Elsevier

Journal of Neuroscience Methods

Volume 225, 30 March 2014, Pages 42-56
Journal of Neuroscience Methods

Computational Neuroscience
Toward a proper estimation of phase–amplitude coupling in neural oscillations

https://doi.org/10.1016/j.jneumeth.2014.01.002Get rights and content

Highlights

  • Boundary conditions are determined for appropriate use of standard PAC algorithms.

  • Oscillation-triggered coupling (OTC) estimates PAC by treating oscillations as events.

  • The occurrence of high-power phase- and frequency-specific oscillations explains PAC.

  • OTC can separate phase-locked oscillatory activity from spiking-related activity.

Abstract

Background

The phase–amplitude coupling (PAC) between distinct neural oscillations is critical to brain functions that include cross-scale organization, selection of attention, routing the flow of information through neural circuits, memory processing and information coding. Several methods for PAC estimation have been proposed but the limitations of PAC estimation as well as the assumptions about the data for accurate PAC estimation are unclear.

New method

We define boundary conditions for standard PAC algorithms and propose “oscillation-triggered coupling” (OTC), a parameter-free, data-driven algorithm for unbiased estimation of PAC. OTC establishes a unified framework that treats individual oscillations as discrete events for estimating PAC from a set of oscillations and for characterizing events from time windows as short as a single modulating oscillation.

Results

For accurate PAC estimation, standard PAC algorithms require amplitude filters with a bandwidth at least twice the modulatory frequency. The phase filters must be moderately narrow-band, especially when the modulatory rhythm is non-sinusoidal. The minimally appropriate analysis window is ∼10 s. We then demonstrate that OTC can characterize PAC by treating neural oscillations as discrete events rather than continuous phase and amplitude time series.

Comparison with existing methods

These findings show that in addition to providing the same information about PAC as the standard approach, OTC facilitates characterization of single oscillations and their sequences, in addition to explaining the role of individual oscillations in generating PAC patterns.

Conclusions

OTC allows PAC analysis at the level of individual oscillations and therefore enables investigation of PAC at the time scales of cognitive phenomena.

Introduction

The mammalian brain is a complex system with a distributed organization of sensory, motor, and executive computation centers across large areas of the cortex. While the distributed organization allows for parallel and specialized processing of information, it requires a mechanism for binding information from different computations into a coherent, unitary mental experience (von der Malsburg, 1981, Engel and Singer, 2001). The multipurpose, functional organization of local brain circuits also requires a mechanism for achieving dynamic, context-dependent cognitive and attentional control, a mechanism for the efficient routing of information between different brain computation centers, as well as a robust and efficient mechanism for coding the information in the dynamics of neural discharge (Phillips and Singer, 1997, Kelemen and Fenton, 2010). Various forms of neural synchrony, the coordinated synchronized activation of same-function cells and the active desynchronization of different-function cells have been proposed as this fundamental mechanism of neural computation (von der Malsburg and Schneider, 1986, Buzsaki, 2010). In the recent decade, phase–amplitude synchrony of field potential oscillations, the coupling between the phase of a slow oscillation and the amplitude of a faster oscillation, has received significant attention as a candidate synchronizing mechanism and is the subject of the present work.

In phase–amplitude coupling (PAC), the amplitude of a fast signal (e.g. gamma 30–100 Hz) is modulated by the phase of a slow signal (e.g. theta 5–12 Hz). This interaction is sometimes called “nesting” because the fast oscillation is precisely fitted within the cycle of the slower oscillation (Lakatos et al., 2005). The term phase–amplitude cross-frequency coupling (CFC) has also been used for this phenomenon, because the interaction happens between two distinct oscillatory bands (Bragin et al., 1995). This particular property makes PAC principally different from other synchrony measures such as amplitude synchrony (assessed by cross-correlation) or phase synchrony (assessed by phase locking statistics) because it reflects the dynamical relationship between two oscillations that are generated by distinct neurophysiological mechanisms. As the oscillations have different biophysical origins, the consequent PAC is not easily attributed to the spurious occurrence of synchrony caused by volume conduction, selection of reference or synchronized noise. The concept of a cross-scale organization of neural activity (Jensen and Colgin, 2007, Le Van Quyen, 2011) offers a possible neural mechanism for integrating information between several functionally distinct networks, to accomplish perceptual binding, selective attention, cognitive control and the recruitment of computational and representational cell assemblies. Neural activity in macroscopic (slow oscillations), mesoscopic (high frequency oscillations) and microscopic (single neuron activity) scales are braided together such that a progressively faster activity occurs within a specific, short time window of a slower activity. Indeed, several conceptual and theoretical frameworks have been proposed for the computational role of PAC (Canolty and Knight, 2010). Given the growing interest, and the substantial value in PAC as a mechanism for neural computation it is important for the broader neuroscience community to understand how to accurately measure and interpret PAC, and appreciate the limitations of the current methods.

This paper is written in two parts. The first part is an analysis of the standard approach to computing PAC. We examine the assumptions and by parametric analyses, identify the filter and temporal requirements for estimating PAC accurately. The second part introduces a novel approach to estimate, measure and characterize PAC. It operates on two time scales, one is global, and like traditional methods it is only robust when applied to long time series of data, on the order of many seconds. The approach also allows the characterization of PAC on short time scales, as short as a single oscillation.

Section snippets

Materials and methods

Multiple algorithms for quantifying PAC have been proposed (Fig. 1). The common starting point of all algorithms is an extraction of the phase and the amplitude information from the sampled signal x(t). This can be accomplished by band-pass filtering the signal into the bands of interest, for example theta 7–9 Hz and fast gamma 62–100 Hz followed by the Hilbert transform (Fig. 1A–C). There are other methods for extraction of phase and amplitude information, for example convolution of the signal

Results

Part I

Properties of standard PAC algorithms

We investigated the boundary conditions for the appropriate estimation of phase–amplitude coupling in LFP recordings. We demonstrated the importance of filter properties and analysis window size for estimating PAC. Because these properties define the time–frequency resolution of the analyses, it is necessary to consider them carefully. Phase filters should be narrow band to obtain meaningful phase information but not excessively narrow to distort non-sinusoidal shapes of rhythms such as

Acknowledgements

Supported by NIMH Grants R01MH084038 and R01MH099128.

References (50)

  • O. Jensen et al.

    Cross-frequency coupling between neuronal oscillations

    Trends Cogn Sci

    (2007)
  • Y. Kajikawa et al.

    How local is the local field potential?

    Neuron

    (2011)
  • M.A. Kramer et al.

    Sharp edge artifacts and spurious coupling in EEG frequency comodulation measures

    J Neurosci Methods

    (2008)
  • M. Le Van Quyen

    The brainweb of cross-scale interactions

    New Ideas Psychol

    (2011)
  • M. Le Van Quyen et al.

    Comparison of Hilbert transform and wavelet methods for the analysis of neuronal synchrony

    J Neurosci Methods

    (2001)
  • L.W. Leung et al.

    Spectral analysis of hippocampal unit train in relation to hippocampal EEG

    Electroencephalogr Clin Neurophysiol

    (1983)
  • K. Mizuseki et al.

    Theta oscillations provide temporal windows for local circuit computation in the entorhinal–hippocampal loop

    Neuron

    (2009)
  • W.D. Penny et al.

    Testing for nested oscillation

    J Neurosci Methods

    (2008)
  • C.E. Schroeder et al.

    Low-frequency neuronal oscillations as instruments of sensory selection

    Trends Neurosci

    (2009)
  • A.B. Tort et al.

    Theta-associated high-frequency oscillations (110–160 Hz) in the hippocampus and neocortex

    Prog Neurobiol

    (2013)
  • N. Axmacher et al.

    Cross-frequency coupling supports multi-item working memory in the human hippocampus

    Proc Natl Acad Sci USA

    (2010)
  • M.A. Belluscio et al.

    Cross-frequency phase–phase coupling between theta and gamma oscillations in the hippocampus

    J Neurosci

    (2012)
  • J.I. Berman et al.

    Variable bandwidth filtering for improved sensitivity of cross-frequency coupling metrics

    Brain Connect

    (2012)
  • A. Bragin et al.

    Gamma (40–100 Hz) oscillation in the hippocampus of the behaving rat

    J Neurosci

    (1995)
  • G. Buzsaki et al.

    Neuronal oscillations in cortical networks

    Science

    (2004)
  • Cited by (0)

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