Phase-amplitude coupling

Authors: Soheila Samiee, Thomas Donoghue, Francois Tadel, Sylvain Baillet

This tutorial introduces the concept of phase-amplitude coupling (PAC) and the metrics used in Brainstorm to estimate it. Those tools are illustrated first on simulated recordings. In separate tutorials, we illustrate how to use them on resting-state MEG recordings and rat intra-cranial signals.

Introduction

Phase-amplitude coupling

The oscillatory activity in multiple frequency bands is observed in different levels of organization from micro-scale to meso-scale and macro-scale. Studies have been shown that brain functions are achieved with simultaneous oscillations in different frequency bands [Schutter and Knyazev, 2012]. Classical studies in this field were only focused on rhythms in each of these frequency bands, and it has been reported that these rhythms are linked to perception and cognition [Cohen, 2008]. However, it is revealed that not only examining brain activity in each single frequency band, but also the relation and interaction between oscillations in different bands, can be informative in understanding brain function. Thus, this concept increasingly received interest especially in the field of cognitive neuroscience. This interaction between several oscillations is also known as cross-frequency coupling (CFC).

Two forms of recognized CFC in brain rhythms are: phase amplitude coupling (PAC), and phase-phase coupling (PPC). In the first type, which is also called nested oscillations, the phase of the lower frequency oscillation (nesting) drives the power of the coupled higher frequency oscillation (nested), that results in synchronization of amplitude envelope of faster rhythms with the phase of slower rhythms. The second form is amplitude independent phase locking between n cycles of high frequency oscillation and m cycles of low frequency one. That's why it is also called n:m phase synchrony [Palva et al., 2005].

Among these two types, phase-amplitude coupling received more interests. It has been shown that behavioral tasks can modulate the phase amplitude coupling [Voytek et al., 2010], and also it is potentially involved in sensory integration, memory process, and attentional selection [Lisman and Idiart, 1995, Lisman, 2005, Schroeder and Lakatos, 2009]. This coupling is observed in several brain regions including hippocampus, basal ganglia, and neocortex; and these observations are reported in rats, mice, sheep, and monkeys, as well as humans [Tort et al., 2010].

Following figure shows a schematic of phase amplitude coupling. In the top signal, we have the sum of a fast and slow oscillations, where the power of fast oscillation's envelope changes with the phase of the slower oscillation, which is a sample of PAC. The bottom signal shows only the fast oscillation and the variation in its power. As it is obvious from comparison of two signals, the fast rhythm's power is always maximum, at a certain phase of slower oscillation, this phase is called coupling phase.

pac_schematic1.jpg

Measures of cross frequency phase amplitude coupling can monitor the relationship between the activities that modulate low frequency oscillations like sensory or motor inputs, and the local cortical activities such as local computations that are correlated to amplitude of higher frequency oscillation [Canolty and Knight, 2010].

All these interesting features of this coupling resulted in proposing several methods for its measuring. Each of these methods has certain limitations and also advantages over the others, and can be used for a particular purpose; that's why no preferred standard method has been chosen for this estimation yet [Tort et al., 2010]. One of these methods, which is implemented in Brainstorm, is called Mean Vector Length (MVL), proposed by Canolty et al. (2006). This method and the step by step instruction of using it is described in this section of the tutorial.

A measure of PAC: Mean Vector Length (Modulation Index)

Canolty et al. (2006) pointed out that a time series defined in the complex plane by $$A_{f_A}. e^{i \phi_{f_p}}$$ could be used to extract a phase-amplitude coupling measure. In this formula $$A_{f_A}$$ is the envelope of fast oscillation, and $$\phi_{f_p}$$ is the phase of slow oscillation.

Therefore, after filtering in fast and slow oscillation, and extracting the phase of slow, and the amplitude of fast rhytm; each instantaneous fast oscillation amplitude component in time is represented by the length of the complex vector, whereas the slow oscillation phase of the same time point is represented by the vector angle (see following figure).

mvl_step3.jpg mvl_steps.jpg

At the absence of phase-amplitude coupling, the plot of the $$A_{f_A} .e^{i \phi_{f_p}}$$ time series in the complex plane is characterized by a roughly uniform circular density of vector points, symmetric around zero, because the $$A_{f_A}$$ values (averaged over cycles of slow oscillation) are approximately the same for all phases. If there is modulation of the $$f_A$$ amplitude by the $$f_P$$ phase, the $$A_{f_A}$$ would be higher at certain phases than others. This higher amplitude for certain angles will lead to a “bump” in the polar plot of the $$A_{f_A}.e^{i \phi_{f_p}}$$, leading to loss of symmetry around zero. This loss of symmetry can be inferred by measuring the length of the vector obtained from the mean over all points in the complex plane. It is thus assumed that a symmetric distribution as it occurs during lack of coupling leads to a small mean vector length (because the points in the different phases would cancel each other), whereas the existence of coupling leads to a larger mean vector length [Tort et al. 2010]. For more detail read [Canolty et al, 2006].

References

Canolty RT, Edwards E, Dalal SS, Soltani M, Nagarajan SS, Kirsch HE, Berger MS, Barbaro NM, Knight RT (2006). High gamma power is phase-locked to theta oscillations in human neocortex, Science, 313(5793), 1626-1628.

Canolty RT, Knight RT (2010). The functional role of cross-frequency coupling. Trends in cognitive sciences, 14(11), 506-515

Cohen MX (2008). Assessing transient cross-frequency coupling in EEG data. Journal of neuroscience methods, 168(2), 494-499.

Palva JM, Palva S, Kaila K (2005). Phase synchrony among neuronal oscillations in the human cortex. The Journal of Neuroscience, 25(15), 3962-3972.

Schutter DJ, Knyazev GG(2012). Cross-frequency coupling of brain oscillations in studying motivation and emotion. Motivation and emotion, 36(1), 46-54.

Tort AB, Komorowski R, Eichenbaum H, Kopell N (2010). Measuring phase-amplitude coupling between neuronal oscillations of different frequencies. Journal of neurophysiology, 104(2), 1195-1210.

Voytek B, Canolty RT, Shestyuk A, Crone NE, Parvizi J, Knight RT (2010). Shifts in gamma phase–amplitude coupling frequency from theta to alpha over posterior cortex during visual tasks.Frontiers in human neuroscience, 4.

Simulate signals

You can generate a synthesized data containing cross-frequency phase-amplitude coupling, with your preferred parameters. The model used for data generation is a simple method introduced in [Tort et al. 2010]. In this section, we generate a dataset of synthesized signal and analyze it with available phase-amplitude coupling estimation tool in brainstorm.

Process options

PAC estimation

To extract the phase-amplitude coupling from this signal:

Process options

Input options:

Estimator options:

Loop options: Should be left at default options unless you know how to use them.

Output options:

File contents

The files saved by this process have the same structure as the time-frequency files, with an additional "sPAC" field. To review its contents, right-click on the PAC file > File > View file contents.

file_contents.gif

Some of the relevent fields in the maxPAC files:

Recommendations

PAC estimation using the MVL algorithm

In order to have a reliable result from this method it is required to use a signal which length is at least ten cycles of the slowest oscillation in your low oscillation band.

Considering this point is more important in analysis of real databases, where the noise level (and/or background brain activity) can be higher than synthesized data, and the coupling intensity can be low. Thus, if you want to examine the coupling for slow oscillations in [2, 14] Hz, it would be better to use a signal with minimum length of 10 cycles of the slowest oscillation, which would be 10 x 0.5 = 5 S.





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Tutorials/TutPac (last edited 2015-01-29 20:15:28 by ?SoheilaSamiee)