Figure 4 - uploaded by Coen Zandvoort
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Phase-amplitude coupling and bicoherence in the human electro-encephalographic data. Illustrative coupling estimates examples of the electro-encephalographic data of single participant (channel 17 of subject 8). Left-hand plots represent the mean and right-hand plots the ratio values using the surrogate data. A) Phase-amplitude coupling (PAC) as a function of the amplitude component and its bandwidth. The low-frequency component was fixed at 10 Hz as this frequency corresponded to the power peak in the alpha range. B-D) The PAC representations based on a broader (2:1-ratio), equalling (1:1-ratio), or narrowed (0.5:1-ratio) bandwidth underlines the importance of using filter settings in a 1:1-ratio. Here, the broad-band smearing results in merging multiple peaks. E) Bicoherence spectrally localise the peaks 11 and 22 Hz like the PAC-estimates with a narrowed bandwidth. PAC: phase-amplitude coupling; fW : filter width; f1: low frequency; f2: high frequency.
Source publication
Two measures of cross-frequency coupling (CFC) are Phase-Amplitude Coupling (PAC) and bicoherence. The estimation of PAC with meaningful bandwidth for the high frequency amplitude is crucial in order to avoid misinterpretations. While recommendations on the bandwidth of PAC's amplitude component exist, there is no consensus yet. Here, we show that...
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Background
Two measures of cross-frequency coupling are phase-amplitude coupling (PAC) and bicoherence. The estimation of PAC with meaningful bandwidth for the high-frequency amplitude is crucial in order to avoid misinterpretations. While recommendations on the bandwidth of PAC's amplitude component exist, there is no consensus yet. Theoretical re...
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Citations
... The theory for this can be found in Zandvoort and Nolte (2020) and is presented here in more detail. In the Fourier FIGURE 3 | Upper row: the absolute value of PLV as a function of coherence (upper left) and as a function of scaled coherence (upper right) for a 500 simulated Gaussian distributed random data sets each consisting of 10 7 realizations. ...
A large variety of methods exist to estimate brain coupling in the frequency domain from electrophysiological data measured, e.g., by EEG and MEG. Those data are to reasonable approximation, though certainly not perfectly, Gaussian distributed. This work is based on the well-known fact that for Gaussian distributed data, the cross-spectrum completely determines all statistical properties. In particular, for an infinite number of data, all normalized coupling measures at a given frequency are a function of complex coherency. However, it is largely unknown what the functional relations are. We here present those functional relations for six different measures: the weighted phase lag index, the phase lag index, the absolute value and imaginary part of the phase locking value (PLV), power envelope correlation, and power envelope correlation with correction for artifacts of volume conduction. With the exception of PLV, the final results are simple closed form formulas. In an excursion we also discuss differences between short time Fourier transformation and Hilbert transformation for estimations in the frequency domain. We tested in simulations of linear and non-linear dynamical systems and for empirical resting state EEG on sensor level to what extent a model, namely the respective function of coherency, can explain the observed couplings. For empirical data we found that for measures of phase-phase coupling deviations from the model are in general minor, while power envelope correlations systematically deviate from the model for all frequencies. For power envelope correlation with correction for artifacts of volume conduction the model cannot explain the observed couplings at all. We also analyzed power envelope correlation as a function of time and frequency in an event related experiment using a stroop reaction task and found significant event related deviations mostly in the alpha range.
... As a side note, the choice of the filter bandwidth for the phase and amplitude is still debated. While some previous studies recommended filtering the amplitude with a bandwidth twice as large as the one used for phase (2:1 ratio) [48], a recent study suggests that a 1:1 ratio might be better as this could prevent smearing [61]. ...
... The triangular freq-freq representation depicts coupling strength across many possible combinations of amplitude frequency bounds, where the x-axis corresponds to the starting frequency and the y-axis to the ending frequency. Here, the PAC is maximum for an amplitude range of [61,79] hz. ...
Despite being the focus of a thriving field of research, the biological mechanisms that underlie information integration in the brain are not yet fully understood. A theory that has gained a lot of traction in recent years suggests that multi-scale integration is regulated by a hierarchy of mutually interacting neural oscillations. In particular, there is accumulating evidence that phase-amplitude coupling (PAC), a specific form of cross-frequency interaction, plays a key role in numerous cognitive processes. Current research in the field is not only hampered by the absence of a gold standard for PAC analysis, but also by the computational costs of running exhaustive computations on large and high-dimensional electrophysiological brain signals. In addition, various signal properties and analyses parameters can lead to spurious PAC. Here, we present Tensorpac, an open-source Python toolbox dedicated to PAC analysis of neurophysiological data. The advantages of Tensorpac include (1) higher computational efficiency thanks to software design that combines tensor computations and parallel computing, (2) the implementation of all most widely used PAC methods in one package, (3) the statistical analysis of PAC measures, and (4) extended PAC visualization capabilities. Tensorpac is distributed under a BSD-3-Clause license and can be launched on any operating system (Linux, OSX and Windows). It can be installed directly via pip or downloaded from Github (https://github.com/EtienneCmb/tensorpac). By making Tensorpac available, we aim to enhance the reproducibility and quality of PAC research, and provide open tools that will accelerate future method development in neuroscience.
