Abstract
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, and η, with η a 1/f α noise process. The γ process is constructed as a product of a latent and unobserved high-frequency process x with 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.
Highlights
Cross frequency coupling (CFC) is a statistical relation between the phase or amplitude of a low frequency and the phase or amplitude of a high frequency
The rationale behind this proposal is based on the experimental observations that (i) relatively slow frequency oscillations tend to be coordinated over large regions of neural tissue, unlike higher frequency oscillations [1, 2], and (ii) oscillatory activity reflects changes in the excitability of neural tissue [3]
Experimental studies have shown that the nature of phase-amplitude CFC can be altered by predictive cues and attentional demands; the phase of the low-frequency oscillation can be reset such that a stimulus of attentional interest arrives at the phase of maximal excitability [11]
Summary
Cross frequency coupling (CFC) is a statistical relation between the phase or amplitude of a low frequency and the phase or amplitude of a high frequency. Focus is placed upon phase-amplitude CFC, which can be thought of as the correlation of the amplitude of a relatively highfrequency oscillation (γ) with the phase of a lower frequency oscillation (θ). The rationale behind this proposal is based on the experimental observations that (i) relatively slow frequency oscillations tend to be coordinated over large regions of neural tissue, unlike higher frequency oscillations [1, 2], and (ii) oscillatory activity reflects changes in the excitability of neural tissue [3]. Experimental studies have shown that the nature of phase-amplitude CFC can be altered by predictive cues and attentional demands; the phase of the low-frequency oscillation can be reset such that a stimulus of attentional interest arrives at the phase of maximal excitability [11]. Phase-amplitude CFC has been implicated in learning and memory [6, 12], and the dynamics of phaseamplitude CFC have been shown to change over the course of a cognitive task [8]
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