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

Abstract

The human brain consists of anatomically distant neuronal assemblies that are interconnected via a myriad of synapses. This anatomical network provides the neurophysiological wiring framework for functional connectivity (FC), which is essential for higher-order brain functions. While several studies have explored the scale-specific FC, the scale-free (i.e., multifractal) aspect of brain connectivity remains largely neglected. Here we examined the brain reorganization during a visual pattern recognition paradigm, using bivariate focus-based multifractal (BFMF) analysis. For this study, 58 young, healthy volunteers were recruited. Before the task, 3-3 min of resting EEG was recorded in eyes-closed (EC) and eyes-open (EO) states, respectively. The subsequent part of the measurement protocol consisted of 30 visual pattern recognition trials of 3 difficulty levels graded as Easy, Medium, and Hard. Multifractal FC was estimated with BFMF analysis of preprocessed EEG signals yielding two generalized Hurst exponent-based multifractal connectivity endpoint parameters, H(2) and ΔH15; with the former indicating the long-term cross-correlation between two brain regions, while the latter captures the degree of multifractality of their functional coupling. Accordingly, H(2) and ΔH15 networks were constructed for every participant and state, and they were characterized by their weighted local and global node degrees. Then, we investigated the between- and within-state variability of multifractal FC, as well as the relationship between global node degree and task performance captured in average success rate and reaction time. Multifractal FC increased when visual pattern recognition was administered with no differences regarding difficulty level. The observed regional heterogeneity was greater for ΔH15 networks compared to H(2) networks. These results show that reorganization of scale-free coupled dynamics takes place during visual pattern recognition independent of difficulty level. Additionally, the observed regional variability illustrates that multifractal FC is region-specific both during rest and task. Our findings indicate that investigating multifractal FC under various conditions – such as mental workload in healthy and potentially in diseased populations – is a promising direction for future research.

Multiple-Resampling Cross-Spectral Analysis: An Unbiased Tool for Estimating Fractal Connectivity With an Application to Neurophysiological Signals

“…We observed a strong increase in cross-spectral slope in increased mental activity when compared to an idle state. This is in line with previous results identifying an increase in the bivariate Hurst exponent due to performing a cognitive task ( Stylianou et al, 2021 ). The observed results imply that long-range cooperation among distinct brain regions strengthened while performing the word generation task.…”

“…Along these lines, in an earlier study we presented a novel method for analyzing bivariate (multi)fractality, with statistical tests for assessment of genuine scale-free coupled dynamics included ( Stylianou et al, 2020 ). In that and a following paper ( Stylianou et al, 2021 ) we introduced the notion of extrinsic and intrinsic bivariate fractality, referring to the cases when H xy is equal or smaller than the average of H x and H y , respectively. In contrast to extrinsic fractality, the presence of intrinsic fractality implies that the properties of the bivariate processes cannot only be explained from those of the univariate processes.…”

“…Nevertheless, the vast majority of previous studies considered univariate fractal dynamics and not long-term correlations in interregional connections. On the other hand, only a handful of studies analyzed fractal brain connectivity ( Achard et al, 2008 ; Wang and Zhao, 2012 ; Stylianou et al, 2020 ; La Rocca et al, 2021 ) and even less assessed its changes due to performing a cognitive task ( Ciuciu et al, 2014 ; Stylianou et al, 2021 ). Our results contribute to the growing body of literature suggesting that fractal brain connectivity has functional significance as it can differentiate between various mental states, in which capacity MRCSA could prove as a valuable tool in future studies.…”

“…Multifractality has been confirmed in many physiological processes such as heart rate variability ( Ivanov et al, 1999 ) or cerebral hemodynamics ( Shimizu et al, 2004 ). Importantly, functional brain connectivity has also been shown recently to express not only fractal but indeed multifractal dynamics on the level of global network topological properties ( Racz et al, 2018a , 2020 ) as well as individual connections ( Racz et al, 2018b ; Stylianou et al, 2020 , 2021 ). The presented MRCSA algorithm by itself is only capable of characterizing the global monofractal character of functional coupling, however, by utilizing a sliding window approach one can actually obtain a trajectory/distribution of local cross-spectral exponents over time.…”

“…The power-law relationship is commonly characterized in the obtained fractal scaling exponent, which is referred to as the Hurst exponent ( H ) or the spectral slope (β) in the time and frequency domains, respectively, with an explicit equivalence between the two ( Eke et al, 2000 ; Kristoufek, 2014 ). Given that identifying such long-term couplings between various brain regions can reveal novel implications on the functional organization of the brain – that cannot be identified otherwise via single-scale or scale dependent analyses –, fractal connectivity studies gained growing interest recently ( Achard et al, 2008 ; Ciuciu et al, 2014 ; Stylianou et al, 2020 , 2021 ; La Rocca et al, 2021 ).…”