Inter-Avalanche Intervals and a Temporal-Scaling Signature in EEG Criticality

To investigate whether the temporal organization of resting-state electroencephalography (EEG) is consistent with statistical properties emphasized in crucial-event (CE) theory by examining the quiescent periods between neuronal avalanches, known as inter-avalanche intervals (IAI).

Resting-state EEG from healthy adults and traumatic brain injury (TBI) patients was transformed into avalanche rasters using a subject-specific z-score threshold treated as an inferred model parameter. For each subject, IAI distributions were fitted with power law, lognormal, Weibull, and exponential models using maximum likelihood estimation with Monte Carlo Kolmogorov-Smirnov (KS) testing and strict tail selection. Renewal behavior was evaluated through autocorrelation analysis, Ljung-Box testing, and phase shuffled surrogates. Modified Diffusion Entropy Analysis (MDEA) provided an independent estimate of the CE exponent μ. Simulated avalanche rasters with known scaling were also used to test whether the threshold optimization procedure could recover IAI statistics under varying noise conditions.

Optimized thresholds revealed stable power-law scaling (1 < τ < 3, KS p ≥ 0.2) with near-zero autocorrelation, consistent with renewal-like temporal organization. Across subjects, μ fell within a similar numerical range to τ but showed weaker separation between cohorts, indicating that the two metrics capture complementary aspects of temporal structure rather than numerically interchangeable estimates. In contrast, τ captured systematic differences between TBI and healthy groups, reflecting compressed quiescent periods and reduced temporal variability in TBI.

IAI timing exhibits temporal statistics consistent with CE theory.

The framework offers a threshold-optimized approach for quantifying temporal scaling in EEG across cohorts and recording conditions.