The scale-invariant, temporal profile of neuronal avalanches in relation to cortical γ–oscillations

Abstract

Miller et al.The temporal profile of neuronal avalanches 2 ABSTRACT Activity cascades are found in many complex systems. In the cortex, they arise in the form of neuronal avalanches which capture ongoing and evoked neuronal activities at many spatial and temporal scales. The scale-invariant nature of avalanches suggests that the brain is in a critical state, yet predictions from critical theory on the temporal unfolding of avalanches have yet to be confirmed in vivo. Here we show in awake nonhuman primates that the temporal profile of avalanches, which describes how avalanches initiate locally, extend spatially and shrink as they evolve in time, follows a symmetrical, inverted parabola spanning up to hundreds of milliseconds. Parabolas of different durations can be collapsed with a scaling exponent close to 2 supporting critical generational models of neuronal avalanches. Spontaneously emerging, transient γ-oscillations coexist with and modulate these avalanche parabolas thereby providing a temporal segmentation to inherently scale-invariant, critical dynamics. Our results identify avalanches and oscillations as dual principles in the temporal organization of brain activity. Significance StatementThe most common framework for understanding the temporal organization of brain activity is that of oscillations, or "brain waves". In oscillations, distinct physiological frequencies emerge at well-defined temporal scales, dividing brain activity into time segments underlying cortex function. Here, we identify a fundamentally different temporal parsing of activity in cortex. In awake Macaque monkeys, we demonstrate the motif of an inverted parabola that governs the temporal unfolding of brain activity in the form of neuronal avalanches. This symmetrical motif is scale-invariant, that is, it is not tied to time segments, and exhibits a scaling exponent close to 2 in line with prediction from theory of critical systems. We suggest that oscillations provide a Miller et al.The temporal profile of neuronal avalanches 3 transient "wrinkle" of regularity in an otherwise scale-invariant temporal organization pervading cortical activity at numerous scales.

Self-Organized Criticality in the Brain

“…Further support that spike avalanches in dissociated cultures differ from LPF avalanches in vivo comes from the mean size vs. duration scaling exponent. This exponent was found to be 2, which is in line with expectations for a critical branching process [71], but ranges between 1-1.5 for spike-based avalanches with bimodal distributions even at large Δt [146,147]. This is more in line with expectations for a noise process wherein size simply grows more linearly with duration [73,79].…”

“…Figure 11). Recent analysis in vivo in the prefrontal cortex of awake nonhuman primates further confirmed this precise relationship between avalanche dynamics and γ-oscillations [71].…”

“…These original scaling operations for avalanches involved >10 h of continuous recordings in vitro, which is difficult to achieve under standard experimental conditions. Recently, Miller et al [71,77] extended this scaling analysis of LFP-based avalanches. They identified a scaling exponent of two for an avalanche waveform and a mean size vs. duration relationship in line with predictions for a critical branching process.…”

“…[Reproduced under CC-NY license from (Levina and Priesemann, 2017).] γoscillations (Miller et al, 2019). To summarize, in vivo experiments in rodents and nonhuman primates, as well as developmentally well controlled in vitro experiments using organotypic cortex cultures and acute cortex slices demonstrate a precise regulation between up-states, nested oscillations and neuronal avalanches that involves fast GABA-mediated inhibition, slow-glutamate mediated excitation and the neuromodulator dopamine.…”

The recovery of parabolic avalanches in spatially subsampled neuronal networks at criticality

“…By measuring locally synchronized neuronal activity using the local field potential (LFP) and tracking the spatiotemporal spread of LFP cascades with microelectrode arrays, power-law distributions for both size, S, and duration, T, 𝑃𝑃(𝑆𝑆) ~ 𝑆𝑆 −𝛼𝛼 and 𝑃𝑃(𝑇𝑇) ~ 𝑇𝑇 −β were revealed, with exponents α ≈ 3/2 and β ≈ 2 respectively, in addition to a critical branching parameter of σ ≅ 1, and significant correlation of neuronal activity within and between 16,17 neuronal cascades (for review see 18 ). These hallmarks of fast, neuronal synchronization in the form of avalanches were subsequently confirmed in the normal brain for ongoing and evoked LFP cascades in the cortex of nonhuman primates [19][20][21][22] and in humans using magnetoencephalography 23,24 . Their sensitivity to even slight pharmacological alterations in the balance of excitation and inhibition 7,18,22,25 and changes during pathological conditions such as epilepsy [26][27][28][29] or changes in brain states such as sleep 30,31 and sleep deprivation [32][33][34][35] , firmly indicate that these avalanches represent neuronal synchronization of cell assemblies in the normal brain.…”