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

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.

Classifying epileptic phase-amplitude coupling in SEEG using complex-valued convolutional neural network

EEG phase-amplitude coupling (PAC), the amplitude of high-frequency oscillations modulated by the phase of low-frequency oscillations (LFOs), is a useful biomarker to localize epileptogenic tissue. It is commonly represented in a comodulogram of coupling strength but without coupled phase information. The phase-amplitude coupling is also found in the normal brain, and it is difficult to discriminate pathological phase-amplitude couplings from normal ones. This study proposes a novel approach based on complex-valued phase-amplitude coupling (CV-PAC) for classifying epileptic phase-amplitude coupling. The CV-PAC combines both the coupling strengths and the coupled phases of low-frequency oscillations. The complex-valued convolutional neural network (CV-CNN) is then used to classify epileptic CV-PAC. Stereo-electroencephalography (SEEG) recordings from nine intractable epilepsy patients were analyzed. The leave-one-out cross-validation is performed, and the area-under-curve (AUC) value is used as the indicator of the performance of different measures. Our result shows that the area-under-curve value is .92 for classifying epileptic CV-PAC using CV-CNN. The area-under-curve value decreases to .89, .80, and .88 while using traditional convolutional neural networks, support vector machine, and random forest, respectively. The phases of delta (1-4 Hz) and alpha (8-10 Hz) bands are different between epileptic and normal CV-PAC. The phase information of CV-PAC is important for improving classification performance. The proposed approach of CV-PAC/CV-CNN promises to identify more accurate epileptic brain activities for potential surgical intervention.

Transcerebral information coordination in directional hippocampus-prefrontal cortex network during working memory based on bimodal neural electrical signals

Working memory (WM) is a kind of advanced cognitive function, which requires the participation and cooperation of multiple brain regions. Hippocampus and prefrontal cortex are the main responsible brain regions for WM. Exploring information coordination between hippocampus and prefrontal cortex during WM is a frontier problem in cognitive neuroscience. In this paper, an advanced information theory analysis based on bimodal neural electrical signals (local field potentials, LFPs and spikes) was employed to characterize the transcerebral information coordination across the two brain regions. Firstly, LFPs and spikes were recorded simultaneously from rat hippocampus and prefrontal cortex during the WM task by using multi-channel in vivo recording technique. Then, from the perspective of information theory, directional hippocampus-prefrontal cortex networks were constructed by using transfer entropy algorithm based on spectral coherence between LFPs and spikes. Finally, transcerebral coordination of bimodal information at the brain-network level was investigated during acquisition and performance of the WM task. The results show that the transfer entropy in directional hippocampus-prefrontal cortex networks is related to the acquisition and performance of WM. During the acquisition of WM, the information flow, local information transmission ability and information transmission efficiency of the directional hippocampus-prefrontal networks increase over learning days. During the performance of WM, the transfer entropy from the hippocampus to prefrontal cortex plays a leading role for bimodal information coordination across brain regions and hippocampus has a driving effect on prefrontal cortex. Furthermore, bimodal information coordination in the hippocampus → prefrontal cortex network could predict WM during the successful performance of WM.

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.

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.

Multiscale Wavelet Transfer Entropy with Application to Corticomuscular Coupling Analysis

OBJECTIVE

Functional coupling between the motor cortex and muscle activity is commonly detected and quantified by cortico-muscular coherence (CMC) or Granger causality (GC) analysis, which are applicable only to linear couplings and are not sufficiently sensitive: some healthy subjects show no significant CMC and GC, and yet have good motor skills. The objective of this work is to develop measures of functional cortico-muscular coupling that have improved sensitivity and are capable of detecting both linear and non-linear interactions.

METHODS

A multiscale wavelet transfer entropy (TE) methodology is proposed. The methodology relies on a dyadic stationary wavelet transform to decompose electroencephalogram (EEG) and electromyogram (EMG) signals into functional bands of neural oscillations. Then, it applies TE analysis based on a range of embedding delay vectors to detect and quantify intra- and cross-frequency band cortico-muscular coupling at different time scales.

RESULTS

Our experiments with neurophysiological signals substantiate the potential of the developed methodologies for detecting and quantifying information flow between EEG and EMG signals for subjects with and without significant CMC or GC, including non-linear cross-frequency interactions, and interactions across different temporal scales. The obtained results are in agreement with the underlying sensorimotor neurophysiology.

CONCLUSION

These findings suggest that the concept of multiscale wavelet TE provides a comprehensive framework for analyzing cortex-muscle interactions.

SIGNIFICANCE

The proposed methodologies will enable developing novel insights into movement control and neurophysiological processes more generally.

Measuring spectrally-resolved information transfer

Information transfer, measured by transfer entropy, is a key component of distributed computation. It is therefore important to understand the pattern of information transfer in order to unravel the distributed computational algorithms of a system. Since in many natural systems distributed computation is thought to rely on rhythmic processes a frequency resolved measure of information transfer is highly desirable. Here, we present a novel algorithm, and its efficient implementation, to identify separately frequencies sending and receiving information in a network. Our approach relies on the invertible maximum overlap discrete wavelet transform (MODWT) for the creation of surrogate data in the computation of transfer entropy and entirely avoids filtering of the original signals. The approach thereby avoids well-known problems due to phase shifts or the ineffectiveness of filtering in the information theoretic setting. We also show that measuring frequency-resolved information transfer is a partial information decomposition problem that cannot be fully resolved to date and discuss the implications of this issue. Last, we evaluate the performance of our algorithm on simulated data and apply it to human magnetoencephalography (MEG) recordings and to local field potential recordings in the ferret. In human MEG we demonstrate top-down information flow in temporal cortex from very high frequencies (above 100Hz) to both similarly high frequencies and to frequencies around 20Hz, i.e. a complex spectral configuration of cortical information transmission that has not been described before. In the ferret we show that the prefrontal cortex sends information at low frequencies (4-8 Hz) to early visual cortex (V1), while V1 receives the information at high frequencies (> 125 Hz).

Prospective empirical test suite for energy practitioners

OBJECTIVE

To design a set of measures which were portable and cost-effective that scientists could use to determine competence of Energy Practitioners so that qualified practitioners could be employed in improving ongoing research accuracy.

DESIGN

This was a prospective study with sample of convenience.

SUBJECTS

213 subjects, 185 women and 28 men, were tested in this study.

OUTCOME MEASURES

Empirical outcome measures included Triaxial Extra Low Frequency Magnetic Field meter, Data Logging Multimeter, RF Field Spectrum Analyzer, Acoustimeter, Broadcast Frequency counter, digital pH meter, digital TDS meter, GDV and physiology suite including heart rate variability, galvanic skin response, respiration, EMG, EKG, temperature and blood volume pulse. Additional questions on ethics and body reading were included in the test.

RESULTS

Results suggest a range of tests which could be used to determine practitioner competence. Many of the energy practitioners tested consistently produced changes in the areas being measured past the error rate of the devices being used. Across the 13 measures, practitioner success ranged from 56.8% on the Acoustimeter to 100% on the Broadcast Frequency Counter measures with 95% CI. Tri Axial ELF magnetic field meter showed significance with practitioners producing oscillations of amplitude from the L hand at p< 0.01 with and effect size D of 1.5 and R hand p< 0.001 and an effect size D of 1.6. Practitioners demonstrated the ability to produce a change in pH beyond ±.1pH in 10 minutes at a Mean of 0.5 and a SD of 0.4 at a 95% CI of 0.48-0.58 and changes in TDS beyond+/-2% at a Mean of 36.7 and a SD of 35.2 at a 95% CI of 31.9-41.5. Other measures are discussed in detail.

CONCLUSIONS

This test presents a possible way to demonstrate a level of practitioner competence and improve the selection of energy practitioners for use in scientific studies of energy healing in the areas of full spectrum healing, laying-on-of-hands healing, Reiki, Qi Gong and Tai Chi.

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.

Functional Integration and Segregation in Multiplex Brain Networks for Alzheimer's Disease

Growing evidence links impairment of brain functions in Alzheimer's disease (AD) with disruptions of brain functional connectivity. However, whether the AD brain shows similar changes from a dynamic or cross-frequency view remains poorly explored. This paper provides an effective framework to investigate the properties of multiplex brain networks in AD considering inter-frequency and temporal dynamics. Using resting-state EEG signals, two types of multiplex networks were reconstructed separately considering the network interactions between different frequency bands or time points. We further applied multiplex network features to characterize functional integration and segregation of the cross-frequency or time-varying networks. Finally, machine learning methods were employed to evaluate the performance of multiplex-network-based indexes for detection of AD. Results revealed that the brain networks of AD patients are disrupted with reduced segregation particularly in the left occipital area for both cross-frequency and time-varying networks. However, the alteration of integration differs among brain regions and may show an increasing trend in the frontal area of AD brain. By combining the features of integration and segregation in time-varying networks, the best classification performance was achieved with an accuracy of 92.5%. These findings suggest that our multiplex framework can be applied to explore functional integration and segregation of brain networks and characterize the abnormalities of brain function. This may shed new light on the brain network analysis and extend our understanding of brain function in patients with neurological diseases.

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.

Linear and Nonlinear EEG-Based Functional Networks in Anxiety Disorders

Electrocortical network dynamics are integral to brain function. Linear and nonlinear connectivity applications enrich neurophysiological investigations into anxiety disorders. Discrete EEG-based connectivity networks are unfolding with some homogeneity for anxiety disorder subtypes. Attenuated delta/theta/beta connectivity networks, pertaining to anterior-posterior nodes, characterize panic disorder. Nonlinear measures suggest reduced connectivity of ACC as an executive neuro-regulator in germane "fear circuitry networks" might be more central than considered. Enhanced network complexity and theta network efficiency at rest define generalized anxiety disorder, with similar tonic hyperexcitability apparent in social anxiety disorder further extending to task-related/state functioning. Dysregulated alpha connectivity and integration of mPFC-ACC/mPFC-PCC relays implicated with attentional flexibility and choice execution/congruence neurocircuitry are observed in trait anxiety. Conversely, state anxiety appears to recruit converging delta and beta connectivity networks as panic, suggesting trait and state anxiety are modulated by discrete neurobiological mechanisms. Furthermore, EEG connectivity dynamics distinguish anxiety from depression, despite prevalent clinical comorbidity. Rethinking mechanisms implicated in the etiology, maintenance, and treatment of anxiety from the perspective of EEG network science across micro- and macroscales serves to shed light and move the field forward.

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.