Elsevier

Journal of Neuroscience Methods

Volume 250, 30 July 2015, Pages 137-146
Journal of Neuroscience Methods

Basic Neuroscience
Effects of time lag and frequency matching on phase-based connectivity

https://doi.org/10.1016/j.jneumeth.2014.09.005Get rights and content

Abstract

The time- and frequency-varying dynamics of how brain regions interact is one of the fundamental mysteries of neuroscience. In electrophysiological data, functional connectivity is often measured through the consistency of oscillatory phase angles between two electrodes placed in or over different brain regions. However, due to volume conduction, the results of such analyses can be difficult to interpret, because mathematical estimates of connectivity can be driven both by true inter-regional connectivity, and by volume conduction from the same neural source. Generally, there are two approaches to attenuate artifacts due to volume conduction: spatial filtering in combination with standard connectivity methods, or connectivity methods such as the weighted phase lag index that are blind to instantaneous connectivity that may reflect volume conduction artifacts. The purpose of this paper is to compare these two approaches directly in the presence of different connectivity time lags (5 or 25 ms) and physiologically realistic frequency non-stationarities. The results show that standard connectivity methods in combination with Laplacian spatial filtering correctly identified simulated connectivity regardless of time lag or changes in frequency, although residual volume conduction artifacts were seen in the vicinity of the “seed” electrode. Weighted phase lag index under-estimated connectivity strength at small time lags and failed to identify connectivity in the presence of frequency mismatches or non-stationarities, but did not misidentify volume conduction as “connectivity.” Both approaches have strengths and limitations, and this paper concludes with practical advice for when to use which approach in context of hypothesis testing and exploratory data analyses.

Introduction

Brain functional connectivity is a topic of growing interest in neuroscience (Sporns, 2010, Hutchison et al., 2013, Cabral et al., 2014). In humans, functional connectivity can be measured using either hemodynamic (fMRI) or electrophysiological (MEG or EEG) techniques. Noninvasive electrophysiological measurements of functional connectivity have two main advantages: They measure changes in connectivity in a time-frame that matches that of many cognitive/perceptual processes (tens to hundreds of ms), and they can be more easily linked to underlying neurophysiology compared to the hemodynamic response.

The main disadvantage of measuring electrophysiological functional connectivity is that there is a potential confound of volume conduction. Volume conduction is the phenomenon that electromagnetic fields generated at a location in the brain will propagate through tissues (brain, skull, skin, etc.) and will be recorded from several electrodes. Volume conduction is a double-edged sword: Without it, non-invasive M/EEG would not be possible; because of it, functional connectivity measurements can be confounded.

The question is thus how to dissociate volume conduction from true interactions between brain regions when estimating functional connectivity. Broadly speaking, there are two approaches for this dissociation. The first approach is to develop data analysis methods that are blind to the potential influence of volume conduction. This has led to methods such as (corrected) imaginary coherence (Nolte et al., 2004, Sekihara et al., 2011) and (weighted) phase-lag-index (Stam et al., 2007, Vinck et al., 2011). The second approach is to apply spatial filters to the data that strongly attenuate volume conduction and therefore permit the valid interpretation of standard connectivity analysis methods. The most commonly used scalp-level spatial filter for this approach is the surface Laplacian (Srinivasan et al., 2006).

It appears that these two approaches reflect different “camps” of thinking about how to perform connectivity analyses. The purpose of this paper is to examine the advantages and disadvantages of these two approaches for EEG connectivity analyses. Part of the motivation for this study is based on informal scientific interactions (i.e., those that do not take place in peer-reviewed publications); I frequently hear or read researchers offering advice or demanding re-analyses of connectivity findings based on their idea of how best to address the volume conduction issue. In many cases, these suggestions seem to be based on a poor understanding of the advantages and limitations of different approaches and connectivity analysis methods. This misunderstanding can lead to misguided interpretations of findings, good-intentioned but poor advice, or inappropriate reviewer demands.

There are many methods to quantify functional connectivity in M/EEG time series. The focus of this paper is on phase-based connectivity methods, because they are widely used in the literature, and because phase-based connectivity is more often highlighted in theoretical and computational discussions of how disparate neural circuits might interact (Bush and Sejnowski, 1996, Varela et al., 2001, Fries, 2005). Two phase-based connectivity methods will be compared here: phase clustering and weighted phase lag index. Phase clustering is based on the circular variance of phase angle differences; phase lag index, in contrast, is based on the average number of phase angle differences that are positive or negative in the complex plane (that is, pointing up or down with respect to the horizontal real axis).

Phase clustering and phase lag index are sometimes mistakenly considered to be roughly equivalent with the latter being insensitive to volume conduction. This is true only in the narrow situation of tight clustering with a time lag close to π/2 (or −π/2), and very little noise. In real data, there are at least two phenomena that produce notable differences between phase clustering and phase lag index. The first is small time lags, which, in combination with noise, can cause a distribution of phase angles to be close to 0 or π. Phase clustering is insensitive to time lags, but phase lag index will produce lower estimates of connectivity as the distribution gets closer to 0 or π. This can be particularly problematic if the time lag or the amount of noise differs over time or across conditions. The second phenomenon is violations of frequency stationarity. Frequency stationarity means that the frequency characteristics of a signal remain constant over time. Although EEG is often conceptualized (or, at least, analyzed) as comprising temporally overlapping stationary oscillators, in fact the frequency structure of EEG changes dynamically over time: different brain regions oscillate at different sub-frequencies (e.g., peak alpha can be 8 Hz in one region and 9 Hz in another region) (Tognoli and Kelso, 2013), peak oscillation frequency varies as a function of task demands (Roberts et al., 2013, Haegens et al., 2014), and peak frequency can fluctuate over time due to endogenous and experimental factors (Ahissar et al., 2001, Foffani et al., 2005, Ray and Maunsell, 2010, Cohen, 2014a). Although part of the frequency non-stationarities might simply reflect measurement noise, non-stationarities are a meaningful feature of brain function that should be considered and incorporated into analyses, rather than ignored (Kaplan et al., 2005).

The idea of this study was to simulate EEG data that include a time period of frequency band-specific synchronization of several hundred ms. Data were simulated in two brain dipoles and then projected onto 64 points on the scalp, thus simulating a typical 64-channel EEG recording setup. Thereafter, data were re-referenced to the average of all electrodes, or were spatially filtered using the Laplacian. Real EEG data were also used from a previously published study. Functional connectivity was then estimated via phase clustering and weighted phase lag index. The two independent variables were the time lag between the simulated interactions (5 or 25 ms) and the frequency stationarity and matching of the two dipoles.

I argue in this paper that the choice of phase-based functional connectivity analyses for EEG data should be based in part on the relative aversion to Type-I vs. Type-II errors, which in turn should be guided by whether the analyses are relatively hypothesis-driven vs. exploratory. To quell suspense, the results of analyses of simulated and real EEG data show: (1) weighted phase lag index should be preferred in exploratory studies whereas phase clustering should be preferred in hypothesis-driven studies; (2) if one is interested in the time course of changes in connectivity, phase clustering should be preferred, because even minor violations of frequency stationarity cause connectivity estimation errors for weighted phase lag; (3) the surface Laplacian renders connectivity estimates robust to time lag and frequency non-stationarities, although the Laplacian remains open to volume conduction confounds for closely positioned electrodes (<∼5 cm when using a standard 64-channel cap).

Matlab code to produce these simulations and analyze the results are posted online (www.mikexcohen.com/Cohen_phaseConnectivityComparison.zip). Readers are encouraged to inspect the results for themselves, modify parameters, etc.

Section snippets

Methods for estimating phase-based connectivity

Inter-site phase clustering (ISPC; also known as phase-locking value/factor, phase coherence, and several other terms; ISPC is preferred here because it is a description of the analysis rather than an interpretation of the result; see Cohen, 2014b) is defined as the length of the average of phase angle difference vectors from two electrodes: n−1eip, where n is the number of data points (here, trials), e is the natural exponential, i is the imaginary operator (the square root of −1), and p is

Selected dipoles, scalp projections, and reconstructions

Fig. 2b–d shows the topographical distributions of the individual leadfield projections from each of two selected “activation dipoles,” the summed leadfield projections, and their Laplacian. Time series were then generated at the two dipoles as tapered alpha (10 Hz) oscillations. Time–frequency and beamforming analyses revealed that the topographical and spatial distributions of the results mapped well onto the individual dipole locations (Fig. 2a). These are not surprising results, but

Phase clustering vs. weighted phase lag index for EEG connectivity

These results paint a nuanced picture of ISPC vs. wPLI for measuring functional connectivity. ISPC is robust both to time lags and to frequency non-stationarities, but can also be misled by volume conduction artifacts. WPLI, on the other hand, is insensitive to volume conduction artifacts, but can underestimate the strength of connectivity with realistically small time lags and can produce uninterpretable connectivity time courses in the presence of frequency mismatches or non-stationarities

Acknowledgments

Thanks to Daan van Es for assistance with data collection. This work was funded by a VIDI grant from the NWO (452-09-003) (Dutch Science Funding Agency).

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