha oscillations as recorded with MEG can be viewed as noise-perturbed damped harmonic oscillations. This provides evidence for the hypothesis that these oscillations reflect filtered noise and hence do not possess limit-cycle dynamics. To illustrate the use of the model, we apply it to two data-sets in which a decrease in alpha power can be observed across conditions. The associated differences in the estimated model parameters show that observed decreases in alpha power are associated with different kinds of changes in the dynamics. Thus, the model parameters are useful dynamical biomarkers for spontaneous human alpha oscillations.

The influence of the astrocyte field on neuronal dynamics and synchronization

Astrocytes can sense local synaptic release of glutamate by metabotropic glutamate receptors. Receptor activation in turn can mediate transient increases of astrocytic intracellular calcium concentration through inositol 1,4,5-trisphosphate production. Notably, the perturbation of calcium concentration can propagate to other adjacent astrocytes. Astrocytic calcium signaling can therefore be linked to synaptic information transfer between neurons. On the other hand, astrocytes can also modulate neuronal activity by feeding back onto synaptic terminals in a fashion that depends on their intracellular calcium concentration. Thus, astrocytes can also be active partners in neuronal network activity. The aim of our study is to provide a computationally simple network model of mutual neuron-astrocyte interactions, in order to investigate the possible roles of astrocytes in neuronal network dynamics. In particular, we focus on the information entropy of neuronal firing of the whole network, considering how it could be affected by neuron-glial interactions.

Alpha entrainment in human electroencephalogram and magnetoencephalogram recordings

Visual stimulation by repetitive flashes of light can lead to an entrainment of the alpha rhythm in electroencephalogram recordings (also called photic driving). We report a comparison of simultaneously recorded electric and magnetic data in a photic driving experiment, adapted to the individual alpha rhythm of 10 healthy volunteers. We show that there is a stronger frequency entrainment in magnetoencephalogram than in electroencephalogram recordings in all volunteers, which indicates a possible tangential brain activity underlying the dominant entrainment effect. The entrainment in the magnetoencephalogram lasts over significantly more frequencies and is most effective in the region around the individual alpha and a half alpha. For different channels, we found different degrees of entrainment showing topological and time-varying properties.

EEG alpha oscillations: the inhibition-timing hypothesis

The traditional belief is that the event-related alpha response can solely be described in terms of suppression or event-related desynchronization (ERD). Recent research, however, has shown that under certain conditions alpha responds reliably with an increase in amplitudes (event-related synchronization or ERS). ERS is elicited in situations, where subjects withhold or control the execution of a response and is obtained over sites that probably are under, or exert top-down control. Thus, we assume that alpha ERS reflects top-down, inhibitory control processes. This assumption leads over to the timing aspect of our hypothesis. By the very nature of an oscillation, rhythmic amplitude changes reflect rhythmic changes in excitation of a population of neurons. Thus, the time and direction of a change - described by phase - is functionally related to the timing of neuronal activation processes. A variety of findings supports this view and shows, e.g., that alpha phase coherence increases between task-relevant sites and that phase lag lies within a time range that is consistent with neuronal transmission speed. Another implication is that phase reset will be a powerful mechanism for the event-related timing of cortical processes. Empirical evidence suggests that the extent of phase locking is a functionally sensitive measure that is related to cognitive performance. Our general conclusion is that alpha ERS plays an active role for the inhibitory control and timing of cortical processing whereas ERD reflects the gradual release of inhibition associated with the emergence of complex spreading activation processes.

A coherence-based technique for separating phase-locked from non-phase-locked power spectrum estimates during intermittent stimulation

In addition to evoked responses, which are phase-locked to the stimuli, the stimulation may also change the ongoing EEG in a time-locked manner. This change has been investigated in event-related synchronization/desynchronization (ERS/ERD) studies by comparing the spectra before and during stimulation or alternatively by using the intertrial variance method (IVM). In the present work, a technique based on the coherence estimate (kappa(y)(2)(f)) between the stimulation signal and the EEG is proposed for separating the ongoing EEG activity spectrum from that of the evoked responses. Furthermore, a statistical criterion is applied to reduce spurious spectral peaks. The performance of this procedure was assessed through simulation and illustrated with EEG during photic stimulation. For simulated data (signal-to-noise-ratio of 0.995 within 10-12.5 Hz) kappa(y)(2)(f) led to a non-phase-locked spectrum estimate with an average normalized error of 12.4%, which is reduced to only 0.2% after applying the statistical criterion. The methodology proposed is asymptotically equivalent to the IVM but it does not require previous filtering the EEG data. Kappa(y)(2)(f) together with the statistical correction criterion allows investigating the entrainment within a narrow-band range, particularly in frequencies close to that of the alpha peak. Hence it is useful in ERS/ERD studies. Moreover, it can be also used for characterizing frequencies within the gamma band.

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.

The functional significance of mu rhythms: translating "seeing" and "hearing" into "doing"

Existing evidence indicates that mu and other alpha-like rhythms are independent phenomena because of differences in source generation, sensitivity to sensory events, bilateral coherence, frequency, and power. Although mu suppression and enhancement echo sensorimotor processing in frontoparietal networks, they are also sensitive to cognitive and affective influences and likely reflect more than an idling brain state. Mu rhythms are present at early stages of human development and in other mammalian species. They exhibit adaptive and dynamically changing properties, including frequency acceleration and posterior-to-anterior shifts in focus. Furthermore, individuals can learn to control mu rhythms volitionally in a very short period of time. This raises questions about the mu rhythm's open neural architecture and ability to respond to cognitive, affective, and motor imagery, implying an even greater developmental and functional role than has previously been ascribed to it. Recent studies have suggested that mu rhythms reflect downstream modulation of motor cortex by prefrontal mirror neurons, i.e., cells that may play a critical role in imitation learning and the ability to understand the actions of others. It is proposed that mu rhythms represent an important information processing function that links perception and action-specifically, the transformation of "seeing" and "hearing" into "doing." In a broader context, this transformation function results from an entrainment/gating mechanism in which multiple alpha networks (visual-, auditory-, and somatosensory-centered domains), typically producing rhythmic oscillations in a locally independent manner, become coupled and entrained. A global or 'diffuse and distributed alpha system' comes into existence when these independent sources of alpha become coherently engaged in transforming perception to action.

Evaluating the entrainment of the alpha rhythm during stroboscopic flash stimulation by means of coherence analysis

Two major conflicting hypotheses propose that alpha rhythm activity should be either the output of a linear filter having a white noise as input or reflect the output of a nonlinear oscillator. External stimulation can be employed to test for nonlinearity in alpha genesis, since an entrainment of such rhythmic activity (shift in the alpha peak) could only be explained by nonlinear relationships. Flash photic stimulation has been used to investigate such entrainment. Nevertheless, only entrainments due to the second harmonic of the stimulation could be suitably measured. Aiming at overcoming this limitation, a coherence-based technique is proposed for evaluating the strength of responses due to rhythmic stimulation. It was applied to the occipital EEG derivations of 12 normal subjects during stroboscopic stimulation. Entrainment of alpha rhythm by the second harmonic of the stimulation occurred in 75% of the subjects, whilst no spectral shifts were observed for the remained that exhibited broadband alpha peak at rest. However, stimulating with fundamental frequency close to that peak led to entrainment in all subjects. These differences in the degree of synchronization due to stimulation at the first and second harmonics should reflect complex nonlinear mechanisms in alpha genesis.

The physical basis of alpha waves in the electroencephalogram and the origin of the "Berger effect"

Synchronised activity, differing in phase in different populations of neurons, plays an important role in existing theories on the function of brain oscillations (e.g., temporal correlation hypothesis). A prerequisite for this synchronisation is that stimuli are capable of affecting (resetting) the phase of brain oscillations. Such a change in the phase of brain waves is also assumed to underlie the "Berger effect": when observers open their eyes, the amplitude of EEG oscillations in the alpha band (8-13 Hz) decreases significantly. This finding is usually thought to involve a desynchronisation of activity in different neurons. For functional interpretations of brain oscillations in the visual system, it therefore seems to be crucial to find out whether or not the phase of brain oscillations can be affected by visual stimuli. To answer this question, we investigated whether alpha waves are generated by a linear or a nonlinear mechanism. If the mechanism is linear - in contrast to nonlinear ones - phases cannot be reset by a stimulus. It is shown that alpha-wave activity in the EEG comprises both linear and nonlinear components. The generation of alpha waves basically is a linear process and flash-evoked potentials are superimposed on ongoing alpha waves without resetting their phase. One nonlinear component is due to light adaptation, which contributes to the Berger effect. The results call into question theories about brain-wave function based on temporal correlation or event-related desynchronisation.

Detection and description of non-linear interdependence in normal multichannel human EEG data

OBJECTIVES

This study examines human scalp electroencephalographic (EEG) data for evidence of non-linear interdependence between posterior channels. The spectral and phase properties of those epochs of EEG exhibiting non-linear interdependence are studied.

METHODS

Scalp EEG data was collected from 40 healthy subjects. A technique for the detection of non-linear interdependence was applied to 2.048 s segments of posterior bipolar electrode data. Amplitude-adjusted phase-randomized surrogate data was used to statistically determine which EEG epochs exhibited non-linear interdependence.

RESULTS

Statistically significant evidence of non-linear interactions were evident in 2.9% (eyes open) to 4.8% (eyes closed) of the epochs. In the eyes-open recordings, these epochs exhibited a peak in the spectral and cross-spectral density functions at about 10 Hz. Two types of EEG epochs are evident in the eyes-closed recordings; one type exhibits a peak in the spectral density and cross-spectrum at 8 Hz. The other type has increased spectral and cross-spectral power across faster frequencies. Epochs identified as exhibiting non-linear interdependence display a tendency towards phase interdependencies across and between a broad range of frequencies.

CONCLUSIONS

Non-linear interdependence is detectable in a small number of multichannel EEG epochs, and makes a contribution to the alpha rhythm. Non-linear interdependence produces spatially distributed activity that exhibits phase synchronization between oscillations present at different frequencies. The possible physiological significance of these findings are discussed with reference to the dynamical properties of neural systems and the role of synchronous activity in the neocortex.

Coherence between one random and one periodic signal for measuring the strength of responses in the electro-encephalogram during sensory stimulation

Coherence between a pulse train representing periodic stimuli and the EEG has been used in the objective detection of steady-state evoked potentials. This work aimed to quantify the strength of the stimulus responses based on the statistics of coherence estimate between one random and one periodic signal, focusing on the confidence limits and power of significance tests in detecting responses. To detect the responses in 95% of cases, a signal-to-noise ratio of about -7.9 dB was required when using 48 windows (M) in the coherence estimation. The ratio, however, increased to -1.2 dB when M was 12. The results were tested in Monte Carlo simulations and applied to EEGs obtained from 14 subjects during visual stimulation. The method showed differences in the strength of responses at the stimulus frequency and its harmonics, as well as variations between individuals and over cortical regions. In contrast to those from the parietal and temporal regions, results for the occipital region gave confidence limits (with M = 12) that were above zero for all subjects, indicating statistically significant responses. The proposed technique extends the usefulness of coherence as a measure of stimulus responses and allows statistical analysis that could also be applied usefully in a range of other biological signals.

Photic driving in the electroencephalogram of children and adolescents: harmonic structure and relation to the resting state

In order to identify latent bioelectrical oscillators, 15 normal subjects (aged 9-17 years, 8 males, 7 females) were subjected to intermittent photic stimulation. The EEG amplitude spectra corresponding to the 11 fixed frequencies of stimulation presented (3-24 Hz) were combined to form "profiles" of the driving reaction in the right occipital area. The driving response varied with frequency, and was demonstrable in 70-100% of cases (using as criterion peak amplitudes 20% larger than those of the neighbors). The strongest responses were observed at the frequency closest to the alpha peak of the resting EEG. A secondary profile maximum was in the theta band. In 10 subjects, this maximum exceeded half the alpha peak (with an average of 72.4% of the alpha peak), while in the resting spectra, theta amplitudes were much lower than the alpha maxima. This responsiveness in theta activity seems to be characteristic of prepubertal and pubertal subjects. The profiles and resting EEG spectra showed a highly significant Pearson's correlation, with the peak in the theta band of the profiles being the main difference observed between them. The correlation coefficient was significantly correlated with the ratio of the maxima in the theta and alpha bands (R = -0.77, P<0.001). The correlation coefficient between profile and resting spectrum may be a useful indicator in screening methods used to reveal latent cerebral oscillators. Profiles for the second and third harmonics were correlated with those of the first harmonic (fundamental frequency), when considering the corresponding EEG frequencies. Peak frequencies in all three profiles were close to those of the individual's background alpha rhythm, and peak amplitudes in higher harmonics were not much lower than those of the fundamental frequency (mean values of 84 and 63%, for second and third harmonics, respectively).