Neuronal Oscillations with Non-sinusoidal Morphology Produce Spurious Phase-to-Amplitude Coupling and Directionality

Abstract

Neuronal oscillations support cognitive processing. Modern views suggest that neuronal oscillations do not only reflect coordinated activity in spatially distributed networks, but also that there is interaction between the oscillations at different frequencies. For example, invasive recordings in animals and humans have found that the amplitude of fast oscillations (>40 Hz) occur non-uniformly within the phase of slower oscillations, forming the so-called cross-frequency coupling (CFC). However, the CFC patterns might be influenced by features in the signal that do not relate to underlying physiological interactions. For example, CFC estimates may be sensitive to spectral correlations due to non-sinusoidal properties of the alpha band wave morphology. To investigate this issue, we performed CFC analysis using experimental and synthetic data. The former consisted in a double-blind magnetoencephalography pharmacological study in which participants received either placebo, 0.5 or 1.5 mg of lorazepam (LZP; GABAergic enhancer) in different experimental sessions. By recording oscillatory brain activity with during rest and working memory (WM), we were able to demonstrate that posterior alpha (8–12 Hz) phase was coupled to beta-low gamma band (20–45 Hz) amplitude envelope during all sessions. Importantly, bicoherence values around the harmonics of the alpha frequency were similar both in magnitude and topographic distribution to the cross-frequency coherence (CFCoh) values observed in the alpha-phase to beta-low gamma coupling. In addition, despite the large CFCoh we found no significant cross-frequency directionality (CFD). Critically, simulations demonstrated that a sizable part of our empirical CFCoh between alpha and beta-low gamma coupling and the lack of CFD could be explained by two-three harmonics aligned in zero phase-lag produced by the physiologically characteristic alpha asymmetry in the amplitude of the peaks relative to the troughs. Furthermore, we showed that periodic signals whose waveform deviate from pure sine waves produce non-zero CFCoh with predictable CFD. Our results reveal the important role of the non-sinusoidal wave morphology on state of the art CFC metrics and we recommend caution with strong physiological interpretations of CFC and suggest basic data quality checks to enhance the mechanistic understanding of CFC.

On cross-frequency phase-phase coupling between theta and gamma oscillations in the hippocampus

“…Though a very weak but true coupling effect cannot be discarded, based on our analysis of sawtooth waves (Figure 4 and Figure 4—figure supplement 2), we believe these results can be explained by theta harmonics, which would remain phase-locked to the fundamental frequency under small time shifts. Sharp signal deflections have been previously recognized to generate artifactual phase-amplitude coupling (Kramer et al, 2008; Scheffer-Teixeira et al, 2013; Tort et al, 2013; Aru et al, 2015; Lozano-Soldevilla et al, 2016). Interestingly, Hyafil (2015) recently suggested that the non-sinusoidality of alpha waves could underlie the 1:2 phase-locking between alpha and beta observed in human EEG (Nikulin and Brismar, 2006; see also Palva et al, 2005).…”

Oscillatory Dynamics of Prefrontal Cognitive Control

“…For example, Parkinson rigidity has been linked to elevated CFC between the basal ganglia and motor cortex [94]. However, it is currently unclear whether this effect might constitute an artifact of the non-sinusoidal characteristics of beta rhythms in PD [95]. Furthermore, another recent report demonstrated that low frequency tACS that was frequency- and phase-matched to the tremor frequency could reduce the shaking through phase cancellation [96].…”

Discriminating Valid from Spurious Indices of Phase-Amplitude Coupling

“…Note that, due to frequency smoothing as a result of estimating the envelope for the fast frequencies, the harmonic contributions are often “bleeding” together in the PAC plot. Therefore, great care must be taken when interpreting measures of PAC, in particular in the frequency bands of the higher harmonics, additionally taking into account the effective frequency smoothing (Kramer et al, 2008; Aru et al, 2015; Cole et al, 2016; Jones, 2016; Lozano-Soldevilla et al, 2016). In particular, Cole et al (2016) and Sheremet et al (2016) provide concrete examples from respective intracranial human and hippocampal rat recordings in which nonsinusoidal oscillations contribute to estimates of PAC.…”