Full Length ArticlesA method for event-related phase/amplitude coupling
Highlights
► Event-related phase/amplitude coupling (ERPAC) enables time-resolved coupling. ► ERPAC is easy to instantiate for human and animal electrophysiology. ► ERPAC provides novel insight into the timing of brain dynamics. ► ERPAC can be used to assess the timing of coupling across brain regions.
Introduction
The mammalian neo- and archicortices generate electrophysiological oscillatory rhythms (Buzsáki and Draguhn, 2004, Engel et al., 2001) that interact to facilitate communication (Fries, 2005, Fröhlich and McCormick, 2010, Sirota et al., 2008). The amplitude and phase of these rhythms are typically assessed in an event-related manner across trials or subjects. There is emerging evidence that frequency-specific rhythms are often nested within other frequency bands (Kramer et al., 2008a, Roopun et al., 2008, Tort et al., 2009; see Canolty and Knight, 2010 for a review). There are multiple forms of coupling dynamics: phase/amplitude (Canolty et al., 2006, Cohen et al., 2009, Griesmayr et al., 2010, Lakatos et al., 2008, Miller et al., 2010, Osipova et al., 2008, Tort et al., 2009, Voytek et al., 2010a), phase/phase (Canolty et al., 2007, Darvas et al., 2009, Palva et al., 2005, Tass et al., 1998), and amplitude-to-amplitude (Bruns and Eckhorn, 2004, Voytek et al., 2010b). It is proposed that phase/amplitude coupling (PAC) reflects interactions between local microscale (Colgin et al., 2009, Quilichini et al., 2010) and systems-level macroscale neuronal ensembles (Canolty et al., 2010, Fries, 2005, Lisman and Idiart, 1995) that index cortical excitability and network interactions (Vanhatalo et al., 2004). From a behavioral viewpoint PAC has been shown to track learning and memory (Axmacher et al., 2010, Lisman and Idiart, 1995, Tort et al., 2009). PAC magnitude also fluctuates at an extremely low (< 0.1 Hz) rate at rest (Foster and Parvizi, 2012).
Currently PAC calculation algorithms compute a value averaged across a semi-arbitrary time window (Canolty et al., 2006, Cohen and van Gaal, in press, Voytek et al., 2010a) (see Cohen, 2008, Penny et al., 2008, Tort et al., 2010 for methodological details). The minimum length of this time window is bounded by the frequency of the coupling phase, as at least one full cycle is needed to calculate the distribution of values of the coupling amplitude. However, the PAC metric is sensitive to noise, and recent simulations have made use of > 200 cycles to get a reliable PAC estimate (Tort et al., 2010). This means, for example, that if one is investigating PAC between theta phase (4–8 Hz) and high gamma amplitude (80–150 Hz), the best temporal resolution one could achieve at 4 Hz would be 250 ms (one full cycle). However, 50 s or more might be required for reliable estimates (250 ms/cycle × 200 cycles). This requires researchers to use block designs (Voytek et al., 2010a), use long trial windows at the cost of temporal resolution (Tort et al., 2009), or to concatenate time series across trials (Tort et al., 2009) which could introduce spurious PAC due to edge artifacts (see Kramer et al., 2008b). These limitations present a problem for analyzing subcomponents of a task such as encoding, delay, and retrieval periods during working memory.
Here we demonstrate a novel approach for assessing time-resolved, event-related PAC (ERPAC). We provide results from subdural electrocorticographic (ECoG) data from three human subjects with implanted electrodes (Jacobs and Kahana, 2010) to demonstrate the utility of the ERPAC analysis procedure. We show that this method can be used to assess PAC both within local cortical regions as well as between distant sites. We observed couplings between multiple frequencies occurring at different time scales that evolved across trials and were independent of evoked responses. ERPAC provides a method for assessing sub-second coupling dynamics supporting cortical processing.
Section snippets
Data collection
We analyzed data from three patients with intractable epilepsy who were implanted with chronic subdural electrodes for approximately one week as part of a pre-operative procedure to localize the epileptogenic focus. Data were recorded at the Johns Hopkins School of Medicine where the surgeons determined electrode placement and treatment solely on the clinical needs of each patient. All subjects gave informed consent in accordance with the Johns Hopkins Medicine Institutional Review Boards. ECoG
Event-related amplitude and phase changes
An analysis of the effect of visual stimulus types (attended targets and standard non-targets) on event-related spectral perturbation (ERSP) in visual cortex (Fig. 1a) reveals an early latency (< 100 ms) increase in high frequency γ (80–150 Hz) and low frequency δ (1–4 Hz) and θ (4–8 Hz) activity for both stimulus types (Fig. 1b; p < 0.001, corrected for multiple comparisons). Upon visual inspection, it appears that γ and α (8–12 Hz) amplitudes are greater in response to targets compared to
Discussion
We describe a PAC method that provides time-resolved calculation of event-related PAC (ERPAC). Because it is based on correlation and regression techniques, it is intuitive and straightforward to instantiate. While other methods exist for examining time-resolved phase/phase or amplitude/amplitude relationships (Bruns and Eckhorn, 2004, Darvas et al., 2009), this method combines a circular (phase) and linear (amplitude) variable with improved temporal resolution permitting within-trial changes
Conflict of interest statement
The authors declare no competing financial or other interests.
Acknowledgments
We thank Aurelie Bidet-Caulet, Maya Cano, Ryan Canolty, Adeen Flinker, John Long, Avgusta Shestyuk, Frederic Theunissen, Adriano Tort, and Jonathan Wallis for useful conversations about the manuscript and methods. B.V. is funded by the American Psychological Association Diversity Program in Neuroscience (5-T32-MH18882). B.V. and R.T.K. are funded by the NINDS grant NS21135 and R.T.K. by the NINDS grant PO40813. N.E.C is funded by NINDS grant NS40596.
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