Abstract
Cross-frequency interactions, a form of oscillatory neural activity, are thought to play an essential role in the integration of distributed information in the brain. Indeed, phase-amplitude interactions are believed to allow for the transfer of information from large-scale brain networks, oscillating at low frequencies, to local, rapidly oscillating neural assemblies. A promising approach to estimating such interactions is the use of transfer entropy (TE), a non-linear, information-theory-based effective connectivity measure. The conventional method involves feeding instantaneous phase and amplitude time series, extracted at the target frequencies, to a TE estimator. In this work, we propose that the problem of directed phase-amplitude interaction detection is recast as a phase TE estimation problem, under the hypothesis that estimating TE from data of the same nature, i.e., two phase time series, will improve the robustness to the common confounding factors that affect connectivity measures, such as the presence of high noise levels. We implement our proposal using a kernel-based TE estimator, defined in terms of Renyi’s α entropy, which has successfully been used to compute single-trial phase TE. We tested our approach on the synthetic data generated through a simulation model capable of producing a time series with directed phase-amplitude interactions at two given frequencies, and on EEG data from a cognitive task designed to activate working memory, a memory system whose underpinning mechanisms are thought to include phase–amplitude couplings. Our proposal detected statistically significant interactions between the simulated signals at the desired frequencies for the synthetic data, identifying the correct direction of the interaction. It also displayed higher robustness to noise than the alternative methods. The results attained for the working memory data showed that the proposed approach codes connectivity patterns based on directed phase–amplitude interactions, that allow for the different cognitive load levels of the working memory task to be differentiated.
Highlights
Biological neural systems exhibit rhythmic activity across many scales, from the spiking activity of individual neurons to the electric potentials generated by large populations of neurons, measurable from the scalp in the form of electroencephalographic (EEG) recordings [1]
The results show that the proposed approach captures strong and statistically significant phase-amplitude-directed interactions around the target frequencies used to generate the simulated data
The central idea behind our proposal is to recast the problem of detecting directed phase-amplitude coupling (PAC) as that of estimating directed interactions between phase time series
Summary
Biological neural systems exhibit rhythmic activity across many scales, from the spiking activity of individual neurons to the electric potentials generated by large populations of neurons, measurable from the scalp in the form of electroencephalographic (EEG) recordings [1]. The most widely studied instance of CFC is the modulation of the amplitude envelope of high-frequency oscillations by the phase evolution of low-frequency activity, known as phase-amplitude coupling (PAC) [2,3,4]. Phase-amplitude interactions are commonly assessed using electrophysiological data through metrics of statistical dependency, such as the modulation index, mean vector length, and variations in the concept of mutual information [8,9,10] They are unable to capture the directionality and delay of phase-amplitude interactions, quantities that are intrinsic to the concept of information being sent from one neural assembly to another [1,5,11]. Transfer entropy (TE) is a model-free connectivity measure that estimates the directed interaction, or information flow, between two dynamical systems [14,15] It is specially well-suited to exploratory analysis in neuroscience because of its ability to detect unknown non-linear interactions [16, 17]. It has been argued that filtering before TE computation negatively affects the results of TE [19,20], leading to false positives, and that it may not have the desired frequency-specific effects [1]
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