Untangling cross-frequency coupling in neuroscience

Abstract

Cross-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.

Encephalography Connectivity on Sources in Male Nonsmokers after Nicotine Administration during the Resting State

“…In the online supplementary material (S1), we discuss a checklist extracted from Aru et al [12] with the purpose of mitigating false positives generated in our connectivity (rPDC algorithm) and phase-amplitude CFC (VL algorithm) analyses.…”

“…In addition, for the phase-amplitude CFC analysis we employed the mean resultant vector length (VL) algorithm [10]. Unfortunately, terminology is not consistently used throughout the literature; for instance, the ‘mean vector length' in Tort et al [5] is ‘Canolty's modulation index (MI)', while Tort's ‘modulation index (MI)' [5,11,12] is the Kullback-Leibler divergence. VL as defined in Miyakoshi et al [10] is constructed in parallel to an index termed ‘phase-locking-value (PLV)' elsewhere.…”

“…VL as defined in Miyakoshi et al [10] is constructed in parallel to an index termed ‘phase-locking-value (PLV)' elsewhere. Although Kullback-Leibler divergence is considered the gold standard [5], a recent paper challenged its sensitivity to spectral changes [12]. We consider VL to be a more robust measure of phase-amplitude CFC since restriction to the largest (top 2%) of the observed amplitudes probably causes a good tolerance to noise.…”

Components of the Language-Ready Brain

“…With larger neuronal populations oscillating at lower frequencies and smaller populations doing so at higher frequencies, CFC would enable their synchronization. In particular, it has been shown that via "phase-amplitude" CFC the phase of the lower frequency modulates the amplitude of the higher frequency component, a process claimed to be involved in information transfer for faculties such as memory (Tort et al, 2009, though see Aru et al, 2015 for current limitations of phase-amplitude modeling).…”

“…Using laminar electrodes to measure activity in monkey primate visual cortex, Spaak et al (2012) found that α phase in infragranular layers modulates γ amplitude in supergranular layers (see also Friston, 2008); similar to how thalamic nuclei oscillating at the α band synchronize distant cortical regions oscillating at higher frequencies. As Aru et al (2015) note, the most elegant theory to account for these findings is that periodic membrane potential fluctuations generate low frequency oscillations which subsequently gate the incidence of higher frequency activity in a phase-specific fashion. From a functional perspective, the above nested γ cycles could act as multiplexing mechanisms (Buzsáki, 2006, p. 356) for sustaining working memory representations by sending multiple representations as a single complex message to be recovered and "unpacked" downstream (see for empirical support, and Baddeley et al, 2014 for a review of working memory mechanisms); precisely as is seen in labeling and phasal transfer.…”