Towards a proper estimation of phase synchronization from time series

Instantaneous phase of rhythmic behaviour under volitional control

The phase of signals representing cyclic behavioural patterns provides valuable information for understanding the mechanisms driving the observed behaviours. Methods usually adopted to estimate the phase, which are based on projecting the signal onto the complex plane, have strict requirements on its frequency content, which limits their application. To overcome these limitations, input signals can be processed using band-pass filters or decomposition techniques. In this paper, we briefly review these approaches and propose a new one. Our approach is based on the principles of Empirical Mode Decomposition (EMD), but unlike EMD, it does not aim to decompose the input signal. This avoids the many problems that can occur when extracting a signal's components one by one. The proposed approach estimates the phase of experimental signals that have one main oscillatory component modulated by slower activity and perturbed by weak, sparse, or random activity at faster time scales. We illustrate how our approach works by estimating the phase dynamics of synthetic signals and real-world signals representing knee angles during flexion/extension activity, heel height during gait, and the activity of different organs involved in speech production.

Studying time-resolved functional connectivity via communication theory: on the complementary nature of phase synchronization and sliding window Pearson correlation

Time-resolved functional connectivity (trFC) assesses the time-resolved coupling between brain regions using functional magnetic resonance imaging (fMRI) data. This study aims to compare two techniques used to estimate trFC, to investigate their similarities and differences when applied to fMRI data. These techniques are the sliding window Pearson correlation (SWPC), an amplitude-based approach, and phase synchronization (PS), a phase-based technique. To accomplish our objective, we used resting-state fMRI data from the Human Connectome Project (HCP) with 827 subjects (repetition time: 0.7s) and the Function Biomedical Informatics Research Network (fBIRN) with 311 subjects (repetition time: 2s), which included 151 schizophrenia patients and 160 controls. Our simulations reveal distinct strengths in two connectivity methods: SWPC captures high-magnitude, low-frequency connectivity, while PS detects low-magnitude, high-frequency connectivity. Stronger correlations between SWPC and PS align with pronounced fMRI oscillations. For fMRI data, higher correlations between SWPC and PS occur with matched frequencies and smaller SWPC window sizes (~30s), but larger windows (~88s) sacrifice clinically relevant information. Both methods identify a schizophrenia-associated brain network state but show different patterns: SWPC highlights low anti-correlations between visual, subcortical, auditory, and sensory-motor networks, while PS shows reduced positive synchronization among these networks. In sum, our findings underscore the complementary nature of SWPC and PS, elucidating their respective strengths and limitations without implying the superiority of one over the other.

Abrupt phase changes coupled with waning in amplitude of neural oscillation lead to phase-locking in the auditory evoked responses

Neural oscillations on the human auditory cortex measured with the magnetoencephalography were band-pass filtered between 3 and 16 Hz and then divided into instantaneous phases and amplitudes by the Hilbert transformation. Spontaneously, the amplitudes fluctuated, i.e. waxed and waned; The phases rotated at around 6 Hz most of the time, but abruptly accelerated or decelerated when the amplitudes waned close to zero. After auditory stimuli, the amplitudes and the phases were coupled in the same way as spontaneously. Amounts and directions of the accelerations or decelerations were thereby specific so that the phases subsequently took mostly the same value, i.e. were locked, at around the time of N100 peaks in the auditory evoked responses. In short, the auditory evoked responses emerged from spontaneous oscillations by abrupt phase changes coupled with waning in amplitudes and phase-locking thereafter.

Different Methods to Estimate the Phase of Neural Rhythms Agree But Only During Times of Low Uncertainty

Rhythms are a common feature of brain activity. Across different types of rhythms, the phase has been proposed to have functional consequences, thus requiring its accurate specification from noisy data. Phase is conventionally specified using techniques that presume a frequency band-limited rhythm. However, in practice, observed brain rhythms are typically nonsinusoidal and amplitude modulated. How these features impact methods to estimate phase remains unclear. To address this, we consider three phase estimation methods, each with different underlying assumptions about the rhythm. We apply these methods to rhythms simulated with different generative mechanisms and demonstrate inconsistency in phase estimates across the different methods. We propose two improvements to the practice of phase estimation: (1) estimating confidence in the phase estimate, and (2) examining the consistency of phase estimates between two (or more) methods.

Different methods to estimate the phase of neural rhythms agree, but only during times of low uncertainty

Rhythms are a common feature of brain activity. Across different types of rhythms, the phase has been proposed to have functional consequences, thus requiring its accurate specification from noisy data. Phase is conventionally specified using techniques that presume a frequency band-limited rhythm. However, in practice, observed brain rhythms are typically non-sinusoidal and amplitude modulated. How these features impact methods to estimate phase remains unclear. To address this, we consider three phase estimation methods, each with different underlying assumptions about the rhythm. We apply these methods to rhythms simulated with different generative mechanisms and demonstrate inconsistency in phase estimates across the different methods. We propose two improvements to the practice of phase estimation: (1) estimating confidence in the phase estimate, and (2) examining the consistency of phase estimates between two (or more) methods.

Delay Analysis in Closed-Loop EEG Phase-Triggered Transcranial Magnetic Stimulation

The recent development of closed-loop EEG phase-triggered transcranial magnetic stimulation (TMS) has advanced potential applications of adaptive neuromodulation based on the current brain state. Closed-loop TMS involves instantaneous acquisition of the EEG rhythm, timing prediction of the target phase, and triggering of TMS. However, the accuracy of EEG phase prediction algorithms is largely influenced by the system's transport delay, and their relationship is rarely considered in related work. This paper proposes a delay analysis that considers the delay of the closed-loop EEG phase-triggered TMS system as a primary factor in the validation of phase prediction algorithms. An in-silico validation using real EEG data was performed to compare the performance of commonly used algorithms. The experimental results indicate a significant influence of the total delay on the algorithm performance, and the performance ranking among algorithms varies at different levels of delay. We conclude that the delay analysis framework should be widely adopted in the design and validation of phase prediction algorithms for closed-loop EEG phase-triggered TMS systems.

Ion dynamic characterization using phase-resolved laser-induced fluorescence spectroscopy in a Hall effect thruster

Significant information on the dynamics of the plasma constituents in Hall effect thrusters can be obtained using minimally intrusive techniques, such as laser-induced fluorescence (LIF) diagnostics. Indeed, LIF provides an excellent tool to determine the ion velocity distribution function with high spatial resolution. Even in a steady-state operation, recording time-resolved maps of the velocity distribution is relevant due to persisting time-dependent features of the thruster discharge. One of the preeminent phenomena that render the ion velocity distribution to be time dependent is commonly attributed to the breathing mode, characterized by pronounced oscillations in the discharge current. The goal of this work is to propose a new technique for plasma dynamic studies based on LIF spectroscopy with phase-resolution during the breathing period. For this purpose, the Hilbert transform is used to define the instantaneous phase of oscillation of the thruster current. Ion velocity distribution modification over assigned phases of oscillation is measured simultaneously and in real-time thanks to a fully numerical analysis of the data.

Uncovering the organization of neural circuits with Generalized Phase Locking Analysis

Despite the considerable progress of in vivo neural recording techniques, inferring the biophysical mechanisms underlying large scale coordination of brain activity from neural data remains challenging. One obstacle is the difficulty to link high dimensional functional connectivity measures to mechanistic models of network activity. We address this issue by investigating spike-field coupling (SFC) measurements, which quantify the synchronization between, on the one hand, the action potentials produced by neurons, and on the other hand mesoscopic "field" signals, reflecting subthreshold activities at possibly multiple recording sites. As the number of recording sites gets large, the amount of pairwise SFC measurements becomes overwhelmingly challenging to interpret. We develop Generalized Phase Locking Analysis (GPLA) as an interpretable dimensionality reduction of this multivariate SFC. GPLA describes the dominant coupling between field activity and neural ensembles across space and frequencies. We show that GPLA features are biophysically interpretable when used in conjunction with appropriate network models, such that we can identify the influence of underlying circuit properties on these features. We demonstrate the statistical benefits and interpretability of this approach in various computational models and Utah array recordings. The results suggest that GPLA, used jointly with biophysical modeling, can help uncover the contribution of recurrent microcircuits to the spatio-temporal dynamics observed in multi-channel experimental recordings.

An extended Hilbert transform method for reconstructing the phase from an oscillatory signal

Rhythmic activity is ubiquitous in biological systems from the cellular to organism level. Reconstructing the instantaneous phase is the first step in analyzing the essential mechanism leading to a synchronization state from the observed signals. A popular method of phase reconstruction is based on the Hilbert transform, which can only reconstruct the interpretable phase from a limited class of signals, e.g., narrow band signals. To address this issue, we propose an extended Hilbert transform method that accurately reconstructs the phase from various oscillatory signals. The proposed method is developed by analyzing the reconstruction error of the Hilbert transform method with the aid of Bedrosian's theorem. We validate the proposed method using synthetic data and show its systematically improved performance compared with the conventional Hilbert transform method with respect to accurately reconstructing the phase. Finally, we demonstrate that the proposed method is potentially useful for detecting the phase shift in an observed signal. The proposed method is expected to facilitate the study of synchronization phenomena from experimental data.

Modelling neural entrainment and its persistence: influence of frequency of stimulation and phase at the stimulus offset

Neural entrainment, the synchronization of brain oscillations to the frequency of an external stimuli, is a key mechanism that shapes perceptual and cognitive processes.Objective.Using simulations, we investigated the dynamics of neural entrainment, particularly the period following the end of the stimulation, since the persistence (reverberation) of neural entrainment may condition future sensory representations based on predictions about stimulus rhythmicity.Methods.Neural entrainment was assessed using a modified Jansen-Rit neural mass model (NMM) of coupled cortical columns, in which the spectral features of the output resembled that of the electroencephalogram (EEG). We evaluated spectro-temporal features of entrainment as a function of the stimulation frequency, the resonant frequency of the neural populations comprising the NMM, and the coupling strength between cortical columns. Furthermore, we tested if the entrainment persistence depended on the phase of the EEG-like oscillation at the time the stimulus ended.Main Results.The entrainment of the column that received the stimulation was maximum when the frequency of the entrainer was within a narrow range around the resonant frequency of the column. When this occurred, entrainment persisted for several cycles after the stimulus terminated, and the propagation of the entrainment to other columns was facilitated. Propagation also depended on the resonant frequency of the second column, and the coupling strength between columns. The duration of the persistence of the entrainment depended on the phase of the neural oscillation at the time the entrainer terminated, such that falling phases (fromπ/2 to 3π/2 in a sine function) led to longer persistence than rising phases (from 0 toπ/2 and 3π/2 to 2π).Significance.The study bridges between models of neural oscillations and empirical electrophysiology, providing insights to the mechanisms underlying neural entrainment and the use of rhythmic sensory stimulation for neuroenhancement.

Phase-based causality analysis with partial mutual information from mixed embedding

Instantaneous phases extracted from multivariate time series can retain information about the relationships between the underlying mechanisms that generate the series. Although phases have been widely used in the study of nondirectional coupling and connectivity, they have not found similar appeal in the study of causality. Herein, we present a new method for phase-based causality analysis, which combines ideas from the mixed embedding technique and the information-theoretic approach to causality in coupled oscillatory systems. We then use the introduced method to investigate causality in simulated datasets of bivariate, unidirectionally paired systems from combinations of Rössler, Lorenz, van der Pol, and Mackey-Glass equations. We observe that causality analysis using the phases can capture the true causal relation for coupling strength smaller than the analysis based on the amplitudes can capture. On the other hand, the causality estimation based on the phases tends to have larger variability, which is attributed more to the phase extraction process than the actual phase-based causality method. In addition, an application on real electroencephalographic data from an experiment on elicited human emotional states reinforces the usefulness of phases in causality identification.

Benchmarking real-time algorithms for in-phase auditory stimulation of low amplitude slow waves with wearable EEG devices during sleep

Auditory stimulation of EEG slow waves (SW) during non-rapid eye movement (NREM) sleep has shown to improve cognitive function when it is delivered at the up-phase of SW. SW enhancement is particularly desirable in subjects with low-amplitude SW such as older adults or patients suffering from neurodegeneration such as Parkinson disease (PD). However, existing algorithms to estimate the up-phase suffer from a poor phase accuracy at low EEG amplitudes and when SW frequencies are not constant. We introduce two novel algorithms for real-time EEG phase estimation on autonomous wearable devices. The algorithms were based on a phase-locked loop (PLL) and, for the first time, a phase vocoder (PV). We compared these phase tracking algorithms with a simple amplitude threshold approach. The optimized algorithms were benchmarked for phase accuracy, the capacity to estimate phase at SW amplitudes between 20 and 60 V, and SW frequencies above 1 Hz on 324 recordings from healthy older adults and PD patients. Furthermore, the algorithms were implemented on a wearable device and the computational efficiency and the performance was evaluated on simulated sleep EEG, as well as prospectively during a recording with a PD patient. All three algorithms delivered more than 70% of the stimulation triggers during the SW up-phase. The PV showed the highest capacity on targeting low-amplitude SW and SW with frequencies above 1 Hz. The testing on real-time hardware revealed that both PV and PLL have marginal impact on microcontroller load, while the efficiency of the PV was 4% lower than the PLL. Active auditory stimulation did not influence the phase tracking. This work demonstrated that phase-accurate auditory stimulation can be delivered during home-based sleep interventions with a wearable device also in populations with low-amplitude SW.

Indirect Estimation of Breathing Rate from Heart Rate Monitoring System during Running

Recent advances in wearable technologies integrating multi-modal sensors have enabled the in-field monitoring of several physiological metrics. In sport applications, wearable devices have been widely used to improve performance while minimizing the risk of injuries and illness. The objective of this project is to estimate breathing rate (BR) from respiratory sinus arrhythmia (RSA) using heart rate (HR) recorded with a chest belt during physical activities, yielding additional physiological insight without the need of an additional sensor. Thirty-one healthy adults performed a run at increasing speed until exhaustion on an instrumented treadmill. RR intervals were measured using the Polar H10 HR monitoring system attached to a chest belt. A metabolic measurement system was used as a reference to evaluate the accuracy of the BR estimation. The evaluation of the algorithms consisted of exploring two pre-processing methods (band-pass filters and relative RR intervals transformation) with different instantaneous frequency tracking algorithms (short-term Fourier transform, single frequency tracking, harmonic frequency tracking and peak detection). The two most accurate BR estimations were achieved by combining band-pass filters with short-term Fourier transform, and relative RR intervals transformation with harmonic frequency tracking, showing 5.5% and 7.6% errors, respectively. These two methods were found to provide reasonably accurate BR estimation over a wide range of breathing frequency. Future challenges consist in applying/validating our approaches during in-field endurance running in the context of fatigue assessment.

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.

From Univariate to Multivariate Coupling Between Continuous Signals and Point Processes: A Mathematical Framework

Time series data sets often contain heterogeneous signals, composed of both continuously changing quantities and discretely occurring events. The coupling between these measurements may provide insights into key underlying mechanisms of the systems under study. To better extract this information, we investigate the asymptotic statistical properties of coupling measures between continuous signals and point processes. We first introduce martingale stochastic integration theory as a mathematical model for a family of statistical quantities that include the phase locking value, a classical coupling measure to characterize complex dynamics. Based on the martingale central limit theorem, we can then derive the asymptotic gaussian distribution of estimates of such coupling measure that can be exploited for statistical testing. Second, based on multivariate extensions of this result and random matrix theory, we establish a principled way to analyze the low-rank coupling between a large number of point processes and continuous signals. For a null hypothesis of no coupling, we establish sufficient conditions for the empirical distribution of squared singular values of the matrix to converge, as the number of measured signals increases, to the well-known Marchenko-Pastur (MP) law, and the largest squared singular value converges to the upper end of the MP support. This justifies a simple thresholding approach to assess the significance of multivariate coupling. Finally, we illustrate with simulations the relevance of our univariate and multivariate results in the context of neural time series, addressing how to reliably quantify the interplay between multichannel local field potential signals and the spiking activity of a large population of neurons.

Examining the optimal timing for closed-loop auditory stimulation of slow-wave sleep in young and older adults

Study Objectives

Closed-loop auditory stimulation (CLAS) is a method for enhancing slow oscillations (SOs) through the presentation of auditory clicks during sleep. CLAS boosts SOs amplitude and sleep spindle power, but the optimal timing for click delivery remains unclear. Here, we determine the optimal time to present auditory clicks to maximize the enhancement of SO amplitude and spindle likelihood.

Methods

We examined the main factors predicting SO amplitude and sleep spindles in a dataset of 21 young and 17 older subjects. The participants received CLAS during slow-wave-sleep in two experimental conditions: sham and auditory stimulation. Post-stimulus SOs and spindles were evaluated according to the click phase on the SOs and compared between and within conditions.

Results

We revealed that auditory clicks applied anywhere on the positive portion of the SO increased SO amplitudes and spindle likelihood, although the interval of opportunity was shorter in the older group. For both groups, analyses showed that the optimal timing for click delivery is close to the SO peak phase. Click phase on the SO wave was the main factor determining the impact of auditory stimulation on spindle likelihood for young subjects, whereas for older participants, the temporal lag since the last spindle was a better predictor of spindle likelihood.

Conclusions

Our data suggest that CLAS can more effectively boost SOs during specific phase windows, and these differ between young and older participants. It is possible that this is due to the fluctuation of sensory inputs modulated by the thalamocortical networks during the SO.

What Can Local Transfer Entropy Tell Us about Phase-Amplitude Coupling in Electrophysiological Signals?

Modulation of the amplitude of high-frequency cortical field activity locked to changes in the phase of a slower brain rhythm is known as phase-amplitude coupling (PAC). The study of this phenomenon has been gaining traction in neuroscience because of several reports on its appearance in normal and pathological brain processes in humans as well as across different mammalian species. This has led to the suggestion that PAC may be an intrinsic brain process that facilitates brain inter-area communication across different spatiotemporal scales. Several methods have been proposed to measure the PAC process, but few of these enable detailed study of its time course. It appears that no studies have reported details of PAC dynamics including its possible directional delay characteristic. Here, we study and characterize the use of a novel information theoretic measure that may address this limitation: local transfer entropy. We use both simulated and actual intracranial electroencephalographic data. In both cases, we observe initial indications that local transfer entropy can be used to detect the onset and offset of modulation process periods revealed by mutual information estimated phase-amplitude coupling (MIPAC). We review our results in the context of current theories about PAC in brain electrical activity, and discuss technical issues that must be addressed to see local transfer entropy more widely applied to PAC analysis. The current work sets the foundations for further use of local transfer entropy for estimating PAC process dynamics, and extends and complements our previous work on using local mutual information to compute PAC (MIPAC).

Phase Synchrony Analysis of Rolling Bearing Vibrations and Its Application to Failure Identification

As the failure-induced component (FIC) in the vibration signals of bearings transmits through housings and shafts, potential phase synchronization is excited among multichannel signals. As phase synchrony analysis (PSA) does not involve the chaotic behavior of signals, it is suitable for characterizing the operating state of bearings considering complicated vibration signals. Therefore, a novel PSA method was developed to identify and track the failure evolution of bearings. First, resonance demodulation and variational mode decomposition (VMD) were combined to extract the mono-component or band-limited FIC from signals. Then, the instantaneous phase of the FIC was analytically solved using Hilbert transformation. The generalized phase difference (GPD) was used to quantify the relationship between FICs extracted from different vibration signals. The entropy of the GPD was regarded as the indicator for quantifying failure evolution. The proposed method was applied to the vibration signals obtained from an accelerated failure experiment and a natural failure experiment. Results showed that phase synchronization in bearing failure evolution was detected and evaluated effectively. Despite the chaotic behavior of the signals, the phase synchronization indicator could identify bearing failure during the initial stage in a robust manner.

Persistence of EEG Alpha Entrainment Depends on Stimulus Phase at Offset

Neural entrainment is the synchronization of neural activity to the frequency of repetitive external stimuli, which can be observed as an increase in the electroencephalogram (EEG) power spectrum at the driving frequency, -also known as the steady-state response. Although it has been systematically reported that the entrained EEG oscillation persists for approximately three cycles after stimulus offset, the neural mechanisms underpinning it remain unknown. Focusing on alpha oscillations, we adopt the dynamical excitation/inhibition framework, which suggests that phases of entrained EEG signals correspond to alternating excitatory/inhibitory states of the neural circuitry. We hypothesize that the duration of the persistence of entrainment is determined by the specific functional state of the entrained neural network at the time the stimulus ends. Steady-state visually evoked potentials (SSVEP) were elicited in 19 healthy volunteers at the participants’ individual alpha peaks. Visual stimulation consisted of a sinusoidally-varying light terminating at one of four phases: 0, π/2, π, and 3π/2. The persistence duration of the oscillatory activity was analyzed as a function of the terminating phase of the stimulus. Phases of the SSVEP at the stimulus termination were distributed within a constant range of values relative to the phase of the stimulus. Longer persistence durations were obtained when visual stimulation terminated towards the troughs of the alpha oscillations, while shorter persistence durations occurred when stimuli terminated near the peaks. Source localization analysis suggests that the persistence of entrainment reflects the functioning of fronto-occipital neuronal circuits, which might prime the sensory representation of incoming visual stimuli based on predictions about stimulus rhythmicity. Consequently, different states of the network at the end of the stimulation, corresponding to different states of intrinsic neuronal coupling, may determine the time windows over which coding of incoming sensory stimulation is modulated by the preceding oscillatory activity.

Mapping atmospheric waves and unveiling phase coherent structures in a global surface air temperature reanalysis dataset

In the analysis of empirical signals, detecting correlations that capture genuine interactions between the elements of a complex system is a challenging task with applications across disciplines. Here, we analyze a global dataset of surface air temperature (SAT) with daily resolution. Hilbert analysis is used to obtain phase, instantaneous frequency, and amplitude information of SAT seasonal cycles in different geographical zones. The analysis of the phase dynamics reveals large regions with coherent seasonality. The analysis of the instantaneous frequencies uncovers clean wave patterns formed by alternating regions of negative and positive correlations. In contrast, the analysis of the amplitude dynamics uncovers wave patterns with additional large-scale structures. These structures are interpreted as due to the fact that the amplitude dynamics is affected by processes that act in long and short time scales, while the dynamics of the instantaneous frequency is mainly governed by fast processes. Therefore, Hilbert analysis allows us to disentangle climatic processes and to track planetary atmospheric waves. Our results are relevant for the analysis of complex oscillatory signals because they offer a general strategy for uncovering interactions that act at different time scales.

The Influence of EEG References on the Analysis of Spatio-Temporal Interrelation Patterns

The characterization of the functional network of the brain dynamics has become a prominent tool to illuminate novel aspects of brain functioning. Due to its excellent time resolution, such research is oftentimes based on electroencephalographic recordings (EEG). However, a particular EEG-reference might cause crucial distortions of the spatiotemporal interrelation pattern and may induce spurious correlations as well as diminish genuine interrelations originally present in the dataset. Here we investigate in which manner correlation patterns are affected by a chosen EEG reference. To this end we evaluate the influence of 7 popular reference schemes on artificial recordings derived from well controlled numerical test frameworks. In this respect we are not only interested in the deformation of spatial interrelations, but we test additionally in which way the time evolution of the functional network, estimated via some bi-variate interrelation measures, gets distorted. It turns out that the median reference as well as the global average show the best performance in most situations considered in the present study. However, if a collective brain dynamics is present, where most of the signals get correlated, these schemes may also cause crucial deformations of the functional network, such that the parallel use of different reference schemes seems advisable.

Uncovering temporal regularity in atmospheric dynamics through Hilbert phase analysis

Uncovering meaningful regularities in complex oscillatory signals is a challenging problem with applications across a wide range of disciplines. Here, we present a novel approach, based on the Hilbert transform (HT). We show that temporal periodicity can be uncovered by averaging the signal in a moving window of appropriated length, τ, before applying the HT. As a case study, we investigate global gridded surface air temperature (SAT) datasets. By analyzing the variation of the mean rotation period, T¯, of the Hilbert phase as a function of τ, we discover well-defined plateaus. In many geographical regions, the plateau corresponds to the expected 1-yr solar cycle; however, in regions where SAT dynamics is highly irregular, the plateaus reveal non-trivial periodicities, which can be interpreted in terms of climatic phenomena such as El Niño. In these regions, we also find that Fourier analysis is unable to detect the periodicity that emerges when τ increases and gradually washes out SAT variability. The values of T¯ obtained for different τs are then given to a standard machine learning algorithm. The results demonstrate that these features are informative and constitute a new approach for SAT time series classification. To support these results, we analyze the synthetic time series generated with a simple model and confirm that our method extracts information that is fully consistent with our knowledge of the model that generates the data. Remarkably, the variation of T¯ with τ in the synthetic data is similar to that observed in the real SAT data. This suggests that our model contains the basic mechanisms underlying the unveiled periodicities. Our results demonstrate that Hilbert analysis combined with temporal averaging is a powerful new tool for discovering hidden temporal regularity in complex oscillatory signals.

Reducing the Effect of Spurious Phase Variations in Neural Oscillatory Signals

The phase-reset model of oscillatory EEG activity has received a lot of attention in the last decades for decoding different cognitive processes. Based on this model, the ERPs are assumed to be generated as a result of phase reorganization in ongoing EEG. Alignment of the phase of neuronal activities can be observed within or between different assemblies of neurons across the brain. Phase synchronization has been used to explore and understand perception, attentional binding and considering it in the domain of neuronal correlates of consciousness. The importance of the topic and its vast exploration in different domains of the neuroscience presses the need for appropriate tools and methods for measuring the level of phase synchronization of neuronal activities. Measuring the level of instantaneous phase (IP) synchronization has been used extensively in numerous studies of ERPs as well as oscillatory activity for a better understanding of the underlying cognitive binding with regard to different set of stimulations such as auditory and visual. However, the reliability of results can be challenged as a result of noise artifact in IP. Phase distortion due to environmental noise artifacts as well as different pre-processing steps on signals can lead to generation of artificial phase jumps. One of such effects presented recently is the effect of low envelope on the IP of signal. It has been shown that as the instantaneous envelope of the analytic signal approaches zero, the variations in the phase increase, effectively leading to abrupt transitions in the phase. These abrupt transitions can distort the phase synchronization results as they are not related to any neurophysiological effect. These transitions are called spurious phase variation. In this study, we present a model to remove generated artificial phase variations due to the effect of low envelope. The proposed method is based on a simplified form of a Kalman smoother, that is able to model the IP behavior in narrow-bandpassed oscillatory signals. In this work we first explain the details of the proposed Kalman smoother for modeling the dynamics of the phase variations in narrow-bandpassed signals and then evaluate it on a set of synthetic signals. Finally, we apply the model on ongoing-EEG signals to assess the removal of spurious phase variations.

Non-linear auto-regressive models for cross-frequency coupling in neural time series

We address the issue of reliably detecting and quantifying cross-frequency coupling (CFC) in neural time series. Based on non-linear auto-regressive models, the proposed method provides a generative and parametric model of the time-varying spectral content of the signals. As this method models the entire spectrum simultaneously, it avoids the pitfalls related to incorrect filtering or the use of the Hilbert transform on wide-band signals. As the model is probabilistic, it also provides a score of the model “goodness of fit” via the likelihood, enabling easy and legitimate model selection and parameter comparison; this data-driven feature is unique to our model-based approach. Using three datasets obtained with invasive neurophysiological recordings in humans and rodents, we demonstrate that these models are able to replicate previous results obtained with other metrics, but also reveal new insights such as the influence of the amplitude of the slow oscillation. Using simulations, we demonstrate that our parametric method can reveal neural couplings with shorter signals than non-parametric methods. We also show how the likelihood can be used to find optimal filtering parameters, suggesting new properties on the spectrum of the driving signal, but also to estimate the optimal delay between the coupled signals, enabling a directionality estimation in the coupling.

Neural oscillations synchronize information across brain areas at various anatomical and temporal scales. Of particular relevance, slow fluctuations of brain activity have been shown to affect high frequency neural activity, by regulating the excitability level of neural populations. Such cross-frequency-coupling can take several forms. In the most frequently observed type, the power of high frequency activity is time-locked to a specific phase of slow frequency oscillations, yielding phase-amplitude-coupling (PAC). Even when readily observed in neural recordings, such non-linear coupling is particularly challenging to formally characterize. Typically, neuroscientists use band-pass filtering and Hilbert transforms with ad-hoc correlations. Here, we explicitly address current limitations and propose an alternative probabilistic signal modeling approach, for which statistical inference is fast and well-posed. To statistically model PAC, we propose to use non-linear auto-regressive models which estimate the spectral modulation of a signal conditionally to a driving signal. This conditional spectral analysis enables easy model selection and clear hypothesis-testing by using the likelihood of a given model. We demonstrate the advantage of the model-based approach on three datasets acquired in rats and in humans. We further provide novel neuroscientific insights on previously reported PAC phenomena, capturing two mechanisms in PAC: influence of amplitude and directionality estimation.

A robust statistical framework for instantaneous electroencephalogram phase and frequency estimation and analysis

OBJECTIVE

The instantaneous phase (IP) and instantaneous frequency (IF) of the electroencephalogram (EEG) are considered as notable complements for the EEG spectrum. The calculation of these parameters commonly includes narrow-band filtering, followed by the calculation of the signal's analytical form. The calculation of the IP and IF is highly susceptible to the filter parameters and background noise level, especially in low analytical signal amplitudes. The objective of this study is to propose a robust statistical framework for EEG IP/IF estimation and analysis.

APPROACH

Herein, a Monte Carlo estimation scheme is proposed for the robust estimation of the EEG IP and IF. It is proposed that any EEG phase-related inference should be reported as an average with confidence intervals obtained by repeating the IP and IF estimation under infinitesimal variations (selected by an expert), in algorithmic parameters such as the filter's bandwidth, center frequency and background noise level. In the second part of the paper, a stochastic model consisting of the superposition of narrow-band foreground and background EEG is used to derive analytically probability density functions of the instantaneous envelope (IE) and IP of EEG signals, which justify the proposed Monte Carlo scheme.

MAIN RESULTS

The instantaneous analytical envelope of the EEG, which has been empirically used in previous studies, is shown to have a fundamental impact on the accuracy of the EEG phase contents. It is rigorously shown that the IP/IF estimation quality highly depends on the IE and any phase/frequency interpretations in low IE are statistically unreliable and require a hypothesis test.

SIGNIFICANCE

The impact of the proposed method on previous studies, including time-domain phase synchrony, phase resetting, phase locking value and phase amplitude coupling are studied with examples. The findings of this research can set forth new standards for EEG phase/frequency estimation and analysis techniques.

On the estimation of phase synchronization, spurious synchronization and filtering

Phase synchronization, viz., the adjustment of instantaneous frequencies of two interacting self-sustained nonlinear oscillators, is frequently used for the detection of a possible interrelationship between empirical data recordings. In this context, the proper estimation of the instantaneous phase from a time series is a crucial aspect. The probability that numerical estimates provide a physically relevant meaning depends sensitively on the shape of its power spectral density. For this purpose, the power spectrum should be narrow banded possessing only one prominent peak [M. Chavez et al., J. Neurosci. Methods 154, 149 (2006)]. If this condition is not fulfilled, band-pass filtering seems to be the adequate technique in order to pre-process data for a posterior synchronization analysis. However, it was reported that band-pass filtering might induce spurious synchronization [L. Xu et al., Phys. Rev. E 73, 065201(R), (2006); J. Sun et al., Phys. Rev. E 77, 046213 (2008); and J. Wang and Z. Liu, EPL 102, 10003 (2013)], a statement that without further specification causes uncertainty over all measures that aim to quantify phase synchronization of broadband field data. We show by using signals derived from different test frameworks that appropriate filtering does not induce spurious synchronization. Instead, filtering in the time domain tends to wash out existent phase interrelations between signals. Furthermore, we show that measures derived for the estimation of phase synchronization like the mean phase coherence are also useful for the detection of interrelations between time series, which are not necessarily derived from coupled self-sustained nonlinear oscillators.

Real-time multi-signal frequency tracking with a bank of notch filters to estimate the respiratory rate from the ECG

Measuring the instantaneous frequency of a signal rapidly and accurately is essential in many applications. However, the instantaneous frequency by definition is a parameter difficult to determine. Fourier-based methods introduce estimation delays as computations are performed in a time-window. Instantaneous methods based on the Hilbert transform lack robustness. State-of-the-art adaptive filters yield accurate estimates, however, with an adaptation delay. In this study we propose an algorithm based on short length-3 FIR notch filters to estimate the instantaneous frequency of a signal at each sample, in a real-time manner and with very low delay. The output powers of a bank of the above-mentioned filters are used in a recursive weighting scheme to estimate the dominant frequency of the input. This scheme has been extended to process multiple inputs containing a common frequency by introducing an additional weighting scheme upon the inputs. The algorithm was tested on synthetic data and then evaluated on real biomedical data, i.e. the estimation of the respiratory rate from the electrocardiogram. It was shown that the proposed method provided more accurate estimates with less delay than those of state-of-the-art methods. By virtue of its simplicity and good performance, the proposed method is a worthy candidate to be used in biomedical applications, for example in health monitoring developments based on portable and automatic devices.

On the dynamics of Liesegang-type pattern formation in a gaseous system

Liesegang pattern formations are widely spread in nature. In spite of a comparably simple experimental setup under laboratory conditions, a variety of spatio-temporal structures may arise. Presumably because of easier control of the experimental conditions, Liesegang pattern formation was mainly studied in gel systems during more than a century. Here we consider pattern formation in a gas phase, where beautiful but highly complex reaction-diffusion-convection dynamics are uncovered by means of a specific laser technique. A quantitative analysis reveals that two different, apparently independent processes, both highly correlated and synchronized across the extension of the reaction cloud, act on different time scales. Each of them imprints a different structure of salt precipitation at the tube walls.

Graph analysis of functional brain networks: practical issues in translational neuroscience

The brain can be regarded as a network: a connected system where nodes, or units, represent different specialized regions and links, or connections, represent communication pathways. From a functional perspective, communication is coded by temporal dependence between the activities of different brain areas. In the last decade, the abstract representation of the brain as a graph has allowed to visualize functional brain networks and describe their non-trivial topological properties in a compact and objective way. Nowadays, the use of graph analysis in translational neuroscience has become essential to quantify brain dysfunctions in terms of aberrant reconfiguration of functional brain networks. Despite its evident impact, graph analysis of functional brain networks is not a simple toolbox that can be blindly applied to brain signals. On the one hand, it requires the know-how of all the methodological steps of the pipeline that manipulate the input brain signals and extract the functional network properties. On the other hand, knowledge of the neural phenomenon under study is required to perform physiologically relevant analysis. The aim of this review is to provide practical indications to make sense of brain network analysis and contrast counterproductive attitudes.

Parametric estimation of cross-frequency coupling

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We revisit the general linear model (GLM) approach to cross-frequency coupling.

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Continuous time series were split into epochs for parametric statistical tests.

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The GLM and permutation tests produced similar results in experimental data.

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The GLM offers a good trade-off between computation time and statistical power.

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Other predictors such as amplitude-amplitude coupling can be easily included.

Background

Growing experimental evidence suggests an important role for cross-frequency coupling in neural processing, in particular for phase-amplitude coupling (PAC). Although the details of methods to detect PAC may vary, a common procedure to estimate the significance level is the comparison of observed values to those of at least 100 surrogate time series. When scanning large parts of the frequency spectrum and multiple recording sites, this could amount to very large computation times.

New method

We demonstrate that the general linear model (GLM) allows for a parametric estimation of significant PAC. Continuous recordings are split into epochs, of a few seconds duration, on which an F-test can be performed. We compared its performance against traditional non-parametric permutation tests in both simulated and experimental data.

Results

Our method was able to reproduce findings of phase-amplitude coupling in local field potential recordings obtained from the subthalamic nucleus in patients with Parkinson's disease. We also show that PAC may be detected between the subthalamic nucleus and cortical motor areas.

Comparison with existing method(s)

Although the GLM slightly underestimated significance compared to permutation tests in the simulations, for experimental data the two methods produced highly similar results. Computation times were drastically lower for the GLM. Furthermore, we demonstrate that the GLM can be easily extended by including additional predictors such as low-frequency amplitude to test for amplitude-amplitude coupling.

Conclusions

The GLM forms an adequate and computationally efficient approach for detecting cross-frequency coupling with the flexibility to add other explanatory variables of interest.

Directional influence between the human amygdala and orbitofrontal cortex at the time of decision-making

There is a growing consensus that the brain makes simple choices, such as choosing between an apple and an orange, by assigning value to the options under consideration, and comparing those values to make a choice. There is also a consensus that value signals computed in orbitofrontal cortex (OFC) and amygdala play a critical role in the choice process. However, the nature of the flow of information between OFC and amygdala at the time of decision is still unknown. In order to study this question, simultaneous local field potentials were recorded from OFC and amygdala in human patients while they performed a simple food choice task. Although the interaction of these circuits has been studied in animals, this study examines the effective connectivity directly in the human brain on a moment-by-moment basis. A spectral conditional Granger causality analysis was performed in order to test if the modulation of activity goes mainly from OFC-to-amygdala, from amygdala-to-OFC, or if it is bi-directional. Influence from amygdala-to-OFC was dominant prior to the revealed choice, with a small but significant OFC influence on the amygdala earlier in the trial. Alpha oscillation amplitudes analyzed with the Hilbert-Huang transform revealed differences in choice valence coincident with temporally specific amygdala influence on the OFC.

Toward a proper estimation of phase-amplitude coupling in neural oscillations

BACKGROUND

The phase-amplitude coupling (PAC) between distinct neural oscillations is critical to brain functions that include cross-scale organization, selection of attention, routing the flow of information through neural circuits, memory processing and information coding. Several methods for PAC estimation have been proposed but the limitations of PAC estimation as well as the assumptions about the data for accurate PAC estimation are unclear.

NEW METHOD

We define boundary conditions for standard PAC algorithms and propose "oscillation-triggered coupling" (OTC), a parameter-free, data-driven algorithm for unbiased estimation of PAC. OTC establishes a unified framework that treats individual oscillations as discrete events for estimating PAC from a set of oscillations and for characterizing events from time windows as short as a single modulating oscillation.

RESULTS

For accurate PAC estimation, standard PAC algorithms require amplitude filters with a bandwidth at least twice the modulatory frequency. The phase filters must be moderately narrow-band, especially when the modulatory rhythm is non-sinusoidal. The minimally appropriate analysis window is ∼10s. We then demonstrate that OTC can characterize PAC by treating neural oscillations as discrete events rather than continuous phase and amplitude time series.

COMPARISON WITH EXISTING METHODS

These findings show that in addition to providing the same information about PAC as the standard approach, OTC facilitates characterization of single oscillations and their sequences, in addition to explaining the role of individual oscillations in generating PAC patterns.

CONCLUSIONS

OTC allows PAC analysis at the level of individual oscillations and therefore enables investigation of PAC at the time scales of cognitive phenomena.

Adaptive filtering methods for identifying cross-frequency couplings in human EEG

Oscillations have been increasingly recognized as a core property of neural responses that contribute to spontaneous, induced, and evoked activities within and between individual neurons and neural ensembles. They are considered as a prominent mechanism for information processing within and communication between brain areas. More recently, it has been proposed that interactions between periodic components at different frequencies, known as cross-frequency couplings, may support the integration of neuronal oscillations at different temporal and spatial scales. The present study details methods based on an adaptive frequency tracking approach that improve the quantification and statistical analysis of oscillatory components and cross-frequency couplings. This approach allows for time-varying instantaneous frequency, which is particularly important when measuring phase interactions between components. We compared this adaptive approach to traditional band-pass filters in their measurement of phase-amplitude and phase-phase cross-frequency couplings. Evaluations were performed with synthetic signals and EEG data recorded from healthy humans performing an illusory contour discrimination task. First, the synthetic signals in conjunction with Monte Carlo simulations highlighted two desirable features of the proposed algorithm vs. classical filter-bank approaches: resilience to broad-band noise and oscillatory interference. Second, the analyses with real EEG signals revealed statistically more robust effects (i.e. improved sensitivity) when using an adaptive frequency tracking framework, particularly when identifying phase-amplitude couplings. This was further confirmed after generating surrogate signals from the real EEG data. Adaptive frequency tracking appears to improve the measurements of cross-frequency couplings through precise extraction of neuronal oscillations.

Coding of repetitive transients by auditory cortex on posterolateral superior temporal gyrus in humans: an intracranial electrophysiology study

Evidence regarding the functional subdivisions of human auditory cortex has been slow to converge on a definite model. In part, this reflects inadequacies of current understanding of how the cortex represents temporal information in acoustic signals. To address this, we investigated spatiotemporal properties of auditory responses in human posterolateral superior temporal (PLST) gyrus to acoustic click-train stimuli using intracranial recordings from neurosurgical patients. Subjects were patients undergoing chronic invasive monitoring for refractory epilepsy. The subjects listened passively to acoustic click-train stimuli of varying durations (160 or 1,000 ms) and rates (4-200 Hz), delivered diotically via insert earphones. Multicontact subdural grids placed over the perisylvian cortex recorded intracranial electrocorticographic responses from PLST and surrounding areas. Analyses focused on averaged evoked potentials (AEPs) and high gamma (70-150 Hz) event-related band power (ERBP). Responses to click trains featured prominent AEP waveforms and increases in ERBP. The magnitude of AEPs and ERBP typically increased with click rate. Superimposed on the AEPs were frequency-following responses (FFRs), most prominent at 50-Hz click rates but still detectable at stimulus rates up to 200 Hz. Loci with the largest high gamma responses on PLST were often different from those sites that exhibited the strongest FFRs. The data indicate that responses of non-core auditory cortex of PLST represent temporal stimulus features in multiple ways. These include an isomorphic representation of periodicity (as measured by the FFR), a representation based on increases in non-phase-locked activity (as measured by high gamma ERBP), and spatially distributed patterns of activity.

IDENTIFICATION OF NONLINEAR OSCILLATORY ACTIVITY EMBEDDED IN BROADBAND NEURAL SIGNALS

Oscillatory phenomena in the brain activity and their synchronization are frequently studied using mathematical models and analytic tools derived from nonlinear dynamics. In many experimental situations, however, neural signals have a broadband character and if oscillatory activity is present, its dynamical origin is unknown. To cope with these problems, a framework for detecting nonlinear oscillatory activity in broadband time series is presented. First, a narrow-band oscillatory mode is extracted from a broadband background. Second, it is tested whether the extracted mode is significantly different from linearly filtered noise, modelled as a linear stochastic process possibly passed through a static nonlinear transformation. If a nonlinear oscillatory mode is positively detected, further analysis using nonlinear approaches such as the phase synchronization analysis can potentially bring new information. For linear processes, however, standard approaches such as the coherence analysis are more appropriate and provide sufficient description of underlying interactions with smaller computational effort. The method is illustrated in a numerical example and applied to analyze experimentally obtained human EEG time series from a sleeping subject.

Evolution of genuine cross-correlation strength of focal onset seizures

To quantify the evolution of genuine zero-lag cross-correlations of focal onset seizures, we apply a recently introduced multivariate measure to broad band and to narrow-band EEG data. For frequency components below 12.5 Hz, the strength of genuine cross-correlations decreases significantly during the seizure and the immediate postseizure period, while higher frequency bands show a tendency of elevated cross-correlations during the same period. We conclude that in terms of genuine zero-lag cross-correlations, the electrical brain activity as assessed by scalp electrodes shows a significant spatial fragmentation, which might promote seizure offset.

Dysfunction of fronto-limbic brain circuitry in depression

BACKGROUND

depression is characterized by a stable negative bias toward emotional stimuli. This bias is associated with abnormal activities in emotion-processing regions (such as the amygdala) and cognitive-control regions (such as the dorsolateral prefrontal cortex [DLPFC]). However, it remains unclear whether the emotion-processing and cognitive-control regions affect negative cognitive bias independently or reciprocally.

EXPERIMENTAL PROCEDURE

a functional magnetic resonance imaging (fMRI) study of 16 depressed patients and 16 matched control subjects was conducted during an emotion-interference task.

RESULTS

the accuracies were significantly lower in the depressed group than in the control group when subjects attended to the happy and the neutral faces. Compared with control participants, depressed patients showed abnormal activity in bilateral amygdala and the right DLPFC. In addition, a significant correlation was found between the right amygdala and the right DLPFC when subjects observed the happy faces.

CONCLUSIONS

the results suggest that the dysfunction in positive emotion-processing and cognitive-control regions may reciprocally affect negative cognitive bias. Additionally, altered positive emotional interference processing in the fronto-limbic brain circuitry might be another cause of negative cognitive bias that finally leads to depression.

Time-frequency characterization of electrocorticographic recordings of epileptic patients using frequency-entropy similarity: a comparison to other bi-variate measures

Expert evaluation of electrocorticographic (ECoG) recordings forms the linchpin of seizure onset zone localization in the evaluation of epileptic patients for surgical resection. Numerous methods have been developed to analyze these complex recordings, including uni-variate (characterizing single channels), bi-variate (comparing channel pairs) and multivariate measures. Developing reliable algorithms may be helpful in clinical tasks such as localization of epileptogenic zones and seizure anticipation, as well as enabling better understanding of neuronal function and dynamics. Recently we have developed the frequency-entropy (F-E) similarity measure, and have tested its capability in mapping the epileptogenic zones. The F-E similarity measure compares time-frequency characterizations of two recordings. In this study, we examine the method's principles and utility and compare it to previously described bi-variate correspondence measures such as correlation, coherence, mean phase coherence and spectral comparison methods. Specially designed synthetic signals were used for illuminating theoretical differences between the measures. Intracranial recordings of four epileptic patients were then used for the measures' comparative analysis by creating a mean inter-electrode matrix for each of the correspondence measures and comparing the structure of these matrices during the inter-ictal and ictal periods. We found that the F-E similarity measure is able to discover spectral and temporal features in data which are hidden for the other measures and are important for foci localization.

Inter-brain synchronization during social interaction

During social interaction, both participants are continuously active, each modifying their own actions in response to the continuously changing actions of the partner. This continuous mutual adaptation results in interactional synchrony to which both members contribute. Freely exchanging the role of imitator and model is a well-framed example of interactional synchrony resulting from a mutual behavioral negotiation. How the participants' brain activity underlies this process is currently a question that hyperscanning recordings allow us to explore. In particular, it remains largely unknown to what extent oscillatory synchronization could emerge between two brains during social interaction. To explore this issue, 18 participants paired as 9 dyads were recorded with dual-video and dual-EEG setups while they were engaged in spontaneous imitation of hand movements. We measured interactional synchrony and the turn-taking between model and imitator. We discovered by the use of nonlinear techniques that states of interactional synchrony correlate with the emergence of an interbrain synchronizing network in the alpha-mu band between the right centroparietal regions. These regions have been suggested to play a pivotal role in social interaction. Here, they acted symmetrically as key functional hubs in the interindividual brainweb. Additionally, neural synchronization became asymmetrical in the higher frequency bands possibly reflecting a top-down modulation of the roles of model and imitator in the ongoing interaction.

Firing patterns and synchronization in nonsynaptic epileptiform activity: the effect of gap junctions modulated by potassium accumulation

Several lines of evidence point to the modification of firing patterns and of synchronization due to gap junctions (GJs) as having a role in the establishment of epileptiform activity (EA). However, previous studies consider GJs as ohmic resistors, ignoring the effects of intense variations in ionic concentration known to occur during seizures. In addition to GJs, extracellular potassium is regarded as a further important factor involved in seizure initiation and sustainment. To analyze how these two mechanisms act together to shape firing and synchronization, we use a detailed computational model for in vitro high-K(+) and low-Ca(2+) nonsynaptic EA. The model permits us to explore the modulation of electrotonic interactions under ionic concentration changes caused by electrodiffusion in the extracellular space, altered by tortuosity. In addition, we investigate the special case of null GJ current. Increased electrotonic interaction alters bursts and action potential frequencies, favoring synchronization. The particularities of pattern changes depend on the tortuosity and array size. Extracellular potassium accumulation alone modifies firing and synchronization when the GJ coupling is null.

Adaptive tracking of EEG oscillations

Neuronal oscillations are an important aspect of EEG recordings. These oscillations are supposed to be involved in several cognitive mechanisms. For instance, oscillatory activity is considered a key component for the top-down control of perception. However, measuring this activity and its influence requires precise extraction of frequency components. This processing is not straightforward. Particularly, difficulties with extracting oscillations arise due to their time-varying characteristics. Moreover, when phase information is needed, it is of the utmost importance to extract narrow-band signals. This paper presents a novel method using adaptive filters for tracking and extracting these time-varying oscillations. This scheme is designed to maximize the oscillatory behavior at the output of the adaptive filter. It is then capable of tracking an oscillation and describing its temporal evolution even during low amplitude time segments. Moreover, this method can be extended in order to track several oscillations simultaneously and to use multiple signals. These two extensions are particularly relevant in the framework of EEG data processing, where oscillations are active at the same time in different frequency bands and signals are recorded with multiple sensors. The presented tracking scheme is first tested with synthetic signals in order to highlight its capabilities. Then it is applied to data recorded during a visual shape discrimination experiment for assessing its usefulness during EEG processing and in detecting functionally relevant changes. This method is an interesting additional processing step for providing alternative information compared to classical time-frequency analyses and for improving the detection and analysis of cross-frequency couplings.