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

Neural Synchrony and Network Dynamics in Social Interaction: A Hyper-Brain Cell Assembly Hypothesis

Mounting neurophysiological evidence suggests that interpersonal interaction relies on continual communication between cell assemblies within interacting brains and continual adjustments of these neuronal dynamic states between the brains. In this Hypothesis and Theory article, a Hyper-Brain Cell Assembly Hypothesis is suggested on the basis of a conceptual review of neural synchrony and network dynamics and their roles in emerging cell assemblies within the interacting brains. The proposed hypothesis states that such cell assemblies can emerge not only within, but also between the interacting brains. More precisely, the hyper-brain cell assembly encompasses and integrates oscillatory activity within and between brains, and represents a common hyper-brain unit, which has a certain relation to social behavior and interaction. Hyper-brain modules or communities, comprising nodes across two or several brains, are considered as one of the possible representations of the hypothesized hyper-brain cell assemblies, which can also have a multidimensional or multilayer structure. It is concluded that the neuronal dynamics during interpersonal interaction is brain-wide, i.e., it is based on common neuronal activity of several brains or, more generally, of the coupled physiological systems including brains.

Theta-Nested Gamma Oscillations in Next Generation Neural Mass Models

Theta-nested gamma oscillations have been reported in many areas of the brain and are believed to represent a fundamental mechanism to transfer information across spatial and temporal scales. In a series of recent experiments in vitro it has been possible to replicate with an optogenetic theta frequency stimulation several features of cross-frequency coupling (CFC) among theta and gamma rhythms observed in behaving animals. In order to reproduce the main findings of these experiments we have considered a new class of neural mass models able to reproduce exactly the macroscopic dynamics of spiking neural networks. In this framework, we have examined two set-ups able to support collective gamma oscillations: namely, the pyramidal interneuronal network gamma (PING) and the interneuronal network gamma (ING). In both set-ups we observe the emergence of theta-nested gamma oscillations by driving the system with a sinusoidal theta-forcing in proximity of a Hopf bifurcation. These mixed rhythms always display phase amplitude coupling. However, two different types of nested oscillations can be identified: one characterized by a perfect phase locking between theta and gamma rhythms, corresponding to an overall periodic behavior; another one where the locking is imperfect and the dynamics is quasi-periodic or even chaotic. From our analysis it emerges that the locked states are more frequent in the ING set-up. In agreement with the experiments, we find theta-nested gamma oscillations for forcing frequencies in the range [1:10] Hz, whose amplitudes grow proportionally to the forcing intensity and which are clearly modulated by the theta phase. Furthermore, analogously to the experiments, the gamma power and the frequency of the gamma-power peak increase with the forcing amplitude. At variance with experimental findings, the gamma-power peak does not shift to higher frequencies by increasing the theta frequency. This effect can be obtained, in our model, only by incrementing, at the same time, also the stimulation power. An effect achieved by increasing the amplitude either of the noise or of the forcing term proportionally to the theta frequency. On the basis of our analysis both the PING and the ING mechanism give rise to theta-nested gamma oscillations with almost identical features.

Assignment of Empirical Mode Decomposition Components and Its Application to Biomedical Signals

Objectives: Empirical mode decomposition (EMD) is a frequently used signal processing approach which adaptively decomposes a signal into a set of narrow-band components known as intrinsic mode functions (IMFs). For multi-trial, multivariate (multiple simultaneous recordings), and multi-subject analyses the number and signal properties of the IMFs can deviate from each other between trials, channels and subjects. A further processing of IMFs, e.g. a simple ensemble averaging, should determine which IMFs of one signal correspond to IMFs from another signal. When the signal properties have similar characteristics, the IMFs are assigned to each other. This problem is known as correspondence problem.

Methods: From the mathematical point of view, in some cases the correspondence problem can be transformed into an assignment problem which can be solved e.g. by the Kuhn-Munkres algorithm (KMA) by which a minimal cost matching can be found. We use the KMA for solving classic assignment problems, i.e. the pairwise correspondence between two sets of IMFs of equal cardinalities, and for pairwise correspondences between two sets of IMFs with different cardinalities representing an unbalanced assignment problem which is a special case of the k-cardinality assignment problem.

Results: A KMA-based approach to solve the correspondence problem was tested by using simulated, heart rate variability (HRV), and EEG data. The KMA-based results of HRV decomposition are compared with those obtained from a hierarchical cluster analysis (state-of-the-art). The major difference between the two approaches is that there is a more consistent assignment pattern using KMA. Integrating KMA into complex analysis concepts enables a comprehensive exploitation of the key advantages of the EMD. This can be demonstrated by non-linear analysis of HRV-related IMFs and by an EMD-based cross-frequency coupling analysis of the EEG data.

Conclusions: The successful application to HRV and EEG analysis demonstrates that our solutions can be used for automated EMD-based processing concepts for biomedical signals.

Time-frequency Techniques in Biomedical Signal Analysis

Objectives: This review outlines the method -ological fundamentals of the most frequently used non-parametric time-frequency analysis techniques in biomedicine and their main properties, as well as providing decision aids concerning their applications.

Methods: The short-term Fourier transform (STFT), the Gabor transform (GT), the S-transform (ST), the continuous Morlet wavelet transform (CMWT), and the Hilbert transform (HT) are introduced as linear transforms by using a unified concept of the time-frequency representation which is based on a standardized analytic signal. The Wigner-Ville dis -tribution (WVD) serves as an example of the ‘quadratic transforms’ class. The combination of WVD and GT with the matching pursuit (MP) decomposition and that of the HT with the empirical mode decomposition (EMD) are explained; these belong to the class of signal-adaptive approaches.

Results: Similarities between linear transforms are demonstrated and differences with regard to the time-frequency resolution and interference (cross) terms are presented in detail. By means of simulated signals the effects of different time-frequency resolutions of the GT, CMWT, and WVD as well as the resolution-related properties of the inter -ference (cross) terms are shown. The method-inherent drawbacks and their consequences for the application of the time-frequency techniques are demonstrated by instantaneous amplitude, frequency and phase measures and related time-frequency representations (spectrogram, scalogram, time-frequency distribution, phase-locking maps) of measured magnetoencephalographic (MEG) signals.

Conclusions: The appropriate selection of a method and its parameter settings will ensure readability of the time-frequency representations and reliability of results. When the time-frequency characteristics of a signal strongly correspond with the time-frequency resolution of the analysis then a method may be considered ‘optimal’. The MP-based signal-adaptive approaches are preferred as these provide an appropriate time-frequency resolution for all frequencies while simultaneously reducing interference (cross) terms.

Cortical Correlates of Human Balance Control

Balance control is a fundamental component of human every day motor activities such as standing or walking, and its impairment is associated with an increased risk of falling. However, in humans the exact neurobiological mechanisms underlying balance control are still unclear. Specifically, although previous studies have identified a number of cortical regions that become significantly activated during real or imagined balancing, the interactions within and between the relevant cortical regions remain to be investigated. The working hypothesis of this study is that cortical networks contribute to an optimization of balance control, and that this contribution can be revealed by partial directed coherence—a time-variant, frequency-selective and directed functional connectivity analysis tool. Electroencephalographic activity was recorded in 37 subjects during single-leg balancing on a stable as well as an unstable surface. Results of this study show that in the transition from balancing on a stable surface to an unstable surface, two topographically delimitable connectivity networks (weighted directed networks) are established; one associated with the alpha and one with the theta frequency band. The theta network sequence can be described as a set of subnetworks (modules) comprising the frontal, central and parietal cortex with individual temporal and spatial developments within and between those modules. In the alpha network, the occipital electrodes O1 and O2 act as a source, and the interactions propagate predominantly in the directions from occipital to parietal and to centro-parietal areas. These important findings indicate that balance control is supported by at least two functional cortical networks.

Total variation for the analysis of event-related potentials

BACKGROUND

Event-related potential waveforms are often analysed in the time-domain for changes of striking morphological features, like amplitudes or latencies of extrema, at the expense of missing less obvious changes in overall morphology.

NEW METHOD

The measure of total variation can capture a variety of changes in curve morphology. We show analytical examples, and the application to two sets of EEG data (n₁=41, n₂=19) difficult to analyse with more traditional methods.

RESULTS

Total variation can be used to identify the effects of experimental manipulations on event-related potential waveforms, and can additionally be used to identify the respective time windows by means of hierarchical subdivision of longer signals.

COMPARISON WITH EXISTING METHODS

The ANOVA of total variation provided additional insights into effects already hinted at by the ANOVA of global field power in the first experiment, and identified a number of interactions missed by an ANOVA of amplitude as well as a topographic ANOVA in the second one.

CONCLUSIONS

The analysis of total variation can be an interesting complement to more traditional analyses, especially when changes are hard to assess with traditional methods, e.g. in the absence of pronounced extrema, or the presence of noise or large interindividual variations of latency.

Cerebral and neural regulation of cardiovascular activity during mental stress

Background

Mental arithmetic has been verified inducing cerebral and cardiovascular responses. However, the mechanism and sequential responses are still ambiguous. This study aims to reveal the mechanism of cardiovascular and autonomic responses and the related scalp positions that regulate the autonomic nerves system (ANS) during MA task.

Methods

34 healthy male subjects aged between 19 and 27 years old (mean age 23.6 ± 2.3 years) were recruited in. Electrocardiogram, impedance cardiography, beat-to-beat blood pressure and electroencephalography were measured simultaneously and continuously during the experiments. And the analysis of time–frequency, approximate entropy and Pearson correlation coefficient were adopted. For statistical comparison, paired t test is utilized in the study.

Results

The results showed that mental arithmetic task increased heart rate (from 72.35 ± 1.88 to 80.38 ± 2.34), blood pressure (systolic blood pressure: from 112.09 ± 3.23 to 126.79 ± 3.44; diastolic blood pressure: from 74.15 ± 1.93 to 81.20 ± 1.97), and cardiac output (from 8.71 ± 0.30 to 9.68 ± 0.35), and the mental arithmetic induced physiological responses could be divided into two stages, the first stage (10–110 s) and late stage (150–250 s). The high frequency power component (HF) of HRV decreased during MA, but the normalized low frequency power component (nLF) and LF/HF ratio of HRV increased only at the late stage. Moreover, during first stage, the correlations between approximate entropy of electroencephalography at Fp2, Fz, F4, F7 and the corresponding time–frequency results of HF were significant. During the late stage, the correlations between approximate entropy of electroencephalography at Fp2, Fz, C3, C4 and the corresponding nLF was significant.

Conclusions

Our results demonstrated that (1) mental stress induces time-dependent ANS activity and cardiovascular response. (2) Parasympathetic activity is lower during mental arithmetic task, but sympathetic nerve is activated only during late stage of mental arithmetic task. (3) Brain influences the cardiac activity through prefrontal and temporal cortex with the activation of ANS during mental arithmetic.

Misidentifications of specific forms of cross-frequency coupling: three warnings

Cross-frequency coupling (CFC) between neural oscillations has received increased attention over the last decade, as it is believed to underlie a number of cognitive operations in different brain systems. Coupling can take different forms as it associates the phase, frequency, and/or amplitude of coupled oscillations. These specific forms of coupling are a signature for the underlying network physiology and probably relate to distinct cognitive functions. Here I discuss three caveats in data analysis that can lead to mistake one specific form of CFC for another: (1) bicoherence assesses the level of phase-amplitude and not of phase-phase coupling (PPC) as commonly accepted; (2) a test for phase-amplitude coupling (PAC) can indeed signal phase-frequency coupling (PFC) when the higher frequency signal is extracted using a too narrow band; (3) an oscillation whose frequency fluctuates may induce spurious amplitude anticorrelations between neighboring frequency bands. I indicate practical rules to avoid such misidentifications and correctly identify the specific nature of cross-frequency coupled signals.

Cross-frequency coupling in real and virtual brain networks

Information processing in the brain is thought to rely on the convergence and divergence of oscillatory behaviors of widely distributed brain areas. This information flow is captured in its simplest form via the concepts of synchronization and desynchronization and related metrics. More complex forms of information flow are transient synchronizations and multi-frequency behaviors with metrics related to cross-frequency coupling (CFC). It is supposed that CFC plays a crucial role in the organization of large-scale networks and functional integration across large distances. In this study, we describe different CFC measures and test their applicability in simulated and real electroencephalographic (EEG) data obtained during resting state. For these purposes, we derive generic oscillator equations from full brain network models. We systematically model and simulate the various scenarios of CFC under the influence of noise to obtain biologically realistic oscillator dynamics. We find that (i) specific CFC-measures detect correctly in most cases the nature of CFC under noise conditions, (ii) bispectrum (BIS) and bicoherence (BIC) correctly detect the CFCs in simulated data, (iii) empirical resting state EEG show a prominent delta-alpha CFC as identified by specific CFC measures and the more classic BIS and BIC. This coupling was mostly asymmetric (directed) and generally higher in the eyes closed (EC) than in the eyes open (EO) condition. In conjunction, these two sets of measures provide a powerful toolbox to reveal the nature of couplings from experimental data and as such allow inference on the brain state dependent information processing. Methodological advantages of using CFC measures and theoretical significance of delta and alpha interactions during resting and other brain states are discussed.

Time-variant partial directed coherence in analysis of the cardiovascular system. A methodological study

Time-variant partial directed coherence (tvPDC) is used for the first time in a multivariate analysis of heart rate variability (HRV), respiratory movements (RMs) and (systolic) arterial blood pressure. It is shown that respiration-related HRV components which also occur at other frequencies besides the RM frequency (= respiratory sinus arrhythmia, RSA) can be identified. These additional components are known to be an effect of the 'half-the-mean-heart-rate-dilemma' ('cardiac aliasing' CA). These CA components may contaminate the entire frequency range of HRV and can lead to misinterpretation of the RSA analysis. TvPDC analysis of simulated and clinical data (full-term neonates and sedated patients) reveals these contamination effects and, in addition, the respiration-related CA components can be separated from the RSA component and the Traube-Hering-Mayer wave. It can be concluded that tvPDC can be beneficially applied to avoid misinterpretations in HRV analyses as well as to quantify partial correlative interaction properties between RM and RSA.

Assessing directed interactions from neurophysiological signals--an overview

The study of synchronization phenomena in coupled dynamical systems is an active field of research in many scientific disciplines including the neurosciences. Over the last decades, a number of time series analysis techniques have been proposed to capture both linear and nonlinear aspects of interactions. While most of these techniques allow one to quantify the strength of interactions, developments that resulted from advances in nonlinear dynamics and in information and synchronization theory aim at assessing directed interactions. Most of these techniques, however, assume the underlying systems to be at least approximately stationary and require a large number of data points to robustly assess directed interactions. Recent extensions allow assessing directed interactions from short and transient signals and are particularly suited for the analysis of evoked and event-related activity.

A time-variant processing approach for the analysis of alpha and gamma MEG oscillations during flicker stimulus generated entrainment

Repetitive flicker stimulation (photic driving) offers the possibility to study the properties and coupling characteristics of stimulation-sensitive neuronal oscillators by means of the MEG/EEG analysis. With flicker frequencies in the region of the individual alpha band frequency, the dynamics of the entrainment process of the alpha oscillation, as well as the dynamics of the accompanying gamma oscillations and the coupling between the oscillations, are investigated by means of an appropriate combination of time-variant analysis methods. The Hilbert and the Gabor transformation reveal time-variant properties (frequency entrainment, phase locking, and n:m synchronization) of the entrainment process in the whole frequency range. Additionally, time-variant partial directed coherence is applied to identify ocular saccadic interferences and to study the directed information transfer between the recording sites of the simultaneously derived MEG/EEG data during the entrainment. The MEG data is the focus of this methodological study as the entrainment effects of the alpha oscillation are stronger in MEG than in the EEG. The occipital brain region (visual cortex) was mainly investigated and the dynamics of the alpha entrainment quantified. It can be shown that at the beginning of this entrainment, a transient, strongly phase-locked "40-Hz" gamma oscillation occurs.

Time-variant analysis of linear and non-linear phase couplings of and between frequency components of EEG burst patterns in full-term newborns

Time-variant (tv) phase-locking and synchronization characteristics of and between low-frequency (≤ 1.5 Hz) and high-frequency EEG oscillations (≥ 3.5 Hz) of the tracé alternant (TA) pattern in full-term newborns have been quantified to explore the origin of quadratic phase coupling (QPC, as non-linear phase coupling measure) between the frequency ranges 1 - 1.5 Hz ⇔ 3.5 - 4.5 Hz, which characterize the specific interactions of oscillations during the TA's burst activity. Using the Gabor transformation two measures of linear phase coupling, the phase-locking index (PLI) and the n:m phase synchronization index (PSI) have been determined. Phase-locking within the frequency ranges 1 -1.5 Hz and 3.5 - 4.5 Hz, and synchronization between both frequency ranges exists. These phase characteristics are significant 2 sec after burst onset and are associated with the maximum-values of the QPC(1 - 1.5 Hz ⇔ 3.5 - 4.5 Hz) which demonstrates that a specific neuronal coordination between the dynamics of phases and of amplitude-frequency dependencies must be underlying.

Phase synchronisation of the three leg joints in quiet human stance

Quiet human stance is a dynamic multi-segment phenomenon. In literature, coupled ankle and hip actions are in the focus and examinations are usually restricted to frequency contributions below 4 Hz. Very few studies point to the knee playing an active role, and just one study gives evidence of higher frequency contributions. In order to investigate the dynamic coupling of all three leg joints in more depth, we revisited an experimental data set on quiet human stance. Since phase synchronisation is a strong indicator of non-linear coupling behind, we used the phase synchronisation index (PSI) to quantify the degree of leg joint coupling as a function of frequency. One main result is that we did not find any synchronisation between ankle and hip across the whole frequency range examined up to 8 Hz. In contrast, there is significant synchronisation between ankle and knee at a couple of frequencies between 1.25 Hz and 8 Hz when looking at the kinematics. Their joint torques rather synchronise below 2 Hz. There is also synchronisation between knee and hip kinematics above 6 Hz, however, only significant at one frequency bin in our data set. From this, we would infer that the multiple mechanical degrees of freedom contributing to quiet human stance should be chosen according to, thus map, physiology. Thereby, the knee is indispensable and bi-articular muscles play a central role in organising quiet human stance. Examining the non-stationarity of phase synchronisations will probably advance the understanding of self-organisation of quiet human stance.

On the stability of the n:m phase synchronization index

Synchronization analysis of multitrial EEG or (magneto encephalogram) MEG signals is an excellent approach to detect functional connectivity between different neuronal oscillators. In our current research, the n:m phase synchronization index (n:m PSI ) is of special interest. We prove the existence of stable and unstable synchronies dependent upon the analysis frequencies and show that they lie closely together in the frequency domain. Thus, a plot of the time-frequency plane of the n:m PSI automatically violates the sampling theorem and accordingly, the method cannot be considered as a black box. A frequency-tiling approach is presented that can detect robust synchronies while ignoring the unstable ones. The improved synchrony detection is evaluated in numerical experiments on using both simulated and real-life data. It can be demonstrated that the transient synchronization events between MEG oscillations in distant frequency ranges can be detected and that compactly textured EEG synchronization patterns can be reliably characterized.

Coordination of the EEG and the heart rate of preterm neonates during quiet sleep

Aim of this study was to confirm that EEG bursts are associated with heart rate (HR) accelerations, and to investigate the synchronicity between quadratic phase couplings (QPC) courses of the EEG and HR before and during burst activity during quiet sleep in preterm newborns. The time-courses of QPC between frequency components of the EEG ([0.25-1.0 Hz]<-->[4.0-6.0 Hz]) as well as between the Mayer-Traube-Hering (MTH) wave and the frequency component of the HR associated to the respiratory sinus arrhythmia (RSA) ([0.02-0.15 Hz]<-->[0.4-1.5 Hz]) were investigated in five preterm neonates. During quiet sleep, the EEG alternates between burst and interburst activity. The burst onsets were used to trigger an averaging procedure for the EEG, HR, and QPC courses. It can be demonstrated that the envelopes of the EEG rise after the burst onset accompanied by an acceleration of HR before or at the burst maximum. The QPC courses show that the HR's QPC increases before or at the burst onset whereas the increase of the EEG's QPC is delayed. The synchronous changes of EEG and HR as well as of the corresponding QPC courses indicate a coupling between cortical, thalamocortical and neurovegetative brain structures. Such a coupling might be mediated by the MTH waves in the blood pressure.

Coupling of mesoscopic brain oscillations: recent advances in analytical and theoretical perspectives

Oscillatory brain activities have been traditionally studied in the context of how oscillations at a single frequency recorded from a single area could reveal functional insights. Recent advances in methodology used in signal analysis have revealed that cross-frequency coupling, within or between functional related areas, is more informative in determining the possible roles played by brain oscillations. In this review, we begin by describing the cellular basis of oscillatory field potentials and its theorized as well as demonstrated role in brain function. The recent development of mathematical tools that allow the investigation of cross-frequency and cross-area oscillation coupling will be presented and discussed in the context of recent advances in oscillation research based on animal data. Particularly, some pitfalls and caveats of methods currently available are discussed. Data generated from the application of examined techniques are integrated back into the theoretical framework regarding the functional role of brain oscillations. We suggest that the coupling of oscillatory activities at different frequencies between brain regions is crucial for understanding the brain from a functional ensemble perspective. Effort should be directed to elucidate how cross-frequency and area coupling are modulated and controlled. To achieve this, only the correct application of analytical tools may shed light on the intricacies of information representation, generation, binding, encoding, storage and retrieval in the brain.