Higher-order spectrum in understanding nonlinearity in EEG rhythms

Stratified Multivariate Multiscale Dispersion Entropy for Physiological Signal Analysis

Multivariate entropy quantification algorithms are becoming a prominent tool for the extraction of information from multi-channel physiological time-series. However, in the analysis of physiological signals from heterogeneous organ systems, certain channels may overshadow the patterns of others, resulting in information loss. Here, we introduce the framework of Stratified Entropy to prioritize each channels' dynamics based on their allocation to respective strata, leading to a richer description of the multi-channel time-series. As an implementation of the framework, three algorithmic variations of the Stratified Multivariate Multiscale Dispersion Entropy are introduced. These variations and the original algorithm are applied to synthetic time-series, waveform physiological time-series, and derivative physiological data. Based on the synthetic time-series experiments, the variations successfully prioritize channels following their strata allocation while maintaining the low computation time of the original algorithm. In experiments on waveform physiological time-series and derivative physiological data, increased discrimination capacity was noted for multiple strata allocations in the variations when benchmarked to the original algorithm. This suggests improved physiological state monitoring by the variations. Furthermore, our variations can be modified to utilize a priori knowledge for the stratification of channels. Thus, our research provides a novel approach for the extraction of previously inaccessible information from multi-channel time series acquired from heterogeneous systems.

Identification of nonlinear features in cortical and subcortical signals of Parkinson's Disease patients via a novel efficient measure

This study offers a novel and efficient measure based on a higher order version of autocorrelative signal memory that can identify nonlinearities in a single time series. The suggested method was applied to simultaneously recorded subthalamic nucleus (STN) local field potentials (LFP) and magnetoencephalography (MEG) from fourteen Parkinson's Disease (PD) patients who underwent surgery for deep brain stimulation. Recordings were obtained during rest for both OFF and ON dopaminergic medication states. We analyzed the bilateral LFP channels that had the maximum beta power in the OFF state and the cortical sources that had the maximum coherence with the selected LFP channels in the alpha band. Our findings revealed the inherent nonlinearity in the PD data as subcortical high beta (20-30 Hz) band and cortical alpha (8-12 Hz) band activities. While the former was discernible without medication (p=0.015), the latter was induced upon the dopaminergic medication (p<6.10-4). The degree of subthalamic nonlinearity was correlated with contralateral tremor severity (r=0.45, p=0.02). Conversely, for the cortical signals nonlinearity was present for the ON medication state with a peak in the alpha band and correlated with contralateral akinesia and rigidity (r=0.46, p=0.02). This correlation appeared to be independent from that of alpha power and the two measures combined explained 34 % of the variance in contralateral akinesia scores. Our findings suggest that particular frequency bands and brain regions display nonlinear features closely associated with distinct motor symptoms and functions.

Applications of Higher Order Statistics in Electroencephalography Signal Processing: A Comprehensive Survey

Electroencephalography (EEG) is a noninvasive electrophysiological monitoring technique that records the electrical activities of the brain from the scalp using electrodes. EEG is not only an essential tool for diagnosing diseases and disorders affecting the brain, but also helps us to achieve a better understanding of brain's activities and structures. EEG recordings are weak, nonlinear, and nonstationary signals that contain various noise and artifacts. Therefore, for analyzing them, advanced signal processing techniques are required. Second order statistical features are usually sufficient for analyzing most basic signals. However, higher order statistical features possess characteristics that are missing in the second order; characteristics that can be highly beneficial for analysis of more complex signals, such as EEG. The primary goal of this article is to provide a comprehensive survey of the applications of higher order statistics or spectra (HOS) in EEG signal processing. Therefore, we start the survey with a summary of previous studies in EEG analysis followed by a brief mathematical description of HOS. Then, HOS related features and their applications in EEG analysis are presented. These applications are then grouped into three categories, each of which are further explored thoroughly with examples of prior studies. Finally, we provide some specific recommendations based on the literature survey and discuss possible future directions of this field.

Methodological Considerations on the Use of Different Spectral Decomposition Algorithms to Study Hippocampal Rhythms

Local field potential (LFP) oscillations are primarily shaped by the superposition of postsynaptic currents. Hippocampal LFP oscillations in the 25- to 50-Hz range (“slow γ”) are proposed to support memory retrieval independent of other frequencies. However, θ harmonics extend up to 48 Hz, necessitating a study to determine whether these oscillations are fundamentally the same. We compared the spectral analysis methods of wavelet, ensemble empirical-mode decomposition (EEMD), and Fourier transform. EEMD, as previously applied, failed to account for the θ harmonics. Depending on analytical parameters selected, wavelet may convolve over high-order θ harmonics due to the variable time-frequency atoms, creating the appearance of a broad 25- to 50-Hz rhythm. As an illustration of this issue, wavelet and EEMD depicted slow γ in a synthetic dataset that only contained θ and its harmonics. Oscillatory transience cannot explain the difference in approaches as Fourier decomposition identifies ripples triggered to epochs of high-power, 120- to 250-Hz events. When Fourier is applied to high power, 25- to 50-Hz events, only θ harmonics are resolved. This analysis challenges the identification of the slow γ rhythm as a unique fundamental hippocampal oscillation. While there may be instances in which slow γ is present in the rat hippocampus, the analysis presented here shows that unless care is exerted in the application of EEMD and wavelet techniques, the results may be misleading, in this case misrepresenting θ harmonics. Moreover, it is necessary to reconsider the characteristics that define a fundamental hippocampal oscillation as well as theories based on multiple independent γ bands.

Theta-gamma cascades and running speed

Oscillations in the hippocampal local field potential at theta and gamma frequencies are prominent during awake behavior and have demonstrated several behavioral correlates. Both oscillations have been observed to increase in amplitude and frequency as a function of running speed. Previous investigations, however, have examined the relationship between speed and each of these oscillation bands separately. Based on energy cascade models where "…perturbations of slow frequencies cause a cascade of energy dissipation at all frequency scales" (Buzsaki G. Rhythms of the Brain, 2006), we hypothesized that cross-frequency interactions between theta and gamma should increase as a function of speed. We examined these relationships across multiple layers of the CA1 subregion, which correspond to synaptic zones receiving different afferents. Across layers, we found a reliable correlation between the power of theta and the power of gamma, indicative of an amplitude-amplitude relationship. Moreover, there was an increase in the coherence between the power of gamma and the phase of theta, demonstrating increased phase-amplitude coupling with speed. Finally, at higher velocities, phase entrainment between theta and gamma increases. These results have important implications and provide new insights regarding how theta and gamma are integrated for neuronal circuit dynamics, with coupling strength determined by the excitatory drive within the hippocampus. Specifically, rather than arguing that different frequencies can be attributed to different psychological processes, we contend that cognitive processes occur across multiple frequency bands simultaneously with organization occurring as a function of the amount of energy iteratively propagated through the brain. NEW & NOTEWORTHY Often, the theta and gamma oscillations in the hippocampus have been believed to be a consequence of two marginally overlapping phenomena. This perspective, however, runs counter to an alternative hypothesis in which a slow-frequency, high-amplitude oscillation provides energy that cascades into higher frequency, lower amplitude oscillations. We found that as running speed increases, all measures of cross-frequency theta-gamma coupling intensify, providing evidence in favor of the energy cascade hypothesis.

Online Epileptic Seizure Prediction Using Wavelet-Based Bi-Phase Correlation of Electrical Signals Tomography

Considerable efforts have been made in order to predict seizures. Among these methods, the ones that quantify synchronization between brain areas, are the most important methods. However, to date, a practically acceptable result has not been reported. In this paper, we use a synchronization measurement method that is derived according to the ability of bi-spectrum in determining the nonlinear properties of a system. In this method, first, temporal variation of the bi-spectrum of different channels of electro cardiography (ECoG) signals are obtained via an extended wavelet-based time-frequency analysis method; then, to compare different channels, the bi-phase correlation measure is introduced. Since, in this way, the temporal variation of the amount of nonlinear coupling between brain regions, which have not been considered yet, are taken into account, results are more reliable than the conventional phase-synchronization measures. It is shown that, for 21 patients of FSPEEG database, bi-phase correlation can discriminate the pre-ictal and ictal states, with very low false positive rates (FPRs) (average: 0.078/h) and high sensitivity (100%). However, the proposed seizure predictor still cannot significantly overcome the random predictor for all patients.

Hypovigilance detection for UCAV operators based on a hidden Markov model

With the advance of military technology, the number of unmanned combat aerial vehicles (UCAVs) has rapidly increased. However, it has been reported that the accident rate of UCAVs is much higher than that of manned combat aerial vehicles. One of the main reasons for the high accident rate of UCAVs is the hypovigilance problem which refers to the decrease in vigilance levels of UCAV operators while maneuvering. In this paper, we propose hypovigilance detection models for UCAV operators based on EEG signal to minimize the number of occurrences of hypovigilance. To enable detection, we have applied hidden Markov models (HMMs), two of which are used to indicate the operators' dual states, normal vigilance and hypovigilance, and, for each operator, the HMMs are trained as a detection model. To evaluate the efficacy and effectiveness of the proposed models, we conducted two experiments on the real-world data obtained by using EEG-signal acquisition devices, and they yielded satisfactory results. By utilizing the proposed detection models, the problem of hypovigilance of UCAV operators and the problem of high accident rate of UCAVs can be addressed.

Experimental observation of a theoretically predicted nonlinear sleep spindle harmonic in human EEG

OBJECTIVE

To investigate the properties of a sleep spindle harmonic oscillation previously predicted by a theoretical neural field model of the brain.

METHODS

Spindle oscillations were extracted from EEG data from nine subjects using an automated algorithm. The power and frequency of the spindle oscillation and the harmonic oscillation were compared across subjects. The bicoherence of the EEG was calculated to identify nonlinear coupling.

RESULTS

All subjects displayed a spindle harmonic at almost exactly twice the frequency of the spindle. The power of the harmonic scaled nonlinearly with that of the spindle peak, consistent with model predictions. Bicoherence was observed at the spindle frequency, confirming the nonlinear origin of the harmonic oscillation.

CONCLUSIONS

The properties of the sleep spindle harmonic were consistent with the theoretical modeling of the sleep spindle harmonic as a nonlinear phenomenon.

SIGNIFICANCE

Most models of sleep spindle generation are unable to produce a spindle harmonic oscillation, so the observation and theoretical explanation of the harmonic is a significant step in understanding the mechanisms of sleep spindle generation. Unlike seizures, sleep spindles produce nonlinear effects that can be observed in healthy controls, and unlike the alpha oscillation, there is no linearly generated harmonic that can obscure nonlinear effects. This makes the spindle harmonic a good candidate for future investigation of nonlinearity in the brain.

Continuous EEG-based dynamic markers for sleep depth and phasic events

Sleep architecture is characterized by classifying polysomnographic epochs into mutually exclusive stages. Notwithstanding the clinical importance of staging, it has the drawback of representing sleep as a discrete process. Metrics based on the electroencephalogram (EEG) are needed to supplement conventional sleep staging by allowing a description of sleep in terms of unitary, continuous markers. Traditional linear and nonlinear techniques for achieving this goal have not proved sufficient. Employing recurrence analysis, we developed a method for capturing and quantifying the dynamical states of the brain during sleep. The method yields markers for continuously determining sleep depth, for detecting sleep-specific phasic events, and for objectively defining potentially useful sleep markers and indices. Recurrence markers captured the coarse- and fine-grained temporal activity of the sleep EEG, thereby permitting continuous quantitation of brain electrical activity on any desired time scale. The markers were validated with respect to the tonic behavior (time scale of seconds) of the sleep EEG by establishing that they disambiguated the stages of sleep that are defined solely on the basis of EEG activity. Validation of the markers over time scales of milliseconds was achieved by showing that common types of sleep-EEG phasic events could be detected by recurrence analysis. The method was also used to define a generalized EEG arousal index that quantified previously unrecognized sleep-stage-dependent deterministic properties of brain electrical activity. Using nonlinear analysis that quantified the recurrence properties of the EEG, we described a novel method for producing dynamic markers of brain states during sleep.