Neuronal avalanches and critical dynamics of brain waves

TL;DR

This paper presents a theoretical framework linking nonlinear wave dynamics to neuronal avalanches, showing that brain activity across different states exhibits scale-free power laws explained by wave interactions.

Contribution

It introduces a novel analytical model connecting brain wave spectra with neuronal avalanches through nonlinear wave Hamiltonian dynamics.

Findings

Analytical expressions match experimental neuronal avalanche data.

Neuronal avalanches are manifestations of nonlinear wave processes.

Wave interactions produce scale-free power laws in brain activity.

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 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 was never reported in the physical literature and may be applicable to many physical systems that involve wave processes and not just to neuronal avalanches.