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/f2 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/f2 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 in time and 2) rapidly firing, temporally correlated cells that generate UP-DOWN states.
Highlights
Power laws appear in a large variety of settings throughout nature and often signify that there is a simple process at the origin of what appears to be a very complex phenomenon
We found that electrophysiological recordings, taken from pharmacologically intractable epilepsy patients with microelectrodes implanted in a variety of cerebral areas, display a surprisingly universal 1/f2 power law in the frequency spectrum of local field potentials (LFPs) activity
Using the simplified model discussed in the methods section above, we focus on searching for solutions of Eq 3 that have a 1/v2 functional dependence
Summary
Power laws appear in a large variety of settings throughout nature and often signify that there is a simple process at the origin of what appears to be a very complex phenomenon. Power laws have been witnessed within the brain in electroencephalographic (EEG) and magnetoencephalographic (MEG) recordings while studying a wide variety of brain function [5,6,7]. Much more local measurements of cerebral activity may be recorded by a single microelectrode. Connecting local behavior, such as that displayed by single-neuron activity and LFP measurements, to more global measurements such as EEG recordings, is one of the great challenges to our understanding of the brain
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