Theoretical Analysis of Field Potentials in Anisotropic Ensembles of Neuronal Elements

Abstract

Synchronous excitation of an ensemble of elements in the nervous system generates field potentials in and around the ensemble. Experimental analysis of these potentials can provide information about neuronal function. This paper derives a theoretical relationship between field potentials and the volume source current density produced by transmembrane currents of members of the neuronal ensemble, under typical experimental conditions. It is shown to be plausible that the potentials produced by a dense bounded ensemble of excited neuronal elements are adequately represented by Poisson's equation. The ensemble is envisaged as embedded in an anisotropic conductive medium. When the ensemble possesses some anatomical symmetry and is synchronously excited, Poisson's equation may be solved to give the field potential as a one-dimensional weighted integral of the volume source current density. The weighting is a function of the conductivity tensor, the neuronal population geometry, and the location of the observation point relative to the source points. When the neuronal elements are represented by a core conductor model, the field potentials may be computed and are shown to agree with experiments. The present theory should facilitate field potential analysis by demonstrating effects of anisotropy and ensemble geometry in a three-dimensional conductive medium.

The Amplitude and Timing of the BOLD Signal Reflects the Relationship between Local Field Potential Power at Different Frequencies

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On the magnetic field and the electrical potential generated by bioelectric sources in an anisotropic volume conductor

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