Neuronal avalanches: Sandpiles of self-organized criticality or critical dynamics of brain waves?

Abstract

Analytical expressions for scaling of brain wave spectra derived from the general nonlinear wave Hamiltonian form show excellent agreement with experimental “neuronal avalanche” data. The theory of the weakly evanescent nonlinear brain wave dynamics [Phys. Rev. Research 2, 023061 (2020); J. Cognitive Neurosci. 32, 2178 (2020)] reveals the underlying collective processes hidden behind the phenomenological statistical description of the neuronal avalanches and connects together the whole range of brain activity states, from oscillatory wave-like modes, to neuronal avalanches, to incoherent spiking, showing that the neuronal avalanches are just the manifestation of the different nonlinear side of wave processes abundant in cortical tissue. In a more broad way these results show that a system of wave modes interacting through all possible combinations of the third order nonlinear terms described by a general wave Hamiltonian necessarily produces anharmonic wave modes with temporal and spatial scaling properties that follow scale free power laws. To the best of our knowledge this has never been reported in the physical literature and may be applicable to many physical systems that involve wave processes and not just to neuronal avalanches.

Graphical abstract

Keywords

nonlinear waves / critical exponent / Hamiltonian system / neuronal avalanches / critical dynamics

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Conflict of interest statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Author contributions

VLG and LRF developed the theoretical formalism, performed the analytic calculations and performed the numerical simulations. Both VLG and LRF contributed to the final version of the manuscript.

Funding

LRF and VLG were supported by NSF grant ACI-1550405, UCOP MRPI grant MRP17454755 and NIH grant R01 AG054049.

Data availability statement

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

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