Macroscopic models of local field potentials and the apparent 1/f noise in brain activity

TL;DR

This paper presents a macroscopic model based on Maxwell's equations suggesting ionic diffusion causes the 1/f noise in brain local field potentials, reconciling conflicting experimental findings and explaining frequency scaling.

Contribution

The paper introduces a first-principles macroscopic formalism that attributes the 1/f noise in LFPs to ionic diffusion, providing a unified explanation for diverse experimental observations.

Findings

Ionic diffusion explains the 1/f power spectral structure of LFPs.

The model accounts for frequency-dependent conductivity and permittivity.

A proposed measurement method can test the model's predictions.

Abstract

The power spectrum of local field potentials (LFPs) has been reported to scale as the inverse of the frequency, but the origin of this "1/f noise" is at present unclear. Macroscopic measurements in cortical tissue demonstrated that electric conductivity (as well as permittivity) is frequency dependent, while other measurements failed to evidence any dependence on frequency. In the present paper, we propose a model of the genesis of LFPs which accounts for the above data and contradictions. Starting from first principles (Maxwell equations), we introduce a macroscopic formalism in which macroscopic measurements are naturally incorporated, and also examine different physical causes for the frequency dependence. We suggest that ionic diffusion primes over electric field effects, and is responsible for the frequency dependence. This explains the contradictory observations, and also reproduces the 1/f power spectral structure of LFPs, as well as more complex frequency scaling. Finally, we suggest a measurement method to reveal the frequency dependence of current propagation in biological tissue, and which could be used to directly test the predictions of the present formalism.