Neuronal Shot Noise and Brownian $1/f^2$ Behavior in the Local Field Potential

TL;DR

This paper shows that local field potentials in the human brain exhibit a universal $1/f^2$ power spectrum, modeled as neuronal shot noise, revealing underlying cellular activity patterns and their contributions to Brownian noise.

Contribution

It introduces a quantitative shot noise model for LFPs that explains the origin of $1/f^2$ Brownian noise in neural signals, with two analytical solutions.

Findings

LFP power spectra exhibit ubiquitous $1/f^2$ scaling.

The shot noise model explains Brownian noise in neural signals.

Two cellular activity patterns produce the observed noise characteristics.

Abstract

We demonstrate that human electrophysiological recordings of the local field potential (LFP) from intracranial electrodes, acquired from a variety of cerebral regions, show a ubiquitous $1/f^2$ scaling within the power spectrum. We develop a quantitative model that treats the generation of these fields in an analogous way to that of electronic shot noise, and use this model to specifically address the cause of this $1/f^2$ Brownian noise. The model gives way to two analytically tractable solutions, both displaying Brownian noise: 1) uncorrelated cells that display sharp initial activity, whose extracellular fields slowly decay and 2) rapidly firing, temporally correlated cells that generate UP-DOWN states.