Bridging Neuronal Avalanches and Crucial Events: Evidence for Temporal Criticality in EEG

Neuronal avalanches (NA) are widely studied as manifestations of self-organized criticality (SOC) in neural systems, yet their relationship to crucial events (CE), a hallmark of self-organized temporal criticality (SOTC), remains unexplored. This study provides empirical evidence that NA exhibit CE characteristics through power-law scaling and renewal properties. EEG data from 109 healthy participants, 11 TBI patients, and 47 subjects performing cognitive tasks revealed that inter-avalanche intervals follow an inverse power-law (IPL) distribution (τ), validating the NA-CE link. Power-law fits were validated via Kolmogorov-Smirnov tests (p > 0.2) and log-likelihood comparisons against log-normal/exponential models, and renewal dynamics were confirmed via correlation analysis. A strong correlation between τ and CE exponent µ (r =0.38-0.63, FDR-adjusted p < 0.05) confirms that CE and NA waiting times share the same power-law dynamics. Furthermore, the inverse correlation between τ and SNZ (r = -0.18 to -0.45) reveals a metastable trade-off: shorter inter-avalanche intervals (higher τ) weaken size-duration scaling (lower SNZ), reflecting a balance in excitation-inhibition, which is critical for neural adaptability. These findings unify NA and CE under the SOTC framework, offering novel insights into brain criticality and its disruption in neurological disorders.Clinical Relevance-In traumatic brain injury, altered τ and SNZ values reflect disrupted criticality, positioning them as biomarkers for diagnosis. The inverse τ-SNZ correlation mirrors impaired neural balance, measurable via low-cost EEG, enabling non-invasive monitoring and personalized interventions.