scholarly journals Mutual Information of Multiple Rhythms for EEG Signals

2020 ◽  
Vol 14 ◽  
Author(s):  
Antonio José Ibáñez-Molina ◽  
María Felipa Soriano ◽  
Sergio Iglesias-Parro
Keyword(s):  
Time Series ◽  
Mutual Information ◽  
A Priori ◽  
Basic Mechanism ◽  
Frequency Component ◽  
Brain Functioning ◽  
Single Method ◽  
Spatiotemporal Scales ◽  
Frequency Coupling ◽  
Cross Frequency Coupling

Electroencephalograms (EEG) are one of the most commonly used measures to study brain functioning at a macroscopic level. The structure of the EEG time series is composed of many neural rhythms interacting at different spatiotemporal scales. This interaction is often named as cross frequency coupling, and consists of transient couplings between various parameters of different rhythms. This coupling has been hypothesized to be a basic mechanism involved in cognitive functions. There are several methods to measure cross frequency coupling between two rhythms but no single method has been selected as the gold standard. Current methods only serve to explore two rhythms at a time, are computationally demanding, and impose assumptions about the nature of the signal. Here we present a new approach based on Information Theory in which we can characterize the interaction of more than two rhythms in a given EEG time series. It estimates the mutual information of multiple rhythms (MIMR) extracted from the original signal. We tested this measure using simulated and real empirical data. We simulated signals composed of three frequencies and background noise. When the coupling between each frequency component was manipulated, we found a significant variation in the MIMR. In addition, we found that MIMR was sensitive to real EEG time series collected with open vs. closed eyes, and intra-cortical recordings from epileptic and non-epileptic signals registered at different regions of the brain. MIMR is presented as a tool to explore multiple rhythms, easy to compute and without a priori assumptions.

scholarly journals An extension of Phase Linearity Measurement for revealing cross frequency coupling among brain areas

2019 ◽  
Vol 16 (1) ◽  
Author(s):  
Pierpaolo Sorrentino ◽  
Michele Ambrosanio ◽  
Rosaria Rucco ◽  
Fabio Baselice
Keyword(s):  
A Priori ◽  
Behavioral Responses ◽  
Real Data ◽  
Frequency Synchronization ◽  
Brain Areas ◽  
Neural Ensembles ◽  
Frequency Coupling ◽  
Cross Frequency Coupling ◽  
Reconstructed Data

Abstract Background Brain areas need to coordinate their activity in order to enable complex behavioral responses. Synchronization is one of the mechanisms neural ensembles use to communicate. While synchronization between signals operating at similar frequencies is fairly straightforward, the estimation of synchronization occurring between different frequencies of oscillations has proven harder to capture. One specifically hard challenge is to estimate cross-frequency synchronization between broadband signals when no a priori hypothesis is available about the frequencies involved in the synchronization. Methods In the present manuscript, we expand upon the phase linearity measurement, an iso-frequency synchronization metrics previously developed by our group, in order to provide a conceptually similar approach able to detect the presence of cross-frequency synchronization between any components of the analyzed broadband signals. Results The methodology has been tested on both synthetic and real data. We first exploited Gaussian process realizations in order to explore the properties of our new metrics in a synthetic case study. Subsequently, we analyze real source-reconstructed data acquired by a magnetoencephalographic system from healthy controls in a clinical setting to study the performance of our metrics in a realistic environment. Conclusions In the present paper we provide an evolution of the PLM methodology able to reveal the presence of cross-frequency synchronization between broadband data.

scholarly journals Detection of cross-frequency coupling between brain areas: an extension of phase-linearity measurement

2020 ◽  
Author(s):  
Pierpaolo Sorrentino ◽  
Michele Ambrosanio ◽  
Rosaria Rucco ◽  
Joana Cabral ◽  
Leonardo L. Gollo ◽  
...  
Keyword(s):  
Large Scale ◽  
Brain Activity ◽  
A Priori ◽  
Broad Band ◽  
Main Idea ◽  
Theoretical Explanation ◽  
Frequency Synchronization ◽  
Brain Areas ◽  
Frequency Coupling ◽  
Cross Frequency Coupling

AbstractThe current paper proposes a method to estimate phase to phase cross-frequency coupling between brain areas, applied to broadband signals, without any a priori hypothesis about the frequency of the synchronized components. N:m synchronization is the only form of cross-frequency synchronization that allows the exchange of information at the time resolution of the faster signal, hence likely to play a fundamental role in large-scale coordination of brain activity. The proposed method, named cross-frequency phase linearity measurement (CF-PLM), builds and expands upon the phase linearity measurement, an iso-frequency connectivity metrics previously published by our group. The main idea lies in using the shape of the interferometric spectrum of the two analyzed signals in order to estimate the strength of cross-frequency coupling. Here, we demonstrate that the CF-PLM successfully retrieves the (different) frequencies of the original broad-band signals involved in the connectivity process. Furthermore, if the broadband signal has some frequency components that are synchronized in iso-frequency and some others that are synchronized in cross-frequency, our methodology can successfully disentangle them and describe the behaviour of each frequency component separately. We first provide a theoretical explanation of the metrics. Then, we test the proposed metric on simulated data from coupled oscillators synchronized in iso- and cross-frequency (using both Rössler and Kuramoto oscillator models), and subsequently apply it on real data from brain activity, using source-reconstructed Magnetoencephalography (MEG) data. In the synthetic data, our results show reliable estimates even in the presence of noise and limited sample sizes. In the real signals, components synchronized in cross-frequency are retrieved, together with their oscillation frequencies. All in all, our method is useful to estimate n:m synchronization, based solely on the phase of the signals (independently of the amplitude), and no a-priori hypothesis is available about the expected frequencies. Our method can be exploited to more accurately describe patterns of cross-frequency synchronization and determine the central frequencies involved in the coupling.

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

2017 ◽  
Vol 13 (12) ◽  
pp. e1005893 ◽  
Author(s):  
Tom Dupré la Tour ◽  
Lucille Tallot ◽  
Laetitia Grabot ◽  
Valérie Doyère ◽  
Virginie van Wassenhove ◽  
...  
Keyword(s):  
Time Series ◽  
Non Linear ◽  
Auto Regressive ◽  
Frequency Coupling ◽  
Cross Frequency Coupling

scholarly journals Periodic Non-Sinusoidal Activity Can Produce Cross-Frequency Coupling in Cortical Signals in the Absence of Functional Interaction Between Neural Sources

2016 ◽  
Author(s):  
Edden M. Gerber ◽  
Boaz Sadeh ◽  
Andrew Ward ◽  
Robert T. Knight ◽  
Leon Y. Deouell
Keyword(s):  
Frequency Component ◽  
High Frequency Component ◽  
Functional Interaction ◽  
Scalp Eeg ◽  
Periodic Potentials ◽  
Frequency Coupling ◽  
Eeg Recordings ◽  
Low Amplitude ◽  
Cross Frequency Coupling ◽  
Intracranial Recordings

AbstractThe analysis of cross-frequency coupling (CFC) has become popular in studies involving intracranial and scalp EEG recordings in humans. It has been argued that some cases where CFC is mathematically present may not reflect an interaction of two distinct yet functionally coupled neural sources with different frequencies. Here we provide two empirical examples from intracranial recordings where CFC can be shown to be driven by the shape of a periodic waveform rather than by a functional interaction between distinct sources. Using simulations, we also present a generalized and realistic scenario where such coupling may arise. This scenario, which we term waveform-dependent CFC, arises when sharp waveforms (e.g., cortical potentials) occur in a periodic manner throughout parts of the data. Since the waveforms are repeated periodically, they constitute a slow wave that is inherently phase-aligned with the high-frequency component carried by the same waveforms. We submit that such behavior of the data, which seems to be present in various cortical signals, cannot be interpreted as reflecting functional modulation between distinct neural sources without additional evidence. In addition, we show that even low amplitude periodic potentials that cannot be readily observed or controlled for, are sufficient for significant CFC to occur.

scholarly journals Non-linear Auto-Regressive Models for Cross-Frequency Coupling in Neural Time Series

2017 ◽  
Author(s):  
Tom Dupré la Tour ◽  
Lucille Tallot ◽  
Laetitia Grabot ◽  
Valérie Doyère ◽  
Virginie van Wassenhove ◽  
...  
Keyword(s):  
Time Series ◽  
Model Selection ◽  
High Frequency ◽  
Goodness Of Fit ◽  
Model Based ◽  
Non Linear ◽  
Auto Regressive ◽  
Frequency Coupling ◽  
Cross Frequency Coupling ◽  
Driving Signal

AbstractWe 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.Author SummaryNeural 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.

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

2021 ◽  
Vol 15 ◽  
Author(s):  
Chi-Hung Juan ◽  
Kien Trong Nguyen ◽  
Wei-Kuang Liang ◽  
Andrew J. Quinn ◽  
Yen-Hsun Chen ◽  
...  
Keyword(s):  
Spectral Analysis ◽  
Temporal Dynamics ◽  
A Priori ◽  
Sensory Stimuli ◽  
Electrophysiological Data ◽  
Study Results ◽  
Non Linear ◽  
Neural Entrainment ◽  
Frequency Coupling ◽  
Cross Frequency Coupling

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.

scholarly journals Untangling cross-frequency coupling in neuroscience

2014 ◽  
Author(s):  
Juhan Aru ◽  
Jaan Aru ◽  
Viola Priesemann ◽  
Michael Wibral ◽  
Luiz Lana ◽  
...  
Keyword(s):  
Time Series ◽  
Brain Function ◽  
Neural Dynamics ◽  
Spatial And Temporal Scales ◽  
Total Absence ◽  
Road Map ◽  
Frequency Components ◽  
Frequency Coupling ◽  
Cross Frequency Coupling ◽  
Practical Recommendations

AbstractCross-frequency coupling (CFC) has been proposed to coordinate neural dynamics across spatial and temporal scales. Despite its potential relevance for understanding healthy and pathological brain function, the standard CFC analysis and physiological interpretation come with fundamental problems. For example, apparent CFC can appear because of spectral correlations due to common non-stationarities that may arise in the total absence of interactions between neural frequency components. To provide a road map towards an improved mechanistic understanding of CFC, we organize the available and potential novel statistical/modeling approaches according to their biophysical interpretability. While we do not provide solutions for all the problems described, we provide a list of practical recommendations to avoid common errors and to enhance the interpretability of CFC analysis.HighlightsFundamental caveats and confounds in the methodology of assessing CFC are discussed.Significant CFC can be observed without any underlying physiological coupling.Non-stationarity of a time-series leads to spectral correlations interpreted as CFC.We offer practical recommendations, which can relieve some of the current confounds.Further theoretical and experimental work is needed to ground the CFC analysis.

scholarly journals Mutual Information in Frequency and Its Application to Measure Cross-Frequency Coupling in Epilepsy

2018 ◽  
Vol 66 (11) ◽  
pp. 3008-3023 ◽  
Author(s):  
Rakesh Malladi ◽  
Don H. Johnson ◽  
Giridhar P. Kalamangalam ◽  
Nitin Tandon ◽  
Behnaam Aazhang
Keyword(s):  
Mutual Information ◽  
Frequency Coupling ◽  
Cross Frequency Coupling

scholarly journals A Time-Series Model of Phase Amplitude Cross Frequency Coupling and Comparison of Spectral Characteristics with Neural Data

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Kyle Q. Lepage ◽  
Sujith Vijayan
Keyword(s):  
Time Series ◽  
High Frequency ◽  
Spectral Characteristics ◽  
Low Frequency ◽  
Time Series Model ◽  
High Frequency Component ◽  
Frequency Oscillation ◽  
Low Frequency Oscillation ◽  
Frequency Coupling ◽  
Cross Frequency Coupling

Stochastic processes that exhibit cross-frequency coupling (CFC) are introduced. The ability of these processes to model observed CFC in neural recordings is investigated by comparison with published spectra. One of the proposed models, based on multiplying a pulsatile function of a low-frequency oscillation (θ) with an unobserved and high-frequency component, yields a process with a spectrum that is consistent with observation. Other models, such as those employing a biphasic pulsatile function of a low-frequency oscillation, are demonstrated to be less suitable. We introduce the full stochastic process time series model as a summation of three component weak-sense stationary (WSS) processes, namely,θ,γ, andη, withηa1/fαnoise process. Theγprocess is constructed as a product of a latent and unobserved high-frequency processxwith a function of the lagged, low-frequency oscillatory component (θ). After demonstrating that the model process is WSS, an appropriate method of simulation is introduced based upon the WSS property. This work may be of interest to researchers seeking to connect inhibitory and excitatory dynamics directly to observation in a model that accounts for known temporal dependence or to researchers seeking to examine what can occur in a multiplicative time-domain CFC mechanism.

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