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Evolving functional network properties and synchronizability during human epileptic seizures
Kaspar A. Schindler, Stephan Bialonski, Marie-Therese Horstmann, Christian E. Elger, Klaus Lehnertz
TL;DR
The paper asks how functional network topology and synchronizability evolve during human epileptic seizures. Using time-resolved statistical and spectral analysis of EEG-derived functional networks across one-hundred seizures, it finds a transient shift toward regular topology, reduced synchronizability during seizures, and recovery before seizure end.
Problem
The mechanisms underlying seizure initiation, spreading, and termination remain uncertain, motivating analysis of seizure dynamics through complex-network properties.
Method
The study analyzes time-resolved statistical and spectral properties of functional seizure networks derived from multichannel EEG using sliding-window correlations and Laplacian spectra.
Results
Across one-hundred seizures, topology shifted from more random toward more regular and back toward more random, while synchronizability decreased during seizures and increased before seizure end.
Takeaways & Limitations
The findings support studying seizure dynamics as evolving complex networks and suggest that increasing neuronal synchronization may participate in seizure termination.
Abstract
from arXiv · showhide
We assess electrical brain dynamics before, during, and after one-hundred human epileptic seizures with different anatomical onset locations by statistical and spectral properties of functionally defined networks. We observe a concave-like temporal evolution of characteristic path length and cluster coefficient indicative of a movement from a more random toward a more regular and then back toward a more random functional topology. Surprisingly, synchronizability was significantly decreased during the seizure state but increased already prior to seizure end. Our findings underline the high relevance of studying complex systems from the view point of complex networks, which may help to gain deeper insights into the complicated dynamics underlying epileptic seizures.
I. INTRODUCTION
The paper frames seizures as dynamics of complex brain networks, where functional topology and synchronization may change over time. It studies these statistical and spectral network properties to clarify seizure evolution, including initiation and termination.
- Complex-network analysis relates connection structure to the dynamics of interacting systems, including brain networks represented by electrophysiological or imaging-based nodes.
- Average shortest path length L measures network compactness, whereas cluster coefficient C measures the tendency of nodes to form local clusters.
- Regular graphs have high L and C, while randomly interconnected graphs have low L and C.
- Synchronized dynamics depend on both network statistics and the Laplacian eigenvalue spectrum, not solely on connection structure.
- The study examines time-resolved statistical and spectral properties of functional seizure networks in human epileptic brains.
- The reported pattern shifts from more random topology toward greater regularity during seizures and back toward randomness before seizure termination, while synchronizability decreases during seizures and rises before they end.
II. METHODS
The study constructs time-resolved functional networks from multichannel EEG using lagged correlations and connected-graph thresholding. It then tracks topology and Laplacian-based synchronizability across seizure-related windows.
- EEG recordings from 60 patients included one-hundred focal onset seizures, with n = 53 ± 21 channels and seizure origins in different anatomical regions.
- Functional links connect bipolar EEG channels according to cross-correlation, regardless of their anatomical connectivity.
- A 2.5 s sliding window containing 500 sampling points and no overlap estimates time-resolved maximum-lag correlation matrices.
- Adaptive thresholding selects the highest threshold producing a connected graph, with connectivity assessed through the Laplacian's second-smallest eigenvalue λmin.
- The analysis computes average shortest path length L, cluster coefficient C, normalized edge density ǫ, and ratios C/Cr and L/Lr against degree-preserving random graphs.
- Synchronizability is measured by the Laplacian eigenratio S = λmax/λmin, where smaller S indicates better synchronizability.
III. RESULTS
Across 100 focal-onset seizures, functional network measures followed a concave-like trajectory toward a more regular topology before returning toward a more random organization. Synchronizability decreased during seizures, while increasing before electrographic seizure termination; lag analysis indicated activity propagation rather than passive volume conduction.
- Network density: Edge density slowly increased during the second half of seizures and reached an average post-seizure value almost twofold higher than the pre-seizure value.The largest eigenvalue λmax(w) showed a time course resembling edge-density dynamics.
- Consistency: The concave-like evolution of C and L was consistent across investigated seizures and independent of anatomical onset location.Variability across seizures from the same patient was low.
- Synchronizability: Highest eigenratio S occurred in the middle of seizures, indicating lowest synchronizability, followed by increasing synchronizability before electrographic seizure end.The eigenratio dynamics were largely dominated by the smallest non-vanishing eigenvalue λmin(w).
- Functional topology: Normalized cluster coefficient and average shortest path length increased during the first half of seizures, then gradually decreased again.This pattern occurred independently of anatomical seizure origin and was more pronounced for the normalized cluster coefficient.
- Volume-conduction control: Maximum-correlation time lags peaked between 5–50ms, indicating propagation along anatomical pathways rather than passive electromagnetic field effects.A zero-lag peak would have been expected from enhanced volume conduction alone.
IV. CONCLUSION
Across seizures, functional network topology shifted transiently toward greater regularity before returning toward randomness, while globally synchronized-state stability increased before seizure end. Interpretation remains constrained by alternative passive mechanisms and reliance on cross-correlation-based interdependences.
- Conclusion: Functional topology shifted from more random toward more regular and then back toward more random during seizures, regardless of anatomical onset location.The authors describe this as a relative transient evolution in graph properties across investigated seizures.
- Conclusion: Synchronizability initially decreased during seizures but increased already before seizure termination.The result concerns the stability of the globally synchronized state inferred from network spectral properties.
- Conclusion: The displayed distribution covers absolute maximum-correlation lags from 0 to 225 ms because the probability approaches zero at larger lags.The full analysis-window interval is 0–2499 ms, with finer resolution at smaller time lags.
- Conclusion: Global neuronal synchronization significantly increased during the second half of seizures and before seizures stopped.This finding was obtained in a previous analysis of the same data using the eigenvalue spectrum of the zero-lag correlation matrix.
- Conclusion: The observed topology changes may reflect either an active brain process supporting seizure abortion or a passive consequence of intense neuronal firing.The proposed passive mechanism involves saturation of highly connected hubs, affecting local-substructure connections and global synchronizability.
- Conclusion: The findings are restricted to interdependences assessed with cross-correlation, leaving nonlinear and directional interaction analyses for future work.The authors state that additional time-series techniques may provide further information.