A Test for Criticality in Spontaneous Human Brain Organoid Activity: Power-Law Rejection, Session-Level Heterogeneity, and Evidence of Temporal Clustering

Cortical tissue is often reported to operate near a critical point, a dynamical regime in which spontaneous activity organizes into cascades, or neuronal avalanches, whose sizes follow a power-law distribution. Whether cultured human brain organoids reproduce this signature is not well established, and testing it requires care: the standard avalanche definition assumes a preparation that returns to true silence between events, an assumption that does not hold for every tissue. This paper reports a criticality test on a continuous, 39,031-reading passive recording spanning 5.5 hours of active observation across two sessions, collected from a human neurosphere culture (fs652) accessed through the FinalSpark Neuroplatform. Exact-silence avalanche extraction was attempted first and produced a small number of implausibly long events, the largest spanning 27,373 consecutive readings, because the tissue returned to exact zero activity in only 0.04% of readings. This extraction was discarded as physically meaningless, and threshold-based extraction was used instead, at five thresholds spanning the 75th to above the 99th percentile of the activity distribution. Pooling both sessions, event magnitudes were better described by an exponential or lognormal distribution than by a power law at every threshold, with log-likelihood ratios between -34 and -171 and p<0.0001 throughout. Splitting the same test by session produced a materially different picture: the shorter first session (105 minutes, lower mean activity) favoured a power law over an exponential at every threshold tested, while the longer second session (225 minutes, higher mean activity) rejected it as clearly as the pooled data did. This session-level heterogeneity is reported as a primary finding in its own right, alongside a statistical explanation (small-sample bias) and a physiological explanation (state-dependent dynamics), neither adjudicated by the present data. Event timing, measured independently of magnitude, showed a coefficient of variation between 2.35 and 2.67 across three sampling resolutions, well above the value of 1.0 expected under a Poisson process, indicating strong temporal clustering that held regardless of the magnitude result. The zero-touching problem encountered here is reported as a methodological finding relevant to any avalanche analysis of tissue with a non-negligible baseline firing rate.