Scale-Free Coupled Dynamics in Brain Networks Captured by Bivariate Focus-Based Multifractal Analysis

Abstract

While most connectivity studies investigate functional connectivity (FC) in a scale-dependent manner, coupled neural processes may also exhibit broadband dynamics, manifesting as power-law scaling of their measures of interdependence. Here we introduce the bivariate focus-based multifractal (BFMF) analysis as a robust tool for capturing such scale-free relations and use resting-state electroencephalography (EEG) recordings of 12 subjects to demonstrate its performance in reconstructing physiological networks. BFMF was employed to characterize broadband FC between 62 cortical regions in a pairwise manner, with all investigated connections being tested for true bivariate multifractality. EEG channels were also grouped to represent the activity of six resting-state networks (RSNs) in the brain, thus allowing for the analysis of within- and between- RSNs connectivity, separately. Most connections featured true bivariate multifractality, which could be attributed to the genuine scale-free coupling of neural dynamics. Bivariate multifractality showed a characteristic topology over the cortex that was highly concordant among subjects. Long-term autocorrelation was higher in within-RSNs, while the degree of multifractality was generally found stronger in between-RSNs connections. These results offer statistical evidence of the bivariate multifractal nature of functional coupling in the brain and validate BFMF as a robust method to capture such scale-independent coupled dynamics.

Multifractal Functional Connectivity Analysis of Electroencephalogram Reveals Reorganization of Brain Networks in a Visual Pattern Recognition Paradigm

“…This series of tests reveal the qualitative nature of bivariate multifractality, which is assessed independently from its quantitative changes in this study. The complete account of the testing procedure followed in this study was reported elsewhere ( Stylianou et al, 2021 ). We expanded the test yielding a distinction between extrinsic and intrinsic multifractality referred to as bivariate-univariate Hurst comparison.…”

“…The scale-free coupled dynamics were estimated with bivariate focus-based multifractal analysis (BFMF), introduced by Mukli and colleagues (Mukli et al, 2018). The applicability of BFMF for multifractal FC estimation was demonstrated previously (Stylianou et al, 2021). Here we only provide a summary of the method, while further details are found in the references mentioned above.…”

“…Various statistical approaches have been applied and/or developed for characterizing the linear and nonlinear aspects of the coupled neural activities ( Bastos and Schoffelen, 2016 ). A common limitation of these methods is that they capture interdependence on a single scale, despite the fact that the scale-free (or fractal) nature of the connections has already been demonstrated in various modalities such as EEG ( Wang and Zhao, 2012 ; Stylianou et al, 2021 ), fMRI ( Ciuciu et al, 2014 ) and magnetoencephalography ( Achard et al, 2008 ). The univariate scale-free behavior of neural dynamics has already been shown both regionally ( Popivanov et al, 2006 ) and globally ( Stam and de Bruin, 2004 ).…”

“…While estimating FC at a given time scale reflect the coupling between oscillatory (narrowband) components at specific cross-spectrum frequencies, our current approach assumes a significant scale-free (broadband) component of the cross-spectrum; a signature of statistical dependency spanning a broad range of frequencies (scales). Moreover, the true multifractal nature of coupled dynamics was recently validated in resting-state EEG ( Stylianou et al, 2021 ). Scale-free FC estimators allow for capturing how the long-term memory and multifractality of the coupled dynamics are spatially distributed across brain networks; topological aspects that otherwise would remain obscured.…”

Two-Tiered Response of Cardiorespiratory-Cerebrovascular Network to Orthostatic Challenge

“…There is an abundance of such bivariate methods that have been utilized in recent studies of physiological networks (Bashan et al, 2012;Bartsch et al, 2015;Zanetti et al, 2019), for a review see Schulz et al (2013). The relatively short time series (150 data points) were insufficient for adopting alternative bivariate measures such as symbolic transfer entropy (Dickten and Lehnertz, 2014;Lucchini et al, 2020), Granger causality (Faes et al, 2008) or measures of scale-free coupled dynamics (Stylianou et al, 2021) with suitable surrogate testing capable of identifying causal relationships (Schreiber and Schmitz, 1996). Adequate data representation is also necessary for using fractal models based on capturing spatio-temporal cross-dependencies between coupled physiological processes in order to identify physiological networks by utilizing fractional differencing operators (Xue et al, 2016;Bogdan, 2019).…”