Wavelet Bicoherence Research Articles

Effect of sleep-disordered breathing on stable electroencephalographic characteristics during night sleep in patients with arterial hypertension

Introduction. Obstructive sleep apnea (OSA) is the most common sleep-disordered breathing condition. A significant number of OSA patients often present with cardiovascular comorbidities, particularly arterial hypertension. OSA is associated with changes in bioelectrical activity of the brain, such as slowing of electroencephalographic activity in the cortex and reduced interhemispheric synchronization. These changes can become pathophysiological markers of sleep-disordered breathing.Aim. To investigate the effect of sleep-disordered breathing on a range of quantitative electroencephalogram (EEG) characteristics during nighttime sleep in patients with arterial hypertension and clinically significant OSA.Materials and methods. The material for this retrospective study consisted of 84 polysomnographic records of patients predominantly diagnosed with arterial hypertension. Patients were divided into three groups based on the apneahypopnea index (AHI). Polysomnographic records were used to assess the synchronization measure of brain electrical activity between occipital EEG leads. The synchronization measure was evaluated using a method based on wavelet bicoherence calculation.Results. Statistically significant differences were observed in the low-frequency ranges Δf1-Δf4: 0.2-1.0 Hz, 0.8-1.6 Hz, 1.0-2.0 Hz, 1.0-4.0 Hz. In these frequencies, the interhemispheric synchronization measure significantly decreased with increasing severity of apnea.Conclusion. To determine the severity of obstructive sleep apnea, a parameter based on the synchronization measure evaluated from symmetrical occipital EEG signals in the frequency ranges 0.2-1.0 Hz, 0.8-1.6 Hz, 1.0-2.0 Hz, and 1.0-4.0 Hz can be considered. This may serve as the basis for developing and implementing new diagnostic tools for assessing the severity of sleep-disordered breathing in practice.

Compensatory mechanisms of reduced interhemispheric EEG connectivity during sleep in patients with apnea

We performed a mathematical analysis of functional connectivity in electroencephalography (EEG) of patients with obstructive sleep apnea (OSA) (N = 10; age: 52.8 ± 13 years; median age: 49 years; male/female ratio: 7/3), compared with a group of apparently healthy participants (N = 15; age: 51.5 ± 29.5 years; median age: 42 years; male/female ratio: 8/7), based on the calculation of wavelet bicoherence from nighttime polysomnograms. Having observed the previously known phenomenon of interhemispheric synchronization deterioration, we demonstrated a compensatory increase in intrahemispheric connectivity, as well as a slight increase in the connectivity of the central and occipital areas for high-frequency EEG activity. Significant changes in functional connectivity were extremely stable in groups of apparently healthy participants and OSA patients, maintaining the overall pattern when comparing different recording nights and various sleep stages. The maximum variability of the connectivity was observed at fast oscillatory processes during REM sleep. The possibility of observing some changes in functional connectivity of brain activity in OSA patients in a state of passive wakefulness opens up prospects for further research. Developing the methods of hypnogram evaluation that are independent of functional connectivity may be useful for implementing a medical decision support system.

Intracortical synchronization pattern on the preclinical and clinical stages of absence epilepsy (analysis of wavelet bicoherence in WAG/Rij rats)

Intracortical synchronization pattern on the preclinical and clinical stages of absence epilepsy (analysis of wavelet bicoherence in WAG/Rij rats)

Continuous Wavelet Analysis of Matter Clustering Using the Gaussian-derived Wavelet

Continuous wavelet analysis has been increasingly employed in various fields of science and engineering due to its remarkable ability to maintain optimal resolution in both space and scale. Here, we introduce wavelet-based statistics, including the wavelet power spectrum, wavelet cross correlation, and wavelet bicoherence, to analyze the large-scale clustering of matter. For this purpose, we perform wavelet transforms on the density distribution obtained from the one-dimensional Zel’dovich approximation and then measure the wavelet power spectra and wavelet bicoherences of this density distribution. Our results suggest that the wavelet power spectrum and wavelet bicoherence can identify the effects of local environments on the clustering at different scales. Moreover, we apply the statistics based on the three-dimensional isotropic wavelet to the IllustrisTNG simulation at z = 0, and investigate the environmental dependence of the matter clustering. We find that the clustering strength of the total matter increases with increasing local density except on the largest scales. Besides, we notice that the gas traces dark matter better than stars on large scales in all environments. On small scales, the cross correlation between the dark matter and gas first decreases and then increases with increasing density. This is related to the impacts of the active galactic nucleus feedback on the matter distribution, which also varies with the density environment in a similar trend to the cross correlation between dark matter and gas. Our findings are qualitatively consistent with previous studies on matter clustering.

Change in brain electrical activity connectivity in migraine patients without aura

Objective: In this study, we consider how the structure of the brain EEG activity changes in patients with migraine, compared with virtually healthy volunteers without complaints of acute or chronic headache. Materials and Methods. The study of the connectivity of EEG activity was carried out on the basis of an objective assessment of pairwise synchronization between different recording channels, for which we used a method based on wavelet bicoherence. Results. Within the framework of the performed experimental study, we demonstrated an increased reactivity in the structure of connections in brain electrical activity of the patients experiencing a weak visual impact. Conclusion. A prospective study could determine the value of the described diagnostic procedure in support of the clinical decision on appropriate pharmacological and non-pharmacological prophylactic measures.

Novel Instantaneous Wavelet Bicoherence for Vibration Fault Detection in Gear Systems

Higher order spectra exhibit a powerful detection capability of low-energy fault-related signal components, buried in background random noise. This paper investigates the powerful nonlinear non-stationary instantaneous wavelet bicoherence for local gear fault detection. The new methodology of selecting frequency bands that are relevant for wavelet bicoherence fault detection is proposed and investigated. The capabilities of wavelet bicoherence are proven for early-stage fault detection in a gear pinion, in which natural pitting has developed in multiple pinion teeth in the course of endurance gearbox tests. The results of the WB-based fault detection are compared with a stereo optical fault evaluation. The reliability of WB-based fault detection is quantified based on the complete probability of correct identification. This paper is the first attempt to investigate instantaneous wavelet bicoherence technology for the detection of multiple natural early-stage local gear faults, based on comprehensive statistical evaluation of the industrially relevant detection effectiveness estimate—the complete probability of correct fault detection.

Age-dependent cross frequency coupling features from children to adults during general anesthesia

BackgroundThe frequency coupling characteristics in electroencephalogram (EEG) induced by anesthetics have been well studied in adults, but the investigation of the age-dependent cross frequency coupling features from children to adults is still lacking. MethodsWe analyzed EEG signals recorded from pediatric to adult patients (n = 131), separated into six age groups: <1 year (n = 15), 1–3 years (n = 23), 3–6 years (n = 19), 6–12 years (n = 18), 12–18 years (n = 16), and 18–45 years (n = 40). Age related EEG power and cross frequency coupling analysis (phase amplitude coupling (PAC) and quadratic phase coupling) of data from maintenance of a surgical state of anesthesia (MOSSA) was conducted. Also, for patients of ages less than 6 years, we analyzed the performance of cross frequency coupling derived indices in distinguishing the states of wakefulness, MOSSA, and recovery of consciousness (ROC). Results(1) During MOSSA, EEG power substantially increased with age from infancy to 3–6 years then decreased with age in the theta-gamma frequency bands. The infant group (<1 year) had the highest slow oscillation (SO) power among all age groups. (2) The distinct PAC pattern is absent in patients less than 1 year of age both in SO-alpha and delta-alpha frequency band coupling during propofol induced unconsciousness. The modulation index between delta and alpha oscillations in MOSSA increased with age. (3) Wavelet bicoherence derived indices reach their peaks in the 3–6 years group and then decrease with age growth. (4) The Diag_En index (normalized entropy of the diagonal bicoherence entries of the bicoherence matrix) performed the best at distinguishing different states for ages less than 6 years (p<0.05). ConclusionsThe combination of propofol induction and sevoflurane maintenance exhibited age-dependent EEG power spectra, PAC, and bicoherence, likely related to brain development. These observations suggest new rules for infant and child brain state monitoring during general anesthesia are needed.

On the characterization of cognitive tasks using activity-specific short-lived synchronization between electroencephalography channels

Accurate characterization of brain activity during a cognitive task is challenging due to the dynamically changing and the complex nature of the brain. The majority of the proposed approaches assume stationarity in brain activity and disregard the systematic timing organization among brain regions during cognitive tasks. In this study, we propose a novel cognitive activity recognition method that captures the activity-specific timing parameters from training data that elicits maximal average short-lived pairwise synchronization between electroencephalography signals. We evaluated the characterization power of the activity-specific timing parameter triplets in a motor imagery activity recognition framework. The activity-specific timing parameter triplets consist of latency of the maximally synchronized signal segments from activity onset Δt, the time lag between maximally synchronized signal segments τ, and the duration of the maximally synchronized signal segments w. We used cosine-based similarity, wavelet bi-coherence, phase-locking value, phase coherence value, linearized mutual information, and cross-correntropy to calculate the channel synchronizations at the specific timing parameters. Recognition performances as well as statistical analyses on both BCI Competition-III dataset IVa and PhysioNet Motor Movement/Imagery dataset, indicate that the inter-channel short-lived synchronization calculated using activity-specific timing parameter triplets elicit significantly distinct synchronization profiles for different motor imagery tasks and can thus reliably be used for cognitive task recognition purposes.

Novel Higher-Order Spectral Cross-Correlation Technologies for Vibration Sensor-Based Diagnosis of Gearboxes.

Novel vibration sensor-based diagnostic technologies, built on the higher order wavelet spectral cross-correlation (WSC), are proposed, investigated and applied to gearbox vibration diagnosis for the first time in worldwide terms. The proposed WSC-based technologies do not feature any constrains in selection of signal spectral components, relations between which are analysed. That is a radical improvement in comparison with the higher-order spectra (HOS). The WSC technologies are applied for an experimental diagnosis of a local gear tooth fault of a helical gearbox that is developed during a long duration gearbox endurance test. Differences between the applied technologies and advantages of the novel WSC approach over the classical HOS are explained in detail. Superiority of the WSC technologies is justified by high validity comprehensive experimental comparison with the HOS technologies: i.e., the wavelet bicoherence and the wavelet tricoherence.

Characterizing the orientation selectivity in V1 and V4 of macaques by quadratic phase coupling

Objective. Orientation selectivity is one of the significant characteristics of neurons in the primary visual cortex (V1). Some neurons in extrastriate visual cortical areas also exhibit certain orientation selectivity. But it is still not well understood that how the orientation selectivity generates. Most previous studies about the orientation selectivity are based on the spike firing rate. However, the spikes are prone to be biased by the detection and sorting algorithms. Then, in this paper, the local field potential (LFP) is adopted to investigate the mechanism of orientation selectivity. Approach. We used the quadratic phase coupling (QPC), which was calculated by wavelet bicoherence, to describe the characteristics of orientation selectivity available in V1 and V4. The raw wideband neural signals were recorded by two chronically implanted multi-electrode arrays, which were placed in V1 and V4 respectively in two macaques performing a selective visual attention task. Main results. There is a strong correlation between the total bicoherence (TotalBic), which is a quantization for the overall QPC of frequency pairs in gamma band, and the grating orientation. Furthermore, the QPC distribution at the non-preferred orientation is mainly concentrated in the low frequencies (30–40 Hz) of gamma; while the QPC distribution at the preferred orientation concentrates in both the low frequencies and high frequencies (60–80 Hz) of gamma. In addition, the TotalBic of the gamma-band LFP between V1 and V4 varies with the grating orientations, indicating that the QPC is available in the feedforward link and the gamma-band LFP in V1 modulates the QPC in V4. Significance. The QPC reflects the orientations of the sinusoidal grating and describes the interaction of gamma-band LFP between different brain regions. Our results suggest that the QPC is an alternative avenue to explore the mechanism for generating orientation selectivity of visual neurons effectively.

A New Instantaneous Wavelet Bicoherence for Local Fault Detection of Rotating Machinery

Practical vibration signals resulting from fault-included rotating machinery are nonlinear and nonstationary in nature, which bring new challenges for the linear representations and the stationarity assumption methods. Wavelet bicoherence (WB) is considered an effective method for these nonlinear signals analysis. However, the current WB model ignores the phase information of the nonlinear signals and is often estimated by integrating over the finite-time interval. Thus, its direct application may cause spurious bicoherence peaks and the transient information loss of the nonstationary signals. To overcome these limitations, a new instantaneous WB model is established to extend the application of WB for nonstationary signal analysis. In this method, the instantaneous biphase information is used first for bispectrum calculation, and then, the algorithm based on ensemble average of instantaneous phase randomization is introduced to eliminate the spurious bicoherence. Finally, the bicoherence is estimated in the time-frequency domain. The effectiveness of the proposed method is validated by mathematical discussion, simulations, and experiments. Results illustrate that, compared with the commonly used method, the proposed method provides an alternative solution for local fault detection of rotating machinery.

Results Suggestive of the Brain Trying to Re-Organizee Itself and Recover During the Early Stages of an Epileptic Seizure?

It literally “boggles the mind” to try to imagine the chaos that must be occurring in the brain during an epileptic seizure! No wonder seizures are often referred to as ‘brainstorms’! This paper presents some results of my studies analyzing the EEGs of patients suffering seizures, during the brainstorms themselves. Then, based on cross-frequency coupling strength computations, contour plot snapshots are presented which suggest to me that they may be showing the brain ‘struggling’ to regain control. Results are presented in graphical form for the progression of four epileptic seizures. There are two each from two patients, during the first dozen or two seconds after onset, for seizures lasting roughly three-quarters of to a full minute. Much longer time studies were done for each in my four recent SSRN e-papers, covering pre-seizure and post-seizure epochs as well. Using the metric of harmonic wavelet bicoherence, MATLAB contour plots of cross-frequency coupling of EEG oscillations were created. A short sequence of such plots is presented for each seizure, stepped forward in time by a second (or sometimes less), from a contour plot at or near seizure onset. Each sequence shows how the pattern of cross-frequency coupling soon after seizure onset morphs into noticeable, somewhat dramatic, frequency sub-band coupling. This coupling may be driven/modulated by narrow, lower-frequency sub-bands, as suggested by key contour plots. My conjectures may well spring mostly from my imagination/wishful thinking, and are likely premature, at the very least. But, for these seizures from two different patients with a specific, common type of seizure, complex partial, I seem to see a distinct pattern of brain activity, 'fighting' to reset itself, to escape the seizure. There appears to be a ‘characteristic’ spiking frequency for each seizure, which might identify a specific type(s) and location(s) of neurons responsible for this? Perhaps such knowledge could eventually lead to more effective treatment options? Much further work needs to be done, though.

Identification of the formation of resonant tones in compressible cavity flows

Identification of the fluid dynamic mechanisms responsible for the formation of resonant tones in a cavity flow is challenging. Time-frequency non-linear analysis techniques were applied to the post-processing of pressure signals recorded on the floor of a rectangular cavity at a transonic Mach number. The results obtained, confirmed that the resonant peaks in the spectrum were produced by the interaction of a carrier frequency (and its harmonics) and a modulating frequency. High-order spectral analysis, based on the instantaneous wavelet bi-coherence method, was able to identify, at individual samples in the pressure–time signal, that the interaction between the fundamental frequency and the amplitude modulation frequency was responsible for the creation of the Rossier–Heller tones. The same technique was also able to correlate the mode switching phenomenon, as well as the deactivation of the resonant tones during the temporal evolution of the signal.

Using Contour Plots of Bicoherence to Illustrate and Investigate Cross-Frequency Coupling of EEG Oscillations

My 12/2017 SSRN e-paper investigated possible cross-frequency phase-phase coupling of scalp-recorded EEG signals. Essentially, the quadratic-coupling metric of harmonic wavelet bicoherence was applied to 1-hr blocks of data centered at identified seizures, with results presented in graphical form. That paper was motivated in part by earlier studies of delta-theta band and theta-gamma band couplings. The former studied correlations between delta-theta couplings and depth of anesthesia during surgery, using this metric; the latter demonstrated such theta-gamma couplings in rat hippocampus. In this paper MATLAB figures of contour plots of bicoherence were chosen to better illustrate and investigate cross-frequency phase-phase coupling of EEG oscillations. The graphical framework is a frequency vs. frequency matrix, 0.5-50 Hz, with colored contour plots of bicoherence, for frequency steps of 1 Hz. To demonstrate ‘proof of concept’ in a limited amount of space, some restrictions from the previous paper were made.

Vibration diagnosis of a gearbox by wavelet bicoherence technology

Vibration diagnosis of a gearbox by wavelet bicoherence technology

Enhanced Gamma Activity and Cross-Frequency Interaction of Resting-State Electroencephalographic Oscillations in Patients with Alzheimer's Disease.

Cognitive impairment, functional decline and behavioral symptoms that characterize Alzheimer’s disease (AD) are associated with perturbations of the neuronal network. The typical electroencephalographic (EEG) features in AD patients are increased delta or theta rhythm and decreased alpha or beta rhythm activities. However, considering the role of cross-frequency couplings in cognition, the alternation of cross-frequency couplings in AD patients is still obscure. This study aims to explore the interaction dynamics between different EEG oscillations in AD patients. We recorded the resting eye-closed EEG signals in 8 AD patients and 12 healthy volunteers. By analyzing the wavelet power spectrum and bicoherence of EEG, we found enhanced gamma rhythm power in AD patients in addition to the increased delta and decreased alpha power. Furthermore, an enhancement of the cross-frequency coupling strength between the beta/gamma and low-frequency bands was observed in AD patients compared to healthy controls (HCs). We propose that the pathological increase of ongoing gamma-band power might result from the disruption of the GABAergic interneuron network in AD patients. Furthermore, the cross-frequency overcouplings, which reflect the enhanced synchronization, might indicate the attenuated complexity of the neuronal network, and AD patients have to use more neural resources to maintain the resting brain state. Overall, our findings provide new evidence of the disturbance of the brain oscillation network in AD and further deepen our understanding of the central mechanisms of AD.

Regenerative chatter identification in grinding using instantaneous nonlinearity indicator of servomotor current signal

Chatter is considered as one of the most important causes of instability in the precision grinding process. Suffering from the influence of nonlinearity and changed machining condition, regenerative chatter signal is nonlinear and non-stationary in nature, which makes the linear representations and stationary assumed methods not appropriate. Wavelet bicoherence is considered as an effective method for these nonlinear signals analysis. However, current wavelet bicoherence is often estimated by integrating over the finite time interval. This procedure may result to the loss of the time information; hence, it is not appropriate for chatter signal that cannot be assumed to be stationary. In this paper, an instantaneous nonlinearity indicator-based method is proposed for regenerative chatter identification in grinding by using the servomotor current signal. Firstly, the nonlinearity of servomotor current affected by regenerative chatter is discussed. After that, a non-stationary wavelet bicoherence is proposed for the quadratic nonlinear coupling detection of these nonlinear and non-stationary signals. On this basis, an instantaneous nonlinearity indicator is further established for regenerative chatter identification. The effectiveness of the proposed method is verified by simulations and experiments, and the results show that, compared with the commonly used wavelet bicoherence and continuous wavelet transform, this method can not only describe the non-stationary chatter signal in time-frequency domain but also extract the true nonlinear coupling component resulted from regenerative chatter.

Vibration diagnostics of rolling bearings by novel nonlinear non-stationary wavelet bicoherence technology

Rolling element bearings are widely used in almost all complex engineering structures. Failure of bearings could lead to a failure of the whole structure. Therefore, early damage diagnosis of bearings is of great importance for the structural integrity of the complex engineering structures.The novel nonlinear non-stationary wavelet bicoherence technology is applied for the first time in worldwide terms for rolling bearing condition monitoring.High effectiveness of early bearing diagnostics by the technology has been experimentally revealed, which has been further substantiated using the Fisher criterion.

Gamma (30-80Hz) bicoherence distinguishes seizures in the human epileptic brain.

We have applied wavelet bicoherence (BIC) analysis to human iEEG data to characterize non-linear frequency interactions in the human epileptic brain. Bicoherence changes were most prominent in the gamma (30-80 Hz) frequency band, and allowed for the differentiation between seizure and non-seizure states in all patients studied (n=3). While gamma band BIC values increased during seizure activity, this trend was only observed in a select number of electrode(s) located on the implanted patient subdural grids. Several studies have suggested that fast frequencies may play a role in the process of seizure genesis. While the small patient numbers limit the significance of our study, our results highlight the bicoherence of the gamma frequency band (30-80 Hz) as an ictal identifier, and suggest an active role of this fast frequency during seizures.

A Wavelet Bicoherence-Based Quadratic Nonlinearity Feature for Translational Axis Condition Monitoring

The translational axis is one of the most important subsystems in modern machine tools, as its degradation may result in the loss of the product qualification and lower the control precision. Condition-based maintenance (CBM) has been considered as one of the advanced maintenance schemes to achieve effective, reliable and cost-effective operation of machine systems, however, current vibration-based maintenance schemes cannot be employed directly in the translational axis system, due to its complex structure and the inefficiency of commonly used condition monitoring features. In this paper, a wavelet bicoherence-based quadratic nonlinearity feature is proposed for translational axis condition monitoring by using the torque signature of the drive servomotor. Firstly, the quadratic nonlinearity of the servomotor torque signature is discussed, and then, a biphase randomization wavelet bicoherence is introduced for its quadratic nonlinear detection. On this basis, a quadratic nonlinearity feature is proposed for condition monitoring of the translational axis. The properties of the proposed quadratic nonlinearity feature are investigated by simulations. Subsequently, this feature is applied to the real-world servomotor torque data collected from the X-axis on a high precision vertical machining centre. All the results show that the performance of the proposed feature is much better than that of original condition monitoring features.