Noise and Brownian 1 / f 2 Behavior in the Local Field Potential

Potential J.N. Milstein 1,∗ F. Mormann , I. Fried , and C. Koch 1 1 California Institute of Technology, Pasadena, Ca. 91125 2 Department of Neurosurgery, David Geffen School of Medicine and Semel Institute of Neuroscience and Human Behavior, University of California, Los Angeles, Ca. 90095 and 3 Functional Neurosurgery Unit, Tel-Aviv Medical Center and Sackler Faculty of Medicine, Tel-Aviv University, 69978 Tel-Aviv, Israel 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 and 2) rapidly firing, temporally correlated cells that generate UP-DOWN states.