Phase-amplitude Cross-frequency Coupling Research Articles

Rhythmic Temporal Cues Coordinate Cross-frequency Phase-amplitude Coupling during Memory Encoding.

Accumulating evidence suggests that rhythmic temporal cues in the environment influence the encoding of information into long-term memory. Here, we test the hypothesis that these mnemonic effects of rhythm reflect the coupling of high-frequency (gamma) oscillations to entrained lower-frequency oscillations synchronized to the beat of the rhythm. In Study 1, we first test this hypothesis in the context of global effects of rhythm on memory, when memory is superior for visual stimuli presented in rhythmic compared with arrhythmic patterns at encoding [Jones, A., & Ward, E. V. Rhythmic temporal structure at encoding enhances recognition memory, Journal of Cognitive Neuroscience, 31, 1549-1562, 2019]. We found that rhythmic presentation of visual stimuli during encoding was associated with greater phase-amplitude coupling (PAC) between entrained low-frequency (delta) oscillations and higher-frequency (gamma) oscillations. In Study 2, we next investigated cross-frequency PAC in the context of local effects of rhythm on memory encoding, when memory is superior for visual stimuli presented in-synchrony compared with out-of-synchrony with a background auditory beat (Hickey et al., 2020). We found that the mnemonic effect of rhythm in this context was again associated with increased cross-frequency PAC between entrained low-frequency (delta) oscillations and higher-frequency (gamma) oscillations. Furthermore, the magnitude of gamma power modulations positively scaled with the subsequent memory benefit for in- versus out-of-synchrony stimuli. Together, these results suggest that the influence of rhythm on memory encoding may reflect the temporal coordination of higher-frequency gamma activity by entrained low-frequency oscillations.

126. Challenges Identifying Peak Frequencies of Cross-Frequency Phase-Amplitude Coupling: Implications for Frequency Personalization of tACS in Clinical Trials

126. Challenges Identifying Peak Frequencies of Cross-Frequency Phase-Amplitude Coupling: Implications for Frequency Personalization of tACS in Clinical Trials

Biomimetic Deep Learning Networks With Applications to Epileptic Spasms and Seizure Prediction.

In this study, we present a novel biomimetic deep learning network for epileptic spasms and seizure prediction and compare its performance with state-of-the-art conventional machine learning models. Our proposed model incorporates modular Volterra kernel convolutional networks and bidirectional recurrent networks in combination with the phase amplitude cross-frequency coupling features derived from scalp EEG. They are applied to the standard CHB-MIT dataset containing focal epilepsy episodes as well as two other datasets from the Montefiore Medical Center and the University of California Los Angeles that provide data of patients experiencing infantile spasm (IS) syndrome. Overall, in this study, the networks can produce accurate predictions (100%) and significant detection latencies (10 min). Furthermore, the biomimetic network outperforms conventional ones by producing no false positives. Biomimetic neural networks utilize extensive knowledge about processing and learning in the electrical networks of the brain. Predicting seizures in adults can improve their quality of life. Epileptic spasms in infants are part of a particular seizure type that needs identifying when suspicious behaviors are noticed in babies. Predicting epileptic spasms within a given time frame (the prediction horizon) suggests their existence and allows an epileptologist to flag an EEG trace for future review.

Effect of Phase Clustering Bias on Phase-Amplitude Coupling for Emotional EEG.

Emotions are thought to be related to distinct patterns of neural oscillations, but the interactions among multi-frequency neural oscillations during different emotional states lack full exploration. Phase-amplitude coupling is a promising tool for understanding the complexity of the neurophysiological system, thereby playing a crucial role in revealing the physiological mechanisms underlying emotional electroencephalogram (EEG). However, the non-sinusoidal characteristics of EEG lead to the non-uniform distribution of phase angles, which could potentially affect the analysis of phase-amplitude coupling. Removing phase clustering bias (PCB) can uniform the distribution of phase angles, but the effect of this approach is unknown on emotional EEG phase-amplitude coupling. This study aims to explore the effect of PCB on cross-frequency phase-amplitude coupling for emotional EEG. The technique of removing PCB was implemented on a publicly accessible emotional EEG dataset to calculate debiased phase-amplitude coupling. Statistical analysis and classification were conducted to compare the difference in emotional EEG phase-amplitude coupling prior to and post the removal of PCB. Emotional EEG phase-amplitude coupling values are overestimated due to PCB. Removing PCB enhances the difference in coupling strength between fear and happy emotions in the frontal lobe. Comparable emotion recognition performance was achieved with fewer features after removing PCB. These findings suggest that removing PCB enhances the difference in emotional EEG phase-amplitude coupling patterns and generates features that contain more emotional information. Removing PCB may be advantageous for analyzing emotional EEG phase-amplitude coupling and recognizing human emotions.

Local field potentials and single unit dynamics in motor cortex of unconstrained macaques during different behavioral states

Different sleep stages have been shown to be vital for a variety of brain functions, including learning, memory, and skill consolidation. However, our understanding of neural dynamics during sleep and the role of prominent LFP frequency bands remain incomplete. To elucidate such dynamics and differences between behavioral states we collected multichannel LFP and spike data in primary motor cortex of unconstrained macaques for up to 24 h using a head-fixed brain-computer interface (Neurochip3). Each 8-s bin of time was classified into awake-moving (Move), awake-resting (Rest), REM sleep (REM), or non-REM sleep (NREM) by using dimensionality reduction and clustering on the average spectral density and the acceleration of the head. LFP power showed high delta during NREM, high theta during REM, and high beta when the animal was awake. Cross-frequency phase-amplitude coupling typically showed higher coupling during NREM between all pairs of frequency bands. Two notable exceptions were high delta-high gamma and theta-high gamma coupling during Move, and high theta-beta coupling during REM. Single units showed decreased firing rate during NREM, though with increased short ISIs compared to other states. Spike-LFP synchrony showed high delta synchrony during Move, and higher coupling with all other frequency bands during NREM. These results altogether reveal potential roles and functions of different LFP bands that have previously been unexplored.

Repetitive sensorimotor mu-alpha phase-targeted afferent stimulation produces no phase-dependent plasticity related changes in somatosensory evoked potentials or sensory thresholds.

Phase-dependent plasticity has been proposed as a neurobiological mechanism by which oscillatory phase-amplitude cross-frequency coupling mediates memory process in the brain. Mimicking this mechanism, real-time EEG oscillatory phase-triggered transcranial magnetic stimulation (TMS) has successfully induced LTP-like changes in corticospinal excitability in the human motor cortex. Here we asked whether EEG phase-triggered afferent stimulation alone, if repetitively applied to the peaks, troughs, or random phases of the sensorimotor mu-alpha rhythm, would be sufficient to modulate the strength of thalamocortical synapses as assessed by changes in somatosensory evoked potential (SEP) N20 and P25 amplitudes and sensory thresholds (ST). Specifically, we applied 100 Hz triplets of peripheral electrical stimulation (PES) to the thumb, middle, and little finger of the right hand in pseudorandomized trials, with the afferent input from each finger repetitively and consistently arriving either during the cortical mu-alpha trough or peak or at random phases. No significant changes in SEP amplitudes or ST were observed across the phase-dependent PES intervention. We discuss potential limitations of the study and argue that suboptimal stimulation parameter choices rather than a general lack of phase-dependent plasticity in thalamocortical synapses are responsible for this null finding. Future studies should further explore the possibility of phase-dependent sensory stimulation.

The frontooccipital interaction mechanism of high-frequency acoustoelectric signal.

Based on acoustoelectric effect, acoustoelectric brain imaging has been proposed, which is a high spatiotemporal resolution neural imaging method. At the focal spot, brain electrical activity is encoded by focused ultrasound, and corresponding high-frequency acoustoelectric signal is generated. Previous studies have revealed that acoustoelectric signal can also be detected in other non-focal brain regions. However, the processing mechanism of acoustoelectric signal between different brain regions remains sparse. Here, with acoustoelectric signal generated in the left primary visual cortex, we investigated the spatial distribution characteristics and temporal propagation characteristics of acoustoelectric signal in the transmission. We observed a strongest transmission strength within the frontal lobe, and the global temporal statistics indicated that the frontal lobe features in acoustoelectric signal transmission. Then, cross-frequency phase-amplitude coupling was used to investigate the coordinated activity in the AE signal band range between frontal and occipital lobes. The results showed that intra-structural cross-frequency coupling and cross-structural coupling co-occurred between these two lobes, and, accordingly, high-frequency brain activity in the frontal lobe was effectively coordinated by distant occipital lobe. This study revealed the frontooccipital long-range interaction mechanism of acoustoelectric signal, which is the foundation of improving the performance of acoustoelectric brain imaging.

Phase-amplitude coupling of Go/Nogo task-related neuronal oscillation decreases for humans with insufficient sleep.

Phase-amplitude coupling (PAC) across frequency might be associated with the long-range synchronization of brain networks, facilitating the spatiotemporal integration of multiple cell assemblies for information transmission during inhibitory control. However, sleep problems may affect these cortical information transmissions based on cross-frequency PAC, especially when humans work in environments of social isolation. This study aimed to evaluate changes in the theta-beta/gamma PAC of task-related electroencephalography (EEG) for humans with insufficient sleep. Here, we monitored the EEG signals of 60 healthy volunteers and 18 soldiers in the normal environment, performing a Go/Nogo task. Soldiers also participated in the same test in isolated cabins. These measures demonstrated theta-beta PACs between the frontal and central-parietal, and robust theta-gamma PACs between the frontal and occipital cortex. Unfortunately, these PACs significantly decreased when humans experienced insufficient sleep, which was positively correlated with the behavioral performance of inhibitory control. The evaluation of theta-beta/gamma PAC of Go/Nogo task-related EEG is necessary to help understand the different influences of sleep problems in humans.

Cross-frequency coupling between slow harmonics via the real brainstem oscillators: An in vivo animal study.

Brain waves of discrete rhythms (gamma to delta frequency ranges) are ubiquitously recorded and interpreted with respect to probable corresponding specific functions. The most challenging idea of interpreting varied frequencies of brain waves has been postulated as a communication mechanism in which different neuronal assemblies use specific ranges of frequencies cooperatively. One promising candidate is cross-frequency coupling (CFC), in which some neuronal assemblies efficiently utilize the fastest gamma range brain waves as an information carrier (phase-amplitude CFC); however, phase-phase CFC via the slowest delta and theta waves has rarely been described to date. Moreover, CFC has rarely been reported in the animal brainstem including humans, which most likely utilizes the slowest waves (delta and theta ranges). Harmonic waves are characterized by the presence of a fundamental frequency with several overtones, multiples of the fundamental frequency. Rat brainstem waves seemed to consist of slow harmonics with different frequencies that could cooperatively produce a phase-phase CFC. Harmonic rhythms of different frequency ranges can cross-couple with each other to sustain robust and resilient consonance via real oscillators, notwithstanding any perturbations.

Comparative analysis of multifaceted neural effects associated with varying endogenous cognitive load

Contemporary neuroscience has firmly established that mental state variation concurs with changes in neural dynamic activity in a complex way that a one-to-one mapping cannot describe. To explore the scenario of the multifaceted changes in neural dynamics associated with simple mental state variation, we took cognitive load – a common cognitive manipulation in psychology – as a venue to characterize how multiple neural dynamic features are simultaneously altered by the manipulation and how their sensitivity differs. Electroencephalogram was collected from 152 participants performing stimulus-free tasks with different demands. The results show that task demand alters wide-ranging neural dynamic features, including band-specific oscillations across broad frequency bands, scale-free dynamics, and cross-frequency phase-amplitude coupling. The scale-free dynamics outperformed others in indexing cognitive load variation. This study demonstrates a complex relationship between cognitive dynamics and neural dynamics, which points to a necessity to integrate multifaceted neural dynamic features when studying mind-brain relationship in the future.

Transcranial Alternating Current Stimulation Alters Auditory Steady-State Oscillatory Rhythms and Their Cross-Frequency Couplings.

Auditory cortical plasticity deficits in schizophrenia are evidenced with electroencephalographic (EEG)-derived biomarkers, including the 40-Hz auditory steady-state response (ASSR). Aiming to understand the underlying oscillatory mechanisms contributing to the 40-Hz ASSR, we examined its response to transcranial alternating current stimulation (tACS) applied bilaterally to the temporal lobe of 23 healthy participants. Although not responding to gamma tACS, the 40-Hz ASSR was modulated by theta tACS (vs sham tACS), with reductions in gamma power and phase locking being accompanied by increases in theta-gamma phase-amplitude cross-frequency coupling. Results reveal that oscillatory changes induced by frequency-tuned tACS may be one approach for targeting and modulating auditory plasticity in normal and diseased brains.

Using linear parameter varying autoregressive models to measure cross frequency couplings in EEG signals.

For years now, phase-amplitude cross frequency coupling (CFC) has been observed across multiple brain regions under different physiological and pathological conditions. It has been suggested that CFC serves as a mechanism that facilitates communication and information transfer between local and spatially separated neuronal populations. In non-invasive brain computer interfaces (BCI), CFC has not been thoroughly explored. In this work, we propose a CFC estimation method based on Linear Parameter Varying Autoregressive (LPV-AR) models and we assess its performance using both synthetic data and electroencephalographic (EEG) data recorded during attempted arm/hand movements of spinal cord injured (SCI) participants. Our results corroborate the potentiality of CFC as a feature for movement attempt decoding and provide evidence of the superiority of our proposed CFC estimation approach compared to other commonly used techniques.

Vagus Nerve Stimulation Modulates Phase-Amplitude Coupling in Thalamic Local Field Potentials

ObjectiveThe antiseizure effects of vagus nerve stimulation (VNS) are thought to be mediated by the modulation of afferent thalamocortical circuitry. Cross-frequency phase-amplitude coupling (PAC) is a mechanism of hierarchical network coordination across multiple spatiotemporal scales. In this study, we leverage local field potential (LFP) recordings from the centromedian (CM) (n = 3) and anterior (ATN) (n = 2) nuclei in five patients with tandem thalamic deep brain stimulation and VNS to study neurophysiological changes in the thalamus in response to VNS. Materials and MethodsBipolar LFP data were recorded from contact pairs spanning target nuclei in VNS “on” and “off” states. ResultsActive VNS was associated with increased PAC between theta, alpha, and beta phase and gamma amplitude in CM (q < 0.05). Within the ATN, PAC changes also were observed, although these were less robust. In both nuclei, active VNS also modulated interhemispheric bithalamic functional connectivity. ConclusionsWe report that VNS is associated with enhanced PAC and coordinated interhemispheric interactions within and between thalamic nuclei, respectively. These findings advance understanding of putative neurophysiological effects of acute VNS and contextualize previous animal and human studies showing distributed cortical synchronization after VNS.

Cross-frequency phase-amplitude coupling in repetitive movements in patients with Parkinson's disease.

Bradykinesia is a cardinal motor symptom in Parkinson's disease (PD), the pathophysiology of which is not fully understood. We analyzed the role of cross-frequency coupling of oscillatory cortical activity in motor impairment in patients with PD and healthy controls. High-density EEG signals were recorded during various motor activities and at rest. Patients performed a repetitive finger-pressing task normally, but were slower than controls during tapping. Phase-amplitude coupling (PAC) between β (13-30 Hz) and broadband γ (50-150 Hz) was computed from individual EEG source signals in the premotor, primary motor, and primary somatosensory cortices, and the primary somatosensory complex. In all four regions, averaging the entire movement period resulted in higher PAC in patients than in controls for the resting condition and the pressing task (similar performance between groups). However, this was not the case for the tapping tasks where patients performed slower. This suggests the strength of state-related β-γ PAC does not determine Parkinsonian bradykinesia. Examination of the dynamics of oscillatory EEG signals during motor transitions revealed a distinctive motif of PAC rise and decay around press onset. This pattern was also present at press offset and slow tapping onset, linking such idiosyncratic PAC changes to transitions between different movement states. The transition-related PAC modulation in patients was similar to controls in the pressing task but flattened during slow tapping, which related to normal and abnormal performance, respectively. These findings suggest that the dysfunctional evolution of neuronal population dynamics during movement execution is an important component of the pathophysiology of Parkinsonian bradykinesia.NEW & NOTEWORTHY Our findings using noninvasive EEG recordings provide evidence that PAC dynamics might play a role in the physiological cortical control of movement execution and may encode transitions between movement states. Results in patients with Parkinson's disease suggest that bradykinesia is related to a deficit of the dynamic regulation of PAC during movement execution rather than its absolute strength. Our findings may contribute to the development of a new concept of the pathophysiology of bradykinesia.

Reduced Cross-Frequency Coupling and Daytime Sleepiness in Obstructive Sleep Apnea Patients.

Simple SummaryObstructive sleep apnea (OSA) is one of the most common breathing-related sleep disorders. The processes that take place in specific areas of the brain during distinct sleep stages and specific respiratory events are suspected to be impaired in OSA patients. These brain processes may be described in complex (mathematical) terms. Using one of these descriptions (phase–amplitude cross-frequency coupling), we demonstrated in electroencephalographic (EEG) recordings of OSA patients that the process sequences in certain areas of the brain are altered in distinct sleep stages of OSA patients compared to patients who do not suffer from clinically relevant OSA. In addition, we were able to find a physiological marker that assesses the severity of daytime sleepiness, one of the main symptoms of OSA. This study supports the hypothesis that OSA is a neuronal/neuromuscular disorder. Thus, it contributes to a better understanding of the so-far-unexplained cause for the development of OSA and opens new possibilities for the exploration of alternative therapeutic approaches.Obstructive sleep apnea (OSA) is associated with sleep-stage- and respiratory-event-specific sensorimotor cortico-muscular disconnection. The modulation of phase–amplitude cross-frequency coupling (PACFC) may influence information processing throughout the brain. We investigated whether sleep-stage-specific PACFC is impaired at the sensorimotor areas in OSA patients. C3 and C4 electrode EEG polysomnography recordings of 170 participants were evaluated. Different frequency band combinations were used to compute CFC modulation index (MI) to assess if MI differs between OSA and non-significant OSA patients in distinct sleep stages. We tested if the CFC-MI could predict daytime sleepiness in OSA. Theta–gamma CFC-MI at cortical sensorimotor areas was significantly reduced during all sleep stages; the delta–alpha CFC-MI was significantly reduced during REM and N1 while increasing during N2 in patients with respiratory disturbance index (RDI) > 15/h compared to those with RDI ≤ 15/h. A sleep stage classification using MI values was achieved in both patient groups. Theta–gamma MI during N2 and N3 could predict RDI and Epworth Sleepiness Scale, while delta–alpha MI during REM predicted RDI. This increase in disconnection at the cortical sensorimotor areas with increasing respiratory distress during sleep supports a cortical motor dysfunction in OSA patients. The MI provides an objective marker to quantify subjective sleepiness and respiratory distress in OSA.

Cross-Frequency Brain Network Dynamics Support Pitch Change Detection.

Processing auditory sequences involves multiple brain networks and is crucial to complex perception associated with music appreciation and speech comprehension. We used time-resolved cortical imaging in a pitch change detection task to detail the underlying nature of human brain network activity, at the rapid time scales of neurophysiology. In response to tone sequence presentation to the participants, we observed slow inter-regional signaling at the pace of tone presentations (2-4 Hz) that was directed from auditory cortex toward both inferior frontal and motor cortices. Symmetrically, motor cortex manifested directed influence onto auditory and inferior frontal cortices via bursts of faster (15-35 Hz) activity. These bursts occurred precisely at the expected latencies of each tone in a sequence. This expression of interdependency between slow/fast neurophysiological activity yielded a form of local cross-frequency phase-amplitude coupling in auditory cortex, which strength varied dynamically and peaked when pitch changes were anticipated. We clarified the mechanistic relevance of these observations in relation to behavior by including a group of individuals afflicted by congenital amusia, as a model of altered function in processing sound sequences. In amusia, we found a depression of inter-regional slow signaling toward motor and inferior frontal cortices, and a chronic overexpression of slow/fast phase-amplitude coupling in auditory cortex. These observations are compatible with a misalignment between the respective neurophysiological mechanisms of stimulus encoding and internal predictive signaling, which was absent in controls. In summary, our study provides a functional and mechanistic account of neurophysiological activity for predictive, sequential timing of auditory inputs.SIGNIFICANCE STATEMENT Auditory sequences are processed by extensive brain networks, involving multiple systems. In particular, fronto-temporal brain connections participate in the encoding of sequential auditory events, but so far, their study was limited to static depictions. This study details the nature of oscillatory brain activity involved in these inter-regional interactions in human participants. It demonstrates how directed, polyrhythmic oscillatory interactions between auditory and motor cortical regions provide a functional account for predictive timing of incoming items in an auditory sequence. In addition, we show the functional relevance of these observations in relation to behavior, with data from both normal hearing participants and a rare cohort of individuals afflicted by congenital amusia, which we considered here as a model of altered function in processing sound sequences.

Phase-Amplitude Coupling Brain Networks in Children with Attention-Deficit/Hyperactivity Disorder.

In cognitive neuroscience, there is an increasing interest in identifying and understanding the synchronization of distinct neural oscillations with different frequencies that might support dynamic communication within the brain. This study explored the cross-frequency phase-amplitude coupling brain network characteristics of resting-state electroencephalograms between 30 children with attention-deficit/hyperactivity disorder (ADHD) and 30 age-matched typically developing children. Compared with control group, children with ADHD show increased coupling intensity and altered distribution patterns of dominant paired channels, especially in the δ-γH, θ-γH, α-γH, βL-γH, and βH-γH coupling networks. Regarding graph theory properties, the characteristic path length, the mean clustering coefficient, the global efficiency, and the mean local efficiency significant difference in many cross-frequency coupling networks, especially in the δ-γH, θ-γH, α-γH, βL-γH, and βH-γH coupling networks. The area under the receiver operating characteristic curve (AUC) in low-frequency coupling with a high-gamma frequency was larger than that in coupling with low-gamma frequency (AUC values of δ-γL, θ-γL, α-γL, βL-γL, βH-γL, δ-γH, θ-γH, α-γH, βL-γH, and βH-γH were 0.794, 0.722, 0.666, 0.570, 0.881, 0.992, 0.998, 0.998, 0.989, and 0.974, respectively). These findings demonstrate altered coupling intensity and disrupted topological organization of coupling networks, support the altered brain network theory in children with ADHD. The coupling intensity and graph theory properties of low-frequency coupling with high-gamma frequency were promising resting-state electroencephalogram biomarkers of ADHD in children.

Toward the Identification of Neurophysiological Biomarkers for Alzheimer's Disease in Down Syndrome: A Potential Role for Cross-Frequency Phase-Amplitude Coupling Analysis.

Cross-frequency coupling (CFC) mechanisms play a central role in brain activity. Pathophysiological mechanisms leading to many brain disorders, such as Alzheimer's disease (AD), may produce unique patterns of brain activity detectable by electroencephalography (EEG). Identifying biomarkers for AD diagnosis is also an ambition among research teams working in Down syndrome (DS), given the increased susceptibility of people with DS to develop early-onset AD (DS-AD). Here, we review accumulating evidence that altered theta-gamma phase-amplitude coupling (PAC) may be one of the earliest EEG signatures of AD, and therefore may serve as an adjuvant tool for detecting cognitive decline in DS-AD. We suggest that this field of research could potentially provide clues to the biophysical mechanisms underlying cognitive dysfunction in DS-AD and generate opportunities for identifying EEG-based biomarkers with diagnostic and prognostic utility in DS-AD.

Phase-Amplitude Coupling Features Accurately Classify Multiple Sub-States Within a Seizure Episode.

Epilepsy is frequently characterized by convulsive seizures, which are often followed by a postictal EEG suppression state (PGES). The ability to automatically detect and monitor seizure progression and postictal state can allow for early warning of seizure onset, timely intervention in seizures themselves, as well as identification of major complications in epilepsy such as status epilepticus and sudden unexpected death in epilepsy (SUDEP). To test whether it is possible to reliably differentiate these ictal and postictal states, we investigated 52 seizure records (both intracranial and scalp EEG) from 19 patients. Phase-amplitude cross-frequency coupling was calculated for each recording and used as an input to a convolutional neural network model, achieving the mean accuracy of 0.890.09 across all classes, with the worst class accuracy of 0.73 for one of the later ictal sub-states. When the trained model was applied to SUDEP patient data, it classified seizure recordings as primarily interictal and PGES-like state (70% and 26%, respectively), highlighting the fact that in SUDEP patients seizures primarily exist in postictal states and don't show the ictal sub-state evolution. These results suggest that using frequency coupling markers with a machine learning algorithm can reliably identify ictal and postictal sub-states, which can open up opportunities for novel monitoring and management approaches in epilepsy.

Estimating Phase Amplitude Coupling between Neural Oscillations Based on Permutation and Entropy

Cross-frequency phase–amplitude coupling (PAC) plays an important role in neuronal oscillations network, reflecting the interaction between the phase of low-frequency oscillation (LFO) and amplitude of the high-frequency oscillations (HFO). Thus, we applied four methods based on permutation analysis to measure PAC, including multiscale permutation mutual information (MPMI), permutation conditional mutual information (PCMI), symbolic joint entropy (SJE), and weighted-permutation mutual information (WPMI). To verify the ability of these four algorithms, a performance test including the effects of coupling strength, signal-to-noise ratios (SNRs), and data length was evaluated by using simulation data. It was shown that the performance of SJE was similar to that of other approaches when measuring PAC strength, but the computational efficiency of SJE was the highest among all these four methods. Moreover, SJE can also accurately identify the PAC frequency range under the interference of spike noise. All in all, the results demonstrate that SJE is better for evaluating PAC between neural oscillations.