Identifying Phase-Amplitude Coupling in Cyclic Alternating Pattern using Masking Signals

Auditory cues modulate the short timescale dynamics of STN activity during stepping in Parkinson's disease

BACKGROUND

Gait impairment has a major impact on quality of life in patients with Parkinson's disease (PD). It is believed that basal ganglia oscillatory activity at β frequencies (15-30 Hz) may contribute to gait impairment, but the precise dynamics of this oscillatory activity during gait remain unclear. Additionally, auditory cues are known to lead to improvements in gait kinematics in PD. If the neurophysiological mechanisms of this cueing effect were better understood they could be leveraged to treat gait impairments using adaptive Deep Brain Stimulation (aDBS) technologies.

OBJECTIVE

We aimed to characterize the dynamics of subthalamic nucleus (STN) oscillatory activity during stepping movements in PD and to establish the neurophysiological mechanisms by which auditory cues modulate gait.

METHODS

We studied STN local field potentials (LFPs) in eight PD patients while they performed stepping movements. Hidden Markov Models (HMMs) were used to discover transient states of spectral activity that occurred during stepping with and without auditory cues.

RESULTS

The occurrence of low and high β bursts was suppressed during and after auditory cues. This manifested as a decrease in their fractional occupancy and state lifetimes. Interestingly, α transients showed the opposite effect, with fractional occupancy and state lifetimes increasing during and after auditory cues.

CONCLUSIONS

We show that STN oscillatory activity in the α and β frequency bands are differentially modulated by gait-promoting oscillatory cues. These findings suggest that the enhancement of α rhythms may be an approach for ameliorating gait impairments in PD.

Cross-Frequency Coupling and Intelligent Neuromodulation

Cross-frequency coupling (CFC) reflects (nonlinear) interactions between signals of different frequencies. Evidence from both patient and healthy participant studies suggests that CFC plays an essential role in neuronal computation, interregional interaction, and disease pathophysiology. The present review discusses methodological advances and challenges in the computation of CFC with particular emphasis on potential solutions to spurious coupling, inferring intrinsic rhythms in a targeted frequency band, and causal interferences. We specifically focus on the literature exploring CFC in the context of cognition/memory tasks, sleep, and neurological disorders, such as Alzheimer's disease, epilepsy, and Parkinson's disease. Furthermore, we highlight the implication of CFC in the context and for the optimization of invasive and noninvasive neuromodulation and rehabilitation. Mainly, CFC could support advancing the understanding of the neurophysiology of cognition and motor control, serve as a biomarker for disease symptoms, and leverage the optimization of therapeutic interventions, e.g., closed-loop brain stimulation. Despite the evident advantages of CFC as an investigative and translational tool in neuroscience, further methodological improvements are required to facilitate practical and correct use in cyborg and bionic systems in the field.

A Novel Framework in Quantifying Oscillatory Coupling to Gait Disturbance in Parkinson's Disease

Phase-amplitude coupling (PAC) based on the uniform phase empirical mode decomposition (UPEMD) is proposed to improve the accuracy of PAC assessment. The framework is applied to investigate the mechanism and improvement measure of gait disturbance for Parkinson's disease (PD). Hβ modulation is suppressed at the time of contralateral heel strikes and rebounds when the contralateral foot rests on the ground and the ipsilateral foot is raised. Prominent PACs exist between δ and Lβ/Hβ activities. Auditory cue improves the gait; meanwhile, it enhances the Hβ modulation, and suppresses the δ-Lβ/Hβ PACs, which may rebound toward the before-cue stage afterward. Our findings suggest the proposed UPEMD-PAC is a useful framework in quantifying PAC with pre-determined frequencies, whereas the δ-Lβ/Hβ PACs in the subthalamic nucleus serve as potential biomarkers for gait disturbance in PD. Clinical Relevance- This manifests the efficacy of auditory cues on gait disturbance. The proposed framework may be useful in diagnosing the severity of motor impairment.

Sleep Dynamic Analysis Technology Based on Cross-Phase-Amplitude Transfer Entropy in Multiple Brain Regions

Information flow existed across brain regions, and varies dynamically during sleep. In evaluating brain communication and neural-oscillation connectivity across spatiotemporal scales, the phase-amplitude coupling (PAC) is well-explored. However, the directional connectivity is still a deficiency. In this work, we propose a cross-phase-amplitude transfer entropy method in quantifying the characteristics of multi-regional sleep dynamics. The simulation of multivariate nonlinear and nonstationary signals verifies both effectiveness and veracity of the proposed algorithm. The results achieved in sleep EEG of healthy adults indicate that the direction of PAC is from the occipital lobe to the frontal lobe in the Awake and N1 sleep stages. And the flow of PAC turns to the opposite direction for the other sleep stages, i.e., frontal-to-occipital lobe. Besides, the δ-θ/α PAC gradually strengthens with the deepening of the sleep. Of note, the PAC results in the REM sleep stage vary across different frequency pairs. The obtained results support the proposed method as a reliable tool in evaluating brain functions during sleep with brain signals. Clinical Relevance- This manifests the brain communication and neuron-oscillation connectivity across spatiotemporal scales. The proposed framework may be useful in identifying multi-regional sleep dynamics.

Frequency Nesting Interactions in the Subthalamic Nucleus Correlate With the Step Phases for Parkinson’s Disease

Gait disturbance in Parkinson’s disease (PD) can be ameliorated by sound stimulation. Given that excessive β synchronization in basal ganglia is linked to motor impairment in PD, whether the frequency nesting interactions are associated with the gait problem is far from clear. To this end, the masking phase-amplitude coupling (PAC) method was proposed to overcome the trade-off between intrinsic nonlinearity/non-stationarity and demand for predetermined frequencies, normally extracted by the filter. In this study, we analyzed LFPs recorded from 13 patients (one female) with PD during stepping with bilateral deep brain electrodes implanted in the subthalamic nucleus (STN). We found that not only high-frequency oscillation (100–300 Hz) was modulated by β (13–30 Hz) but also β and γ amplitude were modulated by their low-frequency components in δ/θ/α and δ/θ/α/β bands. These PAC values were suppressed by sound stimulation, along with an improvement in gait. We also showed that gait-related high-β (Hβ) modulation in the STN was sensitive to auditory cues, and Hβ gait-phase modulation increased with a metronome. Meanwhile, phase-locking values (PLVs) across all frequencies were significantly suppressed around contralateral heel strikes, manifesting the contralateral step as a critical gait phase in gait initiation for PD. Only the PLVs around contralateral steps were sensitive to auditory cues. Our results support masking PAC as an effective method in exploring frequency nesting interactions in LFPs and reveal the linkages between sound stimulation and couplings related to gait phases in the STN. These findings raise the possibility that nesting interactions in the STN work as feasible biomarkers in alleviating gait disorders.

Alpha and high gamma phase amplitude coupling during motor imagery and weighted cross-frequency coupling to extract discriminative cross-frequency patterns

Motor imagery modulates specific neural oscillations like actual movement does. Representatively, suppression of the alpha power (e.g., event-related desynchronization [ERD]) is the typical pattern of motor imagery in the motor cortex. However, in addition to this amplitude-based feature, the coupling across frequencies includes important information about the brain functions and the existence of such complex information has been reported in various invasive studies. Yet, the interaction across multiple frequencies during motor imagery processing is still unclear and has not been widely studied, particularly concerning the non-invasive signals. In this study, we provide empirical evidence of the comodulation between the phase of alpha rhythm and the amplitude of high gamma rhythm during the motor imagery process. We used electroencephalography (EEG) in our investigation during the imagination of left- or right-hand movement recorded from 52 healthy subjects, and quantified the ERD of alpha and phase-amplitude coupling (PAC) which is a relative change of modulation index to the base line period (before the cue). As a result, we found that the coupling between the phase of alpha (8-12 Hz) and the amplitude of high gamma (70-120 Hz) and this PAC decreases during motor imagery and then rebounds to the baseline like alpha ERD (r = 0.29 to 0.42). This correlation between PAC and ERD was particularly stronger in the ipsilateral area. In addition, trials that demonstrated higher alpha power during the ready period (before the cue) showed a larger ERD during motor imagery and similarly, trials with higher modulation index during the ready period yielded a greater decrease in PAC during imagery. In the classification analysis, we found that the effective phase frequency that showed better decoding accuracy in left and right-hand imagery, varied across subjects. Motivated by result, we proposed a weighted cross-frequency coupling (WCFC) method that extracts the maximal discriminative feature by combining band power and CFC. In the evaluation, WCFC with only two electrodes yielded a performance comparable to the conventional algorithm with 64 electrodes in classifying left and right-hand motor imagery. These results indicate that the phase-amplitude frequency plays an important role in motor imagery, and that optimizing this frequency ranges is crucial for extracting information features to decode the motor imagery types.

An automatic sleep disorder detection based on EEG cross-frequency coupling and random forest model

Objective. Sleep disorders are medical disorders of a subject's sleep architecture and based on their severity, they can interfere with mental, emotional and physical functioning. The most common ones are insomnia, narcolepsy, sleep apnea, bruxism, etc. There is an increased risk of developing sleep disorders in elderly like insomnia, periodic leg movements, rapid eye movement behavior disorders, sleep disorder breathing, etc. Consequently, their accurate diagnosis and classification are important steps towards an early stage treatment that could save the life of a patient.Approach. The electroencephalographic (EEG) signal is the most sensitive and important biosignal, which is able to capture the brain sleep activity that is sensitive to sleep. In this study, we attempt to analyze EEG sleep activity via complementary cross-frequency coupling (CFC) estimates, which further feed a classifier, aiming to discriminate sleep disorders. We adopted an open EEG database with recordings that were grouped into seven sleep disorders and a healthy control. The EEG brain activity from common sensors has been analyzed with two basic types of CFC.Main results. Finally, a random forest (RF) classification model was built on CFC patterns, which were extracted from non-cyclic alternating pattern epochs. Our RF^CFCmodel achieved a 74% multiclass accuracy. Both types of CFC, phase-to-amplitude and amplitude-amplitude coupling patterns contribute to the accuracy of the RF model, thus supporting their complementary information.Significance. CFC patterns, in conjunction with the RF classifier proved a valuable biomarker for the classification of sleep disorders.

Predicting Grating Orientations With Cross-Frequency Coupling and Least Absolute Shrinkage and Selection Operator in V1 and V4 of Rhesus Monkeys

Orientation selectivity, as an emergent property of neurons in the visual cortex, is of critical importance in the processing of visual information. Characterizing the orientation selectivity based on neuronal firing activities or local field potentials (LFPs) is a hot topic of current research. In this paper, we used cross-frequency coupling and least absolute shrinkage and selection operator (LASSO) to predict the grating orientations in V1 and V4 of two rhesus monkeys. The experimental data were recorded by utilizing two chronically implanted multi-electrode arrays, which were placed, respectively, in V1 and V4 of two rhesus monkeys performing a selective visual attention task. The phase-amplitude coupling (PAC) and amplitude-amplitude coupling (AAC) were employed to characterize the cross-frequency coupling of LFPs under sinusoidal grating stimuli with different orientations. Then, a LASSO logistic regression model was constructed to predict the grating orientation based on the strength of PAC and AAC. Moreover, the cross-validation method was used to evaluate the performance of the model. It was found that the average accuracy of the prediction based on the combination of PAC and AAC was 73.9%, which was higher than the predicting accuracy with PAC or AAC separately. In conclusion, a LASSO logistic regression model was introduced in this study, which can predict the grating orientations with relatively high accuracy by using PAC and AAC together. Our results suggest that the principle behind the LASSO model is probably an alternative direction to explore the mechanism for generating orientation selectivity.

On the use of patterns obtained from LSTM and feature-based methods for time series analysis: application in automatic classification of the CAP A phase subtypes

The cyclic alternating pattern is a marker of sleep instability identified in the electroencephalogram signals whose sequence of transient variations compose the A phases. These phases are divided into three subtypes (A1, A2, and A3) according to the presented patterns. The traditional approach of manually scoring the cyclic alternating pattern events for the full night is unpractical, with a high probability of miss classification, due to the large quantity of information that is produced during a full night recording. To address this concern, automatic methodologies were proposed using a long short-term memory to perform the classification of one electroencephalogram monopolar derivation signal. The proposed model is composed of three classifiers, one for each subtype, performing binary classification in a one versus all procedure. Two methodologies were tested: feed the pre-processed electroencephalogram signal to the classifiers; create features from the pre-processed electroencephalogram signal which were fed to the classifiers (feature-based methods). It was verified that the A1 subtype classification performance was similar for both methods and the A2 subtype classification was higher for the feature-based methods. However, the A3 subtype classification was found to be the most challenging to be performed, and for this classification, the feature-based methods were superior. A characterization analysis was also performed using a recurrence quantification analysis to further examine the subtypes characteristics. The average accuracy and area under the receiver operating characteristic curve for the A1, A2, and A3 subtypes of the feature-based methods were respectively: 82% and 0.92; 80% and 0.88; 85% and 0.86.

Waveform changes with the evolution of beta bursts in the human subthalamic nucleus

OBJECTIVE

Phasic bursts of beta band synchronisation have been linked to motor impairment in Parkinson's disease (PD). However, little is known about what terminates bursts.

METHODS

We used the Hilbert-Huang transform to investigate beta bursts in the local field potential recorded from the subthalamic nucleus in nine patients with PD on and off levodopa.

RESULTS

The sharpness of the beta waveform extrema fell as burst amplitude dropped. Conversely, an index of phase slips between waveform extrema, and the power of concurrent theta activity increased as burst amplitude fell. Theta activity was also increased on levodopa when beta bursts were attenuated. These phenomena were associated with reduction in coupling between beta phase and high gamma activity amplitude. We discuss how these findings may suggest that beta burst termination is associated with relative desynchronization of the beta drive, increase in competing theta activity and increased phase slips in the beta activity.

CONCLUSIONS

We characterise the dynamical nature of beta bursts, thereby permitting inferences about underlying activities and, in particular, about why bursts terminate.

SIGNIFICANCE

Understanding the dynamical nature of beta bursts may help point to interventions that can cause their termination and potentially treat motor impairment in PD.

Matrix of Lags: A tool for analysis of multiple dependent time series applied for CAP scoring

BACKGROUND

Multiple methods have been developed to assess what happens between and within time series. In a particular type of these series, the previous values of the currently observed series are contingent on the lagged values of another series. These cases can commonly be addressed by regression. However, a model selection criteria should be employed to evaluate the compromise between the amount of information provided and the model complexity. This is the basis for the development of the Matrix of Lags (MoL), a tool to study dependent time series.

METHODS

For each input, multiple regressions were applied to produce a model for each lag and a model selection criterion identifies the lags that will populate an auxiliary matrix. Afterwards, the energy of the lags (that are in the auxiliary matrix) was used to define a row of the MoL. Therefore, each input corresponds to a row of the MoL. To test the proposed tool, the heart rate variability and the electrocardiogram derived respiration were employed to perform the indirect estimation of the electroencephalography cyclic alternating pattern (CAP) cycles. Therefore, a support vector machine was fed with the MoL to perform the CAP cycle classification for each input signal. Multiple tests were carried out to further examine the proposed tool, including the effect of balancing the datasets, application of other regression methods and employment of two feature section models. The first was based on sequential backward selection while the second examined characteristics of a return map.

RESULTS

The best performance of the subject independent model was attained by feeding the lags, selected by sequential backward selection, to a support vector machine, achieving an average accuracy, sensitivity, specificity and area under the receiver operating characteristic curve of, respectively, 77%, 71%, 82% and 0.77.

CONCLUSIONS

The developed model allows to perform a measurement of a characteristic marker of sleep instability (the CAP cycle) and the results are in the upper bound of the specialist agreement range with visual analysis. Thus, the developed method could possibly be used for clinical diagnosis.

Cross-Channel Phase-Amplitude Transfer Entropy Conceptualize Long-Range Transmission in sleep: a case study

A causal algorithmic framework quantifying cross-channel phase-amplitude transfer entropy was proposed to measure long-range transmission dynamics between frontal and occipital brain areas during sleep. To this end, a noise-assisted multivariate empirical mode decomposition method was used to guarantee the consistent scales across multivariate signals. On the other side, transfer entropy was applied to measure information transfers from a low-frequency phase to a high-frequency amplitude across different brain regions. Our results showed δ phase may modulate either θ or α amplitude. The frontal cortex transferred information to the occipital brain area more than its inverse direction during Awake and N3 sleep stages, whereas N1 was more likely of serving as a transition state. On the other side, the information flow transferred from the occipital area to the frontal cortex surpassed its inverse flow in the N2 sleep stage. The proposed causal algorithmic framework facilitated identifying information flow and driving force across brain regions in sleep.

An ADMM Approach to Masked Signal Decomposition Using Subspace Representation

Signal decomposition is a classical problem in signal processing, which aims to separate an observed signal into two or more components, each with its own property. Usually, each component is described by its own subspace or dictionary. Extensive research has been done for the case where the components are additive, but in real-world applications, the components are often non-additive. For example, an image may consist of a foreground object overlaid on a background, where each pixel either belongs to the foreground or the background. In such a situation, to separate signal components, we need to find a binary mask which shows the location of each component. Therefore, it requires solving a binary optimization problem. Since most of the binary optimization problems are intractable, we relax this problem to the approximated continuous problem and solve it by alternating optimization technique. We show the application of the proposed algorithm for three applications: separation of text from a background in images, separation of moving objects from a background undergoing global camera motion in videos, and separation of sinusoidal and spike components in 1-D signals. We demonstrate in each case that considering the non-additive nature of the problem can lead to a significant improvement.

Self-Adaptive Fault Feature Extraction of Rolling Bearings Based on Enhancing Mode Characteristic of Complete Ensemble Empirical Mode Decomposition with Adaptive Noise

Originally, a rolling bearing, as a key part in rotating machinery, is a cyclic symmetric structure. When a fault occurs, it disrupts the symmetry and influences the normal operation of the rolling bearing. To accurately identify faults of rolling bearing, a novel method is proposed, which is based enhancing the mode characteristics of complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN). It includes two parts: the first is the enhancing decomposition of CEEMDAN algorithm, and the second is the identified method of intrinsic information mode (IIM) of vibration signal. For the first part, the new mode functions (CIMFs) are obtained by combing the adjacent intrinsic mode functions (IMFs) and performing the corresponding Fast Fourier Transform (FFT) to strengthen difference feature among IMFs. Then, probability density function (PDF) is used to estimate FFT of each CIMF to obtain overall information of frequency component. Finally, the final intrinsic mode functions (FIMFs) are obtained by proposing identified method of adjacent PDF based on geometrical similarity (modified Hausdorff distance (MHD)). FIMFs indicate the minimum amount of mode information with physical meanings and avoid interference of spurious mode in original CEEMDAN decomposing. Subsequently, comprehensive evaluate index (Kurtosis and de-trended fluctuation analysis (DFA)) is proposed to identify IIM in FIMFs. Experiment results indicate that the proposed method demonstrates superior performance and can accurately extract characteristic frequencies of rolling bearing.

Fault Diagnosis for a Bearing Rolling Element Using Improved VMD and HT

The variational mode decomposition (VMD) method for signal decomposition is severely affected by the number of components of the VMD method. In order to determine the decomposition modal number, K, in the VMD method, a new center frequency method of the multi-threshold is proposed in this paper. Then, an improved VMD (MTCFVMD) algorithm based on the center frequency method of the multi-threshold is obtained to decompose the vibration signal into a series of intrinsic modal functions (IMFs). The Hilbert transformation is used to calculate the envelope signal of each IMF component, and the maximum frequency value of the power spectral density is obtained in order to effectively and accurately extract the fault characteristic frequency and realize the fault diagnosis. The rolling element vibration data of the motor bearing is used to test the effectiveness of proposed methods. The experiment results show that the center frequency method of the multi-threshold can effectively determine the number, K, of decomposed modes. The proposed fault diagnosis method based on MTCFVMD and Hilbert transformation can effectively and accurately extract the fault characteristic frequency, rotation frequency, and frequency doubling, and can obtain higher diagnostic accuracy.

Robust Fetal Heart Beat Detection via R-Peak Intervals Distribution

Monitoring fetal heart rate during pregnancy is essential to assist clinicians in making more timely decisions. Non-invasive monitoring of fetal heart activities using abdominal ECGs is useful for diagnosis of heart defects. However, the extracted fetal ECGs are usually too weak to be robustly detected. Thus, it is a necessity to enhance fetal R-peak since their peaks may be hidden within the signal due to the immaturity of the fetal cardiovascular system. Therefore, to improve the detection of the fetal heartbeat, a novel fetal R-peak enhancement technique was proposed to statistically generate the weighting mask according to the distribution of the neighboring temporal intervals between each pair of peaks. Two sets of simulations were designed to validate the reliability of the method: challenges with different levels of (1) noise contamination and (2) R-peak interval changing rate. The simulation results showed that the weighting mask improved the accuracy of the R-peak detection rate by 25% and decreased the false alarm rate by 20% with white noise contamination, and ensured high R-peak detection rate (>80%), especially with mild noise contamination (noise amplitude ratio <1.5 and noise rate per minute <25%). For the simulations with continuous R-peak intervals changing, the masking process can still effectively eliminate noise contamination especially when the amplitude of the sinusoidal fetal R-R intervals is lower than 50 ms. For the real fetus ECGs, the detection rate was increased by 3.498%, whereas the false alarm rate was decreased by 3.933%. Next, we implemented the fetal R-peak enhancement technique to investigate fractal regulation and multiscale entropy of the real fetal heartbeat intervals. Both scaling exponent (∼0.6 to ∼1 in scale 4-15) and entropy measure (scale 6-10) increased with gestational ages (22-40 weeks). The results confirmed fractal slope and complexity of fetal heartbeat intervals can reflect the maturation of fetus organism.

A Revised Hilbert⁻Huang Transform and Its Application to Fault Diagnosis in a Rotor System

As a classical method to deal with nonlinear and nonstationary signals, the Hilbert–Huang transform (HHT) is widely used in various fields. In order to overcome the drawbacks of the Hilbert–Huang transform (such as end effects and mode mixing) during the process of empirical mode decomposition (EMD), a revised Hilbert–Huang transform is proposed in this article. A method called local linear extrapolation is introduced to suppress end effects, and the combination of adding a high-frequency sinusoidal signal to, and embedding a decorrelation operator in, the process of EMD is introduced to eliminate mode mixing. In addition, the correlation coefficients between the analyzed signal and the intrinsic mode functions (IMFs) are introduced to eliminate the undesired IMFs. Simulation results show that the improved HHT can effectively suppress end effects and mode mixing. To verify the effectiveness of the new HHT method with respect to fault diagnosis, the revised HHT is applied to analyze the vibration displacement signals in a rotor system collected under normal, rubbing, and misalignment conditions. The simulation and experimental results indicate that the revised HHT method is more reliable than the original with respect to fault diagnosis in a rotor system.

Cross-Frequency Transfer Entropy Characterize Coupling of Interacting Nonlinear Oscillators in Complex Systems

The purpose of this study is to introduce a method in quantifying cross-frequency information transfer to characterize directional couplers between irregular oscillations in complex systems. Importantly, the method should be able to reflect the intrinsic mechanism of interacting oscillations faithfully. Six types of interacting oscillators, including phase-amplitude, amplitude-amplitude, and component-amplitude cross-frequency transfer entropy as well as their inverse transfer entropies, are within our scope in untangling the brain connectivity. Challenges with nonlinear and nonstationary patterns are designed to validate the robustness of the proposed method. We suggest this approach could be effective in identifying driving and responding elements of interacting oscillators across different time scales. Meanwhile, an atlas of interacting oscillators in sleep is constructed. High-frequency amplitude can inversely drive low-frequency phase stronger than the standard phase-amplitude coupling, and the low-frequency amplitude can be the driving force to the high-frequency amplitude in addition to the low-frequency phase. Unlike the standard phase-amplitude coupling, the proposed cross-frequency transfer entropy is applicable to quantify the interactions across phases, amplitudes, or even the components without methodological adjustments. Meanwhile, the exploration of causal relationship enables the identification of the driving force of information flow.