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 ΔH ₁₅; 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 ΔH ₁₅ 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 ΔH ₁₅ 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.

Keywords: brain networks; electroencephalography; functional connectivity; multifractal; visual pattern recognition.

FIGURE 1

Measurement protocol for obtaining electroencephalography records during resting states and subsequent visual pattern recognition. First, resting-state recordings were made in 180 s periods with eyes closed and eyes open, respectively. Then, the subject performed a pattern recognition task in a block of 30 trials, each consisting of a 10 s or less of active period and a 10 s passive period. In the active period, participants were presented a large-size image (A) and its cropped sub-region (B) and were required to click on (A) at the position of (B) if found (The picture of Figure 1 was taken from https://alphacoders.com/users/profile/97828).

FIGURE 2

Multifractal time series analysis and its endpoint parameters. On the upper panels, a representative pair of 2048 datapoint-long EEG segments (from Subject01) is displayed along with the windowing scheme for a smaller (s = 64, shown in yellow) and larger (s = 128, shown in purple) scale, which illustrates the calculation of covariance scaling function [S_XY(q,s) displayed in the lower panel] according to Eq. 1. The Focus (red disk) is used as a reference point when simultaneously fitting linear models in the log-log transform of the S_XY(q,s) vs s, the essential step of BFMF. The slope of each linear regression line represents the generalized Hurst exponent [H(q)] (shown for q = –15, +2, +15). H(2) describes the long-term cross-correlation between the signals X and Y, while the degree of multifractality (ΔH₁₅) is captured in the difference between H(q) values at the extreme [i.e., minimal (–15) and maximal (15)] statistical moments.

FIGURE 3

State-dependent weighted node degree topology of H(2) and ΔH₁₅ brain networks. The color bars represent the values of the local node degrees.

FIGURE 4

State-dependent weighted global node degree distribution of H(2) and ΔH₁₅ brain networks. Significance marked by asterisk (*). Figure was created using Gramm (Morel, 2018).

FIGURE 5

Localization of significantly different weighted node degrees for every between state comparison of the H(2) and ΔH₁₅ brain networks. The colormap is based on the absolute difference of the node degrees of the states under investigation (e.g., | D_O2,EC - D_O2,EO|). Only the significantly different nodes are shown.

FIGURE 6

Within-state differences of node degrees in every state. Red: only H(2) network comparison was significant, Orange: only ΔH₁₅ network comparison was significant, Blue: both H(2) and ΔH₁₅ networks comparisons were significant.

FIGURE 7

Average success rate and reaction time for different difficulty levels. Significant differences are marked by asterisk (*). Figure was created using Gramm (Morel, 2018).

FIGURE 8

Scatter plots of the reaction time vs global node degree for Easy (orange) and Hard (blue) task in ΔH₁₅ networks and their Spearman’s correlation (r). Figure was created using Gramm (Morel, 2018).