# Universal mechanism of low-frequency brain rhythm formation through nonlinear coupling of high-frequency spiking-like activity

## TL;DR

This paper proposes a universal nonlinear coupling mechanism involving surface brain modes that explains the emergence of synchronized low-frequency brain rhythms from high-frequency activity, supported by numerical simulations.

## Contribution

It introduces a novel physical model of brain surface modes and demonstrates how nonlinear coupling produces low-frequency rhythms from high-frequency activity.

## Key findings

- Low-frequency rhythms emerge via nonlinear coupling of surface modes.
- Numerical simulations show a transition from damped to oscillatory regimes with increased forcing.
- Resonant coupling produces low-frequency brain wave patterns.

## Abstract

A universal mechanism of emergence of synchronized low frequency brain wave field activity is presented as a result of nonlinear coupling with flat frequency neuronal forcing. The mechanism utilizes a unique dispersion properties of weakly-evanescent wave--like brain surface modes that are predicted to exist within a inhomogeneous and anisotropic physical brain tissue model. These surface modes are able to propagate in thin inhomogeneous layers with frequencies that are inverse proportional to wave numbers. The resonant and non-resonant terms of nonlinear coupling between multiple modes produce both synchronous spiking-like high frequency wave activity as well as low frequency wave rhythms. The relatively narrow localized frequency response of the non-resonant coupling can be expressed by terms similar to phase coupling in oscillatory systems. Numerical simulation of forced multiple mode dynamics shows as forcing increases a transition from damped to oscillatory regime that is then silenced off as over excitation is reached. The resonant nonlinear coupling results in emergence of low frequency rhythms with frequencies that are several orders of magnitude below the linear frequencies of modes taking part in the coupling.