Dissociating harmonic and non-harmonic phase-amplitude coupling in the human brain

Optogenetic stimulation of medial septal glutamatergic neurons modulates theta-gamma coupling in the hippocampus

Hippocampal cross-frequency theta-gamma coupling (TGC) is a basic mechanism for information processing, retrieval, and consolidation of long-term and working memory. While the role of entorhinal afferents in the modulation of hippocampal TGC is widely accepted, the influence of other main input to the hippocampus, from the medial septal area (MSA, the pacemaker of the hippocampal theta rhythm) is poorly understood. Optogenetics allows us to explore how different neuronal populations of septohippocampal circuits control neuronal oscillations in vivo. Rhythmic activation of septal glutamatergic neurons has been shown to drive hippocampal theta oscillations, but the role of these neuronal populations in information processing during theta activation has remained unclear. Here we investigated the influence of phasic activation of MSA glutamatergic neurons expressing channelrhodopsin II on theta-gamma coupling in the hippocampus. During the experiment, local field potentials of MSA and hippocampus of freely behaving mice were modulated by 470 nm light flashes with theta frequency (2-10) Hz. It was shown that both the power and the strength of modulation of gamma rhythm nested on hippocampal theta waves depend on the frequency of stimulation. The modulation of the amplitude of slow gamma rhythm (30-50 Hz) prevailed over modulation of fast gamma (55-100 Hz) during flash trains and the observed effects were specific for theta stimulation of MSA. We discuss the possibility that phasic depolarization of septal glutamatergic neurons controls theta-gamma coupling in the hippocampus and plays a role in memory retrieval and consolidation.

[Formula: see text]-[Formula: see text]: A Nonparametric Model for Neural Power Spectra Decomposition

The power spectra estimated from the brain recordings are the mixed representation of aperiodic transient activity and periodic oscillations, i.e., aperiodic component (AC) and periodic component (PC). Quantitative neurophysiology requires precise decomposition preceding parameterizing each component. However, the shape, statistical distribution, scale, and mixing mechanism of AC and PCs are unclear, challenging the effectiveness of current popular parametric models such as FOOOF, IRASA, BOSC, etc. Here, ξ- π was proposed to decompose the neural spectra by embedding the nonparametric spectra estimation with penalized Whittle likelihood and the shape language modeling into the expectation maximization framework. ξ- π was validated on the synthesized spectra with loss statistics and on the sleep EEG and the large sample iEEG with evaluation metrics and neurophysiological evidence. Compared to FOOOF, both the simulation presenting shape irregularities and the batch simulation with multiple isolated peaks indicated that ξ- π improved the fit of AC and PCs with less loss and higher F1-score in recognizing the centering frequencies and the number of peaks; the sleep EEG revealed that ξ- π produced more distinguishable AC exponents and improved the sleep state classification accuracy; the iEEG showed that ξ- π approached the clinical findings in peak discovery. Overall, ξ- π offered good performance in the spectra decomposition, which allows flexible parameterization using descriptive statistics or kernel functions. ξ- π is a seminal tool for brain signal decoding in fields such as cognitive neuroscience, brain-computer interface, neurofeedback, and brain diseases.

Analysis of Amplitude Modulation of EEG Based on Holo-Hilbert Spectrum Analysis During General Anesthesia

OBJECTIVE

The study aims to investigate the relationship between amplitude modulation (AM) of EEG and anesthesia depth during general anesthesia.

METHODS

In this study, Holo-Hilbert spectrum analysis (HHSA) was used to decompose the multichannel EEG signals of 15 patients to obtain the spatial distribution of AM in the brain. Subsequently, HHSA was applied to the prefrontal EEG (Fp1) obtained during general anesthesia surgery in 15 and 34 patients, and the α-θ and α-δ regions of feature (ROFs) were defined in Holo-Hilbert spectrum (HHS) and three features were derived to quantify AM in ROFs.

RESULTS

During anesthetized phase, an anteriorization of the spatial distribution of AMs of α-carrier in brain was observed, as well as AMs of α-θ and α-δ in the EEG of Fp1. The total power ([Formula: see text]), mean carrier frequency ([Formula: see text]) and mean amplitude frequency ([Formula: see text]) of AMs changed during different anesthesia states.

CONCLUSION

HHSA can effectively analyze the cross-frequency coupling of EEG during anesthesia and the AM features may be applied to anesthesia monitoring.

SIGNIFICANCE

The study provides a new perspective for the characterization of brain states during general anesthesia, which is of great significance for exploring new features of anesthesia monitoring.

The detection of absence seizures using cross-frequency coupling analysis with a deep learning network

High frequency oscillations are important novel biomarkers of epileptogenic tissue. The interaction of oscillations across different time scales is revealed as cross-frequency coupling (CFC) representing a high-order structure in the functional organization of brain rhythms. New artificial intelligence methods such as deep learning neural networks can provide powerful tools for automated analysis of EEG. Here we present a Stacked Sparse Autoencoder (SSAE) trained to recognize absence seizure activity based on the cross-frequency patterns within scalp EEG. We used EEG records from the Temple University Hospital database. Absence seizures (n = 94) from 12 patients were taken into analysis along with segments of background activity. Half of the records were selected randomly for network training and the second half were used for testing. Power-to-power coupling was calculated between all frequencies 2-120 Hz pairwise using the EEGLAB toolbox. The resulting CFC matrices were used as training or testing inputs to the autoencoder. The trained network was able to recognize background and seizure segments (not used in training) with a sensitivity of 96.3%, specificity of 99.8% and overall accuracy of 98.5%. Our results provide evidence that the SSAE neural networks can be used for automated detection of absence seizures within scalp EEG.

Over and above frequency: Gamma oscillations as units of neural circuit operations

Gamma oscillations (∼30-150 Hz) are widespread correlates of neural circuit functions. These network activity patterns have been described across multiple animal species, brain structures, and behaviors, and are usually identified based on their spectral peak frequency. Yet, despite intensive investigation, whether gamma oscillations implement causal mechanisms of specific brain functions or represent a general dynamic mode of neural circuit operation remains unclear. In this perspective, we review recent advances in the study of gamma oscillations toward a deeper understanding of their cellular mechanisms, neural pathways, and functional roles. We discuss that a given gamma rhythm does not per se implement any specific cognitive function but rather constitutes an activity motif reporting the cellular substrates, communication channels, and computational operations underlying information processing in its generating brain circuit. Accordingly, we propose shifting the attention from a frequency-based to a circuit-level definition of gamma oscillations.

Chronological changes in phase-amplitude coupling during epileptic seizures in temporal lobe epilepsy

OBJECTIVE

To analyze chronological changes in phase-amplitude coupling (PAC) and verify whether PAC analysis can diagnose epileptogenic zones during seizures.

METHODS

We analyzed 30 seizures in 10 patients with mesial temporal lobe epilepsy who had ictal discharges with preictal spiking followed by low-voltage fast activity patterns on intracranial electroencephalography. We used the amplitude of two high-frequency bands (ripples: 80-200 Hz, fast ripples: 200-300 Hz) and the phase of three slow wave bands (0.5-1 Hz, 3-4 Hz, and 4-8 Hz) for modulation index (MI) calculation from 2 minutes before seizure onset to seizure termination. We evaluated the accuracy of epileptogenic zone detection by MI, in which a combination of MI was better for diagnosis and analyzed patterns of chronological changes in MI during seizures.

RESULTS

MI_{Ripples/3-4 Hz} and MI_{Ripples/4-8 Hz} in the hippocampus were significantly higher than those in the peripheral regions from seizure onset. Corresponding to the phase on intracranial electroencephalography, MI_{Ripples/3-4 Hz} decreased once and subsequently increased again. MI_{Ripples/4-8 Hz} showed continuously high values.

CONCLUSIONS

Continuous measurement of MI_{Ripples/3-4 Hz} and MI_{Ripples/4-8 Hz} could help identify epileptogenic zones.

SIGNIFICANCE

PAC analysis of ictal epileptic discharges can help epileptogenic zone identification.

Direct modulation index: A measure of phase amplitude coupling for neurophysiology data

Neural communication across different spatial and temporal scales is a topic of great interest in clinical and basic science. Phase-amplitude coupling (PAC) has attracted particular interest due to its functional role in a wide range of cognitive and motor functions. Here, we introduce a novel measure termed the direct modulation index (dMI). Based on the classical modulation index, dMI provides an estimate of PAC that is (1) bound to an absolute interval between 0 and +1, (2) resistant against noise, and (3) reliable even for small amounts of data. To highlight the properties of this newly-proposed measure, we evaluated dMI by comparing it to the classical modulation index, mean vector length, and phase-locking value using simulated data. We ascertained that dMI provides a more accurate estimate of PAC than the existing methods and that is resilient to varying noise levels and signal lengths. As such, dMI permits a reliable investigation of PAC, which may reveal insights crucial to our understanding of functional brain architecture in key contexts such as behaviour and cognition. A Python toolbox that implements dMI and other measures of PAC is freely available at https://github.com/neurophysiological-analysis/FiNN.

Understanding Harmonic Structures Through Instantaneous Frequency

The analysis of harmonics and non-sinusoidal waveform shape in time-series data is growing in importance. However, a precise definition of what constitutes a harmonic is lacking. In this paper, we propose a rigorous definition of when to consider signals to be in a harmonic relationship based on an integer frequency ratio, constant phase, and a well-defined joint instantaneous frequency. We show this definition is linked to extrema counting and Empirical Mode Decomposition (EMD). We explore the mathematics of our definition and link it to results from analytic number theory. This naturally leads to us to define two classes of harmonic structures, termed strong and weak, with different extrema behaviour. We validate our framework using both simulations and real data. Specifically, we look at the harmonic structures in shallow water waves, the FitzHugh-Nagumo neuronal model, and the non-sinusoidal theta oscillation in rat hippocampus local field potential data. We further discuss how our definition helps to address mode splitting in nonlinear time-series decomposition methods. A clear understanding of when harmonics are present in signals will enable a deeper understanding of the functional roles of non-sinusoidal oscillations.

Harmoni: a Method for Eliminating Spurious Interactions due to the Harmonic Components in Neuronal Data

Cross-frequency synchronization (CFS) has been proposed as a mechanism for integrating spatially and spectrally distributed information in the brain. However, investigating CFS in Magneto- and Electroencephalography (MEG/EEG) is hampered by the presence of spurious neuronal interactions due to the non-sinusoidal waveshape of brain oscillations. Such waveshape gives rise to the presence of oscillatory harmonics mimicking genuine neuronal oscillations. Until recently, however, there has been no methodology for removing these harmonics from neuronal data. In order to address this long-standing challenge, we introduce a novel method (called HARMOnic miNImization - Harmoni) that removes the signal components which can be harmonics of a non-sinusoidal signal. Harmoni's working principle is based on the presence of CFS between harmonic components and the fundamental component of a non-sinusoidal signal. We extensively tested Harmoni in realistic EEG simulations. The simulated couplings between the source signals represented genuine and spurious CFS and within-frequency phase synchronization. Using diverse evaluation criteria, including ROC analyses, we showed that the within- and cross-frequency spurious interactions are suppressed significantly, while the genuine activities are not affected. Additionally, we applied Harmoni to real resting-state EEG data revealing intricate remote connectivity patterns which are usually masked by the spurious connections. Given the ubiquity of non-sinusoidal neuronal oscillations in electrophysiological recordings, Harmoni is expected to facilitate novel insights into genuine neuronal interactions in various research fields, and can also serve as a steppingstone towards the development of further signal processing methods aiming at refining within- and cross-frequency synchronization in electrophysiological recordings.

Automatic decomposition of electrophysiological data into distinct nonsinusoidal oscillatory modes

Neurophysiological signals are often noisy, nonsinusoidal, and consist of transient bursts. Extraction and analysis of oscillatory features (such as waveform shape and cross-frequency coupling) in such data sets remains difficult. This limits our understanding of brain dynamics and its functional importance. Here, we develop iterated masking empirical mode decomposition (itEMD), a method designed to decompose noisy and transient single-channel data into relevant oscillatory modes in a flexible, fully data-driven way without the need for manual tuning. Based on empirical mode decomposition (EMD), this technique can extract single-cycle waveform dynamics through phase-aligned instantaneous frequency. We test our method by extensive simulations across different noise, sparsity, and nonsinusoidality conditions. We find itEMD significantly improves the separation of data into distinct nonsinusoidal oscillatory components and robustly reproduces waveform shape across a wide range of relevant parameters. We further validate the technique on multimodal, multispecies electrophysiological data. Our itEMD extracts known rat hippocampal θ waveform asymmetry and identifies subject-specific human occipital α without any prior assumptions about the frequencies contained in the signal. Notably, it does so with significantly less mode mixing compared with existing EMD-based methods. By reducing mode mixing and simplifying interpretation of EMD results, itEMD will enable new analyses into functional roles of neural signals in behavior and disease.

NEW & NOTEWORTHY We introduce a novel, data-driven method to identify oscillations in neural recordings. This approach is based on empirical mode decomposition and reduces mixing of components, one of its main problems. The technique is validated and compared with existing methods using simulations and real data. We show our method better extracts oscillations and their properties in highly noisy and nonsinusoidal datasets.

Detecting Phase-Synchrony Connectivity Anomalies in EEG Signals. Application to Dyslexia Diagnosis

Objective Dyslexia diagnosis is a challenging task, since traditional diagnosis methods are not based on biological markers but on behavioural tests. Although dyslexia diagnosis has been addressed by these tests in clinical practice, it is difficult to extract information about the brain processes involved in the different tasks and, then, to go deeper into its biological basis. Thus, the use of biomarkers can contribute not only to the diagnosis but also to a better understanding of specific learning disorders such as dyslexia. In this work, we use Electroencephalography (EEG) signals to discover differences among controls and dyslexic subjects using signal processing and artificial intelligence techniques. Specifically, we measure phase synchronization among channels, to reveal the functional brain network activated during auditory processing. On the other hand, to explore synchronicity patterns risen by low-level auditory processing, we used specific stimuli consisting in band-limited white noise, modulated in amplitude at different frequencies. The differential information contained in the functional (i.e., synchronization) network has been processed by an anomaly detection system that addresses the problem of subjects variability by an outlier-detection method based on vector quantization. The results, obtained for 7 years-old children, show that the proposed method constitutes an useful tool for clinical use, with the area under ROC curve (AUC) values up to 0.95 in differential diagnosis tasks.

Targeting neural oscillations with transcranial alternating current stimulation

Neural oscillations at the network level synchronize activity between regions and temporal scales. Transcranial alternating current stimulation (tACS), the delivery of low-amplitude electric current to the scalp, provides a tool for investigating the causal role of neural oscillations in cognition. The parameter space for tACS is vast and optimization is required in terms of temporal and spatial targeting. We review emerging techniques and suggest novel approaches that capitalize on the non-sinusoidal and transient nature of neural oscillations and leverage the flexibility provided by a customizable electrode montage and electrical waveform. The customizability and safety profile of tACS make it a promising tool for precision intervention in psychiatric illnesses.

Revealing the Dynamic Nature of Amplitude Modulated Neural Entrainment With Holo-Hilbert Spectral Analysis

Patterns in external sensory stimuli can rapidly entrain neuronally generated oscillations observed in electrophysiological data. Here, we manipulated the temporal dynamics of visual stimuli with cross-frequency coupling (CFC) characteristics to generate steady-state visual evoked potentials (SSVEPs). Although CFC plays a pivotal role in neural communication, some cases reporting CFC may be false positives due to non-sinusoidal oscillations that can generate artificially inflated coupling values. Additionally, temporal characteristics of dynamic and non-linear neural oscillations cannot be fully derived with conventional Fourier-based analyses mainly due to trade off of temporal resolution for frequency precision. In an attempt to resolve these limitations of linear analytical methods, Holo-Hilbert Spectral Analysis (HHSA) was investigated as a potential approach for examination of non-linear and non-stationary CFC dynamics in this study. Results from both simulation and SSVEPs demonstrated that temporal dynamic and non-linear CFC features can be revealed with HHSA. Specifically, the results of simulation showed that the HHSA is less affected by the non-sinusoidal oscillation and showed possible cross frequency interactions embedded in the simulation without any a priori assumptions. In the SSVEPs, we found that the time-varying cross-frequency interaction and the bidirectional coupling between delta and alpha/beta bands can be observed using HHSA, confirming dynamic physiological signatures of neural entrainment related to cross-frequency coupling. These findings not only validate the efficacy of the HHSA in revealing the natural characteristics of signals, but also shed new light on further applications in analysis of brain electrophysiological data with the aim of understanding the functional roles of neuronal oscillation in various cognitive functions.

Methodological considerations for studying neural oscillations

Neural oscillations are ubiquitous across recording methodologies and species, broadly associated with cognitive tasks, and amenable to computational modelling that investigates neural circuit generating mechanisms and neural population dynamics. Because of this, neural oscillations offer an exciting potential opportunity for linking theory, physiology and mechanisms of cognition. However, despite their prevalence, there are many concerns-new and old-about how our analysis assumptions are violated by known properties of field potential data. For investigations of neural oscillations to be properly interpreted, and ultimately developed into mechanistic theories, it is necessary to carefully consider the underlying assumptions of the methods we employ. Here, we discuss seven methodological considerations for analysing neural oscillations. The considerations are to (1) verify the presence of oscillations, as they may be absent; (2) validate oscillation band definitions, to address variable peak frequencies; (3) account for concurrent non-oscillatory aperiodic activity, which might otherwise confound measures; measure and account for (4) temporal variability and (5) waveform shape of neural oscillations, which are often bursty and/or nonsinusoidal, potentially leading to spurious results; (6) separate spatially overlapping rhythms, which may interfere with each other; and (7) consider the required signal-to-noise ratio for obtaining reliable estimates. For each topic, we provide relevant examples, demonstrate potential errors of interpretation, and offer suggestions to address these issues. We primarily focus on univariate measures, such as power and phase estimates, though we discuss how these issues can propagate to multivariate measures. These considerations and recommendations offer a helpful guide for measuring and interpreting neural oscillations.