Tensorpac: An open-source Python toolbox for tensor-based phase-amplitude coupling measurement in electrophysiological brain signals

Abstract

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.

Shaping information processing: the role of oscillatory dynamics in a working-memory task

“…This measure reflects the degree to which the phase of each frequency is aligned across trials. In addition, we used the Tensorpac toolbox (Combrisson et al, 2020) to compute a time-resolved measure of phase-amplitude coupling (PAC) on source level. This algorithm measures PAC across trials (rather than across time).…”

Measuring Phase-Amplitude Coupling Based on the Jensen-Shannon Divergence and Correlation Matrix

“…In the previous simulation analysis, we only considered additive white Gaussian noise. In fact, the noise content may be much more complex and stronger in real EEG recordings, such as the sharp waveform of spikes and large artifacts [51,[72][73][74][75]. Specifically, movement artifacts are inevitable and unexpected during prolonged recordings (~24 hours) for closed loop applications [23,76].…”

“…The traditional and frequently used methods to measure the PAC include PLV [47], MVL [35], KLmi [26], and GLM [48]. Recently, some new methods have also been developed in the literature, such as driven autoregressive Measuring Phase-Amplitude Coupling Based on the Jensen-Shannon Divergence and Correlation Matrix Zhaohui Li, Xiaochen Bai, Rui Hu, and Xiaoli Li N (DAR) models [49], bispectrum [50], Gaussian-copula [51], mutual information [25], and adaptive decomposition [52].…”

Sigma Oscillations Protect or Reinstate Motor Memory Depending on their Temporal Coordination with Slow Waves

“…We tested, using the tensorPac (68) open-source Python toolbox, whether and when the phase of the 0.3-2 Hz oscillatory signal was coupled with the amplitude of the signal in the 7-30 Hz frequency range # (see supplemental Table S1.4) in relation with either the auditory cue onset or the negative peak of the SWs. The phase of the signal from -0.5 to 2.5 sec around the auditory cue onset and signal from -1 to 2 sec around the negative peak of the SWs was extracted from the filtered signal within the 0.3 -2 Hz SO frequency band.…”

“…The preferred phase (PP), which reflects whether the amplitude of the signal in a given frequency band is modulated by the phase of the signal in another band, was also computed using tensorPac (68) opensource Python toolbox. Based on our a priori hypotheses, these analyses focused on the amplitude of the signal in the sigma band and the phase of the SO.…”