A fast statistical significance test for baseline correction and comparative analysis in phase locking

TORUS GRAPHS FOR MULTIVARIATE PHASE COUPLING ANALYSIS

Angular measurements are often modeled as circular random variables, where there are natural circular analogues of moments, including correlation. Because a product of circles is a torus, a d-dimensional vector of circular random variables lies on a d-dimensional torus. For such vectors we present here a class of graphical models, which we call torus graphs, based on the full exponential family with pairwise interactions. The topological distinction between a torus and Euclidean space has several important consequences. Our development was motivated by the problem of identifying phase coupling among oscillatory signals recorded from multiple electrodes in the brain: oscillatory phases across electrodes might tend to advance or recede together, indicating coordination across brain areas. The data analyzed here consisted of 24 phase angles measured repeatedly across 840 experimental trials (replications) during a memory task, where the electrodes were in 4 distinct brain regions, all known to be active while memories are being stored or retrieved. In realistic numerical simulations, we found that a standard pairwise assessment, known as phase locking value, is unable to describe multivariate phase interactions, but that torus graphs can accurately identify conditional associations. Torus graphs generalize several more restrictive approaches that have appeared in various scientific literatures, and produced intuitive results in the data we analyzed. Torus graphs thus unify multivariate analysis of circular data and present fertile territory for future research.

How to Evaluate Phase Differences between Trial Groups in Ongoing Electrophysiological Signals

A growing number of studies endeavor to reveal periodicities in sensory and cognitive functions, by comparing the distribution of ongoing (pre-stimulus) oscillatory phases between two (or more) trial groups reflecting distinct experimental outcomes. A systematic relation between the phase of spontaneous electrophysiological signals, before a stimulus is even presented, and the eventual result of sensory or cognitive processing for that stimulus, would be indicative of an intrinsic periodicity in the underlying neural process. Prior studies of phase-dependent perception have used a variety of analytical methods to measure and evaluate phase differences, and there is currently no established standard practice in this field. The present report intends to remediate this need, by systematically comparing the statistical power of various measures of "phase opposition" between two trial groups, in a number of real and simulated experimental situations. Seven measures were evaluated: one parametric test (circular Watson-Williams test), and three distinct measures of phase opposition (phase bifurcation index, phase opposition sum, and phase opposition product) combined with two procedures for non-parametric statistical testing (permutation, or a combination of z-score and permutation). While these are obviously not the only existing or conceivable measures, they have all been used in recent studies. All tested methods performed adequately on a previously published dataset (Busch et al., 2009). On a variety of artificially constructed datasets, no single measure was found to surpass all others, but instead the suitability of each measure was contingent on several experimental factors: the time, frequency, and depth of oscillatory phase modulation; the absolute and relative amplitudes of post-stimulus event-related potentials for the two trial groups; the absolute and relative trial numbers for the two groups; and the number of permutations used for non-parametric testing. The concurrent use of two phase opposition measures, the parametric Watson-Williams test and a non-parametric test based on summing inter-trial coherence values for the two trial groups, appears to provide the most satisfactory outcome in all situations tested. Matlab code is provided to automatically compute these phase opposition measures.

Mid-Task Break Improves Global Integration of Functional Connectivity in Lower Alpha Band

Numerous efforts have been devoted to revealing neurophysiological mechanisms of mental fatigue, aiming to find an effective way to reduce the undesirable fatigue-related outcomes. Until recently, mental fatigue is thought to be related to functional dysconnectivity among brain regions. However, the topological representation of brain functional connectivity altered by mental fatigue is only beginning to be revealed. In the current study, we applied a graph theoretical approach to analyse such topological alterations in the lower alpha band (8~10 Hz) of EEG data from 20 subjects undergoing a two-session experiment, in which one session includes four successive blocks with visual oddball tasks (session 1) whereas a mid-task break was introduced in the middle of four task blocks in the other session (session 2). Phase lag index (PLI) was then employed to measure functional connectivity strengths for all pairs of EEG channels. Behavior and connectivity maps were compared between the first and last task blocks in both sessions. Inverse efficiency scores (IES = reaction time/response accuracy) were significantly increased in the last task block, showing a clear effect of time-on-task in participants. Furthermore, a significant block-by-session interaction was revealed in the IES, suggesting the effectiveness of the mid-task break on maintaining task performance. More importantly, a significant session-independent deficit of global integration and an increase of local segregation were found in the last task block across both sessions, providing further support for the presence of a reshaped topology in functional brain connectivity networks under fatigue state. Moreover, a significant block-by-session interaction was revealed in the characteristic path length, small-worldness, and global efficiency, attributing to the significantly disrupted network topology in session 1 in comparison of the maintained network structure in session 2. Specifically, we found increased nodal betweenness centrality in several channels resided in frontal regions in session 1, resembling the observations of more segregated global architecture under fatigue state. Taken together, our findings provide insights into the substrates of brain functional dysconnectivity patterns for mental fatigue and reiterate the effectiveness of the mid-task break on maintaining brain network efficiency.