Canonical bicoherence analysis of dynamic EEG data

Bicoherence has been used in quantifying quadratic phase coupling (QPC) in electroencephalography (EEG) signals. However, for high-dimensional EEG signals, the calculations of traditional auto– and cross–bicoherences of signals from multiple electrodes are computationally very expensive. This has been compounded by the recognition of the non-stationary character of EEG signals. This paper introduces a new approach, the time-varying canonical bicoherence (CBC) by short-time weighted Fourier transforms, for analyzing QPC nonlinearities of dynamic EEG signals. This new method shows both computational efficiency and simple interpretation of estimated canonical bicoherences. The canonical bicoherence analysis of EEG records, during a human visual stimulus-driven cognitive process, put into evidence of quadratic phase couplings of Beta waves and Delta waves in the frontal regions.     

Spreading of epileptic afterdischarges between entorhinal cortex and hippocampus in acute experiments and the kindling model of epilepsy in the rat--comparing different methods of analysis

Spreading of epileptiform activity in the central nervous system is one of the fundamental problems in epileptology. The patterns of spreading of after-discharges in the hippocampus and entorphinal cortex were studied in acute experiments and using the kindling model of epileptogenesis. Three methods were used to determine the time relations between EEG signals from different brain areas; visual inspections, average amount of mutual information (AAMI) and phase spectrum method. The analysis methods used are adequate for quantification of the degree of coupling between different EEG signals during an afterdischarge, but should be used jointly since different signal features are taken into consideration by different methods. During an afterdischarge only at the beginning the focal area is clearly leading the other brain areas; thereafter the pattern becomes more complex.     

Peak and averaged bicoherence for different EEG patterns during general anaesthesia

Background  

Changes in nonlinear neuronal mechanisms of EEG generation in the course of general anaesthesia have been extensively investigated in research literature. A number of EEG signal properties capable of tracking these changes have been reported and employed in anaesthetic depth monitors. The degree of phase coupling between different spectral components is a marker of nonlinear EEG generators and is claimed to be an important aspect of BIS. While bicoherence is the most direct measure of phase coupling, according to published research it is not directly used in the calculation of BIS, and only limited studies of its association with anaesthetic depth and level of consciousness have been published. This paper investigates bicoherence parameters across equal band and unequal band bifrequency regions, during different states of anaesthetic depth relating to routine clinical anaesthesia, as determined by visual inspection of EEG.     

Quantification of transient quadratic phase couplings within EEG burst patterns in sedated patients during electroencephalic burst-suppression period

The time dynamics of the quadratic phase coupling within burst patterns during electroencephalic burst-suppression has been quantified. It can be shown that a transient quadratic phase coupling (QPC) exists between the frequency ranges 0 to 2.5 and 3 to 7.5 Hz and between the frequency ranges 0 to 2.5 and 8 to 12 Hz. The QPC can be explained by an amplitude modulation, where the slow rhythm modulates the rhythmic activities with a higher frequency. By means of time-variant bicoherence analysis, a strong phase-locking between the modulating and the modulated component can be identified. The phase-locking is demonstrable within the first 250 ms after the burst onset and comes up to the maximum between 750 and 1250 ms. The effect is maintained over the whole first part of the burst (2 s) with a decreasing tendency after 1250 ms. All these effects cannot be found in the EEG before entering the burst suppression period (BSP). The transient coupling phenomena in the EEG bursts during BSP can be regarded as indicators for short-term interrelations between the underlying electrophysiologic processes.     

Coupled oscillators for modeling and analysis of EEG/MEG oscillations.

This study presents three EEG/MEG applications in which the modeling of oscillatory signal components offers complementary analysis and an improved explanation of the underlying generator structures. Coupled oscillator networks were used for modeling. Parameters of the corresponding ordinary coupled differential equation (ODE) system are identified using EEG/MEG data and the resulting solution yields the modeled signals. This model-related analysis strategy provides information about the coupling quantity and quality between signal components (example 1, neonatal EEG during quiet sleep), allows identification of the possible contribution of hidden generator structures (example 2, 600-Hz MEG oscillations in somatosensory evoked magnetic fields), and can explain complex signal characteristics such as amplitude-frequency coupling and frequency entrainment (example 3, EEG burst patterns in sedated patients).     

Analysis and modeling of time-variant amplitude–frequency couplings of and between oscillations of EEG bursts

Low-frequency (0.5-2.5 Hz) and individually defined high-frequency (7-11 or 8-12 Hz; 11-15 or 14-18 Hz) oscillatory components of the electroencephalogram (EEG) burst activity derived from thiopental-induced burst-suppression patterns (BSP) were investigated in seven sedated patients (17-26 years old) with severe head injury. The predominant high-frequency burst oscillations (>7 Hz) were detected for each patient by means of time-variant amplitude spectrum analysis. Thereafter, the instantaneous envelope (IE) and the instantaneous frequency (IF) were computed for these low- and high-frequency bands to quantify amplitude-frequency dependencies (envelope-envelope, envelope-frequency, and frequency-frequency correlations). Time-variant phase-locking, phase synchronization, and quadratic phase couplings are associated with the observed amplitude-frequency characteristics. Additionally, these time-variant analyses were carried out for modeled burst patterns. Coupled Duffing oscillators were adapted to each EEG burst and by means of these models data-based burst simulations were generated. Results are: (1) strong envelope-envelope correlations (IE courses) can be demonstrated; (2) it can be shown that a rise of the IE is associated with an increase of the IF (only for the frequency bands 0.5-2.5 and 7-11 or 8-12 Hz); (3) the rise characteristics of all individually averaged envelope-frequency courses (IE-IF) are strongly correlated; (4) for the 7-11 or 8-12 Hz oscillation these associations are weaker and the variation between the time courses of the patients is higher; (5) for both frequency ranges a quantitative amplitude-frequency dependency can be shown because higher IE peak maxima are accompanied by stronger IF changes; (6) the time range of significant phase-locking within the 7-11 or 8-12 Hz frequency bands and of the strongest quadratic phase couplings (between 0.5-2.5 and 7-11 or 8-12 Hz) is between 0 and 1,000 ms; (7) all phase coupling characteristics of the modeled bursts accord well with the corresponding characteristics of the measured EEG burst data. All amplitude-frequency dependencies and phase locking/coupling properties described here are known from and can be discussed using coupled Duffing oscillators which are characterized by autoresonance properties.     

Coupling between Intrinsic Prefrontal HbO2 and Central EEG Beta Power Oscillations in the Resting Brain

There is increasing interest in the intrinsic activity in the resting brain, especially that of ultraslow and slow oscillations. Using near-infrared spectroscopy (NIRS), electroencephalography (EEG), blood pressure (BP), respiration and heart rate recordings during 5 minutes of rest, combined with cross spectral and sliding cross correlation calculations, we identified a short-lasting coupling (duration [Formula: see text] s) between prefrontal oxyhemoglobin (HbO2) in the frequency band between 0.07 and 0.13 Hz and central EEG alpha and/or beta power oscillations in 8 of the 9 subjects investigated. The HbO2 peaks preceded the EEG band power peaks by 3.7 s in 6 subjects, with moderate or no coupling between BP and HbO2 oscillations. HbO2 and EEG band power oscillations were approximately in phase with BP oscillations in the 2 subjects with an extremely high coupling (squared coherence [Formula: see text]) between BP and HbO2 oscillation. No coupling was identified in one subject. These results indicate that slow precentral (de)oxyhemoglobin concentration oscillations during awake rest can be temporarily coupled with EEG fluctuations in sensorimotor areas and modulate the excitability level in the brains' motor areas, respectively. Therefore, this provides support for the idea that resting state networks fluctuate with frequencies of between 0.01 and 0.1 Hz (Mantini et.al. PNAS 2007).     

Bispectral analysis does not differentiate between anaesthesia EEG and a linear random process]

Bispectral analysis of the electroencephalogram (EEG) has been used to monitor depth of anaesthesia. In the majority of publications this has involved the use of the so called BIS-Index TM (Aspect Medical Systems, Inc.). The exact relationship of this index to such bispectral parameters as the bispectrum and bicoherence has not yet been reported. If the EEG is considered as a linear random process, bicoherence is trivial, i.e. it is independent of the EEG frequency. The aim of this study was to determine the proportion of EEG epochs with non-trivial bicoherence during isoflurane/N20 anaesthesia. We reanalyzed 25.5 hours of digitalised EEG signal from 9 patients undergoing gynaecological surgery. The test developed by Hinich for Gaussian distribution and linearity was then applied. The test was validated using various synthetic surrogate data: Gaussian random data, the z-component of the Lorenz attractor, the phase randomized EEG and the phase randomized z-component of the Lorenz attractor. The percentage of epochs (8.192 s, 1024 data points) with non-trivial bicoherence was: Lorenz data 95.4%, phase randomized Lorenz data 9.4%, synthetic Gaussian data 14.8%, original EEG 9.1%, phase randomized EEG 5.1%. The original EEG data were not found to contain a higher percentage of epochs with non-trivial bicoherence than the phase randomized data and the synthetic Gaussian data. We conclude that bispectral analysis does not substantially add to the information obtained with other methods of quantitative EEG analysis.     

Reduction theories elucidate the origins of complex biological rhythms generated by interacting delay-induced oscillations

Time delay is known to induce sustained oscillations in many biological systems such as electroencephalogram (EEG) activities and gene regulations. Furthermore, interactions among delay-induced oscillations can generate complex collective rhythms, which play important functional roles. However, due to their intrinsic infinite dimensionality, theoretical analysis of interacting delay-induced oscillations has been limited. Here, we show that the two primary methods for finite-dimensional limit cycles, namely, the center manifold reduction in the vicinity of the Hopf bifurcation and the phase reduction for weak interactions, can successfully be applied to interacting infinite-dimensional delay-induced oscillations. We systematically derive the complex Ginzburg-Landau equation and the phase equation without delay for general interaction networks. Based on the reduced low-dimensional equations, we demonstrate that diffusive (linearly attractive) coupling between a pair of delay-induced oscillations can exhibit nontrivial amplitude death and multimodal phase locking. Our analysis provides unique insights into experimentally observed EEG activities such as sudden transitions among different phase-locked states and occurrence of epileptic seizures.     

Measuring the directionality of coupling: phase versus state space dynamics and application to EEG time series

Measuring the directionality of coupling between dynamical systems is one of the challenging problems in nonlinear time series analysis. We investigate the relative merit of two approaches to assess directionality, one based on phase dynamics modeling and one based on state space topography. We analyze unidirectionally coupled model systems to investigate the ability of the two approaches to detect driver-responder relationships and discuss certain problems and pitfalls. In addition we apply both approaches to the intracranial electroencephalogram (EEG) recorded from one epilepsy patient during the seizure-free interval to demonstrate the general suitability of directionality measures to reflect the pathological interaction of the epileptic focus with other brain areas.     

Automatic classification of EEG segments and extraction of representative ones by dynamic clusters method

Use of the dynamic clusters method for automatic extraction of compressed information about recorded EEG signal is presented. The computer first divides the record into quasi-stationary segments by means of adaptive segmentation. Second, the extracted segments are classified by a method of dynamic clusters into homogeneous classes. One part of the used clustering algorithm permits to specify and draw the most typical class members, which may represent the whole studied EEG signal and may be used as input for the further phase of the automatic EEG analysis, i.e. for the classification of the whole EEG records. The above procedure was applied to a 75 sec long EEG record of anaesthetized cat intoxicated by CO.     

Deterministic chaos and the first positive Lyapunov exponent: a nonlinear analysis of the human electroencephalogram during sleep

Under selected conditions, nonlinear dynamical systems, which can be described by deterministic models, are able to generate so-called deterministic chaos. In this case the dynamics show a sensitive dependence on initial conditions, which means that different states of a system, being arbitrarily close initially, will become macroscopically separated for sufficiently long times. In this sense, the unpredictability of the EEG might be a basic phenomenon of its chaotic character. Recent investigations of the dimensionality of EEG attractors in phase space have led to the assumption that the EEG can be regarded as a deterministic process which should not be mistaken for simple noise. The calculation of dimensionality estimates the degrees of freedom of a signal. Nevertheless, it is difficult to decide from this kind of analysis whether a process is quasiperiodic or chaotic. Therefore, we performed a new analysis by calculating the first positive Lyapunov exponent L ₁ from sleep EEG data. Lyapunov exponents measure the mean exponential expansion or contraction of a flow in phase space. L ₁ is zero for periodic as well as quasiperiodic processes, but positive in the case of chaotic processes expressing the sensitive dependence on initial conditions. We calculated L ₁ for sleep EEG segments of 15 healthy men corresponding to the sleep stages I, II, III, IV, and REM (according to Rechtschaffen and Kales). Our investigations support the assumption that EEG signals are neither quasiperiodic waves nor a simple noise. Moreover, we found statistically significant differences between the values of L ₁ for different sleep stages. All together, this kind of analysis yields a useful extension of the characterization of EEG signals in terms of nonlinear dynamical system theory.     

A Computational Predictor of Human Episodic Memory Based on a Theta Phase Precession Network

In the rodent hippocampus, a phase precession phenomena of place cell firing with the local field potential (LFP) theta is called “theta phase precession” and is considered to contribute to memory formation with spike time dependent plasticity (STDP). On the other hand, in the primate hippocampus, the existence of theta phase precession is unclear. Our computational studies have demonstrated that theta phase precession dynamics could contribute to primate–hippocampal dependent memory formation, such as object–place association memory. In this paper, we evaluate human theta phase precession by using a theory–experiment combined analysis. Human memory recall of object–place associations was analyzed by an individual hippocampal network simulated by theta phase precession dynamics of human eye movement and EEG data during memory encoding. It was found that the computational recall of the resultant network is significantly correlated with human memory recall performance, while other computational predictors without theta phase precession are not significantly correlated with subsequent memory recall. Moreover the correlation is larger than the correlation between human recall and traditional experimental predictors. These results indicate that theta phase precession dynamics are necessary for the better prediction of human recall performance with eye movement and EEG data. In this analysis, theta phase precession dynamics appear useful for the extraction of memory-dependent components from the spatio–temporal pattern of eye movement and EEG data as an associative network. Theta phase precession may be a common neural dynamic between rodents and humans for the formation of environmental memories.     

Shifted Coupling of EEG Driving Frequencies and fMRI Resting State Networks in Schizophrenia Spectrum Disorders

Introduction

The cerebral resting state in schizophrenia is altered, as has been demonstrated separately by electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) resting state networks (RSNs). Previous simultaneous EEG/fMRI findings in healthy controls suggest that a consistent spatiotemporal coupling between neural oscillations (EEG frequency correlates) and RSN activity is necessary to organize cognitive processes optimally. We hypothesized that this coupling is disorganized in schizophrenia and related psychotic disorders, in particular regarding higher cognitive RSNs such as the default-mode (DMN) and left-working-memory network (LWMN).

Methods

Resting state was investigated in eleven patients with a schizophrenia spectrum disorder (n = 11) and matched healthy controls (n = 11) using simultaneous EEG/fMRI. The temporal association of each RSN to topographic spectral changes in the EEG was assessed by creating Covariance Maps. Group differences within, and group similarities across frequencies were estimated for the Covariance Maps.

Results

The coupling of EEG frequency bands to the DMN and the LWMN respectively, displayed significant similarities that were shifted towards lower EEG frequencies in patients compared to healthy controls.

Conclusions

By combining EEG and fMRI, each measuring different properties of the same pathophysiology, an aberrant relationship between EEG frequencies and altered RSNs was observed in patients. RSNs of patients were related to lower EEG frequencies, indicating functional alterations of the spatiotemporal coupling.

Significance

The finding of a deviant and shifted coupling between RSNs and related EEG frequencies in patients with a schizophrenia spectrum disorder is significant, as it might indicate how failures in the processing of internal and external stimuli, as commonly seen during this symptomatology (i.e. thought disorders, hallucinations), arise.     

Fronto-Central Theta Oscillations Are Related to Oscillations in Saccadic Response Times (SRT): An EEG and Behavioral Data Analysis

The phase reset hypothesis states that the phase of an ongoing neural oscillation, reflecting periodic fluctuations in neural activity between states of high and low excitability, can be shifted by the occurrence of a sensory stimulus so that the phase value become highly constant across trials (Schroeder et al., 2008). From EEG/MEG studies it has been hypothesized that coupled oscillatory activity in primary sensory cortices regulates multi sensory processing (Senkowski et al. 2008). We follow up on a study in which evidence of phase reset was found using a purely behavioral paradigm by including also EEG measures. In this paradigm, presentation of an auditory accessory stimulus was followed by a visual target with a stimulus-onset asynchrony (SOA) across a range from 0 to 404 ms in steps of 4 ms. This fine-grained stimulus presentation allowed us to do a spectral analysis on the mean SRT as a function of the SOA, which revealed distinct peak spectral components within a frequency range of 6 to 11 Hz with a modus of 7 Hz. The EEG analysis showed that the auditory stimulus caused a phase reset in 7-Hz brain oscillations in a widespread set of channels. Moreover, there was a significant difference in the average phase at which the visual target stimulus appeared between slow and fast SRT trials. This effect was evident in three different analyses, and occurred primarily in frontal and central electrodes.     

Multivariate and multiorgan analysis of cardiorespiratory variability signals: the CAP sleep case.

Signals from different systems are analyzed during sleep on a beat-to-beat basis to provide a quantitative measure of synchronization with the heart rate variability (HRV) signal, oscillations of which reflect the action of the autonomic nervous system. Beat-to-beat variability signals synchronized to QRS occurrence on ECG signals were extracted from respiration, electroencephalogram (EEG) and electromyogram (EMG) traces. The analysis was restricted to sleep stage 2. Cyclic alternating pattern (CAP) periods were detected from EEG signals and the following conditions were identified: stage 2 non-CAP (2 NCAP), stage 2 CAP (2 CAP) and stage 2 CAP with myoclonus (2 CAP MC). The coupling relationships between pairs of variability signals were studied in both the time and frequency domains. Passing from 2 NCAP to 2 CAP, sympathetic activation is indicated by tachycardia and reduced respiratory arrhythmia in the heart rate signal. At the same time, we observed a marked link between EEG and HRV at the CAP frequency. During 2 CAP MC, the increased synchronization involved myoclonus and respiration. The underlying mechanism seems to be related to a global control system at the central level that involves the different systems.     

Alteration of phase–phase coupling between theta and gamma rhythms in a depression-model of rats

Alterations in oscillatory brain activity are strongly correlated with cognitive performance in various physiological rhythms, especially the theta and gamma rhythms. In this study, we investigated the coupling relationship of neural activities between thalamus and medial prefrontal cortex (mPFC) by measuring the phase interactions between theta and gamma oscillations in a depression model of rats. The phase synchronization analysis showed that the phase locking at theta rhythm was weakened in depression. Furthermore, theta-gamma phase locking at n:m (1:6) ratio was found between thalamus and mPFC, while it was diminished in depression state. In addition, the analysis of coupling direction based on phase dynamics showed that the unidirectional influence from thalamus to mPFC was diminished in depression state only in theta rhythm, while it was partly recovered after the memantine treatment in a depression model of rats. The results suggest that the effects of depression on cognitive deficits are modulated via profound alterations in phase information transformation of theta rhythm and theta-gamma phase coupling.     

Functional interactions in hierarchically organized neural networks studied with spatiotemporal firing patterns and phase-coupling frequencies

A scalable hardware/software hybrid module--called Ubidule--endowed with bio-inspired ontogenetic and epigenetic features is configured to run a neural networks simulation with developmental and evolvable capabilities. We simulated the activity of hierarchically organized spiking neural networks characterized by an initial developmental phase featuring cell death followed by spike timing dependent synaptic plasticity in presence of background noise. An upstream 'sensory' network received a spatiotemporally organized external input and downstream networks were activated only via the upstream network. Precise firing sequences, formed by recurrent patterns of spikes intervals above chance levels, were observed in all recording conditions, thus suggesting the build-up of a connectivity able to sustain temporal information processing. The activity of a Ubinet--a network of Ubidules--is analyzed by means of virtual electrodes that recorded neural signals similar to EEG. The analysis of these signals was compared with a small set of human recordings and revealed common patterns of shift in quadratic phase coupling. The results suggest some interpretations of changes and plasticity of functional interactions between cortical areas driven by external stimuli and by learning/cognitive     

EEG--indicator of impairment and recovery of the dendrite structure in the plexiform layer of the cerebral cortex

The connection between EEG spectrum and structural changes of plexiform layer apical dendrites was revealed during the period of recovery from the deep anesthesia. On the initial phase of recovery when the multiply varicose dendritic enlargements are present, an additional peak in EEG spectrum emerged in a delta-band under weak DC action (10 microA); on the late phase of recovery when the structure of the plexiform layer apical dendrites became normal the peak in EEG spectrum under weak DC action emerged in a tetha-band. Thus, by the absence or appearance of the tetha-rhythm in the cerebral cortex in the response to it direct stimulation we can evaluate the morphological condition of the Plexiform layer apical dendrites.     

Transmission of stimulus-locked responses in two oscillators with bistable coupling

Numerous electroencephalography (EEG) and magnetoencephalography (MEG) studies aim at identifying the chronological order of activation of brain areas. This paper demonstrates that the timing sequence obtained with the gold standard for EEG/MEG analysis (averaging across trials) may not correlate at all with the actual transmission of a stimulus effect within a pathway formed by connected brain areas. This is shown by studying transmission of stimulus-locked responses in a model that shares basic features with stimulated neuronal rhythms: in two phase oscillators with bistable coupling and noise one oscillator is stimulated. The model presents a mechanism that causes a response clustering, i.e., a switching between two different responses across trials, without extinction of the averaged response (calculated over all trials). Transmission times are calculated for all trials as well as for the two clusters separately with standard averaged responses and with a stochastic phase resetting analysis. The stochastic phase resetting analysis provides reliable estimates of the transmission time. In contrast, transmission times calculated by averaging across trials correspond to the phase difference in the different stable synchronized states (when calculated for the two clusters separately) or their weighted superposition (when calculated over all trials). The standard method does not detect the time elapsing during the transmission of the stimulus action. The results presented here call into question many findings reported in the evoked response literature.