Abstract
Neural avalanches are a prominent form of brain activity characterized by network-wide bursts whose statistics follow a power-law distribution with a slope near 3/2. Recent work suggests that avalanches of different durations can be rescaled and thus collapsed together. This collapse mirrors work in statistical physics where it is proposed to form a signature of systems evolving in a critical state. However, no rigorous statistical test has been proposed to examine the degree to which neuronal avalanches collapse together. Here, we describe a statistical test based on functional data analysis, where raw avalanches are first smoothed with a Fourier basis, then rescaled using a time-warping function. Finally, an F ratio test combined with a bootstrap permutation is employed to determine if avalanches collapse together in a statistically reliable fashion. To illustrate this approach, we recorded avalanches from cortical cultures on multielectrode arrays as in previous work. Analyses show that avalanches of various durations can be collapsed together in a statistically robust fashion. However, a principal components analysis revealed that the offset of avalanches resulted in marked variance in the time-warping function, thus arguing for limitations to the strict fractal nature of avalanche dynamics. We compared these results with those obtained from cultures treated with an AMPA/NMDA receptor antagonist (APV/DNQX), which yield a power-law of avalanche durations with a slope greater than 3/2. When collapsed together, these avalanches showed marked misalignments both at onset and offset time-points. In sum, the proposed statistical evaluation suggests the presence of scale-free avalanche waveforms and constitutes an avenue for examining critical dynamics in neuronal systems.
Highlights
Neural avalanches are a form of brain dynamics observed both in vivo and in vitro and characterized by bursts of activity whose statistics follow a power-law distribution (Plenz and Thiagarajan, 2007)
We examined whether neuronal avalanches of different durations can be collapsed together (Sethna et al, 2001; Friedman et al, 2012)
One implication of avalanche collapse is that they form a key signature of criticality in neuronal systems, as they reflect a fractal property of activity at different timescales (Beggs and Timme, 2012)
Summary
Neural avalanches are a form of brain dynamics observed both in vivo and in vitro and characterized by bursts of activity whose statistics follow a power-law distribution (Plenz and Thiagarajan, 2007). Several physical systems that evolve in a critical state exhibit power-law scaling (Bak et al, 1987). Whether such power-law scaling reflects criticality in neuronal recordings, remains debated (Touboul and Destexhe, 2010; Klaus et al, 2011; Beggs and Timme, 2012). This debate is fueled by the presence of power-law scaling in stochastic systems that are not in a critical state (Benayoun et al, 2010). This scaling property suggests the presence of similar avalanche dynamics across a range of temporal scales
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