Spurious cross-frequency amplitude-amplitude coupling in nonstationary, nonlinear signals

Time-domain methods for quantifying dynamic cerebral blood flow autoregulation: Review and recommendations. A white paper from the Cerebrovascular Research Network (CARNet)

Cerebral Autoregulation (CA) is an important physiological mechanism stabilizing cerebral blood flow (CBF) in response to changes in cerebral perfusion pressure (CPP). By maintaining an adequate, relatively constant supply of blood flow, CA plays a critical role in brain function. Quantifying CA under different physiological and pathological states is crucial for understanding its implications. This knowledge may serve as a foundation for informed clinical decision-making, particularly in cases where CA may become impaired. The quantification of CA functionality typically involves constructing models that capture the relationship between CPP (or arterial blood pressure) and experimental measures of CBF. Besides describing normal CA function, these models provide a means to detect possible deviations from the latter. In this context, a recent white paper from the Cerebrovascular Research Network focused on Transfer Function Analysis (TFA), which obtains frequency domain estimates of dynamic CA. In the present paper, we consider the use of time-domain techniques as an alternative approach. Due to their increased flexibility, time-domain methods enable the mitigation of measurement/physiological noise and the incorporation of nonlinearities and time variations in CA dynamics. Here, we provide practical recommendations and guidelines to support researchers and clinicians in effectively utilizing these techniques to study CA.

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.

EEG emotion recognition based on cross-frequency granger causality feature extraction and fusion in the left and right hemispheres

EEG emotion recognition based on Granger causality (GC) brain networks mainly focus on the EEG signal from the same-frequency bands, however, there are still some causality relationships between EEG signals in the cross-frequency bands. Considering the functional asymmetric of the left and right hemispheres to emotional response, this paper proposes an EEG emotion recognition scheme based on cross-frequency GC feature extraction and fusion in the left and right hemispheres. Firstly, we calculate the GC relationship of EEG signals according to the frequencies and hemispheres, and mainly focus on the causality of the cross-frequency EEG signals in left and right hemispheres. Then, to remove the redundant connections of the GC brain network, an adaptive two-stage decorrelation feature extraction scheme is proposed under the condition of maintaining the best emotion recognition performance. Finally, a multi-GC feature fusion scheme is designed to balance the recognition accuracy and feature number of each GC feature, which comprehensively considers the influence of the recognition accuracy and computational complexity. Experimental results on the DEAP emotion dataset show that the proposed scheme can achieve an average accuracy of 84.91% for four classifications, which improved the classification accuracy by up to 8.43% compared with that of the traditional same-frequency band GC features.

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.

A Waveform-Independent Measure of Recurrent Neural Activity

Rhythmic neural activity, so-called oscillations, plays a key role in neural information transmission, processing, and storage. Neural oscillations in distinct frequency bands are central to physiological brain function, and alterations thereof have been associated with several neurological and psychiatric disorders. The most common methods to analyze neural oscillations, e.g., short-time Fourier transform or wavelet analysis, assume that measured neural activity is composed of a series of symmetric prototypical waveforms, e.g., sinusoids. However, usually, the models generating the signal, including waveform shapes of experimentally measured neural activity are unknown. Decomposing asymmetric waveforms of nonlinear origin using these classic methods may result in spurious harmonics visible in the estimated frequency spectra. Here, we introduce a new method for capturing rhythmic brain activity based on recurrences of similar states in phase-space. This method allows for a time-resolved estimation of amplitude fluctuations of recurrent activity irrespective of or specific to waveform shapes. The algorithm is derived from the well-established field of recurrence analysis, which, in comparison to Fourier-based analysis, is still very uncommon in neuroscience. In this paper, we show its advantages and limitations in comparison to short-time Fourier transform and wavelet convolution using periodic signals of different waveform shapes. Furthermore, we demonstrate its application using experimental data, i.e., intracranial and noninvasive electrophysiological recordings from the human motor cortex of one epilepsy patient and one healthy adult, respectively.

Localizing Spectral Interactions in the Resting State Network Using the Hilbert–Huang Transform

Brain synchronizations are orchestrated from neuronal oscillations through frequency interactions, such as the alpha rhythm during relaxation. Nevertheless, how the intrinsic interaction forges functional integrity across brain segregations remains elusive, thereby motivating recent studies to localize frequency interactions of resting-state fMRI (rs-fMRI). To this point, we aim to unveil the fMRI-based spectral interactions using the time-frequency (TF) analysis; however, Fourier-based TF analyses impose restrictions on revealing frequency interactions given the limited time points in fMRI signals. Instead of using the Fourier-based wavelet analysis to identify the fMRI frequency of interests, we employed the Hilbert–Huang transform (HHT) for probing the specific frequency contribution to the functional integration, called ensemble spectral interaction (ESI). By simulating data with time-variant frequency changes, we demonstrated the Hilbert TF maps with high spectro-temporal resolution and full accessibility in comparison with the wavelet TF maps. By detecting amplitude-to-amplitude frequency couplings (AAC) across brain regions, we elucidated the ESI disparity between the eye-closed (EC) and eye-open (EO) conditions in rs-fMRI. In the visual network, the strength of the spectral interaction within 0.03–0.04 Hz was amplified in EC compared with that in EO condition, whereas a canonical connectivity analysis did not present differences between conditions. Collectively, leveraging from the instantaneous frequency of HHT, we firstly addressed the ESI technique to map the fMRI-based functional connectivity in a brand-new AAC perspective. The ESI possesses potential in elucidating the functional connectivity at specific frequency bins, thereby providing additional diagnostic merits for future clinical neuroscience.

Epileptogenic Zone Location of Temporal Lobe Epilepsy by Cross-Frequency Coupling Analysis

Epilepsy is a chronic brain disease with dysfunctional brain networks, and electroencephalography (EEG) is an important tool for epileptogenic zone (EZ) identification, with rich information about frequencies. Different frequency oscillations have different contributions to brain function, and cross-frequency coupling (CFC) has been found to exist within brain regions. Cross-channel and inter-channel analysis should be both focused because they help to analyze how epilepsy networks change and also localize the EZ. In this paper, we analyzed long-term stereo-electroencephalography (SEEG) data from 17 patients with temporal lobe epilepsy. Single-channel and cross-channel CFC features were combined to establish functional brain networks, and the network characteristics under different periods and the localization of EZ were analyzed. It was observed that theta–gamma phase amplitude coupling (PAC) within the electrodes in the seizure region increased during the ictal (p < 0.05). Theta–gamma and delta–gamma PAC of cross-channel were enhanced in the early and mid-late ictal, respectively. It was also found that there was a strong cross-frequency coupling state between channels of EZ in the functional network during the ictal, along with a more regular network than interictal. The accuracy rate of EZ localization was 82.4%. Overall, the combination of single-channel and multi-channel cross-band coupling analysis can help identify seizures and localize EZ for temporal lobe epilepsy. Rhythmic coupling reveals a relationship between the functional network and the seizure status of epilepsy.

Measuring Phase-Amplitude Coupling Based on the Jensen-Shannon Divergence and Correlation Matrix

Phase-amplitude coupling (PAC) measures the relationship between the phase of low-frequency oscillations (LFO) and the amplitude of high-frequency oscillations (HFO). It plays an important functional role in neural information processing and cognition. Thus, we propose a novel method based on the Jensen-Shannon (JS) divergence and correlation matrix. The method takes the amplitude distributions of the HFO located in the corresponding phase bins of the LFO as multichannel inputs to construct a correlation matrix, where the elements are calculated based on the JS divergence between pairs of amplitude distributions. Then, the omega complexity extracted from the correlation matrix is used to estimate the PAC strength. The simulation results demonstrate that the proposed method can effectively reflect the PAC strength and slightly vary with the data length. Moreover, it outperforms five frequently used algorithms in the performance against additive white Gaussian noise and spike noise and the ability of detecting PAC in wide frequency ranges. To validate our proposed method with real data, it was applied to analyze the local field potential recorded from the dorsomedial striatum in a male Sprague-Dawley rat. It can replicate previous results obtained with other PAC metrics. In conclusion, these results suggest that our proposed method is a powerful tool for measuring the PAC between neural oscillations.

Brain network features based on theta-gamma cross-frequency coupling connections in EEG for emotion recognition

Emotion recognition is a hot topic in the field of cognitive neuroscience and interpersonal interaction, and EEG feature selection is an important classification technology. At present, the mainstream method of EEG feature selection is to extract non-interactive features of channels such as power spectral density, or correlation features among local multi-channels. With the application of complex network graph theory, the connection network between multiple brain regions is gradually included in feature selection. However, in the process of brain network construction, most of the current connections adopt simple signal phase or amplitude synchronization. In recent years, it has been found that in the process of emotion, memory, learning, and other advanced cognitive processes, the large-scale connection and communication between the brain regions are mainly completed by the cross-frequency coupling(CFC) between the low-frequency phase and the high-frequency amplitude of neural oscillations. Based on this, we use CFC to update the connection mode, reconstruct the brain network, and extract features for emotion recognition research. Our results show that the EEG network based on CFC performs better than other EEG synchronization networks in emotion classification. Moreover, the combination of global features and local features of the brain network, as well as the dynamic network features with continuous time-windows, can effectively improve the accuracy of emotion recognition. This study provides a new idea of network connection for the follow-up study of emotion recognition and other advanced cognitive activities and makes a pioneering exploration for further research on feature selection of emotion recognition and related neural circuits at the brain network level of functional connectivity.

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.

EEG, MEG and neuromodulatory approaches to explore cognition: Current status and future directions

Neural oscillations and their association with brain states and cognitive functions have been object of extensive investigation over the last decades. Several electroencephalography (EEG) and magnetoencephalography (MEG) analysis approaches have been explored and oscillatory properties have been identified, in parallel with the technical and computational advancement. This review provides an up-to-date account of how EEG/MEG oscillations have contributed to the understanding of cognition. Methodological challenges, recent developments and translational potential, along with future research avenues, are discussed.

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.

The dynamic properties of a brain network during working memory based on the algorithm of cross-frequency coupling

Working memory (WM) refers to a memory system with limited energy for short-term maintenance and plays an important role in cognitive functions. At present, research regarding WM mostly focuses on the coordination between neural signals in the signal microelectrode channel. However, how neural signals coordinate the coding of WM at the network level is rarely studied. Cross-frequency coupling (CFC) reflects the coordinated effect between different frequency components (e.g., theta and gamma) of local field potentials (LFPs) during WM. In this study, we try to map the changes that occur in the brain networks during WM at the level of CFC between theta-gamma of LFPs. First, a 16-channel brain network by using the CFC between theta-gamma of LFPs during WM was constructed. Then, the dynamic properties of the brain network during WM were analyzed based on graph theory. Experimental results show that the LFPs power increased at the WM state than at resting stat, but decreased across learning; the CFC between theta-gamma increased with learning days and phase-amplitude coupling (PAC) in the WM state was higher than that in free choice state and rest state; the changes of average degree, average shortest path length and global efficiency had significant difference on learning days. We can indicate that the CFC between theta-gamma in the network plays an important role in the WM formation. Furthermore, correct storage of WM information will not change local information transmission and the small-world attribute, while, it can increase the network connection and efficiency of information transmission.

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.

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.

Possible Implication of the CA2 Hippocampal Circuit in Social Cognition Deficits Observed in the Neuroligin 3 Knock-Out Mouse, a Non-Syndromic Animal Model of Autism

Autism spectrum disorders (ASDs) comprise a heterogeneous group of neuro-developmental abnormalities with a strong genetic component, characterized by deficits in verbal and non-verbal communication, impaired social interactions, and stereotyped behaviors. In a small percentage of cases, ASDs are associated with alterations of genes involved in synaptic function. Among these, relatively frequent are mutations/deletions of genes encoding for neuroligins (NLGs). NLGs are postsynaptic adhesion molecules that, interacting with their presynaptic partners neurexins, ensure the cross talk between pre- and postsynaptic specializations and synaptic stabilization, a condition needed for maintaining a proper excitatory/inhibitory balance within local neuronal circuits. We have focused on mice lacking NLG3 (NLG3 knock-out mice), animal models of a non-syndromic form of autism, which exhibit deficits in social behavior reminiscent of those found in ASDs. Among different brain areas involved in social cognition, the CA2 region of the hippocampus has recently emerged as a central structure for social memory processing. Here, in vivo recordings from anesthetized animals and ex vivo recordings from hippocampal slices have been used to assess the dynamics of neuronal signaling in the CA2 hippocampal area. In vivo experiments from NLG3-deficient mice revealed a selective impairment of spike-related slow wave activity in the CA2 area and a significant reduction in oscillatory activity in the theta and gamma frequencies range in both CA2 and CA3 regions of the hippocampus. These network effects were associated with an increased neuronal excitability in the CA2 hippocampal area. Ex vivo recordings from CA2 principal cells in slices obtained from NLG3 knock-out animals unveiled a strong excitatory/inhibitory imbalance in this region accompanied by a strong reduction of perisomatic inhibition mediated by CCK-containing GABAergic interneurons. These data clearly suggest that the selective alterations in network dynamics and GABAergic signaling observed in the CA2 hippocampal region of NLG3 knock-out mice may account for deficits in social memory reminiscent of those observed in autistic patients.

Parsing Hippocampal Theta Oscillations by Nested Spectral Components during Spatial Exploration and Memory-Guided Behavior

Theta oscillations reflect rhythmic inputs that continuously converge to the hippocampus during exploratory and memory-guided behavior. The theta-nested operations that organize hippocampal spiking could either occur regularly from one cycle to the next or be tuned on a cycle-by-cycle basis. To resolve this, we identified spectral components nested in individual theta cycles recorded from the mouse CA1 hippocampus. Our single-cycle profiling revealed theta spectral components associated with different firing modulations and distinguishable ensembles of principal cells. Moreover, novel co-firing patterns of principal cells in theta cycles nesting mid-gamma oscillations were the most strongly reactivated in subsequent offline sharp-wave/ripple events. Finally, theta-nested spectral components were differentially altered by behavioral stages of a memory task; the 80-Hz mid-gamma component was strengthened during learning, whereas the 22-Hz beta, 35-Hz slow gamma, and 54-Hz mid-gamma components increased during retrieval. We conclude that cycle-to-cycle variability of theta-nested spectral components allows parsing of theta oscillations into transient operating modes with complementary mnemonic roles.

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Spectral profiling of single theta waves enables studying inter-cycle variability

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Theta spectral components feature different spiking patterns and ensembles

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Co-firing in theta cycles nesting mid-gamma undergo enhanced offline reactivation

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Theta components relate differently to learning and memory retrieval demands

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.

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

Judiciously classifying phase-A subtypes in cyclic alternating pattern (CAP) is critical for investigating sleep dynamics. Phase-amplitude coupling (PAC), one of the representative forms of neural rhythmic interaction, is defined as the amplitude of high-frequency activities modulated by the phase of low-frequency oscillations. To examine PACs under more or less synchronized conditions, we propose a nonlinear approach, named the masking phase-amplitude coupling (MPAC), to quantify physiological interactions between high (α/lowβ) and low (δ) frequency bands. The results reveal that the coupling intensity is generally the highest in subtype A1 and lowest in A3. MPACs among various physiological conditions/disorders (p < 0.0001) and sleep stages (p < 0.0001 except S4) are tested. MPACs are found significantly stronger in light sleep than deep sleep (p < 0.0001). Physiological conditions/disorders show similar order in MPACs. Phase-amplitude dependence between δ and α/lowβ oscillations are examined as well. δ phase tent to phase-locked to α/lowβ amplitude in subtype A1 more than the rest. These results suggest that an elevated δ-α/lowβ MPACs can reflect some synchronization in CAP. Therefore, MPAC can be a potential tool to investigate neural interactions between different time scales, and δ-α/lowβ MPAC can serve as a feasible biomarker for sleep microstructure.

Anterior Thalamic High Frequency Band Activity Is Coupled with Theta Oscillations at Rest

Cross-frequency coupling (CFC) between slow and fast brain rhythms, in the form of phase–amplitude coupling (PAC), is proposed to enable the coordination of neural oscillatory activity required for cognitive processing. PAC has been identified in the neocortex and mesial temporal regions, varying according to the cognitive task being performed and also at rest. PAC has also been observed in the anterior thalamic nucleus (ATN) during memory processing. The thalamus is active during the resting state and has been proposed to be involved in switching between task-free cognitive states such as rest, in which attention is internally-focused, and externally-focused cognitive states, in which an individual engages with environmental stimuli. It is unknown whether PAC is an ongoing phenomenon during the resting state in the ATN, which is modulated during different cognitive states, or whether it only arises during the performance of specific tasks. We analyzed electrophysiological recordings of ATN activity during rest from seven patients who received thalamic electrodes implanted for treatment of pharmacoresistant focal epilepsy. PAC was identified between theta (4–6 Hz) phase and high frequency band (80–150 Hz) amplitude during rest in all seven patients, which diminished during engagement in tasks involving an external focus of attention. The findings are consistent with the proposal that theta–gamma coupling in the ATN is an ongoing phenomenon, which is modulated by task performance.