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 $\mu$. 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 ($1 < \tau < 3$, KS $p \geq 0.2$) with near-zero autocorrelation, consistent with renewal-like temporal organization. Across subjects, $\mu$ fell within a similar numerical range to $\tau$ but showed weaker separation between cohorts, indicating that the two metrics capture complementary aspects of temporal structure rather than numerically interchangeable estimates. In contrast, $\tau$ 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.