Emergence of stable functional networks in long-term human electroencephalography

Abstract

Functional connectivity networks have become a central focus in neuroscience because they reveal key higher-dimensional features of normal and abnormal nervous system physiology. Functional networks reflect activity-based coupling between brain regions that may be constrained by relatively static anatomical connections, yet these networks appear to support tremendously dynamic behaviors. Within this growing field, the stability and temporal characteristics of functional connectivity brain networks have not been well characterized. We evaluated the temporal stability of spontaneous functional connectivity networks derived from multi-day scalp encephalogram (EEG) recordings in five healthy human subjects. Topological stability and graph characteristics of networks derived from averaged data epochs ranging from 1 s to multiple hours across different states of consciousness were compared. We show that, although functional networks are highly variable on the order of seconds, stable network templates emerge after as little as ∼100 s of recording and persist across different states and frequency bands (albeit with slightly different characteristics in different states and frequencies). Within these network templates, the most common edges are markedly consistent, constituting a network "core." Although average network topologies persist across time, measures of global network connectivity, density and clustering coefficient, are state and frequency specific, with sparsest but most highly clustered networks seen during sleep and in the gamma frequency band. These findings support the notion that a core functional organization underlies spontaneous cortical processing and may provide a reference template on which unstable, transient, and rapidly adaptive long-range assemblies are overlaid in a frequency-dependent manner.

Figure 1.

Construction of functional networks from multivariate scalp EEG recordings. A, Example 5 s of EEG data recorded from 19 electrodes (broadband, 0.5–55 Hz). B, For each 1-s interval for each electrode pair, the cross-correlation is calculated. Two example traces recorded from O1 and T5 electrode tracings here. The maximum absolute value of the cross-correlation (blue circle) determines the significance of the coupling. (Note that, for evaluation of specific frequency bands, coherence was computed for each frequency band of interest using the multitaper method.) C, Example binary adjacency matrices derived from five 1-s epochs. Significant electrode coupling is represented in black and given a value of 1. D, Example weighted adjacency matrix generated from averaging n-binary matrices, where n ranged from 1 to 5000, representing 1 s to ∼83 min recording epochs. E, Average matrices derived from same epoch lengths are visualized, characterized, and compared.

Figure 2.

Forward model simulation of volume conduction. We implemented a four-shell spherical head model, placing 514 radially oriented dipole sources on the upper half of the innermost sphere (methods adapted from Nunez and Srinivasan, 2005). We simulated 500 time steps, assigning each dipole source uncorrelated pink noise. We then measured the coupling (see Materials and Methods, Network construction) between sensors at the scalp surface (outer sphere). A, Example voltage map on cortex (left) and scalp (right) demonstrating blurring of voltage signal on the scalp surface compared with cortex. B, Distribution of maximum absolute value of the cross-correlation between scalp voltage signals as a function of geodesic distance on the scalp. Green (red) circles indicate edges (non-edges) in the resulting functional network, and filled black circles indicate the maximum absolute value of the correlation occurred at zero time lag.

Figure 3.

Visualization of functional network similarity and epoch length. A, Example binary functional networks derived from 1-s epochs in a single subject during REM sleep. Marked variability in network topology is evident. B, Example weighted average networks derived from varying epoch lengths from the same subject during REM sleep. The width of the edge is drawn proportional to its weight (scaled to the frequency of the most common edge). The most persistent edges present in each of these networks (those with weights above the 95th percentile) are shown on the right in red. Variability between networks derived from 5, 10, 25, and 50 s epochs is evident. A recurrent network template (left) and core topology (right) emerges in networks generated from 100 s epochs that remains stable across networks derived from longer (500 s) epochs.

Figure 4.

Functional network stability and epoch length. Functional network stability is plotted as the average 2D cross-correlation (y-axis) for all networks derived from increasing epoch lengths (x-axis) across 48 h samples for each subject. Mean ± SD cross-correlation for networks derived from randomly selected and averaged 1 s epochs for each subject are shown in light gray. Networks are highly variable for epochs <20 s but rapidly stabilize with increasing epoch lengths and achieve near-maximal cross-correlation values for epochs >100 s. Mean cross-correlation for shuffled (dark gray) and random data (black) remain near zero for all simulated epoch lengths. Networks derived from the same state of consciousness (wake, N1, N2, N3, and REM) are more similar than networks compared between different states of consciousness (purple). Functional networks derived from wakefulness are significantly less stable than those derived from all sleep states (p < 0.02).

Figure 5.

Functional network stability across subjects and states. Average networks derived from the entire recording session for each subject for each state of consciousness. The widths of the edges are drawn proportional to the frequency with which the edges appear in the sample (scaled to the frequency of the most common edge). Consistent functional network topologies are evident in each subject across all states. The most common edges present in each subject (those with weights above the 95th percentile) are shown in red. Although functional networks are stable across time for each subject, they vary considerable across subjects.

Figure 6.

Functional network stability across frequency bands. A, Average networks derived from the entire recording session in a single subject in each frequency band of interest [delta (0.5–4 Hz), theta (4–8 Hz), alpha (8–12 Hz) beta (12–20 Hz), and gamma (20–50 Hz)]. The widths of the edges are drawn proportional to the frequency with which the edge appears in the sample. Consistent functional network topologies are evident across all frequencies. The most stable edges (those with weights above the 95 percentile) are shown in red. B, Functional network stability is plotted as the average 2D cross-correlation (y-axis) for all networks derived from increasing epoch lengths (x-axis) for each frequency band and mixed frequency bands compared with each other. Networks are highly variable for epochs <20 s but rapidly stabilize with increasing lengths and achieve near-maximal cross-correlation values for epochs >100 s. Similar curves are seen for each frequency band. Networks compared within the same frequency are more similar then networks compared from different frequency bands (plotted in gray). C, Top, Empirical cumulative distribution function of density measures for all 1 s networks for each frequency band and all subjects. Graph characteristics vary significantly between frequency bands (p < 0.0001 for all comparisons). Sparsest networks were seen in the low gamma and theta bands for each subject.

Figure 7.

Signal coupling across frequencies is not synchronous. Left, Example EEG data from two electrodes that are highly coupled on average. Strong coupling was apparent between the same electrode pair at each frequency band, although not necessarily at the same time. Here, in the delta band, coupling is strongest in the first second, whereas in the alpha band, coupling is strong in the third second, and in the beta band, coupling is strong in the second and third seconds. Right, Example EEG data from two electrodes that are not highly coupled on average. Coupling is not strong between this electrode pair at any frequency band.

Figure 8.

Functional network stability and graph characteristics across subjects and states. A, Functional network stability plotted as the average 2D cross-correlation for all networks derived from increasing epoch lengths. Networks are markedly less similar between subjects than within the same subject but more similar than random or shuffled networks. B, Top, Empirical cumulative distribution function of density measures for all 1 s networks for each state and all subjects. Bottom, Empirical cumulative distribution function of clustering coefficient values of 1 s networks for each state and all subjects. Graph characteristics vary significantly between states (p < 0.0001 for all comparisons). Similar distributions were seen for each subject. Sparsest networks with lowest clustering were present in N3, followed by N2 in each subject. Densest networks with highest clustering are present during wakefulness in each subject. REM and N1 states had intermediate values, which were near-equivalent to wake values in one subject.