Abstract
The analysis of human brain functional networks is achieved by computing functional connectivity indices reflecting phase coupling and interactions between remote brain regions. In magneto- and electroencephalography, the most frequently used functional connectivity indices are constructed based on Fourier-based cross-spectral estimation applied to specific fast and band-limited oscillatory regimes. Recently, infraslow arrhythmic fluctuations (below the 1 Hz) were recognized as playing a leading role in spontaneous brain activity. The present work aims to propose to assess functional connectivity from fractal dynamics, thus extending the assessment of functional connectivity to the infraslow arrhythmic or scale-free temporal dynamics of M/EEG-quantified brain activity. Instead of being based on Fourier analysis, new Imaginary Coherence and weighted Phase Lag indices are constructed from complex-wavelet representations. Their performances are first assessed on synthetic data by means of Monte-Carlo simulations, and they are then compared favorably against the classical Fourier-based indices. These new assessments of functional connectivity indices are also applied to MEG data collected on 36 individuals both at rest and during the learning of a visual motion discrimination task. They demonstrate a higher statistical sensitivity, compared to their Fourier counterparts, in capturing significant and relevant functional interactions in the infraslow regime and modulations from rest to task. Notably, the consistent overall increase in functional connectivity assessed from fractal dynamics from rest to task correlated with a change in temporal dynamics as well as with improved performance in task completion, which suggests that the complex-wavelet weighted Phase Lag index is the sole index is able to capture brain plasticity in the infraslow scale-free regime.
Highlights
(iii) The Complex Wavelet W-ICOH and W-wPLI perform significantly better than the Fourier-based F-COH and F-wPLI first when the signals show very large scaling exponents β in their f −β power spectral density behavior, as is the case with fractional Brownian motion (fBm)-like time series and second when additive noise in the form of smooth and slow trends are superimposed to data with scale-free dynamics, which is a situation commonly observed in recordings collected from neuroimaging techniques
We have introduced the notion of functional connectivity assessment from fractal dynamics for MEG data, defined as functional connectivity associated with the largeband infraslow arrhythmic cross-temporal dynamics, in contradistinction with the classical functional connectivities associated with the band-limited rapid oscillatory rhythms (α−, β−, γ − bands)
While Fourier-based tools are natural to use to assess functional connectivity in band-limited rapid oscillatory rhythms, it was shown, using simulated synthetic data and mostly on MEG data, that the assessment of functional connectivity for large-band slow scale-free cross-temporal dynamics is better achieved by complex wavelet based indices
Summary
At the turn of the 21st century, the large-band infraslow activity of the brain (typically below 1 Hz), which for long had been considered as either instrumental or head-movement noise, received growing interest; it has been documented as a prominent part of recorded electromagnetic brain signals and a critical component of brain activity (Gong et al, 2003; Stam and De Bruin, 2004; Vanhatalo et al, 2004; Miller et al, 2009; Werner, 2010) This large-band infraslow activity in the brain differs significantly from band-limited oscillations in the sense that it is not characterized by specific frequencies or scales of times but rather corresponds to arrhythmic, or scale-free, temporal dynamics. Altered scale-free brain dynamics has been reported in a specific condition, such as Alzheimer’s disease for which larger selfsimilarity exponents were reported in multiple brain areas (e.g., lateral temporal lobes, insula, etc.) involved early in the neurodegenerative process (Maxim et al, 2005)
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