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.
Highlights
Physiological systems are integrated through a series of intricate connections giving rise to networks of dynamically interacting elements
Even though many of these methodologies have been proven invaluable for the investigation of scale-specific interactions, they largely neglect the plausible broadband nature of the functional coupling itself. This may, become relevant, as many biological processes have been shown to express broadband, scale-free dynamics; examples include the variability of heart rate (Ivanov et al, 1999, 2004; Nunes Amaral et al, 2001; Bartsch et al, 2005), spontaneous brain activity (Ivanov et al, 2009; Lin et al, 2020) or gait variability (Bartsch et al, 2007), to name a few. While these biological functions may contain narrowband components that can be of interest, their broadband dynamics indicate scale-free behavior (Eke et al, 2000)
Utilizing a combination of dynamic graph theoretical analysis and multifractal time series analysis, we recently revealed that both global (Racz et al, 2018a,b) and local (Racz et al, 2019) properties of functional brain networks fluctuate according to a multifractal pattern, which may be affected in pathological conditions (Racz et al, 2020)
Summary
Physiological systems are integrated through a series of intricate connections giving rise to networks of dynamically interacting elements. Even though many of these methodologies have been proven invaluable for the investigation of scale-specific interactions, they largely neglect the plausible broadband nature of the functional coupling itself (i.e. coupling that spans across a wide range of frequencies) This may, become relevant, as many biological processes have been shown to express broadband, scale-free dynamics; examples include the variability of heart rate (Ivanov et al, 1999, 2004; Nunes Amaral et al, 2001; Bartsch et al, 2005), spontaneous brain activity (Ivanov et al, 2009; Lin et al, 2020) or gait variability (Bartsch et al, 2007), to name a few. The ubiquity of the univariate fractal dynamics in physiological processes warrants the application of bivariate scale-free time series analysis to study the complexity of coupling between such processes
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