Article Figures & Data
Figures
- Figure 1.
Quantifying PAC: a, The raw signal. b, c, The temporal evolution of phase (b) and power (c) are typically identified using a discrete Fourier transform, wavelet transformations, or a bandpass filter followed by a Hilbert transformation. d, e, The relationship between phase and amplitude envelope can be quantified by the phase relationship between the two signals (e.g., coherence; d; Osipova et al., 2008) or by considering the nonuniformity of the phase distribution of fast-frequency power with respect to the slow oscillations (e; Tort et al., 2010).
- Figure 2.
Periodic nonsinusoidal signals expressed as Fourier series. a, A periodic nonsinusoidal signal (blue line) constructed by a sigmoidal function applied to sinusoidal signal:
. The signal can be expressed as a sum of sinusoids
. i.e. the periodic signal can be expressed as a sum of sinusoids at the harmonic frequencies. The green line shows the sum of the first 10 harmonics. b, The first 10 harmonics. c, The coefficient for amplitude and phase (αi and
). d, The PAC for the signal is sensitive to the higher harmonics and can therefore produce a spurious phase-to-power coupling. e, Examples of nonsinusoidal functions of some neuronal relevance: periodic pulses, a saw-tooth function, and a clipped sinusoidal signal. - Figure 3.
Gamma oscillations are modulated by theta phase in the rat hippocampus. a, The PAC measure applied to the LFP of rat data reveals phase-amplitude coupling. b, Gamma oscillations coupled to the phase of the theta oscillations are directly visible in the unfiltered LFPs. c, A histogram demonstrating the neuronal firing is modulated by gamma band oscillations. Reprinted by permission from Macmillan Publishers Ltd. (Colgin et al., 2009).
- Figure 4.
Gamma power in superficial cortical layers is coupled to alpha phase in deeper layers. a, Epochs of data in the alpha range are phase aligned according to the peaks in each epoch. For each epoch, the time–frequency representation of power is calculated and averaged. These data were obtained from laminar recordings in visual cortex of the monkey. Note that coupling was stronger across sites than within sites. This would not have been the case if the coupling was explained by nonsinusoidal alpha oscillations. b, The PAC measure applied to the data from the deep and superficial layers. Reproduced with permission from Cell Press (Spaak et al., 2012).
- Figure 5.
An MEG study in which subjects were asked to encode (‘Remember’) or ignore (‘No-Remember’) upcoming visual stimulus. The ‘Remember’ condition was associated with less alpha power (a) but stronger PAC (b). Given that PAC goes up when alpha power goes down, the coupling is not likely to be explained by higher harmonics of the alpha oscillations. Reproduced with permission from Macmillan Publishers Ltd. (Park et al., 2016).
In this issue
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- Article
- Abstract
- Significance Statement
- Detecting phase-amplitude coupling
- The problem: spurious identification PAC coupling
- How are nonsinusoidal oscillations generated?
- Three examples of reliable phase-to-amplitude coupling
- Does broadband gamma activity warrant special caution?
- Conclusion
- Acknowledgments
- Footnotes
- References
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